DEPARTMENT OF CHEMICAL AND METALLURGICAL ENGINEERING Heat Transfer Laboratory The University of Michigan Ann Arbor, Michigan THE CONDENSING OF STEAM ON HORIZONTAL SINGLE-START AND TRIPLE-START CORRUGATED TUBES Report No. 61 Edwin H. Young Professor of Chemical and Metallurgical Engineering George T. S. Chen Ranvir Aggarwal Research Assistants Project 30911 UOP WOLVERINE TUBE DIVISION of UNIVERSAL OIL PRODUCTS COMPANY ALLEN PARK, MICHIGAN NOVEMBER 1969

TABLE OF CONTENTS Page List of Tables List of Figures Abstract Introduction iii vii 1 1 Previous Work Equipment and Test Procedure Results Discussion of Results Pressure Drop Considerations Summary of Results Conclusions Literature Cited Figures Appendices 3 5 7 9 13 17 19 21 23 51 Appendix I... Summary of the Calculated Cn, Individual Uo, and Cumulative Uo Values for the 1-inch Bare 90-10 Cupro-Nickel Tubes in a Single Vertical Row and in the Center Row of Three Vertical Rows Appendix II........ Summary of the Calculated Ch, Individual Uo, and Cumulative Uo Values for the 1-inch Triple-Start 90-10 Cupro-Nickel Corrugated Tubes in a Single Vertical Row 53 59 i

TABLE OF CONTENTS (Continued) Appendix III......... 63 Summary of the Calculated Cn, Individual Uo, and Cumulative Uo Values for the Center Row of 1-inch Triple-Start 90-10 Cupro-Nickel Corrugated Tubes in Three Vertical Rows Appendix IV......... 67 Computer Output from the Program in Appendix V, Pages 162-167, of Report No. 60, Which Calculates the Point Values of Uo, hcond, hi and Q, Using the Equations Presented in Table 3 For Steam Condensing at 212~F on 1-inch Bare Tubes Appendix V.......... 73 Computer Output from the Program in Appendix V, Pages 162-167, of Report No. 60, Which Calculates the Point Values of Uo, hcond, hi and Q, For Steam Condensing at 212~F on Hypothetical 1-inch SingleStart and on The Triple-Start Corrugated 90-10 Cupro-Nickel Tubes Appendix VI....... 79 Computer Output from the Program in Appendix V, Pages 162-167, of Report No. 60, Which Calculates the Point Values of Uo, hcond, hi and Q, For a Hypothetical 1-inch Triple-Start Corrugated Tube Having the Same O. D. and I. D. as The Single-Start Corrugated Tubes of Report No. 60 Appendix VII......... 85 Computer Program for Condenser Stage Design Calculations Appendix VIII........... 93 Steam Condensing Design Calculations for A Hypothetical Stage in a Desalination Plant ii

LIST OF TABLES Table Page 1 Values of the Sieder-Tate Constant, Ci, for Predicting the Inside Heat Transfer Coefficient for the Four Tubes of Report No. 60....... 4 2 Tube Dimensions and Characteristics of The TripleStart and Single-Start Corrugated Tubes Investigated. 5 3 Summary of the C Equations e..... 10 4 Characteristics of the Hypothetical Single-Start Corrugated Tube.. o...... 12 5 Dimensions and Characteristics of the Three Tubes and the MSF Stage Conditions Used in the Stage Calculations by the Computer Program in Appendix VII. 14 6 Results of an MSF Stage Design Using Three Different Tubes.. o.. o... 15 I-1 Condensing Coefficient Correction Factor, Cn, for Condensation of Steam at 212~F on 1 to 7 1-inch Bare 90-10 Cupro-Nickel Tubes in a Single Vertical Row.. 54 1-2 Individual Tube 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 Single Vertical Row........ 55 I-3 Cumulative 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 Single Vertical Row o....... 56 1-4 Individual Tube Overall Heat Transfer Coefficients, U0, for Condensation of Steam at 212~F with a Water Velocity of 6. 0 ft/sec on 1 to 7 1-inch Single-Start Corrugated 90-10 Cupro-Nickel Tubes in Three Vertical Rows (Abstracted from Report No. 60).. 57 I- 5 Cumulative Overall Heat Transfer Coefficients, Uo, for Condensation of Steam at 212~F with a Water Velocity of 6. 0 ft/sec on 1 to 7 1-inch Single-Start Corrugated 90-10 Cupro-Nickel Tubes in Three Vertical Rows (Abstracted from Report No. 60).. 58 iii

LIST OF TABLES (Continued) Table Page II-1 Condensing Coefficient Correction Factor, Cn, for Condensation of Steam at 212~F on 1 to 7 1-inch Triple-Start Corrugated Tubes in a Single Vertical Row......... 60 11-2 Individual Tube Overall Heat Transfer Coefficients, Uo, for Condensation of Steam at 212~F on 1 to 7 1-inch Triple-Start Corrugated 90-10 Cupro-Nickel Tubes in a Single Vertical Row........ 61 II-3 Cumulative Overall Heat Transfer Coefficients, Uo, for Condensation of Steam at 212~F on 1 to 7 1-inch Triple-Start Corrugated 90-10 Cupro-Nickel Tubes in Multiple Vertical Rows.. o... 62 III-1 Condensing Coefficient Correction Factor, Cn, for Condensation of Steam at 212~F on 1 to 7 1-inch Triple-Start Corrugated Tubes in Maltiple Vertical Rows......... 64 III-2 Individual Tube Overall Heat Transfer Coefficients, Uo, for Condensation of Steam at 212~F on 1 to 7 1-inch Triple-Start Corrugated 90-10 Cupro-Nickel Tubes in Multiple Vertical Rows..... 65 III-3 Cumulative Overall Heat Transfer Coefficients, UO, for Condensation of Steam at 212~F on 1 to 7 1-inch Triple-Start Corrugated 90-10 Cupro-Nickel Tubes in a Single Vertical Row........66 IV-1 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steaming Condensing at 212~F, Without Fouling, Using Equation (3).. 68 IV-2 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steaming Condensing at 212~F, Without Fouling, Using Equation (7)... 69 IV-3 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steaming Condensing at 212~F, With 0. 0005 Fouling, Using Equation (3)... 70 iv

LIST OF TABLES (Continued) Table Page IV-4 Calculated Point Values for 1-inch Bare 90-10 CuproNickel Tubes With Steaming Condensing at 212~F, With 0. 0005 Fouling, Using Equation (7).... 71 V-1 Calculated Point Values for The Hypothetical 1-inch Single-Start Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, Without Fouling, Using Table 4........ 74 V-2 Calculated Point Values for The 1-inch Triple-Start Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, Without Fouling, Using Table 2 and Equation (13)........ 75 V-3 Calculated Point Values for The Hypothetical 1-inch Single-Start Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, With 0. 0005 Fouling, Using Table 4...... 76 V-4 Calculated Point Values for The 1-inch Triple-Start Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, With 0. 0005 Fouling Using Table 2 and Equation (13)........ 77 VI-1 Calculated Point Values for The 1-inch Single-Start Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, Without Fouling, Using Equation (4)........ o 80 VI-2 Calculated Point Values for The Hypothetical 1-inch Triple-Start Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, Without Fouling Using Equation (13).. e. o.... 81 VI-3 Calculated Point Values for The 1-inch Single-Start Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, With 0. 0005 Fouling, Using Equation (4)....... 82 VI-4 Calculated Point Values for The Hypothetical 1-inch Triple-Start Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, With 0. 0005 Fouling, Using Equation (13)........ o 83 v

LIST OF TABLES (Continued) Table Page VIII-1 Design Calculations for a 3/4-inch Bare Tube for an MSF Desalination Plant Stage..... 94 VIII-2 Design Calculations for a Hypothetical 1-inch Single-Start Corrugated Tube for an MSF Desalination Plant Stage....... 95 VIII-3 Design Calculations for a 1-inch Triple-Start Corrugated Tube for an MSF Desalination Plant Stage 96 vi

LIST OF FIGURES Figure Page 1 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 i-inch 0. D., 18 Gage, 90-10 Cupro-Nickel Tubes in a Vertical Row. (Fig. 18, page 64, of Report 60)....... 25 2 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 Single-Start Corrugated 1-inch 0. D., 18 Gage, 90-10 Cupro-Nickel Tubes in a Vertical Row. (Fig. 23, page 69, of Report 60)....... 26 3 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., 20 Gage, Copper Tubes in a Vertical Row. (Fig. 25, page 71, of Report 60).. 27 4 Summary of the Condensing Coefficient Correction Factors for Tubeside Water Velocities of 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 8 Single-Start Corrugated 5/8-inch O.D., 20 Gage, Copper Tubes in a Vertical Row. (Fig. 26, page 72, of Report 60). 28 5 Sections of the 1-inch Single-Start and Triple-Start Corrugated 90-10 Cupro-Nickel Tubes. Triple-Start, Upper Specimen; Single-Start, Lower Specimen.... 29 6 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 7 Bare 1-inch O.D., 18 Gage, 90-10 Cupro-Nickel Tubes in a Single Vertical Row.. a 30 7 Individual Tube Overall Heat Transfer Coefficients for a Tubeside Water Velocity of 6. 0 feet per second and Condensation of Steam at 212~F on 1 to 7 Bare 1-inch 0. D., 18 Gage, 90-10 Cupro-Nickel Tubes in a Single Vertical Row.......... 31 vii

LIST OF FIGURES (Continued) Figure Page 8 Cumulative Overall Heat Transfer Coefficients for a Tubeside Water Velocity of 6. 0 feet per second and Condensation of Steam at 212~F on 1 to 7 Bare 1-inch O.D., 18 Gage, 90-10 Cupro-Nickel Tubes in a Single Vertical Row.......... 31 9 Condensing Coefficient Correction Factors for a Tubeside Water Velocity of 3. 5 feet per second and Condensation of Steam at 212~F on 1 to 7 Triple-Start Corrugated 1-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes in a Single Vertical Row......... 32 10 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 7 Triple-Start Corrugated 1-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes in a Single Vertical Row.......... 33 11 Summary of the Condensing Coefficient Correction Factors for Tubeside Water Velocity of 3. 5 and 6. 0 feet per second and Condensation of Steam at 212~F on 1 to 7 Triple-Start Corrugated 1-inch 0. D., 20 Gage, 90-10 Cupro-Nickel Tubes in a Single Vertical Row...... 34 12 Individual Tube Overall Heat Transfer Coefficients for a Tubeside Water Velocity of 3. 5 feet per second and Condensation of Steam at 212~F on 1 to 7 Triple-Start Corrugated 1-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes in a Single Vertical Row.......... 35 13 Individual Tube Overall Heat Transfer Coefficients for a Tubeside Water Velocity of 6. 0 feet per second and Condensation of Steam at 212~F on 1 to 7 Triple-Start Corrugated 1-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes in a Single Vertical Row.......... 36 14 Cumulative Overall Heat Transfer Coefficients for a Tubeside Water Velocity of 3. 5 feet per second and Condensation of Steam at 212~F on 1 to 7 Triple-Start Corrugated 1-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes in a Single Vertical Row.......... 37 viii

LIST OF FIGURES (Continued) Figure Page 15 Cumulative Overall Heat Transfer Coefficients for a Tubeside Water Velocity of 6. 0 feet per second and Condensation of Steam at 212~F on 1 to 7 Triple-Start Corrugated 1-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes in a Single Vertical Row......... 38 16 Condensing Coefficient Correction Factors for a Tubeside Water Velocity of 3. 5 feet per second and Condensation of Steam at 212~F on 1 to 7 Triple-Start Corrugated i-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes, Center Row of the Three Vertical Rows... 39 17 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 7 Triple-Start Corrugated 1-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes, Center Row of the Three Vertical Rows... 40 18 Summary of the Condensing Coefficient Correction Factors for Tubeside Water Velocity of 3. 5 and 6.0 feet per second and Condensation of Steam at 212~F on 1 to 7 Triple-Start Corrugated I-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes, Center Row of the Three Vertical Rows.......... 41 19 Individual Tube Overall Heat Transfer Coefficients for Tubeside Water Velocity of 3. 5 feet per second and Condensation of Steam at 212~F on 1 to 7 Triple-Start Corrugated i-inch O.D., 20 Gage, 90-10 Cupro- Nickel Tubes, Center Row of the Three Vertical Rows.... 42 20 Individual Tube Overall Heat Transfer Coefficients for Tubeside Water Velocity of 6.0 feet per second and Condensation of Steam at 212~F on 1 to 7 Triple-Start Corrugated 1-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes, Center Row of the Three Vertical Rows... 43 21 Cumulative Overall Heat Transfer Coefficients for Tubeside Water Velocity of 3. 5 feet per second and Condensation of Steam at 212~F on 1 to 7 Triple-Start Corrugated 1-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes, Center Row of the Three Vertical Rows......... 44 ix

LIST OF FIGURES (Continued) Figure Page 22 Cumulative Overall Heat Transfer Coefficients for Tubeside Water Velocity of 6. 0 feet per second and Condensation of Steam at 212~F on 1 to 7 Triple-Start Corrugated 1-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes, Center Row of the Three Vertical Rows... 45 23 Modified Wilson Plot for Triple-Start Corrugated 1-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes...... 46 24 Pressure Drop Data Versus Tubeside Water Velocity for the 1-inch Triple-Start Corrugated Tubes Studied in This Report and Four Other Types of Tubes Studied in Previous Report.......... 47 25 Moody Friction Factor Plot from the Tubeside Pressure Drop Data Appearing in Figure 24......... 48 26 Individual Tube Overall Heat Transfer Coefficients for a Tubeside Water Velocity of 6. 0 feet per second and Condensation of Steam at 212~F on 1 to 7 Bare 1-inch 0. D., 18 Gage, 90-10 Cupro-Nickel Tubes, Center Row of the Three Vertical Rows.......... 49 27 Cumulative Overall Heat Transfer Coefficients for a Tubeside Water Velocity of 6. 0 feet per second and Condensation of Steam at 212~F on 1 to 7 Bare 1-inch O. D., 18 Gage, 90-10 Cupro-Nickel Tubes, Center Row of the Three Vertical Rows.......... 49 x

ABSTRACT Experimental heat transfer data are presented for steam condensing at 212~F on the outside of horizontal 1-inch, 90-10 Cupro-Nickel triplestart corrugated tubes with two tube-support plates. The differences between the performance of a single vertical row of tubes and of the center row of three vertical rows of horizontal tubes in the test condenser are presented. The experimental results are compared with the results presented in the previous publication covering earlier research work. Data obtained on a single vertical row of horizontal bare Cupro-Nickel tubes without tube-support plates are also reported. INTRODUCTION This investigation is an extension of the work published under the title "The Condensing of Steam on Horizontal Corrugated and Bare Tubes," Report No. 60, September 1968, which was limited to single-start corrugated tubes and bare tubes. The investigation was extended to include the heat transfer performance of 1-inch, 90-10 Cupro-Nickel triple-start corrugated tubes with two tube- support plates with steam condensing at 212~F. 1

PREVIOUS WORK In the earlier investigation, Young, McParland, Chen and Young established that in the modified Nusselt equation for steam condensing h = 0.725 C m k3 2 n N D gX n NBD Atf - 1/4 The correction factor Cn is a function of the number of tubes in a vertical row. The experimental data indicated that C has the following form: C = A (N)B n where N is the number of tubes in a vertical row. The constants A and B have to be determined experimentally for the particular type of tubes of interest. The results of that investigation are summarized in Figure 1' for 1-inch bare tubes; Figure 2 for 1-inch single-start corrugated tubes; Figure 3 for 5/8-inch bare tubes; and Figure 4 for 5/8-inch single- start corrugated tubes. The Cn equations recommended by the authors of Report No. 60 for design use for these tubes are: (1) (2) 1-inch bare tubes: 1-inch single-start corrugated tubes: 0. 170 C = 1.07(N) n (3) (4) C n = 1.45(N) = 1.20 N)0557 5/8-inch bare tubes: C n (5) Literature cited will be found on page 21. Figures are presented in section beginning on page 23. 3

5/8-inch single-start corrugated tubes: C = 1.11 (N) (6) n In Report No. 60, the Sieder-Tate equation, with appropriate constant, was used as the basis for correlatingthe tube-side heat transfer performance of the above bare and corrugated tubes from experimental heat transfer data obtained on a concentric pipe heat exchanger. The Sieder-Tate constants for the above four tubes are summarized in the following table: TABLE 1 Values of the Sieder-Tate Constant, Ci, for Predicting the Inside Heat Transfer Coefficient for the Four Tubes of Report No. 60 Tube C. 1 5/8-inch Bare Copper 0. 02468 5/8-inch Single-Start Corrugated Copper 0. 06730 1-inch Single-Start Corrugated 90-10 Cupro-Nickel 0. 05786 1-inch Bare 90-10 Cupro-Nickel 0.02642 The calculated values of Cn were made using the steam condensing experimental data collected on seven to nine tubes in a vertical row. The resulting Cn values always appeared to be a linear function of N when plotted on the log-log scale. The extrapolation of Cn up to N = 25 tubes in a vertical row is believed to be valid for design purposes. (2) Eissenberg) also studied the steam condensing heat transfer performance of similar type corrugated tubes. Since the operating condition and the equipment configuration of their work are different from that of this investigation, no attempt was made to compare their results with that of this investigation. Since the publication of Report No. 60, a question has been raised concerning the vertical alignment of the tubes investigated in that report and concerning the straightness of the individual tubes. These points are discussed in a later section of this current report. 4

EQUIPMENT AND TEST PROCEDURE The basic equipment and test procedure used in this investigation are the same as described in Report No. 60(1). The reader is referred to that report for complete details. The dimensions and characteristics of the triple-start corrugated tubes studied in this investigation along with the single-start corrugated tubes of Report No. 60 are given in Table 2. Figure 5 presents sections of the single-start and triple-start corrugated tubes. TABLE 2 Tube Dimensions and Characteristics of The Triple-Start and Single-Start Corrugated Tubes Investigated Triple-Start Single-Start Tube outside diameter, in. 0.9900 0.9370 Tube inside diameter, in. 0.9132 0.8220 Tube wall thickness, in. 0.0384 0.0575 Tube length, in. 71.375 72.156 Tube material 90-10 Cupro-Nickel Thermal conductivity, BTU/hr-ft-~F 26.0 26.0 Helix Pitch 0. 375" 0. 250" Depth 0. 030" 0. 031" Start Three One Initially, further test data was collected on the existing bundle of bare tubes left in the steam condenser at the completion of the previous investigation. Later two equally spaced support plates were installed to hold the tubes in place in the condenser. The support baffles were made of 1/8-inch thick steel plate with holes properly drilled to support the tubes and were spaced 24 inches apart. The edges of the baffles were partially cut out to allow the steam to pass through the baffles. 5

RESULTS Before the tube-support baffles were installed, the two side vertical rows of the three vertical rows of horizontal bare 1-inch 0. D. tubes still remaining in the steam condensing test section from the previous investigation were removed and further test data collected with steam condensing at 212~F with a tube-side water velocity of 6 feet per second. Tables I-1, I-2 and 1-3 in Appendix I contain C, U for each individual tube, and U cumulative, respectively. Figure 6 presents a plot of the C values tabulated in Table I-1; Figure 7 presents a plot of the individual U values tabulated in Table 1-2; and Figure 8 presents a plot of the cumulative U values tabulated in Table 1-3. o After the 1-inch O.D. bare tubes were removed, the tube-support baffles were installed in the condenser test section. A single vertical row of 1-inch triple-start corrugated tubes was installed in the steam condenser test section. Data were collected with steam condensing at 212~F with tube-side water velocities of 3-1/2 and 6 feet per second. Tables II-1, 11-2, and II-3 in Appendix II contain C, U for each individual tube and U cumulative, respectively. Figures 9, 10 and 11 present plots of C; Figures 12 and 13 present plots of U individual; and Figures 14 and 15n present plots of U cumulative using the values tabulated in Tables II-1, II-2, and 11-3, respectively. After collecting the experimental test data on the single vertical row of horizontal triple-start corrugated tubes, two side rows of triplestart corrugated tubes were added with one row on each side of the existing row. Test data were collected on the center row with steam condensing at 212~F on all three rows with tube-side water velocities of 3-1/2 and 6 feet per second. Tables III-1, III-2 and III-3 in Appendix III contain C, U individual and U cumulative, respectively. Figures 16, 17 and 18present plots of C; Figures 19 and 20 present plots of U individual; and Figures 21 and 22 present plots of U cumulative using the values tabulated in Tables III-i, 11-2 and III-3, respectively. The determination of the Sieder-Tate constant and tube-side pressure drop curve for the 1-inch triple-start corrugated tubes used in this investigation was made by the UOP Wolverine Tube Division in their Engineering and Development Laboratories in Allen Park, Michigan. Figure 23 presents the modified Wilson plot curve that establishes the Sieder- Tate constant for the inside of the triple-start corrugated tube as 0.05058. Figure 24 presents the tube-side pressure drop data for the triplestart corrugated tube superimposed on Figure 38, page 84, of Report No. 60. Figure 25 gives the corresponding Moody friction factor for the triple-start corrugated tube superimposed on Figure 39, page 85, of Report No. 60. Appendices will be found beginning on page 51. 7

DISCUSSION OF RESULTS In the earlier section of this report entitled "Previous Work" on page 3, reference was made to the fact that a question has been raised concerning the vertical alignment and straightness of the tubes investigated and reported in Report No. 60. Figure 1 presents all of the data collected with 3. 5, 4. 7, 5. 3 and 6. 0 feet per second water velocities through the center row of the three vertical rows of 1-inch bare, 18 gage, 90-10 CuproNickel tubes with steam condensing at 101~F and 212~F. Equation 3, page 3, is the equation of the recommended line for C under these conditions. n Figure 7 and Figure 8 present plots of individual U and cumulative U values, respectively, obtained with a water velocity of 6. 0 leet per second and steam condensing at 212~F on the center vertical row of tubes after removing the two side rows of tubes. Figures 26 and 27 present plots of individual U and cumulative U values respectively, obtained with a water velocity of 6. 6 feet per second and steam condensing at 212~F before removing the two side rows of tubes. The data used for the preparation of Figures 26 and 27 appeared in Table IV-9, page 152, of Report No. 60. This data was abstracted and is presented as Tables 1-4 and 1-5 of Appendix I of this report. The dotted curves appearing in Figures 26 and 27 are the solid lines appearing in Figures 7 and 8, respectively, for comparison purposes. A comparison of the single row data in Figure 7 with the data with two side rows shown in Figure 26 indicates that the presence of the two side rows of tubes had a marked effect on the overall heat transfer coefficients with log-mean temperature differences of approximately 43~F to 47~F. A comparison of the performance of corresponding tubes in Figures 7 and 26 indicates Tube No. 2 and No. 6 are in marked disagreement; No. 7 is in partial disagreement, while the rest of the individual tubes are within experimental agreement. The only explanation that can be offered at this time is that there must have been some interference between the center row and the side rows of tubes. A similar comparison can be made on the cumulative Uo basis by comparing Figure 8 with Figure 27, and another by comparing Figure 8 with Figure 7, and Figure 27 with Figure 26. A comparison of Figure 7 with Figure 8, and Figure 26 with Figure 27, indicates that the performance of an individual tube is submerged in the cumulative performance of the tube row to such an extent that Cn plot given in Figure 1 gives no clear indication of the performance of the individual tubes. The question as to the degree of vertical alignment of the rows and the straightness of the tubes and subsequently their effect on the heat transfer performance cannot be fully answered on the basis of the data collected to date. In order to answer these questions, it would be necessary to re-tube the steam condenser with three rows of bare tubes with the two tube-support baffles in place and collect more experimental data. In the meantime, it is recommended that Equation 3 be used for design purposes. A study of the effect of using the equation for a 9

single row in comparison with using Equation 3 was made. Figure 6 presents the Cn plot for the data collected on the single row. This C equation is presented in Table 3 as Equation 7. TABLE 3 Summary of the C Equations -inch Bare Tube, Sinle Row 1-inch Bare Tube, Single Row Equation for 6.0 ft/sec data (Fig. 6) C = 1.22 n (ID Equation Equation Equation 1-inch Triple-Start Corrugated Tube, Single Row for 3. 5 ft/sec data (Fig. 9) C = 1.40 (P n for 6.0 ft/sec data (Fig. 10) C = 1.48 (l1 n for Combined Data (Fig. 11) C = 1.43 (1! n 1-inch Triple-Start Corrugated Tube, Three Rows 0. 0895 0. 0620 T) )0.0795 ) 0. 0708 0.0708 J) (7) (8) (9) (10) (11) (12) (13) Equation for 3. 5 ft/sec data Equation for 6. 0 ft/sec data Equation Recommended for Design Use (Fig. 16) (Fig. 17) (Fig. 18) 0. O968 C = 1.47 (N)9 n 0. 1097 C = 1.52(N) n 0 = 1.48 1050 C = 1.48 (N) n The Cn equation for the single row of tubes and Equation 3 for three rows were used in the design computer program given in Appendix V of Report No. 60, pages 161-167. Appendix IV of this report presents the calculated results for non-fouling and a 0. 0005 fouling factor for steam condensing at 212~F with a water velocity of 6. 0 feet per second. A comparison of the results for Equation 3 without fouling given in Table IV-1 with corresponding Cn equation for a single row of tubes given in Table IV-2 indicates that the use of Equation 3 results in 4. 5 percent more steam being condensed. On the other hand, a comparison of Table IV-3 with Table IV-4 with 0. 0005 fouling indicates 3. 5 percent more steam being condensed. Thus, the use of Equation 3 results in a prediction of approximately 4 percent more steam condensed. A similar study of the performance of a single vertical row of triplestart corrugated tubes versus the performance of the middle vertical row of three rows with two tube-support plates was also made. Figures 9, 10, and 11 present C plots for the single row using the data in Table II-1. The n 10

resulting Cn equations are summarized in the middle of Table 3. Figures 12 through 15 present plots of the individual and cumulative Uo values from Tables II-2 and II-3. A comparison of Figures 12 and 13 with Figure 7 indicates that the use of two tube- support plates resulted in a more consistent pattern of performance. A comparison of Figures 14 and 15 with Figure 8 supports this conclusion. Figures 16, 17 and 18 present Cn plots for the center row of a threerow bundle of triple-start corrugated tubes using the data in Table III-1. The resulting Cn equation is summarized at the bottom of Table 3. Figures 19 through 22 present plots of the individual and cumulative Uo values from Tables III-2 and III-3. A comparison of Figures 19 and 20 for triple-start corrugated tubes with Figure 26 for one-inch bare tubes further indicates that the use of the two tube-support plates resulted in a more consistant pattern of performance. A similar comparison of Figures 21 and 22 with Figure 27 also supports this conclusion. Further comparisons must be made between the single row and multiple row results for the triple-start corrugated tubes. The individual tube performances given in Figures 12 and 13 for a single row must be compared with those given in Figures 19 and 20 for the center row of three rows, respectively. Likewise, the cumulative performances given in Figures 14 and 15 for a single row must be compared with those given in Figures 21 and 22 for the center row, respectively. If such a comparison is made, it will be noted that in all cases, without exception, the center row in a three row bundle always gives slightly higher overall heat transfer coefficients than the single row. Since the tubes studied were identical in both instances and the operating conditions were the same, the differences in overall heat transfer performance must be due to the steam-side condensing behavior. Furthermore, it is believed that the performance of the center vertical row of tubes in a three row bundle is physically more representative of the performance of a row of tubes in an actual steam condensing bundle. It is recommended that the Cn equation obtained from the center row of a simulated bundle be used for design purposes. This logic is the basis for justifying the recommendation of Equation 3 for bare tubes. The triple-start corrugated tube studied in this investigation had a 50 percent thicker wall than the single-start tube studied and reported in Report No. 60. A direct comparison between these two tubes is not strictly valid. A direct comparison should be made on tubes having similar inside diameter, outside diameter and wall thickness. A hypothetical single-start tube having the same inside diameter, outside diameter, and wall thickness as the triple- start corrugated tube was assumed and comparison performance calculations made. The results are reported in Appendix V. Table 4 presents the characteristics of the hypothetical single-start corrugated tube. This hypothetical tube differs from the triple-start tube in Table 2 only in the number of corrugation starts, The Ci value and Cn equations for this tube were obtained by interpolating the values presented in Report No. 60 and in this report. 11

TABLE 4 Characteristics of the Hypothetical Single-Start Corrugated Tube Outside Diameter, inches 0.9900 Inside Diameter, inches 0.9132 Average Tube Wall, inches 0. 0384 Tube Material 90-10 CuNi Thermal Conductivity, Btu/ft-hr-~F 26. 0 Helix Pitch, inches 0. 375 Depth, inches 0.030 Start One Sieder-Tate Constant 0.0550 0. 204 C Equation C = 1.505(N) n n Appendix V contains design calculations for the hypothetical 1-inch single-start and the triple-start 90-10 Cupro-Nickel corrugated tubes for 10, 15, 20, 25 and 30 tubes in a vertical row with steam condensing at 212~F with a tube-side water velocity of 3. 5 feet per second with and without fouling. An examination of these tables indicates that without fouling the single- start tubes will condense approximately 18 percent more steam than the triplestart tubes with 25 tubes in a vertical row under the same condition. For the same condition and arrangement but with a 0. 0005 fouling factor on the tubeside, the triple-start tubes condense approximately 10 percent more steam than the single-start tubes. Another interesting hypothetical comparison can be made if one assumes that a triple-start corrugated tube could be made that had the identical outside diameter, identical inside diameter and correspondingly identical wall thickness as the single-start corrugated tube. If it is further assumed that (a) the Sieder-Tate constant has the same value as reported herein, and (b) the Cn equation is the same as that reported herein, then corresponding computer design calculations can be made. Such calculations were made and are presented in Table VI-1 and Table VI-2 for no fouling and Tables VI-3 and VI-4 for a fouling factor of 0. 0005. A comparison of Table VI-1 with Table VI-2 and Table VI-3 with Table VI-4 indicates that the single-start corrugated tube would condense approximately 17 percent more steam at 212~F than the hypothetical triple-start corrugated tube without fouling and would condense approximately 10 percent more steam at 212~F with a 0. 0005 fouling factor with tubeside water velocities of 3. 5 feet per second. 12

PRESSURE DROP CONSIDERATIONS The previous section indicated that hypothetical 1-inch singlestart corrugated tubes would condense 18 percent more steam with no fouling and 10 percent more steam with a 0. 0005 fouling factor if pressure drop considerations were ignored. The pressure drop of the single-start corrugated tube, from Figure 24, is approximately 44 percent higher per unit length than the triple- start tube with a 3. 5 feet-per- second water velocity. A more useful comparison can be made for equal pressure drop conditions for a stage of an MSF (multi-stage flash) distillation plant. A computer design program prepared by UOP Wolverine Tube Division was used for making the design calculations. The computer program is listed in Appendix VII. The characteristics of the tubes studied in the design comparison are presented in Table 5 along with the MSF recovery stage design conditions. The Sieder-Tate constant for the 3/4-inch bare tube of Table 5 was obtained by interpolating the constant for the 5/8-inch bare tube in Report No. 55(3) and for the 1-inch bare tube in Report No. 60. The Cn equation for this tube was also obtained in a similar manner. The friction factor equation for this tube was obtained by fitting an equation to the bottom curve of Figure 25, page 48 of this report. The hypothetical 1-inch single-start corrugated tube of Table 5 is the same tube presented in Table 4 with additional information concerning the tube-side friction factor. This friction factor was obtained by cross-plotting the relative roughness (E /D)of Moody(4) for the 5/8-inch and 1-inch single-start corrugated tubes of Report No. 60 and extrapolating to the inside diameter indicated in Table 4. All of the information given in Table 5 for the 1-inch triple-start corrugated tube was reported earlier in this report. The performance of 3/4-inch outside diameter bare tubes in the steam condensing application is used as a basis of comparison. Table VIII- 1 of Appendix VIII summarizes the calculations for the 3/4-inch bare tube; Table VII-2 summarizes the calculations for the 1-inch outside diameter hypothetical single-start corrugated tubes; and Table VIII-3 summarizes the calculations for the 1-inch outside diameter triple-start corrugated tubes. It should be noted that a 0. 0003 fouling factor was used for the MSF stage calculations. For comparison purposes, Table 6, page 15, summarizes the calculation results for the 3/4-inch bare tubes, the 1-inch single-start and 1-inch triple-start corrugated tubes. An examination of Table 6 indicates that approximately 24 percent less weight of tubing is required for the hypothetical 1-inch single-start corrugated tube and approximately 17 percent less for the 1-inch triple-start corrugated tubing as compared with 3/4-inch bare tubing. Table 6 further indicates that the stage length required for the hypothetical single-start corrugated tube stage length is 37 percent shorter than for the 3/4-inch bare tube and the triple-start corrugated tube stage length is 20 percent shorter. 13

TABLE 5 Dimensions and Characteristics of the Three Tubes and the MSF Stage Conditions Used in the Stage Calculations by the Computer Program in Appendix VII Condenser Duty, Btu/hr Condensing Temperature, ~F Tubeside Brine Inlet Temperature, ~F Tubeside Brine Outlet Temperature, ~F Log Mean Temperature Difference Tube Designation 4^ 29, 950,000 212.70 201.42 205.25 Brine Concentration, Wt. % Solid Total Tubeside Brine Flow Rate, lbs/hr Tubefield Layout Tube Pitch, inches Tubefield Shape 5. 0 8, 191,000 Triangular 1.25 (nom. O. D.) Circular 9.23 Tube, O.D., inches Average tube wall, inches Tube material Tubeside Fouling Resistance, hr-ft2- F/Btu Sieder-Tate Constant C Equation n 3/4" Bare 0. 750 0. 0384 90-10 CuNi 0. 0003 0. 0251 C = 1.158(N)09 n f= 0.316 025 (Re0 25 Hypothetical 1" Corrugated (single- start) 1" Corrugated (triple- start) 0.990 0. 0384 90-10 CuNi 0. 0003 0. 0550 C = 1.505(N) n 0.990 0. 0384 90-10 CuNi 0. 0003 0. 0505 C =1.48(N)105 n f= 0. 386 101 L (Re)0.16 Friction Factor Equation f = 0. 10

TABLE 6 Results of an MSF Stage Design Using Three Different Tubes Tube Designation 3/4" Bare Hypothetical 1" Corrugated (single- start) 1" Corrugated (triple- start) Tubeside Pressure Drop per Stage, psi Tubeside Velocity, ft/sec Tube Length per Stage, ft Total No. of Tubes per Stage Total Tube Length per Stage, ft Overall Heat Transfer Coefficient, Uo Tubeside Heat Transfer Coefficient, h. 1 Condensing Heat Transfer Coefficient, h o Tube Weight per Stage, lbs Percent of Tube Weight 0.70 6.0 9.0 2,456 21,998 0.70 3.7 5. 7 2, 162 12,390 751 1,010 0.70 4. 3 7. 2 1,880 13, 503 927 3, 019 3, 427 6, 085 83 2, 099 2, 695 7,332 100 2,941 5, 171 5, 583 76 15

SUMMARY OF RESULTS The previous two sections of this report indicated that pressure drop consideration must be taken into account when evaluating single- start and triple-start corrugated tubes in desalination applications in comparison with bare tubes. With the same water velocity of 3. 5 feet per second, the single-start corrugated tubes would condense approximately 18 percent more steam at 212~F than the triple-start corrugated tubes without fouling, or approximately 10 percent more with a fouling factor of 0. 0005, but with a 44 percent higher pressure drop. On the other hand, if one considers an actual desalination design application and introduces an equal pressure drop constraint and equal LMTD constraint for an MSF stage with steam condensing at 212~F, the tube-side water velocity would then be different for the single- start corrugated tubes and the triple- start corrugated tubes, i. e., 3. 7 feet per second for the single-start corrugated tubes and 4. 3 feet per second for the triple-start corrugated tubes, respectively. At these water velocities, the single-start corrugated tubes would condense approximately 8 percent more steam per unit length than the triple- start corrugated tubes with a fouling factor of 0. 0003 as would be used in the heat recovery section of an MSF desalination plant. Under these operating conditions, the length of tubes required per stage would be 5. 7 feet and 7. 2 feet, respectively, and the corresponding total number of tubes per stage, as indicated in Table 6, would be 2, 162 and 1,880. The use of 1-inch single-start corrugated tubes would amount to approximately 9 percent saving in tube weight over the use of triple-start corrugated tubes in this design application with the two indicated constraints. The corresponding comparison of both single-start and triple-start corrugated tubes with the use of 3/4-inch bare tubes was made by referring to Table 6 and presented on page 15. 17

CONCLUSIONS The single-start and triple-start corrugated tubes are both significantly better for condensing steam than corresponding bare tubes. The increased pressure drop resulting from the internal corrugation requires that a larger diameter corrugated tube be used in place of the normally used bare tubes and that lower water velocities be used with the corrugated tubes. Consequently, the use of corrugated tubes for desalination applications requires that great care be taken in the design of MSF plants with such tubes. Complete economic studies must be made of plant designs for specific applications in order to determine the relative economic merits of corrugated tubes over bare tubes. 19

LITERATURE CITED 1. Young, Edwin H., McParland, Patrick J., Chen, George T. S. and Young, David H., "The Condensing of Steam on Horizontal Corrugated and Bare Tubes," Report No. 60, Heat Transfer Laboratory, Department of Chemical and Metallurgical Engineering, The University of Michigan, September 1968. 2. Eissenberg, D. M., Oak Ridge National Laboratory, "The Multitube Condenser Test, " Paper No. 6, Symposium on Enhanced Tubes for Distillation Plants, Office of Saline Water, U.S. Department of the Interior, March 11-12, 1969, Washington, D. C. 3. Briggs, Dale E. and Young, Edwin H., "The Condensing of Low Pressure Steam on Horizontal Titanium Tubes," Report No. 55, Heat Transfer Laboratory, Department of Chemical and Metallurgical Engineering, The University of Michigan, December 1963. 4. Moody, L. F., Trans. ASME, Vol. 66, pp. 671-684, 1944. 21

FIGURES 23

3. 2.5 2.0 t" > oBE~ E 0.9 0 0.o 9 o 3.5FPS 0.8- 4.7 FPS < 5.3FPS 0 7 o7 6.0 FPS 0.6 I I I I I I I 1 2 3 4 5 6 7 8 Tubes in a Vertical Row Figure 1. 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 0. D., 18 Gage, 90-10 Cupro-Nickel Tubes in a Vertical Row. (Fig. 18, page 64, of Report 60)

3. 2.5 o - z0 o - 8n 0 L 0 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 1 2 3 4 5 6 7 8 9 10 Tubes in a Vertical Row Figure 2. 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 0F and 212~F on 1 to 7 Single-Start Corrugated 1-inch O.D., 18 Gage, 90-10 Cupro-Nickel Tubes in a Vertical Row. (Fig. 23, page 69, of Report 60)

3. 0 I I I I I I I I 2. 5 2.0 - 1.5H i C =120(N)00557 __._______ 48- - - 1~ n = -i6 8 e.Mwwm_ I - Iq Q - C n r) -q LO1 0. 9 o 60 FPS o 8.9FPS < 11.6 FPS 0.8 0.a7 0. 6 I I I I I I I I 1 2 3 4 5 6 7 8 9 10 Tubes in a Vertical Row Figure 3. 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 0. D., 20 Gage, Copper Tubes in a Vertical Row. (Fig. 25, page 71, of Report 60)

3.0 2.5 2.0 1.5 C n R) OD 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 4. Summary of the Condensing Coefficient Correction Factors for Tubeside Water Velocities of 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 8 Single-Start Corrugated 5/8-inch O. D., 20 Gage, Copper Tubes in a Vertical Row. (Fig. 26, page 72, of Report 60)

Figure,5. Sections of the I-inch S'ingle-Start and Triple-Start Corrugated 90-10 Cupro-N.icekel Tubes, Triple-Start, Upper Specimen; Si. ngleStart, Lower Speci-men. 29

3.0 2.5 2.0 1.5 C n 0 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 6. 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 7 Bare i-inch 0. D., 18 Gage, 90-10 Cupro-Nickel Tubes in a Single Vertical Row.

Uo Tube Number Figure 7. Individual Tube Overall Heat Transfer Coefficients for a Tubeside Water Velocity of 6.0 feet per second and Condensation of Steam at 212~F on 1 to 7 Bare 1-inch O.D., 18 Gage, 90-10 Cupro-Nickel Tubes in a Single Vertical Row. Uo 2 3 4 5 6 7 Tubes In a Vertical Row Figure 8. Cumulative Overall Heat Transfer Coefficients for a Tubeside Water Velocity of 6.0 feet per second and Condensation of Steam at 212~F on 1 to 7 Bare 1-inch O.D., 18 Gage, 90-10 Cupro-Nickel Tubes in a Single Vertical Row. 31

3.0 C n Lro 1.0 0.9 0.8 0.7 0.6 1 _f 4 5 A Figure 9. -f8 9 10 Tubes in a Vertical Row Condensing Coefficient Correction Factors for a Tubside Water Velocity of 3.5 feet per second and Condensation of Steam at 212oF on i to 7 TripleStart Corrugated l-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes in a Single Vertical Row.

3.0 2.5 2.0 1.05 C = 1.48(N) 0795 n C 0 0. 0. ).1.6 1 2 3 4 5 Tubes In r\/t;irn,n 6 7 8 9 In Figure 10. Condensing CoeffIcdI o W Start feet Coefficient Correction Factors for a Tubeside Water Velocit Start Corrugated I-i and Condensation of Steam at 212 1 o 7 Trle Single Vertical Row.. 20 Gage le90 up ro- Nic kel Tube s in a mu

3.0 2.5 2.0 1.5 I 1.43 00708 C = 1.43 (N) n C f n 1.0 - 0.9 o 3-12 ft/sec. 0.8 -, 6 ft/sec. 0.8 -- 0.7 0.6 1 2 3 4 5 6 7 8 igure 11. Sum m y o t Tubes In a Vertical Row Figure 11. Summary of th C d d -e ensing Coefficient Correction Factors for Tubeside Water Velocity of 3. 5 and 6. 0 feet per Second and Condensaion o Steam at 2Cupr on 1 to 7 TripleStart Corrugated i-inch O.D. 0 Gage. 90-10o Cupro-Nickel Tubes in a Single Vertical Row. 2 9 10

I 1 I' 0 Uo I I 0 0 0 0 0 0 2 3 4 5 6 7 Tube Number Figure 12. Individual Tube Overall Heat Transfer Coefficients for a Tubeside Water Velocity of 3.5 feet per second and Condensation of Steam at 212~F on 1 to 7 Triple-Start Corrugated 1-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes in a Single Vertical Row. 55

1500 14001300 1200 Uo Gb 1100 0 o 0 ^^1 Io~~~~~0 1000 o o 900 800-I II 2 3 4 5 6 7 Tube Number Figure 13. Individual Tube Overall Heat Transfer Coefficients for a Tubeside Water Velocity of 6.0 feet per second and Condensation of Steam at 212~F on 1 to 7 Triple-Start Corrugated 1-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes in a Single Vertical Row. 36

I I 0 I I 100- Uo % t 1000 900 800 I1 I 2 3 4 5 6 7 Tubes In a Vertical Row Figure 14. Cumulative Overall Heat Transfer Coefficients for a Tubeside Water Velocity of 3.5 feet per second and Condensation of Steam at 212~F on 1 to 7 Triple-Start Corrugated 1-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes in a Single Vertical Row.

0 I Uo I I I 3 4 5 6 7 Tubes In a Vertical Row Figure 15. Cumulative Overall Heat Transfer Coefficients for a Tubeside Water Velocity of 6.0 feet per second and Condensation of Steam at 212~F on 1 to 7 Triple-Start Corrugated 1-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes in a Single Vertical Row. 38

3.0 2.5 2.0 1.51 C = 1.47 (N)0-068 n C n I 1.0 0.9 0.8 0.7 0.6 2 3 4 5 6 7 6 Figure 16. Conensing Coefficient CorrestI a Vertia o 8 35 feet per Second andCondec Factors f - I W V i' * i <u1es, Center Row 1.0

3.0 2.5 C = 1.52 (N)0.1097 n 1.5 C n 0 1.0 0.9 0.8 0.7 0.6 1 2 3 4 c Figure 17. 6 7 8 Tubes In a Vertical Row 7 /C ondensi g C oefficient C o r e i..a. r fTd 6. 0 f e e t p e r s e o n d a n d CInd e nFa ct o r f oS t a a l 2T o t o T ri e. St a t Corrugated Ii-inch D C ndensation of Ste1.... atrVloito the Three Vertica i Row, GaSe at 212oS o Tues, -cr RoTb of ~ C-enter Row of 9 10

3.0 I I I I I I I 2.5F _ — f% 2.0C 1.48 (N). 0105) 1.5A L 0 a C n -H M 1.0K 0.9 o 3-1/2 ft/sec., 6 ft/sec. 0.8 0.17 I I I I I 0.6 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 Velocity of 3. 5 and 6. 0 feet per second and Condensation of Steam at 212~F on 1 to 7 Triple-Start Corrugated 1-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes, Center Row of the Three Vertical Rows.

1500 1400 1300 1200 Uo 0 I o10 0 0 0 1000o 0 0 0 0 900 0 800- I 2 3 4 Tube Number 5 6 7 Figure 19. Individual Tube Overall Heat Transfer Coefficients for Tubeside Water Velocity of 5.5 feet per second and Condensation of Steam at 212~F on 1 to 7 Triple-Start Corrugated 1-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes, Center Row of the Three Vertical Rows. 42

0 0 0 0 O O 0 0 8 Uo QD 9 0 o 0 II 0 2 3 4 5 6 7 Tube Number Figure 20. Individual Tube Overall Heat Transfer Coefficients for Tubeside Water Velocity of 6.0 feet per second and Condensation of Steam at 212~F on 1 to 7 Triple-Start Corrugated 1-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes, Center Row of the Three Vertical Rows. 43

I Uo 0 1100 1000 900 800 1 Figure 21. 0 0 7 Tubes In a Vertical Row Cumulative Overall Heat Transfer Coefficients for Tubeside Water Velocity of 35.5 feet per second ana Condensation of Steam at 212~F on 1 to 7 Triple-Start Corrugated 1-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes, Center Row of the Three Vertical Rows. 44

1500C 8 1400 o CD 0 1300 9 o o 9 0 0 0 8 1200+ o Uo -i I 100 1000 900+ 800' 2 3 4 5 6 7 Tubes In a Vertical Row Figure 22. Cumulative Overall Heat Transfer Coefficients for Tubeside Water Velocity of 6.0 feet per second and Condensation of Steam at 212~F on 1 to 7 Triple-Start Corrugated 1-inch O.D., 20 Gage, 90-10 Cupro-Nickel Tubes, Center Row of the Three Vertical Rows. 45

er C' V) Co O"\ I - CDo i j. 100 90 80 70 u0 50 40 30 20 10 0 I I I I I I I I I I I I I I I I I _ ~ —^r"'"^o~~~~~~~~~~~~~~~ WW —o^ —c0 woo r = n nqncI I.j - U. V./VU 1 1 l l l I I I 4_ I I I II I I I 0 0.2 0.4 0.o 0.8 1.0 1.2 1.4 1.6 0.833[(0 03333 0'14 08 0. 3333 14 Modified Wilson Plot for Triple-Start Corrugated 1-inch 0. D., 20 Gage, 90-10 Cupro-Nickel Tubes. 1.8 Figure 23.

10. 0 5.0 40 3.0 I I I I I I I I I I I 1 1 11 2.0 1.0._ 0 I= Q) 0a) V) a) CD I 0 5 0.4 0.3 i 0. 2 0.1 0.05 0.04 0.03 0002 0 0.01 I I I I I I I I I I I I 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 (ft/sec) Figure 24. Pressure Drop Data Versus Tubeside Water Velocity for the 1-inch Triple-Start Corrugated Tubes Studied in This Report and Four Other Types of Tubes Studied in Previous Report.

1.0 I I I I I I I I I I I I lI I I I I I I I I_ 0.5h 0. 4 0.3 h 002[ lQ ~- - II 0: L 0 I4co U0 LL0 ( ( 0.1 ). 05 )3 04 5/8" SingBle-Start Corrugated i o-o-oao'CDo: -e-oo — f = 0. 17574 R 014334 1" Single-Start Corrugated e - 00-oo0 —d-o-~ o 0 [ Tripie-Sta f - 0. 14879 aIooCorrugated 0.0o-^obo., f = 0.386 A " Bai o 5/8" B 1 R 0032793 e 1 i2 0. 16243 aRe re lare Im 0 03I Bare 0.02 n 01 I I I I' I I I I I I I I I I l l I I. I I I I I I MO v....B.. I m.,I 3, 000 104 105 106 Reynolds Number Figure 25. Moody Friction Factor Plot from the Tubeside Pressure Drop Data Appearing in Figure 24.

1000O 900 \,-FROM FIGURE 7 \ N, **I%-,0 Uo 0 8 800H 0 0 0 o 0 0 0 8 9 0~~~ O 8 a 9 700 I 2 3 4 Tube Number 5 6 7 Figure 26. Individual Tube Overall Heat Transfer Coefficients for a Tubeside Water Velocity of 6.0 feet per second and Condensation of Steam at 212~F on 1 to 7 Bare 1-inch O.D., 18 Gage, 90-10 CuproNickel Tubes, Center Row of the Three Vertical Rows. I UUU 900 I I I II.1 I FROM FIGURE 8 Ho 0 8 0 0 Uo 800H 700' I 2 3 4 5 6 7 Tubes In a Vertical Row Figure 27. Cumulative Overall Heat Transfer Coefficients for a Tubeside Water Velocity of 6.0 feet per second and Condensation of Steam at 212~F on 1 to 7 Bare 1-inch O.D., 18 Gage, 90-10 CuproNickel Tubes, Center Row of the Three Vertical Rows. 49

APPENDICES 51

APPENDIX I Summary of the Calculated C, Individual Uo, and Cumulative Uo Values for the 1-inch Bare 90-10 Cupro-Nickel Tubes in a Single Vertical Row and in the Center Row of Three Vertical Rows 53

TABLE I- 1 Condensing Coefficient Correction Factor, C, for Condensation of Steam at 212~F on 1 to 7 1-inch Bare 90-10 Cupro-Nickei Tubes in a Single Vertical Row C n Run No. Velocity ft. /sec. 206153A 6.16 206153B 6.12 206155A 6.05 206155B 6.05 206156A 6.03 206156B 6.03 \Jn 206157A 6.03 206157B 6.03 206158A 6.09 206158A 6.10 206159A 6.15 206159B 6.15 206164A 6.08 206164B 6.08 206165A 6.14 206165B 6.14 LMTD OF 43 46 49 49 46 46 46 46 46 46 44 44 46 46 43 43 1 1.30 1.01 1.10 1.09 1.19 1.27 1.22 1.27 1.19 1.17 1.10 1.11 1.31 1.36 1.31 1.33 2 1.32 1.17 1.17 1.16 1.30 1.34 1.26 1.32 1.28 1.22 1.17 1.14 1.36 1.38 1.34 1.33 3 1.40 1.25 1.24 1.24 1.38 1.44 1.34 1.37 1.30 1.27 1.25 1.20 1.44 1.43 1.42 1.40 4 1.45 1.30 1.28 1.28 1.42 1.46 1.37 1.40 1.31 1.28 1.28 1.24 1.46 1.47 1.44 1.44 5 6 7 1.50 1.34 1.33 1.33 1.45 1.48 1.42 1.43 1.35 1.31 1.33 1.28 1.50 1.52 1.49 1.49 1.51 1.34 1.35 1.35 1.46 1.49 1.44 1.45 1.36 1.32 1.35 1.31 1.51 1.52 1.49 1.49 1.53 1.36 1.37 1.37 1.48 1.50 1.46 1.46 1.37 1.33 1.37 1.33 1.52 1.54 1.51 1.49

TABLE I-2 Individual Tube Overall Heat Transfer Coefficients, U, for Condensation of Steam at 212~F on 1 to 7 1-inch Bare 90-10 Cupro-Nickel Tubes in a Single Vertical Row U o Run No. Velocity ft. /sec. 206153A 6.16 206153B 6.12 206155A 6.05 206155B 6.05 206156A 6.03 206156B 6.03 \ji 206157A 6.03 206157B 6.03 206158A 6.09 206158B 6.10 206159A 6.15 206159B 6.15 206164A 6.08 206164B 6.08 206165A 6.14 206165B 6. 14 LMTD ~F 43 46 49 49 46 46 46 46 46 46 44 44 46 46 43 43 1 2 959 851 875 872 910 936 918 936 914 907 892 897 949 962 961 965 839 831 785 780 848 842 812 832 834 809 808 781 843 840 845 839 3 851 799 779 784 828 859 817 806 775 780 799 776 848 829 852 842 4 5 6 7 819 771 753 752 786 783 773 774 745 736 757 762 792 805 794 806 824 758 763 762 783 780 790 777 762 743 784 754 803 809 813 823 769 688 713 718 741 738 750 741 710 687 730 734 751 753 751 847 753 720 708 715 746 739 726 734 692 707 725 714 740 749 766 732

TABLE 1-3 Cumulative Overall Heat Transfer Coefficients, U, for Condensation of Steam at 212~F on 1 to 7 I-inch Bare 90-10 Cupro-Nickel fubes in a Single Vertical Row U o Run No. Velocity LMTD 1 2 3 4 5 6 ft. /sec. ~F 206153A 6.16 43 959 899 883 867 859 844 82 206153B 6.12 46 851 841 827 813 802 783 77 206155A 6.05 49 875 830 813 798 791 778 7( 206155B 6.05 49 872 826 812 797 790 778 7E 206156A 6.03 46 910 879 862 844 831 816 8C 206156B 6.03 46 936 889 879 855 840 823 81 206157A 6.03 46 918 865 849 830 822 810 79 206157B 6.03 46 936 864 858 837 825 811 8C 206158A 6.09 46 914 784 841 817 806 790 77 206158B 6.10 46 907 858 832 808 795 777 7( 206159A 6.15 44 892 850 833 814 808 795 78 206159B 6.15 44 897 839 818 804 794 784 77 206164A 6.08 46 949 896 880 858 847 831 81 206164B 6.08 46 962 901 877 859 849 833 82 206165A 6.14 43 961 903 886 863 853 836 82 206165B 6.14 43 965 902 882 863 855 837 82 7 8 58 )9 )6 31 )8 )0 74 [8:6'6'2

TABLE 1-4 Individual Tube Overall Heat Transfer Coefficients, Uo, for Condensation of Steam at 212~F with a Water Velocity of 6.0 ft/sec on 1 to 7 1-inch Single-Start Corrugated 90-10 Cupro-Nickel Tubes in Three Vertical Rows (Abstracted from Report No. 60) U o Run No. Velocity ft. /sec. 206108A 6.10 206108B 6.11 206110A 6.04 206110B 6.04 206130A 5.99 206130B 5.99 206132A 6.04 206132B 6.00 206134A 5.99 206134B 6.00 206136A 6.01 206136B 6.02 LMTD oF 43 63 45 45 48 48 47 46 47 47 46 46 1 868 878 871 870 855 852 859 857 856 861 884 875 2 780 784 761 758 767 768 733 781 748 721 754 753 3 845 813 789 805 784 777 772 801 775 775 789 790 4 781 793 771 783 762 747 748 757 757 739 765 770 5 836 832 798 804 787 781 783 804 769 759 798 787 6 846 796 762 768 769 769 725 740 733 737 750 747 7 786 795 771 777 770 751 749 762 745 748 763 780

TABLE I-5 Cumulative Overall Heat Transfer Coefficients, UO, for Condensation of Steam at Water Velocity of 6.0 ft/sec on 1 to 7 1-inch Single-Start Corrugated 90-10 Cupro-Nickel Tubes in Three Vertical Rows (Abstracted from Report No. 60) 212~F with a U o Run No. Velocity ft. /sec. LMTD ~F 1 2 3 4 5 6 7 206108A 206108B 206110A 206110B 206130A 206130B,,I, 206132A 00 206132B 206134A 206134B 206136A 206136B 6.10 6.11 6.04 6.04 5.99 5.99 6.04 6.00 5.99 6.00 6.01 6.02 43 43 45 45 48 48 47 46 47 47 46 46 868 878 871 870 855 852 859 857 856 861 884 875 824 831 816 814 811 810 796 819 802 791 819 814 821 825 807 811 802 799 788 813 793 779 809 806 811 817 798 804 792 786 778 799 784 769 798 797 816 820 798 804 791 785 779 800 781 767 798 795 821 816 792 798 784 779 770 790 773 762 791 787 816 813 789 795 782 775 767 786 769 760 787 786

APPENDIX II Summary of the Calculated Cn, Individual Uo, and Cumulative Uo Values for the 1-inch Triple-Start 90-10 Cupro-Nickel Corrugated Tubes in a Single Vertical Row 59

TABLE II-1 Condensing Coefficient Correction Factor, C, for Condensation of Steam at 212~F on 1 to 7 1-inch Triple-Start Corrugate& Tubes in a Single Vertical Row C n Run No. Velocity LMTD 1 2 3 4 5 6 7 ft. /sec. F 206177A 3.55 42 1.38 1.45 1.52 1.55 1.57 1.57 1.58 206177B 3.55 42 1.37 1.46 1.51 1.55 1.56 1.57 1.58 206178A 3.56 39 1.58 1.58 1.62 1.63 1.63 1.63 1.63 206178B 3.56 39 1.50 1.51 1.55 1.57 1.58 1.58 1.59 206179A 3.56 41 1.54 1.53 1.57 1.59 1.59 1.59 1.60 206179B 3.57 41 1.55 1.54 1.57 1.58 1.59 1.59 1.60 206180A 3.54 39 1.50 1.50 1.53 1.55 1.57 1.58 1.58 206180B 3.54 39 1.50 1.50 1.55 1.57 1.58 1.58 1.58 206181A 3.53 41 1.51 1.54 1.60 1.62 1.64 1.64 1.65 206181B 3.53 41 1.52 1.54 1.59 1.61 1.62 1.63 1.64 206182A 3.56 41 1.37 1.46 1.53 1.56 1.57 1.57 1.57 206182B 3.56 41 1.40 1.48 1.53 1.57 1.58 1.59 1.60 O 206183A 3.56 42 1.28 1.36 1.43 1.50 1.51 1.52 1.54 206183B 3.56 41 1.25 1.35 1.42 1.47 1.49 1.50 1.52 206184A 3.58 41 1.27 1.36 1.43 1.46 1.48 1.49 1.51 206184B 3.58 41 1.25 1.36 1.43 1.47 1.49 1.50 1.51 206185A 3.56 42 1.26 1.38 1.45 1.49 1.49 1.50 1.51 206185B 3.56 42 1.24 1.36 1.43 1.46 1.45 1.48 1.49 206186A 3.58 43 1.27 1.37 1.45 1.48 1.45 1.46 1.47 206186B 3.58 43 1.26 1.37 1.43 1.45 1.48 1.50 1.51 206168A 6.01 41 1.51 1.56 1.64 1.68 1.70 1.71 1.72 206168B 6.01 41 1.51 1.54 1.63 1.67 1.69 1.71 1.73 206169A 6.01 42 1.49 1.56 1.62 1.67 1.69 1.71 1.70 206169B 6.01 42 1.47 1.54 1.62 1.67 1.70 1.71 1.72 206170A 6.02 44 1.46 1.54 1.61 1.67 1.70 1.71 1.72 206170B 6.02 44 1.50 1.58 1.65 1.69 1.70 1.71 1.72 206172A 6.01 43 1.48 1.53 1.62 1.66 1.69 1.71 1.72 206172B 6.01 43 1.45 1.53 1.62 1.66 1.69 1.71 1.72 206173A 6.00 39 1.47 1.53 1.61 1.66 1.69 1.71 1.72 206173B 6.00 39 1.48 1.54 1.62 1.66 1.70 1.72 1.72 206175A 6.01 42 1.46 1.54 1.63 1.68 1.72 1.73 1.74 206175B 6.01 42 1.46 1.53 1.62 1.67 1.70 1.72 1.73 206176A 5.99 40 1.56 1.56 1.61 1.65 1.70 1.72 1.73 206176B 5.99 40 1.57 1.59 1.64 1.67 1.71 1.73 1.74

TABLE II-2 Individual Tube Overall Heat Transfer Coefficients, U, for Condensation of Steam at 0 212~F on 1 to 7 1-inch Triple-Start Corrugated 90-10 Cupro-Nickel Tubes in a Single Vertical Row U o Run No. Velocity ft. /sec. 206177A 3.55 206177B 3.55 206178A 3.56 206178B 3.56 206179A 3.56 206179B 3.57 206180A 3.54 206180B 3.54 206181A 3.53 206181B 3.53 206182A 3.56 206182B 3.56 206183A 3.56 206183B 3.56 206184A 3.58 206184B 3.58 206185A 3.56 206185B 3.56 206186A 3.58 206186B 3.58 LMTD ~F 42 42 39 39 41 41 39 39 41 41 41 41 42 41 41 41 42 42 43 43 1 1144 1140 1228 1202 1206 1209 1197 1198 1188 1193 1151 1159 1109 1097 1114 1106 1101 1093 1103 1097 2 1018 1024 1052 1028 1024 1027 1021 1022 1032 1025 1027 1039 991 999 1000 1006 1015 1007 997 999 3 988 983 1017 995 989 986 980 999 1011 1004 1005 991 966 967 970 975 977 963 972 955 4 946 941 967 951 949 939 942 941 957 950 945 951 942 937 924 929 939 913 924 901 5 899 902 921 914 897 900 920 910 922 918 897 920 902 885 892 894 848 829 784 893 6 867 860 875 874 863 874 868 870 878 880 873 880 868 857 854 856 856 871 846 861 7 851 849 863 861 862 863 862 857 872 876 829 850 865 852 847 842 837 841 824 832 HN H 206168A 206168B 206169A 206169B 206170A 206170B 206172A 206172B 206173A 206173B 206175A 206175B 206176A 206176B 6.01 6.01 6.01 6.01 6.02 6.02 6.01 6.01 6.00 6.00 6.01 6.01 5.99 5.99 41 1418 41 1416 42 1402 42 1393 44 1376 44 1395 43 1390 43 1378 39 1410 39 1415 42 1389 42 1387 40 1447 40 1448 1210 1194 1214 1207 1196 1215 1192 1204 1214 1221 1217 1203 1187 1216 1197 1203 1170 1189 1175 1182 1186 1186 1201 1201 1195 1199 1164 1167 1151 1127 1138 1143 1141 1128 1120 1124 1147 1147 1155 1143 1142 1133 1064 1095 1081 1083 1077 1050 1087 1093 1118 1118 1109 1098 1120 1121 1058 1063 1045 1053 1037 1032 1051 1053 1074 1070 1051 1062 1086 1073 1015 1036 944 1010 992 985 1010 1012 1019 1020 1011 1014 1023 1011

TABLE II-3 Cumulative Overall Heat Transfer Coefficients, U, for Condensation of Steam at 1 to 7 1-inch Triple-Start Corrugated 90-10 Cupro-Nickel Tubes in Multiple Verti( 212~F on cal Rows U o Run No. Velocity ft. /sec. LMTD ~F 1 2 3 4 5 6 7 206187A 206187B 206188A 206188B 206189A 206189B 206190A 206190B 206191A 206191B 206192A 206192B 206193A 206193B 206194A 206194B 206195A 206195B 206196A 206196B ON Ix) 3.35 3.35 3.32 3.33 3.34 3.34 3.31 3.31 3.31 3.32 3.21 3.21 3.21 3.21 3.18 3.21 3.23 3.23 3.21 3.21 6.13 6.14 6.14 6.12 6.15 6.16 6.15 6.15 6.16 6.16 6.15 6.15 6.12 6.12 41 1126 41 1162 39 1145 39 1155 40 1171 40 1164 38 1177 38 1176 41 1158 41 1158 38 1152 38 1163 39 1157 40 1154 38 1144 38 1144 40 1148 40 1147 39 1155 39 1153 42 1386 42 1378 43 1339 43 1378 46 1428 46 1434 45 1442 45 1445 46 1448 46 1445 45 1449 45 1454 42 1451 42 1444 1076 1104 1100 1097 1110 1105 1118 1108 1104 1101 1096 1101 1096 1098 1087 1091 1092 1091 1102 1098 1309 1308 1281 1298 1320 1331 1334 1337 1336 1329 1345 1344 1350 1345 1063 1073 1070 1066 1088 1080 1079 1076 1070 1067 1063 1066 1063 1066 1056 1060 1058 1059 1047 1058 1282 1279 1254 1266 1279 1288 1291 1296 1294 1285 1298 1294 1305 1310 1048 1056 1055 1053 1066 1056 1060 1058 1050 1049 1047 1051 1046 1051 1043 1045 1043 1045 1036 1041 1264 1251 1235 1240 1250 1261 1264 1270 1275 1265 1272 1270 1285 1286 1022 1029 1028 1026 1051 1038 1043 1043 1032 1038 1032 1036 1031 1032 1031 1031 1026 1029 1024 1028 1251 1231 1213 1222 1223 1236 1238 1246 1262 1245 1261 1261 1266 1271 1012 1019 1019 1016 1037 1025 1030 1032 1020 1020 1019 1023 1017 1019 1019 1019 1014 1016 1011 1016 1239 1217 1201 1208 1212 1221 1226 1230 1244 1228 1241 1239 1249 1256 1003 1007 1007 1003 1024 1013 1019 1022 1009 1009 1006 1012 997 1006 1009 1010 1002 1006 998 1004 1225 1204 1189 1195 1194 1203 1209 1213 1225 1210 1223 1221 1231 1237 206199A 206199B 206200A 206200B 206201A 206201B 206202A 206202B 206203A 200203B 206204A 206204B 20620-5A 206205B

APPENDIX III Summary of the Calculated Cn, Individual Uo, and Cumulative Uo Values for the Center Row of 1-inch Triple-Start 90-10 Cupro-Nickel Corrugated Tubes in Three Vertical Rows 63

TABLE III-1 Condensing Coefficient Correction Factor, C, for Condensation of Steam at 212~F on 1 to 7 1-inch Triple-Start CorrugatedlTubes in Multiple Vertical Rows C n Run No. Velocity LMTD 1 2 3 4 5 6 7 ft. /sec. F 206187A 3.35 41 1.38 1.49 1.61 1.67 1.68 1.73 1.76 206187B 3.35 41 1.49 1.58 1.64 1.70 1.71 1.75 1.78 206188A 3.32 39 1.42 1.55 1.61 1.68 1.69 1.73 1.76 206188B 3.33 39 1.45 1.54 1.60 1.67 1.68 1.72 1.74 206189A 3.34 40 1.51 1.59 1.68 1.73 1.78 1.81 1.83 206189B 3.34 40 1.49 1.58 1.66 1.70 1.73 1.77 1.80 206190A 3.31 38 1.51 1.59 1.63 1.68 1.72 1.76 1.79 216190B 3.31 38 1.51 1.56 1.62 1.68 1.72 1.76 1.80 206191A 3.31 41 1.48 1.57 1.63 1.68 1.72 1.75 1.78 206191B 3.32 41 1.48 1.57 1.62 1.68 1.72 1.76 1.79 206192A 3.21 38 1.47 1.56 1.61 1.68 1.72 1.75 1.78 206192B 3.21 38 1.51 1.57 1.62 1.69 1.73 1.77 1.80 206193A 3.21 39 1.51 1.57 1.63 1.69 1.74 1.77 1.76 206193B 3.21 40 1.50 1.59 1.65 1.71 1.74 1.78 1.80 206194A 3.18 38 1.45 1.53 1.59 1.66 1.71 1.75 1.78 206194B 3.21 38 1.45 1.54 1.60 1.67 1.71 1.75 1.79 206195A 3.23 40 1.47 1.56 1.61 1.68 1.71 1.75 1.77 206195B 3.23 40 1.47 1.55 1.61 1.68 1.72 1.76 1.79 206196A 3.21 39 1.48 1.58 1.66 1.64 1.69 1.73 1.75 206196B 3.21 39 1.47 1.56 1.60 1.66 1.71 1.74 1.77 206199A 6.13 42 1.45 1.55 1.65 1.73 1.80 1.85 1.89 206199B 6.14 42 1.43 1.55 1.65 1.70 1.75 1.80 1.83 206200A 6.14 43 1.36 1.50 1.60 1.68 1.72 1.77 1.81 206200B 6.12 43 1.44 1.54 1.63 1.69 1.74 1.79 1.83 206201A 6.15 46 1.60 1.64 1.72 1.78 1.82 1.86 1.89 206201B 6.16 46 1.58 1.62 1.69 1.75 1.78 1.84 1.86 206202A 6.15 45 1.59 1.64 1.71 1.77 1.80 1.86 1.88 206202B 6.15 45 1.60 1.64 1.72 1.78 1.82 1.87 1.90 206203A 6.16 46 1.62 1.65 1.73 1.81 1.88 1.92 1.94 206203B 6.16 46 1.61 1.64 1.70 1.78 1.83 1.87 1.90 206204A 6.15 45 1.61 1.66 1.72 1.79 1.86 1.90 1.92 206204B 6.15 45 1.62 1.66 1.71 1.78 1.86 1.89 1.92 206205A 6.12 42 1.56 1.62 1.71 1.78 1.85 1.89 1.92 206205B 6.12 42 1.58 1.64 1.70 1.78 1.84 1.88 1.90

TABLE III-2 Individual Tube Overall Heat Transfer Coefficients, U, for Condensation of Steam at 212~F on 1 to 7 1-inch Triple-Start Corrugated 90-10 Cupro-Iickel Tubes in Multiple Vertical Rows U 0 Run No. Velocity LMTD 1 2 3 4 5 6 7 ft. /sec. F 206187A 3.35 41 1126 1026 1037 1003 918 962 949 206187B 3.35 41 1162 1046 1011 1005 921 969 935 206188A 3.32 39 1145 1055 1010 1010 920 974 935 206188B 3.33 39 1155 1039 1004 1014 918 966 925 206189A 3.34 40 1171 1049 1044 1000 991 967 946 206189B 3.34 40 1164 1046 1030 984 966 960 941 206190A 3.31 38 1177 1059 1001 1003 965 975 953 206190B 3.31 38 1176 1040 1012 1004 983 977 962 206191A 3.31 41 1158 1050 1002 990 960 960 943 206191B 3.32 41 1158 1044 999 995 969 955 943 206192A 3.21 38 1152 1040 997 1003 968 954 928 OC 206192B 3.21 38 1163 1039 996 1006 976 958 946 206193A 3.21 39 1157 1035 997 995 971 947 877 206193B 3.21 40 1154 1042 1002 1006 956 954 928 206194A 3.18 38 1144 1030 994 1004 983 959 949 206194B 3.21 38 1144 1038 998 1000 975 959 956 206195A 3.23 40 1148 1036 990 998 958 954 930 206195B 3.23 40 1147 1045 995 1003 965 951 946 206196A 3.21 39 1155 1049 937 1003 976 946 920 206196B 3.21 39 1153 1043 978 990 976 956 932 206199A 6.13 42 1386 1232 1228 1210 1199 1189 1141 206199B 6.14 42 1378 1238 1221 1167 1151 1147 1126 206200A 6.14 43 1339 1223 1200 1178 1125 1141 1117 206200B 6.12 43 1378 1218 1202 1162 1150 1138 1117 206201A 6.15 46 1428 1212 1197 1163 1115 1157 1086 206201B 6.16 46 1434 1228 1202 1180 1136 1146 1095 206202A 6.15 45 1442 1226 1205 1183 1134 1166 1107 206202B 6.15 45 1445 1229 1214 1192 1150 1150 1111 206203A 6.16 46 1448 1224 1210 1219 1210 1154 1114 206203B 6.16 46 1445 1213 1197 1205 1165 1143 1102 206204A 6.15 45 1449 1231 1214 1194 1217 1141 1115 206204B 6.15 45 1454 1234 1194 1198 1225 1129 1113 206205A 6.12 42 1451 1249 1215 1225 1190 1164 1123 206205B 6.12 42 1444 1246 1240 1214 1211 1181 1123

TABLE III- 3 Cumulative Overall Heat Transfer Coefficients, U, for Condensation of Steam at 212~F on 1 to 7 1-inch Triple-Start Corrugated 90-10 Cupro-Nickel Tubes in a Single Vertical Row U 0 Run No. Velocity LMTD 1 2 3 4 5 6 7 ft. /sec. ~F 206177A 3.55 42 1144 1081 1050 1024 999 977 959 206177B 3.55 42 1140 1082 1049 1022 998 975 957 206178A 3.56 39 1228 1140 1099 1066 1037 1010 989 206178B 3.56 39 1202 1115 1075 1044 1018 994 975 206179A 3.56 41 1206 1115 1073 1042 1013 988 970 206179B 3.57 41 1209 1118 1074 1040 1012 989 971 206180A 3.54 39 1197 1109 1066 1035 1012 988 970 206180B 3.54 39 1198 1110 1073 1040 1014 990 971 206181A 3.53 41 1188 1110 1077 1047 1022 998 980 206181B 3.53 41 1193 1109 1074 1043 1018 995 978 206182A 3.56 41 1151 1089 1061 1032 1005 983 961 206182B 3.56 41 1159 1099 1063 1035 1012 990 970 o\ 206183A 3.56 42 1109 1050 1022 1002 982 963 949 206183B 3.56 41 1097 1048 1021 1000 977 957 942 206184A 3.58 41 1114 1057 1028 1002 980 959 943 206184B 3.58 41 1106 1056 1029 1004 982 961 944 206185A 3.56 42 1101 1058 1031 1008 976 956 939 206185B 3.56 42 1093 1050 1021 994 961 946 931 206186A 3.58 43 1103 1050 1024 999 954 936 920 206186B 3.58 43 1097 1048 1017 988 969 951 934 206168A 6.01 41 1418 1314 1275 1244 1208 1183 1159 206168B 6.01 41 1416 1305 1271 1235 1207 1183 1162 206169A 6.01 42 1402 1308 1262 1231 1201 1175 1142 206169B 6.01 42 1393 1300 1263 1233 1203 1178 1154 206170A 6.02 44 1376 1286 1249 1222 1193 1167 1142 206170B 6.02 44 1395 1305 1264 1230 1194 1167 1141 206172A 6.01 43 1390 1291 1256 1222 1195 1171 1148 206172B 6.01 43 1378 1291 1256 1223 1197 1173 1150 206173A 6.00 39 1410 1312 1275 1243 1218 1194 1169 206173B 6.00 39 1415 1318 1279 1246 1220 1195 1170 206175A 6.01 42 1389 1303 1267 1239 1213 1186 1161 206175B 6.01 42 1387 1295 1263 1233 1206 1182 1158 206176A 5.99 40 1444 1317 1266 1235 1212 1191 1167 206176B 5.99 40 1448 1332 1277 1241 1217 1193 1167

APPENDIX IV Computer Output from the Program in Appendix V, Pages 162-167, of Report No. 60, Which Calculates the Point Values of Uo, hcond, hi and Q, Using the Equations Presented in Table 3 For Steam Condensing at 212~F on 1-inch Bare Tubes 67

TABLE IV- 1 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steaming Condensing at 212~F, Without Fouling, Using Equation (3) CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE DESIGNATION TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DIAMETER (INCHES) TUBE THERMAL CONDUCTIVITY (BTU/HB-FT-F) 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 TEMPERATUBE (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" BARE 1.00200 0.90080 26.00000 0.26232 0.23583 0.0044257 0. 001622 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 UBES % % RES.% % BTU/HR LB/HR 10 1.58 1015.0 3542.1 28.7% 2091.2 54.0% 17.4% 0.0% 1597.6 1.64 15 1.70 1003.5 3405.8 29.5% 2091.2 53.4% 17.2% 0.0% 1579.5 1.62 20 1.78 994.1 3300.0 30.1% 2091.1 52.9% 17.0% 0.0% 1564.6 1.61 25 1.85 987.8 3231.6 30.6% 2091.0 52.5% 16.9% 0.0% 1554.7 1.60 30 1.91 982.6 3176.7 30.9% 2091.0 52.3% 16.8% 0.0% 1546.5 1.59 68

TABLE IV-2 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steaming Condensing at 212~F, Without Fouling, Using Equation (7) CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE DESIGNATION 1" BARE TUBE OUTSIDE DIAMETER (INCHES) 1.00200 TUBE INSIDE DIAMETER (INCHES) 0.90080 TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) 26.00000 OUTSIDE HEAT TRANSFER AREA (SQFT/FT) 0.26232 INSIDE HEAT TRANSFER AREA (SQFT/FT) 0.23583 FLOW AREA (SQFT) 0.0044257 METAL RESISTANCE (HI/SQFT-F-BTU) 0.0001622 INSIDE SIEDER-TATE CONSTANT 0.02642 FOULING FACTOR (HR-SQFT-F/BTU) 0.0 VAPOR TEMPERATURE (DEG. F) 212.00 LINEAR VELOCITY OF BRINE(FT/SEC) 6.00 MASS VELOCITY OF BRINE (LBS/HR) 5936.61 BRINE TEMPERATURE (DEG. F) 206.00 REYNOLDS NUMBER 129592.31 PRANDTLS NUMBER 1.91 CONSTANT FOR CN: A 1.2200 POWER OF CN: B 0.0895 NO CN UO HCOND HCOND HI HI MET. FOULING Q Q/LAT TUBES X X% RES.% s BTU/HR LB/HR 10 1.50 994.5 3305.0 30.1% 2091.1 52.9% 17.0% 0.0% 1565.3 1.61 15 1.55 971.3 3062.1 31.7% 2091.0 51.7% 16.6% 0.0% 1528.8 1.57 20 1.60 953.6 2893.0 33.0% 2090..8 50.7% 16.3% 0.0% 1500.9 1.54 25 1.63 942.3 2791.2 33.8% 2090.9 50.1% 16.1% 0.0% 1483.1 1.53 30 1.65 930.3 2688.9 34.6% 2090.8 49.5% 15.9% 0.0% 1464.3 1.51 69

TABLE IV- 3 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steaming Condensing at 212~F, With 0. 0005 Fouling, Using Equation (3) CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE DESIGNATION TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DIAMETER (INCHES) TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) 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 NUMBEB PRANDTLS NUMBER CONSTANT FOR CN: A POWER OF CN: B 1" BARE 1.00200 0.90080 26.00000 0.26232 0.23583 0.0044257 0.0001622 0. OUb42 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 % % RES.% % BTU/HR LB/HR 10 1.58 688.3 4009.8 17.2% 2089.2 36.6% 11.8% 34.4% 1083.4 1.11 15 1.70 683.5 3850.8 17.7% 2089.2 36.4% 11.7% 34.2% 1075.8 1.11 20 1.78 680.0 3741.9 18.2% 2089.2 36.2% 11.6% 34.0% 1070.2 1.10 25 1.85 677.2 3659.7 18.5% 2089.2 36.1% 11.6% 33.9% 1065.9 1.10 30 1.91 674.9 3593.9 18.8% 2089.2 35.9% 11.5% 33.7% 1062.3 1.09 70

TABLE IV-4 Calculated Point Values for 1-inch Bare 90-10 Cupro-Nickel Tubes With Steaming Condensing at 212~F, With 0. 0005 Fouling, Using Equation (7) CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE DESIGNATION TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DIAMETER.(INCHES) TUBE THERMAL CONDUCTIVITY (BTU/Hi-FT-F) 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 CNR: _ B 1" BARE 1.00200 0.90080 26.00000 0.26232 0.23583 0.0044257 0.0001622 0.02642 0.00050 212.00 6.00 5936.61 206.00 129592.31 1.91 1.2200 0.0895 NO CN UO HCOND HCOND HI HI MET. FOULING Q Q/LAT T BES % % RES. X BTU/aR LB/HR 10 1.50 680.2 3747.9 18.1% 2089.2 36.2% 11.6% 34.0% 1070.6 1.10 15 1.55 669.9 3456.6 19.4% 2089.1 35.7% 11.5% 33.5% 1054.4 1.08 20 1.60 662.4 3264.3 20.3% 2089.1 35.3% 11.3% 33.1% 1042.5 1.07 25 1.63 656.3 3122.9 21.0% 2089.1 34.9% 11.2% 32.8% 1033.0 1.06 30 1.65 651.3 3012.1 21.6% 2089.1 34.7% 11.1% 32.6% 1025.1 1.05 71

APPENDIX V Computer Output from the Program in Appendix V, Pages 162-167, of Report No. 60, Which Calculates the Point Values of Uo, hcond, hi and Q, For Steam Condensing at 212~F on Hypothetical 1-inch Single-Start and on The Triple-Start Corrugated 90-10 Cupro-Nickel Tubes 73

TABLE V- 1 Calculated Point Values for The Hypothetical 1-inch Single-Start Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, Without Fouling Using Table 4 CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE DESIGNATION TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DDIAMETER (INCHES) TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) 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 HYPO 1" 1-START KORO 0.99000 0.91320 26.00000 0.25918 0.23908 0.0045484 0.0001231 0.05500 0.0 212.00 3.50 3559.02 206.00 76636.13 1.91 1.5050 0.2040 NO CN JO HCOND HCOND HI HI MET. FOULING Q Q/LAT r UBES % % RES.% % BTU/HR LB/HR 10 2.41 1442.4 5528.9 26.1% 2821.0 55.4% 18.5% 0.0% 2243. 2.31 15 2.61 1433.8 5404.8 26.5% 2821.0 55.1% 18.4% 0.0% 2229.7 2.29 20 2.77 1427.7 5318.4 26.8% 2821.0 54.9% 18.3% 0.0% 2220.2 2.28 25 2.90 1422.9 5252.4 27.1% 2820.9 54.7% 18.2% 0.0% 2212.7 2.28 30 3.01 1418.9 5199.1 27.3% 2820.9 54.5% 18.2% 0.0O 2206.6 2.27 74

TABLE V-2 Calculated Point Values for The 1-inch Triple-Start Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, Without Fouling Using Table 2 and Equation (13) CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE DESIGNATION 1" 3-START KORO TUBE OUTSIDE DIAMETER (INCHES) 0.99000 TUBE INSIDE DIAMETER (INCHES) 0.91320 TUBE THERMAL CCNDLCTIVITY (BTU/HR-FT-F) 26.00000 OUTSIDE HEAT TRANSFER AREA (SQFT/FT) 0.25918 INSIDE HEAT TRANSFER AREA (SQFT/FT) 0.23908 FLOW AREA (SQFT) 0.0045484 METAL RESISTANCE ( hR/SQFT-F-eTU) 0.0001231 INSIDE SIEDER-TATE CONSTANT 0.05058 FOULING FACTOR (HR-SCFT-F/BTU) 0.0 VAPOR TEMPERATURE (DEG. F) 212.00 LINEAR VELCCITY CF BPINE(FT/SEC) 3.50 MASS VELOCITY OF BRINE (LBS/HR) 3559.C2 BRINE TEMPERATURE (DEG. F) 206.CC REYNOLDS NUMBER 76636.13 PRANDTLS NUMBER 1.91 CONSTANT FOR CN: A 1.4800 POWER OF CN: B 0.1050 NO CN UO HCOND HCCND HI HI MET. FOULING Q C/LAT TUBES % X RES.2 % BTU/HR LB/HR 10 1.88 1270.9 4152.6 30.6% 2594.0 53.1% 16.3% 0.0% 1976.3 2.03 15 1.97 1243.7 3E76.1 32.1% 2593.9 52.02 15.92 C0% 1934.1 1.99 20 2.03 1223.6 3687.4 33.2% 2593.8 51.1% 15.72 0.02 19C2.8 1.96 25 2.08 1208.6 3554.7 34.0% 2593.7 50.5% 15.5% 0.0% 1879.5 1.93 30 2.12 1195.9 3446. 34.7% 2593.7 50.0% 15.3% 0.0% 1859.7 1.91 75

TABLE V-3 Calculated Point Values for The Hypothetical 1-inch Single-Start Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, With 0. 0005 Fouling Using Table 4 CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE DESIGNATION TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DIAMETER (INCHES) TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) 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 HYPO 1" 1-START KORO 0.99000 0.91320 26.00000 0.25918 0.23908 0.0045484 0.0001231 0.05500 0.00050 212.00 3.50 3559.02 206.00 76636.13 1.91 1.5050 0.2040 NO CN UO HCOND HCOND HI HI MET. FOULING Q Q/LAT r UBES % % RES.% % BTU/HR LB/HR 10 2.41 857.5 6521.5 13.1% 2817.5 33.0% 11.0k 42.9% 1333.4 1.37 15 2.61 854.8 6369.6 13.4% 2817.5 32.9% 11.0% 42.7% 1329.3 1.37 20 2.77 852.9 6264.3 13.6% 2817.5 32.8% 10.9% 42.6% 1326.3 1.36 25 2.90 851.4 6184.0 13.8% 2817.4 32.8% 10.9% 42.6% 1323.9 1.36 30 3.01 850.1 6118.7 13.9% 2817.4 32.7% 10.9% 42.5% 1322.0 1.36 76

TABLE V-4 Calculated Point Values for The 1-inch Triple-Start Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, With 0. 0005 Fouling Using Table 2 and Equation (13) CALCULATICNS CF THE PCINT VALUES OF UC ANE HCCNDO TUBE UOESIGNATIIUN TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DIAMETER (INCHES) TUBE THERMAL CONUCCTIVITY (BTU/HR-FT-F) OUTSIDE HEAT TRANSFER AREA (SQFT/FT) INSIDE HEAT TRANSFER AREA (SQFT/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F —eTU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT-F/BTU) VAPOR TEMPERATURE IDEG. F) LINEAR VELOCITY OF BRINE(FT/SEC) MASS VELCCITY OF BRINE (LBS/hR) BRINE TEMPERATURE (DEG. F) 1" 3-START KORG 0,99000 0.91320 26.000CC 0.25918 0.239C8 0.0045484 0.0001231 0.05058 0.00050 212.00 3.50 3559.C2 206.00 REYNOLDS NUMBER PRANDTLS NUMBER CONSTANT FOR CN: A ffnf;r~n nir f'#,* n 76636.13 1.91 1 4800 n It C f t:buw t Ut- LIN t Us. IUVV NO CN U HCCND HCCND HI tFI MET. FOULING Q, Q/LAT TUBES % % RES.% % 8TU/HR LB/HR 10 1.88 797.9 4835.4 16.5% 2591.2 33.14 1C.2% 39.9% 1240.8 1.28 15 1.97 788.C 4493.1 17.5% 2591.2 33.0% 1C.1% 39.4% 1225.4 1.26 20 2.03 78C.7 4265.5 18.3% 2591.1 32.7t 1C.C% 39.0% 1214.0 1.25 25 2.08 774.9 4097.2 18.9% 2591.1 32.4% S.9% 38.7% 1205.0 1.24 30_ 2. 12 770.0 3964.9 19.4% 2591.1 32.2 9.9S 38.5% 1'197.4 1.23 77

APPENDIX VI Computer Output from the Program in Appendix V, Pages 162-167, of Report No. 60, Which Calculates the Point Values of Uo, hcond, hi and Q, For a Hypothetical 1-inch Triple-Start Corrugated Tube Having the Same O.D. and I. D. as The Single-Start Corrugated Tubes of Report No. 60 79

TABLE VI-1 Calculated Point Values for The 1-inch Single-Start Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, Without Fouling Using Equation (4) CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE DESIGNATION 1" 1-START KORO TUBE OUTSIDE DIAMETER (INCHES) 0.93700 TUBE INSIDE DIAMETER (INCHES) 0.82200 TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) 26.00000 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 0.05786 FOULING FACTOR (HR-SQFT-F/BTU) 0.0 VAPOR TEMPERATURE (DEG. F) 212.00 LINEAR VELOCITY OF BRINE(FT/SEC) 3.50 MASS VELOCITY OF BRINE (LBS/HR) 2883.65 BRINE TEMPERATURE (DEG. F) 206.00 REYNOLDS NUMBER, 68982.63 PRANDTLS NUMBER 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 T UBES % RES.% % BTU/HR LB/HR 10 2.31 1324.6 5491.8 24.1% 3029.9 49.8% 26.0% 0.0% 1949.6 2.01 15 2.51 1317.1 5365.3 24.5% 3029.9 49.6% 25.9% 0.0% 1938.6 1.99 20 2.66 1311.7 5277.1 24.9% 3029.9 49.4% 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% 0.0% 1919.4 1.97 80

TABLE VI- 2 Calculated Point Values for The Hypothetical 1-inch Triple-Start Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, Without Fouling Using Equation (13) CALCULATICNS OF THE POINT VALUES CF UC AND HCCND. TUBE DESIGNATICN HYPO 1" 3-START KCRC TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DIAMETER (INCFES) TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) OUTSIDE HEAT TRANSFER AREA (SQFT/FT) INSIDE HEAT TRANSFER AREt (SCFT/FT) FLCW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-8TU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SCFT-F/BTU) VAPOR TEMPERATURE (DEG. F) LINEAR VELECITY CF ERINE(FT/SEC) MASS VELOCITY CF BRINE (LBS/HP) BRINE TEMPERATURE (DEC. F) REYNOLDS NUMBER PRANDTLS NUMBER CONSTANT FOR CN: A PCWER CF CN: B 0.9370C 0.8220C 26.000OC 0. 24 5 3 1 0.2152C 000.036853 C.00 C 1843 0..05058 212.00 3.50 2883.65 206.00 68982.63 1.91 1. 4800 0. 1050 NO CN UC HCCNk HCCND H I F lET. FOULING C C/LAT TUBES % % RE S.% BTU/HR LB/HR 10 1.88 1167.9 4361.1 26.8t 2648.8 50.3% 23.C% C. O' 1718.S 1.77 15 1.97 1145.1 4C6C.5 2e.2% 2648.7 49.31 22.5% 0.0% 1685.4 1.73 20 2.03 1128.6 3860.6 29.2% 2648.6 48.6% 22.2% 0.0% 1661.2 1.71 25 2.08 1114.3 3698.7 3C.1% 2648.4 48.Q0 21.S% 0.0% 1640.1 1.69 30 2.12 1103.8 3585.6 3C.8% 2648.4 47.5% 21.7% 0.0% 1624.7 1.67 81

TABLE VI-3 Calculated Point Values for The 1-inch Single-Start Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, With 0. 0005 Fouling Using Equation (4) CALCULATIONS OF THE POINT VALUES OF UO AND HCOND. TUBE DESIGNATION TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DIAMETER (INCHES) TUBE THERMAL CONDUCTIVITY (BTU/HR-FT-F) 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" 1-START KORO 0.93700 0.82200 26.00000 0.24531 0.21520 0.0036853 0.0001843 0.05786 0.00050 212.00 3.50 2883.65 206.00 68982.63 1.91 1.4500 0.2030 NO CN UO HCOND HCOND HI HI MET. FOULING Q Q/LAT rUBES % % 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% 15.9k 40.5% 1191.0 1.2.2 25 2.79 807.8 6070.1 13.3% 3026.6 30.4% 15.9% 40.4% 1188.9 1.22 30 2.89 806.6 6 004.9 13.4% 3026.6 30.4% 15.9k 40. 3% 1187.2 1.22 82

TABLE VI-4 Calculated Point Values for The Hypothetical 1-inch Triple-Start Corrugated 90-10 Cupro-Nickel Tubes With Steam Condensing at 212~F, With 0. 0005 Fouling Using Equation (13) CALCULATICNS OF THE POINT VALUES CF UC ANC HCONC. TUBE DESIGNATION TUBE OUTSIDE DIAMETER (INCHES) TUBE INSIDE DIAMETER (INCHES) TUBE THERMAL CONCUCTIVITY (BTU/HR-FT-F) OUTSIDE HEAT TRANSFER AREA (SQFT/FT) INSIDE HEAT TRANSFER AREA (SQFT/FT) FLOW AREA (SQFT) METAL RESISTANCE (HR/SQFT-F-8TU) INSIDE SIEDER-TATE CONSTANT FOULING FACTOR (HR-SQFT-F/BTU) VAPOR TEMPERATURE (CEG. F) LINEAR VELOCITY OF BRINE(FT/SEC) MASS VELCCITY CF BRINE (LBS/hR) BRINE TEMPERATURE (DEG. F) HYPO 1" 3-START KCRC 0.9370C 0.8 2200 26.00000 0.24531 0.21520 0.0036853 0.0001843 0.05058 0.00050 212.CC 3.50 2883.65 206.00 REYNOLDS NUMBER 68982.63 PRANCTLS NUMBER 1.91 CONSTANT FOR CN: A 1.4800 POWER OF CN: B 0.1050 NO CN UO HCONC HCONC HI HI MET. FOULING Q Q/LAT TUBES % % RES.% % BTU/HR LB/HR 10 1.88 753.6 5013.3 15.0% 2646.1 32.5% 14.8% 37.7% 1109.3 1.14 15 1.97 745.1 4656.9 16.0% 2646.1 32.1% 14.6% 37.3% 1096.6 1.13 20 2.03 738.7 4420.0 16.7% 2646.1 31.8% 14.5% 36.9% 1CE7.3 1.12 25 2.08 733.7 4244.9 17.3% 2646.1 31.6% 14.4% 36.7% 1079*9 1.11 30 2.12 729.5 41C7.2 17.8% -. - -. -'T-,....... 7 2646.0 31.42 14.3% 36.5% 1C73.6 1.1C 85

APPENDIX VII Computer Program for Condenser Stage Design Calculations 85

c.CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCcccccccccccccccccccccccccccccCCC C C C STEAM CONDENSER DESIGN PROGRAM C C C cccccccccccccccccccccccCcccccccccccccccccccccccccccccccccccccccccccccccccccccccC C A SUBROUTINE TO TEST THE DIFFERENCE BETWEEN VARIABLES IN C SU(CCESSIVE TRIALS. C LOGICAL TEST TEST(ARG1, ARG2) = ABS((ARG1-ARG2)/ARG1).LT..00025 C 100 READ(2 22)TUNO, T.JBTYPALLOY, 1 STCDI AI,XNXNTFRWF,DO,_ 1 TAO,PW, Z TW1,TW2, DPT, BPT 1_] A.__ AT BRUNWR BETAVNO. XRJN = 15. 0 WRITE (3,41) WRITE (3,71) WRITE (3,72) WRITE (3,74) WRI T(3,42)TUNOSTCTUBTYP,A, ALLOYB,DO,VN,DI,XNAI,XNTNAO,Z, 1 WF PW T, FR WR, TW1 WRITE( 373 ) TW2 DPT, BPT, Q WRITE (3,77) WR I TE ( 3 * 7 7 ) WRITE( 3,75 ) DIM = 1.273238/(DI-'DI ) 131 XMR=(( (DO-)I )/2.0) DO) /(T*(DO+DI)/2.0) AIXNT = AI XNT AOXNT = A;: XNT TWA=( TW 1+TW2 )/2.0 X=. 0/TWA DEN=64.7 291+0. 236 1E-2 WTWA-. 9615E-4*TW A"'TWA+0. 1292E- 6TW A::' 3. 0 1-0.9 06 1E -10' TW A' -:4.0 SRHO=1. 0/DEN CPW AT= 0.9358 +0. 2130E-4* TW A+0.4006hE -6- TW A' TWA-0. 2378 E-9:: TW A':'* 3.0 CWAT=0. 2788+0. 1305E-2':TWA-0. 8 109E-5:'TWA':-TWA+0. 38 32E-7':TW A':3. 0 1-0. 1088E-9': TWA'-*4. 0+0. 1221E-12*TWA".* 5.0 VI SWAT=-0. 1293+0. 1592E3'X+0. 686 E4 X -'XX-0. 8692E 5X'' X 3. 0-0. 4072E8 1' X:.-'4 0+0+ 15 59 E 1 0'-' X' 5 0 RFI=0.0 S = DPT - TVW2 E = BPT-T J1 TDLM = (E-S)/ALOG(E/S) WT = O'XN/((TW2-TW1 )-XNT CPWAT) TW T=( W T/1000 0 ): ( XNT/X N ) G = WT': DIM RE = DI:- G / I SWAT PR = CPWAT'VI SWAT/COAT HII = CWAT STC / QI::(RE*O.8 )*(PR**0.3333) ALPHA = HII VEL=( G'SRHO )/3600.0 DO 7 J=1 200 38 AOTI= BETA AOXNT UtI =Q/( AOTI -: TDLM) AIT = BETA A AIXNT DO 3 I=1, 90 VISWAW = VISANY(TWA + /( AIT* ALPHA ) HIl = HII"'((VISWAT/VISWAW)**0.14) IF (TEST(ALPHA, HI1)) GO TO 4 3 ALPHA = HI1 86

GO TO 12 4 CONTINUE W = AO/AI HI=HI 1 GAMMA = 1.0/(1.O/UOI - FR - W/HI -XMR) IF (GAMMA.LT.O.O) GO TO 36 GO TO 37 36 BETA = BETA + 1.0 GO TO 38 _ 37 DELTF = (UOI TDLM)/GAMi, A TF=ABS((DPT-O.50*DELTF)) VAPOH=1095. 2-0.58*TF PHP=( TF*O. 360452 )" 0.62 0385 CN = A*VN**B HC1=0.725*CN*PHP*((VAPOH/(DO*DELTF*VN ))**0.25 )142.92 IUO = 1.O/(XMR + W/HI + 1.O/HC1 + FR) JnII =UO AOT = Q/(UO*TDLM) TL1 = AOT/AOXNT UO A=UO*AO IF (TEST(BETA, TL1)) GO TO 9 7 BETA = TL1 12 WRITE (3, 31) REVELRUNI GOTO100 9 FF = Z/RE**PW P T=FF*V\EL*VEL*TL1/(9273.6*DI*SRHO) PF=PT/( TL1*XN) TL T=TL1*XNT TTW T=TLT*WF WRITE (3,79) WRITE (3, 10) WRITE (3, 121)REHI1IUOTDLMHC1,AOTTLVEL,UOAO,RUN WRITE (3t50) WRITE (3,51) WTCWATVISWATPR,SRHO,DELTF,TF,PHP,CN,XMR WRITE(3,52) WRITE(3,53 )PT, PF,TLT TTWT, TWT IF( RUN.LT.XRUN)GOTO0100 C INPUT AND OUTPUT FORMATS C 22 FORMAT( I 106XA4,6X,A4/8F10.5/8F10.5/6F10.5,F10.1) 41 FORMAT(1H1,25X,'VAPOR CONDENSING PROGRAM —-— TUBE LENGTH IS A VAR I ABLE' ) 71 FORMAT(1H,25X,'BASIS -— SIEDER-TATE EQUATION FOR TUBESIDE TRANS 1FER COEFFICIENT') 72 FORMAT( 1HO,'FLUID.. SHELL SIDE —CONDENSING STEAM'/ 1'FLUI D...TIJBE SIDE —5% BRINE') 74 FORMAT (1HO,83HTUBE CHARACTERISTICS 1 INPUT DATA AND CONSTANTS) 42 FORMAT( 1HO,'TUNO, TUBE DESIGNATION NO. =',I10,12X, I'STC, SIEDER-TATE CONSTANT =',F10.5/ 1'TJUBTYP, TUBE TYPE =',6X,A4, 12X, __ __1 _'A, CONSTANT IN CN EOUATION =',F10.5/ 1'ALLOY, ALLOY DESIGNATION =',6X,A4,12X, __1 ___'B, POWER IN CN EQUATION =',F10.5/ 1'DO, OUTSIDE DIAMETER, FT. =',F10.5,12X, 1'VN T NO. OF TUBES IN VERTICAL ROW=',F1O.5/ 1'DII, INSIDE DIAMETER, FT. =',F10. 5, 12X __1'XN, NO. OF PASSES =',F1.5/ 1'AI, INSIDE SURFACE AREA, SOFT/FT=',F10.5, 12X,

1'XNT, TOTAL NO. OF TUJBES =',F10.5/ 1'AO, OUTSIDE SURFACE AREA SOFT/FT=I,F10.5,12X,, 1'Z, FRICTION FACTQR EOUA. CONST.=',F10.5/ 1'WF, WEIGHT OF TUBE PER FT. LB/FT='-,F10.5,12X, 1'PWJ, FRICTION FACTOR EOUA.POWER ='FlO.5/ 1'T, THERMAL COND. BT(J/SOFT-HR-F =',F10.5,12X, 1'FR, FOULING RESISTANCE =',FlO.5/ 1'WR, WALL THICKNESS, FT =',F10.5,12X, 1'TW1, T(JBE INLET TEMP. F =',FIO.5) 73 FORMAT(60X,'TW2, TUBE OUTLET TEMP. F =',F10.5/ 1 60X,'DPT, DEW POINT, F =',F10.5/ 1 60X,'BPT, BOILING POINT, F =',F10.5/ 1 60X,'0, HEAT DUTY, BTU/HR ='?,F10.1//) 77 FORMAT( 1lHOt40X,'OUTPUT NOMENCLATURE'/// 1'RE, REYNOLDS NO.',3X, 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1FR 1 75 FORMAT( 1 1 31 FORMAT'HI 1'UDy'TDLMt'HC1'AOT'VEL' UOAO I' RUN'WT ICWAT'VI SWAT,'PR'SRHO I'DE LTF'TF'PHP I CN'XMR'PT'PF'TLT'TTWT'TWT ( 1H 1 X F9. TUBESIDE TRANSFER COEFF.'3X, OVERALL TRANSFER COEFFICIENT'/ LOG MEAN TEMP. DIFF. F',3X, CONDENSING COEFFICIENT', 3X, TOTAL TRANSFER AREA SOFT'/ TUBESIDE VELOCITY FT/SEC',3X PRODUCT OF lO BY AOT',3X, RUN NUMBER'/ FLOW PER TUBE LB/HR', 3X THERMAL COND. OF FLUID',3X, VISCOSITY OF FLUID'/ PRANDTL NUJMBER',3 X, SPECIFIC VOLUME',3X, TEMP. DIFF. ACCROSS FILM'/ TEMP. OF CONDENSATE FILM',3X, PHYSICAL GROUP' 3Xo CORRECTION FACTOR') WALL RESISTANCE',3X, TOTAL PRESSURE DROP PSI',3X, PRESSURE DROP PER FT'/ TOTAL LENGTH OF TUBE FT',3X, TOTAL WEIGHT OF TUBE LB',3X, TOTAL TUBESI[)E FLOW,IKLB/HR'//),10X, 16HDID NOT CONVERGE,54XF5.1, 5X, F4.1) 79 FORMAT (1HO,42X,6HOUJTPIJT) 10 FORMAT (lHO,4XT2HRE,7XT3HHI1,7X, 2HUO,7X,4HTDLM,7X,3HHC1,7X,3HAOT,7 1X, 3HTL1,7X, 3HVEL, 6X,4HUOAO, 7X, 3HRUN) 121 FORMAT( 1X,F8., O1XF7.O 3X,F7. 1,3XF8.2, 2X,F8.1,2XF7.1 4X F7.1.3X 1F6. 2 3X, F7., 3X, F6. 1 ) 50 FORMAT ( 1HO,4X.2HWT7X,4HCWAT,6X, 6HVISWAT, 5X2HPR, 6X4HSPHO 5X, 5HD 1EL TF, 7X, 2HTF, 8X, 3HPHP, 6X, 2HCN, 9X, 3HXMR ) 51 FORMAT ( 1XF6.O4XF7.4,4X, F7.4, 3X,F7.4,3X,F6.4,2XF7.4,4XF7.2,3X 1,F7.4, 2XF7.4,4XF8.6) 52 FORMAT (1HO,4X,2HPTt7XT2HPF,8X,3HTLT,6Xt4HTTWT,6X,3HTWT) 53 FORMAT (2XF7.4,3XF7.4,2X,F7.0,3X, F7. 1,2X,F7.1) CALL SYSTEM END REAL FUNCTION \IAPANY(ARG) A SUJBROUJTINE F(.R CALCULATING HEAT OF VAPORIZATION \/APANY=85. 32-0.0935*ARCG RE TUJRN END REAL FUNCTION PHPANY(ARG) A SUBROUTINE FOR PHYSICAL PROPFRTY GROUP PHPANY=1. 117-0.0004667 ( ARG) 88

RETURN END REAL FUNCTION VISANY(ARG) C C A S.UBROUTINE FOR CALCULATING VISCOSITY. A=1.O/ARG \/I SANY=-O. 1293+159. 2* A+6862. 3'*A*A-86924. O*A*AAA-407 19760. OA* A A"A 1+ 15597 08400.0 O A" A* A*A A RE.TURN END

NOMENCLATURE A Constant in C equation n AI Inside surface area per foot of tube, ft /ft ALLOY Alloy identification number AO Outside surface area per foot of tube, ft /ft 2 AOT Total outside heat transfer area, ft B Power in C equation n BETA Initial estimation of tube length BPT Bubble point temperature, ~F CN C, the Nusselt equation correction factor n CPWAT Specific heat of fluid at average fluid temperature, BTU/lb-~F CWAT Thermal conductivity of fluid at average fluid temperature, BTU/ft-hr- ~F DELTF Temperature difference across condensate film, ~F DEN Density of fluid at average fluid temperature, lb/ft DI Inside diameter, ft DO Outside diameter, ft DPT Dew point temperature, ~F FR Inside fouling resistance, ft -hr-~F/BTU HC1 Condensing heat transfer coefficient, BTU/ft -hr-~F 2 HI1 Tubeside heat transfer coefficient, BTU/ft -hr-~F PF Pressure drop per foot of tube, psi/ft PHP Physical group of fluid at film temperature PR Prandtl number PT Total pressure drop across the stage, psi 90

PW Q RE RUN SRHO STC T TDLM TF TL1 TLT TTWT TUBTYP TUNO TWA TW1 TW2 TWT UO UOAO VAPOH VEL VISWAT NOMENCLATURE (Continued) Friction factor equation power Heat duty, BTU/hr Reynolds number Run number 3 Specific volume of fluid, ft /lb Sieder-Tate constant Tube thermal conductivity, BTU/ft-hr- F Log mean temperature difference, ~F Condensate film temperature, ~F Tube length per stage, ft Total length of tube required, ft Total weight of tube required, lb Tube type number Tube designation number Average fluid temperature, ~F Tube inlet temperature, ~F Tube outlet temperature, ~F Total tubeside fluid flow, Klb/hr 2 Overall heat transfer coefficient, BTU/ft -hr-~F U A o o Latent heat of vaporization at film temperature, BTU/lb Tubeside fluid velocity, ft/sec Viscosity of fluid at average fluid temperature, lb/ft-hr 91

VISWAW VN WF WR WT XMR XN XNT XRUN Z NOMENCLATURE (Continued) Viscosity of fluid at wall temperature, lb/ft-hr Number of tubes in a vertical row Weight per foot of tube, lb Wall thickness, ft Fluid flow per tube, lb/hr Wall resistance to heat transfer, ft -hr-~F/BTU Number of passes Total number of tubes Run counter Friction factor equation constant 92

APPENDIX VIII Steam Condensing Design Calculations for A Hypothetical Stage in a Desalination Plant 93

TABLE VIII- Design Calculations for a 3/4-inch Bare Tube for an MSF Desalination Plant Stage VAPOIR CnNnFNS ITK PR(pi;RAM ---- TlRF FN.TH I A VARTARILF BASTS —--— SIEOER-TATE EQUATION FOR TIJRESIDE TRANSFER COEFFICIENT FLUID...SHELL SIDE —CONDENSING STEAM FLUID...TUBE SIDE —5% BRINE TUBE CHARACTERISTICS INPUT DATA AND CONSTANTS TUNO, TUBE DESIGNATION NO. = 750 STC. SIEDFR-TATE CONSTANT = 0.02510 TUBTYP, TUBE TYPE BARE A, CONSTANT IN CN EQUATION = 1.15800 ALLOY, ALLOY.ESIGNATION = CUNI B, POWER IN CN EQUATION = 0.09300 00, OUTSIDE DIAMETER, FT. = 0.06250 VN, NO. OF TUBES IN VERTICAL ROW= 27.00000 DI, INSIDE )IAMETER, FT. = 0.0561C XN. NO. OF PASSES = 1.00000 AI, INSIDE SURFACE AREA, SQFT/FT= C.17620 XNT, TOTAL NO. OF TUBES =2456.00000 AO, OUTSIDE SURFACE AREA SQFT/FT= 0.1964C Z, FRICTION FACTOR EQUA. CONST.= 0.31640 WF, WEIGHT OF TUBE PER FT. LB/FT= 0.33330 PW, FRICTION FACTOR EQUA.POWER = 0.25000 T, THERMAL COND.BTU/SOFT-HR-F = 26.000)0 FR, FOULING RESISTANCE = 0.00030 WR, WALL THICKNESS, FT = 0.00321 TWI, TUBE INLET TEMP. F = 201.42000 TW2. TUBE OUTLET TEMP. F = 205.25000 DPT, DEW'OINT, F = 212.70000 BPT, BOILING POINT. F = 212.70000 Q, HEAT DUTY, BTU/HR =29950000.0 GUTPUT NOMENCLATURE __RE REYNOLDS NO. HII. TUBESIDE TRANSFER CUEFF. U, OVFRALL TRANSFER COFFFIIFNT TDL~, LOG MEAN TEMP. DIFF. F HCI, CONDENSING COEFFICIENT AOT, TOTAL TRANSFER AREA SOFT VEL * TUBESIDE VELOCITY FT/SEC UnAQ. PRODUCT OF UO BY APT PUN. RUN NUMAER WT, FLOW PER TUBE LR/HR CWAT,THFRMAL COND. OF FLUID VISWAT, VISCOSITY OF FLUID PR -, PRANDTL NU.'1QFR SRHO, SPECIFIC VOLUME DELTF, TEMP. DIFF. ACCROSS FILM TF, TEMP. CF CONOENSATE FILM PkP, PHYSICAL GROUP CN, CORRECTION FACTOR XMf _, WALL RESISTANCE_ PT, TOTAL PRESSURF OROP PSI PF ~ PRESSURE DROP PFR FT TLT, TOTAL LENGTH OF TIJBF FT TTWT, TOTAL WEIGHT OF TUqE LB TWT, TOTAL TUBESIDE FLOW,KLB/HR OUTPUT F HI1 UO TDLM HC1 AOT TL. VEL UOAO RUN 95P21. 2009., 750.9 9.23 2695.1 4320.4 0.0 6.03 147.5 1.0f W_ T CWAT V Iw AT PR SPHO DELTF TF PHP CN XMR.3335. 0.3875 0.7 89S 1.9462 0.0161 2.5730 211.41 4.2733 1.5733 0.000130 PT PF TLT TTWT TWT 0.6996 0.0781 2198Q. 7332.0 8190.9

TABLE VUI-2 Design Calculations for a Hypothetical 1-inch Single-Start Corrugated Tube for an MSF Desalination Plant Stage VAPOR CONDENSING PROGRAM —— TUBE LENGTH IS A VARIABLE BASIS —-SIEDER-TATE EQUATION FOR TUBESIDE TRANSFER COEFFICIENT FLUID...SHELL SIDE —CONDENSING STEAM FLUID...TUBE SIDE —5 BRINE TUBE CHARACTERISTICS INPUT DATA AND CONSTANTS TUNO t TUBE DESIGNATION NO. = 2001 STC, SIEDER-TATE CONSTANT _ 0005500 TUBTYP, TUBE TYPE = KORO A, CONSTANT IN CN EQUATION = 1.50500 ALLOY, ALLOY DESIGNATION 5 CUNI B, POWER IN CN EQUATION " 0.20400 DO 3 -OUTSIDE DIAMETER, FT. = 0.08250 VN, NO. OF TUBES IN VERTICAL ROW= 25.00000 DI, INSIDE DIAMETER, FT. = 0.07610 XN v NO. OF PASSES = 1.00000 AI, INSIDE SURFACE AREA, SQFT/FT- 06.23910 XNT, TOTAL NO. OF TUBES =2162.00000 AO t OUTSIDE SURFACE AREA SQFT/FT= 0.25920 Z, FRICTION FACTOR EQUA. CONST.= 0.10000 -F -- WEIGHT OF TUBE PER FT. LBFT- 0.45060 Pw, FRICTION FACTOR EQUA.POWER = 0.0 T, THERMAL COND.BTU/SQFT-HR-F - 26.00000 FR, FOULING RESISTANCE 0.00030. - R t WALL THICKNESS, FT a 0.00321 TWi t TUBE INLET TEMP. F = 201.42000 TW2 ~ TUBE OUTLET TEMP. F = 205.25000 DPT, DEW POINTe F. 212.70000 BPT, BOILING POINT, F = 212.70000 Q ~ HEAT DUTYt BTU/HR =29950000.0 OUTPUT NOMENCLATURE RE, REYNOLDS NO. HI1 TUBESIDE TRANSFER COEFF. UO ~ OVERALL TRANSFER COEFFICIENT -TDLMO — LOG EAN TEMP. DIFF. F HC1 t CONDENSING COEFFICIENT AOT, TOTAL TRANSFER AREA SQFT VEL, TUBESIDE VELOCITY FT/SEC UOAO, PRODUCT OF UO BY AOT RUN, RUN NUMBER WT t FLOW PER TUBE LB/HR CWAT, THERMAL COND. OF FLUID VISWAT, VISCOSITY OF FLUID PR, PRANDTL NUMBER SRHO ~ SPECIFIC VOLUME DELTF, TEMP. DIFF. ACCROSS FILM — TF- TEMP. OF CONDENSATE FILM PHP ~ PHYSICAL GROUP CN ~ CORRECTION FACTOR XMR, WALL RESISTANCE PT, TOTAL PRESSURE DROP PSI PF, PRESSURE DROP PER FT T-Lr. TOTAL LENGTH OF TUBE FT TTWT, TOTAL WEIGHT OF TUBE LB TWT, TOTAL TUBESIDE FLOW,KLB/HR OUTPUT R- E HIl UO TDLM HC 1 AOT TL 1 VEL UOAO RUN 80244. 2941. 0100.0 9.23 5170.6' 3211.6 5.7 3.72 261.8 3.0 WT CWAT VISWAT PR SPHO DELTF TF PHP CN XMR 3789. 0.3875 0.7899 1.9462 0.0161 1.8031 211.80 4.2761 2.9021 0.000128 PT PF TLT TTWT. TWT 0.6993 0.1220 12390. 5583.1 8190.9 95

TABLE VIII-3 Design Calculations for a 1-inch Triple-Start Corrugated Tube for an MSF Desalination Plant Stage VAPOR CONDENSING PROGRAM —-— TUBE LENGTH IS A VARIABLE BASIS —--— SIEDER-TATE EQUATION FOR TUBESIDE TRANSFER COEFFICIENT FLUID...SHELL SIDE —CONDENSING STEAM FLUID...TUBE SIDE —5 BRINE TUBE CHARACTERISTICS INPUT DATA AND CONSTANTS TUNO, TUBE DESIGNATION NO. = 3000 STC t SIEDER-TATE CONSTANT 0.05050 TUBTYP, TUBE TYPE = KORO A, CONSTANT IN CN EQUATION = 1.4800CO ALLOY, ALLOY DESIGNATION = CUNI B, POWER IN CN EQUATION = 0.10500 DO OUTSIDE DIAMETER, FT. = 0.08250 VN, NO. OF TUBES IN VERTICAL ROW= 24.00000 DI, INSIDE DIAMETER, FT. = O.C7610 XN, NO. OF PASSES = 1.00000 AI INSIDE SURFACE AREA, SOFT/FT= 0.23910 XNT, TOTAL NO. OF TUBES 1880.00000 AO, OUTSIDE SURFACE AREA SOFT/FT= 0.25920 Z, FRICTION FACTOR EQUA. CONST. 0.38620 WF, WEIGHT OF TUBE PER FT. LB/FT= 0.45C60 PW, FRICTION FACTOR EQUA.POWER = 0.16240 T _ THERMAL COND.BTU/SQFT-HR-F = 26.00000 FR, FOULING RESISTANCE = 0.00030 WR. WALL THICKNESS, FT 0O.C0321 TW1I TUBE INLET TEMP. F 201.42000 TW2, TUBE OUTLET TEMP. F = 205.25000 OPT, DEW POINT, F = 212.70000 BPT, BOILING POINT, F _ 212.70000 Q, HEAT DUTY, BTU/HR =29950000.0 OUTPUT NOMENCLATURE RE_ TOLM VEL WT PR TF X MR TLT, REYNOLDS NO.., LOG MEAN TEMP. DIFF. F TUBESIDE VELOCITY FT/SEC, FLOW PER TUBE LB/HR PRANDTL NUMBER, TEMP. OF CONDENSATE FILM, WALL RESISTANCE * TOTAL LENGTH OF TUBE FT HI HC1 UOAC CWAT SRHO PHP PT TTWT, TUBESIDE TRANSFER COEFF. CONDENSING COEFFICIENT, PRCDUCT OF UO BY AOT ~ THERMAL COND. OF FLUID SPECIFIC VOLUME PHYSICAL GROUP, TOTAL PRESSURE DROP PSI TOTAL WEIGHT OF TUBE LB UO t Ua, AOT RUN s VISWAT, OELTF, CN PF TWT OVERALL TRANSFER COEFFICIENT TOTAL TRANSFER AREA SOFT RUN NUMBER VISCOSITY OF FLUID TEMP. DIFF. ACCROSS FILM CORRECTION FACTOR PRESSURE DROP PER FT TOTAL TUBESIDE FLOWKLB/HR OUTPUT RE HI UO TDLM HCI ACT TLI VEL UOAO RUN 92280. 3019. 926.8 9.23 3426.9 3500.0 7.2 4.28 240.2 2.0 WT CWAT VISWAT PR SPkC DELTF TF PHP CN XMR 4357. 0.3875 0.7899 1.9462 0.0161 2.4961 211.45 4.2735 2.0663 0.000128 PT 0.6992 PF TLT TTWT TWT n0.097 13503. t6084.5 819.Q

I3 90 3 9015 03 v 796