UMMU UMR4105 DEPARTMENT OF CHEMICAL AND METALLURGICAL ENGINEERING Heat Transfer Laboratory The University of Michigan Ann Arbor, Michigan THE CONDENSING OF STEAM ON HORIZONTAL CORRUGATED AND BARE TUBES Report No. 60 Edwin H. Young Professor of Chemical and Metallurgical Engineering Patrick J. McParland George T. S. Chen David H. Young Research Assistants Project 1592 WOLVERINE TUBE Division of CALUMET & HECLA CORPORATION A Subsidiary of UNIVERSAL OIL PRODUCTS COMPANY ALLEN PARK, MICHIGAN SEPTEMBER 1968

TABLE OF CONTENTS Page List of Tables.... iv List of Figures o o * * * xiii Abstract. o. o o.. 1 Obj e ctive.... 1 Introduction... o.. 4. 2 Review of the Literature..... 3 Description of Tubes Investigated....... 7 Equipment..... 8 Test Procedure..... 13 Wilson Plot Procedure and Results....... 15 Multiple Tube Data Processing...... 18 Results.. o o... 23 Discussion of Results...... 24 The Effects of Steam Condensing Temperature Level Upon Cn and Design Calculations........ 31 The Effect of LMTD on Cn Values. o.. o 35 The Effect of Tubeside Water Velocity on Cn Values... 36 A Comparison of Tubeside and Steamside Heat Transfer Performances for Corrugated and Bare Tubes.. 37 The Tubeside Pressure Drop........ 42 Conclusions o 44 Recommendations.... o 44 i

TABLE OF CONTENTS (Continued) Page Literature Cited.. o. 45 Figures...... 46 Appendices... o... 86 Appendix I...... 87 Reprint of Paper Published in the AIChE Journal in January 1966, "The Condensing of Low Pressure Steam on Vertical Rows of Horizontal Copper and Titanium Tubes" Appendix II........ 93 Copy of AIChE Preprint 5 "Modified Wilson Plot Techniques for Obtaining Heat Transfer Correlations for Shell-and-Tube Heat Exchangers" and Computer Program and Nomenclature Used by Wolverine Tube to Determine The Seider-Tate Inside Heat Transfer Coefficient Constant in Equation 9 Appendix III........ 118 Computer Program for Analyzing Experimental Multiple Tube Steam Condensing Data, Its Nomenclature and Sample Printout in Tables III-1, Tables III-2, and III-3 Appendix IV... o.... 133 Tables IV-1 through IV-13 Containing the Summary of the Calculated Cn and Uo Values for the 5/8-inch Bare, the 5/8-inch Corrugated, the 1-inch Bare, and the 1-inch Corrugated Tubes Appendix V........ 161 Computer Program with Nomenclature for Calculating Point Values of Cn, hi, hcond, Metal Resistance, Uo and Q With and Without Fouling Appendix VI....... 168 Computer Output from the Program in Appendix V Which Calculates Point Values of U, h cond hi and Q Using the Recommended Cn Equations ii

TABLE OF CONTENTS (C ontinue d) Page Appendix VII........ 185 Computer Output from the Program in Appendix V Which Calculates Point Values of Uo, hcond, hi, and Q Using the Cn Equations for Steam Condensing at 100~F and 212~F and the Recommended Cn Equations iii

LIST OF TABLES Table Page 1 Tube Dimensions and Characteristics of Four Tubes Investigated....... 7 2 Computed Values of the Inside Heat Transfer Coefficient Constant...... 17 3 Calculated Values of Nay as a Function of Ntotal Tubes in a Circular Bundle Using Equation 12. 24 4 Summary of Calculated Uo and hcond and Corresponding Per Cent of Overall Resistances for 25 Bare 1-inch 0. D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling...... 25 5 Summary of Calculated Uo and hcond and Corresponding Overall Resistances for 25 Corrugated 1-inch. D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling.... 27 6 Summary of Calculated Uo and hcond and Corresponding Overall Resistances for 25 Bare 5/8-inch O. D., Schedule 20, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling.. 28 7 Summary of Calculated Uo and hcond and Corresponding Overall Resistances for 25 Corrugated 5/8-inch O.D., Schedule 20, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling.. 29 8 Summary of the Cn Equations at Combined Vacuum and Pressure Steam Condensing Conditions for Various Tubeside Water Velocities...... 30 9 The Effect of Steam Condensing Temperature Level on Cn, hcond, Uo, and Q and the Corresponding Per Cent Difference in Q for 25 Tubes in a Vertical Row Without Fouling for a Temperature Difference Between the Water and Condensing Steam of 6~F. 32 iv

LIST OF TABLES (Continued) Table Page 10 Summary of the Cn Equations at Vacuum and Pressure Conditions for the Combined Data at 3. 5 Feet Per Second, 4. 7 Feet Per Second, and 6. 0 Feet Per Second Water Velocities... 34 11 Summary of Calculated U and hi and Corresponding Per Cent of Overall Resistances for 25 Bare 1-inch O. D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling........ 38 12 Summary of Calculated Uo and hi and Corresponding Per Cent of Overall Resistances for 25 Corrugated l-inch O.D,, Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling...... 38 13 Summary of Calculated U0 and hi and Corresponding Per Cent of Overall Resistances for 25 Bare 5/8-inch O.D., Schedule 20, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling... o o o o. 39 14 Summary of Calculated U and h. and Corresponding Per Cent of Overall Resistances for 25 Corrugated 5/8-inch O.D., Schedule 20, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling.. o... 39 15 Summary of Calculated hcond and hi and Corresponding Per Cent of Overall Resistances for 25 Bare 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling........ 40 16 Summary of Calculated hcond and h. and 7 cond 1 Corresponding Per Cent of Overall Resistances for 25 Corrugated 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling. o... o.. 40 v

LIST OF TABLES (Continued) Table Page 17 18 Summary of Calculated hcond and hi and Corresponding Per Cent of Overall Resistances for 25 Bare 5/8-inch O. D., Schedule 20, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling...... Summary of Calculated hcond and hi and Corresponding Per Cent of Overall Resistances for 25 Corrugated 5/8-inch 0. D., Schedule 20, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling....... Relative Condensing Heat Transfer Performance of Corrugated and Bare Tubes With Water Velocities of 6. 0 and 3. 5 Feet Per Second With No Fouling Relative Condensing Heat Transfer Performance of Corrugated and Bare Tubes With Water Velocities of 6. 0 and 3. 5 Feet Per Second with a 0. 0005 Fouling Factor........ 41 41 19 43 20 43 III- 1 Sample Computer Printout for 5/8-inch Corrugated Copper Tubes... Sample Computer Printout for 1-inch Bare 90-10 Cupro-Nickel Tubes... *. 130 *. 131 III- 2 III- 3 Sample Computer Printout for 1-inch Corrugated 90-10 Cupro-Nickel Tubes 132 IV- 1 Condensing Coefficient Correction Factors, Cn, for Condensation of Steam at 101~F on 1 to 7 1-inch Bare 90-10 Cupro-Nickel Tubes in a Vertical Row..... Condensing Coefficient Correction Factors, Cn, for Condensation of Steam at 212~F on 1 to 7 1-inch Bare 90-10 Cupro-Nickel Tubes in a Vertical Row 134 IV-2 137 IV-3 Condensing Coefficient Correction Factors, Cn, for Condensation of Steam at 101~F on 1 to 7 1-inch Corrugated 90-10 Cupro-Nickel Tubes in a Vertical Row....... 139 vi

LIST OF TABLES (C ontinue d) Table Page IV-4 Condensing Coefficient Correction Factors, Cn, for Condensation of Steam at 212~F on 1 to 7 1-inch Corrugated 90-10 Cupro-Nickel Tubes in a Vertical Row....... 141 IV-5 Condensing Coefficient Correction Factors, Cn, for Condensation of Steam at 101~F on 1 to 9 5/8-inch Bare Copper Tubes in a Vertical Row.. 145 IV-6 Condensing Coefficient Correction Factors, Cn, for Condensation of Steam at 101 F on 1 to 8 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes in a Vertical Row o...... 146 IV-7 Condensing Coefficient Correction Factors, Cn, for Condensation of Steam at 212~F on 1 to 8 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes in a Vertical Row....... 147 IV-8 Overall Heat Transfer Coefficients, Uo, for Condensation of Steam at 101~F gn 1 to 7 1-inch Bare 90-10 Cupro-Nickel Tubes in a Vertical Row. o.. o. 148 IV-9 Overall Heat Transfer Coefficients, Uo, for Condensation of Steam at 212~F on 1 to 7 1-inch Bare 90-10 Cupro-Nickel Tubes in a Vertical Row. 151 IV-10 Overall Heat Transfer Coefficients, Uo, for Condensation of Steam at 101~F on 1 to 7 1-inch Corrugated 90-10 Cupro-Nickel Tubes in a Vertical Row......o 153 IV-11 Overall Heat Transfer Coefficients, Uo, for Condensation of Steam at 212~F on 1 to 7 1-inch Corrugated 90-10 Cupro-Nickel Tubes in a Vertical Row......o 155 IV-12 Overall Heat Transfer Coefficients, Uo, for Condensation of Steam at 101 ~F on 1 to 8 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes in a Vertical Row....... 9. 159 vii

LIST OF TABLES (Continued) Table Page IV-13 Overall Heat Transfer Coefficients, Uo, for Condensation of Steam at 212~F on 1 to 8 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes in a Vertical Row 1....... 160 VI-1 Calculated Point Values for I-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F, Without Fouling...... 169 VI-2 Calculated Point Values for i-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F, With 0.0005 Fouling........ 170 VI- 3 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, Without Fouling........ 171 VI-4 Calculated Point Values for i-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, With 0. 0005 Fouling...... 172 VI-5 Calculated Point Values for i-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F, Without Fouling...... 173 VI-6 Calculated Point Values for i-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F, With 0. 0005 Fouling..... 174 VI-7 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, Without Fouling...... 175 VI-8 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, With 0. 0005 Fouling..... 176 VI-9 Calculated Point Values for 5/8-inch Bare CuproNickel Tubes With Steam Condensing at 100~F, Without Fouling.. o o..... 177 viii

LIST OF TABLES ( Continued) Table Page VI-10 Calculated Point Values for 5/8-inch Bare Cupro-Nickel Tubes With Steam Condensing at 100~F, With 0.0005 Fouling......l 178 VI-11 Calculated Point Values for 5/8-inch Bare Cupro-Nickel Tubes With Steam Condensing at 212~F, Without Fouling........ 179 VI-12 Calculated Point Values for 5/8-inch Bare Cupro-Nickel Tubes With Steam Condensing at 212~F, With 0.0005 Fouling....... 180 VI-13 Calculated Point Values for 5/8-inch Corrugated Cupro-Nickel Tubes With Steam Condensing at 100~F, Without Fouling........ 181 VI-14 Calculated Point Values for 5/8-inch Corrugated Cupro-Nickel Tubes With Steam Condensing at 100~F, With 0. 0005 Fouling........ 182 VI-15 Calculated Point Values for 5/8-inch Corrugated Cupro-Nickel Tubes With Steam Condensing at 212~F, Without Fouling..... 183 VI-16 Calculated Point Values for 5/8-inch Corrugated Cupro-Nickel Tubes With Steam Condensing at 212~F, With 0. 0005 Fouling....... 184 VII-1 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F Without Fouling at Tubeside Velocity of 6.0 ft. /sec........ 186 VII-2 Calculated Point Values for i-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F With 0. 0005 Fouling at Tubeside Velocity of 6.0 ft. /sec......... 187 VII-3 Calculated Point Values for I-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F Without Fouling at Tubeside Velocity of 6.0 ft./sec........ 188 ix

LIST OF TABLES (C ontinue d) Table Page VII-4 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F With 0. 0005 Fouling at Tubeside Velocity of 6 0 ft. /sec,......... 189 VII-5 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F Without Fouling at Tubeside Velocity of 6.0 ft. /sec.. o v.... 190 VII-6 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F With 0.0005 Fouling at Tubeside Velocity of 6. 0 ft. /sec.. o.... 191 VII-7 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F Without Fouling at Tubeside Velocity of 6.0 ft. /sec........ 192 VII-8 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F With 0. 0005 Fouling at Tubeside Velocity of 6.0 ft./sec......... 193 VII-9 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F Without Fouling at Tubeside Velocity of 3. 5 ft. /sec....... 194 VII-10 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F With 0. 0005 Fouling at Tubeside Velocity of 3o 5 ft. /sec....... 195 VII-11 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F Without Fouling at Tubeside Velocity of 3.5 ft. /sec......... 196 x

LIST OF TABLES (Continued) Table Page VII-12 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F With 0.0005 Fouling at Tubeside Velocity of 3.5 ft. /sec....... 197 VII-13 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F Without Fouling at Tubeside Velocity of 3. 5 ft. /sec........ 198 VII-14 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F With 0.0005 Fouling at Tubeside Velocity of 3.5 ft. /sec......... 199 VII-15 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F Without Fouling at Tubeside Velocity of 3. 5 ft. /sec..... o 200 VII-16 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F With 0. 0005 Fouling at Tubeside Velocity of 3.5 ft. /seco..... o. 201 VII-17 Calculated Point Values for 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F Without Fouling at Tubeside Velocity of 3.5 ft. /sec.......... 202 VII-18 Calculated Point Values for 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F With 0. 0005 Fouling at Tubeside Velocity of 3o 5 ft. /sec,...... 203 VII-19 Calculated Point Values for 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F Without Fouling at Tubeside Velocity of 3. 5 ft. /sec,........ 204 xi

LIST OF TABLES (C ontinue d) Table Page VII-20 Calculated Point Values for 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F With 0.0005 Fouling at Tubeside Velocity of 3.5 ft./sec......... 205 VII-21 Calculated Point Values for 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F Without Fouling at Tubeside Velocity of 3.5 ft. /sec.... o.... 206 VII-22 Calculated Point Values for 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F With 0. 0005 Fouling at Tubeside Velocity of 3. 5 ft. /sec......... 207 VII-23 Calculated Point Values for 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F Without Fouling at Tubeside Velocity of 3.5 ft. /sec......... 208 VII-24 Calculated Point Values for 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F With 0. 0005 Fouling at Tubeside Velocity of 3o 5 ft. /sec....... 209 VII-25 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F Without Fouling at Tubeside Velocity of 3.5 ft. /sec......... 210 VII-26 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F Without Fouling at Tubeside Velocity of 3.5 ft. /sec......... 211 xii

LIST OF FIGURES Figure Page 1 Sections of the 1-inch O.D., Schedule 18, Corrugated 90-10 Cupro-Nickel and 5/8-inch O. D., Schedule 20, Corrugated Copp.er Tubes.. 47 2 Overall View of Equipment Showing Test Tubes, Automatic Controls, Potentiometer Set-up, and Manometers......... 48 3 Partial Rear View of Equipment Showing Inlet Pot and Well Insulated Inlet Tube Section. o.. 49 4 Line Diagram of Equipment Showing the Flow of Steam and Water.... o.. 50 5 Elevation Drawing of Condenser, Reboiler, and Make-up Tank With the Condenser Tube Sheets and Reboiler Blind Flanges Removed.... o. 51 6 Detailed Drawing of Condenser Tube Sheets. 52 7 Cross-sectional Drawing of Condenser and Inlet Water Pot..... o. 53 8 Cross-sectional Drawing of Orifice Holder Assembly and Extensions at Each End...... 54 9 Line Diagram of Concentric Tube and Shell Heat Exchanger for Wilson Plot Determination Showing Flow of Steam and Water........ 55 10 Cross-sectional Drawing of Concentric Tube and Shell Heat Exchanger End Fittings and Test Tube Supports........ 56 11 Modified Wilson Plot for the 5/8-inch O. D., Schedule 20, Corrugated Copper Tube... 57 12 Modified Wilson Plot for the 1-inch O.D., Schedule 18, Corrugated 90-10 Cupro-Nickel Tube..... 58 xiii

LIST OF FIGURES (Continued) Figure Page 13 Modified Wilson Plot for the 1-inch O.D., Schedule 18, Bare 90-10 Cupro-Nickel Tube. 59 14 Condensing Coefficient Correction Factors for a Tubeside Water Velocity of 3. 5 feet per second and Condensation of Steam at 101~F and 212~F on 1 to 7 Bare 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row....... 60 15 Condensing Coefficient Correction Factors for a Tubeside Water Velocity of 4. 7 feet per second and Condensation of Steam at 101 F and 212~F on 1 to 7 Bare 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row. o 0.,.. o 61 16 Condensing Coefficient Correction Factors for a Tubeside Water Velocity of 5. 3 feet per second and Condensation of Steam at 101~F and 212~F on 1 to 7 Bare 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row o....... 62 17 Condensing Coefficient Correction Factors for a Tubeside Water Velocity of 6. 0 feet per second and Condensation of Steam at 101 F and 212~F on 1 to 7 Bare 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row...... 63 18 Summary of the Condensing Coefficient Correction Factors for Tubeside Water Velocities of 3. 5, 4. 7, 5. 3, and 6. 0 feet per second and Condensation of Steam at 101~F and 212~F on 1 to 7 Bare 1-inch O.D.,, Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row........ 64 19 Comparison of the Condensing Coefficient Correction Factor Curves for Tubeside Water Velocities at 3. 5, 4. 7, 5. 3, and 6.0 feet per second and Condensation of Steam at 101 F and 212~F on Bare 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row....... 65 xiv

LIST OF FIGURES (Continued) Figure Page 20 Condensing Coefficient Correction Factors for a Tubeside Water Velocity of 3. 5 feet per second and Condensation of Steam at 101~F and 212~F on 1 to 7 Corrugated 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row..... 66 21 Condensing Coefficient Correction Factors for a Tubeside Water Velocity of 4.7 feet per second and Condensation of Steam at 101 F and 212~F on 1 to 7 Corrugated 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row.... 67 22 Condensing Coefficient Correction Factors for a Tubeside Water Velocity of 6. 0 feet per second and Condensation of Steam at 101 F and 212~F on 1 to 7 Corrugated 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row.... 68 23 Summary of the Condensing Coefficient Correction Factors for Tubeside Water Velocities of 3. 5, 4. 0, 4. 7, 5. 3, and 6.0 feet per second and Condensation of Steam at 101~F and 212~F on 1 to 7 Corrugated 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row........ 69 24 Comparison of the Condensing Coefficient Correction Factor Curves for Tubeside Water Velocities at 3. 5, 4.7, and 6. 0 feet per second and Condensation of Steam at 101~F and 212~F on Corrugated 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row........ 70 25 Summary of the Condensing Coefficient Correction Factors for Tubeside Water Velocities of 6.0, 8.9, and 11.6 feet per second and Condensation of Steam at 101~F on 1 to 9 Bare 5/8-inch O. D., Schedule 20, Copper Tubes in a Vertical Row....... 71 26 Summary of the Condensing Coefficient Correction Factors for Tubeside Water Velocities of 4. 0, 4. 7, 5. 5, and 6. 0 feet per second and Condensation of Steam at 101~F and 212~F on 1 to 8 Corrugated 5/8-inch O.D., Schedule 20, Copper Tubes in a Vertical Row.. 72 XV

LIST OF FIGURES (CContinue d) Figure Page 27 Summary of the Condensing Coefficient Correction Factors for Tubeside Water Velocities of 3. 5, 4, 7, 5. 3, and 6. 0 feet per second and Condensation of Steam at 101~F on 1 to 7 Bare 1-inch O. D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row....... 73 28 Summary of the Condensing Coefficient Correction Factors for Tubeside Water Velocities of 3. 5, 4. 7, 5. 3, and 6. 0 feet per second and Condensation of Steam at 212~F on 1 to 7 Bare 1-inch O. D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row....... 74 29 Summary of the Condensing Coefficient Correction Factors for Tubeside Water Velocities of 3. 5, 4. 7, and 6. 0 feet per second and Condensation of Steam at 101~F on 1 to 7 Corrugated 1-inch OoD., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row. o o o. o. 75 30 Summary of the Condensing Coefficient Correction Factors for Tubeside Water Velocities of 3. 5, 4. 0, 4.7, 5.3, and 6.0 feet per second and Condensation of Steam at 212~F on 1 to 7 Corrugated 1-inch O. D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row o... o...o 76 31 Summary of the Condensing Coefficient Correction Factors for a Tubeside Water Velocity of 6. 0 feet per second and Condensation of Steam at 101~F on 1 to 8 Corrugated 5/8-inch O.D., Schedule 20, Copper Tubes in a Vertical Row... o.. o 77 32 Summary of the Condensing Coefficient Correction Factors for a Tubeside Water Velocity of 6.0 feet per second and Condensation of Steam at 212~F on 1 to 8 Corrugated 5/8-inch O.D., Schedule 20, Copper Tubes in a Vertical Row....... 78 xvi

LIST OF FIGURES (Continued) Figure Page 33 Summary of the Condensing Coefficient Correction Factors, Cn, for a Tubeside Water Velocity of 3.5 feet per second and Condensation of Steam at 212~F on 1, 3, 5, and 7 Corrugated 1-inch 0. D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row, Indicating No Significant Effect of LMTD on the Values of Cn....... 79 34 Summary of the Condensing Coefficient Correction Factors, Cn, for a Tubeside Water Velocity of 6. 0 feet per second and Condensation of Steam at 212~F on 1, 3, 5, and 7 Corrugated 5/8-inch O.D., Schedule 20, Copper Tubes in a Vertical Row, Indicating No Significant Effect of LMTD on the Values of Cn. o...... 80 35 Summary of the Condensing Coefficient Correction Factors as a Function of Velocity for Condensation of Steam at 212~F on 1, 3, 5, and 7 Bare 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row...... 81 36 Summary of the Condensing Coefficient Correction Factors as a Function of Velocity for Condensation of Steam at 212~F on 1, 3, 5, and 7 Corrugated 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row........ 82 37 Summary of the Condensing Coefficient Correction Factors as a Function of Velocity for Condensation of Steam at 101~F on 1, 4, 6, and 9 Bare 5/8-inch 0. D., Schedule 20, Copper Tubes in a Vertical Row....... 83 38 Pressure Drop Versus Tubeside Water Velocity for the Four Tubes Studied in This Investigation.. 84 39 Moody Friction Factor Plot from the Tubeside Pressure Drop Data Appearing in Figure 38 o.. 85 xvii

ABSTRACT Experimental heat transfer data are presented for steam condensing at 101~F and 212~F on the outside of horizontal copper and 90-10 Cupro-Nickel tubes in vertical rows. The performance of fiveeighths and one-inch corrugated and bare tubes were investigated. An analysis of the experimental data and the resulting steam condensing coefficient correlations are presented. OBJECTIVE The purpose of this investigation was to establish correlations for predicting steam condensing heat transfer coefficients for multitube bundles of 90-10 Cupro-Nickel corrugated and bare tubes in steam condensing applications. 1

INTRODUCTION This investigation was undertaken to determine experimentally the advantages of using corrugated type tubes in steam condensing applications. An earlier investigation had been undertaken to study the performance of bare titanium tubes in the condensing of low pressure steam. The results of this investigation were presented in Report 55(1)' and in a technical paper published in AIChE Journal in January, 1966(2). A reprint of this paper appears in Appendix I. > In order to evaluate the performance of titanium tubes, experimental data was also collected on 5/8-inch. D. c-pp ^ tubes. This copper tube test data was used in this corrugated tube current investigation. In order to utilize the earlier experimental data obtained on 5/8inch copper tubes, 5/8-inch corrugated tubes were fabricated from copper and studied experimentally. A set of 1-inch bare tubes and a set of 1-inch corrugated tubes fabricated from 90-10 Cupro-Nickel were also studied experimentally with steam condensing at atmospheric pressure and under 28 inches of vacuum. I,'j,% Literature cited will be found on page 45. Appendices will be found beginning on page 86. 2

REVIEW OF THE LITERATURE In 1916, Nusselt(3) derived the equations governing the condensation of pure saturated vapors on wettable condensing surfaces. Nusselt postulated that the resistance to heat transfer was due solely to conduction across the continuous condensate film formed during the condensation process. By considering a force balance between the shear forces resulting from the viscosity of the condensate and gravitational forces resulting from the mass of the condensate, an equation was derived which predicted the thickness of the condensate layer as a function of the angle of the surface with a horizontal plane. Laminar flow and zero vapor velocity were assumed. Using the expression for the condensate film thickness, an equation was derived for the change in heat duty with position for a horizontal tube. By suitable integration of the expression, an equation was developed for the mean heat transfer coefficient for condensation of a pure saturated vapor on the surface of a horizontal tube which is lower in temperature than the saturated vapor. Equation (1) was the equation obtained. 1/4 3 2 h = 0.725 k3 D x (1) m Ow725 eD Atf where h = mean condensing heat transfer coefficient, BTU/hr. -sq. ft. -~F k = thermal conductivity of condensate evaluated at film temperature, BTU/hr. -sq.ft. -~F/ft. p = density of condensate evaluated at film temperature, lb. /cu.ft. g = acceleration due to gravity, taken am 4. 17 x 10 ft. /hr. X = latent heat at baturation temperature, BTU/lb. 1 - viscosity of condensate evaluated St film temperature, lb. /ft. -hr, D = outside diameter of tube, ft. 3

Atf t s t sv = temperature drop across condensate film, t - t, F sv s = outside wall temperature of the tube, ~F = temperature of the saturated vapor, ~F For laminar flow of condensate, the film temperature, tf, is given by 3 t = t - Atf f sv 4 f (2) Experimental investigations of the condensation of pure saturated vapors on single horizontal tubes indicate that Equation (1) predicts values generally within + 10%o of the experimental condensing coefficients. (3) The experimental coefficients are most often higher than the theoretical values. This is attributable to turbulence or rippling in the condensate layer. The average film temperature is often evaluated using Equation (3) when turbulent flow of the condensate is expected. (4) tf 1 = t - sv 2 Atf (3) When several horizontal tubes are placed in a vertical row such that condensate from the upper tubes drops onto the lower tubes, the mean thickness of the condensate film on a particular tube increases from the top tube to the bottom tube. By accounting for the accumulation of condensate from tube to tube, but still assuming laminar flow of the condensate, Equation (4) was derived to predict the average condensing coefficient, h, for n tubes located in a vertical row. (3) m 1/4 h m = 0.725 L (4) 4

where n = number of tubes in a vertical row Equation (3) would be used for calculating t if turbulent flow of condensate is expected. Experimental data taken on multiple horizontal tubes in a vertical row by Katz and Geist(5), Short and Brown(6), and Young and Wohlenberg(7) indicate that Equation (4)/is very conservative. The correction for multiple tube rows of (1/n) is much too severe in view of the high degree of turbulence and splashing with condensate dropping from tube to tube. A turbulence correction factor, C, was added to Equation (4) by Katz, Young and Balekjian(4) to give Equation (5). 1/4 k3 2 h = 0.725 C [ g_ _ (5) m n n pt D At Equation (5) corrects the basic theoretical Nusselt model with the correction factor, C, and gives a means of correlating experimental condensing data for multiple tube arrangements. (4) The correction factor, C, varies with the number of tubes in a vertical row and with the physical n properties of the material being condensed. The surface tension of the condensate film is extremely important. Whenever the cooling surface is not wetted, the condensing vapor tends to form very fine drops which roll off the condensing surface due to the influence of gravity. This phenomena is called dropwise condensation. In dropwise condensation the drops normally agglomerate to form larger drops. Since a significant portion of the cooling surface is always free of liquid, the net resistance to heat transfer is lower than for film condensation. Dropwise condensation is generally associated with the existence of a contaminant on the tube surface. Mercaptans and fatty acids are effective promoters of dropwise condensation.(3) Where tube surfaces are mildly contaminated, mixed condensation may exist. Part of the surface will exhibit filmwise condensation while the remainder of the surface is condensing vapor in a dropwise fashion. This frequently happens with condenser tubes which have been in continuous condensing service for a long time. The existence of any non-condensible gas in the condensing vapor significantly affects the rate of heat transfer due to the buildup of a noncondensible gas around the cooling surface. The concentration of a noncondensible gas around the tube surface forms a barrier through which the 5

condensing vapor must diffuse prior to condensing. The temperature of the free surface of the condensate film will be equal to the saturation temperature of the condensing vapor at a pressure equal to the partial pressure of the condensing vapor at the outer film surface. As the saturation temperature decreases with the decreased partial pressure due to the non-condensible gas, the temperature driving force for heat transfer across the condensing film decreases. The rate of heat transfer also decreases. Experimental work by Othmer(8) and Hampson indicates that as little as 1. 5% air by volume can reduce the condensing coefficient by 50%. The greatest effects occur when there is little motion of vapor across the tubes. Under these conditions, most of the non-condensible gases eventually migrate to the vicinity of the tube surface. An extensive experimental program was made by the British Admiralty in which condensing heat transfer data were obtained for multiple tube arrangements with film and dropwise condensation of steam. (9) Photographic studies indicated that heat fluxes six times the average heat flux were obtained in the drop tracks formed in dropwise condensation when large drops rolled across the surface leaving a "bare" metal surface. About one-fifth of the surface had fresh drop tracks at all times. They concluded that high heat fluxes are sustained for times in the order of seconds in very narrow width tracks. The heat flow through these tracks then diverged in crossing the tube wall because the entire internal surface is utilizable for heat transfer. Because of this, they concluded that very thin metal walls would limit the effectiveness of dropwise condensation. The investigators further determined the effect of condensate inundation on the condensing heat transfer coefficient. By pumping condensate through a perforated tube placed above the test section, the tube on which data were taken could effectively simulate any tube in a vertical row of 22 tubes. For filmwise condensation, the condensing coefficient first decreased with inundation due to a thicker condensate film, and then reversed the trend due to increased turbulence at about the 14th or 15th tube. In dropwise condensation, the effect of inundation was to first increase the condensing coefficient due to enhanced wiping action for the top 6 or 7 tubes followed by a gradual decrease. The coefficient for the simulated 22nd tube in a vertical row was higher than for the top tube. 6

DESCRIPTION OF TUBES INVESTIGATED Two corrugated tubes, 5/8-inch O. D. and 1-inch O. D., and two corresponding bare tubes were studied in a laboratory steam condenser. Figure lrpresents a picture of the two corrugated tubes. Table 1 presents the dimensions and characteristics of the four tubes investigated. The pair of 5/8-inch tubes were fabricated from copper and the pair of 1-inch tubes were fabricated from 90-10 Cupro-Nickel. TABLE 1 Tube Dimensions and Characteristics of Four Tubes Investigated Tube Type 5/8-Inch Bare 5/8-Inch Corrugated 1 -Inch Bare 1 -Inch Corrugated Tube outside diameter, in. Tube inside diameter, in. Tube wall thickness, in. Tube length, in. 0. 6252 0. 5550 0. 0351 72. 156 0.6132 0. 5300 0.0416 72. 156 1.0020 0.9008 0. 0456 72. 156 0.9370 0. 8220 0. 0575 72.156 Tube material Thermal conductivity, BTU/hr-ft - F/ft. Helix: Pitch Depth copper 196 none none copper 196 1/4" 0. 033" 90-10 Cu-Ni 90-10 Cu-Ni 26 none none 26 1/4" 0. 031" Figures are presented in section beginning on page 46 Figures are presented in section beginning on page 46. 7

EQUIPMENT The equipment used in the 5/8-inch bare copper tube investigation is described in the reprint presented in Appendix I. The equipment used in the 5/8-inch corrugated copper tube, the 90-10 Cupro-Nickel 1-inch corrugated tube, and the 90-10 Cupro-Nickel 1-inch bare tube investigations consisted of a condenser, inlet and outlet water pots, reboiler, make-up tank, water preheater, water cooler, line pump, surge tank, manual flowrate valve, steam jet ejector and automatic controls. Figures 2 and 3 show a front and partial rear view of the laboratory equipment. Figure 4 gives a line diagram showing the flow of steam and water. An elevation drawing of the condenser, reboiler and make-up tank is given in Figure 5. Steam was generated by boiling distilled water in the reboiler with 125 psig steam. The vapor flowed upward through an 8-inch line to the condenser where it condensed on the test tubes. The condensate returned to the reboiler through a 4-inch line. Distilled water was used as the coolant in a closed loop. The condenser was constructed of a 6-foot length of 18-inch diameter standard gauge commercial steel pipe. Ring flanges were welded to each end of the pipe. The flanges were made from 2-inch thick plate steel with a bolt circle identical to a standard 18-inch 150-pound flange. Tube sheets were constructed from 2-inch steel plate with both sides surface ground to give a flat surface. Figure 6 gives a detailed drawing of the tube sheets showing the tube layout for the 5/8-inch tubes (Tube Sheet No. 1) and the 1-inch tubes (Tube Sheet No. 2). Tube Sheet No. 1 was constructed to accommodate 25 tubes placed in three vertical rows with the tubes on a 7/8-inch equilateral triangular pitch. Tube Sheet No. 2 was constructed to accommodate nineteen tubes placed in three vertical rows with the tubes on a 1 1/4-inch equilateral triangular pitch. The 5/8-inch and 1-inch tubes were sealed in the tube sheet by expanding them with an expansion tool. An 8-inch by 60-inch section was removed from the top of the condenser. An 8-inch welding tee and two pieces of 8-inch pipe with the bottom half cut off was then welded to the condenser over the open section, as shown in Figure 7. This formed the steam inlet to the condenser. An impingement baffle consisting of a piece of 3-inch pipe cut in half was placed over and 2 inches above the tubes in the condenser. This prevented direct impingement of steam onto the tubes. A 4-inch diameter pipe located at the bottom of the condenser returned the condensate produced in the condenser to the reboiler. Sight glasses were provided for visual observation. One-half inch lines with accompanying valves were placed at the top of the condenser to provide a means of removing non-condensibles during atmospheric operation. These can be seen in Figure 2. The condenser was wrapped with fiberglass insulating material. Corrugated metal asbestos gaskets were used between the tube sheets and ring flanges. 8

The 5/8-inch corrugated tube bundle consisted of twenty-three 5/8-inch O. D. corrugated copper tubes and two 5/8-inch O. D. bare copper tubes. The two bare tubes were inserted at the top of each side vertical row in the tubesheet. The 1-inch corrugated tube bundle consisted of seventeen 1 -inch 0, D. corrugated 90-10 Cupro-Nickel tubes and two i-inch O. D. bare 90-10 Cupro-Nickel tubes. Once again the two bare tubes were inserted at the top of each side vertical row in the tubesheet. The 1-inch bare tube bundle consisted of nineteen 1-inch O. D. bare 90-10 Cupro-Nickel tubes. For the 5/8-inch tubes, the inlet and outlet water pots consisted of 1-foot lengths of 14-inch standard gauge steel pipe with 1-inch steel plates welded to the pipe. The plates closest to the condenser contained tube holes in a pattern identical to the condenser tube sheets. Single O-ring grooves were cut in each hole. A section of 3-inch pipe extended approximately six inches into the other plates. These pipes served as the inlet and outlet water lines. The ends of the pipe within the headers were blanked off and sections cut out of the pipe wall. This was done to insure a more nearly uniform distribution of water flow within the tubes. For the 1-inch tubes, the inlet and outlet water pots consisted of 15-inch lengths of 16-inch standard steel pipe with ring flanges welded to each end of the pipe. The flanges were made from 1 1/2-inch thick plate steel with a bolt circle identical to a standard 16-inch 150-pound flange. Tube sheets were constructed from 1 1/2-inch steel plate. The inlet pot was placed approximately six feet from the condenser while the outlet pot was placed approximately 25 inches from the condenser. Seventy-six-inch lengths of tubes were expanded in the condenser tube sheets such that the tubes extended beyond both ends of the condenser approximately two inches. For the 5/8-inch tube, 6-foot lengths of tubes were placed in the inlet pot (extending approximately one inch into the pot) and joined to the condenser tubes by soldering a connecting coupling between the two. For the 1-inch tubes, 5-inch sections of tube were expanded in the pot flange (extending approximately two inches on either side of the flange) and joined to 6-foot lengths of tube by a soldered coupling. The other ends of the 6-foot lengths were joined to the condenser tubes by soldering couplings between them, This 6-foot entry section of tubes, seen in Figure 3, provided a means of obtaining an established flow pattern before the coolant entered the condenser. The section was tightly wrapped with fiberglass insulation to prevent heat losses. Five-inch lengths of tube were secured in the outlet water pot by O-rings in the 5/8-inch tube experiment and by expansion in the 1-inch tube experiment. Each section was placed in such a manner that the tube extended approximately 1 1/2-inch beyond either side of the pot face. In these positions, the condenser tubes and the pot tubes were joined by placing the orifice sections between them. Each end of the orifice section was connected to the appropriate tube by using a soldered coupling. In the 1-inch tube experiment, reducing couplings were used at the condenser end of the orifice section. 9

The reboiler was constructed of a 6-foot length of 24-inch diameter standard gauge commercial steel pipe. Ring flanges were welded to each end of the pipe. The flanges were constructed from 2-inch plate steel with a bolt circle identical to a standard 24-inch, 150-pound flange. All blind flanges were constructed of similar material. The flanges were bolted together with a corrugated metal asbestos gasket placed between the two flanges. A 6-inch section of 24-inch diameter pipe with accompanying flanges was installed at one end to serve as a steam chest. A 2inch thick steel tube sheet was constructed and welded into place six inches within the shell. The reboiler tube sheet was made to accommodate fortyfive 10-foot long, 3/4-inch O. D. U-bend tubes. Wolverine Type S/T copper Trufin U-bend tubes were rolled into the reboiler tube sheets. Tube supports were provided within the reboiler. High pressure steam (125 psig) was used to vaporize the water in the reboiler. The condensate was returned to the high pressure boiler through a steam trap. A Jerguson gauge installed on the front of the reboiler made it possible to determine the water level in the reboiler, A 25-gallon water make-up tank was located immediately above and slightly behind the reboiler as shown in Figure 5. A 1-inch diameter pipe with a valve connected the make-up tank to the reboiler and permitted the transfer of water to the reboiler during operation. A sparged steam line in the make-up tank makes it possible to preheat and partially de-gas the water before it was allowed to enter the reboiler. A 30-gallon capacity surge tank was placed in the water line after the outlet water pot. A 2-inch diameter pipe with a valve connected the tank to the water line and permitted the exclusion of the tank from the system if so desired. Three pipe lines were incorporated to the top of the surge tank to permit expansion of the coolant water to the atmosphere and also to provide a means of filling the system with water. A 13-foot long, 18-inch diameter heat exchanger was installed in the water line after the surge tank to permit cooling of the water coolant after it left the condenser. The heat exchanger had 12 baffles at 10-inch baffle spacing and 25% baffle cut. End baffle spacing was 12 inches. The bundle consisted of one hundred and seventeen 12-foot long U-bends of 5/8-inch 0. D. Wolverine S/T Tryfin* on 15/16-inch triangular pitch for a total outside surface of 1, 300 ft A 100 gpm, single stage, centrifugal pump driven by a 25 HP motor was installed in the water line between the cooler and the water pre-heater, which was a commercially available Bell and Gossett water heater, Type Registered trademark of the Wolverine Tube. 10

SU, Model 83-2. The pump was used during operation to circulate the water coolant through the closed system. A 3-inch gate-valve was installed in the water line between the preheater and the inlet water pot. This valve served as a manual control of the flowrate of water coolant through the system. A two-stage Schutte and Koerting Model 3TC2 jet ejector with interstage condenser was used to evacuate the condenser-reboiler system on start-up and also permitted the removal of non-condensible gases which leaked into the system during operation. The ejector was connected to the reboiler with a 2-inch diameter pipe containing a 2-inch globe valve. The ejector operated on high pressure steam and process cooling water. Four automatic controllers were installed to assist the operation of the equipment when taking data. The controllers can be seen in Figure 2. One instrument was an inlet cooling water temperature controller. A mercury filled bulb installed in the water line served as the sensing element for the controller. The controller pneumatically actuated a steam valve which regulated the amount of steam entering the water preheater. Two of the instruments were absolute pressure controllers which were used during the operation of the equipment at vacuum conditions. One sensing element was connected to the condenser. The controller used the pressure signal to regulate the amount of steam entering the reboiler through a 3/4-inch pneumatically operated valve so that the desired pressure in the condenser could be maintained. The second pressure controller was installed in the steam jet ejector system to minimize fluctuations in pressure at the ejector dur to variations in the steam flow rate. The control instrument controlled a small bleed valve. By bleeding in small amounts of steam, the pressure in the ejector header could be kept relatively constant. The fourth instrument was used to control the pressure in the condenser when operating at atmospheric pressure conditions. The air lines from the vacuum pressure controller described above were simply installed into this instrument (it worked on the same principle as the vacuum instrument). The steam jet ejector and its controller were not used while the equipment was being operated at atmospheric pressure. The water flow rates in each tube were measured by calibrated orifices placed in 9-inch orifice holders which were located at the outlet end of the test tubes between the condenser and the outlet water pot. Fiveeighths-inch tube extensions were inserted at both ends of the orifice holders. The length of the orifice section was approximately 23 inches. Figure 8 shows the orifice assembly. The orifices were calibrated for each individual assembly. The pressure drop across the orifices were measured with water over mercury manometers. Both 50-inch and 100-inch manometers were used. A manifolded system permitted the same manometer to 11

be used for several orifices. The accuracy of the flow rate measurement was between + 1/4 and + 1/2 percent. Inlet water, outlet water, and condenser steam temperatures were measured with calibrated 30 gauge copper-constantan thermocouples using a Leeds and Northrup K-3 potentiometer and null detector. The inlet water and condenser steam temperatures were also measured with calibrated thermometers. Temperatures could be measured to 0. 01~F. The inlet water thermometer and inlet water thermocouple were placed in the inlet water pot. The exit water thermocouples were located in the orifice holder assemblies as shown in Figure 8. The steam temperature thermometer and thermocouple were placed in the overhead steam line between the reboiler and condenser. The stainless steel sheath extended up-stream along the tube axis for one inch. Thermocouples were placed in two places in the back of the condenser to permit the measurement of the steam temperature. The condenser absolute pressure was determined with a mercury manometer and calibrated barometer. 12

TEST PROCEDURE The order of testing the various tubes in this investigation was to study the 5/8-inch corrugated tube first, the 1-inch corrugated tube second, and the 1-inch bare tube lasto Before the testing began, the equipment was thoroughly de-greased. To do this, a 55-gallon barrel of trichloroethylene was added to the reboiler. The cooling water system was filled with tap water from a hose connected to the overhead line of the surge tank. The line pump was then turned on with the pump bypass valve wide open. The by-pass valve was slowly closed to prevent the tygon tubing in the test tube section from being damaged by sudden surges of water during the pump start-up. While cooling water was flowing through the tubes, the steam line to the reboiler was opened. Trichloroethylene was boiled in the reboiler, condensed on the copper tubes and returned to the reboiler. Since the trichloroethylene temperature was higher than the ambient temperature, some condensation occurred throughout the entire system. This insured a thorough cleaning throughout. The used trichloroethylene was transferred to an empty barrel and a clean barrel of trichloroethylene added for a final cleaning. The cooling water system was then drained and filled -again with tap water through the surge tank. The water was once again allowed to circulate through the system for approximately 30 minutes and was then drained out of the systemo This flushing process was performed three or four times before the testing of each new tube began. During normal operation, the reboiler was 3/4 to 7/8 filled with distilled water through the make-up tank. For the vacuum runs, once the reboiler was filled to the desired level, steam and water to the steam jet ejector were turned on and adjusted to give the optimal evacuation rate. The bleed valve on top of the condenser were always closed during vacuum operation. The line pump was then started with the by-pass valve wide open. After slowly closing the by-pass valve, to reach maximum flow, the manual flowrate valve was adjusted to the desired flowrate. The cooling tower water to the cooler was turned on by adjusting the manual valves in the lines. The ejector was allowed to operate for approximately 30 - 45 minutes to thoroughly evacuate non-condensible gases from the condenserreboiler system. The pressure in the condenser rapidly approached the vapor pressure of the water in the reboiler during this period. With the ejector still pulling a vacuum on the system, the condenser pressure controller was set at the desired pressure setting. The automatically controlled steam valve in the reboiler steam line then opened allowing the water in the reboiler to be heated until the vapor pressure of the water equalled the set point pressure. The system was operating under these conditions for approximately 20 - 30 minutes. This further assisted in de-gassing the water and evacuating the system. The inlet water temperature control was set at the desired inlet water temperature. The steam jet ejector manifold pressure controller was set at a pressure somewhat 13

below the condenser pressure. This minimized the steam bleed and permitted maximum removal of non-condensibles during the period when data were taken. During pressure operation, the procedure was much like that described above except for these alterations. The steam jet ejector was eliminated from the system by closing its line valve. The reboiler steam valve control lines were installed on the atmospheric pressure controller, Also, the bleed valves on top of the condenser were fully opened. The pressure in the condenser was always maintained at 2 - 3 inches of mercury above the atmospheric pressures. At this pressure, steam from the reboiler flowed freely through the bleed valves into the atmosphere and prevented any appreciable quantities of non-condensibles from entering the condenser. During pressure operation the inlet water temperature controller had to be operated manually. During vacuum and pressure operation, the saturated steam temperature was calculated and compared to the measured steam pressure. If the two temperatures agreed within 1/2~F, the system was considered ready for taking data. Heat transfer data were taken when the automatic controllers had stabilized all the control variables at the desired set points. The tube numbering was such that the top tube in the center vertical row was Tube 1, the second tube in the center vertical row was Tube 2, etc. The top tube in each side vertical row was labeled Tube A and Tube B, respectively. The datataking procedure required two people and was taken in this order: inlet water thermocouple, inlet water thermometer, condenser steam thermometer, exit water thermocouple for Tube 1; condenser steam thermocouple, inlet water thermocouple, inlet water thermometer, condenser steam thermometer, exit water thermocouple for Tube 2; condenser steam thermocouple, etc. The pressure drop across the orifice for each tube was measured with a manometer approximately at the same time as the exit water temperature was being measured for the same tube. The condenser pressure relative to atmospheric pressure was measured with a mercury manometer two or three times during the run. Barometer readings were made before and after the runs. All the thermocouple readings were recorded by one man while the other measured the remaining data. Usually two complete sets of data were taken for each set condition. During the course of a run which lasted about 5 - 10 minutes, the inlet water temperature varied approximately + 0. 2~F and the condenser steam temperature varied by approximately + 0. 2~F. The data on Tube A and Tube B was taken prior to the start of each run. Whenever the water level in the reboiler dropped below one-half of the reboiler diameter, make-up water was added from the make-up water tank. The water was heated with steam and at least partially de-gassed before allowing it to flow into the reboiler. A small amount of water was always retained in the make-up tank in order to maintain a vacuum seal. 14

WILSON PLOT PROCEDURE AND RESULTS The Wilson Plot Procedure used in obtaining the values of C. for the tube studied can be found in Appendix II, "Modified Wilson Plot Iechniques for Obtaining Heat Transfer Correlations for Shell and Tube Heat Exchangers," pages 97 through 99. The computer program and nomenclature used in analyzing the data are also given in Appendix II. A line diagram of the equipment used in obtaining the Wilson Plot data is shown in Figure 9. The equipment was located in the Research and Development Laboratories of Wolverine Tube in Allen Park, Michigan, and consisted of a concentric shell and tube heat exchanger, two weigh tanks, two pumps, a pre-heater, and two constant head tanks. To insure minimum fouling on the inside of each tube tested, fresh water was continually used on the tube side. Recirculating water was used on the shell side to enable more precise temperature control. To minimize fouling on the outside of the tubes studied, the shell side water was periodically changed every two or three days. For the 5/8-inch corrugated and bare tubes, the shell of the concentric shell-and-tube heat exchanger was constructed of a 13-foot length of 1-inch I.D. copper tube. A 20-foot length of test tube was inserted into the shell and secured by a threaded fitting at each end of the shell as shown in Figure 10. The test tube, in addition to being supported at each end of the shell, was supported at approximately 3-foot increments by three radially symmetrical brass pins as shown in Figure 10. For the 1-inch corrugated and bare tubes, the heat exchanger was identical to that described above with the exception that the shell was constructed of a 1. 59-inch I. D. copper tube. In this position, the test tube extended two feet beyond the shell at the tube inlet end and five feet beyond the shell at the tube outlet end. The tubeside water flow rate was maintained by a 5 HP Aurora pump, Model K-5. The shellside water was circulated by a 3 HP Aurora pump, Model K-5. Each pump was supplied with a constant head tank on the suction intake end of the pump. To prevent sudden surges of water during start-up, a by-pass line with valve was constructed around each pump. A Bell and Gossett, Type SU Preheater was installed in the shellside water line between the shell-and-tube heat exchanger and the pump. The tubeside and shellside water flow rates were determined using two 50-gallon weigh tanks. An automatic controller-recorder was installed in the inlet shellside water line to control the inlet water temperature. A mercury filled bulb installed in the water line served as the sensing element for the controller. The controller pneumatically activated a 1 1/2-inch steam valve which regulated the amount of steam entering the water preheater, 15

Inlet shellside water, outlet shellside water, inlet tubeside water, and outlet tubeside water temperatures were determined using four calibrated thermometers. All of the experimental Wilson plot data was collected by Wolverine Tube personnel. The experimental procedure used in obtaining the Wilson Plot data was as follows: a set of data were obtained over a wide range of different tubeside flow rates and a constant shellside flow rate. To help insure an accurate heat balance, the temperature difference on the tubeside and the shellside were maintained at a minimum of 10~Fo At equilibrium conditions, experimental data was recorded. This data consisted of tubeside and shellside flow rates, the inlet and outlet temperatures of the shellside water, and the inlet and outlet temperature of the tubeside water. A second set of data was then taken using the above procedure except this time the data were taken over a wide range of different shellside flow rates with a constant tubeside flow rate. A program was prepared for the Wolverine Tube Honeywell 200 digital computer (as shown in Appendix II) and only the + 2%7 heat balance Wilson Plot data were processed using that program. The input data to the program were the water flow rates, the inlet and outlet water temperatures, tube dimensions, thermal conductivity of the tube metal, and an initial estimate for the inside heat transfer coefficient, C.. The necessary physical properties of water were written into the program, The program took the value of C., went through the process outlined in the A. I. Ch. E, preprint of 1968, in Appendix II, pages 97 to 99, and obtained the values of the three functions necessary for the modified Wilson Plot. A least square sub-routine was then used to compute the slope of the best straight line through the processed data and the intercept. The reciprocal of the slope is C.. The assumed value of C. was compared to the calculated value and if it differed by more than 0. 00b5 from the calculated value, the calculated value was used and the process was repeated until the assumed and calculated values agreed within 0. 0005. Three sets of Wilson Plot data were processed: that of the 5/8-inch corrugated copper tube, the 1-inch corrugated 90-10 Cupro-Nickel tube, and the 1-inch bare 90-10 Cupro-Nickel tube. The Wilson Plot results for the 5/8-inch bare copper tube were taken from Report 55(1). Table 2 lists the computed values of the inside heat transfer coefficient constants. The Wilson Plot results for the three sets of data obtained in this investigation are presented graphically in Figures 11-13, pages 57-59. 16

TABLE 2 Computed Values of the Inside Heat Transfer Coefficient Constant Tube 5/8" Bare Copper 5/8" Corrugated Copper 1" Corrugated 90-10 Cupro-Nickel 1" Bare 90-10 Cupro-Nickel Ci 0.02468 0.067301 0.05786 0.026423 Figure No. & Page No. Report 55(1), page 28 Figure 11, page 57 Figure 12, page 58 Figure 13, page 59 17

MULTIPLE TUBE DATA PROCESSING Three sets of heat transfer data were taken on the tubes in the center vertical row of tube bundles. Data was also taken on the top tube on each side row. The data on these two side tubes were used only as a reference and do not appear in Results section of this report. The first set of data were taken on the 5/8-inch corrugated tubes. The second set of data were taken on the 1-inch corrugated tubes. The third set of data were taken on the 1-inch bare tubes, The purpose of taking multiple tube data was to obtain the correction factor, Cn, for Equation 5 as a function of the number of tubes in a vertical row. A computer program was written for the IBM 360 Model 67 digital computer to process the data. The program, along with its nomenclature and a sample printout, is presented in Appendix III. The computer program consisted of four sections. First, the input data for Tube A and Tube B, together with the tube dimensions and characteristics and the value of the inside heat transfer coefficient constant, Ci, were read into the computer and calculations were made. These operations included the calculation for Tube A and Tube B,of the heat duty, logarithmic temperature difference, overall heat transfer coefficient, water velocity, bulk water physical properties, inside heat transfer coefficients, and condensing coefficient by the method described in Equations 5, 6, 7, 8, and 9. The overall heat transfer coefficient is calculated from: U - (6) o A AT o m where U = overall heat transfer coefficient, BTU/hr -sq.ft.-~F 0 Q = total heat transfer, BTU/hr. A = total external heat transfer area, sq. ft. 0 AT = logarithm temperature difference, ~F m 18

The heat duty, Q, is obtained experimentally from Q = Wc (t - t ) p out in (7) where W = water flow rate-lb. /hr. c p t out t. in = specific heat of water - BTU/lb. - F = outlet water temperature, ~F = inlet water temperature, ~F The condensing coefficient can be obtained by rearranging the expression for the overall coefficient in terms of the individual resistances. This gives 1 h m 1 U A 0 o A. h. 1 1 - rm (8) where h = mean condensing coefficient, BTU/hr. -sq. ft. -~F m A. 1 h. 1 = total internal heat transfer surface, sq. ft. = inside heat transfer coefficient r = metal resistance, hr.-sq.ft. (outside area)~F/BTU m The metal resistance, r, is easily calculated from the thermal conductivity of the metal andgthe tube dimensions. Empirical expressions are available for the calculation of h. but they are not sufficiently good for accurate heat transfer work. This is attributable to entrance and exit effects, and other system idiosyncracies. A satisfactory equation as regards to form is the Sieder-Tate Equation, Equation 9. 19

0. 8 1 / 0. 14 hD. D.G c I" k = ci [-/ (9)0 kkIL J k l where D. = tube inside diameter, ft. 1 k = water thermal conductivity at bulk water temperature, BTU/hr. -sq. ft. -~F/ft. C. = inside heat transfer coefficient eonstant, dimensionless 1 G = mass flow rate, lb /hr. -sq. ft. p. = water viscosity at bulk water temperature, lb. /ft. -hr. BL = water viscosity at average wall temperature, lb. /ft. -hr. w The constant, C., must be obtained experimentally. From the condensing coefficient and physical properties of the condensate film, the condensing coefficient correction factor, Cn, was calculated using Equation 5. A printout of the results completed the first section. The remaining three sections of the computer program perform the calculations for the tubes in the center vertical row. In the second section of the program, the input data for the tubes in the center vertical row were read into the computer along with the value of the inside heat transfer coefficient, Ci, and preliminary calculations were made. These preliminary calculations included the calculation for each tube of the heat duty, logarithmic temperature difference, overall heat transfer coefficient, water velocity, bulk water physical properties, inside heat transfer coefficients, and condensing coefficient by the method described above, using Equations 6 through 9. From the condensing coefficient and physical properties of the condensate film, the condensing coefficient constant for Equation 1 was calculated. The average inlet water temperature, water velocity, and steam temperature for all tubes in the center vertical row were also calculated. A printout of the results completed the second section. In the third section of the program, the average inlet water temperature, water velocity, steam temperature, and condensing coefficient constants for each tube were used to predict for each tube what the heat duty, exit water temperature, logarithmic temperature difference, overall heat transfer coefficient, inside heat transfer coefficient and condensing 20

coefficient would have been had the inlet water temperature, water velocity and steam temperature been equal to the average values. These calculations put all the tubes on a consistent basis. A printout of the results completed the third section. The condensing coefficient correction factor was calculated in the fourth section of the computer program. The correction factor is by definition that factor which makes Equation 5 an equality and is calculated from Equation 10: h n m 14 (10) n -1/4 3 2 0.725 k3 n J. D Atf In Equation 10, the mean condensing coefficient, hm, is the mean condensing coefficient for the top n tubes calculated from the experimental data. The correction factor for the top tube was calculated using the values of the heat duty and exit water temperature calculated in the previous section. The overall heat transfer coefficient, logarithmic temperature difference and inside heat transfer coefficients were then calculated and the mean condensing coefficient computed from Equation 8. Equation 11 was used to calculate the temperature drop across the condensing film. U At o m At = h (11) f h m and Equation 3 used to calculate the film temperature. 1 tf = t - - Atf (3) sv 2 f 21

Once the film temperature is known, the quantity with n = 1 1/4 k3 2 0.725 P 1 i D Atf can be calculated and C computed from Equation 10 for the top tube. n To determine Cn for the top two tubes in the center vertical row, the heat duties calculated in the second section for the top two rows were added to give the total heat transferred. Using mean values of the water density and heat capacity for the top two tubes, the average exit water temperature for the top two tubes was calculated. The logarithmic temperature difference, overall heat transfer coefficient and inside heat transfer coefficient were next calculated and the mean condensing coefficient calculated from Equation 8, the temperature drop across the condensing film calculated from Equation 11 and the film temperature calculated from Equation 3. The quantity 1/4 3 2 *0.7 7 2 J D Atf was computed and the correction factor for two tubes in a vertical row calculated from Equation 10. The correction factors for 3, 4...7 or 9 tubes in a vertical row were calculated by adding the heat duties for the top n tubes and following the procedure previously outlined. Appendix IV contains the values of the Cn condensing coefficient correction factors for a vertical row of 1 to 9 copper and titanium tubes, respectively. The results were obtained from experimental data taken at steam temperature of 212~F and 101~F and various inlet water temperatures. The Cn results are also presented in Figures 14 through 37. The Results section, which follows, presents graphically the analysis of the experimental data made on the above basis.

RESULTS As indicated in the previous section of this report, the values of UO and of Cn as determined from Euations 6 through 9 were obtained from the digital computer output using the computer program presented in Appendix III. Samples of computer output for 5/8-inch corrugated, 1-inch bare, and 1-inch corrugated tubes are presented in Tables III-1, 11-2, and III-3 in Appendix III. Approximately 400 experimental runs were made, of which 93% were useable. It was not practical to present all the computer printout for all the experimental runs used in this report. Copies of all the printout are in the research project files and copies are also in the possession of Wolverine Tube, the sponsors of the project, in Allen Park, Michigan. It should be noted that Tables III-1, III-2 and III-3 in Appendix III also present the input experimental test variables and the calculated values of heat duty, LMTD, UO, hi, hcond, and Cn/N1/4. Appendix IV contains Tables IV-1 through IV-13, which present the summary of the Cn and Uo values for the 5/8-inch bare, 5/8-inch corrugated, 1-inch bare, and 1-inch corrugated tubes, respectively. Figures 14 through 37, with the exception of Figures 19 and 24, present graphical plots of the Cn data tabulated in Appendix IV. For most of the data runs, the Cn values for the top tube in the center vertical row were found to be abnormally higher than those of the second tube. The exact reason for this situation was not clear. However, it was suspected that it might be due to the construction of the equipment. These experimental Cn values of the top tube were not used in obtaining the equations given in Figures 14 through 37. 23

DISCUSSION OF RESULTS In order to ascertain the relative fraction of the overall resistance to heat transfer due to the resistance of the steam condensing film, a special computer program was prepared. A copy of this computer program is presented in Appendix V. The program calculates Cn, hi, hcond, metal resistance, Uo, and Q for various fouled and non-fouled point conditions with 5% concentrated sea water as the tubeside coolant. The percentages due to each of the above-named resistances are also calculated. It calculates the above values for five circular bundles having various numbers of tubes in a vertical row. The five circular bundles contain from 400 to 3600 tubes. The average number of tubes in the vertical row are calculated using the following equation: N g= 1/2/ Ntota avg V total (12) where N = total number of tubes in a circular bundle total N = average number of tubes in a vertical row. (See Table 3.) avg TABLE 3 Calculated Values of N as a Function of Ntotal Tubes in a Circular Bundle Using Equation 12 Tubes in a Circular Bundle Using Equation 12 (No. Tubes) Navg Ntotal 400 10 900 15 1600 20 2500 25 3600 30 Sea water properties were obtained from Reference 10. 24

Tables VI-1, 2, 3, and 4, in Appendix VI, present typical computer printout for a 1-inch O. D. bare 90-10 Cupro-Nickel tube with steam condensing at 100~F and 212~F with sea water flowing through the tube at six feet per second, with a 6~F steam to water temperature difference and with no fouling and 0. 0005 fouling. These tables were used in preparing Table 4. Table 4 summarizes the percentage of the total resistances due to the condensing steam film resistance for a circular tube bundle containing 2, 500 1-inch 0. D. bare tubes, i. e., with an average of 25 tubes in a vertical row. The computer program in Appendix V was used for making the calculations. TABLE 4 Summary of Calculated Uo and hcond and Corresponding Per Cent of Overall Resistances for 25 Bare 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling (From Appendix VI,, Tables VI-1 to 4) Condensing Fouling Water AT Uo hcond % Temp. Factor Velocity ~F Resis0F. (ft./sec.) tance due to hcond 100 0 6.0 6 712 2559 27.8 100 0.0005 6.0 6 534 2806 19.0 212 0 6.0 6 988 3232 30.6 212 0.0005 6.0 6 677 3660 18.5 An examination of Table 4 indicates that with no fouling the steam condensing film resistance amounts to approximately 30% of the overall resistance to heat transfer, whereas with 0. 0005 fouling the steam condensing film resistance amounts to approximately 20% of the overall resistance. Since the steam condensing resistance amounts to only 1/5 to 1/4 of the overall resistance after fouling has occurred, there is no justification for introducing the refinements that would result from using the C equations that appear on Figures 14, 15, 16, and 17, which present C 25

plots with water velocity as a variable. Consequently, the Cn equation that correlates all of the data appearing in Figures 14, 15, 16 and 17, as shown in Figure 18, is recommended for design purposes, i. e., Cn = 1.07 (N)0 170. Further justification for this recommendation will be presented later. It should be noted that Figures 14 through 17 present Cn plots for steam condensing at 212~F and 101~F with water flowing through 1-inch 0. D. bare tubes at 3. 5 feet per second, 4. 7 feet per second, 5. 3 feet per second, and 6.0 feet per second, respectively. Figure 19 presents the Cn lines shown in Figures 14, 15, 16, and 17 for comparison purposes. It is evident in this figure that the variations in water velocity introduce no significant effect on the values of Cn. The legitimate question arises as to whether or not the steam condensing temperature level introduces any significant effect. Figure 18 presents all of the Cn values of Figures 14, 15, 16 and 17 for condensing at 212~F and 101~F. It should be noted that in Figure 18, the Cn values for steam condensing at 101~F lie primarily above the recommended Cn line. Further analysis is required to determine whether or not there is any significant temperature level effect. This analysis is presented later in this report. Table 5 summarizes the percentage of the overall resistance due to steam film resistance for a circular tube bundle containing 2, 500 1-inch 0. D. corrugated tubes, i. e., with an average of 25 tubes in a vertical row. The computer program in Appendix V was used for making the calculations. Tables VI-5, 6, 7, and 8, in Appendix VI, contain the printout of the computer calculations which are used as the basis of Table 5. A sea water velocity of 3. 5 feet per second was arbit rarily selected for corrugated tubes because of the higher tubeside pressure drop that results from a water velocity of 6. 0 feet per second with such tubes. One would use such tubes in steam condensing applications with lower water velocities, Pressure drop considerations will be covered in a later section of this report along with heat transfer considerations at the same water velocities. An examination of Table 5 indicates that with no fouling the steam condensing film resistance amounts to approximately 24% of the overall resistance to heat transfer, whereas with 0. 0005 fouling the steam condensing resistance amounts to approximately 14% of the overall resistance. Since the steam condensing film resistance amounts to only 1/6 to 1/4 of the overall resistance after fouling has occurred, there is no justification for introducing the refinements that would result from using the Cn equations that appear on Figures 20, 21 and 22. Consequently, the Cn equation that correlates the 3. 5, 4. 0, 4. 7, 5. 3 and 6. 0 feet per second water velocity results, as shown in Figure 23, is recommended for design purposes, i. e., Cn = 1.45 (N)' 203. The justification for this recommendation appears in a later section of this report. 26

TABLE 5 Summary of Calculated U0 and hcond and Corresponding Overall Resistances for 25 Corrugated 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling (From Appendix VI, Tables VI-5 to 8) Condensing Fouling Water AT Uo hcond % Temp. Velocity ~F Resis(ft. /sec.) tance due to hcond 100~F 0 3.5 6 963 4082 23.6 100~F 0.0005 3.5 6 662 4602 14.4 212~F 0 3.5 6 1308 5210 25.1 212~F 0.0005 3.5 6 808 6070 13.3 It should be noted that Figures 20, 21 and 22 present Cn plots for steam condensing at 212~F and 101~F with water flowing through 1-inch O. D. corrugated tubes at 3. 5 feet per second, 4. 7 feet per second, and 6.0 feet per second, respectively. Figure 24 presents the Cn lines shown in Figures 20, 21, and 22 for comparison purposes. A comparison of Figure 24 with Figure 19 indicates that the 3. 5 feet per second line of Figure 24 is inconsistent with 1-inch 0. D. corrugated tubes as compared with 1-inch O.D. bare tubes. It is believed that since there was no significant velocity effect with 1-inch O.D. bare tubes, there should be no significant velocity effects with 1-inch O. D. corrugated tubes, particularly since the 4. 7 feet per second and 6. 0 feet per second corrugated tube Cn lines compare so favorably. This effect is analyzed further in a later section of this report. Again, the legitimate question arises as to whether or not the steam condensing temperature level introduces any significant effect. Figure 23 presents all of the Cn values of Figures 20, 21, and 22 for condensing at 212~F and 101 F. It should be noted that the Cn values for steam condensing at 212~F on bare 1-inch O. D. tubes are concentrated below the recommended Cn line. A further analysis of this situation is presented in a later section of this report. No experimental heat transfer data were collected on 5/8-inch O.D. bare 90-10 Cupro-Nickel tubes in this investigation. Instead, the experimental data collected on 5/8-inch bare copper tubes and presented in Report 55(1) was assumed to be applicable to 5/8-inch bare 90-10 CuproNickel tubes. The Cn values presented in Report 55(1) and reproduced in 27

Appendix IV are plotted -in Figure 25 for water velocities of 6. 0 feet per second, 8.9 feet per second, and 11.6 feet per second. It should also be noted that all of these experimental results are only for steam condensing at 101~F. No experimental test data was collected at 212~F in that investigation. An examination of Figure 25 indicates that for the three velocities plotted, there is no significant velocity effect. The lack of velocity effect for the 5/8-inch 0. D. bare copper tubes is in agreement with the lack of velocity effect for the 1-inch O. D. bare 90-10 Cupro-Nickel tubes. Table 6 summarizes the percentage of overall resistance due to steam film resistance for a circular tube bundle containing 2, 500 fiveeighths-inch 0. D. bare tubes, i. e., with an average of 25 tubes in a vertical row. Tables VI-9, 10, 11, and 12 in Appendix VI contain the printout of the computer calculations which are used as the basis of Table 6. TABLE 6 Summary of Calculated Uo and hcond and Corresponding Overall Resistances for 25 Bare 5/8-inch O.D., Schedule 20, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling (From Appendix VI, Tables VI-9 to 12) Condensing Temp. 100~F 100~F 212~F 212~F Fouling Water Velocity (ft. /sec. ) 0 0. 0005 0 0. 0005 6. 0 6. 0 6. 0 6. 0 6 6 6 6 Uo 731 548 1015 693 hcond % Resistance due to hcond 2122 34.5 2329 2687 3039 23. 5 37. 8 22. 8 An examination of Table 6 indicates that with no fouling the steam condensing film resistance amounts to approximately 34%. of the overall resistance to heat transfer, whereas with 0. 0005 fouling, the steam condensing film resistance amounts to approximately 23%. Since the steam condensing film resistance amounts to only 1/4 to 1/3 of the overall resistance after fouling has occurred, the Cn equation that appears on 28

Figure 25 is recommended for design purposes, i. e., Cn = 1.20 (N)0- 0557. It was assumed that the Cn equation obtained on bare copper tubes would apply to bare 90-10 Cupro-Nickel tubes. Experimental data were collected on 5/8-inch corrugated copper tubes with steam condensing at 212~F and 101~F at water velocity of 4. 0, 4. 7, 5. 5, and 6. 0 feet per second. The Cn values are plotted in Figure 26. Table 7 summarizes the percentage of overall resistance due to steam film resistance for a circular tube bundle containing 2, 500 fiveeighths-inch O. D. corrugated 90-10 Cupro-Nickel tubes, i.e., with an average of 25 tubes in a vertical row. Tables VI-13, 14, 15, and 16 in Appendix VI contain the printout of the computer calculations which are used as the basis of Table 7. TABLE 7 Summary of Calculated Uo and hcond and Corresponding Overall Resistances for 25 Corrugated 5/8-inch O. D., Schedule 20, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling (From Appendix VI, Tables VI-13 to 16) Condensing Fouling Water AT Uo hcond % Temp. Velocity ~F Resis(ft. /sec. ) tance due to hond 100~F 0 3.5 6 1069 3173 33.7 100~F 0.0005 3.5 6 715 3602 19.9 212~F 0 3.5 6 1447 4051 35.7 212~F 0.0005 3.5 6 866 4765 18.2 An examination of Table 7 indicates that with no fouling the steam condensing resistance amounts to approximately 34% of the overall resistance to heat transfer, whereas with 0. 0005 fouling the steam condensing resistance amounts to approximately 20% of the overall resistance. Since the steam condensing resistance amounts to only 1/5 to 1/3 of the overall resistance after fouling has occurred, there is no justification for introducing additional refinements. Therefore, the Cn equation that correlates all of the data appeari2ng in Figure 26 is recommended for design purposes, i.e., Cn, = 1.11 (N)0 20 29

A comparison of Table 7 and Table 5, which is a comparison of 5/8-inch O. Do corrugated with 1-inch O D. corrugated tubes, indicates that the condensing film resistance is approximately 1/3 of the overall resistance for the 5/8-inch tube, whereas it is 1/4 for the 1-inch tube. With 0.0005 fouling, the corresponding fractions are 1/5 and 1/6. Table 8 contains a summary of the Cn equations obtained at combined vacuum and pressure steam condensing conditions for the various tubeside water velocities studied. TABLE 8 Summary of the Cn Equations at Combined Vacuum and Pressure Steam Condensing Conditions for Various Tubeside Water Velocities Figure No. 1-inch Bare Tubes 14 15 16 17 18 Equation for 3. 5 ft. /sec. data: Equation for 4. 7 ft. /sec. data: Equation for 5. 3 ft. /sec. data: Equation for 6. 0 ft. /sec. data: Equation recommended for design use: Cn = 1.10(N) Cn = 1.18 (N). 146 Cn = 1. 10 (N)0- 179 Cn = 1.04 (N)182 Cn = 1.07 (N)0 170 20 21 22 23 1-inch Corrugated Tubes Equation for 3. 5 ft. /sec. data: Equation for 4. 7 ft. /sec. data: Equation for 6. 0 ft. /sec. data: Equation recommended for design use: C = 1.23 (N)0 208 n Cn = 1.48 (N)0'207 Cn = 1.45 (N)0 198 Cn = 1.45 (N)0-203 n 5/8-inch Bare Tubes"' Equation recommended for design use: 25 Cn = 1.20 (N)0 0557 5/8-inch Corrugated Tubes 26 Equation for all data and the recommended equation for design use: C = 1.11 (N) 00 5/8-inch bare data are for vacuum conditions 30

THE EFFECTS OF STEAM CONDENSING TEMPERATURE LEVEL UPON Cn AND DESIGN CALCULATIONS Figure 27 contains all of the Cn values calculated from the data collected on 1-inch O.D. bare tubes with steam condensing at 101~F and tubeside water velocities of 3. 5, 4. 7, 5. 3, and 6. 0 feet per second. The Cn values are tabulated in Appendix IV, Table IV-1. The same values are shown in Figures 14, 15, 16, 17, and 18. The solid line drawn on Figure 27 best fits the data and has the following equation: Cn = 1.15 (N)0 156 Also presented in Figure 27, as a dotted line, is the recommended equation for design purposes, Cn = 1.07 (N)170. Figure 28 contains all of the Cn values calculated from the data collected on 1-inch O.D. bare tubes with steam condensing at 212~F and tubeside water velocities of 3.5, 4.7, 5.3, and 6.0 feet per second. The Cn values are tabulated in Appendix IV, Table IV-2. The same values are shown in Figures 14, 15, 16, 17, and 18. The solid line drawn on Figure 28 best fits the data and has the following equation: Cn = 1.05 (N)0 174 Also presented in Figure 28, as a dotted line, is the recommended equation for design purposes, Cn = 1.07 (N)0 170 The above three equations were used in the computer program, presented in Appendix V, to determine their effect on design calculations with and without fouling. The printout of the computer calculations are presented in Appendix VII, Tables VII-1 through 8. The calculated results without fouling are summarized in the first section of Table 9. Referring to the summary of the calculations made for 1-inch bare tubes in Table 9, it should be noted that the Uo's and Q's calculated using the Cn equations on Figures 27 and 28 with no fouling differ from the results calculated using the recommended equation by approximately 1. 0% and 0. 3%, respectively. These variations are not considered significant and the recommended equation can be used with confidence. The above percentages are reduced to 0. 6% and 0. 1%, respectively., when a fouling factor of 0. 0005 is introduced into the design calculations as indicated in Tables VII-2, 4, 6 and 8. Figure 29 contains all of the Cn values calculated from the data collected on 1-inch O.D. corrugated tubes with steam condensing at 101~F and tubeside water velocities of 3. 5, 4. 7, and 6. 0 feet per second. The Cn values are tabulated in Appendix IV, Table IV-3. The same values are shown in Figures 20, 21, 22, and 23. The solid line drawn in Figure 29 best fits the data and has the following equation: Cn = 1.30 (N)0@ 26. Also presented in Figure 29, as a dotted line, is the recommended equation for design purposes, Cn = 1.45 (N)0 203 Figure 30 contains all of the Cn values calculated from the data collected on 1-inch O.D. corrugated tubes with steam condensing at 212~F and tubeside water velocities of 3. 5, 4. 0, 4. 7, 5. 3, and 6. 0 feet per second. 31

TABLE 9 The Cn, hcond, for Temperature Condensing Temp. 100~F 100oF' 212~F 22 1 ~F Effect of Steam Condensing Temperature Level on Uo, and Q and the Corresponding Per Cent Difference in Q 25 Tubes in a Vertical Row Without Fouling for a Difference Betweene the Water and Condensing Steam of 6F (From Appendix VII, Tables VII-1 to 24) Equation Cn hcond for Cn 1-inch Bare 90-10 Cupro-Nickel"" 1.15(N)0 156 1.90 2644 1.07(N)0 170 1.85 2559 0 174 1.05(N) 74 1.84 3209 1.07(N)0'170 1.85 3232 Uo Q 718 712 986 988 1131 1120 1551 1555 1.0 0. 3 100~F 100 F212~F 2120OF" 100~F 100oF"' 212~F 2122~F 1-inch Corrugated 90-10 Cupro-Nickel' 1.30(N)0'226 2.69 3910 954 1.45(N)0 203 2.79 4082 963 1.30(N)0'191 2.40 4353 1246 1.45(N)0 203 2.79 5210 1308 5/8-inch Corrugated 90-10 Cupro-Nickel" 1.21(N)0'193 2.25 3394 1093 1.11(N)0'200 2.11 3161 1068 0.99(N)0 220 2.01 3792 1413 0. (N)200 11 4034 1445 1.11(N) 2.11 4034 1445 1403 1418 1834 1925 1053 1029 1361 1392 1. 1 5.0 2. 3 2.4 Recommended Cn Equation Water velocity used was 6. 0 feet per second Water velocity used was 3. 5 feet per second 32

The Cn values are tabulated in Appendix IV, Table IV-4. The same values are shown in Figures 20, 21, 22 and 23. The solid line drawn on Figure 30 best fits the data and has the following equation: Cn = 1.30 (N)0 191. Also presented in Figure 30, as a dotted line, is the recommended equation for design purposes, Cn = 1.45 (N). The above three equations were used in the computer program presented in Appendix V,, to determine their effect on design calculations with and without fouling. The printout of the computer calculations are presented in Appendix VII, Tables VII-9 through VII-16. The calculated results without fouling are summarized in the middle section of Table 9. Referring to the summary of the calculations made for 1-inch corrugated tubes in Table 9, it should be noted that the Uo's and Q's calculated using the Cn equations on Figures 29 and 30 differ from the results calculated using the recommended equation by approximately 1. 1% and 5. 0%, respectively. These percentages are reduced to 0. 6% and 2. 8%, respectively, when a fouling factor of 0. 0005 is introduced into the design calculations, as indicated in Tables VII-10, 12, 14 and 16. Figure 31 contains all of the Cn values calculated from the data collected on 5/8-inch O. D. corrugated tubes with steam condensing at 101 F and a tubeside water velocity of 6. 0 feet per second. The Cn values are tabulated in Appendix IV, Table IV-5. The same values are shown in Figure 26. The solid line drawn in Figure 31 best fits the data and has the following equation: Cn = 1.21 (N)0193. Also presented in Figure 31, as a dotted line, is the recommended equation for design purposes, Cn = 1.11 (N) 2 Figure 32 contains all of the Cn values calculated from the data collected on 5/8-inch O.D. corrugated tubes with steam condensing at 212~F and a tubeside water velocity of 6. 0 feet per second. The Cn values are tabulated in Appendix IV, Table IV-6. The same values are shown in Figure 26. The solid line drawn on Figure 32 best fits the data and has the following equation: Cn = 0.99 (N)0 0. The above three equations were used in the computer program, presented in Appendix V, to determine their effect on design calculations with and without fouling. The printout of the computer calculations are presented in Appendix VII, Tables VII-17 through VII-24. The calculated results without fouling are summarized in the lower section of Table 9. Referring to the summary of the calculations made for 5/8-inch corrugated tubes in Table 9, it should be noted that the Uo's and Q's calculated using the Cn equations on Figures 31 and 32 differ from the results calculated using the recommended equation by approximately 2. 3% and 2.4%, respectively. These percentages are reduced to 1.6% and 1. 2%, respectively, if a fouling factor of 0. 0005 is introduced into the design calculations, as indicated in Tables VII-18, 20, 22 and 24. Since steam condensing data was only collected with steam condensing at 101~F on 5/8-inch bare tubes, a similar analysis cannot be made. The 33

above analysis clearly indicates that the three recommended equations for design purposes can be used with confidence. Table 10 contains a summary of all of the Cn equations used in the above analysis. The above analysis indicates that there is no significant steam condensing temperature level effect on Cn. TABLE 10 Summary of the Cn Equations at Vacuum and Pressure Conditions for the Combined Data at 3. 5 Feet Per Second, 4. 7 Feet Per Second, and 6. 0 Feet Per Second Water Velocities Equation Equation 1-inch Bare Tube for the 100~F Data: for the 212~F Data: C n Cn Cn = 1.15 = 1.05 = 1.07 (N)0. 156 (N)0. 174 (N)0.170 Equation recommended for design use: Equation Equation Equation Equation Equation Equation 1-inch Corrugated Tube for the 100~F Data: for the 212~F Data: recommended for design use: 5/8-inch Corrugated Tube' for the 100~F Data: for the 212~F Data: recommended for design use: Cn Cn Cn n Cn Cn = 1.30 = 1.30 = 1.45 =-1.21 = 0.99 = 1.11 (N) 0 226 (N)0 191 (N)0 203 (N)0 193 (N)0 220 (N)0 200 5/8-inch data for only 6. 0 feet per second water velocity 34

THE EFFECT OF LMTD ON Cn VALUES Examination of some of the Office of Saline Water reports indicated that most of the multistage flash sea water distillation plants were being designed to operate with 5~F or 6~F LMTD's. In the early stages of this investigation, it was found that it was extremely difficult, if not impossible, to obtain accurate reproducible data with 6 to 10~F LMTD's. This was believed to be due to the short length of the test section. At low LMTD's and with 5 to 6 feet per second water velocities, small temperature rises were encountered. The accuracy of results of the analysis of the experimental test data is primarily dependent upon an accurate measurement of the heat duty, Q, which is, in turn, dependent upon the temperature rise of the water. Low LMTD's lead to low heat duties and, therefore, introduced large experimental errors. It was found experimentally that very accurate reproducible heat duties could be obtained with large LMTD's in the neighborhood of 20 to 40~F. Figure 33 presents plots of Cn versus LMTD for 1, 3, 5, and 7 corrugated 1-inch 0. D. tubes in a vertical row with steam condensing at 212~F and a tubeside water velocity of 3. 5 feet per second. The numerical values of Cn are presented in Appendix IV, Table IV-4. Examination of this figure clearly indicates that there is no significant effect of LMTD on the Cn values. Figure 34 presents a similar plot for 5/8-inch O. D. corrugated tubes with steam condensing also at 212~F but with a tubeside water velocity of 6.0 feet per second. The Cn values are presented in Appendix IV, Table IV-6. It should be noted that there is only a limited amount of data in Table IV-6. Although a slight dependency of Cn value upon LMTD is apparently indicated in Figure 34, it is not believed to be conclusive due to the small amount of experimental data. Therefore, based on the evidence shown in Figure 33, it is believed that the Cn equations obtained from high LMTD data is applicable to condensation of steam at low LMTD's, i. e., 4~ to 12~F. 35

THE EFFECT OF TUBESIDE WATER VELOCITY ON C VALUES n For the purpose of design applications, it was decided early in this investigation that it was necessary to determine the dependence of Cn upon water velocity since it would be very advantageous to the designer if one equation for Cn could be used for all water velocities for a particular tube. To determine this dependence, all the data for the 1-inch bare and corrugated tubes were taken at four different water velocities, approximately 3. 5, 4. 7, 5. 3, and 6. 0 feet per second. The Cn values obtained on the 1-inch bare tubes at atmospheric pressure steam condensing conditions were plotted against water velocity and are shown for 1, 3, 5, and 7 tubes in a vertical row in Figure 35. This figure indicates that the difference between the values of Cn at 3. 5, 4.7, 5. 3, and 6. 0 feet per second water velocity are not significant. The Cn values obtained on the 1-inch corrugated tubes condensing steam at 212~F were plotted against water velocity and are shown in Figure 36. The values of Cn in this figure at the 3. 5 feet per second water velocity appear to be lower than the values corresponding to the other four water velocities. To show the significance of this difference, the Cn equation for the 3. 5 feet per second data (shown on Figure 20) and the recommended Cn equation (shown on Figure 23) were used to calculate point values of Uo and Q, assuming no fouling, using the computer program in Appendix V. It was found that the difference in the values of Q as predicted by the two Cn equations is approximately5 per cent. These calculated results are found in Tables VII-25 and VII-26 in Appendix VII. It was concluded that the 3. 5 feet per second water velocity data collected on 1-inch corrugated tubes is inconsistent with all the water velocity results collected on the tubes and shown in Figures 35, 36, and 37. This is the justification for the recommendation of the Cn equation shown in Figure 24 to be used for design calculations. The study of velocity effects was undertaken with 1-inch tubes after the heat transfer data had been collected on the 5/8-inch corrugated tubes. Therefore, there are no 5/8-inch O. D. corrugated tube experimental data as a function of velocity available for making a velocity effect analysis. An analysis was made of the experimental steam condensing data collected on 5/8-inch O. D. copper bare tubes presented in Report 55( ). Heat transfer data was collected on the copper tubes with water velocities of 5.9 to 25.5 feet per second with steam condensing at 101 ~F. The Cn values as a function of velocity for 1, 4, 6, and 9 tubes in a vertical row are presented in Figure 37. An examination of this figure indicates no significant effect of velocity upon Cn, It is believed that the Cn correlations recommended in this report for design purposes are valid and do not require the inclusion of any tubeside water velocity term. 36

A COMPARISON OF TUBESIDE AND STEAMSIDE HEAT TRANSFER PERFORMANCES FOR CORRUGATED AND BARE TUBES The purpose of this investigation was to study the steamside condensing heat transfer performance of corrugated tubes. The overall performance of corrugated and bare tubes is in part determined by the tubeside heat transfer performance. The tubeside heat transfer performance of the two corrugated tubes and the two bare tubes reported in this investigation are summarized in Tables 11 through 18 for point conditions involving 2, 500 tubes in a circular bundle with steam condensing at 100~F and 212~F. The computer program used for making the calculations is presented in Appendix V and the computer printout can be found in Appendix VI, Tables VI-1 through VI-16. Calculations in these tables were made for a tubeside water velocity of 3. 5 feet p-er second in the corrugated tubes and 6. 0 feet per second in the bare tubes with no fouling and 0. 0005 fouling. In all the calculations a AT of 6~F was used. Tables 11 through 18 report the calculated Uo's, hi's and corresponding per cent of the overall resistance due to the tubeside resistance. An examination of these tables indicates: a) Tubeside resistance of 5/8-inch and 1-inch O. D. bare tubes amounts to 50 to 60 per cent with no fouling and 33 to 45 per cent with fouling; b) Tubeside resistance of 5/8-inch and 1-inch O. D. corrugated tubes amounts to 43 to 58 per cent with no fouling and 26 to 40 per cent with fouling; c) Steam condensing side resistance of 5/8-inch and 1-inch O.D. bare tubes amounts to 28 to 38 per cent with no fouling and 18 to 24 per cent with fouling; d) Steam condensing side resistance of 5/8-inch and 1-inch O.D. corrugated tubes amounts to 23 to 36 per cent with no fouling and 13 to 20 per cent with fouling. Tables 15 through 18 present the exact calculated per cent distribution of the heat transfer coefficients for comparison purposes. These four tables obviously indicate that the tubeside water film resistance is the major resistance to heat transfer. Tables 11 through 14 indicate that even though the water velocity through the corrugated tubes is only 3. 5 feet per second as compared with 6. 0 feet per second through the bare tubes, the tubeside heat transfer coefficient for the corrugated tubes is running 45 per cent higher than those for the bare tubes. The corresponding 37

steamside heat transfer coefficients are running 60 per cent higher for the corrugated tubes than those of the bare tubes. In spite of these differences, Tables 11 through 18 indicate that the percentage distribution of film resistances are still approximately the same. TABLE 11 Summary of Calculated Uo and hi and Corresponding Per Cent of Overall Resistances for 25 Bare 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling (From Appendix VI, Tables VI-1 to 4) Condensing Temp. ~F Fouling Water Factor Velocity (ft. /sec.) AT ~F 6 U h. % o 1 Resistance due to hi 712 1319 60.0 100 0 6. 0 100 0. 0005 6. 0 6. 0 6.0 6 6 6 534 1318 988 2091 45.1 52. 5 36. 1 212 0 212 0. 0005 677 2089 TABLE 12 Summary of Calculated Uo and hi and Corresponding Per Cent of Overall Resistances for 25 Corrugated 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling (From Appendix VI, Tables VI-5 to 8) Condensing Temp. ~F Fouling Water Factor Velocity (ft. /sec. ) AT ~F Uo hi % Resistance due to h. 1 100 0 100 0. 0005 3. 5 3. 5 3. 5 3. 5 6 6 963 662 1911 1908 3030 3027 49.2 39. 5 49. 2 30.4 212 0 6 1308 212 0. 0005 6 808 38

TABLE 13 Summary of Calculated Uo and hi and Corresponding Per Cent of Overall Resistances for 25 Bare 5/8-inch O. D., Schedule 20, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling (From Appendix VI, Tables VI-9 to 12) Condensing Temp. ~F 100 Fouling Water Factor Velocity (ft. /sec.) 0 6.0 AT UO hi % ~F Resistance due to hi 6 731 1488 56.0 100 0. 0005 0 6.0 6.0 6.0 6 548 1486 6 1015 2359 6 693 2357 42. 0 49.0 33. 5 212 212 0. 0005 TABLE 14 Summary of Calculated Uo and hi and Corresponding Per Cent of Overall Resistances for 25 Corrugated 5/8-inch O. D., Schedule 20, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling (From Appendix VI, Tables VI-13 to 16) Condensing Temp. ~F 100 Fouling Water Factor Velocity (ft. /sec. ) AT Uo hi % ~F Resistance due to hi 6 1069 2426 51.0 0 3. 5 100 212 212 0. 0005 0 0. 0005 3. 5 3. 5 3. 5 6 715 2422 6 1447 3846 6 866 3843 34.2 43. 5 26 1 39

TABLE 15 Summary of Calculated hcond and hi and Corresponding Per Cent of Overall Resistances for 25 Bare 1-inch O. D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling (From Appendix VI, Tables VI-1 to 4) Condensing Temp. ~F 100 100 212 212 Fouling Water Factor Velocity (ft. /sec. ) AT % ~F Resistance due to hcond 6 27.8 0 0. 0005 0 0. 0005 6. 0 6.0 6. 0 6. 0 Resistance due to h. 1 60.0 45.1 52. 5 36.1 6 6 6 19. 0 30. 6 18.5 TABLE 16 Summary of Calculated hcond and hi and Corresponding Per Cent of Overall Resistances for 25 Corrugated 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling (From Appendix VI, Tables VI-5 to 8) Condensing Temp. OF Fouling Water Factor Velocity (ft. /sec.) AT % ~F Resistance due to hcond 6 23.6 100 100 212 212 0 0. 0005 0 0. 0005 3. 5 3. 5 3. 5 3. 5 % Resistance due to h. 1 57.5 39. 5 49.2 30.4 6 6 6 14.4 25.1 13.3 40

TABLE 17 Summary of Calculated hcond and hi and Corresponding Per Cent of Overall Resistances for 25 Bare 5/8-inch O. D., Schedule 20, 90-10 Cupro-Nickel Tubes in a Vertical Row With and Without Fouling (From Appendix VI, Tables VI-9 to 12) Condensing Temp. ~F 100 Fouling Water Factor Velocity (ft. /sec.) AT % ~F Resistance due to hcond 6 34.5 Resistance due to hi 56.0 0 6. 0 100 212 212 0. 0005 0 0. 0005 6. 0 6.0 6.0 6 23.5 42.0 49.0 33. 5 6 6 37. 8 22. 8 TABLE 18 Summary of Calctilated hcond and hi and Corresponding Per Cent of Overall Resistances for 25 Corrugated 5/8-inch O. D., Schedule 20, 90-10 Cupro-Nickel Tubes it a Vertical Row With atnd Without Fouling (From Appendix VI, Tables VI-13 to 16) Condensing Temp. OF 100 100 212 212 Fouling Factor Water Velocity (ft. /sec ) AT % ~F Resistance due to hcond 6 33.7 0 3.4 % Resistance due to hi 51.0 34.2 43.5 26.1 o. 0o05 3.4 6 6 6 19.9 35. 7 18. 2 3,5 0. 0005 3.5 41

THE TUBESIDE PRESSURE DROP The determination of the proper water velocity to be used with corrugated tubes in steam condensing applications requires an economic analysis. Such an analysis is beyond the scope of this report. Figure 38 presents a plot of the tubeside pressure drop in pounds per square inch per foot of tube length as a function of tubeside water velocity in feet per second at the temperatures indicated for the four tubes studied in this investigation. The pressure drop information appearing in Figure 38 has been converted to a Moody Friction Factor plot as shown in Figure 39.(11) An examination of Figure 38 indicates that the water velocity flowing through the inside of a corrugated tube must be reduced considerably to give a pressure drop per foot of tube comparable to that of the corresponding bare tube. On the other hand, the heat transfer performance of the corrugated tubes with the same water velocity as flowing through the corresponding bare tubes is considerably higher. This is shown in Table 19 with no fouling and in Table 20 with a 0. 0005 fouling factor. Table 19 indicates that with no fouling and a water velocity of 6. 0 ft. per second the corrugated tubes produce 44. 0 to 62. 6% more condensate per foot of tube length and 53. 5 to 72. 5% more condensate with a water velocity of 3. 5 feet per second. The corresponding figures with a 0. 0005 fouling factor presented in Table 20 are 23. 0 to 34. 5% with a 6. 0 feet per second water velocity and 30. 0 to 43. 5% with 3. 5 feet per second water velocity. Consequently, adjustments must be made and the designer has considerable choices as to what these adjustments might be. One recommended possibility consists of using a larger diameter corrugated tube in place of the bare tube with a somewhat lower water velocity. Without making any detail economic analysis, an arbitrary decision was made to compare the overall heat transfer performance of the corrugated tubes at a water velocity of 3. 5 feet per second with the overall heat transfer performance of the bare tubes at a water velocity of 6. 0 feet per second. 42

TABLE 19 Relative Condensing Heat Transfer Performance of Corrugated and Bare Tubes With Water Velocities of 6. 0 and 3. 5 Feet Per Second With No Fouling (Tsv = 212~F, AT = 6~F, 25 Tubes in a Vertical Row) hcond Uo W lb. /ft. -hr. Velocity = 6. 0 ft. /sec.; Fouling = 0 5/8-inch Bare 5/8-inch Corrugated 1-inch Bare 1-inch Corrugated 2359 5917 2091 4660 2687 3853 3232 4580 1015 1671 988 1516 1.02 1.66 1.60 2.30 (+62. 6%) (+44. 0%) Velocity = 3. 5 ft. /sec.; Fouling = 0 5/8-inch Bare 5/8-inch Corrugated 1-inch Bare 1-inch Corrugated 1534 3847 1389 3030 2880 4051 3494 5210 819 1447 795 1308 0.83 1.43 1.29 1.98 (+72. 5%) (+53. 5%) TABLE 20 Relative Condensing Heat Transfer Performance of torrugated and Bare Tubes With Water Velocities of 6. 0 and 3. 5 Feet Per Second With a 0. 0005 Fouling Factor (Tsv = 212~F, AT = 6~F, 25 Tubes in a Vertical Row) hcond Uo W lb. /ft. -hr. 0. 0005 Velocity = 6.0 ft. /sec.; Fouling = 5/8-inch Bare 5/8-inch Corrugated l-rinch Bare 1-inch Cdrrugated 2357 5912 2089 4656 3039 4630 3660 5445 693 945 677 889 0.70 0.94 1.10 1.35 (+34. 5%) (+23. 0%) Velo ciity 6 0 ft. I/ec. o tolinfi t, {. 0005 5/8-Inch Bare 5/ 8 ^ich Corrugated l-inch Bare 1-inch Cotrugated 1532 3843 1388 3027 3194 4765 3866 6070 593 866 578 808 0.60 0.86 0.94 1.22 (+43, 5%) (+430. O%) 43

CONCLUSIONS It was concluded that corrugated 90-10 Cupro-Nickel tubes have distinct heat transfer performance advantages on both tubeside and steam condensing side over bare 90-10 Cupro-Nickel tubes in steam condensing applications. It was further concluded that the steam condensing coefficient correction factor, Cn, is not a function of steam condensing temperature level, LMTD, or tubeside water velocity. RECOMMENDATIONS It is recommended that the users of the tubeside heat transfer correlations, pressure drop correlations and the steamside condensing coefficient correlations presented in this report for 90-10 Cupro-Nickel tubes determine the optimum diameter of the corrugated tube and tubeside water velocity to be used in steam condensing applications from economic considerations. 44

LITERATURE CITED 1 Report No. 55, The University of Michigan, Office of Research Administration, 01592-149-T, "The Condensing of Low Pressure Steam on Horizontal Titanium Tubes, " December 1963. 2. Young, Edwin H. and Briggs, Dale E., A.I. Ch.E. Journal, Vol. 12, No. 1, pp. 31-35, 1966. 3. Jakob, M., Heat Transmission, Vol. 1, John Wiley and Sons, N.Y., N.Y., 1949. 4. Katz, D. L., Young, E. H., and Balekjian, G., Pet. Ref., Vol. 33, No. 11, pp. 175-178, 1954. 5. Katz, D. L. and Geist, J. M., Trans. ASME, Vol. 70, No. 11, pp. 907-914, 1948. 6. Short, B. E. and Brown, H. E., Institution of Me chanical Engineers and ASME Proceedings of the General Discussion on Heat Transfer, Section I, London, pp. 27-31, 1951. 7. Young, F. L. and Wohlenberg, W. J., Trans. ASME, Vol. 64, No. 11, pp. 787-794, 1942. 8. McAdams, W. H., Heat Transmission, McGraw-Hill, 3rd Edition, 1954. 9. Watson, R. G. H., Brunt, J. J. and Birt, D. G. P., "Dropwise Condensation of Steam, " International Developments in Heat Transfer, Part II," ASME, N.Y., N.Y., 1961. 10. Office of Saline Water, U. S. Dept. of Interior Saline Water Conversion Engineering Data Book, Prepared by the M. W. Kellogg Company, N.Y., N.Y., July 1965. 11. Moody, L. F., Trans. ASME, Vol. 66, pp. 671-684, 1944. 45

FIGURES 46

Figure 1. Sections of the 1-inch O.D., Schedule 18, Corrugated 90-10 Cupro-Nickel and 5/8-inch 0. D., Schedule 20, Corrugated Copper Tubes. 47

Figure 2. Overall View of Equipment Showing Test Tubes, Automatic Controls, Potentiometer Set-up, and Manometers. 48

Figure 3. Partial Rear View of Equipment Showing Inlet Pot and Well Insulated Inlet Tube Section. 49

Steam Bleed - Steam Steam Jet Ejector Un 0 SYMBOLS -APRCO TRCO -2 Control Valve Pressure Recorder Controller Temperature Recorder Controller Pressure Element I -t~ Thermocouple Temperature Element Orfice Air Line Figure 4. Line Diagram of Equipment Showing the Flow of Steam and Water.

8" STD. SCH. STEEL PIPE 1" STD. SCH. STEEL PIPE 4 STD. SCH. STEEL PIPE ///////////I///////////////// Figure S. Elevation Drawing of Condenser, Reboiler, and Make-up Tank With the Condenser Tube Sheets and Reboiler Blinrd Fldhges kemoVedd 51

25" Diameter 25" Diameter 22 1/4" Bolt Circle 22 1/4" Bolt Circle 16 1 1/4" Holes 16 11/8" Holes 010 \~ 00 O/\o \ oo /0\ 0 o0 o 0 oo 0 CONDENSER TUBE SHEET NO. 1 CONDENSER TUBE SHEET NO. 2 For 5/8" Tubes For 1" Tubes Figure 6. Detailed Drawing of Condenser Tube Sheets.

Steam Header II I5 F be w = j ~ l | 18" Condenser Pot Condensate Return Line ^- 1/2" -- 2 --- -- I Figure 7. Cross-sectional Drawing of Condenser and Inlet Water Pot.

Y COPPER TUBING COPPER-CONSTANTAN THERMOCOUPLE STAINLESS STEEL SHEATH %"13BWG COPPER Q-i (JI 5/8" 20OBWG 1" 5/8" 20BWG S 20BWG COPPER INSERT 0.375" DIA. HOLE IN ORFICE Figure 8. Cross-sectional Drawing of Orifice Holder Assembly and Extensions at Each End.

Shell ID, 5/8" test tube; L 000" Shell ID, 1" test tube; L 592" TS2 Tube Side Pump Constant Head Tank Tube Side TRC Temperature Recorder Controller FRC Flow Recorder Controller TS1 Temperature Shell Side Water, In TS2 Temperature Shell Side Water, Out TT1 temperature Tube Side Water, In tT2 Temperature Tube Side Water, Out Figure 9. Line Diagram of Concentric Tube and Shell Heat Exchanger for Wilson Plot betermination Showing Flow of Steam and Water. 55

Shell Test Section Support and Center Line Positioning Pins - Three Sets at 3'K Increments Test Tube U T v r\\\\\\\I\\v 1 / 1 U-'End Connector Figure 10. Cross-sectional Drawing of Concentric Tube and Shell Heat Exchanger End Fittings and Test Tube Supports.

-—.l 60 er ZL ~L 50 m cnq w 40 r_ <^" 30 LU V, I 2 20 Un -j I r E L. I I I I I I I I I E I { I { I I I I I I I[ C. = 0. 067301 p i L 10_ I - S O 0 I I I I I I I I I1 I I I I I I I I I I 0.2 04 0.6 0.8 1.0 1.2 1.4 L6 L8 2.0 2.4 I O/ \KS / 0 7740 0. 3333 j 0"10. 14ir D 1 0.8 0.3333 /J 0.14 (S /) ( S) (L) ][((\) (P) (wT) ] Figure 11. Modified Wilson Plot for the 5/8-inch O.D., Schedule 20, Corrugated Copper Tube.

I I I I i I I I I I I I I I 400 350 300 cy Ln 3 m^ 250 LC QI. Cy% 200 LA k I3 L. 150 1 1 E L= 1I /j0 C. = 0,05786 1o 1 1I o 100 I = 50 - 0 I I I I I I I I I I I I I I 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 /OD(I "ss ) 0.9976 / )0-3333/ s)0.-14 ID (1 08 3333, 0. 14] Figure 12. Modified Wilson Plot for the 1-inch 0. D., Schedule 18, Corrugated 90-10 Cupro-Nickel Tube 58

aqn.L TlaPl-N-ojdnO 01-06 a Ieg'81 alnpaqoS' aI' 0 so *: UT- aq1 JOJ OidC uosTIM PaJTPOI *~"IT I nF.ITJ )~~'()0 1 38 alx )]. [ r.(.0 ol) F(171 (it.) ( I S W(a\1,M7 H - _ 1 LM^^ ^^ W T A (]1 ^^ro1^ >L^ W'''A^JWJ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\d/ -I4~~U LT6Ik j~~ l~ ZT 11 01 6 8 L 9 S P Z I 0 I I I I I I I I I I I I I 0 w~~~~~~~~~~~~~~~~~~~~~~~~ Z9ZO'0"!.3 I I I I I I -- I I I I I - I _ 001 I c -d oC:ooz a — 3 00 _ 0 — 00~. — 0B (A oo O(~lW w 18 _" po %otool 005 009

3.1 2.5 — 0 o 02~~.0- 9-~ 0.8 _ I0 o I I Tubes in a Vertical Row 0.o 0.7 I t 7 Bare 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes ir ert:,cal Row.

Cn 1 2 3 4 Tubes in a Vertical Row 5 6 7 8 9 10 Figure 15. Condensing Coefficient Correction Factors for a Tubeside Water Velocity of 4. 7 feet per second and Condensation of Steam at 101 F and 212~F on 1 to 7 Bare i-inch O. D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row.

3. 2. 1. C n Cr\ 1. 0. 0. 1 2 3 4 5 6 7 8 9 10 Tubes in a Vertical Row Figure 16. Condensing Coefficient Correction Factors for a Tubeside Water Velocity of 5. 3 feet per second and Condensation of Steam at 101 ~F and 212~F on 1 to 7 Bare 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row,

U0. C n LO 0. 9 0. 8 0. 7 0.6 1 Figure 17. Tubes in a Vertical Row Condensing Coefficient Correction Factors for a Tubeside Water Velocity of 6.0 feet per second and Condensation of Steam at 101 F and 212~F on 1 to 7 Bare 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row.

3. 2.5-K 2.0 2. 0 > 0 cn a ig < ~! i D DjD 0.9 - o 3.5 FPS n 07 N~Tubes in a Vertical Row o 3. 5 FPS 0.8 S- 4.7 FPS < 5.3 FPS 0 7 - o 6. 0 FPS 0.6III I I I I I ~~~1 ~ 2 3 4 5 6 7 8 9 10 Tubes in a Vertical Row Figure 18. Summary of the Condensing Coefficient Correction Factors for Tubeside Water Velocities of 3. 5, 4. 7, 5. 3, and 6. 0 feet per second anc Condensation of Steam at 101~F and 212~F on 1 to 7 Bare 1-inch 0. D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row.

C n ul 1 2 3 4 5 6 7 8 9 10 n a Vertical Row Figure 19. Comparison of the Condensing Coefficient Correction Factor Curves for Tubeside Water Velocities at 3. 5, 4. 7, 5. 3, and 6. 0 feet per second and Condensation of Steam at 101 F and 212~F on Bare 1-inch O. D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row.

3. 2. 2. C n (ON ON 0.9 0.8 0.7 0.6 1 2 3 4 5 6 7 8 9 10 Tubes in a Vertical Row Figure 20. Condensing Coefficient Correction Factors for a Tubeside Water Velocity of 3. 5 feet per second and Condensation of Steam at 101 ~F and 212~F on 1 to 7 Corrugated i-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row.

3. 2. 5 1.5 5 C 1. 0 0. 9 0.8 0. 7 0.6 I I I I I I 1 2 3 4 5 6 7 8 9 10 Tubes in a Vertical Row Figure 21. Condensing Coefficient Correction Factors for a Tubeside Water Velocity of 4.7 feet per second and Condensation of Steam at 101 ~F and 212~F on 1 to 7 Corrugated 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row.

2. 2. 1. C n oN 00 1. 0 0.9 0.8 0.7 0.6 1 Figure 22. Tubes in a Vertical Row Condensing Coefficient Correction Factors for a Tubeside Water Velocity of 6. 0 feet per second and Condensation of Steam at 101 ~F and 212~F on 1 to 7 Corrugated I-inch O. D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row.

Cn I 1.0 o 3.5 FPS 0.9- o 4.0FPS > 4.7 FPS 0.8- < 5.3 FPS o 6.0 FPS 0. 7 0.6 0.6 1 1 I I I 1 1 2 3 4 5 6 7 8 9 10 Tubes in a Vertical Row Figure 23. Summary of the Condensing Coefficient Correction Factors for Tubeside Water Velocities of 3. 5, 4. 0, 4. 7, 5. 3, and 6. 0 feet per second and Condensation of Steam at 101 F and 212~F on 1 to 7 Corrugated 1-inch 0. D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row.

o 1. 0.9 0.80. 7 0.6 I I 6I I i I I 1 2 3 4 5 6 7 8 9 10 Tubes in a Vertical Row Figure 24. Comparison of the Condensing Coefficient Correction Factor Curves for Tubeside Water Velocities at 3. 5, 4. 7, and 6. 0 feet per second and Condensation of Steam at 101 F and 212~F on Corrugated 1-inch O. D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row.

3.0, I I 1 I I I I 2.5 2.0[ 1.5h cC =1.20(N)00557 -___ _ 8 A n - - -A e-.- a*-pg~s~ge~ C n 1.o0 0.91 0.8 - o 6.0FPS o 8.9FPS 11. 6FPS I I I I I 007 0 6 I 1 2 3 4 5 6 7 8 9 10 Tubes in a Vertical Row Figure 25. Summary of the Condensing Coefficient Correction Factors for Tubeside Water Velocities of 6.0, 8.9, and 11.6 feet per second and Condensation of Steam at 101~F on 1 to 9 Bare 5/8-inch O. D., Schedule 20, Copper Tubes in a Vertical Row.

3.0 2.5 2.0 1.5 C n 1. 0. 0. 0.7 0.6 1 2 3 4 5 6 7 8 9 10 Tubes in a Vertical Row Figure 26. Summary of the Condensing Coefficient Correction Factors for Tubeside Water Velocities of 4. 0, 4. 7, 5. 5, and 6. 0 feet per second and Condensation of Steam at 101 F and 212~F on 1 to 8 Corrugated 5/8-inch 0. D., Schedule 20, Copper Tubes in a Vertical Row.

c" IK —-U^ ^ —!?< |> > 4.7FPS oB a 8 0 0.8- < 5.3 FPS - o6 0 0.9- o 3.5 FPS t 4.7 FPS 0.8 -- a 5.3 FPS o 6.0 FPS 0. 7 0.6 I I 1 2 3 4 5 6 7 8 9 10 Tubes in a Vertical Row Figure 27. Summary of the Condensing Coefficient Correction Factors for Tubeside Water Velocities of 3. 5, 4. 7, 5. 3, and 6. 0 feet per second and Condensation of Steam at 101~F on 1 to 7 Bare 1-inch O.D., Schedule 18, 90-10 CuproNickel Tubes in a Vertical Row.

3. 2. 2. 1. C n 1I 0. 0. 0. 0. 1 2 3 4 5 6 7 8 9 10 Tibes in a Vertical Row Figure 28. Summary of the Condensing Coefficient Correction Factors for Tubeside Water Velocities of 3. 5, 4. 7, 5. 3, and 6. 0 feet per second and Condensation of Steam at 212~F on 1 to 7 Bare i-inch O.D., Schedule 18, 90-10 CuproNickel Tubes in a Vertical Row.

2. 1. C n 1.0 0. 9 0.8 0.7 0. 6 1 2 3 4 5 6 7 8 9 10 Tubes in a Vertical Row Figure 29. Summary of the Condensing Coefficient Correction Factors for Tubeside Water Velocities of 3. 5, 4. 7, and 6. 0 feet per second and Condensation of Steam at 101 ~F on 1 to 7 Corrugated 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row.

C n 1 2 3 4 5 6 7 8 9 10 Tubes in a Vertical Row Figure 30. Summary of the Condensing Coefficient Correction Factors for Tubeside Water Velocities of 3. 5, 4. 0, 4. 7, 5. 3 and 6. 0 feet per second and Condensation of Steam at 212F on 1 to 7 Corrugated 1-inch O. Do, Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row.

C 0. 9 0.8 0. 7 0,6 I I I i I I! 1 2 3 4 5 6 7 8 9 10 Tubes in a Vertical Row Figure 31. Summary of the Condensing Coefficient Correction Factors for a Tubeside Water Velocity of 6. 0 feet per second and Condensation of Steam at 101 ~F on 1 to 8 Corrugated 5/8-inch O. D., Schedule 20, Copper Tubes in a Vertical Row.

Cn _I O o 8 8 0.9 0 88 8 0.7 0. 0 o. 7 I I I I I I I i 1 2 3 4 5 6 7 8 9 10 Tubes in a Vertical Row Figure 32. Summary of the Condensing Coefficient Correction Factors for a Tubeside Water Velocity of 6. 0 feet per second and Condensation of Steam at 212~F on 1 to 8 Corrugated 5/8-inch O. D., Schedule 20, Copper Tubes in a Vertical Row.

O n C n C n Cn n L. U 0 1 TUBE 1.5 - OI ~ ~ B o o -_8 88 1,0 I I I I I I I _, o ~~~~2.0~ o 0 -- o ~ 3 TUBES ~8 ~~ e ee o 1.5- 8 e - oo o 0 8o 2.0_ o I 1.5 o 5TUBES Lo I I I I 1.0 8 o 8 o o L.5 - 0 7 TUBES 10 15 20 25 30 LMTD(~F) 35 40 45 50 Figure 33. Summary of the Condensing Coefficient Correction Factors, Cn, for a Tubeside Water Velocity of 3. 5 feet per second and Condensation of Steam at 212~F on 1, 3, 5, and 7 Corrugated I-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row, Indicating No Significant Effect of LMTD on the Values of Cn. 79

1. 5 1 TUBE C n 1.0 0.9 8 8 0. 8 C n Cn n _! I I I I I.. -~~~~~~~ ~ ~ ~~~_ ~~~3 TUBES _8 8 8 1.0 2. I I 5 TUBES.5 8 Loo I I I I I I 2.0 7 TUBES L5 a 1. I I I I 10 15 20 25 30 LMTD(~F) 35 40 45 50 Figure 34. Summary of the Condensing Tubeside Water Velocity of Steam at 212~F on 1, 3, 5, Copper Tubes in a Vertical on the Values of Cn* Coefficient Correction Factors, Cn, for a 6. 0 feet per second and Condensation of and 7 Corrugated 5/8-inch O. D., Schedule 20, Row, Indicating No Significant Effect of LMTD 80

C n 2.0 I 1 TUBE i. 5 - o ~8 _.0o I~8 1 l 1 10 2.0~~~s~ I! I I I I -_~~~~~~ ~ ~~~~~~~- 33 TUBES 0 5- ooP3 8 - 1. - 5 10. 0 1.0 I I I I I Ii C n 20 1.5 C n 1 0 2.0 1.5 C n 0 o 5 TUBES CDe J? o I- I I I o CD c G6b ~ 7 TUBES o0 9) o %0 1.0L 3 0 3.5 4.0 4.5 5.0 5.5 TUBE SIDE WATER VELOCITY (FT/SEC) 6.0 6.5 7.0 Figure 35. Summary of the Condensing Coefficient Correction Factors as a Function of Velocity for Condensation of Steam at 212~F on 1, 3, 5, and 7 Bare 1-inch O.D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row. 81

C n n 2. O 2.C I I I I I I o 1 TUBE _ o ~0%_ 0 3 TUBES& 00 0 o 0 1.0 0 0 2.5 I I I I I I 2.5 - g I I I I I I 0 f o - - B < 73 TUBES 1IIII_0 1.5 1.0 I I I I I 2. 5 2.0 00 8 P~_~~~~~~~~~~~~ e & 5TUBES 1.50 1.i I i I I 1. 21II! i C n C n 3.0 3.5 4.0 4.5 5.0 5.5 TUBE SIDE WATER VELOCITY (FT/SEC) 6.0 6.5 7.0 Figure 36. Summary of the Condensing Coefficient Correction Factorm as a Function of Velocity for Condensation of Steam at 212~F on 1, 3, 5, and 7 Corrugated 1-inch 0. D., Schedule 18, 90-10 Cupro-Nickel Tubes in a Vertical Row. 82

C n c n c n Cn 2. o 0 _-~~~~~ ~ ~~- l~~I TUBE 1. 5 L- 5o ~0 1.0 I I I I I 2.0 -^~~~~~~~~~~- 4~~6 TUBES 1, _ 1.5- o _-. 0 0 ~ 0~~~~~ _ _c5 ~ 0 1.o I I I I 2. i 2.0.I-. 6 TUBES 1.5- o _- 9 TUBES 15 o O 5.0 10 0 15.0 TUBE SIDE WATER VELOCITY (FT/SEC) 20 0 25. 0 Figure 37. Summary of the Condensing Coefficient Correction Factors as a Function of Velocity for Condensation of Steam at 101~F on 1, 4, 6, and 9 Bare 5/8-inch O. D., Schedule 20, Copper Tubes in a Vertical Row. 83

10. 0 5.0 4.0 3.0 I I I I 1- I I I I I I I I 2. 0 1.0.IL 0 L. a) =3 V) Q) -_ Q5) I-s h 0.5 0.4 0.3 0.2K 0.1 0.05 0. 04 0.03 0.02 0 0.01 I I I I I I I I I I I I I I I I I 1 2 3 4 5 10 20 30 40 50 Tube Side Water Velocity (ftlsec) Figure 38. Pressure Drop Versus Tubeside Water Velocity for the Four Tubes Studied in This Investigation. 84

1. ni r.... I I.......... Ul 0. 5 0.4 0.3 0. 2 00 Ln 0s.J o II 0" CC' 0 " C to =- C E.) " C 0.1 I 5 - I I i - I I - L I I I II I I I I I 1111 5/8" Corrugated -0 m^ 0-0-0-o-C-D-o-0-oo —- f = 0. 17574 1" Corrugated O 00_ I 0 0 —oO -o —o-Cfo <y 0 0 ). 05 ). 04 )o 03 I I I I I I If. 1 0. 014334 Le J _. 18 1 1 _ f = 0. 14879 R0. 032793 l" Bare o 5/8" Bare I I I I I I I — I 0.02 0.01 I I I I II I I I I I I I I I 3, 000 104 105 106 Reynolds Number Figure 39. Moody Friction Factor Plot from the Tubeside Pressure Drop Data Appearing in Figure 38.

APPENDICES 86

APPENDIX I Reprint of Paper Published in the AIChE Journal in January 1966, "The Condensing of Low Pressure Steam on Vertical Rows of Horizontal Copper and Titanium Tubes" 87

The Condensing of Low Pressure Steam on Vertical Rows of Horizontal Copper and Titanium Tubes EDWIN H. YOUNG and DALE E. BRIGGS University of Michigan, Ann Arbor, Michigan Heat transfer data are presented for condensing steam at 2 in. Hg absolute pressure on the outside of nine copper and nine titanium horizontal tubes in a vertical row. The condensing coefficient correction factor was maximum for the top titanium tube and was 46% higher than the correction factor for the top copper tube. The difference between the correction factors for titanium and copper tubes diminished with the number of tubes in a vertical row to 8% higher than the correction factor for copper tubes with six to nine tubes in a vertical row. The use of titanium tubes for steam condensation in shipboard power plants and in saline water conversion processes is currently of significant interest. The low wettability surface characteristics of titanium tubes tend to give higher condensing coefficients and the high mechanical strength permits the use of thinner tube walls when compared to conventional materials. Favorable erosion and corrosion resistance properties of titanium further add to the benefits of using titanium tubes. REVIEW OF THE LITERATURE In 1916, Nusselt (1) derived the equation governing the condensation of pure saturated vapors on the outside of a horizontal tube with a wettable surface. Equation (1) was obtained by assuming laminar flow of the condensate and no vapor velocity effects: h =0.725[ P (1) T ji D Att For laminar flow of the condensate, the film temperature t, is given by 3 tr = t,, - - tt (2) 4 Experimental investigations of the condensation of pure saturated vapors on single horizontal tubes indicate that Equation (1) predicts values generally within - 10% of the experimental condensing coefficients (2). The experimental coefficients are usually higher than the theoretical values. This is attributable to turbulence or rippling in the condensate layer. When turbulent flow of the condensate is expected, the average film temperature is often evaluated with Equation (3) (3). 1 t = t, t — At (3) 2 When several horizontal tubes are placed in a vertical row so that condensate from the upper tubes drops on the lower tubes, the mean thickness of the condensate film on a particular tube increases from the top tube to the bottom tube. By accounting for the accumulation of condensate from tube to tube, but still assuming laminar flow of the condensate, Nusselt derived Equation (4) to predict the average condensing coefficient hm for n tubes located in a vertical row (1). h,= 0.725[ kgx i/ Ln,u D Atr - (4) Equation (3) would be used for calculating. t if turbulent flow of condensate is expected. Experimental data taken on multiple horizontal tubes in a vertical row by Katz and Geist (4), Short and Brown (5), and Young and Wohlenberg (6) indicate that Equation (4) is very conservative. The correction for multiple tube rows of (l/n)"14 is much too severe in view of the high degree of turbulence and splashing with condensate dropping from tube to tube. A turbulence correction factor C, was added to Equation (4) by Katz, Young, and Balenkjian (3) to give Equation (5). kpggX 1/4 pg 1/4 h. = 0.725 C, [= C [ p5) n, D A t, n y D t tt Equation (5) corrects the basic theoretical Nusselt model with the correction factor Cn and gives a means of correlating experimental condensing data for multiple tube arrangements (3). The correction factor Cn varies with the number of tubes in a vertical row, the physical properties of the condensate, the tube surface, and the vapor velocity. An extensive experimental program was completed by the British Admiralty in which condensing heat transfer data were obtained for multiple tube arrangements with film and dropwise condensation of steam (7). Photographic studies indicated that heat fluxes six times the average heat flux were obtained in the drop tracks formed in dropwise condensation when large drops rolled across the surface leaving a "bare" metal surface. About one-fifth of the surface had fresh drop tracks at all times. They concluded that high heat fluxes are sustained for times in the order of seconds in very narrow width tracks. The heat flow through these tracks then diverged in crossing the tube wall because the entire internal surface can be used for heat transfer. Because of this, they concluded that very thin metal walls would limit the effectiveness of dropwise condensation. Vol. 12, No. 1 A.I.Ch.E. Journal 88 Page 31

The investigators further determined the effect of condensate inundation on the condensing heat transfer coefficient. By pumping condensate through a perforated tube placed above the test section, the tube on which data were taken could effectively simulate any tube in a vertical row of twenty-two tubes. For filmwise condensation, the condensing coefficient first decreased with inundation due to a thicker condensate film, and then reversed the trend due to increased turbulence at about the fourteenth or fifteenth tube. In dropwise condensation, the effect of inundation was first to increase the condensing coefficient due to enhanced wiping action for the top six or seven tubes followed by a gradual decrease. The coefficient for the simulated twentysecond tube in a vertical row was higher than for the top tube. The existence of any noncondensible gas in the condensing vapor significantly reduces the rate of heat transfer due to the buildup of noncondensible gas around the condensing surface. Experimental work by Othmer (8) and Hampson (9) indicates that as little as 1.5% air by volume can reduce the condensing coefficient by 50%. The greatest effect occurs when there is little motion of vapor across the tubes. Under these conditions, most of the noncondensible gases eventually migrate to the vicinity of the tube. EQUIPMENT AND TEST PROCEDURE The equipment in this investigation consisted of a condenser, inlet and outlet water headers, reboiler, make-up tank, water preheater, pump, two-stage steam jet ejector, and automatic controllers. Figure 1 is a line diagram showing the flow of steam and water. Steam was generated by boiling distilled water in the reboiler with 150 lb./sq. in. gauge steam. The vapor flowed to the condenser where it condensed on the test tubes. The condensate was returned to the reboiler. Water from the cooling tower system was used as the coolant. The condenser was 6 ft. long and 18 in. in diameter. O rings were used to seal the tubes in the tube sheets to permit changing. An impingement baffle was placed over and 2 in. above the tubes in the condenser to prevent direct impingement of steam onto the tubes. The reboiler was 6 ft. long and 24 in. in diameter. High pressure steam (150 lb./sq. in. gauge) was used to vaporize the water in the reboiler. The condensate was returned to the high pressure boiler through a steam trap. Four automatic controllers were installed to assist in the operation of the equipment when taking data. One instrument controlled the water flow rate. A second instrument served as an inlet cooling water temperature controller. The controller pneumatically actuated a steam valve which regulated the amount of steam entering the water preheater. The remaining two instruments were absolute pressure controllers. One sensing element was connected to the condenser. The controller used the pressure signal to regulate the amount of steam entering the reboiler through a 3/4 in. pneumatically operated valve so that the desired pressure in the condenser could be maintained. The second pressure controller was installed in the steam jet ejector system to minimize fluctuations in pressure at the ejector due to variations in the steam flow rate. The control instrument controlled a small bleed valve. By bleeding in small amounts of air, the pressure in the ejector header could be kept relatively constant. The water flow rates in each tube were measured by calibrated orifices placed in orifice holders which were located at the outlet end of the test tubes between the condenser and the exit water header. The orifices were calibrated for each tube tested. The pressure drop across the orifices was measured with water over mercury manometers. Both 50- and 100-in. manometers were used. A manifolded system permitted the same manometer to be used for several orifices. The accuracy of the flow rate measurement was between ~4 and /o%. Inlet water, outlet water, and condenser steam temperatures were measured with calibrated 30 gauge copper-constantan thermocouples with a Leeds and Northrup K-3 potentiometer. Temperatures could be measured to 0.01~F. The inlet water thermocouple was placed in the inlet water header. The exit water thermocouples were located in the orifice holder assemblies within stainless steel sheaths extended upstream along the tube axis for 1 in. Thermocouples were placed in two places in the back of the condenser to permit the measurement of the steam temperature. The condenser absolute pressure was determined with a mercury manometer and calibrated barometer. During normal operation, the reboiler was one-half to twothirds filled with distilled water through the water make-up tank. Once the reboiler was filled to the desired level, steam and water to the steam jet ejector were turned on and adjusted to give the maximum evacuation rate. The ejector was allowed to operate for approximately 30 to 45 min. to evacuate thoroughly noncondensible gases from the condenser-reboiler system. The pressure in the condenser rapidly approached the vapor pressure of the water in the reboiler during this period. With the ejector still pulling a vacuum on the system, the condenser pressure controller was set at the desired pressure setting. The automatically controlled steam valve in the reboiler steam line then opened, allowing the water in the reboiler to be heated until the vapor pressure of the water equalled the set point pressure. The system was operated under these conditions for approximately 20 to 30 min. This further assisted in degassing the water and evacuating the system. The cooling water controller was next set to the desired total water flow rate and the inlet water temperature controller set at the desired inlet water temperature. The steam jet ejector manifold pressure controller was set at a pressure somewhat below the condenser pressure. This minimized the air bleed and permitted maximum removal of noncondensible gases during the period when data were taken. There was a very small amount of air leakage into the system. Before data were taken, the saturated steam temperature was calculated on the basis of the absolute pressure indicated by the manometer and compared to the steam temperature measured with a thermocouple. If the two temperatures agreed within % ~F., the system was considered ready for taking data. If the temperature calculated from the absolute pressure in the condenser was greater than ~F. above the measured temperature, an excessive amount of air still remained in the system and evacuation was continued until satisfactory agreement was obtained. Heat transfer data were taken when the automatic controllers had stabilized all the control variables at the desired set points. MULTIPLE TUBE DATA PROCESSING AND RESULTS The overall heat transfer coefficient for each tube was calculated from 11.0......... C~~(U -.0IlICO ICIXl'.0n.IUIK IICIA I w-uu Q U o AT Ao ATm (6) where the heat duty Q was obtained experimentally from Fig. 1. Line diagram of equipment showing the flow of steam and water. Q = W Cp (tout -tin) (7) Page 32 A.I.Ch.E. Journal 89 January, 1966

TABLE 1. TUBE DIMENSIONS AND CHARi Copper Average for Top vertical tube row Tube type Tube O. D., in. Tube I. D., in. Tube wall thickness, in. Tube length, in. Thermal conductivity, B.t.u./(hr.) (sq. ft.)( 0F. )/ft. plain 0.6252 0.5550 plain 0.6252 0.5550 ACTERISTICS erties of the condensate film, the condensing coefficient constant was calculated from Equation (10). The average Titanium inlet water temperature, water velocity, and steam temAverage perature for all nine tubes were also calculated. A printout for of the results completed the first section. Top vertical In the second section of the program, the average inlet tube row water temperature, water velocity, steam temperature, and condensing coefficient constants for each tube were plain plain used to predict for each tube what the heat duty, exit 0.6287 0.6271 water temperature, logarithmic temperature difference, 0.5592 0.5581 overall heat transfer coefficient, inside heat transfer co0.0347 0.0345 efficient, and condensing coefficient would have been had 72156 72 156 the inlet water temperature, water velocity, and'steam temperature been equal to the average values. These calculations put all the tubes on a consistent basis. A print10 10 out of the results completed the second section. The condensing coefficient correction factor was calculated in the third section of the computer program. The 0) was used to correction factor is by definition that factor which makes in Equation (8) Equation (5) an equality and is calculated from Equation t used in the in- (11): 0.0351 0.0351 72.156 72.156 196 196 A modified Wilson plot technique (ii obtain a realistic value of the coefficient for the narticular experimental equipment vestigation. This was done in preference to using an arbitrary value from the technical literature. The modified Wilson plot technique took into account the variation in the average temperature drop across the condensing film with changes in water velocity. It did not take into account the variation of the temperature drop across the condensing film from one end of a tube to the other end. The intent of the investigation was to look at the average condensing heat transfer coefficients with titanium and copper tubes. Wilson plot data were obtained on the top tube in the vertical row for each alloy tube. The tube dimensions are given in Table 1. With the use of the average value of C, for the two sets of data, the inside heat transfer coefficient became h. Cn (11) 0.725 [ Lp2g 1/4 n u D At, h = 0.0248 [ DIG C k, < k /lu^J (8) The condensing coefficient and the condensing coefficient constant were calculated with Equations (9) and (10), respectively, for all the Wilson plot data. 1 1 A, A.^~'U: A^"'- (9) h. U. Ah, From Equation (5) with n = 1 for the top tube hm C = (10) p fD Atf Two sets of heat transfer data were taken on the nine tubes in a vertical row. The first set of data were taken on copper tubes and the second set of titanium tubes. The original data appear in reference 10. The purpose of taking multiple tube data was to obtain the correction factor C, for Equation (5) as a function of the number of tubes in a vertical row for the condensation of steam at 2 in. Hg absolute pressure. A computer program was written for the IBM 7090 digital computer to process the data. The computer program consisted of three sections. In the first section the input data, including the average value of the inside heat transfer coefficient constant, were read into the computer and preliminary calculations were made. These operations included the calculation for each tube of the heat duty, logarithmic temperature difference, overall heat transfer coefficient, water velocity, bulk water physical properties, inside heat transfer coefficient, and condensing coefficient from Equation (9). From the condensing coefficient and physical prop In Equation (11), the mean condensing coefficient h, is the mean condensing coefficient for the top n tubes calculated from the experimental data. The correction factor for the top tube was calculated with the values of the heat duty and exit water temperature calculated in the previous section. The overall heat transfer coefficient, logarithmic temperature difference, and inside heat transfer coefficients were then calculated and the mean condensing coefficient computed from Equation (9). Equation (12) was used to calculate the temperature drop across the condensing film At,=U At, (12) h, and Equation (3) was used to calculate the film temperature. Once the film temperature was known, the quantity with n = 1 0.725 kgp' g X 11/4 0.725 1 DAt1 p, D Att was calculated and Cn computed from Equation (11) for the top tube. To determine C, for the top two tubes in the vertical row, the heat duties calculated in the second section of the computer program for the top two rows were added to give the total heat transferred. With the mean values of the water density and heat capacity for the top two tubes, we calculated the average exit water temperature for the top two tubes. The logarithmic temperature difference, overall heat transfer coefficient, and inside heat transfer coefficient were calculated next and the mean condensing coefficient was calculated from Equation (9), the temperature drop across the condensing film was calculated from Equation (12), and the film temperature was calculated from Equation (3). The quantity 0.725 [ 2 L D At 2,u D Atf was computed and the correction factor for two tubes in a vertical row was calculated from Equation (11). The correction factors for 3, 4....9 tubes in a vertical row were calculated by adding the heat duties for the top n tubes and by following the procedure previously outlined. The computer program and typical calculated results can be found in reference 10. Vol. 12, No. 1 A.I.Ch.E. Journal 90 Page 33

DISCUSSION OF RESULTS Tables 2* and 3 give the values of the condensing coefficient correction factors for a vertical row of one to nine copper and titanium tubes, respectively. The results were obtained from experimental data taken at a steam pressure of approximately 2 in. Hg absolute and an inlet water temperature of 75~F. Average values of C, for each water velocity are given in Tables 4 and 5 for copper and titanium tubes, respectively. The results are also presented in Figures 2 and 3. Average values of Cn for all the data as a function of the number of tubes in a vertical row are given in Table 4 for copper tubes and Table 5 for titanium tubes. As can be seen in Figures 2 and 3, the condensing coefficient correction factor C, is higher for titanium tubes than for copper tubes. The maximum value of C, for titanium tubes occurs for the top tube where C, is 46% higher than the value for the top copper tube. The difference in C, diminishes to a more or a less constant value of approximately 8% greater with six to nine tubes in a vertical row. Inundation drastically reduces the effectiveness of titanium tubes with essentially all the improvement being a result of the increase on the top tube. In Figures 2 and 3, there appears to be a consistent trend in which for a given number of tubes in a vertical row C, varies with the tube-side water velocity (or condensate loading as both are directly related). For low and high velocities the correction factor is higher than for intermediate velocities. This is attributable in part to the varying degrees of turbulence in the condensate film depending upon the tube condensate flow rate, as previously mentioned. The maximum deviations from the mean values in Figures 2 and 3 are 5.3 and 6.3%, respectively. Visual observation of low pressure steam condensing on the nine titanium tubes in vertical row revealed that as could best be seen, only filmwise condensation was occurring. Visual observation of the top tube was limited and it could be possible that partial dropwise condensation was occurring on this tube. The generally lower wettability of the titanium tube surface increases the condensing coefficient but not to the point where dropwise condensation will persist for multiple tube arrangements. * Tables 2 through 5 have been deposited as document 8560 with the American Documentation Institute, Photoduplication Service, Library of Congress, Washington 25, D. C., and may be obtained for $1.25 for photoprints or 35-mm. microfilm. 20 - 1.9 k 8l c 17 h Water Velocity o 6.5 ft /sec A 94 ft/sec o 13.3 ft./sec v 16.3 ft/sec o 209 ft/sec * 24.9 ft/sec - overoge Maximum deviation 6.3 % o v v o * o. * 0 l I I i 1 1 i 1 [ 16 1.5 k,4 I 2 3 4 5 6 7 8 9 TUBES IN VERTICAL. ROW Fig. 3. Condensing coefficient correction factors for condensation of steam at 2 in. Hg absolute pressure on one to nine titanium tubes in a vertical row. ACKNOWLEDGMENT Permission by the Wolverine Tube Division of Calumet and Hecla, Inc., to publish this paper is appreciated. William D. Hancock, Boris Tarunteav, and Hans G. Schwallbach assisted in the construction of the experimental equipment and the collection of the experimental data. NOTATION Ai = total internal heat transfer surface, sq. ft. Ao = total external heat transfer area, sq. ft. C = condensing coefficient constant which is equivalent to 0.725 C,, dimensionless C, - inside heat transfer coefficient constant, dimensionless C, = turbulence correction factor, dimensionless cp = specific heat of water, B.t.u./(lb.) (~F.) D = outside diameter of tube, ft. D i= tube inside diameter, ft. G = mass flow rate, lb./(hr.) (sq. ft.) g - acceleration due to gravity, taken as 4.17 x 10" ft./hr.2 hi = inside heat transfer coefficient, B.t.u./(hr.) (sq. ft.) (F.) hm = mean condensing coefficient, B.t.u./(hr.) (sq. ft.) (~F.) k = thermal conductivity of condensate evaluated at film temperature, B.t.u./(hr.) (sq. ft.) (~F.)/ft. ki = water thermal conductivity at bulk water temperature, B.t.u./(hr.) (sq. ft.) (~F.)/ft. n = number of tubes in a vertical row Q = total heat transfer, B.t.u./hr. rm = metal resistance, hr./sq. ft. (outside area) ~F./ B.t.u. ti, = inlet water temperature, ~F. tf = average condensing film temperature, ~F. tolt = outlet water temperature, ~F. t, = outside wall temperature of the tube, ~F. t,v = temperature of the saturated vapor, ~F. Uo = overall heat transfer coefficient, B.t.u./(hr.) (sq. ft.) (F.) W = water flow rate, lb./hr. Greek Letters Atf = temperature drop across condensate film, t,,,- t,, OF. 16 1.5 r 1.4 IX r X I I X 7 Water Velocity o 5.9 ft/sec a 8.9 ft/sec - 11.6 ft/sec v 16.7 ft/sec o 20.2 ft/sec * 25.5 ft/sec - - overage - Maximum deviation 5.3 % * o ~ o o _ o ^ A A Ao X O 0 0EI_ 13 1.2 2 3 4 5 6 7 8 9 TUBES IN VERTICAL ROW Fig. 2. Condensing coefficient correction factors for condensation of steam at 2 in. Hg absolute pressure on one to nine copper tubes in a vertical row. Page 34 A.I.Ch.E. Journal 91 January, 1966

T, = logarithm temperature difference, ~F. X latent heat at saturation temperature, B.t.u./lb. At, = water viscosity at bulk water temperature, lb./ (ft.) (hr.), = viscosity of condensate evaluated at film, temperature, lb./(ft.) (hr.) Mu, = water viscosity at average inside wall temperature, lb./(ft.) (hr.) p = density of condensate evaluated at film temperature, lb./cu. ft. LITERATURE CITED 1. Nusselt, W., Z. Ver. Deut. Ing., 60, 541, 569 (1916). 2. Jakob, M., "Heat Transmission," Vol. 1, Wiley, New York (1949). 3. Katz, D. L., E. H. Young, and G. Balekjian, Petrol. Ref., 33, No. 11, 175-178 (1954). 4. Katz, D. L., and J. M. Geist, Trans. Am. Soc. Mech. Engrs., 70, No. 11, 907-914 (1948). 5. Short, B. E., and H. E. Brown, in "Proceedings of the General Discussion on Heat Transfer," Sect. I, pp. 27-31, Am. Soc. Mech. Engrs. and Inst. Mech. Engrs. (London) (1951). 6. Young, F. L., and W. J. Wohlenberg, Trans. Am. Soc. Mech. Engrs., 64, No. 11, 787-794 (1942). 7. Watson, R. G. H., J. J. Brunt, and D. G. P. Birt, in "International Developments in Heat Transfer," Pt. II, Am. Soc. Mech. Engrs., New York (1961). 8. Othmer, D. F., Ind. Eng. Chem., 21, 576 (1929). 9. Hampson, H., in "Proceedings of the General Discussion on Heat Transfer," Am. Soc. Mech. Engrs. and Inst. Mech. Engrs. (London) (1951). 10. Briggs, D. E., and E. H. Young, Rept. No. 55, 01592-149-T, Office Res. Admin., Univ. Michigan, Ann Arbor (December, 1963). Manuscript received September 30, 1964; revision received June 18, 1965; paper accepted July 23, 1965. Paper presented at A.I.Ch.E. Boston meeting. Vol. 12, No. 1 A.I.Ch.E. Journal 92 Page 35

APPENDIX II Copy of AIChE Preprint 5 "Modified Wilson Plot Techniques for Obtaining Heat Transfer Correlations for Shell-and-Tube Heat Exchangers" and Computer Program and Nomenclature Used by Wolverine Tube to Determine The Seider- Tate Inside Heat Transfer Coefficient Constant in Equation 9 93

MODIFIED WILSON PLOT TECHNIQUES FOR OBTAINING HEAT TRANSFER CORRELATIONS FOR SHELL-ANDTUBE HEAT EXCHANGERS AIChE PREPRINT 5 D. E. Briggs and E. H. Young The University of Michigan, Ann Arbor, Michigan I PS ^1 4_ ) Presented at the TENTH NATIONAL HEAT TRANSFER CONFERENCE A.I.Ch.E.-A.S.M.E. Philadelphia, Pennsylvania August 11-14, 1968 rreprinted for the conference by AMERICAN INSTITUTE OF CHEMICAL ENGINEERS 345 East 47 Street, New York, New York 10017 Preprinting this paper does not release it for publication. All rights are reserved by the sponsoring society, Members AIChE, ASME Nonmem bers $.75 1.50 94

INTRODUCTION The separation of individual heat transfer resistances from the overall heat transfer resistance of the system is extremely important in obtaining heat transfer correlations for forced convection, condensation, and boiling. To develop shell-side heat transfer correlations for concentric pipe and shell-and-tube heat exchangers, accurate shell-side heat transfer coefficients are needed. Accurate condensation and boiling heat transfer coefficients are required to obtain correlations suitable for design purposes. Local heat transfer coefficients can be found by direct measurement of the temperature drop across a convective or condensate film by using thermocouples located in the wall of the tube and in the bulk stream. This method works well for single resistance heated tubes for which thermocouples can be attached to the tube wall without disturbing the fluid flow in the vicinity of the thermocouple. The accuracy of the process is directly related to the temperature drop across the heat transfer film. In the design of heat transfer equipment, overall convective film,'10 condensing, or boiling coefficients are usually preferred to local coefUtl ficients. Although local coefficients can be suitably integrated over the tube length to give the average film coefficient for the whole tube, i. e., as with a boiling refrigerant inside a tube, this cannot be conveniently done for many systems and configurations. The large number of tubes and the baffle arrangement in shell-and-tube heat exchangers makes it impossible to put a sufficient number of thermocouples inside the shell without seriously affecting the flow of the shell-side fluid. A useful technique for determining individual resistances from an overall resistance was devised by Wilson in 1915. Wilson was interested in determining the effects of water temperature and velocity on the overall coefficient for a steam condenser. Wilson's technique was used by Katz and Geist in 1948 to obtain condensing coefficients for six finned tubes in a vertical row. The technique was used by Knudsen and Katz in 1950 to develop tube-side and shell-side heat transfer coefficient correlations for concentric pipe heat exchangers. In 1952, Williams and Katz4 used the same procedure to evaluate tube-side and shell-side heat transfer coefficient correlations for shell-and-tube heat exchangers. In 1957, Young and Wall modified the procedure and obtained shell-side and tube-side heat transfer correlations for concentric pipe heat exchangers. EXISTING WILSON PLOT PROCEDURE FOR NO PHASE CHANGES In the method used by Young and Wall' for finned tubes, the finresistance procedure was employed. Their modification involved the use of the Sieder and Tate equation for the outside and inside heat transfer coefficients: 0.8 1/3 0.14 h' D (D G\ c k ) ( o eq = -C.- ) koo (1) and 0.8 1/3 hk D ) i ( k 3 ( 1 x -, \ W / 0.14 (2) Equations (1) and (2) were solved for h' and h., respectively, and were subo 1 stituted into the following overall heat transfer relationship: 1 1 1 A U- = - + rfin + rm + h A- - o o 1 1 (3) 3 2

The substitutions give: ( U~- rfin - rm) = In using this procedure, tube-side Wilson plot data are obtained by maintaining the shell-side bulk temperature and flow rate constant while collecting field test data at several different tube-side fluid flow rates. For these conditions, Equation (5) has the mathematical form: 0.8 1/3 0.14 k D G\ \L\ c --- ( P Deq eq (D) (- k) (1w ) o o o A o 0.8 0.8 1/3 0.14 + y = mx + b (6) (4) where: A C G-. - i -(- i) ( ) i i 0.14 y = ( - rfin - r ) (7) If the tube-side fluid flow rate varies, the viscosity ratios will vary even if the bulk fluid temperature and the shell-side flow rates are held constant. In order to make the expression for the outside heat transfer coefficient constant, it is necessary to multiply Equation (4) (a ~-0.14 I'D by the expression ( _)1. This substitution gives 0^ 7w o m = ci (8) x = (U - Jrfin - rm)(-)0 o 0 1 k (D G ()e 8 ( 3 + eq 0 0 0.14 A. ( ) 0 0.8 1/3 0.14 i i i 1 (9) 0.14 and the intercept: Ai w o k. D.G C 1 1 i Di (~. (c k /k (5) 1/3 0.14 (5) 1 1 k D G ~~0. 8 t I3 (10)

Tube-side Wilson plot results are obtained by a linear regression of the function y on x. The reciprocal of the slope of the least squared deviation line through the data is equal to the inside heat transfer coefficient correlation constant, C.. The value of the outside heat transfer coefficient correlation constant, C, can be calculated from o Equation (10). The above procedure of Young and Wall was applied to the test data of Williams and Katz' 9. In the technique, an initial estimate of the constant, C., for Equation (2) is made in order to determine the wall temperatures from the experimental data. The Wilson plot functions are calculated and the slope of the least squared deviation line through the data determined. The reciprocal of the slope of the line is equal to the calculated value of C.. If the assumed and calculated values of C. 1 1 differ by more than some allowable error, a re-estimated value is taken as the assumed value and the procedure repeated. Convergence of the assumed and calculated values of C. to within 0. 05 percent is usually obtained within 4 or 5 trials. Figure 1 presents Wilson plot results typical of this method for the data. The data were processed with an "-1 IBM 7090 digital computer. The linear regression of y on x was effected with a subroutine. Calculated values of C. for Equation (2) are given in Table I. TABLE I Calculated Values of the Inside Heat Transfer Correlation Constant Obtained by the Wilson Plot Method as Modified by Young and Wall for Data Taken on a 6-inch Heat Exchanger with Water on the Shell-and-Tube Sides Shell-side heat transfer correlations can be obtained in several ways. The constant, C, for Equation (1) can be evaluated from the value of the intercept found in the tube-side regression analysis, but there is no guarantee that the resulting correlation will be valid over a wide range of Reynolds numbers without calculating C from the intercept values for several sets of tube-side Wilson plot data each with a different shell-side flow rate. The values of C for each set of data should o be averaged to give the correlation expressed by Equation (1). If the tube-side correlation is established by a Wilson plot method, a shellside correlation can be devised by taking data at several different shellside flow rates, evaluating the shell-side coefficient from Equation (3) and plotting the function yshell versus x shell: (h'D ) o eq Yshe11 = In ( s^hell ~~- 1/3 -. 140 0 (11) shell (12) Runs 24A- 24D 25A-25D 26A-26D 27A-27D 28A-28D C. 1 0. 02665 0.02431 0.02540 0. 02558 0. 02508 Average 0.02540 The slope, P, of the least squared deviation line through the processed data [Yshell' xshell] is equal to the exponent of the Reynolds number and the exponential of the intercept (where Re = 1) is equal to the shell-side correlation constant, C, in Equation (13): 7 6

h' D D G o eq = C o0 Dc(eG L 0 o ( P 1/3 0. (k) (-i ) 0 0 0.14 (13) The value of the exponent P varies from about 0. 6 at low Reynolds numbers (Re <1000) to approximately 0.9 at high Reynolds numbers (Re> 10, 000). This is evident on j-factor plots covering a wide range of Reynolds numbers Shell-side correlations can also be obtained by taking heat transfer data with a constant bulk fluid temperature on the tube-side and making shell-side Wilson plot calculations. In this instance, Equation (4) is multiplied by 0.14 ( - ) 14, and the procedure outlined in the tube-side Wilson plots \w 1 technique is followed. The shell-side Reynolds number exponent, 0.8, in Equation (4) could be replaced, but the best value to use is seldom known a priori. MODIFIED WILSON PLOT TECHNIQUE FOR NO PHASE CHANGES There are two distinct disadvantages to the traditional Wilson plot 00o techniques and the modified technique of Young and Wall. Firstly, the data are troublesome to obtain because of the constant flow rate and constant average bulk fluid temperature requirements. Secondly, a considerable number of data are required for accurate tube- and shell-side heat transfer correlations. It would be very desirable to have available a type of regression analysis procedure which could determine the values of the constants Ci, C, and P in Equation (14) in a least square deviation sense while obviating the disadvantages of the traditional Wilson plot procedures. ating the disadvantages of the traditional Wilson plot procedures. Upon examination of Equation (14) it is obvious that a linear regression analysis scheme is impossible except for plain tubes under conditions where the group (/w )0. 14 is essentially unity and where the value of P is known. For finned tubes, the shell-side coefficient must be known to evaluate the fin resistance. If the viscosity ratio groups and the shell- side Reynolds number exponent are to be included in addition to relaxing the flow rate and fluid temperature conditions, a non-linear regression analysis procedure must be used. A non-linear regression analysis can be effected by using successive linear regressions in a trial and error procedure. Multiplying Equation (14) by P 1/3 0.14 _(<\ () (a) kD gives P 1/3 0.14 ( i )[ k (D ) (~) (:) ] = 0 0 0 P 1/3 0.14 1 o eq o k G&) ] C L k DG )O. 8 ( ) 1/3 ( 0. 14'.h G- (-"1 () 1 111~~~ (15) ( - rfin- rm ) =' o 1 k f0^ f-^Y/3 ^ 0.14 + C ~0 (D L k ( ( + ) 0 0 0 which again is of the form y = mx + b (6) A o (14) k (DiG.8 ( )1/3 0.14 Ai1i D i [1 k Lw i i 8

where p 1/3 0.14 Y~m = - r P 1/3 0.14 A kD G\/c \ /\ 0 1Sm - 0.8 1/3 0.14 i i ( i (16) (8) (17) value of the inside heat transfer coefficient and subsequently the wall temperatures and the viscosity ratio functions. If the least squared deviation value of C. obtained by the linear regression differs from the assumed value by more than some allowable error, C. is re-estimated and the calculations repeated until satisfactory agreement between the assumed and calculated values is attained. The shell-side coefficient for each run is calculated using Equation (3) and the functions y shell and x shel calculated. A linear regression of y shell on x shel gives the least squared deviation values of P and C. If the calculated value of P differs from the assumed value of P by more than the specified maximum amount, P is re-estimated and all the calculations repeated until satisfactory agreement between the assumed and calculated values is reached. The values of C obtained from the two linear regression analyses should o agree closely. The non-linear regression procedure can be considered as being a further modification of the original Wilson plot procedure in which the equations are transformed into a form suitable for a linear regression analysis. Figures 2 and 3 give the linear regression analysis results for the data presented in Figure 1. Figure 2 indicates that all the experimental data in Figure 1 can be correlated together giving a greater statistical meaning to the results. Figure 3 presents the shell-side correlation obtained in the process of evaluating the inside heat transfer coefficient constant. The heat transfer correlations for the finned tube heat exchanger with water on both sides become and b - 0 (18) As indicated by Mickley, Sherwood, and Reed, the transformation of Equation (14) into Equation (15) is mathematically permissible and although it may appear to give an improved or inferior correlation of the data when plotted, the correlation is in fact unaltered. The advantage of such a transformation is that it puts Equation (15) into a form suitable for effecting a linear regression of y on x giving the least square values of m and b or of more importance, their reciprocals, C. and C, 1 o respectively. The evaluation of the functions y and x requires an initial estimate of P and C.. The constant C. is used to calculate an estimated i 1 0.8 Nu. = 0. 02589 Re. 1 1 Pr. --- 1 / w 0.14 (19) o and 0.9389 1/3 / 0.14 Nu = 0.01809 Re Pr 0'0 0 lw 0 (20) 10 11

Agreement between the assumed and calculated values of C. and P were within 0.05 and 0. 1 percent, respectively. The values of the shell-side correlation constant calculated from the intercept values of Figures 2 and 3 agreed within 0. 5 percent. Wilson plot data for oil and glycerine on the shell-side of Bundle 6 of Reference (4) were also analyzed. The results obtained by the two methods are given in Tables II and III. As the shell-side resistance is controlling with oil and glycerine on the shell-side, it is difficult to obtain good tube-side Wilson plot results with only 4 data points. By correlating all the data for a particular shell-side fluid together as shown in Figures 4 and 5 significantly better results are obtained. The calculated value of the constant, C., for oil on the shell-side agreed with the value obtained for water on the shell-side and the value of C. for glycerine on the shell-side agreed within 6 percent. Figures 6 and 7 give shell-side correlations for oil and glycerine, respectively. These correlations were obtained in the process of effecting the linear regression analysis for P. As can be seen from Figures 6 and 7, there is very good agreement between the two correlations as there should be. Figure 8 presents the results given in Figures 3, 6 and 7. Whenever heat transfer data taken over a wide range of shell-side Reynolds numbers, i.e., 10-100,000, are correlated together, Equation (13) is no longer a satisfactory correlating equation for the shell-side coefficient since the power to which the Reynolds number should be raised to represent the data changes with Reynolds numbers as is evident in Figure 8 and on most j-factor plots. Equation (13) can be modified by making the Reynolds power a function of the Reynolds number as, for example, in 0.14 TABLE II Calculated Values of the Inside Heat Transfer Correlation Constant Obtained by the Wilson Plot Technique Modified by Young and Wall for Data Taken on a 6-Inch Diameter Heat Exchanger with Water on the Tube-side 0 0 Shell-side Fluid Oil Glycerine Run Numbers 32A-32D 33A-33D 34A- 34D 35A-35D 36A-36D 37A- 37D 38A-38D 72A-72D 73A-73D 81A-81D 87A-87D 0. 01406 0.01974 0.01450 0.01661 0.02010 0. 02374 0.02549 0.01563 0. 01134 Average 0. 01801 0.02385 0.01680 Average 0. 02032 Ci from Young and Wall Modification (P + Plx In Re ) 1/3 Nu = C Re Pr fM o oo o \ (21) 12

Equation (21) has been used to represent the shell-side heat transfer coefficient in the modified version of the Wilson plot technique with satisfactory results. The procedure parallels the method outlined. 10 Other shell-side correlation models, such as proposed by Bell, can also be used with suitable adaptation. MODIFIED WILSON PLOT TECHNIQUE FOR CONDENSATION The Nusselt expression for condensation on a single horizontal plain tube is 1/4 TABLE III Calculated Values of the Inside Heat Transfer Correlation Constant Obtained by the Wilson Plot Technique as Modified by Briggs for Data Taken on a 6-Inch Diameter Heat Exchanger with Water on the Tube-side h 0.72 f P g h = 0.725 1 - D - -t c f f J (22) Beatty3 derived an expression for condensation on horizontal finned tubes using Equation (22) in which for finned tubes the diameter, D, is defined by Shell- side Fluid Run Numbers 0 i —j Oil 32A-73D Ci from Briggs Modification 0. 02588 0. 02439 1/4 (1\ Ar 1. 300 Af _/4 + 1 /4 i D A D 1/4 A L eq r eq (23) Glycerine 80, 81A-81D, 82-86, 87A-87D, 101, 103 where A = A +0A eq r f (24) Equation (22) has been modified for multiple tube arrangements and a turbulence correction factor, C, has been included to account for the n system variance from Equation (22). These changes give for condensation on a multiple tube arrangement of plain or finned tubes, 15

1/4 r kf pf g x h' =N (25) Using Equations (2) and (25) to represent the inside and condensing heat transfer coefficients, respectively, and substituting the expressions for the coefficients into Equation (3) and rearranging gives 1/4 (1 \ rkf f3Pf f 1g - rfin - rN Dt = 0t~ o 2L f a Dtf 1/4 A [k Pf g 1u A LfN D Atf 0.725 C +. 8 1/3 0.14 1 D1 / 1 1 i i which has the required form for a linear regression y = mx + b (27) (U - rfin - rm) = 1/4 0.725 C[ kf pf ] Ao (6) (26) 0.8 1 k(D ) ( )1 1 i /3 0.14 (1) where 0 tN The condensing coefficient represented by the middle group of terms can be held constant with only the greatest of difficulty. Even if the vapor temperature and average tube-side fluid temperature are held constant, the condensing coefficient will vary with changes in the tube-side fluid velocity due to the resultant changes in the temperature drop across the condensing film. Multiplying Equation (26) by 1/4 2 1 kf3 pf gX f N D Atf J 1/4 y (- - = rfin- rm) Lf N D tf 1 C. 1/4 A kf pf2 gk 1 A'i f Na D ttf 0.8 1/3 0.14 D ) (k) ( ) 1 i i (28) (8) (29) (30) b = 1 0.725 C n gives 16 17

A linear regression of the function y above on x gives the least squared deviation values of m and b or more important their reciprocals C. and 0.725 C, respectively. There is, however, a trialn and-error calculation involved due to the presence of the viscosity ratio group in the equation for the inside heat transfer coefficient. As before a value of C. is assumed and calculations made to evaluate the required functions. The calculated and assumed values of C. are compared and the procedure repeated until satisfactory agreement is attained. To illustrate the modified Wilson plot technique, data for condensation of refrigerant 114 on a single horizontal finned tube at two different condensing temperatures were used. Figure 9 presents a traditional Wilson plot for condensation. The intercepts of the lines through the data are supposedly equal to the value of (1/h') + r + rfin o m fin at an infinite water velocity, but as can be seen from Equation (26), this can only be true if the change in (1/ho) with changes in (A /Aihi) is constant. A modified Wilson plot is given in Figure 10. The condensing data for two different temperatures correlate well with a single straight line. The heat transfer correlations obtained by the two methods are given in Figures 9 and 10. arid Equation (13), respectively. Substituting the expressions for h' 0 and hb defined by Equations (13) and (31) into Equation (3) and rearranging gives ( - rfin- rm) P 1/3 0.14 k (D G\c ) o 0 eq ^) (Z) 0 0 0 + (32) A o 2 0.5 i Ab [( ) ( L Multiplying Equation (32) by the group of terms representing h' and 0 excluding C gives P 1/3 0.14 ( —- rfin rm)[ ( ) (_ ) ) WILSON PLOTS FOR BOILING The Wilson plot technique can also be used to separate coefficients in systems where boiling occurs. Heat transfer correlations for boiling refrigerants inside of horizontal tubes and for forced convection on the shell-side of a heat exchanger are 2 0.5 P 1/3 0.14 _A [_%o ( (eq ) (L: ) I i D [eq(L ( w kL [(D G 2 ( J Ax X)] — H )( } (33) which again is of the form y = mx+b hb Di C (DIG a i kL b ii L L t ) (31) 19 18

where P 1/3 0.14 ( - rf- rm) [ ( ) ( ) ( ).4 m = C b P 1/3 0.14 -r ^[(r1) ( k ) (Z) I I 0 xL [(D ) (J \ ] b - C mechanisms. The resulting equations are put into a linear form by suitable manipulations and the required constants are solved for in an iterative fashion using linear regression analyses. It is not the authors' (34) intention to advocate what models should be used but rather to illustrate how given models can be used to analyze data to determine the appropriate constants for the models. There is a significant difference between the (35) choice of models and the evaluation of constants for models. The paper was written to present examples of how one could determine constants for mathematical models from experimental test data. It does take considerable experience in the area of heat transfer to be able to develop a (36) mathematical model to represent heat transfer data. If certain parameters are important to the representation of the data, then the correlation will be inadequate without those parameters. The availability and use of modern digital computers have made rational, comprehensive, and exact analysis of heat transfer data possible (37) with modified Wilson plot techniques. The resulting heat transfer correlations obtained from such techniques are invaluable to the design of heat exchangers. 0 4^ For initial values of Cb and P the trial-and-error calculations can be carried out in a manner analagous to the procedure outlined for no phase change and the constants Cb, C, and P evaluated. O CONCLUSIONS Modified Wilson plot techniques have been developed and successfully used to determine individual heat transfer coefficients from overall heat transfer coefficients for many types of heat transfer processes. The approach consists of developing modified Wilson plot expressions for the individual coefficients which describe the heat transfer 20 21

LITERATURE CITED 1. Wilson, E. E., Trans. Am. Soc. Mech. Engrs., 37, p. 47-82 (1915). 2. Katz, D. L., and J. M. Geist, Trans. Am. Soc. Mech. Engrs., 70, p. 907-194 (1948). 3. Knudsen, J. G. and D. L. Katz, Chem. Engr. Progr., 46, p. 490 (1950). 4. Williams, R. B. and D. L. Katz, Trans. Ama. Soc. Mech. Engrs., 74, p. 1307-1320 (1952). 5. Young, E. H., J. R. Wall, et al., "Development of an Apparatus for the Measurement of Low Bond Resistances in Finned and Bare Duplex Tubing, " Engineering Research Institute, University of Michigan, Report No. 48, Project 1592, 1957. 6. Carrier, W. H. and S. W. Anderson, Heating, Piping and Air Conditioning, p. 75-78, July 1950. 7. Keller, H. H. and E. V. Somers, Trans. Am. Soc. Mech. Engrs., 81, Series C, No. 2, p. 151 (1959). 8. Sieder, E. N. and G. E. Tate, Ind. Eng. Chem., 28, p. 1429-1435 (1936). 9. Briggs, D. E., D. L. Katz, and E. H. Young, Chem. Engr. Progr., 59, No. 11, p. 49 (1963). 10. Bell, K. J., "Final Report of the Cooperative Research Program on Shell and Tube Heat Exchangers, " Bulletin No. 5, University of Delaware Experiment Station (1963). 11. Mickley, H. S., T. K. Sherwood, and C. E. Reed, Applied Mathematics in Chemical Engineering, McGraw-Hill, New York, N.Y. (1957). 12. Jakob, M., Heat Transmission, Vol. 1, John Wiley and Sons, New York, N.Y. (1949). 13. Beatty, K. O., Ph.D. Thesis, The University of Michigan, 1946. 14. Devore, A., Pet. Ref., 38, No. 6(1959). 15. Katz, D. L., E. H. Young and G. Balekjian, Pet. Ref., 33, No. 11 (1954). 16. Altman, M., R. H. Norris and F. W. Staub, Trans. Am. Soc. Mech. Engrs., Journal of Heat Transfer, 82, p. 189 (1960). n 23 22

NOTATION A = equivalent outside heat transfer area of a fin tube, sq. ft. eq Af = fin area of a finned tube, sq. ft. A. = inside heat transfer area, sq. ft. A = outside heat transfer area, sq. ft. o A = root area of a fin tube, sq. ft. b = intercept of line with ordinate Cb = constant for boiling correlation, Equation C. = constant for inside heat transfer correlation i C = turbulence correction factor for condensing coefficient correlation n C = constant for shell-side heat transfer correlation o c = heat capacity of fluid, Btu/lb. -~F P D = tube diameter for condensing correlation; equal to outside diameter of a plain tube and defined by Equation ( ) for a finned tube - ft. D = characteristic length for shell side correlation; root diameter for finned tube bundles - ft. D. = inside diameter of tube, ft. d. = inside diameter of tube, in. 1 G = mass flow rate, lb. /hr. -sq. ft. 8 2 g = gravitation constant, 4.17 x 10 lb. -ft. /lb. -hr. m = boiling heat transfer coefficient, Btu/hr.-sq. ft.-'F h C = condensing heat transfer coefficient, Btu/hr.-sq. ft. -~F h. = inside heat transfer coefficient, Btu/hr. — sq. ft. - ~F h = outside heat transfer coefficient including fin resistance, Btu/hr. - sq. ft. - ~F h' = actual outside heat transfer coefficient, Btu/hr. -sq. ft. -~F o J = mechanical equivalent of heat, 778. 26 ft. -lb. /Btu k - thermal conductivity of fluid, Btu/hr. -sq. ft. -~F L = area of one side of one fin/fin diameter, ft. Lt = tube length, ft. m = slope of least squared deviation line N = mean number of tubes in a vertical row for a condenser a Nu = Nusselt number P = power to which Reynolds number is raised as in Equation (13) P1 = constant determining power to which Reynolds number is to be raised, Equation (21) Pr = Prandtl number Re = Reynolds number r fin = fin resistance, hr. sq. ft.-~F/Btu r = metal resistance, hr. sq. ft. (Outside area) -~F/Btu m t - = average water temperature, ~F w U = overall heat transfer coefficient, Btu/hr. sq. ft.-~F o v = velocity, ft. /sec. x = Wilson plot function x shell = shell-side correlation function shell y = Wilson plot function yshell = shell-side correlation function EAt f = temperature drop across condensing film, ~F Ax = vapor quality change, fraction k = latent heat of condensing vapor, Btu./lb. = viscosity, lb. /ft. -hr. 0 = fin efficiency p = density of fluid, lb. /cu. ft. 0 ON Subscripts f = film i = inside L = liquid o = outside w = wall 24 25

Figure 1 LIST OF CAPTIONS WATER ON SHELL-SIDE AND TUBE-SIDE Figure 1 Wilson Plots as Modified by Young and Wall of Data Obtained NU 0.8 1/3 0.14 with Water on the Shell-side of 6-Inch Diameter Exchanger Re pr ( // Lw 0. with 5/8-Inch Finned Tubes —Bundle 6( Figure 2 Wilson Plot as Modified by Briggs of Data with Water on the 0 Shell-side of a 6-Inch Dianeter Exchanger with 5/8-Inch - 0.20 Finned Tubes —Bundle 6 X / / Figure 3 Shell-side Heat Transfer Correlation for Water on the Shell- o / / / side of a 6-Inch Diameter Exchanger with 5/8-Inch Finned Tubes —Bundle 6 for Reynolds Numbers Between 8000 and 36, 000 0. 0.15 -// Figure 4 Wilson Plot as Modified by Briggs of Data with Oil on the Shell-side of a 6-Inch Dia4eter Exchanger with 5/8-Inch Finned Tubes —Bundle 6 / Figure 5 Wilson Plot as Modified by Briggs of Data with Glycerine on " the Shell-side of a 6-Inch Diameter Exchanger with 5/8-Inch Finned Tubes —Bundle 6 0 Figure 6 Shell-side Heat Transfer Correlation for Oil on the Shell- / side of a 6-Inch Diameter Exchanger with 5/8-Inch Finned Tubes —Bundle 6 for Reynolds Numbers between 20 and 600 o RUNS 24A-24D Ci = 0.0266' Figure 7 Shell-side Heat Transfer Correlation for Glycerine on the Shell-side of a 6-Inch Dianeter Heat Exchanger with 5/8-Inch 005 V RUNS 25A-25D C, =0.02431 Finned Tubes —Bundle 6 for Reynolds Number Between RUNS 26A-26D C =00254( 30-1000 n RUNS 27A-27D Ci -0.02556 Figure 8 Shell-side Heat Transfer Correlation for Three Fluids on the Shell-side of a 6-Inch-Diamyeter Heat Exchanger with 5/8-Inch | RUNS 28A-28D C =0.0250E Finned Tubes —Bundle 6 0)l Figure 9 Wilson Plot for Condensation of Refrigerant 114 on a Single 0 0.1 0.2 03 Horizontal Finned Tube Ao (Ai\014 Figure 10 Wilson Plot as Modified by Briggs for Condensation of Ai W P J Refrigerant 114 on a Single Horizontal Finned Tube _____ I 0 ki Di G0i8 1/3 0.14

Figure 2 400 o I 300. o ~.. 200 aj. 100 E C 0 I!L. WATER ON SHELL-SIDE AND TUBE-SIDE Nui =0.02589 Rei Pri 3 - ) _ k w o RUNS 24A-24D v RUNS 25A-25D - ^ ARUNS 26A-26D a RUNS 27A-27D 4 RUNS I 28A-28 D I I i 17 0 2 3 4 5 b 7 Ao' D l \ C / o 3 - I i 0 CpL/3 P 0-.14 Di \ /., \ k / t,~'/o Figure 3 1000 _r 0 o a1.,oo'- o In WATER ON SHELL-SIDE AND TUBE-SIDE I/3!U 0.14 Nuo =0.01809 Re-9389 Pro (IJr=12.58 o RUNS 24A-24D v RUNS 25 A-25 D A RUNS 26A-26D o RUNS 27A-27D { RUNS 28A-28D 1000 10,000 (Dq G) p o 100,000 108

8 0 0 0 -W - C3, E I c - -1, 6 Figure 4 OIL ON SHELL-SIDE AND WATER ON TUBE-SIDE Nu = 0.02588 ReO8 Pro3 p-'/014 -0 0- 0 A0.0 -, -.., -__ -— +x-~'~o0 4 2 o RUNS 32A-32D V RUNS 33A-33D 0 RUNS 34A-34D A RUNS 35A-35D o RUNS 36A-36D > RUNS 37A-37D < RUNS 38A - 38D x RUNS 72A-72D + RUNS 73A-73D 0 I 0 0.5 1.0 1.5 2.0 2.5 3.0 Ai De q./.2 /o \(o./o 2 A i /i I k iw i Figure 5 - c~ o — l IE a?! 0i _Y 0 — w j: I 0 c oL _ I 1 8 6 GLYCERINE ON SHELL-SIDE WATER ON TUBE-SIDE _ o.o-.-"O Nui = 0.02439 Rei 08Pr3 ()0.14 A RUNS 81A-81D O RUNS 87A-87D o RUNS 80,82-86,101- 103 4 2 0 0.01 0.02 0.03 0.04 0.05 0.06 AO ko ]DoqG 3/I Ai Deq \ / h k /oi LO J ki (Di G\ 0.9CpL( /3 0.14^ 109

Figure 6 5Wv CF 2 6 O -10 9.1 ti o I OIL ON SHELL-SIDE WATER ON TUBE-SIDE N 0. 2619 R 0.662 1/3 ~0.14 Nu0 Re0 Pr0 0 j cr =0.437 /8 o RUNS 32A-32 D v RUNS 33A-33D ORUNS 34A-34D A RUNS 35A-35D o RUNS 36A-36D A' > RUNS 37A-37D,~4 < RUNS 38A-38D x RUNS 72A-72D + RUNS 73A-73D I 10 100 (D ) Figure 7 1000 GLYCERINE ON SHELL-SIDE WATER ON TUBE -SIDE _ 0.6830 -1/3/,, N0.14 Nuo =0.2339 Re60 Pr / )04 m = 1.072 d o cen o ^ —" 31w 0 Z. a.IC o 0h A RUNS 81A-81D o RUNS 87A-87D 0 RUNS 80,82-86,101-103 10 100 (Deq G) \p /o 1000 110

ho Dq Figure 9 0.007 0.8. (k - wo /. )0. \kl___ owo___8 | hi = 228 (l+O011tw) d 0.006 h O.7 [ P g /4: o.~,/" L~ifAt/ 0.005 0.002 REFRIGERAN A VAPOR TEN 0 VAPOR TEN D 0 00 0.004 _ _1 _ o o M 0.0 0'~~ ~ ~ ~ ~ ~ ~ ~~~~~~0.> 0.2 0.3 0.2 0 0_O._ 0 i Ai(I+.Oll )Vi0.8

Figure 10.r I..c __ ki D-_G j IL 0.14 Di iL i i Lw i 112

FORTRAN 200 SOURCQ~tY133TWTN N Ir DArGN - - _ i6MJ -1aTITLE1300 C AoKARr.Il S_ C C JUNE 24. 1968 — _ _ _ CWILSON pO'CNcE{TRCr IP'E —HEAT' EXCHAN~ER."... - - -. 5 /n pP EN 01 TUD 4 — — N-O-m... H................ E -... _. —-—. C CPPET = R... 004N 3 N lN+1 -0 ~ 2 HEAD(, 4r3) sSW (3 5VCW —TSWT-N-3 -Y"e) TN-T -- TR 2 -~3 —T- -RUN C-3N 004 3 N a N+l 006 4 FOR'MA'T? F16T4F6>2I-; —.... 007 CALL FOF(K) -- - - 010 - GO TO (TO) K. Oil 10 STC. 09315' _ _ - ____ 0 2 N=N-1 -............ 013 3 1 M - n 010808... ___............ 014 D AsO 4417 __ ___ __! 4 D —-=0- -n- — _?..............._..... -C-__-TE[T-L-fN-GTHTOR..HEATTRANSFER -"'12,698 FEET -T......A.-..... __ _ c"____ __-___~ " " -* -................... ___ 015 AOT=2.0O.......40 _............._ 016 CPWATf0.999 _ 017 DO 60 I=I.N ___ 020 QstSW(!.36 0-; PWT-TT 1' (' Xi ___ — DEM-T-i-T~ —- (T T-TT I TT- s 2( ITT ( 1 I )I ) i'/A LOG-' ( TSTI(I- T T2!I f/T-r-(SI 1)-TT1 (I )!) 022 U- - U (.I).....DLM....... ]2_3 _ TWBT= TT! TI)'TT2 /2i-O... - -- --- ____. o24 0 ( WwBC5. oT-wT327T........ —. ------ 025 V'ArS-WATi42 07 - 2'4'82'; TWSTr:8-4335-QRT 18 "-r BT=T- — 3 -5r-' 2 026 G W:T S= (Tj*3 1V;) TU — -T W-D —T'____ -63 CTATTT V2 —- WA T o~33 - ----—.-..... 031 PRT(I)srPWAT*Vlw-T7'WfTTTF —---- 032 -W II =vT'wT-sTc-CIn- rrTT-o —,I-I (R-R-'3'' 034 -~'- H J i T -- -- - - — __ -~. —-- 035 A IT s 2 A —....-..-.....-....-... -........ 037 TWI=TWBT*Q/(AIT*ALPHA) 113

040 TWIC:sO;*(TWI-32.0)/9.0 041 VISWAW=?42.0/(2,l482*( (TWIC-8.435)+SQRT(8078.4+(TWIC-8.435)**2 )) 1-120,n) 042 VISRTx =(VISWAT/VlSWAW)**0.14 d 043 - HIX =CwAT(It*STC/DI*(RET(I)**O,8)*(PRt(Il)#0,3333)*VISRTX 6-044 IF(ABS((AI.PHA-HlX -)/ALPHA),LTEPS ) GO TO 8 -— 0-45 - 7 ALPHA=H'TX 046 8 HI(I)=HIX 0471' V I SR' T (" I) vISR TX 050 HC ( I ):1.0/(1.0/Uo( I )-AOT/(AITHI(I) )-RM) C C ANU=PI/4(SHROUD ID*SHROUD ID-TEST OD*TFST OD)1/144 C 05i AN=0:.00340 052 TWPS=(TS1 (I)+TS2(I) )/2*0 053 TWFSC5.0o*(TWBS-32,0)/9,0 054 VISWAS=24?,0/(2,1482*((TWBSC-8,435)+SQRT(8078.4+(TWBSC-A,435) *2 l))-12o0n) 055 GS=SSW(fT)*3600.0/ANU C C DH:SHFLL ID - TUBE OD C 056 PH:=0.032 057 OD=0,n511 060 RES(I)=nH*GS/VISwAS 061 CWAS(I)=0.000299*TWBS+0,3334 062 PRS(I)C=PwAT*VISwAS/CWAS(I) 063 VISRS(I)=(VISWAS/VISWAW)**0.14 064 XAXRE=AIlOG(RES(I)) 065 YAXRF=ALOG((HC(I)*DH/CWAS(I))/(PRS(I)**O,333*VTSRS(I))) 066 5 FORMAT (Hl RUN, 7X9,HX,12X91HY1OX,3HRES,9X,3HRET97X92HH,99X,2HHC, l8X,5HYAXRF,7X95HxAXRE94X,3HHCC) 067 6 FORMAT(lXF5.1,2xFlO.593XFl2*5,3XF9;.13XF9.1,3XF7,i,3XF71,l 13X,F8.3*2X,F8.3,1XF7,0) 070 WRITF(1) XAXRE, YAXRE 071 60 CONTINUF 072 END FTLF 1 073 REwINn 1 074 ITAPE=1 075 CALL LINRFG (PYAXRE,ITAPE) 076 no 16 I=1*N 077 YS=(1.O/UO(I)-RM)*CWAS(I)/DH*RES(I)**P*PRS(I)**033334*VTSRS(I) 100 XS:(On/nI*CWAS(I)/DH*RES(I)**P*PRS(I)**O,3333*V.ISRS(I))/(CWAT(I)/D 1ITRET(I)**0,8*PRT(I)**0,3333*VISRT(I)) -101...RITE' T') XS, YS 102 1'6 CONTINUF 103 END FtLF P 104 - REWINn.'..105 - ITAPE=? 1-06 - CALL LYNRFG (A,B,ITAPE) 107 STCI=1.n/A 114

110 STCO l;n/B 111 DO 99!sl*N 112 HCCUTl)CWAS i)* fV HDl(RESt-PowtY*(Rs()*O,3333)*I SQS(I ) 113 99 CONTINUF 114 WRITE (3,14) 11T WT —-— EWRiT~- STCo —' STCI -- ------ ------ 116 14 FORT --- HA....4X,'-4HSTC'OIZXIHP' —-,'15Xt4HSTCI) I17 15 FORMAT ( X.F —,XO6SX,-9T- 6.TT - 12 o!I F ( A B S I S I c o -;- -2 - I21 - 2r[ —cSTC =-'.'TC I +$T'C')"'/2 0-0.... -.... —-—.. —.. —.. —-.... —........ —-.... ——...-.-.-.-.-.-. —.-.-.-.-.-.-.-. —. 122 GO-TO 31 - -------------- --- -- 123 20 CONTTINlUF - -- - —.- - --- 1 24 R_____WRITE(3.5) 126 READ (1) X'AX3REC' — Y-'X-E. 127 _ _ —W 2AD (2) x-,Y3.. ---------------------------------- 130 32 WRTT3-6-RVN( T),XxSYS-RE-tfRET- ) —, i-'I-) HC'(I)- A XRE-XA-XRE, 1HCC(I) _ _) _... _.... _.... -. 131 33 PAUSE 77777 1 32 END.._.. 115

.FORTRSNoZ0Q SOURE LING N._ LEG__ T TLELTINREG Q0_ S — - UBROTiT fNF L- INR-'E fAB (A TAE) A - - - 002 Z = 0.0 003 SX. _ __X._ 004 SY=0, o0?~....'-=..".................................. O D6 SXYXO.O 007 100 oREAD tiTAPE) -- 610 __ _ CALL — FOF ('I o —Y1 - FG' O. ro!. To.,2).- 012 12 Z=Z+T.0 -0 13- SX S XX -----...........................................................................Y.. _...... 01/6 ___ =SXY-SXVY+X*Y 017 __ _ O-" T O To n o T -....0 0 —' 13 *Y"^XxSY') / (Z'SXX=SX'SX) 021 AR= - (SY*SXX-SX*SXY) / (Z*SXXSXX.... ___ C A-iS T'HF SLOPE AND IS' THE'Y INTERCEPT o_2 ^w'^-r.................... 022 REW I N-1 I TAP E03 RETURN.. OZ4.... - N-.. -.. - 116

NOMENCLATURE RES PRS SSW TSW TS1 TS2 TT1 TT2 VISRS RET PRT HC UO CWAS CWAT VISRT HI YS XS RM DH P OD DI XAXRE YAXRE Re shellside Pr shellside Shellside water flow, lbs. /sec. Tubeside water flow, lbs. /sec. Temperature water in, shellside, ~F Temperature water out, shellside, ~F Temperature water in, tubeside, ~F Temperature water out, tubeside, ~F f n \.14 Viscosity ratio to.14 power h) hellsi Re tubeside Pr tubeside Shellside film coefficient Overall coefficient Thermal conductivity, water, shellside, based on bulk temperature Thermal conductivity water, tubeside, based on bulk temperature Viscosity ratio to.14 power (p, tubesid Inside film coefficient Ordinate Wilson Plot Absicca Wilson Plot Wall resistance Hydraulic diameter Re power shellside Outside diameter, test tube, ft. Inside diameter, test tube, ft. Abcissa, Re shellside power plot Ordinate, Re shellside power plot ide e 117

APPENDIX III Computer Program for Analyzing Experimental Multiple Tube Steam Condensing Data, Its Nomenclature and Sample Printout in Tables III-1, III-2, and III-3 118

001230 08-28-68 001230 08-28-68 0&i230 08-28-68 001230 08-2828-68 001230 08-28-68 002230o CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCcc CCCCCcCCcccccc C THE FOLLOWING PROGRAM IS WRITTEN FOR THE STEAM CONDENSING C C ON MULTIPLE TUBES. _ ____ _ __ __C C THE PROGRAM IS WRITTEN IN FORTRAN IV G-LEVEL. C C TO BE RUN ON THE IBM O/S 360 MODEL 67_____ _ __ C C C THE ORIGINAL ARGORITHM WAS BY MR. DALE BRIGGS. C C C _C_ __ __ BY GEORG__TS, CHEN 1N MARCH 196_ __.....___.._____ CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCccc DIMENSION TTUB E I ( 20,W TUBE(20) TA VG(2QJ,_ DEN201, PR(20.)_,_ _02Q0L, 1 TTUBEO(20), VISCW(20), VISC(20), VEL(20), RE(20), 22 -____ VAPORT(20), TWALL(20), PVEL(2Q0), CNN(20) 0A(?20)_, 3 TUBENO(20), DELTF(20), PTI(20), U0(20), 4..CQN _LA(20QL_ PHYGR2I_. PJ0_. LN20, Q)_...____ 5 TWALLA(20), CONST(20), PTV(20), HO(20), 6 T _.__IWALLOA20L HCDND20Q), EMEt2Q1. P 0L-2014 -.... 7 DELTFA(20), FILMT(20), HOA(20), HG(20),._. 8.....................DCOND( 20...........OA~(_ _,_2 _.) HiL(it2_QL, ____L _. 9 VCOND(20), CPT(20) DOUBLE PRECISION RUNNO, DAY, YEAR, M METAL METAL2, METAL3, METAL4,. _ 1 METAL5, METAL6, METAL7, METAL8 REAL KCOND(20), LMTD(20),LAT(20),KT(20),ID CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCccc C~_ C C STATEMENTS 101 TO 111 ARE FOR TUBES A AND B. C C............................. C. 101 READ(5,20005)ID, OD, TL, TK, CI, N, METAL 1, METAL2, METAL3, METAL4 READ(5,20007)RUNNO, DAY, YEAR WRITE(6,20001)RUNNO, DAY, YEAR_ _______. DO 102 I = 1,2 102 READ(5,20006)TUBENO(I), HG(I), TTUBEI(I), EMF(I), VAPORT(I) WTUBE(1) = EXP((ALOG(HG(1)/11.8979))/1.9866) NO. 12 WTUBE(2) = EXP((ALOG(HG(2)/12.1606))/2.0464) NO. 18 DO 103 I = 1,2 TTUBEO( I ) = (. 31909129E+02)... _ +L0_.7341237E+2 )*E.MF(I). _-i. 1 -(0.24948922E+01)*EMF(I)**2 +(0.10769889E+01)*EMF(I)**3 2. -0.49329147E+00)*EMF(I)**4 +(O.13393543E+00)*EMFIIJ**5 __..__... 3 -(0.18958908E-01)*EMF(I)**6 +(0.10851047E-02)*EMF(I)**7 PTI(IJ =TTUBEI( I)PTO(I) = TTUBEO(I) PTV(I) VAPORT(I)._ ___________________ WTUBE(I) = WTUBE(I)*3600.0,0 103 CONTINUE WRI TE( 6,20028) WRITE(6,20008)OD, ID, TL, TK, METALI, METAL2, METAL3. OD = OD/12.0 _ID = I 0/12.0__ TL = TL/12.0 RM = (OD-ID)/TK/2.0_ DM = (OD-ID)/ALOG(OD/ID) AOT = 3.1416*OD*TL _...___.__.__ AIT = 3.1416*ID*TL ____AMET =___ 3.1416*DM*TL WRITE(6,20009)AOT, AIT, AFLOW, RM, CI AFLOW__. 3.14J6*ID* ID4 __0 DO 105 I = 1,2...._ TAVG(I!) _ (TTUBEI(I) + TTUBEO(I_)J_/2,,___0 CALL WATER(TAVG(I),CPT(I),DEN(I),KT(I),VISC(I),HEAT), _METAL4____

CALL WATER(VAPORT(_ I)-CP,W ATER D WATERKtWA1TAER V, LAT_(l)) 0(I) = WTUBE(I)*CPT(I)*(TTUBEO(I)-TTUBEI(I)) PO(I) = 0(I) LMTD(I) = (TTUBEO(I)-TTUBEI(I))/ALOG((VAPORT(I)-TTUBEI(I))/ 1 (VAPORT(I)-TTUBEO(I))) UO(I) = O(I)/(AOT*LMTD(I)) PR(I) = CPT(I)*VISC(I)/KT(I).............................. ____ RE(I) = ID*WTUBE(I)/(AFLOW*VISC(I)) VEL(I) = WTUBE(I)/(AFLOW*DEN(I)*3600.0) PVEL(I) = VEL(I) TWALLA(I) = TAVG(I) CALL TRIAL(TWALLA(I),TAVG(I),CI,KT(I),RE(I),PR(I),VISC(I), 1 VISCW(I),Q(I),AIT,HI(I),ID,TWALL(I),1) _ HCOND(I) = 1.0/(1.0/UO(I)-AOT*RM/AMET-AOT/(AIT*HI(I))) DELTF(I) = UO(I)*LMTD(I)/HCOND(I) FILMT(I) = VAPORT(I) -DELTF(I)/2.0 CALL WATER( FILMT(I),CP,DCOND(I),KCOND(I),VCOND(I),HEAT) PHYGR(I) = (KCOND(I)*KCOND(I)*KCOND(I)*DCOND(I)*DCOND(I)/ 1 (VCOND(I)*DELTF(I)))**0.25 CN(I) = HCOND(I)/(0.725*PHYGR(I)*(LAT(I)*4.17*10.0**8/OD) 1 **0.25) 105 CNN(I) = CN(I) WRITE(6,20002) WRITE(6,20015) DO 106 I = 1,2 106 WRITE(6,20010)TUBENO(I),WTUBE(I),TTUBEI(I),TTUBEO(I),TAVG(I), 1 CPT(I),DEN(I),VISC(I) WRITE(6,20016) DO 107 I = 1,2 107 WRITE(6,20011)TUBENO(I),KT(I),PR(I),TWALL(I),VISCW(I),VEL(I), 1 RE(I),HI(I) WRITE(6,10005) DO 108 I = 1,2 108 WRITE(6,10002)TUBENO(I),VAPORT(I),LAT(I),0(I),LMTD(I),UO(I), 1 HI(I),HCOND(I) WRITE(6,10001) WRITE(6,20028) WRITE (6,10006) DO 109 I = 1,2 109 WRITE(6,10003)TlJBENO( I),DELTF(I),FILMT(I),KCOND(I),DCOND(I), 1 PHYGR(I) WRI TE( 6,10007) DO 111 I = 1,2 111 WRITE(6,10004)TUBENO(I),HI(I),UO(I),HCOND(I),CN(I) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCXcC C I C C STATEMENTS 200 TO 227 ARE FOR TUBES 1 THROUGH 7. -- C C C ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccCC cccccLC-CL-CcL-C-CC.-Lcccc 200 READ (5,20005)ID,OD,TL,TK,CI,N,METAL5,METAL6,METAL7,METAL8 WRITE(6,20001)RUNNO,DAY,YEAR N = N + 2 SUMVT = 0.0 _ __.__ _.__ _ SUMVEL = 0.0 STIN.0= Q0.0.___.-_ - DO 201 I = 3,N 201 READ (5,20006)TUBENO(I),HG(I),TTUBEI(I),EMF(Il,VAPORTI)......________ — WTUBE(3) = EXP((ALOG(HG(3)/12.4550))/2.0518) NO. 15 WTUBE(4) = EXP((ALOG(HG(4)/12.8193))/2.0380) __. ND_._ 2 WTUBE(5) = EXP((ALOG(HG(5)/12.0399))/2.0213) NO. 11 120

WTUBE(6) = EXP((ALOG(HG(6)/12.7039))/2.0251)......N..._... WTUBE(7) = EXP((ALOG(HG(7)/12.1947))/2.0091) NO. 7 WTUBE(8) = EXP((ALOG(HG(8)/12.8830))/2.0078). N.WTUBE(9) = EXP((ALOG(HG('9)/12.6345))/2.0377) NO. 4 WRITE(6,20028) -.- --- ----- WRITE(6,20008)00, ID,TL,TK,METAL5,METAL6,METAL7,METAL8 DO 202 I = 3,N TTUBEO(I) = (0.31909129E+02) +(0.47341237E+02)*EMF(I) 1 -(0.24948922E+O1)*EMF(I)**2 +(0.10769889E+O1)*EMFI)**3. —--- 2 -(0.49329147E+OO)*EMF(I)**4 +(0.13393543E+00)*EMF(I)**5 -(0.18958908E-01)*EMF(I)**6 +(0.10851047E-02) EMF(I)**7 I I PTI(I) = TTUBEI(I) PTO(I) = TTUBEO(I) PTV(I) = VAPORT(I) WTUBE(I) = WTUBE(I)*3600.0 202 CONTINUE OD = OD/12.0 ID = ID/12.0 TL = TL/12.0 RM = (OD-ID)/TK/2.0 DM = (OD-ID)/ALOG(OD/ID) AOT = 3.1416*OD*TL AIT = 3.1416*ID*TL AMET = 3.1416*DM*TL AFLOW = 3.1416*ID*ID/4.0 WRITE(6,20009)AOT, AIT, AFLOW, RM, CI DO 204 I = 3,N TAVG(I) = (TTUBEI(I) + TTUBEO(I))/2.0 CALL WATER(VAPORT(I),CP,WATERD,WATERK,WATERV,LAT(I)) CALL WATER(TAVG(I),CPT(I),DEN(I),KT(I),VISC(I),HEAT) O(I) = WTUBE(I)*CPT(I)*(TTUBEO(I)-TTUBEI(I)) LMTD(I) = (TTUBEO(I)-TTUBEI(I))/ALOG((VAPORT(I)-TTUBEI(I))/ 1 ((VAPORT(I)-TTUBEO(I))) U( I) = O(I)/(AOT*LMTD(I)) PR(I) = CPT(I)'VISC(I)/KT(I) RE(I) = ID*WTUBE(I)/(AFLOW*VISC( I)) VEL(I) = WTUBE(I)/(AFLOW*DEN( I )3600.0) PVEL(I) = VEL(I) SUMVEL = SUMVEL + VEL(I) STIN = STIN + TTUBEI(I) SUMVT = SUMVT + VAPORT(I) TWALLA(I) = TAVG(I) CALL TRIAL(TWALLA(I),TAVG( I),CI,KT( I ),RE( I),PR(I),VISC(I ), 1 WVISCW(I),0(I),AIT,HI(I),ID,TWALL(I ),1) HCOND( I ) = 1.0/(1.0/O( I )-AOT*RM/AMET-AOT/ ( AITHI ( I ) ) ) DELTF(I) = UO(I) LMTD(I)/HCOND(I) TWALLO(I) = VAPORT( I) - Q(I)/(AOT*HCOND(I)) FILMT(I) = VAPORT(I ) -DELTF(I)/2.0 CALL WATER( FILMT(I),CP,DCOND(I),KCOND(I),VCOND(I),HEAT) PHYGR(I) = (KCOND(I COND(I)KND(I)*KCOND(I)*DCOND(I)*DCOND(I)/ 1 (VCOND(I)*DELTF(I)))**0.25 204 CONST(I) = HCOND(I)*(OD/(4.17*10.0**8*LAT(I)))**0.25/PHYGR(I) XM = N - 2 ATIN = STIN/XM AVGVT = SUMVT/XM AVGVEL = SUMVEL/XM WRI TE( 6,20002) WRITE(6,20015) DO 205 I = 3,N 205 WRITE(6,20010)TUBENO(I),WTUBE(I),TTUBEI(I),TTUBEO(I),TAVG(I), 121

1 CPT( I) IDEN( I)?VISC( I) WRI TE( 6,20016 ) DO 206 I = 3,N 206 WRITE(6,20011 )TUBENO( I ), KT( I ), PR( I ), TWALL( I ), VISCW( I ), VEL( I ), 1 RE(I),HI(I) WR I TE (6,20017) DO 207 I = 3,N 207 WRITE(6,20012)T(JUBENO(I),VAPORT(I),LAT(I),TWALLO(I),DELTF(I ), 1 FILMT(I),KCOND(I),DCOND(I) WRI TE( 6,20018 ) DO 208 I = 3,N 208 WRITE(6,20013)TUBENO( I),VCOND( I ),PHYGR( I),0(I ),LMTD)( I ),UO(I), 1 HI(I),HCOND(I) DO 212 I = 3,N TTUBEI(I) = ATIN VEL(I) = AVGVEL VAPORT(I) = AVGVT 209 WTUBE(I) = DEN( I )AVGVEL*3600.0*AFLOW TTUBEO(I) = 0( I)/(WTUBE( I )*CPT( I))+ATIN TAVG(I) = (TTUBEI( I)+TTUBE[)( I ))/2.0 CALL WATER(TAVG(I),CPT( I ),DEN(I),KT( ),VISC( I ),HEAT) PR(I) = CPT(I)*VISC(I)/KT(I) RE(I) = ID*WTUBE(I)/(AFLOW*VISC(I)) CALL WATER(VAPORT(I),CP,WATERID,WATERK,WATERV,LAT(I)) LMTD(I) = (TTUBEO(I)-TTUBEI( I ) )/ALOG((VAPORT(I)-TTUBEI ( I ) )/ 1 (VAPORT(I)-TTUBEO(I) ) ) 210 CALL TRIAL(TWALLA(I),TAVG(I),CI,KT(I),RE(I),PR(I),VISC(I), 1 VISCW( I ),0( I),AIT,HI (I), ID,TWALL(I ), 1) TWALLO(I) = TWALL(I) + O(I)'RM/AMET DELTF(I) = VAPORT(I) - TWALLO(I) 211 FILMT(I) = VAPORT(I) -DELTF(I)/2.0 CALL WATER( FILMT(I),CP,DCOND(I),KCOND(I),VCOND(I),HEAT) PHYGR(I) = (KCOND( I)*KCUND(I)*KCONl)(I)*DCOND(I)'~DCOND(I)/ 1 (VCOND(I)*DELTF(I)))**0.25 HCOND( I ) = CONST ( I )*PHYGR( I ) (4. 17*10.0**8' LAT ( I )/OD) *'0.25 UO(I) = 1.0/(I.O/HCOND( I ) + AOT*RM/AMET + AOT/(AIT*-HI(I))) DELTFA(I) = UO(I)`*LMTD(I)/HCOND(I) IF(ABS(DELTFA(I)-DELTF(I))/DELTFA(I) - 0.001) 241,241,231 231 DELTF(I) = DELTFA(I) GO TO, 211 241 OA(I) = UO(I) LMTD( I)':AOT IF(ABS(OA(I) - Q(I))/OA(I) - 0.001)212,212, 251 251 0(I) = QA(I) GO TO 209 212 CONTINUE WRI TE( 6,20003) WRITE(6,20015) DO 213 I = 3,N 213 WRITE(6,20010)TUBENO(I),WTUBE(I),TTUBEI(I),TTUBEO(I),TAVG(I), 1 CPT(I),DEN(I),VISC(I) WRI TE( 6,20016) DO 214 I = 3,N 214 WRITE(6,20011)TUBENO(I),KT(I),PR(I),TWALL(I),VISC4W(I ),VEL( I ), 1 RE(I),HI(I) WRI TE( 6,20017) DO 215 I = 3,N 215 WRITE(6,20012)TUBENO(I),VAPORT(I),LAT(I),TWALLO(I),DELTF(I), 1 FILMT(I),KCOND(I),DCOND(I) WRITE( 6,20018) DO 216 I = 3,N 122

216 WRITE(6,20013)TUBENO(I)_VCOND(I),PHYGR(I)..(I) LMT D(_IUO(I), 1 HI(I),HCOND(I) O(1) = 0.0 0(2) = 0.0 SCPT = 0.0 SDEN = 0.0 DO 218 I=3,N __ II = 1-2 O(I) = 0(I-1) + Q(I) P0(I) = 0(I) SDEN = SDEN + DEN(I) DEN(I) = SDEN/II SCPT = SCPT + CPT(I) I)_ ___ _ CPT(I) = SCPT/II WTUBE(I) = DEN(I)*AVGVEL*3600.0*AFLOW*II TTUBEO(I) = TTUBEI(I) + Q(I)/(WTUBE(I)*CPT(I)) TAVG(I) = (TTUBEI(I)+TTUBEO(I))/2.0 CALL WATER(VAPORT(I),CP,WATERD,WATERK,WATERV,LAT(I)) CALL WATER(TAVG(I),CPT(I),DEN(I),KT(I),VISC(I),HEAT) TWALLA(I) = TWALL(I) CALL TRIAL(TWALLA(I),TAVG(I),CI,KT(I),RE(I),PR(I),VISC(I), 1 VISCW(I),Q(I),AIT,HI(I), ID,TWALL(I),II) LMTD(I) = (TTUBEO(I)-TTUBEI(I))/ALOG((VAPORT(I)-TTUBEI(I))/ 1 (VAPORT(I)-TTUBEO(I))) UO(I) = 0(I)/(LMTD(I)*AOT*II) _____ HCOND(I) = 1.0/(1.0/UJO(I)-AOT*RM/AMET-AOT/(AIT*HI(I))) DELTF(I) = UO(I)*LMTD(I)/HCOND(I) FILMT(I) = VAPORT(I) - DELTF(I)/2.0 CALL WATER( FILMT(I),CP,DCOND(I),KCOND(I),VCOND(I),HEAT) PHYGR(I) = (KCOND(I)*KCOND(I)*KCOND(I))*DCOND(I)*DCOND(I)/ 1 (VCOND(I)*DELTF(I)))**0.25 CN(I) = HCOND(I)/(0.725*PHYGR(I):'(LAT(I)*4.17*10.0**8/(OD*II)) 1 **0.25) CNN(I) = CN(I)/(II**0.25) 218 CONSTA(I) = CONST(I)/0.725 WRI TE (6,20004) WRITE(6,20015) ---—.. -i DO 219 I = 3,N 219 WRITE(6,20010)TUBENO(I),WTUBE(I),TTUBEI(I),TTUBEO(I),TAVG(I), 1' CPT(I),DEN(I),VISC(I) WRITE(6,20016) DO 220 I = 3,N 220 WRITE(6,20011)TUBENO(I),KT(I),PR(I),TWALL(I),VISCW(I),VEL(I).. 1 RE(I),HI(I) WRITE(6,20017) DO 221 I = 3,N 221 WRITE(6,20012)TUBENO(I),VAPORT(I),LAT(I),TWALLO(I),DELTF(I), 1 FILMT(I),KCOND(I),DCOND(I).._.WRITE(6,20018) DO 222 I = 3,N 222 WRITE(6,20013)TUBENO(I),VCOND(I),PHYGR(I),Q(I),LMTD(I),UO(I), 1 HI(I),HCOND(I) WRITE(6,20019) DO 223 I = 3,N 223 WRITE(6,20014)TUBENO(I),CNST(I),CONSTAI1CN(I1 __ DO 227 J = 1,2 WRITE(6,20020)RUNNO, DAY,YEAR WRITE(6,20026)METAL1,METAL2,METAL3,METAL4 WRITE(6,20027)METAL5, METAL6,METAL7,METAL8 WRI TE( 6,20021) 123

DO 224 I = 1,2 _ 224 WRITE(6,20022)TUBENO( I),HG(I),PVEL(I),PTI(I),PTO(I),EMF(I),PTV( I), 1 PQ(I) WRI TE( 6,20025) DO 225 I = 3,N 225 WRI TE(6,20022)TUBENO( I),HG(I),PVEL( I ),PTI (I),PTO( I ),EMF( I ),PTV( I), 1 PQ(I) WRI TE( 6,20023) DO 226 I = 1,2 226 WRITE(6,20024)TUBENO(I),LMTD(I),UO(I),HI(I),HCOND(I),CN(I),CNN( I ) WRI TE(6,20025) DO 227 I = 3,N 227 WRITE(6,20024)TUBENO( I ),LMTD( I ),UO( I ),HI ( I ),HCOND( I ),CN( I ),CNN(I)._-___ GO TO 101 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCccc C C C STATEMENTS 10001 TO 20028 ARE INPUT AND OUTPUT FORMATS. C C C 10001 FORMAT(lH1,5X,'THE FOLLOWING RESULTS WERE CACULATED FOR THE RAW D 1ATA ACCORDING TO THE THEORETICAL RELATIONSHIPS OF NUSSELT') 10002 FORMAT(13X,A2,7F15.4) 10003 FORMAT(13X,A2,2F15.3,2F15.5,F15.2) 10004 FORMAT(13X,A2,4X,F15.3,4X,F15.3,2X,F15.3,3X,F15.4) 10005 FORMAT('2',7X,'TUBE NO VAPOR TEMP LAT HEAT HEAT DU-T.. __ 1Y LMTD UO HI H COND'/ 225X,'F BTU/LB BTU/HR F BTU/HR-S 30FT-F BTU/HR-SOFT-F BTU/HR-SOFT-F'/////) 10006 FORMAT( 7X,'TUBE NO DT FILM FILM TEMP C-K 1 C-DENSITY PHYGR'/26X,'F F BTU/ 2HR-FT LB/CUFT'/////) 10007 FORMAT('2',7X,'TUBE NO HI UO 1 H COND CN'/23X,'BTU/HR-SOFT-F BTU/HR-SQFT2F BTU/HR-SOFT-F'/////) 20001 FORMAT(1Hl,30X,'CALC(ULATED RESULTS FOR RUN NUMBER',3A8) 20002 FORMAT(lH1,30X,'CALCULATED RESULTS FOR RAW DATA') 20003 FORMAT(1H1,15X,'CALCULATED RESULTS FOR DATA ADJUSTED TO CONSTANT 1 INLET WATER TEMPERATURE AND CONSTANT VAPOR TEMPERATURES') 20004 FORMAT(1H1,38X,'CALCULATED RESULTS ARE FOR AVERAGE CONDITIONS FOR 1 TOP I TUBES') 20005 FORMAT(5F10.4, I2,8X,4A5) 20006 FORMAT(A2,8X,4F10.4) 20007 FORMAT(3A8) 20008.FORMAT(' TUBE OUTSIDE DIAMETER - INCHES'31X,F10.4/' TUBE INSID 1E DIAMETER - INCHES'32X,F10.4/' TUBE LENTH - INCHES'42X,F10.4/' 2 TUBE THERMAL CONDUCTIVITY - BTU/HR-FT-F'22X,F10.4/' TUBE METAL 3',42X,4A5) 20009 FORMAT(' TUBE OUTSIDE HEAT TRANSFER AREA - SOFT'23X,F10.4/' TU 1BE INSIDE HEAT TRANSFER AREA - SOFT'24X,F10.4/' TUBE FLOW AREA - 2 SOFT'40X,F13.7/' METAL RESISTANCE - BTU/HR-SOFT-F'29X,F13.7/' 3 INSIDE COEFFICIENT CONSTANT'35XF10.5) 20010 FORMAT(13X,A2,F15.0,6F15.3) 20011 FORMAT(13X,A2,F15.3,2F15.2,2F15.3,2F15.2) 20012 FORMAT(13X,A2,F15.3,F15.2,3F15.3,3F15.4,F15.3) 20013 FORMAT( 13X,A2,2F15.3,F15.2,4F15.3) 20014 FORMAT(13X,A2,3F15.4) 20015 FORMAT('2',7X,'TUBE NO W TUBE T TUBE IN T TUBE 0 1UT T-AVG T-CP T-DENSITY T-VISCOSITY' / 2 24X,'LB/HR F F F B 3TU/LB-F LB-CUFT LB/FT-HR'/////) 124

20016 FORMAT( 1H1.7X,'TUBE NO',12X, T-K',3X P R',6X_,T WALL I 9N' _,3X,. 1'TW-VISCOSITY',5X,'T-VELOCITY',12X,'RE',13X,'HI'/ 20X,'BTU/HR-FT.....2',, 29X,' F', _8X_,'_LB/_FT-HR',9X,'FT/SEC,.17X,' BTU/HR-SQFT-'L,//'//_/L _ __20017 FORMAT('2',' TUBE NO VAPOR TEMP LAT HEAT T IWALL OUT DT-FILM T-FILM.... C-K........... DENLT_____ 2Y'/30X,'BTU/LB F F F 3 _ BTU/HR/FT LB/ CUFT'/////)............. 20018 FORMAT('2',' TUBE NO C-VISCOSITY PHYGR HE 1AT DUTY LMTD UO,., HI L..N __._-. 3'/' LB/FT-HT BTU/HR 4 F BTU/HR-SOFT-F BTU/HR-SQFT-F BTU/HR-SOFT-F'.////..1 - ____. 20019 FORMAT('2',' TUBE NO COND CONST CONST/0.725 __1_ CN' _/////) ____ _____ 20020 FORMAT(1H1,/////' SUMMARY SHEET FOR RUN NO.'3A8) 20021 FORMAT(/////' NO ORIFICE VEL T IN T OUT EMF T VAP _ lOR HEAT DUTY'/' IN HG FT/SEC F F M-V 2 F BTU/HR'///) _ ____ 20022 FORMAT( 2X,A2,3X, F5.2,3X,F5.2,2X,F6.2,2X,F6.2,2X,F6.4,2X,F6.2,2X, _____1F9.. 1)..___. ___..... 20023 FORMAT(/////' NO LMTD UO HI H COND CN 1 CN/N-OT' / / / ) 20024 FORMAT(2X,A2,3X,F5.2,3X,F7.1,3X,F7.1,3X,F7.1,3X,F6.4,3X,F6.4) 20025 FORMAT(' ******************************************$************** _ _ 1.*****************' ) 20026 FORMAT_'(____ SIDE_TUBES _'.4A5. __.______. 20027 FORMAT(' CENTER TUBES',4A5) 20028 FORMAT(////////) CALL SYSTEM END CCCCCCCcccCCccccCCCccCCCccCCCCCCCCCCCCCCCCCCCCCCCCCCCcccCCCCCCccCCCCCccCCCCCCCCCc C ___THE..FOLLOWING SUBROUTINE IS WRITTEN FOR THE TRIAL-AND-FRROR c C PROCEDURES FOR FINDING OUT THE CORRECT VISCOSITY ON THE WALL C C WRITTEN IN FORTRAN IV G-LEVEL, ON IBM O/S 360 MODEL 67. - __.C C C C BY GEORGE T. S. CHEN IN MARCH 1968............__C_ C C ccccccccccccccccccccCCCCCCCCCCCCCCCCCCCCCCCCCCccCCCCCCCcLCcC_ CCCCc ccccC cccc SUBROUTINE TRIAL(TT, TA,CI,TH,RE,PR,V,VW,O,A,HI,DI,TWALL,M) 104 CALL WATER(TT,CP,WATERD,WATERK,VW,HEAT) HI = CI*TH*RE**0.80*PR**0.33333*(V/VW)**'0.14/DI TWALL = TA+ Q/(A*HI*M) IF(ABS( TT-TWALL)-0.3)124, 124,114 _ 114 TT_ =_TWALL _ __ ______ —- - GO TO 104 124 RETURN END C C __SUBROUTINE WATER(T, CP. WATER_ D WATERK. WATERV., HEAT)} ____ C - THIS SUBROUTINE IS WRLTTEN FOR THE CALCULATION OF _ ___C C THE PHYSICAL PROPERTIES OF WATER AND STEAM. C C EOUATIONS OBTAINED FROM DALE BRIGG. C C WRITTEN BY GEOTGE T. S. CHEN IN MARCH 1968 C C T # TEMPERATURE C C CP.# SPECIFIC HEAT AS FUNCTION OF TEMPERATURE _.._ ___ C WATERD # DENSITY AS FUNCTION OF TEMPERATURE C 125

C WATERK # THERMAL CONDUCTIVITY AS FUNCTION OF TEMPERATURE c C WATERV # VISCOSITY AS FUNCTION OF TEMPERATURE C C... HEAT. # LATENT HEAT OF VAPORI ZATION.AS_FUNCTIiQN OF TEMPERATUREC..._ CP....... = (0. 10124896E+01).......... -(Q.46678063E-03)*T _ 1 +(0.58540867E-05)*T**2 -( 0.32721741E-07)*T**3 2 +... 0..___.72640.6.1_E- 1._*T__.*_4 _ _____ WATERD = (0.63130000E+02) -(0.11700000E-01)'T WATERK = (0.30377927E+00)..t+0.25267360QE-03)T -- ________ 1 +(0.92050520E-05)*T**2 -(0.75847219E-07)*T**3 2 +(0.17507457.E-09)*T**4....._ _ DUMMY = -(0.21968718E+O1) 1. 1. __ +Q.54722744E+Q3.)./ L-o.,41363-R2E2F+Q5 ZIT*~.0o 2 +(0.16141324E+07)/T**3.0-(0.24764542E+08)/T**4.0 WATERV = EXP(DUMMY) _. HEAT = (O.10952000E+04) -(0.58000000E+OO)*T RETURN END 126

NOMENCLATURE AFLOW AIT AMET AOT ATIN AVGVEL AVGVT CI CN CNN CP CPT DAY, YEAR DCOND DELTF DEN DM EMF FILMT HCOND HEAT HG HI ID KCOND KT Cross-sectional flow area per tube; ft. Total inside heat transfer area per tube; ft. 2 Mean heat transfer area per tube; ft. Total outside heat transfer area per tube; ft. Average inlet temperature of coolant for n tubes in a vertical row; ~F Average coolant velocity for n tubes in a vertical row, ft. /sec. Average vapor temperature for n tubes in a vertical row, ~F Seider-Tate constant for inside heat transfer coefficient Condensing heat transfer coefficient correction factor C /(N)1/4 n Dummy variable Heat capacity of coolant at the average bulk temperature of the coolant; BTU/lb. Date on which run was taken for format Density of the condensate at the film temperature; lbs. /ft. Temperature drop across the condensing film; ~F Density of coolant at the average bulk temperature of the coolant; lbs. /ft. 3 Mean diameter; ft. Thermocouple reading; emf Temperature of the condensing film; ~F 2 Condensing heat transfer coefficient, BTU/hr. -ft. -~F Dummy variable Orifice pressure drop in inches of Hg; ins. of Hg 2 Inside heat transfer coefficient; BTU/hr. -ft. - ~F Tube inside diameter; ins. Thermal conductivity of the condensate at the film temperature; BTU/hr. -ft. - ~OF Thermal conductivity of coolant at average bulk temperature of the coolant; BTU/hr. -ft. -~F 127

NOMENCLATURE (con~tinued) LAT LMTD METALI METAL2 METAL3 METAL4 N OD PHYGR PQ PR PTI PTO PTV PVEL QA, Q RE RM RUNNO SCPT SDEN STIN SUMVEL SUMVT Latent heat of vaporization at the saturated vapor temperature; BTU/lb. Logarithmic temperature differential; ~F Tube description for format statement Tube description for format statement Tube description for format statement Tube description for format statement Number of tubes in a vertical row Tube outside diameter; ins. Physical property group: 3 2 1/4 kf Pf Pf Atf Q Prandtl Number; dimensionless TTUBEI TTUBEO VAPORT VEL Heat duty; BTU/hr. Reynolds Number; dimensionless 2 Metal resistance; hr. /ft. -~F-BTU Run number for output format Summation of the coolant heat capacities for n tubes in a vertical row; BTU/lb. Summation of the coolant densities for n tubes in a vertical row; lbs. /ft. 3 Summation of the coolant inlet temperatures for n tubes in a vertical row; ~F Summation of the velocities for n tubes in a vertical row; ft. /sec. Summation of the vapor temperatures for n tubes in a vertical row; ~F 128

NOMEN CLAT URE ( continued) TAVG TK TL TTUBEI TTUBEO TUBENO TWALLA, TWALL TWALLO UO VAPORT VCOND VEL VISC VISCW WATERD WATERK WTUBE Average bulk temperature of coolant in a tube; ~F Thermal conductivity of tube metal; BTU/hr. -ft. -~F Tube length; ins. Temperature of coolant entering test tubes; ~F Temperature of coolant leaving a tube; ~F Tube number in a vertical row Temperature of coolant at tube wall; ~F Temperature of condensate at the tube outside wall; ~F 2 Overall outside heat transfer coefficient, BTU/hr.-ft. -~F Temperature of saturated vapor; ~F Viscosity of the condensate at the film temperature, lbs. /hr. -ft. Tubeside coolant velocity; ft. /sec. Viscosity of coolant at average bulk temperature of the coolant; lbs. /hr. -ft. Viscosity of coolant at the temperature of the coolant at the tube wall; lbs. /hr. -ft. Dummy variable Dummy variable Coolant flow rate in a tube; lbs. /sec. 129

TABLE III-1 Sample Computer Printout for 5/8-inch Corrugated Copper Tubes SUMMARY SHEET FCR kUN NO. 205E 4 E SEPT.26,19675-1 eARE TUBES _ CCPPE NO. 100 CORRUG/AlED TUBES7 CCPPEf NC. 1300 NO ORIFICE VEL i IN I OUT - EPF T VAPF hEIA CLTY IN HG FT/SEC F F VCL1S F BTU/t-R A 11.41 3.62 EC.30 E8. S 1.2446 99.81 104S1.C B 9.32 3.'4l 8.1 E.~8.39 1.242 1CC.06 8864.C 1 25.61 5.C1 8C.40 90.41 1.255 10CC.20 202S1.E 2 26.24 5.C1 EC.4G _E.E5 1.2826 ICC.09 3952C.C 3 26.09 6.C5 EC.37 C E9.9 1.2E57 S9.92 594E2.a 4 26.56 5.S99 C.3C E.85 1.2E27 ICC.02 79C7S.1 5 25.20 5.97 8C.40 9E.71 1.2793 1CC.09 S8151.7 6 26.81 6.14 80.39 E. 14 1.2664 1CC.CC 116442.7 7 29.29 6.34- 8C.30 E8.6 1 -.255 4 cs 9.28 1347 7 3.5 8 28.59 c6.2 8C.31 E9.27 1.2 64 S9.80 153626.9 NO LMTC UO H I I CONE CN Ch/N-CT F A 15.22 7C0.2 _ 991. 3814.7 1.2431 1.2431 B 14.93 ~C3.3 946.6 2289.5.8137.E137 - -— —-----—` —--- -- 1 14.13 2 14.29 3 14.27 4 14.29 5 14. 33 6 14.40 7 14.45 8 14.45 1467.7 1432.2 14 39.2 1433.2 1418.9 1396. 2 13 E0. 7 1378. I 3752.3 3744.5 374 S. 3747.2 3745.1 3741.2 374C. E 3743. 1 2 E99.8 2701.C 2722.5 27C2.9 2653.6 2 57 7.4 2525.2 2515. 6 ].2C28 1. 481 ]. 5020.60C42 1.6703 1.7059 1.7428 1.7963 1. 2028 1.1336 1.1413 1.1343 1.117C 1.C9CC 1. C715 1.CE61 130

TABLE III-2 Sample Computer Printout for 1-inch Bare 90-10 Cupro-Nickel Tubes SUMMARY SHEE FUOR RUlN N -.2O6UTu AYB-3-1~ 196 8 SIDE TUBES 90/10 CU-NI NO. 200 -CENTER -TUS — -- 07T0CU-NI NU. 20u — NO ORtFIC E VEtL T - TN -T -OUTT -.EF —- F T —V- AVPUR HEAT GUTY IN HG FT/SEC F F M-V F BTU/HR A 20.50 4.87 178.18 186.44 3.6i10 211.05 39290.1 -.. -ZIT'-~. —92 —78.77 — T86 —-2 3-. 65-4 — -2T-15- 38160.1 — *************************************** ******* **$************^************ — wzvr.55 —-4~ I 7I8.;z7 186.-66 3.6264 -Z11.05 —4X0W3 — 2 22.25 4.66 178.27 186.09 3.to20 211.14 77346.1 3 2I.65 4.95- 178.18 185.95 3.6085 21i.144 11471i.1 4 22.25 4.89 178.18 185.92 3.6076 211.05 151757.1 - _...-0 - 4 — 8I1 — 8e-09 1 85. 97- 3.0 90 21-1 -T —- I I 89662.4 -- - 6 22.55 4.89 177.91 185.34 3.593C 211.05 224999.4'-7 —— Z1 8 — 4844 T-77782.185;. 8 —3;. 6067.2 IT-. —-..z63019.9 -N L.MTD - - - —. —-- -- - - -...UU -—.-. H -COUND - -..CN- - C N/N- - -A72i..-54-^ —'.-8729; 9-.. -7.. 1753.3 - 29 39-' 4- I. -C-9 4...91.. 4 8 28.72 842.2 1764.9 2589.9 C.9i61 0.9861 I 28.59 887.6 1759.3 3092.6 1.1386 1.1386 2 28. 75 852.9. — 1757.0-U 2113.9 1.i z yi 1. U245 3 28.80 841.8 1756.7 2605.5 1.3044 0.9912 4 — 2. ~ 83..42..37'53 - 5 - 35.3 ------...1-7 — 0. 9 —5 28.83 834.0 1756.7 2532.8 1.4484 0.9686 6 ~28 —8 823..1 175,.7 I 24 38.0..4694 0.939 7 28.87 825.0 1756.9 2450.8 1.5339 0.9430 131

TABLE III-3 Sample Computer Printout for 1-inch Corrugated 90-10 Cupro-Nickel Tubes............... SUMM ARY SHETFOR-RUN N.........20599& —. - - _....i6 __ BARE TUBES 90/10 CU-NI NO. 200........,... CORRUGAT ED TUBE-S 90/10.U..N...U. -- ---- - NOC ORIFICE VEL T IN T OUT EMF --- T VAP -HEAT DUTY. IN HG FT/SEC F F VOLTS F BTU/HR A 8.15 2.99 76.36 82.01 1.1033 100.74 16696.5... -B 8.08. 2.99 76.46:81..99 1.1030 10069 1637.3 — 1 8.15 3.49 76.48 85.30 1.1783 100.59 -255-5. 2 8.05 3.53 76.40 34.84 1.1680 100.54 50220. 8 3 7. 70 3.5P 76.30 84.92 1.1698 100.51- - T5186.9 - 4 8.35 3.55 76.20 84.93 1.1700 100.64 100443.0 5- - 7.7. 3.47 76. 9 — B4.56 I 16 5.4 1 O.5 —-T.6 - 6 7.98 3.44 76.OP 84.71 1.1649 100.64 149125.7 T -- 8.05 3.50 76.18 85.17 1.1755 100.64 — T1742T.; —. NO LMTD UC HI H COND CN CN/N-QT A 21.43 493.9- 741.9 2820.6 1.1116 1.-11-16 -- B 21.34 486.4 742.2 2587.7 1.0377 1.0377 1 19.56 886.6 1856.3 3150.6 1.3489 1.3489 2 19.66 865.9 1353.8 2912.6 1.5062 1.2666 3 19.67 863.8 1854.8 2886.2 1.6549 1.2574 4 19-.66 865.-9 1855 2907.2- 1.-788-8. —— 26-48 5 19.70 858.4 1853.8 2829.4 1.8504 1.2375 9.I 7T 854. 1853. 47Z. 5 9.0I23 t.Z.24" - 7 19.68 860.7 1856.1 2847.9 2.0237 1.2441 132

APPENDIX IV Tables IV-1 through IV-13 Containing the Summary of the Calculated Cn and Uo Values for the 5/8-inch Bare, the 5/8-inch Corrugated, the 1-inch Bare, and the 1-inch Corrugated Tubes 133

TABLE IV-1 Condensing Coefficient Correction Factors, Cn, for Condensation of Steam at 101~F on 1 to 7 1-inch Bare 90-10 Cupro-Nickel Tubes in a Vertical Row Cn Run No. Velocity ft. /sec. 206074A 3.51 206074B 3.57 206078A 3.62 206078B 3.62 206080B 3.66 206084B 3.64 206086A 3.62 206086B 3.61 206088A 3.61 206091A 3.58 206091B 3.58 206098A 3.62 206098B 3.62 206100B 3.57 206104A 3.60 206104B 3.55 LMTD ~F 24 24 22 22 18 12 23 24 24 24 24 24 24 24 24 24 37 37 32 32 32 32 34 34 35 35 34 34 37 37.1 1.56 1.63 1.14 1.24 1.42 1.87 1.28 1.39 1.30 1.04 1.11 1.50 1.49 1.22 1.12 1.04 1.31 1.34 1.50 1.47 1.29 1.20 1.38 1. 37 1.36 1.26 1.20 1.28 1. 33 1. 33 2 1.50 1. 59 1.02 1.07 1.34 1.68 1.28 1.22 1.02 1.01 1.05 1.42 1.46 1.25 1.15 1.02 1.29 1.31 1.38 1.39 1.29 1.25 1.25 1.21 1.37 1.25 1.25 1.24 1.34 1.28 3 1.62 1.73 1.08 1.13 1.43 1.71 1.33 1.25 1.06 1.09 1.13 1.56 1.57 1.35 1.30 1.12 1.36 1.39 1.47 1.48 1.36 1.34 1.27 1.29 1.44 1.35 1.32 1.35 1.41 1.36 4 1.71 1.78 1.12 1.17 1.47 1.73 1.41 1. 33 1.09 1.15 1.19 1.62 1.62 1.39 1.36 1.19 1.41 1.45 1.51 1.52 1.44 1.41 1.34 1.36 1.48 1.42 1.40 1.42 1.45 1.41 5 1.76 1.84 1.15 1.19 1.51 1.75 1.48 1.41 1.11 1.18 1.22 1.69 1.71 1.45 1.41 1.22 1.47 1.52 1.57 1.60 1.51 1.49 1.37 1.40 1.56 1.47 1.46 1.49 1.50 1.49 6 7 1.79 1.85 1.21 1.25 1.53 1.73 1.51 1.48 1.18 1.26 1.30 1.73 1.75 1.49 1.43 1.27 1.51 1.55 1.61 1.63 1.53 1.51 1.43 1.47 1.63 1.51 1.50 1.53 1.52 1.53 1.83 1.88 1.25 1.29 1.57 1.75 1.56 1.54 1.22 1.31 1.35 1.79 1.80 1.52 1.45 1.32 1.55 1.58 1.64 1.66 1.56 1.55 1.45 1.51 1.66 1.54 1.54 1.56 1.55 1.57 206105A 206105B 206113A 206113B 206115A 206115B 206117A 206117B 206120A 206120B 206122A 206122B 206126A 206126B 3.71 3.71 3.61 3.60 3.64 3. 65 3.61 3. 61 3.65 3. 65 3.65 3. 65 3.60 3. 61

TABLE IV- 1 (Continued) C n Run No. Velocity ft. /sec. 206081A 4.79 206083A 4.76 206083B 4.77 206075A 4.76 206075B 4.75 206076A 4.75 206076B 4.76 206081A 4.79 206079A 4.69 206079B 4.71 206085A 4.76 206085B 4.75 206087A 4.79 206087B 4.79 c"n 206089A 4.75 206099A 4.74 206102A 4.74 206102B 4.74 206103A 4.65 206103B 4.63 LMTD 0F 17 11 11 24 24 23 23 17 22 22 22 22 24 24 24 25 24 24 24 24 34 33 36 36 35 34 33 33 33 33 37 36 1 1.78 1.66 1.90 1. 38 1.45 1.43 1.52 1.78 1.38 1.26 1.37 1.41 1.36 1.37 1.15 1.17 1.41 1.29 1.21 1.31 1.35 1.47 1.19 1.28 1.26 1.24 1.28 1.23 1.32 1.23 1.26 1.31 2 1.68 1.61 1.72 1.35 1.43 1.45 1.52 1.68 1.17 1.13 1.33 1.37 1.34 1.36 1.08 1.23 1.37 1.29 1.21 1. 31 1.44 1.37 1.21 1.27 1.20 1.23 1.27 1.25 1.30 1.25 1.31 1.34 3 1.70 1.68 1.81 1.45 1.51 1.57 1.61 1.70 1.20 1.18 1.44 1.45 1.44 1.45 1.14 1.31 1.45 1.40 1.35 1.41 1.49 1.46 1.34 1.35 1.32 1.33 1.33 1.35 1.37 1.34 1.41 1.42 4 1.74 1.70 1.81 1.51 1.54 1.61 1.65 1.74 1.25 1.23 1.48 1.50 1.49 1.51 1.19 1.36 1.52 1.46 1.40 1.46 1.49 1.52 1.40 1.41 1.39 1.38 1.40 1.40 1.41 1.38 1.49 1.48 5 1.77 1.78 1.84 1.55 1.60 1.67 1.71 1.77 1.27 1.26 1.54 1.56 1.55 1.56 1.21 1.43 1.57 1.53 1.46 1.52 1.51 1.58 1.47 1.49 1.46 1.47 1.45 1.47 1.47 1.46 1.57 1.54 6 7 1.81 1.78 1.81 1.59 1.64 1.72 1.74 1.81 1.32 1.31 1.57 1.61 1.59 1.59 1.25 1.46 1.59 1.58 1.50 1.55 1.56 1.64 1.52 1.55 1.49 1.52 1.50 1.52 1.51 1.50 1.62 1.59 1.85 1.84 1.85 1.63 1.66 1.75 1.77 1.85 1.37 1.36 1.60 1.64 1. 61 1.62 1.29 1.48 1.62 1.61 1.54 1.57 1.59 1.68 1.56 1.60 1.53 1.56 1.53 1.55 1.56 1.52 1.66 1.62 206118A 206118B 206119A 206119B 206121A 206121B 206123B 206123A 206124A 206124B 206128A 206128B 4.80 4.81 4.75 4.75 4.82 4.82 4.78 4.79 4.79 4.79 4.77 4.77

TABLE IV-1 (Continued) Cn Run No. Velocity LMTD 1 2 3 4 5 6 7 ft. /sec. OF 206092A 5.18 24 1.28 1.37 1.48 1.56 1.62 1.67 1.7 206092B 5.18 25 1.24 1.33 1.42 1.49 1.57 1.62 1.6 206093A 5.16 24 1.23 1.23 1.26 1.33 1.39 1.43 1.4~ 206093B 5.16 24 1.15 1.20 1.30 1.36 1.42 1.46 1.4k 206094A 5.18 24 1.26 1.31 1.40 1.46 1.51 1.55 1.5 206094B 5.18 24 1.35 1.36 1.45 1.49 1.54 1.58 1.6( 206095A 5.23 24 1.22 1.27 1.35 1.45 1.51 1.54 1.5 206095B 5.18 24 1.30 1.31 1.40 1.45 1.51 1.54 1.5 206096A 5.24 24 1.11 1.07 1.20 1.23 1.31 1.36 1.42 206096B 5.24 24 1.09 1.08 1' 1.25 1.34 1.39 1.4~ 206097A 5.23 24 1.08 1.06 1.17 1.21 1.30 1.35 1.3' 206097B 5.23 24 1.13 1.14 1.26 1.31 1.40 1.44 1.4c 206101B 5.25 24 1.36 1.36 1.48 1.46 1.50 1.57 1.6] 206106A 6.00 36 1.23 1.24 1.34 1.40 1.48 1.54 1.5 206106B 6.01 36 1.25 1.27 1.37 1.42 1.50 1.54 1.5E 206109B 6.00 26 1.31 1.24 1.30 1.34 1.39 1.42 1.4( 206109A 6.00 26 1.30 1.22 1.30 1.38 1.44 1.47 1.5( 206112A 6.00 32 1.31 1.30 1.38 1.43 1.49 1.52 1.5 206112B 6.01 32 1.26 1.24 1.34 1.41 1.47 1.51 1.5 206114A 5.95 32 1.32 1.29 1.36 1.44 1.51 1.56 1.5E 206114B 5.95 32 1.34 1.31 1.34 1.37 1.46 1.50 1.5 206116A 6.02 34 1.15 1.23 1.34 1.41 1.47 1.52 1.5 206116B 6.02 34 1.11 1.18 1.30 1.37 1.44 1.49 1.5 206127B 5.93 37 1.24 1.26 1.35 1.42 1.49 1.54 1.5( 206127A 5.93 37 1.30 1.26 1.37 1.4B 1.50 1.55 1.5E 3 7? 3 B ) 1 7 7 1 7 3 ) ) 5 3 3? 5 3 6 S

TABLE IV-2 Condensing Coefficient Correction Factors, Cn, for Condensation of Steam at 212~F on 1 to 7 1-inch Bare 90-10 Cupro-Nickel Tubes in a Vertical Row C n Run No. Velocity LMTD 1 2 3 4 5 6 7 ft. /sec. ~F 206053A 3.55 28 1.'32 1.37 1.42 1.45 1.50 1.53 1.59 206053B 3.50 29 1.30 1.33 1.39 1.45 1.53 1.56 1.55 206054A 3.49 29 1.28 1.30 1.36 1.40 1.44 1.46 1.49 206054B 3.50 28 1.33 1.28 1.37 1.40 1.44 1.47 1.5C 206055A 3.73 28 1.42 1.43 1.62 1.64 1.73 1.75 1.8C 206059A 3.63 29 1.23 1.28 1.37 1.43 1.50 1.51 1.56 206059B 3.62 29 1.28 1.32 1.39 1.43 1.51 1.53 1.57 206063A 3.63 29 1.10 1.13 1.23 1.28 1.34 1.37 1.42 206063B 3.61 28 1.19 1.19 1.28 1.32 1.38 1.40 1.4' 206067A 3.63 28 1.24 1.25 1.35 1.39 1.46 1.47 1.51 206067B 3.62 28 1.23 1.31 1.40 1.44 1.50 1.51 1. 5 206111B 3.63 44 1.04 1.10 1.18 1.24 1.31 1.34 1.35 206111A 3.65 43 1.08 1.14 1.23 1.29 1.35 1.39 1.44 206125A 3.56 44 1.06 1.11 1.20 1.25 1.32 1.36 1.41 206125B 3.56 44 1.06 1.11 1.20 1.26 1.32 1.36 1.41 206129A 3.71 44 1.07 1.11 1.19 1.25 1.31 1.35 1.35 206129B 3.71 45 1.05 1.12 1.19 1.24 1.32 1.36 1.35 206131A 3.71 44 1.07 1.11 1.20 1.26 1.32 1.36 1.41 206131B 3.71 44 1.04 1.11 1.20 1.26 1.33 1.38 1.42 206133A 3.62 44 1.13 1.11 1.19 1.24 1.30 1.33 1.37 206133B 3.59 44 1.08 1.10 1.18 1.23 1.31 1.34 1.3q 206135A 3.62 44 1.10 1.12 1.19 1.25 1.32 1.34 1.3206135B 3.50 45 1.07 1.10 1.19 1.24 1.29 1.32 1.32 ) ) 3 I 5.> [ t 7 3 3 D

TABLE IV-2 (Continued) Cn Run No. Velocity LMTD 1 2 3 4 5 6 7 ft. /sec. ~F 206058A 5.50 29 1.35 1.36 1.43 1.48 1.55 1.57 1.6 206058B 5.49 29 1.35 1.37 1.46 1.52 1.60 1.62 1.6 206064A 5.43 29 1:18 1.22 1.31 1.36 1.42 1.46 1.5; 206064B 5.44 28 1.20 1.23 1.32 1.39 1.44 1.47 1.5 206066A 5.36 28 1.19 1.27 1.35 1.41 1.49 1.51 1.5 206066B 5.37 28 1.26 1.30 1.38 1.44 1.53 1.55 1.6 206069A 5.40 29 1.10 1.21 1.31 1.38 1.46 1.49 1.5 206071A 5.36 29 1.14 1.21 1.33 1.40 1.48 1.51 1.5! 206071B 5.36 29 1.11 1.25 1.37 1.42 1.50 1.51 1.5! 206072A 5.34 29 1.09 1.27 1.41 1.50 1.62 1.66 1.7 206062A 4.88 29 1.08 1.13 1.24 1.31 1.37 1.40 1.4 206062B 4.90 28 1.07 1.13 1.21 1.27 1.34 1.37 1.4 206065A 4.87 29 1.07 1.11 1.18 1.25 1.30 1.34 1.3' 206065B 4.85 29 1.06 1.09 1.17 1.24 1.29 1.34 1.4 206068A 4.91 29 1.18 1.18 1.28 1.32 1.39 1.42 1.4' 206068B 4.93 29 1.23 1.27 1.35 1.41 1.47 1.49 1.5z 206070A 4.90 28 1.16 1.22 1.32 1.38 1.47 1.50 1.5 206070B 4.89 28 1.14 1.22 1.30 1.37 1.45 1.47 1.5. 206073B 4.78 28 1.39 1.52 1.62 1.66 1.76 1.78 1.8 206082A 4.88 28 1.08 1.13 1.22 1.28 1.34 1.39 1.4. 206082B 4.89 28 1.15 1.17 1.24 1.31 1.37 1.40 1.4z 206107A 6.12 29 1.19 1.21 1.32 1.38 1.44 1.46 1.5 206107B 6.12 28 1.21 1.25 1.35 1.41 1.49 1.51 1.5( 206108A 6.10 43 1.04 1.10 1.21 1.27 1.36 1.44 1.4~ 206108B 6.11 43 1.06 1.12 1.22 1.29 1.37 1.42 1.4' 206110A 6.04 45 1.07 1.11 1.20 1.26 1.33 1.37 1.4 206110B 6.04 45 1.07 1.11 1.21 1.28 1.35 1.39 1.4z 206130A 5.99 48 1.06 1.12 1.21 1.28 1.34 1.38 1.4 206130B 5.99 48 1.05 1.12 1.21 1.26 1.32 1.37 1.4( 206132A 6.04 47 1.04 1.06 1.15 1.20 1.28 1.31 1.3' 206132B 6.00 46 1.03 1.12 1.22 1.26 1.34 1.37 1.4] 206134A 5.99 47 1.04 1.08 1.17 1.23 1.29 1.32 1.3( 206134B 6.00 47 1.05 1.05 1.13 1.18 1.24 1.29 1.3 206136A 6.01 46 1.11 1.12 1.21 1.27 1.34 1.38 1.42 206136B 6.02 46 1.09 1.11 1.20 1.26 1.33 1.36 1.4] 1 6 2 3 6 1 3 5 7 D 5 2 3 0 7 4 5 3 5 3 4 1 6 8 7 I 3 l 3 0 5 1 6 3 I

TABLE IV-3 Condensing Coefficient Correction Factors, Cn, for Condensation of Steam at 101~F on 1 to 7 1-inch Corrugated 90-10 Cupro-Nickel Tubes in a Vertical Row Cn Run No. Velocity LMTD 1 2 3 4 5 6 7 ft. /sec. O~F 205987A 3.50 27 1.13 1.26 1.39 1.48 1.52 1.56 1.68 205987B 3.50 27 1.12 1.29 1.39 1.49 1.53 1.56 1.69 205988A 3.50 19 1.25 1.43 1.58 1.72 1.77 1.83 1.90 205988B 3.50 19 1.30 1.47 1.63 1.75 1.80 1.85 1.93 205989A 3.52 9 1.31 1.36 1.47 1.60 1.70 1.81 1.98 205989B 3.52 10 1.85 1.70 1.77 1.91 1.92 1.97 2.05 205990A 3.52 19 1.50 1.69 1.85 1.99 2.01 2.09 2.19 205990B 3.52 19 1.42 1.57 1.72 1.87 1.91 1.98 2.11 205991A 3.51 24 1.59 1.77 1.93 2.08 2.12 2.18 2.30 205991B 3.51 24 1.49 1.71 1.89 2.04 2.08 2.13 2.23 205992A 3.37 24 1.30 1.49 1.67 1.84 1.89 1.94 2.04 205992B 3.37 24 1.29 1.49 1.65 1.80 1.86 1.92 2.01,,o 205993A 3.50 20 1.13 1.23 1.34 1.40 1.44 1.50 1.60 205993B 3.50 20 1.13 1.25 1.38 1.47 1.49 1.53 1.63 205994A 3.53 27 1.23 1.37 1.51 1.62 1.66 1.70 1.81 205994B 3.49 27 1.21 1.36 1.50 1.58 1.61 1.65 1.75 205995A 3.50 24 1.29 1.42 1.52 1.61 1.63 1.66 1.75 205995B 3.49 24 1.16 1.32 1.47 1.57 1.60 1.64 1.74 205996A 3.49 27 1.23 1.42 1.55 1.70 1.77 1.82 1.93 205996B 3.49 27 1.30 1.44 1.59 1.73 1.78 1.82 1.93 205997A 3.50 9 1.12 1.11 1.23 1.32 1.37 1.44 1.54 205997B 3.50 10 1.08 1.15 1.22 1.34 1.40 1.46 1.56 205998A 3.50 20 1.35 1.51 1.66 1.79 1.85 1.92 2.02 205998B 3.50 19 1.40 1.59 1.75 1.88 1.93 1.98 2.08 205999A 3.49 25 1.29 1.45 1.59 1.72 1.77 1.82 1.92 205999B 3.49 25 1.30 1.47 1.61 1.73 1.77 1.81 1.91 206000A 3.50 27 1.28 1.48 1.69 1.84 1.87 1.89 1.98 206000B 3.50 27 1.31 1.54 1.71 1.85 1.87 1.89 1.99 206001A 3.49 27 1.29 1.47 1.65 1.79 1.84 1.88 1.98 206001B 3.49 27 1.31 1.52 1.69 1.83 1.87 1.91 2.01 206002A 3.51 9 1.36 1.55 1.65 1.71 1.70 1.70 1.78 206002B 3.51 9 1.30 1.38 1.53 1.54 1.58 1.65 1.72

TABLE IV-3 (Continued) C n Run No. Velocity LMTD 1 2 3 4 5 6 7 ft. /sec. OF 206020A 3.57 24 1.45 1.74 1.95 2.13 2.16 2.20 2.3( 206020B 3.58 24 1.50 1.61 1.77 1.90 1.95 2.04 2.1i 206021A 3.64 26 1.58 1.79 1.98 2.17 2.22 2.26 2.3( 206021B 3.64 26 1.58 1.82 2.00 2.16 2.22 2.26 2.3( 206036B 3.54 24 1.72 1.92 2.09 2.25 2.30 2.35 2.4' 206023A 4.76 25 1.45 1.67 1.85 2.01 2.07 2.12 2.2: 206023B 4.75 25 1.42 1.67 1.86 2.03 2.10 2.14 2.2! 206025A 4.75 25 1.56 1.81 2.03 2.20 2.26 2.30 2.4 206025B 4.76 25 1.57 1.81 2.00 2.16 2.22 2.27 2.3' 206026A 4.74 23 1.48 1.69 1.89 2.05 2.14 2.18 2.2' 206026B 4.74 23 1.41 1.68 1.89 2.06 2.13 2.17 2.2' 206029A 4.75 23 1.44 1.71 1.93 2.11 2.18 2.21 2.3 206029B 4.76 23 1.46 1.73 1.94 2.11 2.18 2.22 2.3 206022A 6.04 26 1.56 1.80 1.99 2.17 2.23 2.26 2.3' 206022B 6.03 26 1.51 1.76 1.96 2.15 2.22 2.34 2.3, 206024A 6.08 26 1.52 1.76 1.97 2.15 2.20 2.22 2.31 206024B 6.08 26 1.49 1.72 1.93 2.12 2.18 2.21 2.3: 206027A 6.11 24 1.38 1.63 1.83 1.99 2.04 2.05 2.1! 206027B 6.11 24 1.36 1.60 1.80 2.00 2.06 2.09 2.1 206028A 6.19 22 1.32 1.71 1.91 2.04 2.10 2.14 2.2! 206028B 6.21 22 1.32 1.56 1.80 1.95 2.02 2.08 2.2( 206030A 6.18 22 1.30 1.55 1.75 1.91 1.94 1.98 2.0' 206030B 6.17 22 1.29 1.54 1.73 1.88 1.95 2.00 2.1( 3 3 6 6 7 3 5 1 7 7 7 1 1 7 8 1 3 I 3 5 9 5 3 3 9 0

TABLE IV-4 Condensing Coefficient Correction Factors, Cn, for Condensation of Steam at 212~F on 1 to 7 1-inch Corrugated 90-10 Cupro-Nickel Tubes in a Vertical Row Cn Run No. Velocity ft. /sec. 205954A 3.45 205954B 3.45 205955A 3.58 205955B 3.58 205956A 3.46 205956B 3.45 205957A 3.46 205957B 3.47 205958A 3.43 205958B 3.45 205959A 3.47 -^ 205959B 3.47 205960A 3.40 205960B 3.40 205961A 3.45 205961B 3.45 205962A 3.45 205962B 3.45 205963A 3.46 205963B 3.46 205964A 3.46 205964B 3.47 205965A 3.45 205965B 3.45 205966A 3.45 205966B 3.45 205967A 3.51 205967B 3.51 205968A 3.45 205968B 3.46 205969A 3.51 205969B 3.51 LMTD ~F 19 19 20 20 20 19 21 21 30 30 30 30 39 39 40 40 39 38 29 28 20 20 28 28 38 38 21 20 40 39 29 29 1 1.52 1. 53 1. 50 1.46 1.25 1.21 1.20 1.31 1. 18 1.13 1.23 1.24 1. 16 1. 15 1.23 1.19 1.29 1.27 1. 36 1. 36 1.27 1.28 1.21 1.23 1.22 1.18 1.16 1.19 1.10 1. 14 1. 14 1.16 2 1.59 1.58 1.54 1.53 1.32 1.28 1.14 1.37 1.23 1.23 1.29 1. 31 1.24 1.25 1. 31 1.26 1.38 1.37 1.43 1.43 1. 37 1.36 1.29 1.33 1.32 1.43 1.36 1.28 1.20 1.23 1. 18 1.32 3 1.68 1.78 1.73 1.73 1.52 1.44 1.33 1.51 1.36 1.36 1.42 1.44 1.37 1.39 1.44 1.39 1.50 1.51 1.57 1.58 1.48 1.48 1.41 1.46 1.44 1. 53 1.46 1.41 1.33 1.34 1.28 1.48 4 1.86 1.97 1.86 1.87 1.65 1. 58 1.47 1.63 1.46 1.48 1.53 1.54 1.49 1. 51 1.56 1.51 1.63 1. 64 1.70 1.70 1.59 1.59 1.52 1.43 1.56 1.62 1. 54 1.52 1.42 1.43 1.32 1.62 5 1.91 2.04 1.88 1.90 1.69 1.60 1. 54 1.67 1.51 1. 53 1.56 1.59 1.54 1.56 1.60 1.55 1.67 1.69 1.73 1.74 1.63 1.63 1.56 1.48 1.59 1.66 1. 58 1.54 1.46 1.47 1.37 1.63 6 7 1.97 2. 12 1.92 1.93 1.71 1.64 1.58 1.71 1.57 1.57 1.60 1.62 1.59 1. 61 1.65 1.60 1.72 1.74 1.78 1.79 1.67 1.67 1.60 1.53 1.63 1.69 1.61 1.57 1. 50 1.51 1.41 1. 68 2.03 2.18 1.92 1.96 1.74 1.69 1.47 1.57 1.50 1.51 1.54 1.56 1.57 1. 60 1. 63 1.57 1.79 1.80 1.83 1.84 1.74 1.73 1.66 1. 61 1.69 1.75 1.66 1. 63 1.56 1.57 1.47 1.73

TABLE IV-4 (Continued) Cn Run No. Velocity LMTD 1 2 3 4 5 6 7 ft. /sec. ~F 205970A 3.50 40 1.26 1.33 1.44 1.55 1.58 1.62 1.6 205970B 3.50 40 1..26 1.33 1.45 1.50 1.55 1.59 1.6 205974A 3.47 41 1.26 1.41 1.55 1.68 1.74 1.79 1.8' 205974B 3.46 40 1.21 1.37 1.51 1.64 1.70 1.75 1.8 205975A 3.45 30 1.20 1.36 1.49 1.62 1.67 1.71 1.7 205975B 3.46 30 1.19 1.34 1.46 1.60 1.67 1.72 1.81 205976A 3.38 18 1.26 1.45 1.59 1.73 1.78 1.81 1.8 205976B 3.44 17 1.22 1.41 1.56 1.70 1.74 1.78 1.8' 205977A 3.56 19 1.37 1.50 1.60 1.71 1.75 1.78 1.8 205977B 3.56 18 1.44 1.52 1.62 1.71 1.76 1.79 1.8 205978A 3.56 39 1.29 1.42 1.53 1.64 1.68 1.72 1.7 205978B 3.56 40 1.21 1.34 1.45 1.57 1.62 1.67 1.7 205979A 3.54 29 1.17 1.29 1.39 1.50 1.55 1.58 1.6 205979B 3.54 30 1.16 1.29 1.40 1.51 1.57 1.61 1.6 205980A 3.62 22 1.13 1.33 1.48 1.59 1.67 1.70 1.7 205980B 3.61 21 1.27 1.44 1.58 1.71 1.74 1.78 1.8 205982B 3.57 25 1.45 1.51 1.63 1.77 1.82 1.87 1.9 205983A 3.47 25 1.66 1.81 2.00 2.17 2.24 2.30 2. 3 205983B 3.47 25 1.73 1.97 2.16 2.32 2.34 2.37 2.4' 205984A 3.50 35 1.40 1.59 1.74 1.90 1.95 1.99 2.0 205984B 3.50 35 1.34 1.50 1.64 1.80 1.86 1.91 1.9 205985A 3.50 25 1.20 1.29 1.45 1.58 1.64 1.68 1.7 205985B 3.50 25 1.31 1.38 1.50 1.63 1.67 1.72 1.8 206003A 3.54 37 1.29 1.41 1.54 1.66 1.70 1.74 1.8 206003B 3.54 37 1.29 1.41 1.53 1.65 1.69 1.73 1.8 206004A 3.54 32 1.27 1.41 1.53 1.65 1.70 1.73 1.8 206005A 3.56 34 1.27 1.37 1.51 1.60 1.65 1.68 1.7 206005B 3.56 34 1.26 1.36 1.49 1.61 1.66 1.69 1.7 206006A 3.59 28 1.24 1.36 1.45 1.58 1.67 1.68 1.7 206006B 3.55 29 1.22 1.31 1.43 1.55 1.61 1.62 1.7 8 5 7 3 9 0 9 7 6 9 9 4 6 8 8 5 4 9 7 5 9 5 1 1 0 0 5 6 4 0

TABLE IV-4 (Continued) Cn Run No. Velocity LMTD 1 2 3 4 5 6 7 ft. /sec. cF 206037A 4.04 29 1.51 1.58 1.72 1.86 1.90 1.93 1.99 206037B 4.04 29 1.50 1.57 1.70 1.84 1.90 1.93 1.99 206040A 4.04 38 1.48 1.52 1.65 1.79 1.85 1.89 1.96 206040B 4.04 37 1.60 1.61 1.75 1.88 1.92 1.97 2.04 206041A 4.06 38 1.44 1.51 1.63 1.76 1.81 1.87 1.94 206041B 4.06 38 1.45 1.54 1.67 1.81 1.86 1.90 1.97 206043A 4.05 38 1.39 1.49 1.62 1.75 1.81 1.86 1.93 206043B 4.05 38 1.41 1.50 1.65 1.77 1.83 1.87 1.94 206045A 4.04 38 1.40 1.51 1.64 1.77 1.81 1.86 1.92 206045B 4.04 38 1.43 1.53 1.66 1.79 1.84 1.87 1.93 206047A 4.04 38 1.46 1.53 1.66 1.79 1.85 1.89 1.95 206047B 4.04 38 1.40 1.50 1.70 1.79 1.84 1.88 1.94 206048A 4.03 39 1.29 1.34 1.47 1.59 1.63 1.66 1.72 206048B 4.02 38 1.31 1.34 1.46 1.58 1.63 1.67 1.73 206031A 4.80 38 1.58 1.66 1.80 1.94 2.00 2.04 2.12 206031B 4.80 38 1.51 1.62 1.77 1.91 1.97 2.05 2.11 206032A 4.80 38 1.50 1.58 1.73 1.88 1.94 1.98 2.05 206032B 4.80 38 1.51 1.60 1.74 1.89 1.95 1.99 2.06 206033A 4.80 38 1.50 1.63 1.77 1.91 1.98 2.04 2.10 206033B 4.80 38 1.63 1.70 1.85 1.99 2.04 2.11 2.16 206034A 4.82 37 1.61 1.72 1.84 1.97 2.01 2.05 2.11 206034B 4.82 37 1.60 1.70 1.82 1.95 1.99 2.03 2.09 206035A 4.82 38 1.55 1.66 1.79 1.92 1.97 2.01 2.08 206035B 4.82 38 1.57 1.68 1.80 1.93 1.98 2.00 2.07 206044A 5.31 40 1.38 1.47 1.61 1.75 1.80 1.84 1.91 206044B 5.30 40 1.39 1.45 1.59 1.72 1.77 1.82 1.88 206046A 5.30 40 1.45 1.52 1.65 1.77 1.83 1.87 1.93 206046B 5.30 39 1.42 1.50 1.64 1.76 1.81 1.85 1.91 206049A 5.32 40 1.39 1.45 1.60 1.72 1.78 1.82 1.88 206049B 5.31 40 1.37 1.43 1.57 1.70 1.75 1.80 1.86 206050A 5.35 40 1.33 1.41 1.58 1.70 1.75 ].79 1.86 206050B 5.35 40 1.31 1.39 1.54 1.64 1.72 1.77 1.84 206051A 5.28 40 1.33 1.41 1.57 1.69 1.74 1.79 1.85 206051B 5.28 40 1.31 1.40 1,56 1.67 1.73 1.79 1.85 206052A 5.30 40 1.34 1.44 1.61 1.72 1.79 1.83 1.90 206052B 5.30 40 1.35 1.44 1.60 1.72 1.79 1.84 1.91

TABLE IV-4 (Continued) Cn Run No. Velocity ft. /sec. 206011B 6.03 206012A 6.04 206012B 6.04 206013A 6.32 206013B 6.32 206014A 6.14 206014B 6.13 206015A 6.13 206015B 6.13 206016A 6.18 206016B 6.18 206017A 6.19 206017B 6.18 206018A 6.15, 206018B 6.16 v 206019A 6.19 206019B 6.19 LMTD OF 39 30 30 39 39 39 39 30 30 20 20 39 39 21 21 21 21 30 29 30 41 41 20 20 39 1 1.38 1.41 1.43 1.52 1.50 1.38 1.37 1.46 1.32 1. 68 1.59 1.50 1.53 1.65 1. 67 1.58 1.59 1.49 1.51 1.49 1.46 1.44 1. 67 1.61 1.39 2 1.53 1.59 1. 59 1.62 1.63 1. 64 1.54 1.61 1.52 1.77 1. 69 1.61 1.62 1.75 1.65 1. 69 1. 65 1.62 1.65 1.59 1.58 1.55 1.74 1. 69 1.57 3 1.69 1.76 1.81 1.80 1.80 1.80 1.70 1.81 1.71 1.92 1.82 1.74 1.78 1.89 1.79 1.86 1.83 1.75 1.77 1.73 1.74 1.71 1.89 1.83 1.74 4 1.86 1.92 1.96 1.97 1.94 1.85 1.84 1.91 1.87 2.05 1.97 1.83 1.90 2.04 1.91 2.03 1.95 1.92 1.94 1.90 1.94 1.87 2.04 1.98 1.88 5 1.90 1.97 2.01 2.00 1.98 1.89 1.90 1.97 1.94 2.12 2.04 1.97 1.94 2.09 1.95 2.06 2.02 1.96 1.99 1.93 1.98 1.93 2.07 2.02 1.95 6 7 1.95 2.01 2.06 2.03 2.02 1.93 1.94 2.01 2.00 2.14 2.07 2.00 1.99 2.12 1.99 2.09 2.06 2.00 2.04 1.99 2.02 1.98 2. 10 2.06 2.00 2.04 2. 10 2. 14 2. 11 2. 09 2. 00 2.02 2.04 2. 09 2.23 2. 16 2.04 2.06 2.21 2.08 2.16 2.15 2.09 2.13 2.06 2.09 2.06 2.16 2.16 2. 08 205981A 205981B 206007A 206008A 206008B 206009A 206009B 206011A 6.32 6.32 6.08 6.07 6.08 6.12 6.13 6.04

TABLE IV-5 Condensing Coefficient Correction Factors, Cn, for Condensation of Steam at 101~'F on 1 to 9 5/8-inch Bare Copper Tubes in a Vertical Row C for n Copper Tubes in a Vertical Row Run No. Vel. 1 2 3 4 5 6 7 8 9 197020A 6.071 1.3292 1.3060 1.3173 1.3243 1.3440 1.3780 1.3898 1.4060 1.4199 197020B 5.854 1.3171 1.3124 1.3092 1.3264 1.3446 1.3608 1.3724 1.3872 1.3985 197020C 5.879 1.2779 1.2969 1.3292 1.3360 1.3602 1.3765 1.3878 1.4055 1.418C 197021A 8. 970 1.2901 1. 2667 1.2946 1. 3299 1.3454 1.3611 1.3687 1.3786 1.3906 197021B 8.907 1.2540 1.2614 1.2927 1.3183 1.3338 1.3502 1.3626 1.3789 1.3974 197021C 8.865 1.2651 1.2612 1.2760 1.2900 1.3098 1.3348 1.3459 1.3625 1.379c 197022A 11.616 1.2466 1.2569 1.2779 1.2926 1.3027 1.3260 1.3190 1.3330 1.3524 197022B 11.608 1.2268 1.2584 1.2652 1.2747 1.2926 1.3112 1.3196 1.3396 1.362 197022C 11.598 1.2640 1.2586 1.2899 1.3009 1.3112 1.3332 1.3500 1.3674 1.386C 197023A 16.415 1.2723 1.2897 1.2998 1.3166 1.3484 1.3697 1.3697 1.3864 1.4067 197023B 16.393 1.3047 1.2680 1.3268 1.3596 1.3887 1.4063 1.4108 1.4246 1.4332 ~lx 197023C 16.391 1.2606 1.2265 1.2447 1.2886 1.3221 1.3299 1.3487 1.3680 1.386: 197024A 20.355 1.3490 1.3331 1.3721 1.3812 1.4039 1.4237 1.4173 1.4315 1.4462 197024B 20.349 1. 3337 1.3263 1.3680 1.3965 1.4217 1.4341 1.4387 1.4486 1.4614 197024C 20.330 1.3410 1.3605 1.4248 1.4608 1.4860 1.5069 1.4875 1.4947 1.503: 197025A 25.440 1.3170 1.3227 1.3610 1.3901 1.4157 1.4371 1.4379 1.4558 1.4711 197025B 25.441 1.3609 1. 3523 1.3954 1.4200 1.4542 1.4761 1.4872 1.4964 1.5064 197025C 25.412 1.3461 1.3424 1.3821 1.4142 1.4444 1.4716 1.4881 1.5002 1.514< 197026A 16.888 1.3393 1.2869 1.3390 1.3664 1.3954 1.4152 1.4254 1.4318 1.4445 197026B 17.006 1.2687 1.2548 1.3164 1.3122 1.3449 1.3727 1.3790 1.3914 1.409; 197026C 17.122 1.2738 1.2902 1.2998 1.3347 1.3653 1.3759 1.3865 1.3997 1.413' 197027A 20.025 1.3417 1.3386 1.3651 1.3827 1.4054 1.4189 1.4295 1.4383 1.450( 197027B 20.012 1.3209 1.2692 1.3244 1.3578 1.3876 1.4094 1.4168 1.4256 1.440; 197027C 20.030 1.3323 1.3329 1.3694 1.3871 1.4106 1.4343 1.4252 1.4356 1.452' 197028A 25.528 1.3564 1.3473 1.3860 1.4088 1.4412 1.4682 1.4695 1.4803 1.494( 197028B 25.526 1.3605 1.3586 1.3923 1.4052 1.4293 1.4505 1.4605 1.4722 1.4875 197028C 25.509 1.3550 1.3561 1.3980 1.4251 1.4559 1.4689 1.4767 1.4870 1.501< 5 ):) 3 I 3 3 3 1 4 9 7 3 9 0 3 9 D 7 9

TABLE IV-6 Condensing Coefficient Correction Factors, Cn, for Condensation of Steam at 101~F on 1 to 8 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes in a Vertical Row C Run No. Velocity LMTD 1 2 3 4 5 ft. /sec. ~F 205889A 2.86 9 1.07 1.21 1.35 1.43 1.48 1. 205882A 3.85 8 1.28 1.43 1.61 1.68 1.74 1. 205879A 4.75 9 1.02 1.19 1.32 1.41 1.47 1. 205879B 4.75 9 1.07 1.21 1.33 1.41 1.46 1. 205878A 5.34 10 1.25 1.36 1.48 1.55 1.60 1. 205878B 5.33 10 1.23 1.35 1.46 1.54 1.58 1. 6 50 78 50 79 63 61 7 8 1.55 1.81 1.56 1.51 1.68 1.65 1. 59 1.85 1.61 1.58 1.71 1.70 205862A 205864A 205865A 205870A 205870B 205871A 205873A 205873B 205873C 205874A 205874B 205874C 205875A 205875B 205876A 205876B 205880A 205880B 205888A 205888B 205888C 205904A 205904B 5.97 6.14 6.11 6.12 6.12 6.67 6.06 6.07 6.07 6.07 6.08 6.08 6.35 6.36 6.38 6.38 5.87 5.89 6.07 5.88 6.09 6.13 6.13 18 1.12 19 1.27 18 1.25 16 1.12 16 1.15 15 1.22 17 1.21 17 1.20 16 1.19 14 1.15 14 1.20 14 1.20 20 1.31 21 1.32 15 1.32 15 1.32 10 1.21 10 1.25 18 1.07 18 1.08 17 1.02 23 1.23 24 1.24 1.31 1.45 1.44 1.30 1.32 1.46 1.37 1.36 1.37 1.28 1.35 1.39 1.44 1.49 1.50 1.52 1.36 1.36 1.25 1.25 1.19 1.44 1.45 1.45 1.61 1.60 1.43 1.45 1.64 1.53 1.52 1.51 1.45 1.50 1.55 1.65 1.66 1.69 1.70 1.51 1.50 1.43 1.45 1.37 1.63 1.64 1. 54 1.72 1.69 1.50 1.53 1.73 1.63 1.63 1.60 1. 56 1.60 1.63 1.75 1.79 1.81 1.84 1.62 1.60 1.50 1.52 1.45 1.75 1.76 1. 59 1.78 1.75 1.52 1. 54 1.80 1.70 1.68 1.67 1. 62 1. 67 1.69 1.82 1.85 1.89 1.92 1.69 1.66 1. 54 1.58 1.50 1.82 1.83 1.63 1.81 1.79 1.56 1.58 1.82 1.74 1.72 1.70 1. 65 1.71 1.73 1.87 1.89 1.93 1.96 1.74 1.71 1.61 1.63 1.56 1.87 1.87 1.68 1.84 1.84 1.57 1.57 1.83 1.78 1.75 1.73 1.67 1.74 1.75 1.89 1.90 1.84 1.85 1.79 1.75 1.67 1.70 1.63 1.92 1.93 1.72 1.88 1.87 1.61 1. 62 1.86 1.82 1.80 1.78 1.73 1.80 1.81 1.93 1.95 1.90 1.90 1.83 1.79 1.70 1.69 1.65 1.96 1.96

TABLE IV-7 Condensing Coefficient Correction Factors, Cn, for Condensation of Steam at 212~F on 1 to 8 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes in a Vertical Row Cn Run No. Velocity LMTD 1 2 3 4 5 6 7 8 ft. /sec. ~F 205881A 3.95 15 0.81 0.96 1.04 1.10 1.16 1.21 1.25 1.28 205881B 3.95 15 0.82 1.96 1.06 1.14 1.19 1.23 1.26 1.29 205896A 4.01 21 0.85 1.01 1.14 1.23 1.28 1.32 1.36 1.40 205896B 4.02 21 0.86 1.02 1.14 1.23 1.30 1.34 1.38 1.41 205886A 4.76 10 0.78 0.95 1.07 1.17 1.23 1.28 1.30 1.33 205886B 4.75 10 0.79 0.94 1.06 1.14 1.21 1.25 1.27 1.31 205886C 4.75 10 0.79 0.94 1.07 1.14 1.22 1.25 1.27 1.31 205900A 5.57 22 0.92 1.08 1.21 1.30 1.36 1.40 1.44 1.48 205900B 5.58 22 0.92 1.08 1.21 1.31 1.37 1.40 1.44 1.49 205902A 5.58 30 0.97 1.13 1.26 1.35 1.41 1.45 1.49 1.53 205902B 5.58 30 0.99 1.14 1.27 1.36 1.42 1.46 1.51 1.55 205891B 6.3 21 0.94 1.09 1.21 1.31 1.36 1.41 1.45 1.49 205892A 6.'4 40 0.99 1.18 1.33 1.43 1.50 1.53 1.57 1.60 205892B 6.3 40 0.98 1.17 1.32 1.43 1.50 1.53 1.57 1.60 205893A 6.4 21 0.95 1.11 1.23 1.33 1.39 1.43 1.47 1.52 205893B 6.4 21 0.95 1.11 1.23 1.32 1.38 1.42 1.47 1.46 205894A 6.3 40 1.01 1.20 1.34 1.44 1.49 1.53 1.58 1.61 205894B 6.3 39 1.01 1.20 1.34 1.44 1.49 1.53 1.58 1.61 205895A 6.5 21 0.97 1.12 1.25 1.35 1.40 1.45 1.49 1.53 205895B 6.5 21 0.97 1.12 1.25 1.34 1.40 1.45 1.49 1.54 205901A 6.4 30 1.00 1.15 1.29 1.39 1.44 1.49 1.53 1.57 205901B 6.4 29 0.97 1.14 1.27 1.37 1.43 1.47 1.52 1.56 205906B 6.2 8 0.81 0.91 0.99 1.07 1.13 1.18 1.21 1.25 205906A 6.3 9 0.82 0.92 1.02 1.12 1.17 1.21 1.23 1.28

TABLE IV-8 Overall Heat Transfer Coefficients, Uo, for Condensation of Steam at 101~F on 1 to 7 1-inch Bare 90-10 Cupro-Nickel Tubes in a Vertical Row U Run No. Velocity LMTD 1 2 3 4 5 6 7 ft. / sec. ~F 206074A 3.51 24 565 540 537 535 532 528 526 206074B 3.57 24 574 552 549 544 541 536 533 206078A 3.62 22 542 498 490 485 480 481 480 206078B 3.62 22 553 506 498 493 487 487 486 206080B 3.66 18 588 558 553 547 542 537 536 206084B 3.64 12 639 611 601 534 588 581 577 206086A 3.62 23 556 532 523 521 520 516 515 206086B 3.61 24 565 524 512 511 511 512 512 206088A 3.61 24 552 492 481 475 467 470 469 206091A 3.58 24 521 489 485 483 478 480 481 206091B 3.58 24 530 496 491 488 483 486 486 206098A 3.62 24 571 542 542 537 535 532 531 206098B 3.62 24 570 546 542 537 536 534 532 206100B 3.57 24 542 521 518 511 509 507 504 206104A 3.60 24 532 511 514 511 508 502 498 206104B 3.55 24 518 489 487 486 481 480 479 206105A 3.71 37 564 535 528 521 519 516 514 206105B 3.71 37 568 538 532 526 525 521 517 206113A 3.61 32 586 551 546 538 535 532 529 206113B 3.60 32 584 551 546 539 538 534 531 206115A 3.64 32 575 549 541 538 537 532 528 206115B 3.65 32 565 543 538 535 536 530 528 206117A 3.61 34 570 530 516 513 507 507 502 206117B 3.61 34 569 524 518 515 511 511 510 206120A 3.65 35 567 543 535 529 528 528 524 206120B 3.65 35 557 529 525 521 518 515 511 206122A 3.65 34 552 530 524 521 519 516 514 206122B 3.65 34 561 530 526 523 522 518 516 206126A 3.60 37 559 536 528 521 517 512 509 206126B 3.61 37 561 530 523 517 517 514 512

TABLE IV-8 (Continued) U 0 Run No. Velocity LMTD 1 2 3 4 5 6 7 ft. /sec. ~F 206081A 4.79 17 718 684 668 659 652 648 645 206083A 4.76 11 734 704 694 684 682 674 673 206083B 4.77 11 752 715 707 696 689 678 675 206075A 4.76 24 649 614 609 602 596 592 589 206075B 4.75 24 656 624 615 606 602 598 593 206076A 4.75 23 657 630 625 617 613 610 606 206076B 4.76 23 668 639 631 623 619 614 609 206081A 4.79 17 718 684 668 659 652 648 645 206079A 4.69 22 652 590 576 568 560 559 559 206079B 4.71 22 639 584 573 567 559 559 559 206085A 4.76 22 662 625 620 612 608 604 600 206085B 4.75 22 664 628 621 614 609 607 602 206087A 4.79 24 655 620 614 607 604 599 594 206087B 4.79 24 655 622 616 610 605 600 595 206089A 4.75 24 617 569 559 553 545 542 540 206099A 4.74 25 618 594 587 580 578 574 568 206102A 4.74 24 645 610 602 597 593 586 582 206102B 4.74 24 629 598 594 589 587 584 580 206103A 4.65 24 622 590 592 583 581 578 575 206103B 4.63 24 635 604 598 592 588 583 579 206118A 4.80 34 659 637 624 608 600 597 591 206118B 4.81 33 675 626 620 613 610 607 604 206119A 4.75 36 623 590 589 584 583 580 577 206119B 4.75 36 637 599 591 585 586 585 582 206121A 4.82 35 642 595 595 591 588 583 581 206121B 4.82 34 640 601 596 589 590 587 585 206123B 4.78 33 650 613 602 596 592 590 586 206123A 4.79 33 643 609 605 597 595 594 588 206124A 4.79 33 657 618 609 599 596 593 591 206124B 4.79 33 643 610 604 595 595 592 585 206128A 4.77 37 635 607 602 598 598 595 592 206128B 4.77 36 642 613 604 597 594 590 587

TABLE IV-8 (Continued) U O Run No. Velocity ft. /sec. LMTD oF 1 2 3 4 5 6 7 206092A 206092B 206093A 206093B 206094A 206094B 206095A 206095B 206096A 206096B 206097A 206097B 206101B 206106A 206106B 206109B 206109A 206112A 206112B 206114A 206114B 206116A 206116B 206127B 206127A 5. 18 5. 18 5.16 5.16 5. 18 5. 18 5.23 5. 18 5.24 5.24 5.23 5.23 5.25 6. 00 6.01 6.00 6.00 6.00 6.01 5.95 5.95 6.02 6.02 5.93 5.93 24 25 24 24 24 24 24 24 24 24 24 24 24 36 36 26 26 32 32 32 32 34 34 37 37 662 65.6 658 645 660 673 659 668 639 636 633 642 680 703 706 755 753 731 721 731 734 693 683 696 708 642 635 621 617 633 641 630 634 593 594 590 606 646 658 666 696 692 684 673 681 684 665 655 656 656 636 628 605 611 626 633 622 627 595 596 588 606 641 652 659 683 682 673 667 668 665 661 652 648 651 632 623 600 605 619 624 622 620 584 588 580 598 624 646 650 670 679 663 661 665 652 654 646 642 641 629 622 598 602 615 618 618 616 587 592 584 602 617 646 649 666 675 660 658 662 653 651 646 640 64B 626 618 593 598 610 614 613 610 584 589 582 598 618 624 617 589 593 605 608 608 606 585 589 580 596 613 643 645 659 668 654 652 658 647 647 643 636 638 639 640 655 663 648 645 651 641 642 639 630 633

Overall Heat Transfer Coefficients, Uo, for Condensation of Steam at 212~F on 1 to 7 1-inch Bare 90-10 Cupro-Nickel Tubes in a Vertical Row U0 Run No. Velocity LMTD 1 2 3 4 5 6 7 ft. /sec. ~F 206053A 3.55 28 804 774 758 746 741 734 734 206053B 3.50 29 795 762 748 740 741 733 729 206054A 3.49 29 790 754 742 730 723 716 711 206054B 3.50 28 800 752 744 732 725 719 714 206055A 3.73 28 839 802 807 793 792 784 782 206059A 3.63 29 800 768 758 751 750 740 737 206059B 3.62 29 809 775 763 752 752 742 740 206063A 3.63 29 772 735 730 723 720 713 713 206063B 3.61 28 790 747 739 729 725 718 717 206067A 3.63 28 800 761 754 744 742 732 728 206067B 3.62 28 798 770 762 751 748 738 736 206111B 3.63 44 711 680 673 666 666 661 660 un 206111A 3.65 43 723 694 687 679 677 673 671 206125A 3.56 44 710 678 671 663 662 658 658 206125B 3.56 44 710 677 671 665 663 659 657 206129A 3.71 44 724 688, 680 672 672 666 663 206129B 3.71 45 718 689 680 671 672 667 664 206131A 3.71 44 726 690 683 676 673 670 668 206131B 3.71 44 717 689 682 676 676 673 670 206133A 3.62 44 732 684 675 666 664 657 655 206133B 3.59 44 719 679 671 663 664 658 655 206135A 3.62 44 724 684 674 667 667 660 658 206135B 3.50 45 714 678 670 662 659 652 644 206062A 4.88 29 868 824 822 816 813 805 803 206062B 4.90 28 867 828 815 808 806 798 798 206065A 4.87 29 865 816 805 799 793 787 787 206065B 4.85 29 859 812 802 795 791 786 790 206068A 4.91 29 898 839 832 819 818 809 809 206068B 4.93 29 913 867 854 843 839 827 824 206070A 4.90 28 895 852 845 837 840 831 829 206070B 4.89 28 888 853 842 834 834 823 825 206073B 4.78 28 940 914 904 889 889 879 879 206082A 4.88 28 872 830 821 811 809 804 800 206082B 4.89 28 891 839 826 820 817 807 804

TABLE IV-9 (Continued) U Run No. Velocity LMTD 1 2 3 4 5 6 7 ft. /sec. ~F 206058A 5.50 29 986 930 913 897 895 882 878 206058B 5.49 29 986 930 917 906 904 894 888 206064A 5.43 29 935 886 874 862 858 850 850 206064B 5.44 28 945 891 881 871 863 855 855 206066A 5.36 28 937 900 885 874 874 863 860 206066B 5.37 28 956 907 894 883 885 873 872 206069A 5.40 29 909 882 872 864 865 855 852 206071A 5.36 29 918 878 875 868 870 858 855 206071B 5.36 29 911 893 887 875 875 859 860 206072A 5.34 29 900 894 893 865 877 872 871 206107A 6.12 29 982 920 915 903 900 887 884 206107B 6.12 28 992 936 926 915 915 902 900 206108A 6.10 43 868 824 821 811 816 821 816 D0 206108B 6.11 43 878 831 825 817 820 816 813 206110A 6.04 45 871 816 807 798 798 792 789 206110B 6.04 45 870 814 811 804 804 798 795 206130A 5.99 48 855 811 802 792 791 784 782 206130B 5.99 48 852 810 799 786 785 779 775 206132A 6.04 47 859 796 788 778 779 770 767 206132B 6.00 46 857 819 813 799 800 790 786 206134A 5.99 47 856 802 793 784 781 773 769 206134B 6.00 47 861 791 779 769 767 762 760 206136A 6.01 46 884 819 809 798 798 791 787 206136B 6.02 46 875 814 806 797 795 787 786

TABLE Iv-10 Overall Heat Transfer Coefficients, Uo, for Condensation of Steam at 101~F on 1 to 7 1-inch Corrugated 90-10 Cupro-Nickel Tubes in a Vertical Row Uo Run No. Velocity LMTD 1 2 3 4 5 6 7 ft. /sec. OF 205987A 3.50 27 784 762 762 758 748 741 754 205987B 3.50 27 782 770 762 760 750 742 757 205988A 3.50 19 863. 849 850 855 844 840 842 205988B 3.50 19 876 859 859 860 850 844 845 205989A 3.52 9 960 917 909 914 914 921 938 205989B 3.52 10 1054 982 964 965 950 943 943 205990A 3.52 19 922 904 901 902 886 886 887 205990B 3.52 19 905 882 879 882 871 867 876 205991A 3.51 24 907 886 884 883 872 866 872 205991B 3.51 24 888 877 876 878 867 859 863 205992A 3.37 24 832 819 824 832 822 817 820 205992B 3.37 24 830 820 821 826 819 813 816 205993A 3.50 20 828 799 792 783 774 770 780 205993B 3.50 20 827 801 802 797 782 776 785 U-1 205994A 3.53 27 815 792 792 790 779 772 780 D. 205994B 3.49 27 806 789 786 780 766 760 768 205995A 3.50 24 842 815 806 800 784 776 782 205995B 3.49 24 807 791 793 793 779 771 778 205996A 3.49 27 814 803 799 807 800 795 802 205996B 3.49 27 832 809 808 812 802 796 802 205997A 3.50 9 910 845 846 848 841 841 851 205997B 3.50 10 894 856 840 846 842 842 852 205998A 3.50 20 887 866 864 866 858 855 861 205998B 3.50 19 898 885 883 883 873 866 870 205999A 3.49 25 840 821 819 822 812 806 811 205999B 3.49 25 843 827 823 824 811 804 809 206000A 3.50 27 825 816 826 830 816 805 809 206000B 3.50 27 832 828 830 832 817 805 811 206001A 3.49 27 826 812 817 821 811 803 809 206001B 3.49 27 832 823 825 828 817 808 813 206002A 3.51 9 972 958 945 933 912 899 900 206002B 3.51 9 956 920 920 899 889 887 889 206020A 3.57 24 883 886 890 895 882 872 875 206020B 3.58 24 893 861 858 859 849 848 858 206021A 3.64 26 912 897 898 904 892 883 886 206021B 3.64 26 914 903 901 904 894 885 887 206036B 3.54 24 931 913 909 909 898 891 895

TABLE IV-10 (Continued) U O Run No. Velocity ft. /sec. LMTD 1 2 3 4 5 6 7 206023A 4.76 206023B 4.75 206025A 4.75 206025B 4.75 206026A 4.74 206026B 4.74 206029A 4.75 206029B 4.76 206022A 6.04 206022B 6.03 206024A 6.08 206024B 6.08 206027A 6.11 206027B 6.11 206028A 6.19 A, 206028B 6.21 206030A 6.18 206030B 6.17 25 979 25 972 25 1012 25 1013 23 997 23 978 23 992 23 997 26 1086 26 1073 26 1079 26 1069 24 1049 24 1043 22 1044 22 1044 22 1039 22 1039 966 966 1002 1002 981 980 992 996 1074 1064 1067 1054 1047 1039 1085 1042 1041 1040 967 970 1008 1002 985 986 1000 1001 1073 1067 1073 1062 1054 1046 1091 1061 1050 1046 972 978 1011 1003 989 992 1006 1007 1079 1076 1080 1072 1059 1063 1086 1065 1057 1054 962 967 998 993 984 981 996 996 1066 1064 1064 1058 1044 1048 1073 1055 1039 1042 953 957 987 983 972 970 984 986 959 963 992 986 974 973 986 987 1052 1068 1047 1044 1025 1033 1060 1048 1025 1032 1055 1057 1048 1050 1030 1038 1066 1055 1033 1038

TABLE IV-11 Overall Heat Transfer Coefficients, Uo, for Condensation of Steam at 212~F on 1 to 7 1-inch Corrugated 90-10 Cupro-Nickel Tubes in a Vertical Row Uo Run No. Velocity LMTD 1 2 3 4 5 67 ft. /sec. ~F 205954A 3.45 19 1276 1219 1196 1212 1196 1190 118 205954B 3.45 19 1280 1218 1226 1240 1229 1225 122 205955A 3.58 20 1280 1210 1219 1219 1196 1185 116 205955B 3.58 20 1268 1210 1218 1222 1201 1188 117 205956A 3.46 20 1185 1129 1148 1154 1136 1121 110 205956B 3.45 19 1173 1118 1123 1134 1115 1104 109 205957A 3.46 21 1162 1046 1076 1090 1083 1073 101 205957B 3.47 21 1205 1142 1141 1141 1126 1116 105 205958A 3.43 30 1092 1028 1025 1028 1016 1011 96 205958B 3.45 30 1077 1032 1032 1037 1025 1015 97 2,05959A 3.47 30 1116 1054 1051 1052 1034 1024 98 I. 205959B 3.47 30 1124 1065 1060 1060 1046 1034 99 ^u- 205960A 3.40 39 1038 982 983 989 977 969 94 205960B 3.40 39 1029 987 990 996 982 974 95 205961A 3.45 40 1068 1015 1012 1016 1000 993 96 205961B 3.45 40 1050 994 991 999 982 974 94 205962A 3.45 39 1091 1039 1032 1037 1022 1014 101 205962B 3.45 38 1087 1036 1035 1041 1028 1019 101 205963A 3.46 29 1166 1109 1103 1107 1090 1080 107 205963B 3.46 28 1167 1108 1107 1108 1093 1082 107 205964A 3.46 20 1192 1142 1132 1130 1116 1105 110 205964B 3.47 20 1193 1141 1134 1134 1116 1106 110 205965A 3.45 28 1113 1059 1053 1054 1036 1027 102 205965B 3.45 28 1112 1066 1062 1016 1004 1000 100 205966A 3.45 38 1070 1020 1015 1018 999 990 99 205966B 3.45 38 1050 1060 1043 1038 1020 1006 100 205967A 3.51 21 1148 1141 1125 1115 1101 1087 108 205967B 3.51 20 1166 1117 1112 1115 1094 1080 107 205968A 3.45 40 1012 971 969 968 953 945 94 205968B 3.46 39 1035 982 974 974 958 949 94 205969A 3.51 29 1091 1021 1012 989 978 972 97 205969B 3.51 29 1096 1075 1082 1091 1067 1057 105 205970A 3.50 40 1084 1023 1014 1013 995 984 98 205970B 3.50 40 1086 1027 1018 997 985 977 97 7 2 3 6 9 7 4;0 9 4 4 3:4 1 7 7 4 7 5 8 6 5 7 6 0 4 2 8 3 9 1 4 3 7

TABLE IV-11 (Continued) Uo Run No. Velocity ft. /sec. 205974A 3.47 205974B 3.46 205975A 3.45 205975B 3.46 205976A 3.38 205976B 3.44 205977A 3.56 205977B 3.56 205978A 3.56 205978B 3.56 205979A 3.54 205979B 3.54 205980A 3.62 205980B 3.61 un 205982B 3. 57 o 205983A 3.47 205983B 3.47 205984A 3.50 205984B 3.50 205985A 3.50 205985B 3.50 206003A 3. 54 206003B 3.54 206004A 3.54 206005A 3.56 206005B 3.56 206006A 3.59 206006B 3.55 LMTD OF 41 40 30 30 18 17 19 18 39 40 29 30 22 21 25 25 25 35 35 25 25 37 37 32 34 34 28 29 38 38 38 38 38 1 1079 1060 ro08 1096 1201 1197 1247 1278 1101 1067 1103 1096 1143 1202 1236 1281 1302 1154 1134 1133 1176 1106 1108 1124 1116 1114 1137 1125 1318 1293 1290 1291 1286 2 1049 1034 1081 1069 1186 1181 1207 1221 1062 1030 1066 1062 1134 1177 1171 1243 1281 1130 1104 1082 1113 1064 1065 1089 1068 1066 1096 1075 1247 1234 1218 1224 1234 3 1045 1034 1078 1062 1181 1180 1192 1201 1050 1021 1052 1051 1139 1173 1160 1242 1278 1126 1100 1091 1106 1058 1056 1082 1064 1059 1079 1068 1236 1226 1212 1215 1222 4 1050 1040 1083 1073 1186 1187 1188 1194 1051 1024 1054 1053 1140 1178 1165 1246 1278 1134 1109 1099 1112 1062 1059 1084 1059 1062 1087 1073 1237 1230 1218 1222 1226 5 1040 1029 1071 1064 1172 1170 1171 1179 1034 1011 1040 1042 1134 1158 1150 1235 1256 1118 1097 1090 1097 1045 1042 1069 1047 1048 1084 1061 1221 1214 1203 1205 1214 6 7 1030 1020 1060 1056 1159 1161 1158 1166 1021 1002 1028 1033 1122 1146 1140 1226 1242 1106 1087 1078 1089 1034 1032 1056 1030 1034 1064 1043 1205 1211 1190 1192 1204 1033 1023 1064 1061 1162 1166 1161 1175 1023 1006 1033 1037 1124 1148 1141 1227 1243 1104 1089 1081 1094 1035 1033 1056 1033 1036 1062 1049 1207 1206 1187 1189 1201 206031A 206031B 206032A 206032B 206033A 4.80 4. 80 4.80 4.80 4.80

TABLE IV-11 (Continued) Uo Run No. Velocity LMTD 1 2 3 4 5 6 7 ft. / sec. ~F 206033B 4.80 38 1334 1261 1250 1251 1233 1225 1217 206034A 4.82 37 1333 1272 1252 1249 1229 1212 1207 206034B 4.82 37 1330 1265 1246 1244 1223 1206 1202 206035A 4.82 38 1310 1250 1235 1234 1216 1201 1198 206035B 4.82 38 1316 1256 1238 1237 1217 1198 1194 206037A 4.04 29 1282 1215 1208 1211 1192 1175 1170 206037B 4.04 29 1277 1211 1200 1204 1189 1176 1171 206040A 4.04 38 1223 1145 1135 1141 1126 1114 1114 206040B 4.04 37 1263 1176 1166 1167 1148 1138 1135 206041A 4.06 38 1209 1142 1130 1133 1119 1110 1109 206041B 4.06 38 1216 1154 1143 1150 1133 1121 1119 206043A 4.05 38 1189 1132 1126 1129 1116 1105 1105 206043B 4.05 38 1199 1139 1133 1136 1121 1109 1108 206045A 4.04 38 1192 1140 1132 1133 1116 1104 1102 206045B 4.04 38 1204 1148 1138 1139 1123 1109 1105 206047A 4.04 38 1214 1146 1135 1140 1126 1112 1110 206047B 4.04 38 1192 1138 1151 1137 1122 1110 1106 206048A 4.03 39 1147 1074 1071 1072 1055 1042 1042 206048B 4.02 38 1155 1075 1067 1069 1055 1044 1044 206044A 5.31 40 1268 1199 1194 1198 1181 1168 1166 206044B 5.30 40 1270 1190 1185 1189 1172 1159 1155 206046A 5.30 40 1295 1220 1208 1207 1190 1175 1173 206046B 5.30 39 1283 1211 1206 1205 1187 1171 1168 206049A 5.32 40 1272 1191 1188 1189 1174 1159 1157 206049B 5.31 40 1260 1182 1177 1179 1164 1152 1151 206050A 5.35 40 1246 1175 1181 1184 1167 1153 1152 206050B 5.35 40 1235 1164 1168 1158 1154 1143 1144 206051A 5.28 40 1245 1174 1176 1175 1162 1148 1147 206051B 5.28 40 1234 1165 1170 1169 1157 1148 1146 206052A 5.30 40 1245 1184 1190 1188 1176 1162 1161 206052B 5.30 40 1250 1184 1187 1188 1177 1164 1163

TABLE IV-11 (Continued) Uo Run No. Velocity ft. /sec. 205981A 6.32 205981B 6.32 206007A 6.08 206008A 6.07 206008B 6.08 206009A 6.12 206009B 6.13 206011A 6.04 206011B 6.03 206012A 6.04 206012B 6.04 206013A 6.32 206013B 6.32 206014A 6.14 U"' 206014B 6.13 206015A 6.13 206015B 6.13 206016A 6.18 206016B 6.18 206017A 6.19 206017B 6.18 206018A 6.15 206018B 6.16 206019A 6.19 206019B 6.19 LMTD oF 30 29 30 41 41 20 20 39 39 30 30 39 39 39 39 30 30 20 20 39 39 21 21 21 21 1 1432 L443 1415 1342 1333 1572 1548 1315 1308 1375 1389 1385 1377 1310 1305 1408 1337 1575 1540 1370 1383 1560 1562 1531 1534 2 1372 1383 1345 1278 1266 1487 1467 1280 1259 1339 1343 1312 1316 1311 1267 1358 1318 1498 1466 1301 1306 1484 1443 1463 1444 3 1355 1365 1331 1276 1264 1474 1455 1280 1260 1342 1362 1316 1315 1304 1266 1367 1330 1486 1448 1285 1300 1470 1428 1456 1448 4 1369 1378 1346 1301 1274 1478 1458 1285 1274 1350 1368 1326 1318 1275 1271 1356 1340 1481 1452 1273 1297 1472 1423 1468 1444 5 1346 1357 1321 1278 1258 1450 1435 1271 1253 1332 1348 1298 1293 1252 1255 1338 1328 1466 1437 1285 1273 1450 1401 1440 1427 6 7 1330 1341 1308 1261 1245 1427 1414 1258 1240 1315 1333 1279 1278 1237 1240 1321 1317 1444 1416 1263 1259 1431 1381 1419 1411 1332 1344 1308 1258 1248 1422 1422 1258 1244 1316 1332 1279 1274 1235 1239 1307 1321 1446 1419 1251 1257 1431 1385 1418 1413

TABLE IV-12 Overall Heat Transfer Coefficients, Uo, for Condensation of Steam'on 1 to 8 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes in a Verti at 101~F cal Row Uo - Run No. Velocity ft. /sec. LMTD ~F 1 2 3 4 5 6 7 8 205889A 205882A 205879A 205879B 205878A 205878B 205862A 205864A 205865A 205870A 205870B 205871A 205873A 205873B 205873C 205874A 205874B 205874C 205875A 205875B 205876A 205876B 205880A 205880B 205888A 205888B 205888C 205904A 205904B 2.86 3.85 4.75 4.75 5.34 5.33 5.97 6.14 6.11 6.12 6.12 6.67 6.06 6.07 6.07 6.07 6.08 6.08 6.35 6.36 6.38 6.38 5.87 5.89 6.07 5.88 6.09 6.13 6.13 9 1139 8 1406 9 1356 9 1394 10 1560 10 1548 18 1366 19 1481 18 1463 16 1396 16 1425 15 1535 17 1446 17 1443 16 1450 14 1444 14 1488 14 1490 20 1506 21 1510 15 1596 15 1604 10 1582 10 1615 18 1334 18 1332 17 1301 23 1408 24 1414 1112 1368 1334 1350 1481 1473 1350 1441 1435 1377 1391 1543 1402 1403 1416 1390 1432 1462 1435 1456 1550 1570 1527 1534 1319 1312 1280 1396 1403 1117 1379 1341 1348 1468 1458 1352 1445 1441 1374 1386 1554 1415 1411 1414 1408 1439 1469 1466 1464 1568 1583 1536 1531 1349 1356 1316 1416 1422 1108 1360 1337 1336 1444 1442 1343 1441 1426 1351 1368 1539 1406 1411 1405 1411 1433 1452 1452 1469 1563 1590 1532 1523 1325 1331 1306 1416 1422 1097 1346 1322 1316 1420 1412 1321 1420 1403 1313 1327 1518 1394 1387 1390 1394 1419 1434 1434 1446 1551 1575 1517 1503 1302 1314 1286 1400 1402 1062 1331 1303 1296 1396 1390 1299 1392 1381 1292 1305 1488 1370 1363 1367 1370 1396 1410 1417 1425 1528 1552 1501 1487 1296 1304 1279 1380 1384 1079 1314 1304 1280 1390 1380 1296 1376 1371 1263 1270 1454 1355 1347 1348 1344 1381 1387 1394 1390 1441 1455 1494 1475 1300 1305 1286 1372 1375 1073 1306 1304 1288 1378 1373 1287 1362 1359 1258 1265 1435 [349 1343 1342 1344 1378 1385 138C 1384 1441 1455 1485 1466 1281 1268 1263 1357 1360

TABLE IV-13 Overall Heat Transfer Coefficients, Uo, for Condensation of Steam on 1 to 8 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes in a Verti at 212~F cal Row Uo Run No. Velocity ft. /sec. 205881A 3.95 205881B 3.95 205896A 4.01 205896B 4.02 205886A 4.76 205886B 4.75 205886C 4.75 205900A 205900B 205902A 205902B oN o 205891B 205892A 205892B 205893A 205893B 205894A 205894B 205895A 205895B 205901A 205901B 205906B 205906A 5. 57 5. 58 5.58 5. 58 6. 3 6.4 6. 3 6.4 6.4 6. 3 6. 3 6. 5 6. 5 6.4 6.4 6. 2 6. 3 LMTD ~F 15 15 21 21 10 10 10 22 22 30 30 21 40 40 21 21 40 39 21 21 30 29 8 9 1 1446 1466 1403 1418 1583 1610 1615 1576 1581 1543 1567 1654 1484 1476 1678 1677 1520 1519 1709 1706 1619 1593 1819 1803 2 3 4 5 6 1446 1443 1402 1408 1609 1604 1614 1557 1565 1517 1525 1631 1489 1481 1660 1654 1517 1518 1670 1665 1583 1580 1740 1719 1425 1450 1418 1424 1638 1633 1648 1576 1578 1526 1533 1635 1513 1507 1665 1661 1523 1523 1680 1677 1597 1584 1717 1727 1409 1444 1422 1428 1657 1631 1637 1577 1582 1522 1533 1639 1517 1512 1667 1655 1523 1526 1680 1678 1596 1587 1726 1759 1406 1433 1411 1421 1650 1638 1645 1562 1569 1506 1516 1619 1503 1502 1652 1642 1503 1503 1663 1663 1578 1572 1729 1742 1398 1422 1394 1405 1636 1623 1626 1544 1546 1486 1495 1602 1471 1475 1633 1625 1479 1481 1644 1643 1557 1554 1724 1723 1394 1406 1383 1395 1610 1596 1595 1533 1534 1474 1485 1592 1457 1460 1621 1615 1466 1470 1630 1635 1546 1543 1700 1698 1383 1394 1381 1388 1601 1591 1592 1527 1535 1464 1476 1584 1441 1441 1615 1570 1451 1455 1624 1628 1536 1532 1705 1700 7 8

APPENDIX V Computer Program with Nomenclature for Calculating Point Values of Cn, hi, hcond, Metal Resistance, UO and Q With and Without Fouling 161

FORTRAN IV G COMPILER MAIN 08-15-68 00:03.06 PAGE 0001 CCCCCCCCCCC CCCCCCCCCCC C C C THE FOLLOWING PROGRAM IS WRITTEN TO CALCULATE THE OVERALL C C HEAT TRANSFER COEFFICIENT FROM THE GIVEN CORELATIONS OF C C INDIVIDUAL TRANSFER COEFFICIENTS, AT CERTAIN VAPOR TEMPERATURE C C AND CERTAIN WATER TEMPERATURE IN THE TUBE SIDE. C C C C BY GEORGE T. S. CHEN IN MAY 1968. C C C CCCCCCCCCCC CCCCCCCCCCC 0001 DIMENSION M(10) 0002 REAL ID,KT,LAT,KCONDIDIN 0003 DOUBLE PRECISION METAL1,METALETA L32META LMETAL4 0004 READ (5,1000) IDIN,ODIN,FF,TKCI,METAL1,MMETAL2,METAL3METAL4 0005 ID = IDIN/12.0 0006 OD = ODIN/12.0 0007 RM = (OD -ID)/(2.0*TK) 0008 AIT = 3.1416*ID 0009 AOT = 3.1416*OD 0010 AFLOW = 3.1416*ID*ID/4.0 0011 AMET = 3.1416*(OD-ID)/ALOG(OD/ID) 0012 READ (5,1002) (M(I), 1=1,5) 0013 20 READ (5,1003) A, B, VEL, VAPORT, TW 0014 IF(A)99,99,17 0015 17 WRITE(6,1001)ODIN IDIN,TKMETAL1,METAL2,METAL3,METAL4,AOTAIT,. 1 AFLOW, RM,CI,FF 0016 CALL BRINE(TW,CPT,DEN,KT, VISCHEAT) 0017 W = VEL*AFLOW*DEN*3600.O 0018 RE = ID*DEN*VEL*3600.0/VISC 0019 PR = CPT*VISC/KT 0020 WRITE(6,1004)VAPORT,VEL,W,TW,RE,PR,A,B 0021 WRITE(6,1005) 0022 CALL WATER(VAPORT,CP,WATERD,WATERK,WATERV,LATI 0023 DO 10 1=1,5 0024 XN = M(I) 0025 CN = A*XN**B 0026 DT = VAPORT - TW 0027 Tl = VAPORT - DT/3.0 0028 11 DELTF = VAPORT - TI 0029 FILMT = VAPORT - DELTF/2.0 0030 CALL WATER(FILMT,CP,DCCND,KCOND,VCOND,HEAT) 0031 HCOND = 0.725*CN* (KCOND*KCOND*KCOND*DCOND*DCOND*LAT*4.17*10.0 1 **8/(XN*VCOND*OD*DELTF) )**0.25 0032 T3 = T1 - RM*AOT*HCOND*DELTF/AMET 0033 T2 = T3 - FF*HCOND*DELTF 0034 CALL BRINE(T2,CP,BRINEDIND,BREK,VISCW,HEAT 0035 HI = CI*RE**0.8*PR**0.33333*(VISC/VISCW)**0.14*KT/ID 0036 UO = 1.0/(1.0/HCOND + AOT/(AIT*HI) + AOT*RM/AMET + FF) 0037 TIC = (HCOND*VAPORT- UO*DT)/HCOND 0038 IF(ABS(T1C - T1) - 0.03)12,12,13 0039 13 T1 = T1C 0040 GO TO 11 0041 12 Q = AOT*UO*DT 0042 RO = 1.0/(UO*AOT) 0043.ET = RM/AMET 162

FORTRAN IV G COMPILER MAIN 0-56 00:3.0 PGE 00 0044 RI = l.0/(HI*AIT) 0045 RC = 1.O/(HCOND*AOT) 0046 PHCOND = RC/RO*100.0 0047 PHI = RI/RO*100.0 0048 PMET = RMET/RO*100.0 0049 PF = FF/(RO*AOTI*100.0 0050 OU = Q/LAT _ 0051 WRITE(6,1006)M(I ),CNUOHCOND PHCOND HI PHI,PMET PF,QDU 0052 10 CONTINUE 0053 GO TO 20 0054 1000 FORMAT(5F10.4,4A5) 0055 1001 FORMAT(1Hl,///' CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. 1 T// 2 TUBE OUTSIDE DIAMETER (INCHES)',F10.5/ 3 " TUBE INSIDE DIAMETER (INCHES)',F10.5/ 4 TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F)',F10.5/ 5' TUBE METAL',4A5/' OUTSIDE HEAT TRANSFER AREA (SQFT/FT),F10.5/ 1' INSIDE HEAT TRANSFER AREA (SQFT/FT)',F10.5/ 2' FLOW AREA (SQFT)',F12.7/ 3' METAL RESISTANCE (HR/SQFT-F-BTU)',F12.7/ 5 INSIDE SIEDER-TATE CONSTANT',F10.5/ 6 " FOULING FACTOR (HR-SQFT-F/BTU)',Fl0.5) 0056 1002 FORMAT(5(8XI2)) 0057 1003 FORMAT(5F10.4) ___ 0058 1004 FORMAT( 1OX,'VAPOR TEMPERATURE (DEG. F)',F10.2/ I 1OX,'LINEAR VELOCITY OF BRINE(FT/SEC)'tF10.2/ 2 10X,'MASS VELOCITY OF BRINE (LBS/HR)',F10.2/ I 1OX,'BRINE TEMPERATURE (DEG. F)',F10.2/ 3 10X'REYNOLDS NUMBER',F10.2/ 4 IOXt'PRANDTLS NUMBER'%F10.2/ 6 1OX,'CONSTANT FOR CN: A',F8.4/ 7 1OX,'POWER OF CN: B',F8.4/ ) 0059 1005 FORMAT(///' NO CN UO HCOND HCOND HI HI MET. FOULI 1NG Q Q/LAT'/' TUBES x X RES 2.% % BTU/HR LB/HR'//) 0060 1006 FORMAT(/2XI2,2XF4.2,1X,F6.1lXF6.1IXtF4.1,'%' tlXF6.1t I IXF4.1,'',1X,.F4.1 %', 2X,F4.1,'',2X,F6.1,3X,F4.2) 0061 99 CALL SYSTEM 0062 END 163

FORTRAN IV G COMPILER BRINE 08-15-68 00:03.19 PAGE 0001 0001 SUBROUTINE BRINE(TI CP, BRINED, BRINEK, BRINEV, HEAT) C PHYSICAL PROPERTIES OF 5% BRINE. C 0002 CP 0.93578C76E+00 + 0,21301210E-04*T 1 +0.400 57057E-06*T**2 - 0.23777602E-09*T**3 0C03 BRINED = 0.6472911 1E+02 +0.23612976E-02*T 1 -0.96149743E-04*T**2 +0.12916280E-06*T**3 -2 -0.90608410E-10*T**4 0004 BRINEK = 0.27882683E+00 + 0.13049617E-02*T 1 -0.81092730E-05*T**2 + 038319286E-07*T**3 2 -0.10878543E-O9*T**4 + 0. 12212887E-12*T**5 0005 X = 1.0/T 0006 BRINEV = -0.12931222E+00 + 0.15922876E+03*X 1 +0.68623125E+04*X**2 - 0.86924000E+05*X**3 1 -0.40719760E+08*X**4 + 0.15597084E+10*X**5 0007 HEAT = (0.10952000E+04) -(0.58000000E+0)*T 0008 RETURN 0009 END 164

FORTRAN IV G COMPILER WATER 08-15-68 00:03.16 PAGE 0001 0001 SUBROUTINE WATER(T. CPWATERD, WATERK, WATERV, HEAT) _ _ _ C PHYSICAL PROPERTIES OF WATER. C 0002 CP = 0.10065384E+01 - 0.15302375E-03*T_ ____ __ I +0.80402242E-06*T**2 - 0.34208369E-09*T**3 0003 WATERD = 0.63277298E+02 -0.22062302E-01*T 1 +0.17648935E-03*T**2 -0. 12005 765E-05*T**3 0___4 2____ W__A2 +0.28273348E-08*T**4 -0.2Z901681E-11*T**5____ __ 0004 WATERK = 0.26081796E+00 + 0.2' 708496E-02*T 1 -0.19852305E-04*T**2 + 0.11187643E-06*T**3 2 -0.32420733E-09*T**4 + 0.36065335E-12*T**5 00C06 WATERV = -0.4459C950E-01 + 0.1110742E+03*X 1 +0.10510937E+05*X**2 - 0.11860300E+06*X**3 2 -0.49631344E+08*X**4 + 0.18674199E+10*X**5 0007 HEAT = (0.10952000E+04) -(0.58000000E+00)*T ____ __ 0008 RETURN 0009 END 165

NOMENCLAT URE A Constant in the equation to calculate C n AFLOW Cross-sectional area of flow; ft. AIT Inside heat transfer areas; ft. AMET Mean heat transfer area; ft. AOT Outside heat transfer area; ft. B Power in the equation to calculate C n CI C. in the Sieder-Tate equation CN Condensing coefficient correction factor CPT Heat capacity of water at TW; BTU/lb. DCOND Density of condensate at FILMT; lbs. /ft. DELTF Temperature difference across the film; ~F DEN Density of water at TW; lbs. /ft. DT VAPORT - TW; OF FF Fouling factor on the inside FILMT Mean temperature of film; ~F HCOND Condensing heat transfer coef,ient; BTU/hr. -ft. 2-_ OF 2 HI Inside heat transfer coefficient; BTU/hr. -ft. -~F ID Inside diameter; ft. KCOND Thermal conductivity of condensate at FILMT; BTU/hr. -ft. -~F KT Thermal conductivity of water at TW; BTU/hr. -ft. -~F LAT Latent heat of vaporization at VAPORT; BTU/lb. N Number of tubes in a vertical row OD Outside diameter; ft. PR Prandtl number Q Heat duty; BTU/hr. RE Reynolds number RM Metal resistance; hr./ft. -~F-BTU Tl Temperature at the outside of tube; ~F T2 Temperature at the inside of tube with fouling; ~F 166

NOMENCLATURE (continued) T2C T3 TK TW UO VAPORT VCOND VEL VisC VISCW T2 calculated The temperature at the inside wall; ~F Thermal conductivity of metal; BTU/hr. -ft. -~F Water temperature; ~F Overall outside heat transfer coefficient; BTU/hr. -ft. 2_ oF Steam temperature; OF Viscosity of condensate at FILMT; lbs. /hr. -ft. Linear velocity of water; ft. /sec. Viscosity of water at TW; lbs. /hr. -ft. Viscosity of water at T2; lbs. /hr. -ft. 167

APPENDIX VI Computer Output from the Program in Appendix V Which Calculates Point Values of Uo, hcond' hi, and Q Using the Recommended Cn Equations Note: The Cn equations are in the following form: C = n A (N)B where A and B are as indicated and N is the number of tubes in a vertical row. 168

TABLE VI- 1 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F, Without Fouling CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE TUBE TUBE TUBE OUTSIDE INSIDE THERMAL METAL DIAMETER (INCHES) DIAMETER (INCHES) CONDUCTIVITY (BTU/HR-FT-F) 1.00200 0. 90080 26.0CC 0O 1" BARE CU-NI OUTSIDE HEAT TRANSFER AREA (SQFT/FT) INSIDE HEAT TRANSFER AREA (SQFT/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-BTU) INSIDE SIEDER-TATE CCNSTANT FOULING FACTOR (HR-SQFT-F/BTU) _ VAPOR TEMPERATURE (DEG. F) __ __ LINEAR VELOCITY OF BRINE(FT/SEC) MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPERATURE (DEG. F) REYNOLDS NUMBER __ ^__ PRANDTLS NUMBER __ CONSTANT FOR CN: A POWER OF CN: B 0.26232 0.23583 0.004t4257 0.0C01622 0.02642 0.0 100.00 6.00 6137.40 94.00 54305.56 5.12 1.0700 0.1700 NO CN UO HCOND HCCND HI HI MET. FOULING Q Q/LAT TUBES % __ % RES.%';_ BTU/HR LB/HR 10 1.58 729.2 2797.5 26.1% 1319.6 61.5% 12.5% 0.0% 1147.7 1.11 15 1.70 721.6 2689.1 26.8% 1319.5 60.8% 12.3% 0.0% 1135.7 1.09 20 1.78 716.1 2614.8 27.4% 1319.4 60.4% 12.2% 0.0% 1127.1 1.09 25 1.85 711.8 2558.6 27.8% 1319.4 60.0% 12.2% 0.0% 1120.3 1.08 30 1.91 708.3 2513.7 28.2% 1319.4 59.7% 12.1% 0.0% 1114.8 1.07 169

TABLE VI-2 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F, With 0. 0005 Fouling CALCULATIONS OF. THE POINT VALUES OF UO AND HCOND. TUBE TUBE TUBE TUBE OUTS IDE INSIDE THERMAL METAL DIAMETER (INCHES) DIAMETER (INCHES) CONDUCTIVITY (BTU/HR-FT-F) 1.00200 0.90080 26.00000 1" BARE CU-NI OUTSIDE HEAT TRANSFER AREA (SQFT/FT) INSIDE HEAT TRANSFER AREA (SQFT/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-STU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT-F/BTU) VAPOR TEMPERATURE (DEG. F) LINEAR VELOCITY OF BRINE(FT/SEC) MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPERATURE (DEG. F) REYNOLDS NUMBER PRANDTLS NUMBER CONSTANT FOR CN: A POWER OF CN: B 0.26232 0.23583 0.0044257 0.0001622 0. 02642 0.00050 100.00 6.00 6137.40 94.00 54005.56 5.12 1.0700 0.1700 NO CN UO HCOND HCOND HI HI MET. FOULING Q Q/LAT TUBES X RES.% % BTU/HR LB/HR 10 1.58 543.4 3074.6 17.7% 1317.7 45.9 2 9.3X 27.2% 855.2 0.82 15 1.70 539.4 2952.7 18.3% 1317.6 45.5% 9.2% 27.0% 849.0 0.82 20 1.78'536.6 2869.2 18.7% 1317.6 45.3t 9.2% 26.8% 844.5 0.81 25 1.85 534.3 2806.2 19.0% 1317.6 45.1% 9.1% 26.7% 841.0 0.81 30 1.91 532.5 2755.8 19.3% 1317.6 45.0 9.1% 26.6% 838.1 0.81 170

TABLE VI-3 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 212 F, Without Fouling CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DIAMETER (INCHES) TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) TUBE METAL OUTSIDE HEAT TRANSFER AREA (SQFT/FT) INSIDE HEAT TRANSFER AREA (SQFT/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-BTU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT-F/BTU) VAPOR TEMPERATURE (DEG. F) LINEAR VELOCITY OF BRINE(FT/SEC) MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPERATURE (DEG. F) REYNOLDS NUMBER ___ _ PRANDTLS NUMBER CONSTANT FOR CN: A POWER OF CN: B ------------- ------------- 1,00200 0. 9O0 80 26.00000 1" BARE CU-NI 0,26232 0.23583 0.0044257 0.0001622 0.02642 0.0 212.00 6.00 5936.61 206.00 129592.31 1.91 1.0700 0.1700 --- _._ —--- NO CN UO HCOND HCOND HI HI MET. FOULING Q Q/LAT TUBES % % RES.% % BTU/HR LB/HR 10 1.58 1015.1 3542.0 28.7% 2091.5 54.0% 17.4% 0.0% 1597.7 1.64 15 1.70 1003.6 3405.8 29.5% 2091.4 53.4% 17.2% 0.0% 1579.5 1.62 20 1.78 994.1 3300.0 30.1% 2091.3 52.94 17.0% 0.0% 1564.7 1.61 25 1.85 987.8 3231.5 30.6% 2091.3 52.5% 16.9% 0.0% 1554.8 1.60 33 1.91 982.6 3176.7 30.9% 2091.2 52.3% 16.8% 0.0% 1546.6 1.59 EXECUTION TERMINATED 171

TABLE VI-4 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, With 0. 0005 Fouling CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DIAMETER ( INCHES) TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) TUBE METAL OUTSIDE HEAT TRANSFER AREA (SQFT/FT) INSIDE HEAT TRANSFER AREA (SQFT/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-BTU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT-F/BTU) VAPOR TEMPERATURE (DEG. F) LINEAR VELOCITY CF BRINE(FT/SEC) MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPERATURE (DEG. F) REYNOLDS NUMBER PRANDTLS NUMBER CONSTANT FOR CN: A POWER OF CN: B w... 1.00200 0. 90080 26.00000 1" BARE CU-NI 0. 26232 0.23583 0.0044257 0.0001622 0.02642 0.00050 212.00 6.00 5936.61 206.00 129592.31 1.91 1.0700 0.1700 NO CN UO HCOND HCOND HI HI MET. FOULING Q Q/LAT TUBES % t RES.L % BTU/HR LB/HR 10 1.58 688.4 4009.8 17.2% 2089.5 36.6% 11.8% 34.4% 1083.4 1.11 15 1.70 683.5 3850.7 17.8% 2089.4 36.4% 11.7% 34.2% 1075.8 1.11 20 1.78'680.0 3741.9 18.2% 2089.4 36.2I 11.6% 34.01 1070.3 1.10 25 1.85 677.2 3659.7 18.5% 2089.4 36.1% 11.6% 33.9% 1065.9 1.10 30 1.91 674.9 3593.9 18.8% 2089.4 35.9% 11.5% 33.7% 1062.3 1.09 EXECUTION TERMINATED 172

TABLE VI-5 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F, Without Fouling CALCULATIONS OF THE POINT. VALUES OF UO AND HCOND. TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DIAMETER (INCHES) TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) TUBE METAL 1" OUTSIDE HEAT TRANSFER AREA (SQFT/FT) INSIDE HEAT TRANSFER AREA (SQFT/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-BTU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT-F/BTU) VAPOR TEMPERATURE (DEG. F) LINEAR VELOCITY OF BRINE(FT/SEC) MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPERATURE (DEG. F) REYNOLDS NUMBER PRANDTLS NUMBER CONSTANT FOR CN: A POWER OF CN: B 0.93700 0.82200 26.00000 KORO CU-NI 0.24531 0.21520 0.0036853 0.0001843 0.05786 0.0 100.00 3.50 2981.18 94.00 28747.43 5.12 1.4500 0.2030 NO CN UO HCOND HCOND HI HI MET. FOULING Q Q/LAT TUBES % % RES.% % BTU/HR LB/HR 10 2.31 975.3 4304.0 22.7% 1911.5 58.2% 19.2% 0.0% 1435.5 1.38 15 2.51 970.1 4204.3 23.1% 1911.5 57.9% 19.1% 0.0% 1427.8 1.38 20 2.66 966.3 4134.9 23.4% 1911.4 57.6% 19.C% 0.0% 1422.3 1.37 25 2.79 963.4 4082.0 23.6% 1911.4 57.5% 18.9% 0.0% 1418.0 1.37 30 2.89 961.0 4039.2 23.8% 1911.4 57.34 18.9% 0.0% 1414.4 1.36 173

TABLE VI-6 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F, With 0. 0005 Fouling CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DIAMETER ( INCHES) TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) TUBE METAL OUTSIDE HEAT TRANSFER AREA (SQFT/FT) INSIDE HEAT TRANSFER AREA (SQFT/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-BTU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT-F/BTU) VAPOR TEMPERATURE (DEG. F) LINEAR VELOCITY OF BRINE(FT/SEC) MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPERATURE (DEG. F) REYNOLDS NUMBER PRANDTLS NUMBER CONSTANT FOR CN: A POWER OF CN: 8 0.93700 0.82200 26. 00000 1" KORO CU-NI 0.24531 0.21520 0.0036853 0.0001843 0.05786 0.00050 100.00 3.50 2981.18 94.00 28747.43 5.12 1.4500 0.2030 NO CN UO HCOND HCOND HI HI MET. FOULING Q Q/LAT TUBES % % RES. % BTU/HR LB/HR 10 2.31 666.7 4858.6 13.7 1908.2 39.8% 13. 1 33.3% 981.3 0.95 15 2.51 664.5 4743.2 14.0 1908.2 39.7% 13.1 33.2% 978.1 0.94 20 2.66'662.9 4663.1 14.2% 1908.2 39.6% 13.0: 33. 1% 975.7 0.94 25 2.79 661.7 4601.9 14.4% 1908.2 39.5% 13.0 33.1% 973.9 0.94 30 2.89 660.6 4552.5 14.5% 1908.2 39.5% 13.0: 33.0% 972.4 0.94 174

TABLE VI-7 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, Without Fouling CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DIAMETER (INCHES) TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) TUBE METAL 1" OUTSIDE HEAT TRANSFER AREA (SQFT/FT) INSIDE HEAT TRANSFER AREA (SQFT/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-BTU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT-F/BTU) VAPOR TEMPERATURE (DEG. F) LINEAR VELOCITY OF BRINE(FT/SEC) MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPERATURE (DEG. F) REYNOLDS NUMBER PRANDTLS NUMBER CONSTANT FOR CN: A POWER OF CN: B 0.93700 0.82200 26.00000 KORO CU-NI 0.24531 0.21520 0,0036853 0.0001843 0.05786 0.0 212.00 3.50 2883.65 206.00 68982.62 1.91 1.4500 0.2030 NO CN UO HCOND HCOND HI HI MET. FOULING Q Q/LAT TUBES % | RES.% BTU/HR LB/HR 10 2.31 1324.6 5491.8 24.1X 3029.9 49.8% 26.0% 0.0% 1949.6 2.01 15 2.51 1317.1 5365.3 24.5Z 3029.9 49.6% 25.9% 0.0 1938.6 1.99 20 2.66 1311,7 5277.1 24.9% 3029.9 49.42 25.8% 0.0 1930.7 1.99 25 2.79 1307.6 5210.1 25.12 3029.8 49.2% 25.72 0.0% 1924.5 1.98 30 2.89 1304.1 5155.7 25.32 3029.8 49.12 25.62 0.0X 9199.4 1.97 EXECUTION TERMINATED 175

TABLE VI-8 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, With 0. 0005 Fouling CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE OUTSIDE DIAMETER (INCHES) 0.93700 TUBE INSIDE DIAMETER (INCHES) 0.82200 TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) 26.00000 TUBE METAL 1" KORO CU-NI OUTSIDE HEAT TRANSFER AREA (SQFT/FT) INSIDE HEAT TRANSFER AREA (SQFT/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-BTU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT-F/BTU) VAPOR TEMPERATURE (DEG. F) LINEAR VELOCITY OF BRINE(FT/SEC) MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPERATURE (DEG. F) REYNOLDS NUMBER PRANDTLS NUMBER _ _~, 0.24531 0.21520 0.0036853 0.0001843 0.05786 0. 00050 212.00 3.50 2883.65 206.00 68982.62 1.91 CONSTANT FOR CN: A 1.4500 POWER OF CN: B 0.2030 NO CN UO HCOND HCOND HI HI MET. FOULING Q Q/LAT TUBES % % RES.% % BTU/HR LB/HR 10 2.31 813.5 6409.1 12.7% 3026.6 30.6% 16.0% 40.7: 1197.3 1.23 15 2.51 811.0 6256.7 13.0% 3026.6 30.5% 15.9% 40.5% 1193.6 1.23 20 2.66'809.2 6151.0 13.2% 3026.6 30.5% 15.9% 40.52 1191.0 1.22 25 2.79 807.8 6070.1 13.32 3026.6 30.4% 15.9% 40.4% 1188.9 1.22 30 2.89 806.6 6004.9 13.4% 3026.6 30.4% 15.9% 40.3% 1187.2 1.22 EXECUTION TERMINATED 176

TABLE VI-9 Calculated Point Values for 5/8-inch Bare Cupro-Nickel Tubes With Steam Condensing at 100~F, Without Fouling LALLULAI LJNSb U- IHM POUINI VALUES Ut- UL ANU HLUNU. lUbtl UUI 5DE DIAMLTK ( NC HE S ) TUbE INSIDE DIAMETER (INCHES) TUBE THERMAL CONC UCTIVITY ({ TU/HR-FT —F) TUBE METAL OUTSIDE HEAT 1RANSFER AREA ( SlF/F ) INSIDE HEAT TKANSFER ARLA (SQF-T/FT) FLOW AREA (SOFT) METAL RESISTANCE (HR/S(~.-T-F-oTU)J INSIDE SIEDER-TATE CuNSTANT FOULING FACTOR (HK-SQFl-f/bTU) VAPuiR' TL'MPt RATUkE (DOe rF-) L.INcAR VELLCIITY uJF - IE(FT/:tL) MASS VELUCIT Y oF IKINt ( LtS/HK) BRINE I E'EPLKATURL ( L: F) RLY'NiL US iNUbcR PAAiDJl'LS NUMBEk CCNS TANT FUi CiuL: A POI~E&R UF CN: b 0.62 520 0. 54880 26.00000 5/b"bAKE tUJ-NI 0. 16368 0. 14368 0.00164217 0.000 1224 0. u2700 0.0 100.00 6.00 2278.01 94.00 3zLULz. 1i 5.12 1.2 UU 0. 5 5 7 0.u551 NO CN 00 H-C,4U thoUNJO hI HI METI. FOULING -;/LA] TUBES, RES.;B i3TU/HK LB/HR 10 1.36 782.2 2o14.0 29.9- i-t8.t 5.~% iL.2 0 U.0 768.2 0.74 15 1.40 760.1 236j. 31.'9 l43d,.4 5d.2~ 9.9 0o.0 746.5 0.72 20 1.42 744, 0 2232.1 33. 3 it48a.3 57.0; 9.7z 0.uOt 730.7 0.70 25 1.44 731.3 2121.9 34. 5, 1i48.2 56.0U 9.g 0.U;U 718.2 0.69 30 1.45 720.8 2036.0 35.4: 1438.1 55.2A 9.4t U.0 1707.9 O.bb 177

TABLE VI-10 Calculated Point Values for 5/8-inch Bare Cupro-Nickel Tubes With Steam Condensing at 100~F, With 0. 0005 Fouling CALCULAI 1UNS UP ItH PUiNI VALULS Ut UU AND Ht.UND. TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DIAMETER (INCHES) TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-FJ TUBE METAL OUTSIDE HEAT TRANSfER AREA (SQFT/FT) INSIDE HEAT TRANSI-ER AREA I (SFT/FT) FLOW AREA (SOFT) METAL RESISTANCE (HR/SQ'F -F-iTU) INSIE S-IEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT- F/BTU) VAPOR TEMPERATURE (DEG. FLINEAR VELOCITY OF BRINE(FT/SEC) MASS VELOCITY OuF 8RINi (LbS/HR) BRINE TEMPERATURE IOEG. F) REYNOLDS NUMBER PRANOTLS NUMBER 0.62520 0. 548 80 26. U000iO 5/8"BARE CU-NI 0.16368 0.14368 0.0016427 0.0001224 0O.UZ100 0.00050 100.00 6.00 2278.01 94.00 - L-ZU 1t 5.12 CONSTANT FOR CN: A 1.2000 POWER OF CN: 6 0.0557 NO CN UO HCUNO HLONU HI HI MET. FOULIN-G Q Q/LAT TUBES % _ RES.% % BTU/HR LB/HR 10 1.36 574.2 2901.4 19.8' 1486.5 44.0% 7.5% 28.7% 563.9 0.54 15 1.40 562.7 2631.6 21.4' 1486.4 43.1% 7.31 28.1; 552.7 0.53 20' 1.42 554.3 2456.3 22.6'? 1486.3 42.5% 7.2% 27.7% 544.3 0.52 25 1.44 547.5 2328.6 23.5% 1466.3 42.0% 7.1 27.4t 537.7 0.52 30 1.45 541.8 2229.5 24.3; 1486.2 41.5% 7.1% 27.1% 532.1 0.51 178

TABLE VI-11 Calculated Point Values for 5/8-inch Bare Cupro-Nickel Tubes With Steam Condensing at 212~F, Without Fouling CALCULATIGNS OF IHL PuONT VALULS UF UO AND LLUNU. TUBE OUTSIDE DIAMETtR (INCHES) 0.b2520 TUBE INSIDE UlAilTtTR ( I tCHLS) 0.54680 TUBE TH1CEMAL CONDUtCTIVITY ( rTJ/Hr-FT-F) 26.00000 TUBE METAL 5/18"'ARE CU-NI OUTSIDE HEAT TRANSFLK AkLRA i(SifT/iFTl) 0.16368 INSIDE HEAT TRANSFER AKtA ( SF:T/i-T) 0. 143 l68 FLOW AREA (SQOT) 0.0016427 MEIAL RESISTANCet (HR/SUOT-F-UTU) )0.0001224 INSI CE SIEDER-TATct CONSTAN r 0. 027o00 FOUL ING FACTOR ( IH-SQOT-F/i3l'U) 0.0 VAPOR TLMPEtATURk (LDE G F- -21.00 LINEAK VELOCITY CF BRINEt(F1/SEC) 6.00 MASS VELOCITY OF BKRINE (LbS/tHR) 2203.49 BRINE TEMPERATURE (DL. F) 206.00 REYNOLDS NUiM3SR 18952.31i PR Ai' DT L S:JUM dER 1.91 CONSTANT FOR CN: A 1.2000 POWER OF LI N:. t 0.0557 NO CN UO hC NUJ HL uND rTI HI MEJ. FOULING Q /L AT TUBE RES ES. BTU/HR Lb/HR 10 1.36 1092.4 3310.5 33.0;2 25'9.6 5z.7 14.34 0.U> 1072.8 1.10 15 1..40 1059. 7 J027.5 35.0/, L359.5 51.2'o 13. 8~ 0. 0 t 1040.6 1.07 20 1.42 1035.3, 2637.0 36.5o 2J59.34 50.U0) 13.5 0.0% 1016b. 1.05 25 1.44 1014.5 2686.7 37.8; Z2359.2 49.0: i3.2^ 0.0% 996.3 1.02 30 1.45 998.4 2?575.7 3b. i' 2.j59.1 48.2% lj.0' 0.0% 980.5 1.01 179

TABLE VI-12 Calculated Point Values for 5/8-inch Bare Cupro-Nickel Tubes With Steam Condensing at 212~F, With 0. 0005 Fouling CALLULATIONS 01- THE OPuiNT VALUJS Uk- UO AND HCUNOu TUBE OUTSIDI: DIArETER ( IiihES) TUBE INSIDE UIAIfETLR IINGLHES) TUbE THERMAL CUOULTIV I T Y (O TU/HK-FT- ) TUBE METAL U. bZt5dU 0. 54880 26. 00000 5/8".l-AkE CU-N1 OUTSIDE HEAl IRANSIFER AREA { SiJ-T/li } INSIDE FIEAT TRANSFtR AREA ( SQt'I-/FT) FLOW ARLA (SOFT) METAL RESISTANLE (HR/SQFIP-F-TU) INSI CE SIEtR'D-TA'It CuNSTANIT FOULING FACTOR (HR-SLFl1-F/bTU) VAPOR TEMPERATURL (DC. F) LINtAR VELOCITY LiF DRINE(FT/StC) i-ASS VELOCITY CF RINt (LbS/HAR) bRINE TEMPERATUkE (J{ 3. F) RtYNOLDS NUMBdtL F RAAiDTLS NUMBL.K CONSTANT FGR C: A POWE'R UF CN: B 0. 16366 u. 14.3 68 0. 0016427 U. 0001 Z24 u. u/ Iuu 0.00050 / 1A. VU. (OUU 2203.49 206.0CO 7d952. 31 1.91 1.2000 0.0557 NO CN UO HLC6iN0 HiCu D HI- H MET. FOUL ING Q Q /LAT TUBES O " %<ES ^ BTU/HR LB/HR 10 1..35 725.8 3767.4 1.Z 2:2357.4 35.1 I 9.5% 36.3,t 712.7 0.73 15 1.40 711.8 343 O. 2(.7' 25i57 3 34. 4 9. 35.t 699.0 0. 72 20 1.42 701.4 3205.9 21.9: 2.51 7.3 33.j9 92 35. 1 b88.8 0.771 25 1.44 6'93.0 3039.3 22. 8 2357.2 33.56 9. I 34.7% 680.6 0.70 30 1.45 686.1 2909.8 23.6% 2357. 33.2Y 9.Ot 34. 3't 673.8 0.69 180

TABLE VI-13 Calculated Point Values for 5/8-inch Corrugated Cupro-Nickel Tubes With Steam Condensing at 100 ~F, Without Fouling LAL.lULAlIIUNS U- IHL Pu-lNI VLLULS bU UU ANU H[,LUilU. TUBE OUTSIDE DIAMETiTcR INCHLS).613Z20 TUBE INSIDE ODIAITLTR (IN CGLS)., 0.53000 TUb:t THERMAL CNiDUCTIVI'TiY (IcfO/f-l-FT-F) 26.00000 TUBE MtTAL 5/8t"KGRO LU-NI OUTSIDE HEAT IRANJSFER FEA-h (S -TI/F] ) 0.16054 INSILE HEAF IRA Sh;< A'LA ( I rF/FJ j O. 13675 FLOti AkREA (SOFT)0.001 i21 METAL RESISTANCE ( hR/S- T-F — TU) 0.0001333 INSIOc SIEDER-TATi LudisTAT 0.06730 FOULING FACTOR ( R-JF 1-F/ SO) 0.0 VAPJR T MP ERATUR (Jc.. t- 10-. —-00 LINEAR VELL LIT LFY OIFB.N(Fl/StL) 3.50 MASS VeLUClIY u brkic (IS/Rt) 1239.36 (_BKINE fLEMPEKLA1UkE (u'b. i-) 94.00,-, -,5............ i. ~, -..,..,........?...... -.-,X, K t rl INUL U SiUi i-' PRtANDTLS,UnlIibc'R CONSIANT F:K CIJ: A PO':tR iOF C-f.: b 1ib J. 4) 5.1 1.11400.2000 NO CN UO HLGONJ HCU HI I MT. FUUL Ii4G Q/LATTUBES:3 " / rTO r S.o 3'U/HR L /Hk 10 1.77 1037.2 3383.0 32.ov 24z64. L 51.cj 15.6 0.0.t i1047.2 1I01 15 1.91 107i8.2 254t.1 33. 1.o 242 45.59 51.4- i5.4' 0.0 1038.6 1.00 20 2.03 1073.,1 3208.2 33.j4 2.O 51.TZ 15.4t U 0.0 1033.6 1.00 2D 2.12 1069.1 3172.6 33. 1 242 6.0 51.06 1ib.3..u- 1029.7 0.99 30 2.20 1064.2 3iL3.3 34.Jg3 425.9 50.8g15 i5.2 0 u.0' 1025.1 0.99 181

TABLE VI-14 Calculated Point Values for 5/8-inch Corrugated Cupro-Nickel Tubes With Steam Condensing at 100~F, With 0. 0005 Fouling CALCULAI 1NS Ut IHE POINI VALULS UF UO AND iHONO. - TUBE OUTSIDE DIAMETtR INCHES) TUBE INSIDE DIAMETER (INCHES) TUBE THERMAL C NJUCTIVITY (BTU/HR-FT-F) TUBE METAL OUTSIDE HEAT TRANSFER AREA (I- f/FTT) INSIDE HEAT TRANSFER AREA (' SOT/FT) FLOW AREA (SOFT) METAL RESISTANCE (HR/SUFT-F-3ITU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT-F/dTU) VAPOR TEMPERATURE (DEo. F) LINEAR VELOCI'TY OF dRINE(FT/SEC) MASS VELOCITY OF BRINc (LOS/HR) BRIN E TEMPERATURE (uc, G F) REYNOLDS NUMBER PRANDTLS NUAMBER CONSTANT FOR CN: A POWER OF tN': b 0.61320 0. 53000 26.00000 5/8'K11RO CU-NI 0. 16054 0. 13875 0.0015321 0. 0001333 0.06730 0.00050 1UU. UU 3.50 12..b36 94.00 18535.45 5. 12 1.1 140 0.2J00 - - - - - - NO CN U0 HCCNDU tlCO.-iJ hil. HI MLT. FOULING Q Q/LAT TUBES' Y RES._;4 BTU/HR LB/HR 10 1.77 722.9 3812.4 L9.*Ju 222*2. 34.5; 10.4/ 36. 696.3 0.67 15 1.91 719.4 3717.5 19.4;o 242Z2 34*.4: 10.3 3 6I.0g 693.0 0.67 20 2.03 716.9 3651.7 19.o, 4422.1 34.2Zg 10.3 35.3Z 690.6 0.67 25. 2.12 715.0 3501.5 1i9.9' 2iZ2.1 34.2 10.2 3 35.7% 688.7 0.66 30 2.20 713.4 35-,1.0 20.0% 2422.1 34.1% i0.2^ 35. 7? 687.1 0.66 182

TABLE VI-15 Calculated Point Values for 5/8-inch Corrugated Cupro-Nickel Tubes With Steam Condensing at 212~F, Without Fouling CALCULA.I INS OF THE PUiNT VALUES Ut UO AND HCUNUO TUBE OUTSIDE DIAlETLR ( iinCHLES) 0.61320 TUBE INSIDE DIAMETER [INCHES) 0.53000 TUdE THERMAL CUNDUCTIVITY (31U/HJR-FT-F) 26.00000 TUBE METAL 5/8_"KUOR CU-NI OUTSIDE HEAT TRANSFER ARtA (SITw]/F ) 0.16054 INSIDE HEAT TRANSFtR AREA ()JFT/FT) 0.13875 FLUW AREA (SUFT) 0.0015321 METAL RESISTANCE (HR/SiIF-F-BTU) 0.0001333 INSIDE S1EDER-TATE CONSTANT 0. 0o730 FOULING FACTOR (HR-SQFt-F/8TU) 0.0 VAPOR TEMPERATURE (JtOG F) 212.00 LINEAR VELOCITY OF oRli FT/:1/SEC) 3.50 MASS VELOCITY OF BRINM (LbS/HR) 1198.81 BRIN E TEMPERATURE (O J,. F) 206.00 REYNOLDS NUMBER 44477.86 PRANOTLS NUM ER 1.91 CONSTANT FC' CN: A 1.1140 POWER OF CN: b 0.2000 NO CN Uj HCONU HCuN HI HI ET. FOULINiG Q QU/LAT TUBES KE R S. bTU/HR LB/HR 10 1.77 1474.7 427J.O 34. 5:. 840.7 44.4?, 21.1 0. 10 420.5 1,46 15 1.91 1462.7 4173.3 35.0).t jU46.6 44.0 Z21.0 0.0I) 1408.9 1.45 20 2.03 1454.0 4104.0 35.44 33846.6 43.7% 20.8:. 0.0; 1400.6 1.44 25 2.12 1447.3 4051.1 35. 71 dt4.5 43.3 C 20.7% 0. 0U 1394.1 1.43 30 2.20 1441.9 4008.4 36.U, 3J8436.5 43.4Y 20.7 0.0; 1388.8 1.43 183

TABLE VI-16 Calculated Point Values for 5/8-inch Corrugated Cupro-Nickel Tubes With Steam Condensing at 212~F, With 0. 0005 Fouling CALLLLATIONS UI THI PUINI VALUtS U0 U ANDU HLUNU. TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DIAMETER (INCHES) TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) TUBE MET AL OUTSIDE HEAT TRANSFER AREA I(SFT/FT) INSIDE HEAT TRANSFER AREA (SWFT/FT) FLOW AREA (SOFT) METAL RESISTANCE (HR/SQFT-F-bTU) INSIDE SIEDER-TATE CONSTANT FOUL'ING FACTOR (HR-SQf —F/8TU) VAPOR TEMPERATURE (bDEG. i-) LINEAR VELUCITY OF BRINE(FT/SEC) MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPERATURE (DEG. F) 0. 61320 0. 53000 26.00000 5/8"KURO CU-NI 0.16054 0.13875 U. UU1)JLi 0.0001333 0. 06130 0. 00050 21.00U 3.50 1198.81 2 06. O00 KLYiNULU) IUMbIOtK PRANDTLS NUMBER CONSTANT FOR LN: A POWER OF CN: b' +'VtI 1 00 1.91 1.1140 — 0.Zou000 NO CN UO HCONJ HCONU HI Hi M ET. FOULING Q/LAT TUBES RES.t 6 bTU/HR LB/HR 10 1.77 875.2 5044.7 17.3t J3842.7 26.4% 12.54 43.84 843.0 0.87 15 1.91 871.3 4918. 717.7 38U42.7 26. 2o 12.5't 43.6t 839.3 0.86 20 2.03 868.5 4831.3 lb.0i 3842.7 26.21 12.4t 43.4% 836.6 0.86 25 2.12 866.4 4764.7 18.27 3842.7 26.1% 12.4t 43.3Z 834.5 0.86 30 2.20 864.6 4710.9 18.4% 3d42.6 26.0% 12.4 4 43.2% 832.8 0.86 184

APPENDIX VII Computer Output from the Program in Appendix V Which Calculates Point Values of Uo, hcond, hi, and Q Using the Cn Equations for Steam Condensing at 100~F and 212~F and the Recommended Cn Equations Note: The Cn equations are in the following form: C = A (N)B n where A and B are as indicated and N is the number of tubes in a vertical row. 185

TABLE VII-1 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F Without Fouling at Tubeside Velocity of 6. 0 ft. /sec. CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE OUTSIDE DIAMETER (INCHES) 1.0000 _TJBE IJNSI.QE__-I A1MEIER.(INCHESR)- - - - -.....9.ii 0__. R TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) 26.00000 _TIUBE-MFTLAL__.... BAREF C1L-Ni OUTSIDE HEAT TRANSFER AREA (SOFT/FT) 0.26232 INSIDE HEAT TRANSFER AREA (SOTFT /FT) O23R3 FLOW AREA (SQFT) 0.0044257 MFTALRES ISTAN CE _.HR/ SQF T-F —RU)_. _. ___ Q. 0001 622_ INSIDE SIEDER-TATE CONSTANT 0.02642 FOULITNG FACTOR _R-SQFT-FjBTUL _ ____.____.0._ Q0__n VAPOR TEMPERATURE (DEG. F) 100.00 LINFAR VFilCITY nF RRTNF(FT/SEPC) 6.00 MASS VELOCITY OF BRINE (LBS/HR) 6137.40 ___ BR INE T EMPERATiEJR ( DEG F__F -....... 94 00 REYNOLDS NUMBER 54005.56 ______-PRANDOTLS NUMBER. __ ___ 5 -____ CONSTANT FOR CN: A 1.1500 POWFR nF CN: R _0.1560 NO CN UO HCOND HCONnf HI HI MFT. FOULING Q Q/L AT TURFS % z RE -S.Z _ BTU/HR I.B /HR __I__ 1.65 _73.4 937.2 25....1319-6. 62.2.. 12..6 - 0 -0 167- _.1-%-!2 15 1.75 72q.6 2803.5 26.0. 1319.6 61.-5 12.-5 O^0? 114.-3 1.11 _Q20. l^ 84_ 72 3.3. 6 26 —7X..13L9 _. ^6-1 X1.A -. 0.0 1 13. * 4 I.I n_-25__-.90 718.3?644L027.21 1319.5 60.d6 2 3 _ _L_- 0.5__ 1.09 30 1-95 714.2 25R9^6 27.^6 1319.4 60.2? 12.72 0,nt 1124.-1 L-.08 186

TABLE VII-2 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F With 0. 0005 Fouling at Tubeside Velocity of 6. 0 ft. /sec. CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE OUTSIDE DIAMETER (INCHES) 1.00200 TUBE INSDE _DIAMETER (INCHE_) __ 0.9 00RO TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) 26.00000 TUBEMETAL _ _ _ _..____1- " BARF CtJ-NI OUTSIDE HEAT TRANSFER AREA (SOFT/FT) 0.26232 INSIDF HFAT TRANSFFR ARFA!SQFT/FTI) 0.235n 3 FLOW AREA (SQFT) 0.0044257 METAL RESSTNE t E HR/SQf T-F_-TB T __ 0000 I 162? INSIDE SIEDER-TATE CONSTANT O.02642 FOIULING FACTOR (HR-SQFT-IF/BTU) __ 0.00050 VAPOR TEMPERATURE (DEG. F) 100.00 LINEAR VELOCITY OF BRINE(FTISFC) 6.00 MASS VELOCITY OF BRINE (LBS/HR) 6137.40 - BRINE _EMPRAThRE M D. F ___ _ _DEG..4. 00__ REYNOLDS NUMBER 54005.56 _P__ 2RANDTILS NUMBER. ___..12....___ 5 1? CONSTANT FOR CN: A 1.1500 POWFR OF CN: R F0. 1560 NO CN UO HCOND HCOND HI HI MET. FOULING 0 Q/LAT TURFS. I RFS, - T. BTUT/HR LB/HR 10__!65__5 4.1_ 32316 L7.0_ 1317..7 463Z 9.9._4 2_741 862.6 0.8315 1.75 543.6 3081.3 17.6t 1317.7 4.9Zq 9-31 27-27 855.- 0=82 _20 __8__5. 9792 37.0 850.4 0. 82 _125 1!90 Q_5 37 7_202 85t 1_3.17_6+i 4. 6 _ 9 86 - 82 30 1.95 535-6 2841.0 18.9Z 1!17.6 45i,?2 9.?T 2?6AR R4-3. 0.81 187

TABLE VII-3 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F Without Fouling at Tubeside Velocity of 6. 0 ft. /sec. CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DIAMETFR (INCHFS) TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) TIlIRFC MFTAI 1.00200 0. 90080 26. 00000 I" RARPF rC —MN OUTSIDE HEAT TRANSFER AREA (SQFT/FT) INSIDE HEAT TRANSFiR AREA (SQFT/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-BRTtU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT-F/RTUI) VAPOR TEMPERATURE (DEG. F) LINEAR VFincfTY OF RRINFiFT/zFC) MASS VELOCITY OF BRINE (LBS/HR) BRINF TEMPERATURE (DEG. F) REYNOLDS NUMBER PRANDTLS NUMBER CONSTANT FOR CN: A PnWFR nF C.N R 0.26232 0. 235R3 0.0044257 0.0001622 0.02642 0.0 100.00 6.on 6137.40 94.00 54005.56 5.12 1.0700 n 1 7nn NO CN UO HCOND HCOND HI HI MET. FOULING Q Q/LAT TUIRFS 2 RES.X BTITU/R L8I/HR 10 1.58 729.2 2797.5 276.1 13196 6152 12-5 0nQT 1147=7 1.11 15 1.70 721.6 2689.1 26.8T 1319.5 60-8A 12-31 00.!!31 7 1._09 20 1.78 716.1 2614.8 27.4T 1319.4 60.4_ 1_2.22 0.0 1127.1 1.0O 25 1.85 711,8 2558.6 27.8! 1319.4 60.o 1?2.2t 0.0 1120.3 1.08 30 191 70A.2t 2513.7 29.?! 1t19.4 59.^7 2.1! n 0.0Z 11T4.8R 1.07 188

TABLE VII-4 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F With 0. 0005 Fouling at Tubeside Velocity of 6. 0 ft. /sec. CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE OUTSIDE TUBE INSIDE TUBE THERMAL TTURF MFTAI DIAMETER (INCHES) DIAMETER (INCHES) CONDUCTIVITY (BTU/HR-FT-F) 1.00200 0.90080 26.00000 It RARE:11 —Ml OUTSIDE HEAT TRANSFER AREA (SQFT/FT) tNSIDF HFAT TRANSFFR AREA (SQFT!FT) FLOW AREA (SQFT) METAL RESISIANCE!HR/RQFT-F l__-__ INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT-F/BTUl) _ VAPOR TEMPERATURE (DEG. F) -I INFAR VEL1CITY nF RRINF(FTI/<EC) MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPERATIURE (DEG. F) _ REYNOLDS NUMBER PRANOTIS NUMBER _ CONSTANT FOR CN: A Pnuwo nf rm RA 0.26232 0.0044257 0.n0001622 0.02642 0.000o50 100.00 6.00 6137.40 94.00 54005.56 5.12 1.0700 (-L 1700 NO CN UO HCOND HCOND HI HI MET. FOULING 0 Q/LAT TUIRES 2 2_ RES-. % BTUIHR LB/HR 10 1.58 543.43 3074.6!17.7 1317.7-459 9.31 27-.2 855.2 0.82 - 5 1.70 39.4 2952-.7 18.3 1317_-6 45=5T 90.2 27.0 849.0 0-82 20 1.78 536.6 2869.2? 18.7 1317,6 45.3% 9q.2 2?6.8R 8445 0.81l -_25 1.85 534.3 2806.2 19.0% 1317.6 45.1% 9.1! 26.7% 841.0 0.81 30 1.91 532.5 2755.R lq^3t 1317.6 45.03 91! 26^,6 83R81 0.81 189

TABLE VII-5 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~ F Without Fouling at Tubeside Velocity of 6. 0 ft. /sec. CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE OUTSIDE DIAMETER (INCHES) 1.00200 TUBE INSIDE DIAMETER (INCHES) 0.90080 TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) 26.00000 TURF MFTAI 1" BARE CU-NI OUTSIDE HEAT TRANSFER AREA (SQFT/FT) 0.26232 INS IF HEAT TRANSFER AREA (SQFTEIT) 0Q.23583 FLOW AREA (SOFT) 0.0044257 METAL RESISTANCE (HR/SQF'T-F-BTU) _ — ____00622INSIDE SIEDER-TATE CONSTANT 0.02642 FOU LING FACTOR (HR-RSQFT-F/BTJ1) 0o.0 VAPOR TEMPERATURE (DEG. F) 212.00 LINEAR VFI1nrITY nl RRTNEFFT/SIFC) 6^n. MASS VELOCITY OF BRINE (LBS/HR) 5936.61 BRINE TEMPERATURE (DEG. F) 206.00 REYNOLDS NUMBER 129592.31 PRANOTLS NUIMRFR -1.9_ CONSTANT FOR CN: A 1.0500 PnWFR nF rN R n l7/n NO CN UO HCOND HCOND HI HI MET. FOULING Q Q/LAT TUBRFS I F RES-. R BTIIIHR LB/HR I0 1_.57 10117 -3500.9 28.9 2091.5 53.8t 17.3% 0.0% 1592.3 1-64 15 16R 1000-.7 337279 9Q.7t 20Q 1.4 53.2 17..12 0-0 1575-.0 -.6 20 1.77 991.7 3273.4 30.33 20913 52.7% 17.0% 00o 1T560_9 1.61?5'184 985.7 3208.9 30.7% 20913 52 4% 6q 0.0% 1551.4 1.60 30 1.90 980.R 3157.1 31-11 2091.7? 5;.?2 16.Rt 0n,0 1543.7 _. Q 190

TABLE VII-6 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F With 0. 0005 Fouling at Tubeside Velocity of 6. 0 ft. /sec. CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DIAMETER (INCHES) TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) TUBE METAL OUTSIDE HEAT TRANSFER AREA (SOFT/FT) INSIDE HEAT TRANSFER AREA (SQFT/IFT FLOW AREA (SQFT) METAL RESISTANCE HR/SQFT-F-BRTlj__J INSIDE SIEDER-TATE CONSTANT FOUL ING FACTOR (HR-SQFT-F/!BTU) VAPOR TEMPERATURE (DEG. F) ITINEAR VEn/CITY OF RRINF(FTISFC} MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPERATURE ( DEG. F) REYNOLDS NUMBER PRANDTLS; NUMBER _ CONSTANT FOR CN: A DPnWRD nF rM. QR 1. 002 00 0 9q0080 - 26.00000 1" BARE CU-NI 0. 26232._73583 0.0044257 0.n001622 0.02642 n. 00050 212.00.C00 5936.61 206-00 129592.31 1.91 1.0500 n- 174n NO CN UO HCOND HCOND HI HI MET. FOULING Q Q/LAT TIJRFBS I RES.% _^ BT'I/HR LB/HR _10 1.5_7 686.9 3961.7 17.3% 2 536.% 1.7 34.3 1081. 111 15 1.68 682.3 81?2.4 17.qt 2?0894 36.3% 11.7% 34-12 1073.9 1-10 20 1.77 678.9,1709,9 18.3? 2089.4 36.1X 1.6t 33.q9 1068-6! 1-10 _25 1.84 676.3 3632.5 18f.6 20q89.4 36.0h 11.6, 331.8! 064.5 1.09 30 1.90 674.1 3570.5 18.9 20?89-4 35^9T 11.5T 3t^7! O61.0 1-nq 191

TABLE VII-7 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F Without Fouling at Tubeside Velocity of 6. 0 ft. /sec. CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DIAMETER (INCHES___ TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) TUBE METAL __ ___ OUTSIDE HEAT TRANSFER AREA (SQF'T/FT) INSIDE HEAT TRANSFFR ARFA (OSQET/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-rBTI!.. INSIDE SIEDER-TATE CONSTANT FOUL IN FACTOR ( HRSOFT-FBTUi - VAPOR TEMPERATURE (DEG. F) I TNFAD VFU nrlTV nh: RRDTNIFMfT/C.Cri 1.00200 26.00000!!BARiE CU-MNL 0.26232 n-?.8tR 0.0044257 n.nn00o A2 0.02642 nt n0 212.00 A 1 C* O MASS VELOCITY OF BRINE (LBS/HR) — ______ BRINE TEMPERATURE A DE GD. -F) REYNOLDS NUMBER __ ___ PRANDUTILIBERLS N _-UM CONSTANT FOR CN: A PnWFR nF fN R 5936.61?nfl nn 1 29592. 31._1.91 1.0700 n- 17nn NO CN UO HCOND HCOND HI HI MET. FOULING Q O/LAT TURFS v __.__ RPF$S t RTIJ/HR L/HR!1 LJ.s58__I_05. _l3542.X) 28.71 2091.5 54.TQ1t7.4ti a0.0. 1597.7 1.6415 1^70 n1003.^A 3408 2R.5 2ZO91.4 53.4Z 17.2 0.0 1579 -5 162 20 1.78 9941, 330X..O30.1 2091_3 52_9 17_0 00! 1 64.7 1.61 _25_ 1.85 9878 323L.5 _306. 091. 525, 169 _0.0 54. 154 1.60 30 1.91 982.6 3176.7 30.9! 2091.3 52?-3 16. R! 00T 1546,^ 1^ EXECUTION TERMINATED 192

TABLE VII-8 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F With 0. 0005 Fouling at Tubeside Velocity of 6. 0 ft. /sec. CALCULATIONS OF THE POINT VALUES OF lUO AND HCOND. TUBE OUTSIDE DIAMETER (INCHES) 1.00200 _ TUBE E__SIDE DIAMETER ( INCHES80} - 0.9.0_ _ TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) 26.00000 _TUBE_ METAL 1'__AE AR__ I-__ OUTSIDE HEAT TRANSFER AREA (SQFT/FT) 0.26232 INSIDE HFAT TRANSFER AREA (SOFT/FT) 10.23583 FLOW AREA (SQFT) 0.0044257 METAL RES.ISTANCE ( HR/SQFT-F-BTU) Q 0.00622 _ _. INSIDE SIEDER-TATE CONSTANT 0.02642 ___FOULING FACTOR (HR-SQFT-F/BTU)1 _.-0 O _ __ _ _ _ VAPOR TEMPERATURE (DEG. F) 212.00 LINEAR VFInCITY nF RRINFIFT/;_EC)} 60.0 MASS VELOCITY OF BRINE (LBS/HR) 5936.61 BRINE TEMPERATURE (DEG. F). 2060 REYNOLDS NUMBER 129592.31 PRANDTLS NUMBER -.1.91 _ CONSTANT FOR CN: A 1.0700 POWER OF CN: R ___ 1700___ NO CN UO HCOND HCONO HI HI MET. FOULI NG Q /LAT TURFS __ _____R____S.% _ _ T RTI. L8/HR 10 1.58 688.4 4009.8 17.2T 2089.5 36.6% 11.8% 34.4! 1083.4 1.11 15 1.70 683.5 3850.7 17.8% 20894 ^6.4+t 1172 344.2 1]07^; 1.1I 20 1.78 680.0 3741.9 18.2% 2089.4 36.2% L1.6% 34.. O 3 10703 _..1J, 25 1.85 677.2 3659.7 18.5% 2089.4 36.1! 11.6T 33.9. 1065.9...lO_ 30 1.91 674.9 3593.9 18^R8?2089.4 35,9Q 1 1.5! 37 3.!'2.3 1 _9__ EXECUTION TFRMINATED 193

TABLE VII-9 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F Without Fouling at Tubeside Velocity of 3. 5 ft. /sec. CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE TUBE TUBE TUBE OUTS IDE INS IDE THERMAL METAL DIAMETER (INCHES) DIAMETER (INCHES) CONDUCTIVITY (BTU/HR-FT-F) 0.93700 0. 82200 26.00000 1" KORO CU-NI OUTSIDE HEAT TRANSFER AREA (SQFT/FT) INSIDE HEAT TRANSFER AREA (SQFT/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-BTU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT-F/BTU) VAPOR TEMPERATURE (DEG. F) LINEAR VELOCITY OF BRINE(FT/SEC) MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPERATURE (DEG. F) 0.24531 0.21520 0.0036853 0.0001843 0.05786 0.0 100.00 3.50 2981.18 94.00 REYNOLDS NUMBER 28747.43 PRANDTLS NUMBER 5.12 CONSTANT FOR CN: A 1.3000 POWER OF CN: B 0.2260 NO CN UO HCOND HCOND HI HI MET. FOULING Q Q/LAT TUBES x % RES.% % BTU/HR LB/HR 10 2.19 959.7 4016.4 23.9% 1911.4 57.2% 18.9% 0.0% 1412.5 1.36 15 2.40 957.0 3968.8 24.1% 1911.3 57.12 18.8% 0.0% 1408.5 1.36 20 2.56 955.0 3935.3 24.3% 1911.3 57.0% 18.8% 0.0% 1405.6 1.36 25 2.69 953.5 3909.5 24.4% 1911.3 56.9% 18.7% 0.0% 1403.3 1.35 30 2.80 952.2 3888.6 24.5% 1911.3 56.8% 18.7% 0.0% 1401.5 1.35 194

TABLE VII-10 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F With 0. 0005 Fouling at Tubeside Velocity of 3. 5 ft. /sec. CALCULATIONS OF THE POINT VALUES OF UO AND HCONO. TUBE TUBE TUBE TUBE OUT S I DE INSIDE THERMAL METAL DIAMETER ( INCHES) DIAMETER (INCHES) CONDUCTIVITY (BTU/HR-FT-F) 0.93700 0.82200 26. 00000 1" KORO CU-NI OUTSIDE HEAT TRANSFER AREA (SQFT/FT) INSIDE HEAT TRANSFER AREA (SQFT/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-BTU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT-F/BTU) VAPOR TEMPERATURE (DEG. F) ___ LLINEAR VELOCITY OF BRINE(FT/SEC) MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPERATURE (DEG. F) REYNOLDS NUMBER PRANDTLS NUMBER CONSTANT FOR CN: A POWER OF CN: B 0.24531 0.21520 0.0036853 0.0001843 0.05786 0.00050 100.00 3.50 2981.18 94.00 28747.43 5.12 1.3000 0.2260 NO CN UO HCOND HCOND HI HI MET. FOULING a Q/LAT TUBES % % __RES.;Z BTU/HR LB/HR 10 2.19 660.1 4526.2 14.6% 1908.2 39.4% 13.0% 33.0% 971.5 0.94 15 2.40 658.9 4471.1 14.7% 1908.2 39.4% 13.0% 32.9% 969.8 0.94 20 2.56b 658.41 4432.4 14.8% 1908.1 39.3% 12.9% 32.9% 968.6 0.93 25 2.69 657.4 4402.7 14.9% 1908.1 39.3% 12.9% 32.9% 967.6 0.93 30 2.80 656.9 4378.5 15.0% 1908.1 39.2% 12.9% 32.8% 966.8 0.93 195

TABLE VII-11 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 100 ~F Without Fouling at Tubeside Velocity of 3. 5 ft. /sec. CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE OUTSIDE DIAMETER ( INCHES) TUBE INSIDE DIAMETER (INCHES) TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) TUBE METAL OUTSIDE HEAT TRANSFER AREA (SQFT/FT) INSIDE HEAT TRANSFER AREA (SQFT/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-BTU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT-F/BTU) VAPOR TEMPERATURE (DEG. F) LINEAR VELOCITY OF BRINE(FT/SEC) MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPERATURE (DEG. F) REYNOLDS NUMBER PRANDTLS NUMBER CONSTANT FOR CN: A POWER OF CN: B 0.93700 0. 82200 26.00000 1" KORO CU-NI 0.24531 0.21520 0.0036853 0.0001843 0.05786 0.0 10c.00 3.50 2981.18 94.00 28747.43 5.12 1.4500 0.2030 NO CN UO HCOND HCONDO HI HI MET. FOULING Q Q/LAT TUBES % % RES.% BTU/HR LB/HR 10 2.31 975.3 4304.0 22.7% 1911.5 58.2% 19.2% 0.0% 1435.5 1.38 15 2.51 970.1 4204.3 23.1% 1911.5 57.S% 19.1% 0.0% 1427.8 1.38 20 2.66 966.3 4134.9 23.4% 1911.4 57.6% 19.0% 0.0% 1422.3 1.37 25 2.79 963.4 4082.0 23.6% 1911.4 57.5% 18.9t 0.0% 1418.0 1.37 30 2.89 961.0 4039.2 23.8% 1911.4 57.3% 18.9% 0.0% 1414.4 1.36 196

TABLE VII-12 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F With 0. 0005 Fouling at Tubeside Velocity of 3. 5 ft. /sec. CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE TUBE TUBE TUBE OUTSIDE INSIDE THERMAL METAL DIAMETER (INCHES) DIAMETER (INCHES) CONDUCTIVITY (BTU/HR-FT-F) 0. 93700 0. 82200 26.00000 1" KORO CU-NI OUTSIDE HEAT TRANSFER AREA (SQFT/FT) INSIDE HEAT TRANSFER AREA (SQFT/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-BTU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT-F/BTU) _ VAPOR TEMPERATURE (DEG. F) LINEAR VELOCITY OF BRINE(FT/SEC) MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPERATURE (DEG. F) REYNOLDS NUMBER PRANDTLS NUMBER CONSTANT FOR CN: A POWER OF CN: B 0.24531 0.21520 0.0036853 0.0001843 0.05786 0.00050 3.50 2981.18 94.00 28747.43 5.12 1.4500 0.2030 NO CN UO HCOND HCOND HI HI MET. FOULING Q Q/LAT TUBES % % RES.% % BTU/HR LB/HR 10 2.31 666.7 4858.6 13.7% 1908.2 39.8% 13.1t 33.3% 981.3 0.95 15 2.51 664.5 4743.2 14.0% 1908.2 39.7% 13.1% 33.2% 978.1 0.94 20 2.66 662.9 4663.1 14.2% 1908.2 39.6% 13.0% 33.1% 975.7 0.94 25 2.79 661.7 4601.9 14.4% 1908.2 39.5% 13.04 33.1% 973.9 0.94 30 2.89 660.6 4552.5 14.5% 1908.2 39.5% 13.0; 33.0% 972.4 0.94 197

TABLE VII-13 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F Without Fouling at Tubeside Velocity of 3. 5 ft. /sec. CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE TUBE TUBE TUBE OUTSIDE INSIDE THERMAL METAL DIAMETER (INCHES) DIAMETER (INCHES) CONDUCTIVITY (BTU/HR-FT-F) 0.93700 0.82200 26.C00000 1" KORO CU-NI OUTSIDE HEAT TRANSFER AREA (SQFT/FT) INSIDE HEAT TRANSFER AREA (SUFT/FT) FLOW AREA (SOFT) METAL RESISTANCE (HR/SQFT-F-BTU) INSIDE SIEDER-TATE CGNSTANT FOULING FACTOR (HR-SQFT-F/TU) _ VAPOR TEMPERATURE (DEG. F) _ LINEAR VE L OCITY OF BRINE(FT/SEC) MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPERATURE (DEG. F) REYNOLDS NUMBER _ PRANDTLS NUMBER__ ___ CONSTANT FOR CN: A POWER OF CN: B 0.24531 0.21520 0.0036853 0.0001843 0.05786 0.0 212.00 3.50 2883.65 206.00 68982.62 1.91 1.30CO 0.1910 NO CN UO HCOND HCOND HI HI MET. FOULING Q Q/LAT TUBES ______ _ % RES. BTU/HR LB/HR 10 2-.2 1269.0 4647.5 27.3% 3n29.6 47.7% 25.0% 0.0% 1867.7 1.92 15 2. 18 1258.8 4514.5 27.9% 3029.6 47.4% 24.8_ 0.0% 1852.8 1.91 20 2.30 1251.6 4422.5 28.3% 3029.5 47.1% 24.6% 0.0% 1842.1 1.89 25 2.40 1245.9 4352.5 28.6% 3029.5 46.9% 24.5% 0.0% 1833.7 1.89 39 2.49 1241.2 4296.2 28.91 3029.5 46.7% 24.4% 0.0% 1826.9 1.88 198

TABLE VII-14 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F With 0. 0005 Fouling at Tubeside Velocity of 3. 5 ft. /sec. CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE TUBE T.UBE TUBE OUTS I DE INS I DE THER MAL METAL DIAMETER (INCHES) DIAMETER (INCHES) CONDUCTIVITY (BTU/HR-FT-F) 0.93700 0.82200 26.00000 1" KURO CU-NI OUTSIDE HEAT TRANSFER AREA (SQFT/FT) INSIDE HEAT TRANSFER AREA (SQFT/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-BTU) INSIDE SIEOER-TATE CONSTANT FOULING FACTOR (HR-SQFT-F/BT U VAPOR TEMPERATURE (DEG. F) LINEAR VELOCITY OF BRINE( FT/SEC) MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPERATURE (DEG. F) REYNOLDS NUMBER PRANOTLS NUMBER CONSTANT FOR CN: A POWER OF CN: B 0.24531 0.21520 0.0036853 0.0001843 0.05786 0.00050 212.00 3.50 2883,65 206.00 68982.62 1.91 1.3000 0.1910 NO CN UO HCOND HCOND HI HI MET. FOULING Q Q/LAT TUBES % % RES.% 4 BTU/HR LB/HR 10 2.02 794.5 5393.7 14.7t 3026.6 29.9% 15.69 39.7% 1169.4 1.20 15 2.18 790.9 5234.2 15.1% 3026.5 29.8% 15.6Z 39.5% 1164.1 1.20 20 2.30 788.4 5124.2 15.4% 3026.5 29.7% 15.5% 39.4% 1160.4 1.19 25 2.40 786.4 5040.3 15.6% 3026.5 29.6% 15.5% 39.3% 1157.4 1.19 30 2.49 784.7 4972.7 15.8% 3026.5 29.6% 15.4% 39.2% 1155.0 1.19 199

TABLE VII-15 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F Without Fouling at Tubeside Velocity of 3. 5 ft. /sec. CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE OUTSIDE TUBE INSIDE TUBE THERMAL TUBE METAL DIAMETER (INCHES) DIAMtTER (INCHES) CONDUCTIVITY (BTU/HR-FT-F) 0. 93700 0.82200 26.00000 1" KORO CU-NI OUTSIDE HEAT TRANSFER AREA (SQFT/FT) INSIDE HEAT TRANSFER AREA (SQFT/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-BTU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT-F/BTU) VAPOR TEMPERATURE (D EG. F) - LINEAR VELOCITY OF BRINE(FT/SEC) MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPERATURE (DEG. F) REYNOLDS NUMBER PRANDTLS NUMBER CONSTANT FUR CN: A POWER OF CN: b 0.24531 0.21520 0.0036853 0.0001843 0.05786 0.0 212.00 3.50 2883.65 206.00 68982.62 1.91 1.4500 0.2030 NO CN UO HCOND HCOND HI HI MET. FOULING Q Q/LAT TUBES %_ % RES.%: BTU/HR LB/HR 10 2.31 1324.6 5491.8 24.1L 3329.9 49.8% 26.0% 0.0O 1949.6 2.01.15 2.51 1317.1 5365.3 24.5% 3C29.9 49.6_ 25.9% n.0% 1938.6 1.99 20 2.66 1311.7 5277.1 24.91 3029.9 49.4I 25.8 0(.0% 1930.7 1.99 25 2.79 1307.6 5210.1 25.1% 3029.8 49.2% _ _ _ ~~~~~~~.__...._... _........................ 25. 7% 0.0 1924.5 1.98 30 2.89 1304.1 5155.7 25.3% 3029.8 49.1; 25.6 EX ECUTION TERMI NAT-ED 0.0% 1919.4 1.97 200

TABLE VII-16 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F With 0. 0005 Fouling at Tubeside Velocity of 3. 5 ft. /sec. CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE OUTSIDE TUBE INSIDE TUBE THERMAL TUBE METAL DIAMETER (INCHES) DIAMETER (INCHES) CONDUCTIVITY (BTU/HR-FT-F) 0.93700 0.82200 26. 00000 1" KORO CU-NI OUTSIDE HEAT TRANSFER AREA (SQFT/FT) INSIDE HEAT TRANSFER AREA (SQFT/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-BTU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT-F/BTU) VAPOR TEMPERATURE (DEG. F) LINEAR VELOCITY CF BRINE(FT/SEC) MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPERATURE (DEG. F) REYNOLDS NUMBER __ P PRANDTLS NUMBER CONSTANT FOR CN: A POWER OF CN: B 0.24531 0.21520 0.0036853 0. 0001843 0.05786 0.00050 212.00 3.50_ 2883.65 206.00 68982.62 1.91 1.4500 0.2030 NO CN UO HCOND HCOND HI HI MET. FOULING Q Q/LAT TUBES ______ ____ RES. BTU/HR LB/HR _1O 2.31 813.5 6409.1 12.7% 3026.6 30.6% 16.0_ 40.7% 1197.3 1.23 15 2.51 811.0 6256.7 13.0% 3026.6 30.5g 1l5.9g 40.5% 1193.6 1.23 20 2.66 809.2 6151.0 13.2% 3026.6 30.5 15.9% 40.5% 1191.0 1.22 _225 2.79 807.8 6070.1 13.3% 3026.6 30.4% 15.9t 40.4% 1188.9 1.22 30 2.89 806.6 6004.9 13.4% 3026.6 30.4% EXECUTION TERMINATED 15.9% 40.3% 1187.2 1.22 201

TABLE VII-17 Calculated Point Values for 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F Without Fouling at Tubeside Velocity of 3. 5 ft. /sec. CALCULATIONS OF THE POINT VALUES OF UJO AND HCOND. TUBE TUBE TUBE TUBE OUTSIDE DIAMETER (INCHFS) INSIDE DIAMETER (INCHFS) THERMAL CONDUCTIVITY (BTU/HR-FT-F) METAL OUTSIDE HEAT TRANSFER AREA (SOFT/FT) INSIDE HEAT TRANSFER AREA (SOFT/FT) FLOW AREA (SOFT) METAL RESISTANCE (HR/SQFT-F-BTU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SOFT-F/BTU) VAPOR TEMPERATURE (DEG. F) LINEAR VELOCITY OF BRINF(FT/SFC) MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPFRATURE (DEG. F) REYNOLDS NUMBER PRANDTLS NUMBER CONSTANT FOR CN: A POWER OF CN: B 0.61320 0.'53000 26. 00000 5/8" KORO CtU-IT 0. 16054 0. 13875 0.0015321 0.00013333 0.06730 0.0 100.00 3.50 1239.36 94.00 18535.45 5. 12 1.2100 0.1930 NO TUBES CN UO HCOND HCOND T H. HI It MET. FOUL ING 0 PFS..? RTU/HR Q/LAT LB/HP 10 1.89 1114.5 3608.9 30.9? 2426.3 53.1 16.07 15 2.04 1105.1 3512.3 31.5T?426.2 52.7T 15.8T 20 2.16'1098.4 3445.4 31.9% 2426.2 52.4T 15.77 25 2.25 1093.2 3394.4 32.2? 2426.2 52.1 15.7T 30 2.33 1088.9 3353.4 32.5T 2426.1 51.91% 15.6. 0.0T 1073.5 0.0? 1064.5 0.0l I 05A.0 0.0? 1053.0 0.0 1048. P 1.04 1.03 1.02 1.*.02 1.01 202

TABLE VII-18 Calculated Point Values for 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 100~F With 0. 0005 Fouling at Tubeside Velocity of 3. 5 ft. /sec. CALCULATIONS OF THF POINT VALUES OF tq A^fD HCOFN. TUBE OUTSIDE DIAMETER (-INCHES) TUBE INSIDE DIAMETER ( INCHES) TUBE THERMAL CONDUCTIVITY ( RTU/HR-FT-F ) TUBE METAL OUTSIDE HEAT TRANSFFR AREA (SOFT/FT) INSIDF HEAT TRANSFER AREA (SOFT/FT) FLOW AREA (SQFT) MFTAL RESISTANCE (HP/SOFT-F-TlJ!) INSIDE SIEDER-TATF CONSTANT FOULING FACTOR (HR-SOFT-F/tT!!) VAPOR TEMPERATURE (DECG. F) LINEAR VELOCITY OF BRINJ(FT/SFC) MASS VELOCITY OF BRINE (LRS/HP) BRINE TEMPERATURF (OFG. F) REYNOLDS NUtMBER PRANDTLS NUMBER CONSTANT FOR CN: A POWER OF CN: B 0.61370 0. 3000 2?^.00000 /fE" KOPO CU-NI 0. 16054 0. 13n75 0.00153?1 0.007301 0. 0050 3 nO 50.23o. 36 a4. 00 3 r 35.45 =. 12 t.21 00 0.!o0 NO TUBES CN UO HCOND HCOND HI T,.HI FT. F.ll ING 9 PF I'I' c r J! / P!_f, 1,T 10 1.89 734.0 4142.0 17.7` 242?.3 35.1 1.t.5 t 6.7wT 5 2.04 730.7 4024.3 14. 10 74'7? 4..'., 6 20 2.16 727.6 3942.9 18.5t 24?2.? 34.7' 10.4t: 3..4w 25 2.25 725.4 3880.9 19.7~ 2422.2 34.*A? 10.4T 6. 30 2.33 723.6 3831.1 1q.9 2422.2 34,*'.4'. 707. 0,6} 703.4.;,, 70. 7 0, 6 A9:, 7 0. A 7 7 *n 0,^ 7 /,KW i 07 O.F i7 203

TABLE VII-19 Calculated Point Values for 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 100 ~F Without Fouling at Tubeside Velocity of 3. 5 ft. /sec. CALCULATIONS OF THE POINT VALUES OF 110 AND HCONO. TUBE TUBE TUBE TUBE OUTSIDE INS IDE THERMAL METAL DIAMETER (INCHES) DIAMETER (INCHES) CONDUCTIVITY (BTU/HR-FT-F) OUTSIDE HEAT TRANSFER AREA (SOFT/FT) INSIDE HEAT TRANSFER AREA (SOFT/FT) FLOW AREA (SOFT) METAL RESISTANCE (HR/SQFT-F-BTJU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SOFT-F/BTU) VAPOR TEMPERATURE (DFG. F) LINEAR VELOCITY OF PRINf{ (FT/SFC ) MASS VELOCITY OF BRINF (LBS/HR) BRINE TFMPFRATURE (DEC. F) REYNOLDS NUtMBER PRANDTLS NUMBER CONSTANT FOR CN: A POWER OF CN: B 0.613: 0 0.,3000?6.00000 5/8~" KORO CU-NI 0. 160(n54 O. 1 397 0, 00n 15 1 0.0001333 0.06730 0.0 100.00 3.50 123g. 36 94.00 IR535.45 ~. 17 1.] lI n 0.?000n NO TUBES CN UO HCONn HCONn I H I HI MET. F:Ut ISN 0 QES.V, V TI/H. 10 1.76 1085.7 3324.0 3?.77?426.] 51~. 15;.6A 15 1.91 1076.9 3243.0 33.2"' 2426.0 51.4 4 15~.4+ 20 2.0? 1671.8 3196.7 33.*5' 24?6.0 51. 1 15.4.' 25 2.11 1067.8 3161.2 33?2426.1 50. 15.3 30 2.19 1062.7 3117.2 34.17 2425.9 50,.7T 15.27 0.0n O I 045. (. O I10.:'377.3 O. 0o, 107.54.0.t l0.3.A O e. O I I ) 7 I. 1 O / t AT L 3 /Ho I.01 I.00 1.00 oc...q 204

TABLE VII-20 Calculated Point Values for 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 100 ~F With 0. 0005 Fouling at Tubeside Velocity of 3. 5 ft. /sec. CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE OUTSIDE DIAMETER (INCHES) 0.61320 TUBE INSIDE DIAMETER (INCHES). 0..._53000 _..... TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) 26.00000 TUBE METAL 5/8" KORO CU-NI OUTSIDE HEAT TRANSFER AREA (SOFT/FT) 0.16054 INSIDE HEAT TRANSFER AREA (SQFTIFT) 0.13875 FLOW AREA (SQFT) 0.0015321 METAL RESISTANCE (_HR/SQFT-F-BTUI) _ 0.0001333 INSIDE SIEDER-TATE CONSTANT 0.06730 FOULING FACTOR (HR-SQFT-F/BTU) 0.00050 VAPOR TEMPERATURE (DEG. F) 100.00 LINEAR VELOCITY OF BRINE(FT/SEC) 3.50 MASS VELOCITY OF BRINE (LBSIHR) 1239.36 ~__ _ _ BRINE TEMPERATURE (DEG. F) 94.00........................... REYNOLDS NUMBER 18535.45 PRANDTLS NUMBER 5.12 CONSTANT FOR CN: A 1.1100 POWER OF CN: B 0.2?000 NO TUBES CN UO HCOND HCOND HI HI MET. FOULING. 0/LAT REFS.T, BTU/HR. LB/HR. 10 1.76 15 1.91:~o?.n 722.3 3795.4 19.0* 718.8 3700.9 19.4T 716.3.3635.4 19.7% 2422.2 34.5% 10.4% 2422.2 34.3% 10.3. 242 22.2 34.2% 10.3% 2422.2 34.1% 10.2% 2422.1 34.0% 10.2% 36.1% 695.8 0.67 35.9% 692.4 0.67 35.8% 690.0 0.67 35.7% 688.1 0,66 35.6% 686.5 0.66 25 2.11 714.4 3585.4 19.9% 30 2.19 712.7 3545.1 20.1% 205

TABLE VII-21 Calculated Point Values for 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F Without Fouling at Tubeside Velocity of 3. 5 ft. /sec. CALCULATIONS OF THE POINT VALUES nF UO AND HCONn. TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DIAMETER (INCHES) TUBE THERMAL CONDUCTIVITY (RTUI/HP-FT-F) TUBE METAL OUTSIDE HEAT TRANSFER AREA (SOFT/FT) INSIDE HEAT TRANSFER AREA (SOFT/FT) FLOW AREA (SOFT) METAL RESISTANCE (HR/SQFT-F-BTU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT-F/BTU) VAPOR TEMPERATURE (nFG. F) LINEAR VELOCITY OF BRINE(FT/SFC) MASS VELOCITY OF BRINF (L3BS/HP) BRINE TEMPERATURE ( FG. F) REYNOLDS NUMBER PRANDTLS NUMBER CONSTANT FOR CN: A POWFR OF CN: B 0.61320 0. 53000?6. 000n 5/q" KORO CU-NT 0.16054 0.13875 0.00 1 53?1 0. 00013 333 0.06730 0.0?12.00 3.50 I 1. q.9tI?(6.00 44477. R6 0.2900 NO TUBES CN UD HCOND HCONN HI )w HI MET. FOULING 0, PqS. I' RTUT/HR 10 1.64 1431.6 3929.9 36.4V 3846.5 43.IT 20.5w 15 1.80 1424.2 3874.8 36.8' 3846.5 42.8t 20?.420 1.91 1417.0 3822.5 37.1y 3846.3 4?.67 20.3w 25 2.01 1412.9 3792.3 37.3T 3846.3 42.5T 20.2T 30 2.09 1409.5 3767.9 37.4w 3846.3 4?.4T?0.2,? 0.0^ 1371. 0.0 1 364.9 0. 1 360. o 0.0' 1357.6 0/t AT L r /. P 1.42 1.41 1.40 1. 4n 1.40 206

TABLE VII-22 Calculated Point Values for 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F With 0. 0005 Fouling at Tubeside Velocity of 3. 5 ft. /sec. CALCULATIONS OF THE POINT VALUES OF tU AND HCOND. TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DIAMETER (INCHES) TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) TUBE METAL OUTSIDE HEAT TRANSFER AREA (SOFT/FT) INSIDE HEAT TRANSFER AREA (SOFT/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-BTU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SOFT-F/BTU) VAPOR TEMPERATURE (DEG. F) LINEAR VELOCITY OF BRINE(FT/SEC) MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPERATURE (DFG. F) REYNOLDS NUMBER PRANDTLS NUMBFR CONSTANT FOR CN: A POWER OF CN: B 0.61320 0.53000 26. 00000 5/8" KRnP CJU-I 0. 16054 0. 13875 0.0015321 0. 000.1333 0.068730 0.00050 21?.00 3. 50 1198.8l?06.00 44477.86 1.01 0.oo00 0.2??00 NO TUBES CN UD HCOND HCOND T.. HI HI MET. FOUlt ING Q RE S.P BTU/qP O/t AT LtB/H 10 1.64 861.2 4612.2 18.77 3842.7 25.39 12.3 T43.1T 15 1.80 858.7 4543.0 18.97 3842.7 25.9w 17.33T 4?2.q 20 1.91 857.0 4494.5 19.1 3842.7 25.8?12.3T 42?.* 25 2.01 855.6 4457.3 19.27 3842.7 25.,9: 12.3T 42. qT 30 2.09 854.5 4427.1 19.3T 3942.7 25.7T 12.?? 42.7T p27.25 0.5 P27,2 O.,AS S2, 5 0.0 5,?4.2 o 0.O q,829. 1 O.r 207

TABLE VII-23 Calculated Point Values for 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F Without Fouling at Tubeside Velocity of 3. 5 ft. /sec. CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE OUTSIDE DIAMETER (INCHES) TURF INSIDE DIAMETER (INCHFS) TUBE THERMAL CONDUCTIVITY (B'TU/HR-FT-F) TUBE METAL OUTSIDE HEAT TRANSFFR AREA (SQFT/FT) INSIDE HEAT TRANSFER ARFA (SOFT/FT) FLOW AREA (SOFT) METAL RESISTANCE fHR/SQFT-F-BTU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT-FB/TU) VAPOR TEMPERATURF (DEG. F) LINEAR VELOCITY OF BRINE(FT/SEC) MASS VELOCITY OF BR'INF (LBS/HP) BRINE TEMPERATURE (PEG. F) REYNOLDS NUMBER PRANDTLS NUMBFR CONSTANT FOR CN: A POWER OF CN: B 0.61320 0. 3000 26.0000 5/f3" KOPO,U —NI 0. 16054 0. 13P75 0.00 153.21.. 0. 000 13:3 0. 0673(0 0.0 212. 00 3.50 1 1O8. q1 206. 00 44477.86 1.q1 1.1100 O.?000 NO TUBES CN UO HCONO HCOND HI 17 H I FT,. FOUIL I r, T FS. T RTTU!/AP 10 1.76 1472.6 4255.1 34.67 3946.7 44.3? 21.10 15 1.91 1460.5 4155.9 35.1?T 3846.6 43.0T?0.0' 20 2.02 1451.9 40P6.9 35.5?' 3846.6 43.7T?0.:R 25 2.11 1445.2 4034.2 35,8. 3846.6 43.5T 20.79 0. n, 14 13.4 0.0 n 140. 0.0 1 I(39q. 5 00- 1 ( 3P -O?, n I/ I AT LR/HP I.4 6 I.4' 1.44..43 30 2.19 1439.7 3991.7 36.1T EXECUTION TERMINATED 3846.6 43.3t 20.6` 0.0) 1.3..7 1.43 208

TABLE VII-24 Calculated Point Values for 5/8-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F With 0. 0005 Fouling at Tubeside Velocity of 3. 5 ft. /sec. CALCULATIONS OF THF POINT VALUES OF tU AND HCOND. TUBE OUTSIDE TUBE INSIDE TUBE THERMAL TUBE METAL DIAMETER (INCHFS) DIAMETER (INCHES) CONDUCTIVITY ( BTt/HR-FT-F ) OUTSIDE HEAT TRANSFER AREA (SOFT/FT) INSIDE HEAT TRANSFER AREA (SOFT/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-r.TU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT-F/BTJU) VAPOR TEMPERATURE (DEG. F) LINEAR VFLOCITY OF PRINE(FT/SFC) MASS VFLOCITY OF BRINF (LBS/HP) BRINE TEMPERATURE (DEG. F) REYNOLDS NUMBER PRANDTLS NUMBER CONSTANT FOR CN: A POWER OF CN: B 0. 1320 0.53000 26. 00000 5/8" KORO CU-NT 0.16054 0. 13875 0.00 15321 0. 0001333 0.06730 0.00050 212.00 3.50 1198.81 206.00 44477. 86 1.1100 0,2000 NO TUBES CN UO HCOND HCOND 2 HI HI MET. FOULIN, Q FS. T. TU/ /t. AT LB/H H 10 1.76 874.5 5022.1 17.4,n 3842.7 26.3? 1?.5,' 43.7 15 1.91 870.6 4896.7 17.8T 3842.7 26.?T 12.5T 43.5T 20 2.02 867.8 4809.7 18.0% 3842.7?6.l? 12.47 43.4T 25 2.11 865.7 4743.4 18.2T 3842.7 26. 1 12.4* 43.3? 842.3 0.87 835 0 0. 86 P33. 8 0,6A 30 2.19 863.9 4689.9 18.4? EXECUTION TERMINATED 3842.7 26.0T 12.4 " 43.? R32?.1 O.6 209

TABLE VII-25 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F Without Fouling at Tubeside Velocity of 3. 5 ft. /sec. CALCULATIONS OF THE POINT VALUES OF UU AND HCOND. TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DIAMETER (INCHES) TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) TUBE METAL OUTSIDE fHEAT TRANSFER AREA (SQFT/FT)INSIDE HEAT TRANSFER AREA (SQFT/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-BTU) INSIDE SIEDER-IATE CUNSTANT FOULING FACTOR (HR-SQFT-F/BTU) U.9 3W7 0. 82200 6. 0( COU 1" KORO CU-NI 0.24531 0.21520 0.0036853 0.0001843 U.'3 f 0.0 VAIUK I tMt KAI UKt lUti. ri LINEAR VELOCITY OF BRINE(FT/SEC) MASS VELOCITY OF BRINE (LBS/HR) BRINE TEMPERATURE (DEG. F) REYNOLDS NUMBER PRANDTLS NUMBER CONSTANT FOR CN: A DOWER OF CN: B AZL.UU 3.50 2883.65 206. 00 68982.63 1.91 1.2300 — 0.2080 NO CN UO HCOND HCONDNDHI HI MET. FOULING Q Q/LAT TUBES % RES.% z BTU/HR LB/HR 10 1.99 1262.1 4556.9 27.7% 3029.6 47.5% 24.84 0.0% 1857.6 1.91 15 2.16 1254.8 4463.8 28.1% 3029.6 47.2% 24.7% 0.0% 1846.9 1.90 20 2.29 1249.7 4398.9 28.4% 3029.5 47.0% 24.6% 0.0% 1839.3 1.89 25 2.40 1245.6 4349.2 28.6% 3029.5 46.9% 24.5% 0.0% 1833.3 1.89 30 2.50 1242.3 4309.1 28.8% EXECUTION TERMINATED 3029.5 46.7% 24.4% 0.0% 1828.5 1.88 210

TABLE VII-26 Calculated Point Values for 1-inch Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F Without Fouling at Tubeside Velocity of 3. 5 ft. /sec. CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE OUTSIDE DIAMETER (INCHES) 0.93700 TUBE INSIDE DIAMETER (INCHES) 0,82200 TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) 26.00000 TUBE METAL I KORO CU-NI OUTSIDE HEAT TRANSFER AREA (SQFT/FT) 0.24531 INSIDE HEAT TRANSFER AREA (SQFT/FT) 0.21520 FLOW AREA (SQFT) 0.0036853 METAL RESISTANCE (HR/SQFT-F-BTU) 0.0001843 INSIDE SIEDER-TATE CONSTANT 0.057S6 FOULING FACTOR (.HR-SQFT-F/3TU) 0.0 VAPOR TEMPERATURE (DEG. F) 212.00 LINEAR VELOCITY OF 3RINE(FT/SEC) 3.50 MASS VELOCITY OF BRINE (LBS/HR) 2883.65 BRINE TEMPERATURE (DEG. F) 206.00 REYNOLDS NUMBER 68982.62 PRANDTLS NUMBER 1.91 CONSTANT FOR CN: A 1.4500 POWER OF CN: B 0.2030 NO TUBES 10 15 20 25 30 I CN UO HCOND HCOND HI 7. HI MET. FOULING Q 7. RES.7 7 % BTU/HR 2.31 1324.6 5491.8 24.1% 2.51 1317.1 5365.3 24.57. 2.66 1311.7' 5277.1 24.97. 2.79 1307.6 5210.1 25.17. 2.89 1304.1 5155.7 25.37. 3029.9 3029.9 3029.9 3029.8 3029.8 49.87. 49.67. 49 47. 49.27. 49.17. 26.07. 25.97. 25.8%Z 25.77. 25.6% 0.07% 0.07. 0 07. O.07. 0.0% 1949.6 1938.6 1930.7 1924.5 1919.4 Q/LAT L3/HR 2.01 1.99 1.99 1.93 1.97 211

UE S.OF MICHIGAN