DEPARTMENT OF CHEMICAL AND METALLURGICAL ENGINEERING Heat Transfer Laboratory The University of Michigan Ann Arbor, Michigan THE CONDENSING OF LOW PRESSURE STEAM ON HORIZONTAL TITANIUM TUBES Report No. 55 Dale, E..'iBgs Instructor in Chemical and Metallurgical Engineering dEdwin He. Young Professor of Chemi:cal. and Metallurgical Engineering Project 1592 WOLVERINE TUBE Division of CALUMET AND HECLA, INCORPORATED ALLEN PARK, MICHIGAN December 1963

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TABLE OF CONTENTS Page List of Tables ii List of Figures iv Abstract 1 Obje ctive 1 Review of the Literature 2 Equipme nt 6 Test Procedure 16 Wilson Plot Procedure and Results 19 Multiple Tube and Data Processing and Results 32 Discussion of Results 41 Conclusions and Recommendations 42 Literature Cited 43 Appendix A 44 Tubeside Wilson Plot Data for Copper and Titanium Tubes Appendix B 47 Modified Wilson Plot Computer Program and a Set of Typical Output Appendix C 52 Condensing Heat Transfer Data for Condensation of Steam at 2 Inches of Mercury Absolute Pressure on 9 Copper and 9 Titanium Tubes in a Vertical Row Appendix D 61 Computer Program for Analysis of Multiple Tube Condensing Data and Typical Computer Calculated Results i

LIST OF TABLES Table Page I Tube Dimensions and Characteristics 28 II Computed Values of the Inside Heat Transfer Coefficient Constant and the Condensing Coefficient Constant for Copper and Titanium Tubes 28 III Condensing Coefficient Correction Factors for Condensation of Steam at 2 Inches Mercury Absolute Pressure on 1-9 Copper Tubes in a Vertical Row 35 IV Condensing Coefficient Correction Factor:s for Condensation of Steam at 2 Inches Mercury Absolute Pressure on 1-9 Titanium Tubes in a Vertical Row 36 V Average Values of Condensing Coefficient Correction Factors for Condensation of Steam at 2 Inches Mercury Absolute Pressure on 1-9 Copper Tubes in.a Vertical Row 37 VI Average Values of Condensing Coefficient Correction Factors for -Condensation of. Steam at 2 Inches Mercury Absolute Pressure on 1-9 Titanium Tubes in.a Vertical Row 37 VII Wilson Plot Data for the Top Copper Tube in the Center Vertical Row, First Set 45 VIII Wilson Plot Data for the Top Copper Tube in the Center Vertical Row, Second Set 45 IX Wilson Plot Data for the Top Titanium Tube in the Center Vertical Row, First Set 46 X Wilson Plot Data for the. Top Titanium Tube in the Center Vertical Row, Second Set 46 XI Modified Wilson Plot Computer Program Written in the Michigan Algorithm Decoder Language 48 XII Typical Wilson Plot Output Calculated with an IBM 7090 Digital Compute r 49

LIST OF TABLES (Continued) Table Page XIII Condensing Heat Transfer Data for Condensation of Steam at 2 Inches of Mercury Absolute Pressure on 9 Copper Tubes in a Vertical Row 53 XIV Condensing Heat Transfer Data for Condensation of Steam at 2 Inches of Mercury Absolute Pressure on 9 Titanium Tubes in.a Vertical Row 57 XV Computer Program Written in the Michigan Algorithm Decoder for the Analysis of Multiple Tube Condensing Data 62 XVI Typical Multiple Tube Analysis Computer Calculated Re sults 64 iii

LIST OF FIGURES Figure Page 1 Overall View of Equipment Showing Test Tubes in the Tube Sheet 7 2 Overall View of Equipment Showing Automatic Controllers, Potentiometer, and Manometers 8 3 Line Diagram of Equipment Show the Flow of Steam and Water 9 4 Elevation Drawing of Condenser, Reboiler, and Make-up Tank with the Condenser Tube Sheets and Reboiler Blind Flange s Removed 10 5 Detailed Drawing of Condenser Tube-Sheets and O-Ring Grooves 11 6 Cross-Sectional Drawing of Condenser and Inlet Water Header 12 7 Cross-Sectional Drawing of Orifice Holder Assembly 15 8 Modified Wilson Plot for the First Set of Copper Tube Data 29, 9 Modified Wilson Plot for the First Set of Titanium Tube Data 29 10 Modified Wilson Plot for the Second Set of Copper Tube Data 30 11 Modified Wilson Plot for the Second Set of Titanium Tube Data 30 12 Condensing Heat Transfer Coefficient Constants Calculated from the Wilson Plot Data Using an Inside Heat Transfer Coefficient Constant of 0.02468 31 13 Condensing Coefficient Correction Factors for Condensation of Steam at 2 Inches of Mercury Absolute Pressure on 1 to 9 Copper Tubes in a Vertical Row 38 14 Condensing Coefficient Correction Factors for Condensation of Steam at 2 Inches of Mercury Absolute Pressure on 1 to 9 Titanium Tubes in a Vertical Row 39 iv

LIST OF FIGURES (Continue d) Figure Page 15 Mean Values of the Condensing Coefficient Correction Factors for Condensation of Steam at 2 Inches of Mercury Absolute Pressure on 1 to 9 Copper and Titanium Tubes in a Vertical Row 40

ABSTRACT Heat transfer data are presented.for condensing steam at 2 inches of mercury absolute pressure on the out-side of 9 copper and 9 titanium horizontal tubes in a vertical row. The condensing coefficient correction factor was maximum for the top titanium tube and was 4.6 per cent higher than the correction factor for the top copper tube. The difference between the correction factors for titanium and copper tubes diminished with the number of tubes in a vertical row to 8 per cent higher than the correction factor for copper tubes with 6 to 9 tubes in a vertical row. OBJECTIVE The purpose of this investigation was to determine the low pressure steam condensing characteristics of horizontal titanium tubes placed in a vertical row where inundation of condensate occurs. Because of the generally low wettability surface characteristics of titanium, it was surmised that condensing heat transfer coefficients would be considerably higher with the possibility of dropwise condensation. The investigation was to further include the condensing characteristics of copper tubes. The copper tube results were to be used as a reference in evaluating the titanium tube condensing behavior. 1

REVIEW OF THE LITERATURE In 1916, Nusselt (1) derived the equations governing the condensation of pure saturated vapors on wettable condensing surfaces. Nusselt postulated thatthe resistance to heat transfer was due solely to conduction across the continuous condensate film formed during the condensation process. By considering a force balance between the shear forces resulting from the viscosity of the condensate and gravitational forces resulting from the mass of the condensate, an equation was derived which predicted the thickness of the condensate layer as a function of the angle of the surface with a horizontal plane. Laminar flow.and zero vapor velocity were assumed. Using the expression for the condensate film thickness, an equation was derived for the change in heat duty with position for a horizontal tube. By suitable integration of the expression, an equation was developed for the mean heat transfer coefficient for condensation of a pure saturated vapor on the surface of a horizontal tube which is lower in temperature than the saturated vapor. Equation (1) was the equation obtained. 1/4 h = 0725 k3p2 m [L DAtE J(1) where h = mean condensing heat transfer coefficient, BTU/hr.-sq.ft.- ~F m k = thermal conductivity of condensate evaluated at film temperature, BTU/hr. - sq. ft. - ~F/ft p = density of condensate evaluated at film temperature, lb. /cu.ft. 8 2 9g = acceleration due to gravity, taken as 4.17 X 10 ft./hr. X = latent heat at saturation temperature, BTU/lb. 1 = viscosity of condensate evaluated at film temperature, lb. /ft. -hr. D = outside diameter of tube, ft. at = temperature drop across condensate film, t - t,F f sv s t = outside wall temperature of the tube, ~F ts = temperature of the saturated vapor, ~F sv

For laminar flow of condensate, the film temperature, tf, is given by 3 t = t - -At (2) tf =tsv 4 f Experimental investigations of the condensation of pure saturated vapors on single horizontal tubes indicate that Equation (1) predicts values generally within +10% of the experimental condensing coefficients. (1) The experimental coefficients are most often higher than the theoretical values. This is attributable to turbulence or rippling in the condensate layer. The average film temperature is often evaluated using Equation (3) when turbulent flow of the condensate is expected.() 1 tf = t - Atf (3) When several horizontal tubes are placed in a vertical row such that condensate from the.upper tubes drops onto the lower tubes, the mean thickness of the condensate film on a particular tube increases from the top tube to the bottom tube. By accounting for the accumulation of condensate from tube to tube, but still assuming laminar flow of the condensate, Equation (4) was derived to predict the average condensing coefficient, h, for n tubes located in a vertical row, (1) 1/4 3 2 h = 0 725 k p g k m n = D (tf where n. number of tubes in a vertical row 3

Equation (3) would be used for calculating t, if turbulent flow of condensate is expected. Experimental data taken on multi ple horizontal tubes in a vertical row by Katz and Geist(3), Short and Brown(4), and Young and Wohlenberg(5) indicate that Equation (4) is very conservative. The correction for multiple tube rows of (11,n)114 is much too severe in view of the high degree of turbulence and splashing with condensate dropping from tube to tube. A turbulence correction factor, Cn2 was added to Equation (4) by Katz, Young and Bale(jian2) to give Equation (5). 1/4 h = 0.725 C k3 2(5) m n L n D ptf Equation (5) corrects the basic theoretical Nusselt model with the correction factor, Cn, and gives a means of correlating experimental condensing data for multiple tube arrangements.(2) The correction factor, Cn, varies with the number of tubes in a vertical row and with the physical properties of the material being condensed. The surface tension of the condensate film is extremely important. Whenever the cooling surface is not wetted, the condensing vapor tends to form very fine drops which roll off the condensing surface due to the influence of gravity. This phenomena is called dropwise condensation. In dropwise condensation the drops normally agglomerate to form larger drops. Since a signifi — cant portion of the cooling surface is always free of liquid, the net resistance to heat transfer is lower than for film condensation. Dropwise condensation is generally associated with the existence of a contaminant on the tube surface. Mer - captans and fatty acids are effective promoters of dropwise condensation.(l) Where tube surfaces are mildly contaminated, mixed condensation may exist. Part of the surface will exhibit filmwise condensation while the remainder of the surface is condensing vapor in a dropwise fashion. This frequently happens with condenser tubes which have been in continuous condensing service for a long time. The existence of any non-condensible gas in the condensing vapor significantly affects the rate of heat transfer due to the buildup of a non-condensible gas around the cooling surface. The concentration of a non-condensible gas around the tube surface forms a barrier through which the condensing vapor must diffuse prior to condensing. The temperature of the free surface of the condensate film will be equal to the saturation temperature of the condensing vapor at a pressure equal to the partial pressure of the condensing vapor at the outer film surface. 4 a

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

EQUIPMENT The equipment in this investigation consisted of a condenser, inlet and outlet water headers, reboiler, make-up tank, water preheater pump, steam jet ejector and automatic controllers Figures 1 and 2 give two views of the equipment and Figure 3 gives a line diagram showing the flow of steam and water. An elevation drawing of the condenser, reboiler and make-up tank is given in Figure 4. Steam was generated by boiling distilled water in the reboiler with 150 psig steam, The vapor flowed upward through an 8 inch line to the condenser where it condensed on the test tubes. The condensate returned to the reboiler through a 2 inch line, Water from the cooling tower system was used as the coolant. The condenser was constructed of a 6 foot length of i186inch diameter standard gauge commercial steel pipe. Ring flanges were welded to each end of the pipe. The flanges were made from 2 inch thick plate steel with a bolt circle identical to a standard 18 inch, 150 pound flange. Tube sheets were con — structed from 2 inch plate steel with both sides surface ground to give a flat surface. Figure 5 gives a detailed drawing of the tube-sheets showing the tube layout and double O-ring grooves. The tube sheets were constructed to accommodate 25 tubes placed in 3 vertical rows with the tubes on a 7/8 inch equilateral triangular pitch. O-rings were used to seal the tubes in the tube sheet. An 8 inch by 60 inch section was removed from the top of the condenser An 8 inch welding tee and two pieces of 8 inch pipe with the bottom half cut off was then welded to the condenser over the open section, as shown in Figure 6. This formed the steam inlet to the condenser. An impingement baffle consisting of a piece of 3 inch pipe cut in half was placed over andl 2 inches above the tubes in the condenser, This prevented direct impingement of steam onto the tubes A 2 inch diameter pipe located at the bottom of the condenser returned the condensate produced in the condenser to the reboiler. Sight glasses were provided for visual observation. These can be seen in Figures 1 and 2. Corrugated metal asbestos gaskets were used between the tube sheets and ring flanges. The inlet and outlet water headers consisted of 1 foot lengths of 14 inch standard gauge steel pipe with 1 inch steel plates welded to the pipe The plates closest to the condenser contained tube holes in a pattern identical to the condenser tube sheets. Single O-ring grooves were cut in each hole. A section of 3 inch pipe extended into the other plates approximately 6 inches. These pipes served as the inlet and outlet water lines. The ends of the pipe within the headers were blanked off and sections cut out of the pipe wall. This was done to insure a more nearly uniform distribution of water flow within the tubes. The inlet and outlet water headers were placed approximately 5 and 25 inches from the condenser respectively In these positions, 8 foot tubes with a 9 inch orifice holder could be placed in the condenser such that the tubes extended into the headers approximately 1 inch. 6

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AIR BLEED PRC ( a s - STEAM 2-STAGE AIR EJECTOR TRC STEAM FRC VAPOR CONDENSER WATER TO COOLING TOWER COOL WATER FROM SUMP PRE-HEATER — OSTER PUMP I | | t I WATER HEADER CONDENSATE TO BOILER TEST CONDENSATE PRC STEAM LEVEL GAUGE -1 CONTROL VALVE REBOILER FRCO FLOWRATE RECORDER CONTROLLER [ PRCO PRESSURE RECORDER CONTROLLER CONDENSATE TO BOILER TRCO TEMPERATURE RECORDER CONTROLLER P PRESSURE ELEMENT / THERMOCOUPLE J TEMPERATURE ELEMENT --- ORFICE -! FLOW ELEMENT -/- AIRLINE Figure 3. Line Diagram of Equipment Show the Flow of Steam and Water

8" STD. SCH. STEEL PIPE 0 / 0 l CONDENSER 0 / ( MAKE-UP N TANK 0 T -2" 0 Q 0 1" STD. SCH. STEEL PIPE REBOILER O TO DRAIN Figure 4. Elevation Drawing of Condenser, Reboiler, and Make-up Tank with the Condenser Tube Sheets and Reboiler Blind Flanges Removed 10

2.000 0.288.716.716.140.140 25" DIA. 22'"BOLT CIRCLE 16 1N"HOLES 221/4''BL t u R,; 5 U \ INSIDDRILLED AND 0 REAMED 41/64" 00 INSIDE 0 0o 25 41/64" HOLES O O ON 7/8" EQUILATERAL SECTION THROUGH CENTER ROW SHOWING TRIANGULAR PITCH TUBE HOLE AND O-RING GROOVES: O -0 0/ SECTION THROUGH OUTER ROW SHOWING CONDENSER TUBE SHEET LAYOUT TUBE HOLE AND O-RING GROOVES Figure 5. Detailed Drawing of Condenser Tube-Sheets and O-Ring Grooves

STEAM LINE STEAM HEADER BAFFLE TUBE SHEET I 1 1411 18" CONDENSER IHEADER 14"' 14" -;l CONDENSATE RETURN LINE 72" 2" Figure 6. Cross-Sectional Drawing of Condenser and Inlet Water Header

The reboiler was constructed of a 6 foot length of 24 inch diameter standard gauge commercial steel pipe. Ring flanges were welded to each end of the pipe. The flanges were constructed from 2 inch plate steel with a bolt circle identical to a standard 24 inch, 150 pound flange. Companion blind flanges were constructed of similar material. The flanges were bolted together with a corrugated metal asbestos gasket placed between the two flanges. A 2.i-nch thick steel tube sheet was constructed and welded into place 6 inches within the shell. The tube sheet was made to accommodate 10, 10 foot long, 3/4 inch O.D. U-bend tubes. The layout is shown in Figure 4. Type S/T copper trufin U-bend tubes were rolled into the tube sheets. Tube supports were provided within the reboiler, A partition plate was welded to the tube sheet between the tube inlet and outlet. An additional piece of metal was welded to the partition plate to form a box such that the condensate could be kept separate from the entering steam. High pressure steam (150 psig) was used to vaporize the water in the reboiler. The condensate was returned to the high pressure boiler through a steam trap. A Jergensen gauge installed on the front of the reboiler made it possible to determine the water level in the reboiler. A 25 gallon water make-up tank was located immediately above and slightly behind the reboiler as shown in Figure 4. A 1 inch diameter pipe with a valve connected the make-up tank to the reboiler and permitted the transfer of water to the reboiler during operation. A sparged steam line in the make-up tank made it possible to preheat and partially de-gas the water before it was allowed to enter the reboiler. A 12 foot long, 15 inch diameter heat exchanger was installed in the inlet water line to permit the preheating of the cooling water to the desired temperatur e. The heat exchanger was converted from a two-tube pass until to a single tube pass unit to reduce the pressure drop. High pressure steam was condensed on the outside of the tubes. The condensate was returned to the high pressure boiler through a steam trap. A 300 gpm submersible pump was modified and installed in the cooling water line immediately after the water preheater. The pump was used during high velocity runs when the main cooling water pump had insufficient head to give the desired water flow rate. A two stage jet ejector with interstage condenser was used to evacuate the condenser-reboiler system on start-up and also permitted the removal of non-condensible gases which leaked into the system during operation. The ejector was connected to the reboiler with a 2 inch diameter pipe containing a 2 inch globe valve, The ejector operated on high pressure steam and process coaling wate r 13

Four automatic controllers were installed to assist in the operation of the equipment when taking data. The controllers can be seen in Figure 2. One instrument controlled the water flow rate. A 2 inch diameter orifice flange with orifice was installed in the inlet water line. The pressure drop across the orifice served as the input signal to the controller. The controller pneumatically actuated a 2 inch globe valve which kept the flow rate at the desired value. A second instrument was an inlet cooling water temperature controller. A mercury filled bulb installed in the water line served as the sensing element for the controller. The controller pneumatically actuated a steam valve which regulated the amount of steam entering the water preheater. The remaining two instruments were absolute pressure controllers. One sensing element was connected to the condenser. The controller used the pressure signal to regulate the amount of steam entering the reboiler through a 3/4 inch pneumatically operated valve so that the desired pressure in the condenser could be maintained. The second pressure controller was installed in the steam jet ejector system to minimize fluctuations in pressure at the ejector due to variations in the steam flow rate. The control instrument controlled a small bleed valve. By bleeding in small amounts of air, the pressure in the ejector header could be kept relatively constant. The water flow rates in each tube were measured by calibrated orifices placed in orifice holders which were located at the outlet end of the test tubes between the condenser and the exit water header. Figure 7 shows the orifice assembly. The orifices were calibrated for each tube tested. The pressure drop across the orifices were measured with water over mercury manometers. Both 50 inch and 100 inch manometers were used. A manifolded system permitted the same manometer to be used for several orifices. The accuracy of the flow rate measurement was between 1/4 and 1/2 percent. Inlet water, outlet water, and condenser steam temperatures were measured with calibrated 30 gauge copper constantan thermocouples using a Leeds and Northrup K-3 potentiometer. Temperatures could be measured to 0.01 ~F. The inlet water thermocouple was placed in the inlet water header. The exit water thermocouples were located in the orifice holder assemblies as shown in Figure 7. The stainless steel sheath extended up-stream along the tube axis for 1 inch. Thermocouples were placed in two places in the back of the condenser to permit the measurement of the steam temperature. The condenser absolute pressure was determined with a mercury manrometer and calibrated barometer. 14

COPPER-.CONSTANTAN THERMOCOUPLE /4" COPPER TUBING STAINLESS STEEL SHEATH 10 "0 Y4"3 13BWG COPPER 5/8" 2OBWG 1" 5/8" 20BWG20BWG COPE 0.375" DIA. HOLE IN ORFICE Figure 7. Cross-Sectional Drawing of Orifice Holder Assembly

TEST PROCEDURE The test equipment was thoroughly degreased upon completion of the construction phase of the investigation. To do this, 9 foot long, 5/8 inch diameter, plain copper tubes were inserted into the condenser through the O-rings in the condenser tube sheets. Each tube sheet had two O-rings. The inlet water heater was placed into position and the tubes pushed into the header through the tube holes containing single O-rings The tubes were pushed into. the header approximately 6 inches. The outlet water header was then placed into position and the tubes pulled back into the outlet water header, leaving approximately 3/4 to 1 inch of tube extending into the headers at both ends A 55 gallon barrel of trichlorethylene was added to the reboiler and the steam line to the reboiler was opened. Cooling water was allowed to flow through the tubes, Trichloroethylene was boiled in the reboiler, condensed on the copper tubes and returned to the reboilero Since the trichlorethylene temperature was higher than the ambient temperature, some condensation occurred throughout the entire system, This insured a thorough cleaning throughout. The used trichlorethylene was transferred to an empty barrel and a clean barrel of trichlorethylene added for a final cleaning. Upon completion of cleaning, the copper tubes were removed. The orifice assemblies were attached to the test tubes with soft solder in the case of copper tubes and with epoxy resin in the case of titanium tubes. The tubes were wiped with trichlorethylene and placed into the condenser and headers as previously described. Vacuum putty was placed around each tube in the condenser to reduce the amount of air leakage into the system. The thermocouple circuit was wired up and the manometer tubing installed. A 24 point thermocouple selector switch was used. Fiber glass insulation was placed around the tubes to minimize heat loss. During normal operation, the reboiler was 1/2 to 2/3 filled with distilled water through the water make-up tank. Once the reboiler was filled to the desired level, steam and water to the steam jet ejector were turned on and adjusted to give the maximum evacuation rate. The ejector was allowed to operate for approximately 30 - 45 minutes to thoroughly evacuate non-condensible gases from the condenser-reboiler system. The pressure in the condenser rapidly approached the vapor pressure of the water in the reboiler during this period. With the ejector still pulling a vacuum on the system, the condenser pressure controller was set at the desired pressure setting. The automatically controlled steam valve in the reboiler steam line then opened allowing the water in the reboiler to be heated until the vapor pressure of the water equalled the set point pressure. The system was operated under these conditions for approximately 20 - 30 minutes. This further assisted in degassing the water and evacuating the system. The cooling water controller was next set to the desired total water flow rate and the inlet water temperature controller set at the desired 16

inlet water temperature., The steam jet ejector manifold pressure controller was set at a pressure somewhat below the condenser pressure.~ This minimized the air bleed and permitted maximum removal of non-condensibles during the period when data were taken, There was always a small amount of air leakage into the system, Prior to taking data, the saturated steam temperature was calculated and compared to the steam temperature measured with a thermocouple. If the two temperatures agreed within 1/2 ~F, the system was considered ready for taking data, If the temperature calculated from the pressure was greater than 1/2'F above the measured temperature, an excessive amount of air still remained in the system and evacuation was continued until satisfactory agreement was obtained. Heat transfer data were taken when the automatic controllers had stabilized all the control variables at the desired set points. The method of taking data depended upon its eventual use. If Wilson plot data were to be taken on the top tube only, the following readings were taken in order: inlet water thermocouple, exit water thermocouple, water flow rate manometer reading, condenser steam thermocouple, and condenser pressure manometer. A total of 10 sets of data were taken for each set point and the readings averaged. If heat transfer data were to be taken on all 9 tubes in the vertical row, the following readings were taken in order: inlet water thermocouple, exit water thermocouple for tube 1, condenser steam thermocouple, exit water thermocouple for tube 2, exit water thermocouple for tube 3, inlet water thermocouple, condenser steam thermocouple, exit water thermocouple for tube 4, exit water thermocouple for tube 5, exit water thermocouple for tube 6, inlet water thermocouple, condenser steam thermocouple, exit water thermocouple for tube 7, exit water thermocouple for tube 8, exit water thermocouple for tube 9, inlet water thermocouple, and condenser steam thermocouple. The pressure drop across the orifice for each tube was measured with a manometer approximately at the same time as the exit water temperature was being measured for the same tube. The condenser pressure relative to atmospheric measure was measured with a mercury manometer 2 or 3 times during the run. Barometer readings were made before and after the runs. The inlet water and condenser steam temperatures were plotted as a function of time in order that the exact values of those temperatures existing when the exit water temperatures were measured could be determined. This procedure was necessary to obtain the most accurate temperature differences between inlet and outlet water temperatures and the most accurate logarithmic temperature differences,. The water temperature rise was used with the water flow rate to determine the heat duty. Usually three complete sets of data were taken for each set condition. During the course of a run which lasted about 5 - 10 minutes, the inlet water temperature varied approximately + 0 o 2 ~F and the condenser steam temperature varied by approximately + 0. 3 ~F. Whenever the water level in the reboiler dropped below 1/4 of the reboiler diameter, make-up water was added from the make-up water tank. The water 17

was heated with steam and at least partially de-gassed before allowing it to flow into the reboiler. A small amount of water was always retained in the make-up tank in order to maintain a vacuum seal. 18

WILSON PLOT PROCEDURE AND RESULTS The main purpose of this investigation was to measure the condensing coefficient for steam on various horizontal tubes at different operating conditions. Direct measurement of the condensing coefficient is a difficult undertaking. To do this, it is necessary to accurately measure the outside wall temperature at several locations. Since only a finite number of measurements can be made, only local coefficients are determined. An alternative procedure is to calculate the condensing coefficient from the overall heat transfer coefficient. The overall heat transfer coefficient is calculated from U = - (6) o A AT o m where U = overall heat transfer coefficient, Btu/hr.-sq. -ft.- ~F Q0 = total heat transfer, Btu/hr. Ao = total external heat transfer area, sq.ft. ATm = logarithm temperature difference ~F The heat duty, Q, is obtained experimentally from Q = W c (t to ) (7) p out in where W = water flow rate-lb. /hr. cp = specific heat of water - Btu/lb.- ~F tout = outlet water temperature, ~F tin = inlet water temperature, OF 19

The condensing coefficient can be obtained by rearranging the expression for the overall coefficient in terms of the individual resistances. This gives 1 1 A 0 h U A,- h. (8) m 0 1 i where hm = mean condensing coefficient, Btu/hr.-sq.ft.- ~F Ai = total internal heat transfer surface, sq.ft. hi = inside heat transfer coefficient rm = metal resistance, hr.-sq. ft. (outside area) ~F/Btu The metal resistance, rm, is easily calculated from the thermal conductivity of the metal and the tube dimensions. Empirical expressions are available for the calculation of hi but they are not sufficiently good for accurate heat transfer work. This is attributable to entrance and exit eff[cts, and other -system idiosyncracies. A satisfactory equation as regards to form is the SiederTate Equation, Equation (9). 0.8 1/3 0.14 =hCi [i ] [ CPl 1 [i3 (9) k where Di -L:tube inside diameter, ftb. k = water thermal conductivity at bulk water temperature, Btu/hr. -sq.ft.- ~F/ft. Ci = inside heat transfer coefficient constant, dimensionless G = mass flow rate, lb. /hr..-sq.ft. CL = water viscosity at bulk water temperature, lb. /ft.-hr. w = water viscosity at average wall temperature, lb./ft.-hr. The constant, C., must be obtained experimentally. 20

A familiar method for determining individual coefficients from the overall coefficient is known as the Wilson Plot technique (8) The general scheme is to hold either the inside or outside coefficient constant while varying the other coefficient. The variation of the overall coefficient is, thereby, due to the varying heat transfer coefficient alone. If the expression for the overall heat transfer coefficient is written as 1 1 A U r = h+ A (10) U m h A. h 0 m 1 1 and the condensing coefficient is assumed to be constant, then Equation (10) takes on the -form y = mx + b (11) where y - rm Uo 1 hm 1 m = 1 A.0 X~~ 0 8 1/3 0.14 21 k l

By plotting r1 U1 A U r gm versus 0.8 1/3 0.14 [ k. D. the slope of the resulting straight line through the data equals 1/C. and the intercept -equals 1 /hm The intercept value corresponds to an infi'nite inside heat transfer coefficient, Experimentally, it is very difficult to hold hm constant since as the inside heat transfer coefficient changes, the wall temperature changes, and consequently, the temperature drop across the condensing film will also change. A modification of the Wilson plot technique can be made to eliminate this problem. Equation (10) is first written in terms of the complete expressions for h and h. 1 1i A D. O I r k p -m 1/4 0,8 /3 0.14(12) 0 3 2 c L g DAtf L [~ 7 where C is the experimentally determined constant to replace the value of 0. 725 in Equation (1). In the expression for h, the variables m 1/4 will vary with changes in the inside heat transfer coefficient. Multiplying ~22

Equation (1 2) bhythi'sgr. o-up Equation (13) is obtained 1/4 1/4 A D. [ ] 3 p _ 1 f +............(13) The group, 1/4 C] can be held sufficiently constant so that Equation (13) has the form y = mx + b (11) which is necessary in the Wilson plot technique. If 1/4 rm] ~ p f 23

is plotted versus 1/4 A D. pAtf 0'8 1/3 0.14 A. k ] -w J. for each data point and a straight line placed through the data in a least square sense, the intercept of the line with the ordinate is 1 1/4 C D D and the slope of the line is 1/C. To obtain the correct values of the function to be plotted requires an iterative procedure. The first step is to assume a value for the inside heat transfer coefficient, C. From the water flow rate and temperatures, the Reynolds number and the water physical properties can be obtained. If 0: 14 [w] is initially taken equal to 1.0, an approximate value of h. can be calculated from 0.8 1/3 0.14 D. i [D k j 1 i)J (14) 24

The inside tube wall temperature is next calculated using Equation (15). t = t + (15) wi wa A.1h. where t average inside wall temperature, oF wi twa = average bulk water temperature, OF The wall temperature, twi, is used to evaluate Pw and a more correct value of hi obtained from Equation (14). Equation (15) is again evaluated to determine if the previous inside wall temperature is sufficiently accurate. If it is not, then the procedure is continued until satisfactory agreement is obtained. Once hi is calculated for the assumed value of Ci, the condensing coefficient can be calculated from Equation (8). The temperature drop across the condensing film, Atf, is then calculated from U AT 0 m At, (16) Af h m and the film temperature, tf, from t = t - -tf (3) sv where t, = average condensing film temperature, ~F t = temperature of saturated vapor, ~F sv 25

The group 1/4 3 2 [A tf 3 is a function of t With the value of that quantity known, the two functions required for the fWilson plot can be evaluated and plotted. A line is placed through the data in a least mean sense and the slope of the line evaluated. The reciprocal of the slope is the constant Ci. If the calculated value of Ci differs significantly from the assumed value, the calculated value is taken and the whole procedure repeated until there is sufficient agreement between the assumed and calculated values of C. The average condensing coefficient constant for all the data can be calculated from the intercept value C = (17) intercept g[ The actual values of the condensing coefficient and the individual values of C are obtained in the process of determining C., 1 A program was prepared for the University of Michigan IBM 7090 digital computer and all the Wilson plot data were processed using that program. The input data to the program were the water flow rate, inlet and outlet water temperatures, steam temperature, tube dimensions, thermal conductivity of the tube metal and an initial estimate for the inside heat transfer coefficient constant, Ci~ The necessary physical properties of steam and water were written into the program. The program took the value of Ci, went through the process outlined and obtained the values of the two functions necessary for the modified Wilson plotL A least square- subroutine was then used to compute the slope of the best straight line through the processed data and the intercept, The reciprocal of the slope is Ci. The assumed value of Ci was compared to the calculated value and if it differed by more than 0 1 per cent, the calculated value was used and the process repeated until the assumed and calculated values agreed within 0.1 per cent26

Four sets of Wilson plot data were processed. All the data were taken with a steam pressure of 2 inches of mercury absolute pressure and an inlet water temperature of 75 ~F. The tube dimensions appear in Table I and the heat transfer data appear in Appendix A. Two sets of data were on a copper tube and two sets were on a titanium tube. In each set the heat transfer data were taken on the top tube in the center vertical row. The first sets of data for the copper and titanium tubes were taken with 25 tubes located in the condenser. The second sets of data were taken with only the 9 tubes in the center vertical row present. Rubber stoppers were used to plug the tube sheet holes not used in the latter runs. The Wilson plot results for the four sets of data are presented graphically in Figures 8-11. The calculated values of the inside heat transfer constant, Ci, and the condensing coefficient constant, C, obtained from the intercept are given in Table II. As can be seen in Table II, the condensing constants in the second sets were higher than in the first. This is attributable to a reduction in the amount of non-condensibles present in the condenser by a factor of 2. Accurate leak rate curves were obtained for the system. Measurements of ejector evacuation rates were also made but they were not very accurate because of the rapid changes in the system pressure. It is estimated that the amounts of non-condensibles present in the first and second sets were less than 0.50 and 0.25 per cent by volume, respectively. The average value of the inside heat transfer coefficient constants appearing in Table II is 0.02468 with maximum deviations of -2.5 per cent and + 3.5 per cent. Most, if not all, the deviation from the average can be attributed to experimental error since straight lines placed through the data in Figures 8-11 with slopes equal to 1/0.02468 appear as reasonable as the least square lines. To determine if the calculated values of the condensing coefficient constant would be reasonable if the inside heat transfer coefficient constant were to be taken as 0.02468, the Wilson plot data were reanalyzed. The results of the analysis are given in Figure 12 with the calculated values of the condensing coefficient plotted versus the amount of condensate produced on the tube in pounds per hour. The amount of condensate produced per hour is directly related to the tube-side water velocity. Exclusive of experimental errors, a trend in the condensing coefficient with the condensate loading can result from an error in the inside heat transfer coefficient due to the wrong coefficient or from an increase in the condensate turbulent level. Any trend due to variations in condensate turbulence is likely to be small. Since there is no obvious trend in the data of each set, the average value for C. adequately represents the data 4 The computer program and a set of typical output data are given in Appendix B. 27

TABLE I Tube Dimensions and Characteristics Copper Titanium Top Average Top Ave rage Tube for Tube for Middle Middle Row Row Tube type plain plain plain plain Tube outside diameter, in. 0,6252 0.6252 0.5287 0,6271 Tube inside diameter, in. 0 5550 0,5550 0.5592 0.5581 Tube wall thickness, in, 0.0351 0o0351 0,0347 0.0345 Tube lengths in. 72.156 72.156 72.156 72,156 Thermal conductivity, BTU/hr. -ft. - ~F/ft. 196 196 10 10 TABLE II Computed Values of the Inside Heat Transfer Coefficient Constant and the Condensing Coefficient Constant for Copper and Titanium Tubes Set C. Deviation Condensing from Constant Average 1st Copper 0.02475 +0.3 0,.7275 1st Titanium 0.02436 -1.3 1.1183 2nd Copper 0,02406 -2.5 0.9709 2nd Titanium 0.02555 +3.5 1.3223 Average 0.02468 28

0.4 i I Ci = 0.02475 x 1. 0.2 RUNS 178733-178736 0.1 19216 1 -192165 192187 -192199 0 I 0 0.1 0.2 0.3 0.4 0.5 0.6 AoDi (k$, )) x/ xl04 0.8 1/3 0.14 Ak (D, G (CP' ) (p Figure 8. Modified Wilson Plot for the First Set of Copper Tube Data 0.4 _ I I Ci = 0.02406 N 0.3 0 =,. 0.2 0.1 RUNS 197020 A - 197028 C 0 I I I I I 0 0.1 0.2 0.3 0.4 0.5 0.6 (k3p29 )'/4 A~Di p tf X 104 Aik' ) pw Figure 9. Modified Wilson Plot for the First Set of Titanium Tube Data 29

0.4 C i 0.02436 0.3 oC 0.2 JE -15 | RUNS 178737-178749 192241 -192244 0. I 0 0.1 0.2 0.3 0.4 0.5 0.6 AoDi ( ) X104 0.8 / 0.14 A k (Di G) (c,)3(-p?) Figure 10. Modified Wilson Plot for the Second Set of Copper Tube Data 0.4,! Ci = 0.02555 0.3 o NV Zi 0.2 - RUNS 197039A - 197054C 0.1 0 I I I i I 0 0.1 0.2 0.3 0.4 0.5 0.6 Ao Di (/ttf )A x10 0.8 1/3 0.14 Figure 11. Modified Wilson Plot for the Second Set of Titanium Tube Data 30

1.50 v v Titanium 2nd set v 1.40 v v vv v 1.30 z z o 1.20 0 z w IS a O 00a I. 1.10 Titanium Ist set 0 0 00 0 o o LL o 0 00 w 0 o Copper 2nd set 0.90 0.80 0 0 Copper I st set 0 o 0.60 0 0 I, I Q 1.00 0 5 10 15 20 25 30 35 40 CONDENSATION RATE Ibs./hr. Figure 12. Condensing Heat Transfer Coefficient Constants Calculated from the Wilson Plot Data Using an Inside Heat Transfer Coefficient Constant of 0.02468

MULTIPLE TUBE DATA PROCESSING AND RESULTS Two sets of heat transfer data were taken on the nine tubes in the center vertical row. The two side rows were excluded. The first set of data were taken on copper tubes and the second set on titanium tubes. The data appear in Appendix C. The purpose of taking multiple tube data was to obtain the correction factor, Cn, for Equation (5), as a function of the number of tubes in a vertical row. A computer program was written for the IBM 7090 digital computer to process the data. The computer program consisted of three sections. In the first section the input data including the average value of the inside heat transfer coefficient were read into the computer and preliminary calculations made. These operations included the calculation for each tube of the heat duty, logarithmic temperature difference, overall heat transfer coefficient, water velocity, bulk water physical properties, inside heat transfer coefficients, and condensing coefficient by the method described in Equation (8). From the condensing coefficient and physical properties of the condensate film, the condensing coefficient constant for Equation (1) was calculated. The average inlet water temperature, water velocity, and steam temperature for all nine tubes were also calculated. A print out of the results completed the first section. In the second section of the program, the average inlet water temperature, water velocity, steam temperature, and condensing coefficient constants for each tube were used to predict for each tube what the heat duty, exit water temperature, logarithmic temperature difference, overall heat transfer coefficient, inside heat transfer coefficient and condensing coefficient would have been had the inlet water temperature, water velocity and steam temperature been equal to the average values. These calculations put all the tubes on a consistent basis. A print out of the results completed the second section. The condensing coefficient correction factor was calculated in the third section of the computer program. The correction factor is by definition that h Cn 1/4 (18) 0.725 kpg X 32

In Equation (18), the mean condensing coefficient, hm, is the mean condensing coefficient for the top n tubes calculated from the experimental data. The correction factor for the top tube was calculated using the values of the heat duty and exit water temperature calculated in the previous section. The overall heat transfer coefficient, logarithmic temperature difference and inside heat transfer coefficients were then calculated and the mean condensing coefficient computed from Equation (8). 1 1 A -h (8) h U A. h. - rm m o i i Equation (16) was used to calculate the temperature drop across the condensing film U At 0 m At = m(16) f h m and Equation (3) used to calculate the film temperature. tf = t - - At (3) sv 2 f Once the film temperature is known, the quantity with n = 1 1/4 k p gk 0.725 D can be calculated and C computed from Equation (18) for the top tube. 33

To determine Cn for the top two tubes in the vertical row, the heat duties calculated in the second section for the top two rows were added to give the total heat transferred. Using mean values of the water density and heat capacity for the top two tubes, the average exit water temperature for the top two tubes was calculated. The logarithmic temperature difference, overall heat transfer coefficient and inside heat transfer coefficient were next calculated and the mean condensing coefficient calculated from Equation (8), the temperature drop across the condensing film calculated from Equation (16) and the film temperature calculated from Equation (3). The quantity 1/4 0. 725[ k3 was computed and the correction factor for two tubes in a vertical row calculated from Equation (18). The correction factors for 3, 4...9 tubes in a vertical row were calculated by adding the heat duties for the top n tubes and following the procedure previously outlined. Tables III and IV give the values of the condensing coefficient correction factors for a vertical row of 1 to 9 copper and titanium tubes respectively. The results were obtained from experimental data taken at a steam pressure of approximately 2 inches of mercury absolute and an inlet water temperature of 75 ~F. Average values of Cn for each water velocity are given in Tables V and VI for copper and titanium tubes, respectively. The results are also presented in Figures 13 and 14. Average values of Cn for all the data as a function of the number of tubes in a vertical row are given in Table V for copper tubes and in Table VI for titanium tubes. These results are shown in Figure 15. The computer program and typical calculated results can be found in Appendix D. 34

TABLE III Condensing Coefficient Correction Factors for Condensation of Steam at 2 Inches Mercury Absolute Pressure on 1-9 Copper Tubes in a Vertical Row G, for n Copper Tubes in a Verticai Row Run No. Vel. 1 2 3 4 5 6 7 8 9 197020A 6.071 1.3292 1.3060 1.3173 1.3243 1.3440 1.3780 1.3898 1.4060 1.4199 197020B 5.854 1.3171 1.3124 1,3092 1.3264 1.3446 1.3608 1.3724 1.3872 1.3985 197020C 5.879 1.2779 1.2969 1.3292 1.3360 1.3602 1.3765 1.3878 1.4055 1.4180 197021A 8.970 1.2901 1.2667 1.2946 1.3299 1.3454 1.3611 1.3687 1.3786 1.3906 197021B 8.907 1.2540 1.2614 1.2927 1.3183 1.3338 1.3502 1.3626 1.3789 1.3974 1970210 8.865 1,2651 1.2612 1.2760 1. 2900 1.3098 1.3348 1.3459 1.3625 1.3799 197022A 11.616 1.2466 1.2569 1.2779 1.2926 1.3027 1.3260 1.3190 1.3330 1.3524 197022B 11.608 1.2268 1.2584 1.2652 1.2747 1.2926 1.3112 1.3196 1.3396 1.3622 1970220 11.598 1.2640 1.2586 1.2899 1.3009 1.3112 1.3332 1.3500 1.3674 1.3860 197023A 16.415 1.2723 1.2897 1.2998 1.3166 1.3484 1.3697 1.3697 1.3864 1.4067 U' 197023B 16.393 1.3047 1.2680 1.3268 1.3596 1.3887 1.4063 1.4108 1.4246 1.4333 197023C 16.391 1.2606 1.2265 1.2447 1.2886 1.3221 1.3299 1.3487 1.3680 1.3863 197024A 20.355 1.3490 1.3331 1.3721 1.3812 1.4039 1.4237 1.4173 1.4315 1.4463 197024B 20.349 1.3337 1.3263 1.3680 1.3965 1.4217 1.4341 1.4387 1.4486 1.4614 197024C 20.330 1.3410 1.3605 1.4248 1.4608 1.4860 1.5069 1.4875 1.4947 1.5033 197025A 25.440 1,3170 1.3227 1.3610 1.3901 1.4157 1.4371 1.4379 1.4558 1.4711 197025B 25.441 1.3609 1.3523 1.3954 1.4200 1.4542 1.4761 1.4872 1.4964 1.5064 1970250 25.412 1.3461 1.3424 1.3821 1.4142 1.4444 1.4716 1.4881 1.5002 1.5149 197026A 16.-888 1.3393 1.2869 1.3390 1.3664 1.3954 1.4152 1.4254 1.4318 1.4447 197026B 17.006 1.2687 1.2548 1.3164 1.3122 1.3449 1.3727 1.3790 1.3914 1.4093 1970260 17.122 1.2738 1.2902 1.2998 1.3347 1.3653 1.3759 1.3865 1.3997 1.4139 197027A 20.025 1.3417 1.3386 1.3651 1.3827 1.4054 1.4189 1.4295 1.4383 1.4500 197027B 20.012 1.3209 1.2692 1.3244 1.3578 1.3876 1.4094 1.4168 1.4256 1.4403 1970270 20.030 1,3323 1.3329 103694 1.3871 1.4106 1.4343 1.4252 1.4356 1.4529 197028A 25.528 1.3564 1.3473 1.3860 1.4088 1.4412 1.4682 1.4695 1.4803 1.4940 197028B 25.526 1.3605 1.3586 1.3923 1.4052 1.4293 1.4505 1.4605 1.4722 1.4877 1970280 25.509 1.3550 1.3561 1.3980 1.4251 1.4559 1.4689 1.4767 1.4870 1.5019

TABLE IV Condensing Coefficient Correction Factors for Condensation of Steam at 2 Inches Mercury Absolute Pressure on 1-9 Titanium Tubes in a Vertical Ro;.C for n Titanium Tubes in a Vertical Row n Run No. Vel. 1 2 3 4 5 6 7 8 9 197039B 6.561 2.0469 1.6098 1.6352 1.5634 1.5538 1.5496 1.5385 1. 568; 1. 5688 197039C 6.458 1.9287 1. 5229 1.5799 1. 5546 1.5538 1.5391 1.5368 1.5618 1.5788 197040A 9.390 1.8320 1.5144 1.5168 1.4904 1.4770 1.4926 1.4997 1.5201 1.5376 197040B 9.298 1.9756 1.6037 1.5480 1.5257 1.5248 1.5447 1.5425 1.5590 1, 5796 197040C 9.312 1.8910 1.5661 1.5418 1.5377 1.5453 1.5582 1.5446 1.5561 1.5634 197041A 13.377 1.8025 1.4776 1.4271 1.4047 1.4071 1.4208 1.4172 1.4383 1.45>C 197041B 13.362 1.9264 1.5651 1.4956 1.4615 1.4680 1.4788 1.4756 1.4932 1.5108 197043A 20.911 1.9215 1.5342 1.4751 1.4568 1.4945 1.5270 1.5156 1.5273 1.5398 197043B 20.819 1.9452 1.6350 1. 5973 1.5322 1.5297 1.5250 1.4897 1.4793 1.4707 197044A 24. 876 1.9854 1.6513 1.6066 1.6021 1.6203 1.6401 1.6456 1,6584 1.6692 197044B 24.884 1.9611 1.6246 1.5593 1.5695 1.5952 1.6131 1.6103 1.6275 1.6447 cY, 197044C 24.904 2.0514 1.6571 1.6309 1.6233 1.6369 1.6497 1.6501 1.6608 1.6774 197048A 13.286 1.8316 1.4979 1.4838 1.4989 1. 5026 1.5047 1.5000 1. 5048 1.5136 197049A 16.258 2.0196 1.2668 1.5406 1.4791 1.5051 1.4960 1.4776 1.4841 1.531; 197049B 16.270 1.8789 1.5202 1.4931 1.4552 1.4884 1.4913 1.4761 1.4810 1.497197049C 16.270 1.8676 1.5168 1.4700 1.4578 1.4698 1.4771 1.4520.4650 1.48:> 197050A 21.020 1.8453 1.5460 1.5389 1.4861 1.5027 1.5013 1.4801 1.4932 I. 519:~ 197050B 21.014 1.8632 1.5307 1.5103 1.4798 1.5032 1.5063 1.4959 1.5247 1.5489 197051A 24.842 1.8360 1.5944 1.6104 1.5915 1.7399 1.7242 1.6945 1.6896 1.6213 197051B 24.848 1.8801 1.6715 1.6510 1.6009 1.6219 1.6426 1.5961 1.6139 1.6340 197051C 24.835 1.9195 1.6065 1.5557 1.5071 1.5370 1.5471 1.5110 1.5419 1.5484 197052B 16.400 1.8383 1.4961 1.4502 1.4533 1i.4794 1.4898 1.4940 1.4991 1,5152 197052C 16.364 1.9092 1. 5958 1.5597 1.4906 1.4954 1.4866 1.4857 1.4893 1 5002 197053A 21.107 1.9730 1.5997 1.5426 1.4852 1.5082 1.4952 1.4849 1.4943 1.5144 197053B 21.035 1.8459 1.4895 1.4848 1.4523 1.4833 1.4953 1.4834 1.4879 I.4974 197054B 24.850 1.9551 1.6027 1.5339 1.5010 1.5360 1.5514 1.5594 1.5833 1.6054 197054C 24.846 1.8983 1.5374 1.4936 1.4726 1.4824 1.5075 1.5251 1.5459 1. 5702 197047A 9.483 1.8539 1.5330 1.5143 1.4747 1.5087 1.5241 1.5302 1.5441 1.5613 197047C 9.516 1,9570 1.5970 1.5409 1.5074 1.4927 1.5016 1.4995 1.5448 1. 5417

TAB LE V Average Values of Condensing Coefficient Correction Factors for Condensation of Steam at 2 Inches Mercury Absolute Pressure on 1-9 Copper Tubes in a Vertical Row C. for n Copper Tubes in a Vertical Row Avg. Vel. ft. /sec. 1 2 3 4 5 6 7 8 9 5,935 1.3081 1.3051 1.3186 1.3289 1.3496 1.3750 1.3833 1.3996 1.4121 8.914 1.2697 1.2631 1.2878 1.3094 1.3287 1.3487 1.3591 1.3733 1.3893 11.607 1.2391 1.2580 1.2777 1.2894 * 1.3022 1.3235 1.3295 1.3467 1.3669 16.702 1.2866 1.2694 1.3044 1.3297 1.3607 1.3783 1.3877 1.4003 1.4157 20.183 1.3364 1.3268 1.3707 1.3943 1.4192 1.4346 1.4358 1.4457 1.4590 25,476 1.3493 1.3466 1.3498 1.4106 1.4401 1.4620 1.4700 1.4819 1.4960 Average 1.3076 1.3013 1.3340 1.3356 1.3801 1.3393 1.4065 1.4195 1.4344 TAB LE VI Average Values of Condensing Coefficient Correction Factors for Condensation of Steam at 2 Inches Mercury Absolute Pressure on 1-9 Titanium Tubes in a Vertical Row C for n Titanium Tubes in a Vertical Row n Avg. Vel. ft. /sec. 1 2 3 4 5 6 7 8 9 6.510 1.9878 1.5664 1.6076 1,5590 1.5538 1.5444 1.5377 1.5593 1.5738 9.400 1.9019 1.5628 1.5324 1.5072 1.5097 1.5242 1.5233 1.5448 1.5567 13.342 1.8535 1.5135 1.4688 1.4550 1.4592 1.4681 1.4643 1.4788 1.4940 16.312 1.9027 1.5511 1.5027 1.4672 1.4876 1.4882 1.4771 1.4837 1.5068 20.984 1.8990 1.5559 1.5248 1.4821 1.5036 1.5084 1.4916 1.5011 1.5144 24.861 1.9359 1.6182 1.5802 1.5585 1.5962 1.6095 1.5990 1.6152 1.6213 Average 1.9135 1.5613 1.5361 1.5048 1.5184 1.5238 1.5155 1.5305 1.5445

Water Velocity o 5.9 ft/sec A 8.9 ft/sec 1.6 o 11.6 ft/sec v 16.7 ft/sec o 20.2 ft/sec * 25.5 ft/sec 1.5 average Maximum deviation-5.3 o * O > 0 1.3 L ~ 1.2 1 2 3 4 5 6 7 8 9 TUBES IN VERTICAL ROW Figure 13. Condensing Coefficient Correction Factors for Condensation of Steam at 2 Inches of Mercury Absolute Pressure on 1 to 9 Copper Tubes in a Vertical Row 38

2.0 Water Velocity o 6.5 ft./sec A 9.4 ft./sec 1.9 o 13.3 ft./sec v 16.3 ft./sec o 20.9 ft/sec * 24.9 ft/sec 1.8 -- average o Maximum deviation 6.3 % 1.7 1.6 - o~00 4 V V a 1.4 1 2 345 678 9 I 2 3 4 ~ 6 7 8 9 TUBES IN VERTICAL ROW Figure 14. Condensing Coefficient Correction Factors for Condensation of Steam at 2 Inches of Mercury Absolute Pre ssure on 1 to 9 Titanium Tubes in a Vertical Row 39

I I i.1 I....I I i i 2.0 1.8 ) 1.6 TITANIUM TUBES 1.4 COPPER TUBES 1.2 1.0 I I I I,I I I I 1 1 2 3 4 5 6 7 8 9 TUBES IN VERTICAL ROW Figure 15. Mean Values of the Condensing Coefficient Correction Factors for Condensation.of Steam at 2 Inches of Mercury Absolute Pressure on 1 to 9 Copper and Titanium Tubes in a Vertical Row 40

DISCUSSION OF RESULTS The results of this investigation are given in Tables III- VI and Figures 13 - 15. As can be seen in Figure 15, the condensing coefficient correction factors, Cn, are higher for titanium tubes than for copper tubes. The maximum value of Cn for titanium tubes occurs for the top tube where Cn is 46 per cent higher than the value for the top copper tube. The difference in Cn diminishes to a more or a less constant value of approximately 8 per cent greater with 6 to 9 tubes in a vertical row. Inundation drastically reduces the effectiveness of titanium tubes with essentially all the improvement being a result of the increase on the top tube. In Figures 12, 13 and 14, there appears to be a consistent trend in which for a given number of tubes in a vertical row Cn varies with the tubeside water velocity (or condensate loading as both are directly related). For low and high velocities the correction factor is higher than for intermediate velocities. This might be attributable in part to an error in the average heat transfer coefficient and in part to varying degrees of turbulence in the condensate film depending upon the tube condensate flow rate. These two factors are closely coupled since it is tentatively assumed that the condensate turbulence effect is constant over the entire range of condensing conditions when taking Wilson plot data. The maximum deviations from the mean values in Figures 13 and 14 are 5.3 and 6.3 per cent, respectively. Visual observation of low pressure steam condensing on the nine titanium tubes in vertical row revealed that as could best be seen, only filmwise condensation was occurring. Visual observation of the top tube was limited and it could be possible that partial dropwise condensation was occurring on this tube. The generally lower wettability of the titanium tube surface increases the condensing coefficient but not to the point where dropwise condensation will persist for multiple tube arrangements. 41

CONCLUSIONS AND RECOMMENDATIONS The slightly higher average condensing coefficients obtainable for titanium tubes (8-10 percent) are compensated'to a certain extent by the low thermal conductivity of the metal (approximately 10 Btu /hr. - sq.ft. - F /ft.) when compared to copper or admiralty condenser tubes. Full advantage of titanium tubes can be realized when compared to the lower thermal conductivity alloy condenser tubes such as cupro-nickel and stainless steel. The greater allowable design stresses permissible with titanium tubes compared to those for the cupro-nickel alloys makes it possible to use considerably thinner tube walls which makes titanium tubes attractive for both improved condensing coefficients and reduced weight. The errosion and corrosion characteristics of titanium further add to the benefits of titanium tube s. To determine if a significant advantage can be realized when using titanium tubes in steam condensing, an actual condenser should be designed with the results presented here and a comparison made to existing conventional condensers. 42

LITERATURE CITED 1. Jakob, M. Heat Transmission, Vol. 1, John Wiley and Sons N. Y., N. Y., 1949. 2. Katz, D. L., Young, E. H., and Balekjian, G., Pet. Ref., Vol. 33, No. 11, pp. 175-178, 1954. 3. Katz, D. L. and Geist, J. M., Trans. ASME, 70, No. 11, pp. 907914, 1948. 4. Short, B. E. and Brown, H. E., Institution of Mechanical Engineers and ASME Proceedings of the General Discussion on Heat Transfer, Section I, London, pp. 27-31, 1951. 5. Young, F. L. and Wohlenberg, W. J., Trans. ASME, Vol. 64, No. 119 pp. 787-794, 1942. 6. McAdams, W. H., Heat Transmission, McGraw-Hill, 3rd Edition, 1954. 7. Watson, R. G. H., Brunt, J. J. and Birt, D. G. P., "Dropwise Condensation of Steam", International Developments in Heat Transfer, Part II, ASME, N.Y., N.Y. 1961. 8. Wilson, E. E., Trans. ASME, Vol. 37, pp. 47-82, 1915. 43

F' APPENDIX A. TUBESIDE WILSON PLOT DATA FOR COPPER AND TITANIUM TUBES 44

TABLE VII Wilson Plot Data for the Top Copper Tube in the Center Vertical Row, First Set RUN NO. W WATER r wATER IN T WATER OUT T STEAM LB/HR F F F 178730 8295 75.850 79.160 100.870 178732 9350 75.760 78.890 100.820 178733 5000 75.620 80.470 100.890 178734 7400 75.600 79.350 100.860 178735 9320 76.030 79.120 100.960 178736 8290 76.220 79.600 100.850 192161C 2930 74.810 81.210 100.000 1921638 3890 74. 830 80.460 100.440 1921648 4840 75.070 80.160 100.760 192165B 5810 75. 120 79.640 100.830 192166A 1781 74.920 83.070 100.590 192187 6935 75.050 79.000 100.960 192188 8200 74.420 78.020 101.030 192189 9320 74.880 78.000 101.080 192190 8150 75.160 78.630 101.080 192191 7000 74.770 78.650 101.060 192192 5955 74.820 79.220 101.160 192193 4980 74.920 79.820 101.070 192194 3770 75.020 80.810 101.060 192195 2890 74. 940 81.610 101.020 192196 5880 74.820 79.220 101.080 192198 6100 75.660 79.880 100.930 192199 7115 75.800 79.550 l01.010 TABLE VIII Wilson Plot Data for the Top Copper Tube in the Center Vertical Row, Second Set RUN NO. W WATER T WATER IN T WATER OUT T STEAM LB/HR F F F 197020A 2345 75.180 83.-250 101.310 1970208 2240 75.200 83.350 101.170 197020C 2260 74.960 83.100 101.240 197021A 3505 75.020 81.710 101.140 1970218 3446 75.090 81.820 101.430 197021C 3421 75.320 82.020 101.320 197022A 4480 74.870 80.710 101. 00 1970228 4490 75.170 80.990 101.530 197022C 4490 75.090 80.930 101.180 197023A 6315 74.930 79.780 101.250 1970238 6300 75.000 79.900 101.190 197023C 6305 75.240 80.010 101.160 197024A 7850 74.810 79.140 100.920 1970248 7850 74.960 79.310 101.350 197024C 7850 74.990 79.320 101.150 197025A 9800 75.010 78.690 101.080 1970258 9800 75.000 78.810 101.500 197025C 9800 74.960 78.740- 101.410 197026A 6500 -74.840 79.674T 100.800 1970268 6540 74.660 79.360 100.780 197026C 6595 74.530 79.250 100.870 197027A 7735 74.730 79.070 100.720 1970278 7735 74.780 79.120 101.000 197027C 7735 74.840 79.180 100.920 197028A 9840 74.990 78.700 100.850 1970288 9840 75.040 78.760 100.910 197028C 9825 75.040 78.750 100.880 45

TABLE IX Wilson Plot Data for the Top Titanium Tube in the Center Vertical Row, First Set RUN NO. W WATER T hATER IN T WATER OUT T STEAM LB/HR F F F 178737 4200 75.220 80.150 100.520 118738 5340 75.060 79.330 100.710 178739 6375 74.990 78.870 100.810 178740 7480 75.130 78.540 100.720 178741 8770 74.990 78.090 100.830 178742 9920 74.940 77.780 100.870 178743 3070 74.830 80.820 100.860 178744 2220 74.840 81.870 100.910 178745 4022 75.440 80.600 101.380 178746 5290 75.110 79.530 101.240 178747 6320 75.000 78.930 101.270;178748 7550 75.000 78.470 101.220 178749 8710 74.900 78.100 101.260 192241 9980 75.070 77.960 101.330 192242 4220 74.920 80.020 101.330 192243 3082 74.770 80.750 101.270 192244 2240 74.850 81.960 101.420 TABLE X Wilson Plot Data for the Top Titanium Tube in the Center Vertical Row, Second Set RUN NO.........WWATER ATER IN T WATER OUT T STEAM LB/HR F F F 197039A 2690 75.230 81.880 101.150 1970398 2656 74.980 81.840 101.240 197039C 2634 74.760 81.660 101.310 197040A 381.... 8 7... 4.950 80.560 101.200 1970408 3761 74.860 80.630 101.250 197040C 3763 74.930 80.650 101.320 197041A 5387 75.170 79.680 100.950 1970418 5368 75.310 79.890 100.990 197041C 5368 75.280 79.760 100.890 1970428 6508 75.210 79.200 101.150 197042C 6525 75.250 79.230 100.970 197043A 8420 74.680 78.180 100.940 1970438 8458 74.680 78.200 101.110 197044A 10110 74.860 77.970 101.110 197044B 10112 75.000 78.080 101.080 197044C 10112 74.990 78.100 100.960 197045A 2774 74.920 81.750 101.220 1970458 2774 74.870 81.730 101.200 197046A 3124 74.990 81.240 100.780 1970468 3098 74.830 81.180 101.100 197047A 3855 75.300 80.820 101.160 1970478 3844 74.840 80.580 101.120 197047C 3873 74.730 80.410 101.180 197048A 5340 74.930 79.490 100.780 197048B 5360 75.060 79.670 100.930 197048C 5359 75.320 79.800 100.940 197049A 6550 75.200 79.320 101.020 197049B 6540 75,350 79.380 101.050 197049C 6540 75.240 79.280 101.060 197050A 8460 75.110 78.520 101.070 1970508 8500 75.000 78.380 100.720 197051A 10110 74.740 77.780 101.060 197051B 10105 74.820 77.870 101.000 197051C 10130 74.900 77.970 101.120 197052A 6605 75.010 78.920 100.840 1970528 6605 75.250 79.230 100.950 197052C 6590 75.200 79.240 100.990 197053A 8530 75.070 78,530 101.040 1970538 8530 75.360 78.720 101.050 197053C 8480 74.900 78.360 101.120 197054A 10130 74.620 77.780 101.060 1970548 10100 74.780 77.880 101.060 197054C 10100 74.760 77.830 101.030 46

APPENDIX B. MODIFIED WILSON PLOT COMPUTER PROGRAM AND A SET OF TYPICAL OUTPUT 47

TABLE XI Modified Wilson Plot Computer Program Written in the Michigan Algorithm Decoder Language SCOMPILE MAU, EXECUTE, DUMP, PUNCH OUJECT C-WP 001 VCTIOR VALULS DATA= $ 11., 5F!0.4.4 VECTOR VALUE -U CAIA = 14, C6, 10.0. 3FIU.3 H$ VECTOR VAL. U:S DATA2 = 2 ZC6 M $ VF.ECTOR VALE.; OU1-I = U 32/ IUBE UIbIDE IU'IAMEIER - INCHES 1 S (:, I 11.4 /. R WILSON PLOT PROGRAM 1311 TJt INATEF TUIMD R INCHE1 $31; F)O.4 22t, T JR!- T i,-I l5C1H F ] 0.44 1~ 2; TJH'e LGTh- INCHE.U', %40, ETD.4 / 14' Tuiit TH" NMAL H(.N;.(CTH.IV ITY - oTU/HR-kI- F' 521., P1.4/ INTEGER I, RUNNO, METALI, METAL2, C. RUNS I2tH TNT-' 3-TEfL H4H, 2Ch _ *$_ b'~i;E43'IURF,JIDI)E HEAI IRAN.1!R AREA - DIMENSION WTUBE(50), TTUBEI(50U, TTUBEO(50), vAPORTM50)I,' H AL UI 43 HM 1 TAVGH 5C), CPT(50), LAT(50), Q(50), LMTD(50),-VISCD50), -/ 191 I4 14Ln ~tiE IUSIE hE~ I~i~~tlii A~c jlF/FT 20. F.10.4~~I - 2 DENI50), KT(50), PR(SC), REI50), VEL(50L, TWALLAI50), 14H T N A INHEL AEA - 3H)F HFH 1Z/h TJ;,F F-LOW AR~ S;-i S0 1. /..... 3 VISCWI50). TWALL(50), TWALLO(50), DELTF(50), FILMT(50) 1H T L i 1 540 13.7 4 KCOND(50) DCONNDT50ST VC"TDISN), PHIIGR(50. FJNCTA(UI )UI I 31 -IL RMIA1 C - *-/TT-'FT-F`29, F13.7 1O I: N L:.O-FFI.CIENT COiNSTAN T 5 FUNCTE(C), RUNNO(S0), 5T2), HIISC0), HCONDD50), U$1$D, E5. O U5 H -' ~ ~~~~~VF('T:;R VALU-~S RFSI! = 7H-AFTER 12~ 18H ITERATIONS9 I 6 A(8), D(8), F(8), F(8I, G(8), HIS), K(8), L(), CONS(50), T AFT 12, ITEATIS, CI 7 MUNDI I- 24H, AONDFT %ING CUNESTAT = F8.5 * IC:], VAI_'j, 2-4 ~; dNN START PRINT FORUAT TITLE II AI-I - El-UT =412OHD RMN ND W TUBE PRINT COMMENT M8S T TH` T TJE HUT T-A VG T-CPL[~ SUMLAT = SC 2T- -i T T TYV I II C F F1TT F B eTU/ READ FORMAT DATA, RUN2$, ID, UD, TL, T,' CI 4 I LI/CUEJ H /FT-HA READ FORMAT DATA2, METALI, METAL2 vECIOR VAL.UH E RESLT A I1, CA, F:4.O, 6F15.3. *$ PRINT FORMAT OUTI, OD, ID, TL, HK, ITETALi, EETAL2 V CI;R VALUTI:H HFADL2 1ZHH2 HUN NO T- THROUGH ALPHA, FOR I = 1, 1, I G. RJN S I PM T ALL IF TW-VISCCOITY T-HELACIT ALPHA READ FORMATT DATAI RUN(I), RUNUTII, wTJBL(I), TTUAEI I), 2 RE ET1 A0 B I TTUBEG(I), VAPORT(I) F LB/FT-HR F1 TTCPHCT I), AXPUETTIT 1~~~~~~~~~~~~~~~~~i/-'IF-FT F LA/FT-MM - F - OD = OD/12.0- 4T/SFCA BIL/P.- E /FA ID = ID/12.0 VECTOR VALUT.S RM.LT2 = $ I9 C6, Fi5.4, F15.3, 2F15T.2. TL = TL/12.0 1 2FI5.3, F15.2 *$ AOT = 3.1416*ODT*TL VEC. TR VALUES. IF-A; = i 1Ci-4'2 HUN NO VAPOR TEMP...... AIT = 3.1416*ID*TL I LOT IIEAT T L I FILM T FILE RM M= (OD-ID)/(TT*2.0) 2 2-K C-DMKENIT_20H D, = (OD-ID)/ELOG.(OD/ID) 3 F F AMFT 3.1416*DM*TL 4 F TU/- FT L/C / AFLOW =3.1416*ID*ID/4.0 4 F tT/'R'i........... ~AF~~~LDACW = U.I3~4T~6HIDEID/4.~ ~VEACTOR VALAE3 R;-:,13 A: 1.9, C6, F15), FrI.2, 3F1VH.$, FIb.4 PRINT FORMAT CUT2, AT, AIT, AFLOW, RM, CI I F15.3 E$ THROUGH UFTA, FOR I = 1, 1. I.G. RUNS VECTOR VALL:E —,tFAD4 - 9,H2 RhN NH C-VI$CHITT TAVGT I) =(TTUcEIII) + TTUBO(IDIT)/2.0 1 PHYCR FUNCT A FUNCT CPTII) = A(I) + A(,J*TAVG(I) + A(2)*TAVTX I).P.2 + H.2 S0UE 1 A(3)*TAVG(I).P.3 + A(4)*TAVG(I).P.4 + A(5)*TAVG(I)I.P.53 /E VISCII) = EXP.( C) + DC(1)/TVG() ()/TAVG(I) P.2 + V/CTOR VTA-PFM RAGI1 M C 19 C6 E M L F19., 2E15H.. MA 1 D(3)/TAVG(I).P.3 + J(4)/TAVG().P.4 H.(5)/TAVG(I).P.5) T RUN NO HEAT DUTY DEN( I-) = F(O) + FT1I*TAVS(I) + F(2I*TAVH(I)IP.2 + LVTLU H COND 1 FI3)*TAT G(I).P.3 + FI4)*TAVGjII. P.4 + DJIS*TAVG(I).P.5 r BTuT/MR KT(I) = G(0) + G(iI* TAvG(i) + G2)*TAV(I I P.2 - sFT-I-.T/i/HR-:FI-F LI,/H-.F'- F /* 1 G(3)*TAVG(I).P.3 + G(4)I TAVG(i ).P.4 + G(5)*TAVG(I).P.5 vECTOR VAL-E. RFSLT, = I9, Cb, FiD.1, Fib.3, 3F15.2 *$ LATIT) = F(O) + E(TI)VA PORTT1) +.(2)*VAPOR'T1I)..2 + V:.CIH' VAL E A..1'124',GE 0, -I.4667bA 63T_ -3 1 E(3T*VAPORT(I).P.3 + EI4)*VAPORT(I).P.4 +:-(5)-VAPORT(I).P.5 8'.'Sgba 6 67E-S:- -.`72i74!4 —07 7.72640616E -10 O.OEO SUMLAT = VUH".AT + LAT(I V T.i VT L'JD.: -L:.2173-;3],'.54722744E23, (I) =?,TUE(I)*CPT(1I)TET t U I -ITTU-TI(II -C113,;.2476454L2ED8, o.QEEO LTDTII (TI-TTLIuTEATIT -TTFFIITI//( IELAGIt.( I1APR T(IT - _,:';. = 15 -..O C, C.C,.C, I TTUBEIETIT /(VIAPT T(I) - TT'o'RPC0I)))) V T,-'," VV t CA.DT UOIT) =11I Ii/I4O0T*LTI )) -LT-TRI',/IlRTV * H. = C.T3 L77-2'TC- 0I..-67I6CE-OIA PR(I) = CPT(I)IVI`THAI /KTCI ) "I- "-',- 3, -C.74d47219E-C7,.17537457E-09, 0.OEOM. RE(1)I = ID*WTUXE(II /AFLOX*VISC(II) TVEI_-I', VLLJFs h =.03 779' 7!,'.3 i'67AD- E-03, RETA VEL(I) WTUI E(I)/XAFLHOW*DFNT)*3600.0) I H.4- 4C5 E-~, --. Tb&4721 - 7, %. 175C7457E-09,.DE ___ AVGLAT SAUMLALT/RUH S F' LE V.LDF` K = 3,I63 1 -' 2 I, 17U(;.CE-dlI, OUEO RET2 THROUGH GAT-IA, FCR I = 1, 1. I.G. RMOS V'T VLF -LA../67)-, C. H?72,":41E0 3 TWALLAHI) TAVG(I) I -CI4IJ6J 8'!', C' l IqL 3Z +'7, -0.24 o,+u-1:-,d I.GEC _ RET1 VISCW(I) - EXP.D(O) + DI1)/TWALLA(I) + D(2)/TWALLA (II.F.2 + TRIl-:: T- O S-IAR19 I Di(3)/TWALLA(I).P.3 + D(4)/TWiALLA(II.P.4 +Hi(5)/TvALLA[I.P.t.,..-.. HITI) = -I*KT(IT*RM (')E.P..8*PRMII.P0C.3333*\/TI~C(I)/ VISCW(I )).P.C.14/1D TWALL(I) = TAVG(I) H Q(i)/(tITEHI(I)) WHENEVER.A-S.(TWALLA(I) - TWALL(I)).G. 0.3 TWALLA(II = TALL(I LC., i..-... FL-. ARF:,. Pi. TRANSFER TO RFTI aHIT HlSl L T!,F HkA1A, S.TFT. END OF CONDITIONAL T9M'T TT L -'-.:=TTL LR —1- 4T TWALLO(I) = TWATLL(I) +,., TiHR/AiLT: I`IAL D:::F,, TRANHSFER AREA, $,.FT. HCCN.(I = 1.N /(1,C/dO(I) -AHT*RI:/AMEIT - AOI/(Tl*THIITT))) T(II T;AiTAT;-JR hEATT CPACIIY OF HATER DELTFIT UC(I)*LI`TD(I/ I/CC'NI)[)';)`A'LT. I:/R L'A.r.ART fI - ROUNTINE F'ILMT(IT VAPORT( I - D~LTF(I)/ 2OC V;,_:F NI::: i:/2. AN COEFFICIENT CAONTIANi CALCULT ED FR'" KCONDI(I = T () 0 )-]iFILiT(IC) + H (TI2 FIL;,'T(IIP.2 + LCT 4:: "RO -'TiNc 1 H(3i*FILT(I)T.P.` + h(4);-FIIL:TTT IIP.4 + I(5)-FILDTTIi.P.5, "-'S-::N-' V"L'Jr OF INLI-:D HILAT 3RAN':FHR COEFFICIENT CON$TIANT DCAN, I TI HI(T + l TE *FILl-!TT T:II + T 2 TF.'L2TI TI ( P. A2 + IC' iFICNT CONSTANT CALCULATED FROM INTERCEPT I K(3)i F IL:,T(I. PH3 + K(4)1 FIL,'T(I).P.4 + K(5)*FILTT() I.P.5 CNZ,. U,'N ";'.:CITNT CONS4TANT TO REPLACE 0.725 VCOND(I)= XP. ( LIII L(I)/FILIT(I) + L(2)/FLIL1T( TI).P.2 + 1 L(3)/FILHTT( I).P.3 + L{4)/FIL4T(II).P.4 + L( I)/ F-ILT.P) PT PECIFTI EDT 7S PHYGR ( = (KCONNI ()*CCONO[I) *KCl:'L')1IHCCANT)/T, CI HCUN$~C L -IPC: N.'IF.'"I, LE/C-.PFT 1 (VCANT I )*TELTF I 1 )).P.0;.2a T4.=. H P k, CNENSATE FIL,! F. CONST(Ii = HrCt,'( I)*(OID/(LAT I I)* 4.7*lG.O.P.8)).P.O.25/ _ NI;'-II." CF:, TRL:/ L T CANSI IT - H 1- -III 1/0/142111 1H4.TAETA.A.D.MI T.E.D./S/~~~~~~~~~~~~~~~~~~~~~~~~~T LI)I A4FIN.CkFT 1 PHYGR(U ):.;:;A )i' F TL IN.R FT. FUICTA(I) =1(1./UO(I) - AT*R/AET )*PYGi(i) 1)',TT- FPORIi I C I v. ATR GAXTE AFUNCIH. II AOT.PHYGR(II.CI/TAI TIlTl TIlT.)) IT C T F'! LT;, STEAM. F -'PLI;Fr L~'F.SEA EXECUTE LSTSA. N(Ft.iNCTE FUNCTA, RUNS, C, 1) FI -!!T -..... — F I-ATCONDC= i G./((0-) *F(4.17*L'.CP.HHAV LAT/O )IT.P.O25) F(A) CIC = 1.,/1(1),T:!:T VIJ r.Ui. T LOS PRINT FOREAT HEADX]UC:,TC V- EL M 1;:UHCT:; V AI.UF FD.R L~ON PLOTS THROUGH Po1, FOR I = 1, I G. RUNS HNS — I5T,- FPR TDFR:E AL COND"CTIVITY OF WATER PAT PR INT PFOIPED1 T. RMESLT 1,UN rI II.M RUNZ TI TI TOOT IITTHDD3I (II, C1F:I.r[N I,.;EFFICIET, iTU/HR.-u. FT.-F. 1 TTUBECDD AITI, TAVIAII CPTI DEN II.I VISCIT I TIHI I $Ir)E r[-iT TRA, F:- R CUEFii ICIE NT, ITU/HR.-HU.FI'.-F..- - - - PkINT DFOR."T MEArtl) HI 1/1,TANT/ FOlR 1IlER4'AL C;P"C-CTTVITY OU CONDENSATE THROUGH P02, FOR I 1, 1,.G. RUNS Tb41E I`I T': IH1A -;F-H. IN. AR FT. PAZ PRINT FORMAT RESLT2,,1 N(I)tIRUNNOli),K[(I),PR (II,IwALL(II Tr1ER-;AL CC4NUCTIV ITY UA CUNDENSAT FILM,,TU/HR.-$5.FT.-F./FT. 1 HISCWlEIT. VAL(II. 1E(I), MiI CCN1DSTANTI FCR D='AsITY OF CONDENSATE PRINT FOR'ATH H HEAl3 T ThFRMAL C NTIUCTIVITY OF' ATR, HTb/MR.-SQ.FT.-F./FT. THRUGH PC3, FOR = 1, 1 I.G. RUNS LT TI-T OP 14 T 1/46. P03 PRINTFC-IMATRFSLT MRUN I)IR!NNOTIVAIAPURT{'I),LAI (II,T,,ALLO(I), L;4T[ L'GARIT HM IC TF'E4PFP'AT L)RF CIFFERENCE, F. I DELTF(I), FILMTP1 1, KCONA(I), COND(I) L() CNSTAN1 FOR VISCOITf OF COADENSATF PRINT FAX.MT HTAD4 TUE OIJTSIDF NIAMHTFR, IN. CR FT. THROIUGH P04, FOR I = 1, 1 I.G. RUNS PHYGR PHYSICAL PH(HPFRTY GRH H P P04 PRINT FORMAT RESLT4, RuN( )I, RUNNO(I, VCUNDTIT, PTHY II, I PFRAIlNIL - OF 14 4HTP F 1 CONS(I)T FIJNCTA(D)T FUNCIT TI HEAT l(ATY,.../AMR. PRINT FORMAT HEALS5 RIHIL DYNF IA DNT'' E - / THROUGH PT5, FOR H = i, 1. I.G. RUN5 R:ETAL RESISTANCE, pR.-$G.FT.(OUTSIDE AREA)-F./oTu PM5 PRINT FORIAT RESLS5, R;jk(I)t, RUNNI( I HI ) ), L41(I)21, HAO(I)T DLXIT -4. OF LTFDT HEAT' FCI ALL MON.- I HIT I, HCONT(I) TTAVU AVERAGF. TUBFSIDE TFMP:RATiURE, F. PRINT CAH'.FNT. -. T ITER AL CCS —%CCII V F I iE HEIAL, Ut3ATHR.-Q.Pi.-F$.DT. PRINT FORMAT RESIT, C, CICL COND.C T1 TUAI LFNCTH, IN.O FT UHENEVER.I.S(CIC - CIC)/CI C 0 G4..24 lITT INLET.4.. T1.F...HAT.. H CI CIC TTURF:O CU;TLET WATFP TF:MPFRATUR ET~ F. TCDAI.A CSTI;4ATIE /ALUL-. (F IN-lDE?,ALL ICM PERAIURL, F. TRAN,%FFR TO RFT2 T,'/LLL a C~T DV~Fo r~~;''L EPRTH, F IXEND P OFC NITHIUOINALL~ CXLIILMTFN VAXLU.F CF 1N4I(14FHALL 1TEAPFMATuRE', F. - ENTA OF CWAnT ITIAN -L 01T2F AELL TE1PFHATUHR, F. VECTOR VALUES TITLE H 110MM AILSAN AFUL nlEM T'NADFLH 44F V T iA/TIR.-HS.F_1.-F. EPLO 1 AITALISIS FSHR 44b4-lu4 MtEAT IHAN.FER'COEFF'CI' NI COHELA 2SF/El STEAl' AM/A THF1AATAE. F. 2ITON -CCNSDXNIHXI42 AC-TA P*$''/l. 4/D M 2210N CONSTANT "b Y~~~~~~~~~~~~~~(.ONDi VISCOSITY OF f'ON.~ t'4CATE~. Lb.~/FT. —HR..LTE. VEL(IT'IT FT./SEE V[C VI:](C4SITY D F: IT IAT:H, L[./FT -99. -—. VI$Cw V~HI —,SITY'F'ATFR-AT WALL TEPERATURE, LR./FT.-HR. - ~Tdr TU1SF. INE FLOW PA[F, LT.,/HR,, 48

TABLE XII Typical Wilson Plot Output Calculated with an IBM 7090 Digital Computer WILSON PLOT ANALYSIS FOR TUBE-SIDE HEAT TRANSFER COEFFICIENT CORRELATION CONSTANT TUBE OUTSIDE DIAMETER - INCHES.6250 TUBE INSIDE DIAMETER - INCHES.5550 TUBE LENGTH - INCHES 72.1560 TUBE THERMAL CONDUCTIVITY - BTU/HR-FT-F 196.0000 TUBE METAL COPPER TUBE OUTSIDE HEAT TRANSFER AREA - SCFT/FT.9839 TUBE INSIDE HEAT TRANSFER AREA - SQFT/FT.8737 TUBE FLOW AREA - SQFT.0016800 METAL RESISTANCE - BTU/HR-SDFT-F.0000149 INSIDE COEFFICIENT CONSTANT.02500 RUN NO W TUBL T TUBE IN T TUBE OUT T-AVG T-CP T-DENSITY T-VISCOSITY LB/HR F F F BTU/LB-F LB/CUFT LB/FT-HR 178730 8295 75.850 79.160 77.505.999 62.223. 2.135 178732 9350 75.760 78.890 77.325.999 62.225 2.140 178733 5000 75.620 80.470 78.045.999 62.217 2.121 178734 7400 75.600 79.350 77.475.999 62.224 2.136 178735 9320 76.030 79.120 77.575.999 62.222 2.133 178736 8290 76.220 79.600 77.910.999 62.218 2.125 192161C 2930 74.810 81.210 78.010.999 62.217 2.122 1921638 3890 74.830 80.460 77.645.999 62.222 2.131 1921648 4840 75.070 80.160 77.615.999 62.222 2.132 1921656 5810 75.120 79.640 77.380.999 62.225 2.138 192166A 1781 74.920 83.070 78.995.999 62.206 2.097 192187 6935 75.050 79.000 77.025.999 62.229 2.148 192188 8200 74.420 78.020 76.220.999 62.238 2.169 192189 9320 74.880 78.000 76.440.999 62.236 2.163 192190 8150 75.160 78.630 76.895.999 62.230 2.151 192191 7000 74.770 78.650 76.710.999 62.232 2.156 192192 5955 74.820 79.220 77.020.999 62.229 2.148 192193 4980 74.920 79.820 77.370.999 62.225 2.139 192194 3770 75.020 80.810 77.915.999 62.218 2.125 192195 2890 74.940 81.610 78.275.999 62.214 2.115 192196 5880 74.820 79.220 77.020.999 62.229 2.148 192198 6100 75.660 79.880 77.770.999 62.220 2.128 192199 7115 75.800 79.550 77.675.999 62.221 2.131

TABLE XII (Continued) RUN NO T-K PR T WALL IN 7W-VISCOSITY T-VELOCITY RE HI BTU/HR-FT F LB/FT-HR FT/SEC BTU/HR-SQFT-F 178730.3497 6.099 86.08 1.93 22.042 106952.392 3661.84 178732.3495 6'.115 85.64 1.94 24.844 120290.727 4023.30 178733.3500 6.053 89.31 1.86 13.288 64892.617 2462.11 178734.3496 6.102 86.96 1.91 19.663 95377.737 3346.49 178735.3497 6.093 85.77 1.93 24.766 120270.862 4018.98 178736.3499 6.065 86.64 1.92 22.030 107415.847 3671.06 192'161C.3500 6.056 91.32 1.81 7.786 38010.936 1610.50 1921638.3498 6.087 90.09 1.84 10.337 50241.693 2012.57 1921648.3497 6.090 89.38 1.86 12.861 62488.694 2393.90 1921658.3496 6.110 88.25 1.88 15.438 74797.695 2762.16 192166A.3506 5.974 94. 0 1.76 4.734 23381.446 1091.22 192187.3494 6.141 86.91 1.91 18.426 88894.336 3169.56 192188.3488 6.211 85.59 1.94 21.784 104074.527 3601.33 192189.3490 6.192 84.77 1.96 24.761 118610.794 3988.92 192190.3493 6.152 85.88 1.93 21.654 104302.220 3598.04 192191.3492 6.168 86.46 1.92 18.598 89381.616 3185.76 192192.3494 6.141 87.68 1.89 15.822 76327.810 2809.36192193.3496 6.111 88.79 1.87.13.233 64104.484 2443.70 192194.3499 6.064 90.60 1.83 10.019 48851.906 1967.10 192195.3502 6.034 92.08 1.81 7.681 37612.589 1596.20.192196.3494 6.141 87.66 1.89 15.623 75366.502 2780.90 192198.3498 6.077 88.00 1.89 16.210 78905.074 2876.51 192199.3498 6.085 81.07 1.91 18.907 91928.070 3246.92 RUN NO VAPOR TEMP LAT HEAT T WALL OUT DT FILM T FILM C-K C-DENSITY 0 F BTU/LB F F F BTU/HR-FT LB/CUFT 118730 100.870 1036.70 86.517 14.314 93.713.3594 62.034 178732 100.820 1036.72 86.110 14.675 93.482.3593 62.036 178733 100.890 1036.68 89.694 11.110 95.335.3603 62.015 178734 100.860 1036.70 87.400 13.410 94.155.3596 62.028 178735 100.960 1036.64 86.229 14.697 93.611.3593 62.035 178736 100.850 1036.71 87.085 13.723 93.988.3595 62.030 192161C 100.000 1037.20 91.622 8.222 95.889.3606 62.008 1921638 100.440 1036.94 90.437 9.887 95.497.3604 62.013 1921648 100.760 1036.76 89.775 10.891 95.314.3603 62.015 1921658 100.830 1036.72 88.671 12.087 94.787.3600 62.021 192166A 100.590 1036.86 94.435 5.896 97.642.3615 61.988 192187 100.960 1036.64 87.345 L3.561 94.180.3596 62.028 192188 101.030 1036.60 86.065 14.922 93.569.3593 62.035 192189 101.080 1036.57 85.240 15.807 93.177.3591 62.040 192190 101.080 1036.57 86.334 14.704 93.728.3594 62.033 192191 101.060 1036.59 86.892 14.116 94.002.3595 62.030 192192 101.160 1036.53 88.103 12.990 94.665.3599 62.022 192193 101.070 1036.58 89.177 11.808 95.166.3602 62.017 192194 101.060 1036.59 90.951 9.987 96.066.3607 62.006 192195 101.0,20 1036.61 92.390 8.466 96.787.3611 61.998 192196 101.080 1036.57 88.071 12.942 94.609.3599 62.023 192198 100.930 1036.66 88.414 12.452 94.704.3599 62.022 192199 101.010 1036.61 87.497 13.462 94.279.3597 62.027

TABLE XII (Continued) RUN NO C-VISCOSITY PHYGR COND C FUNCT A FUNCT 8 L8/FT-HR 178730 1.773 1.629.70443.13372454E-02.12404400E-04 178732 1.778 1.617.73757.12514292E-02.11210015E-04 178733 1.742 1.746.74779.15863888E-02.19775403E-04 178734 1.765 1.658.74641.13473484E-02.13819548E-04 178735 1.775 1.617.72465.12662267E-02.11223358E-04 178736 1.768 1.648.74119.13003189E-02.12517284E-04 192161C 1.732 1.886.72315.21335343E-02.32663172E-04 1921638 1.739 1.799.73661.18061792E-02.24923576E-04 1921648 1.743 1.754.77115.15892956E-02.20438735E-04 1921658 1.753 1.706.76178.14689046E-02.17224404E-04 192166A 1.700 2.063.71368.29545017E-02.52725068E-04 192187 1.764 1.654.73060.13939946E-02.14551559E-04 192188 1.776 1.611.73453.13058577E-02.12475508E-04 192189 1.784 1.586.69398.12966126E-02.11085710E-04 192190 1.773 1.618.71106.13349627E-02.12540418E-04 192191 1.768 1.636.70338.14160007E-02.14323371E-04 192192 1.755 1.675.72043.14891278E-02.16624985E-04 192193 1.745 1.718.71935.16109158-E- 02.19610842E-04 192194 1.729 1.798.72712.18395197E-02.25489170E-04 192195 1.715 1.879.72493.21381909E-02.32825061E-04 192196 1.756 1.676.71349.15044321E-02.16807294E-04 192198 1.754 1.693.73046.14692707E-02.16411893E-04 192199 1.762 1.657.71523.13985849E-02.14236031E-04 RUN NO HEAT DUTY LMTD UO HI H COND BTU/HR F BTU/HR-SQFT-F BTU/HR-SQFT-F BTU/HR-SQFT-F 178730 27425.3 23.326 1195.01 3661.84 1947.42 178732 29232.3 23.460 1266.46 4023.30 2024.62 178733 24222.3 22.759 1081.74 2462.11 2215.95 178734 27718.5 23.335 1207.33 3346.49 2100.91 178735 28766.1 23.351 1252.09 4018.98 1989.34 178736 27988.2 22.898 1242.31 3671.06 2072.91 192161C 18730.6 21.834 871.92 1610.50 2315.53 192163B 21875.8 22.679 980.40 2012.57 2248.91 192164B 24607.6 23.051 1085.00 2393.90 2296.42 1921658 26231.4 23.377 1140.48 2762.16 2205.83 192166A 14498.4 21.336 690.66 1091.22 2499.20 192187 27362.3 23.881 1164.57 3169.56 2050.84 192188 29487.0 24.766 1210.12 3601.33 2008.49 192189 29045.8 24.607 1199.73 3988.92 1867.67 192190 28248.6 24.143 1189.21 3598.04 1952.62 192191 27129.5 24.298 1134.81 3185.76 1953.37 192192 26172.4 24.073 1105.03 2809.36 2047.81 192193 24374.3 23.615 1049.05 2443.70 2098.06 192194 21803.4 23.024 962.51 1967.10 2218.84 192195 19254.2 22.581 866.64 1596.20 2311.67 192196 25842.8 23.993 1094.76 2780.90 2029.58 192198 25712.7 23.096 1131.55 2876.51 2098.76 192199 26650.9 23.285 1163.32 3246.92 2012.09 AFTER 3 ITERATIONS, CI =.02475, CONDENSING CONSTANT =.72746 51

APPENDIX C. CONDENSING HEAT TRANSFER DATA FOR CONDENSATION OF STEAM AT 2 INCHES OF MERCURY ABSOLUTE PRESSURE ON 9 COPPER AND 9 TITANIUM TUBES IN A VERTICAL ROW 52

TABLE XIII Condensing Heat Transfer Data for Condensation of Steam at 2 Inches of Mercury Absolute Pressure on 9 Copper Tubes in a Vertical Row RUN NO. TUBE O-. W WATE& I' WATER IN T WATER OUT T STEAM RUN NO. TURE NO. W WATER T WATER IN T kATER OGT STEAM LB/HR F F F LE/HR F F F 197020A 1 2345 75.180 83.250 101.310 1970218 1 3446 75.090 81.820 101.430 197020A 2 226L 75.280 82.550 10h,290 191021B 2 3330 75.040 81.600 101.340 197020A 3 2232 75.320 82.370 101.270 1970218 3 3312 75.020 80.800 101.240 197020A 4 2250 75.380 82.150 101.220 1970218 4 3312 75.030 80.b20 101.130 197020A 5 2268 75.390 32.100 101.200 1970218 5 3312 75.060 80.460 101.110 197020A 6 2383 75.390 82.030 101.170 1970218 6 3359 75.100 80.380 101.110 197020A 7 2290 75.420 81.880 101.170 * 1970218 7 3359 75.150 80.310 101.100 1970201A 8 2293 75.440 81.920 101.180 1970218 8 3384 75.170 80.330 101.130 197020A 9 2236 75.460 81.960 101.200 1970218 9 3352 75.180 80.380 101.150 RUN NO. TU6E NO. I WATER T WATER IN I WATER OUT T STEAM RUN NO. TUBE NO. W WATER T WATER IN T WATER OUT F STEAM LB/HR F F F LB/HR F F 1970208 1 22460 75.200 83.350 101.170 1970210 1 3421 75.320 I2.020 101.320 1970208 2 2192 75.170 82.580 101.140 197021C 2 331h 75.350 81.230 101.290 1970208 3 2124 75.150 82.300 101.110 197021C 3 3283 75.370 81.010 101.270 1970208 4 2200 75.150 82.080 101.380 197021C 4 3305 75.410 80.830 101.230 197020 5 2196 75.170 82.000 101.080 197021C 5 3283 75.430 80.810 101.230 (i 1970208 6 2196 75.190 81.920 101.080 197021L 6 3359 75.440 80.750 101.220 L1~J 1970208 7 2254 75.170 81.680 101.040 1970210 7 3348 75.490 80.580 101.230 1970208 8 2254 75.120 81.630 101.000 197021C 8 3366 75.520 80.630 101.230 1970208 9 2167 75.070 81.620 100.960 197021C 9 3341 75.540 80.660 101.240 RUN NO. TUBE NO. W WATER T WATER IN T WATER OUT i STEAM RUN NO. TUPE NO. W WA TER, T WATER IN T WATER OUT T STEAM LV/HR F F F LB/HR F F F 19.7020C 1 2260 74.960 83.100 101.240 197022A 1 4480 74.870 80.710 101.100 1970200 2 2221 75.020 82.460 101.240 197022A 2 4345 74.910 79.990 101.250 1970200 3 2196 75.050 82.310 101.230 197022A 3 4327 74.930 79.800 101.390.197020C 4 2200 75.100 82.030 101.230 197022A 4 4349 74.980 79.650 101.520 1970200 5 2203 75.110 82.060 101.230 197022A 5 4309 75.010 79.540 101.500 1970200 6 2214 75.120 81.900 101.220 1970224 6 4388 75.040 79.580 101.480 197020C 7 2214 75.140 81.780 101.160 197022A 7 4352 15.100 79.190 101.480 1970200 3 2232 75.140 81.790 101.150 197022A 8 4406 75.110 79.400 101.490 1970O2 9 2167 75.140 81.770 101.120 197022A 9 4388 75.140 79.500 101.510 RUN NO. TUBE NO. W WATER T WATER IA T WATER OUT F STEAM RUN NO. TU ll NO. W WATER T WATER [N 1 V6ATER OU TrEAM L ~!/hK F F F LB/HR F F F 197021 15 75.020 81.710 101.140 1970228 1 4490 75.170 8(0.990 1970214 2 3370 15.040 80.850 101.070 2970228 2 4356 75.240 90.350 101.450 191321A 3.3 341 75.050 80.730 101.010 1970220 3 4327 75.280 80.010 101.310 1970213 4 3341 75.010 80.640 100.960 1970228 4 4338 75.330 B9.850 101.230 1970218 t 1312 75.000 80.410 100.970 1970228 5 429 s 75.350 73.350 101.250 1970211 6 3314 74.970 80.240 100.980 1970228 6 4)8i 75.380 19.7o0 101.230 197021A 7 3359 14.960 80.100 101.070 1970220 7 4363 75.390 B3.90 109.190 19721A 8 3 34 74.980 80.080 101.luO 1970228 8 4406 75.390 79.590 101.170 1970211 9 1374 75.01(0 80.110 101.250 197022e 9 4360 75.390 73.750 101.150

TABLE XIII (Continued) RUN NO, TUBE NO,.W wATER T WATER IN T WATER OUT T STEAM RUN NO, TUBE NO, i~ WATER T WATER IN t WATER OUT T STEAM LE/HR F F F Lg/HR F F F 197022C I 4490 75,090 80,930 101,180 197024A 1 1850 74,810 79,140 100,920 197022C 2 4350 75,120 80 o 130 101, Z20 19 7024A 2 7546 74,860 78 o 430 101 o 160 197022C 3 4327 75,130 80,020....... 101.270 197024A 3 7603 74,880 78,390 101,40G 19/022C tt tt 3J8 75,170 79,780 101,310 197024a. 4 7607 74,900 78,150 101,550 lqF022C 5 4270 75,200 79~720..... 101o310 191024A 5 7596 74,900 /8,150 [01,ttO [ 97022C o 4381 F5 ~230 79,720 101,300 19 FO2qA 6 7693 74, 9! 0 78 o 050 101 o 400 191022C? 4352 75. 280 79,680 101,21 tO 197024 a, 7 7632 74,890 7?, 710 101 o 290 197022C 8 4599 75,290 79,640 101.320 197024A 8 7744 74,870 77,830 101,260 L97022C 9 4'370 75,310 79,680 - 1-01.3.30 197024A 9 7682 ~4,850 17,810 101,2.30 RUN NO, [U~3E NO. N WATER T ~ATER IN T WATER OUT f S TEAM RUN NO, TUBE NO. W WATER T WATER IN T WATER OUT T,STEAM LB/HR F F F LB/MR F F F 1970Z 3A [ 6315 74. 930 79. 780 101. 250 1970248 7850 74~ 960 19.310 101. 350 191023fi 2 6095 74,960 79, tO0 101. 280 197024B 7535 74,960 78,560 101,430 197023& 3 b116 74.970 78.800 101. 310 1970248 760:3 74.950 78.470 101. 510 197023A 4 6 149 74. 980 78. 680 10 1. 340 197024S 7603 74. 970 78. J~40 101. 530 1970d BA O 60'13 74. 980 78. 760 101. 330 19'70248 7596 74. 980 78. 260 lO 1. 460 19 log 3A 5 6217 74. 980 t8. 570 101.330 197024d 769.3 75. 000 78. 080 101. 340 197073A 7 6 [ 78 74. 950 T8. 260 10 1. 320 [ 970246 7632 75. 020??. 970 101. 290 197023A 8 626~ 74. 920 T8. 360 101. 320 1970248??44 75. 030 77. 950 101. 270 197023A 9 6192 74. 880?8. 390 101. ~2f) 1970248 7675 75. 030 77. 970 lO 1. 240 RUN NO, TUBE NO, W WATER T WATER IN I wATER OUT T STEAM d, UN NO. TUBE NO. W WATER T WATER [N T WATER OUT T STEAM ~_9/HR F F F LB/HR F F F I~ 1970238 6300 75.000 79.900 101.190 197024C 7850 74.990 79.320 101.150:~7o73~ 6o8s 75.o3o 79.o2o tol.32o tgzoz4c 752o 74.91o 78.59o lot.zoo 197023f~ 6106 75. 050?9~ 140 10 [. 450 197024C 758Z 74. 860 78. 510 101.060 197023~ 6138 75.090 78.970 101. 500 197024C 7596 74.880 78.330 100.970 197023B o07~ 75, [ 20 78,940 tO l. 420 19/024C 7589 14,940 78,260 tO0,920 1970238 620o 75.140 78. 740 101. 340 197024C 7690 75. 000 78. 200 100. 870 197023B b tb7 75.170 78. 650 tOl. 270 197024C 762t~ 75.060 77. 820 100. 960 19 70236 62 5 t 75,180 78,540 lO 1,270 197024C 7740 75,060 78,000 101,090 197023)3 o I ~2 75,190 78. 540 101, Z 70 197024C 7675 75,060 78,000 101,220 RUN NO. /Uf~~ NO, W NATrlo, [ It~AT~ZR IN T WATER OUT T STEAM RUN NO. TUBE NO, W WATER T WATER IN [ WATER OUT T STEAM ~_ F, / FIR F F F LZ;/HR F F F I9/OZ3C 030'5 75. 240 80. 010 tO l. 160 197025A 9800 75.010 78. 690 10 I. 080 197023C 50:R~ 75. 230 79.100 10 t.210 197025A 9403 75.020 78. 050 101.120 191023~ 6106 75,220 78,950 10 [. 260 197025A 9482 75,020 77,940 101,160 19702.3C ~5138 75. 240 79,030 10 [, 370 197025A 9529 15,020 17,820 101:250 [ 97023C 6060 75,270 79,000 101,420 197025A 9522 75,020 77,760 101,310 197023C 6199 it5. 290 78. 680 101.470 [ 97025A 9641 75. 010 77. 660 101. 360 197023C 6167 75. 330 78. 800 lO l. 450 197025A 9520 75.000 77.450 101.420 I 97023C 625! 75. 330 78.740 101. 380 197025A 9684 74. 990 77. 540 l 01. tt30 19/OZ3C 61 g2 75. 340 78. 740 101. 300 197025A 9594 74. 980 77. 500 101. 430

TABL XIII {Continued} RUN NO, TUBE NO. W WATER T WAT.ER_..IN. T WATEROiUT T__S.TE.AM. RUN NO. TUBE NO. W WATER T WATER IN T WATERT I TA LB /HR F F F LB/HR FF t1970258 I 9500 75.000 78.8"10 -0i.506 197026C I 6.595 74.530 79.250 oo(7 197025B 2 9403 74. 990 78. 080 101.~440 197026C 2 6332 74.5'10 787540 0. 7 197025B 3 9482 74.990 7...?OO-00 101. 380 197026C 3 6397 74. 500 78. 20 0 0. 7 1970258 4 9540 74. 990 77781_0 101. 240.197026C 4 6412 74.480 7.8.2O0 10.I7 1970Z56.5 9515 74. 980 77. 8 0 101.160 197026C 5 6271 74.460 78.1L70 0.8 197025B 6 9641. 74. 980 77. 660 101.080 197026C 6 6487- 74. 450 77- 840 0. 8 t 970 258 7 9529 74.980 77.550 101. ~,040- 19g7026C 7 6451 7.3 191025B 8 9688 74. 990 778 470 101. 080 197026L2 8 6552 74,.43.0 77._7.51 0.5 1 970258 9 9587 74. 990 77. 470 101.130 197026C 9 6509 74. 430 77. 750 0 4 RUN NO. TUBE NO. iW WATER I WATER IN T:wT.TER U T T STEAM RUN NO. TUBE NO. W WATER T WATER [N T W,,ATER. IU'TA LPB/HR F F F LB/HR F f 197025C 19800 74. 960 78. 740 101.41!0 197027A 1 7735 74. 730 79.'0_70 0.7 197025C 29300 74. 960: /8. 070 101. 440 197027A 2 7416 74. 730 18. 350 0.1 197025C 39490 74.970 77. 960 101.480 19702 7A 3 7484 74. 730 78.180 0./ 19702'5C 49540 74. 970 77. 840 101.4 70 19702 7A 4 7481 74. 740 78. 030 0'9 197025C 59508 74. 970 77. 790 101. 420 197027A 5 7463 74. 750 78. 000 0. 2 197025C 69641 74. 970 77.710 -il-dJ 370 19 702 7A 6 7567: 74.~750 - - 77. 83 0 10.8 197025C 9529 74. 970 77.6_10 1_0[ t290 197027A 7 7513I} _ 74. 760 _77- 77-010 0 4 197025C 9688 74. 970 77. 50 0 10. 6 0 197027A 8 7618 74.760 77 ~7 670 0.3 1 97025C 9 9590 74.970 77.520 101..230 1 9702 7A 9 7560 74. 760 77. 69 0 0.3 RUN NO. TUBE NO. W WATER T WATER IN T WATER_ OUT T STEAM RUN NO. TUBE NO. W WATE__R T WATER IN T WATEROU TSEA LP/HR F F FLB/HR F FF L 97026A 16500 74. 840 79.670 100. 800' 197027B 17735 7.707.2 0 0 197026A4 62359 74.~820 78. 700 100.770 1970278B 7416....74_._790 78. 210 0 0 191026A 3629: 74.810 78. 740 100. 740 1970278 31477 74. 790 78. 291 0 0 197026A 46293 74,780?8,510 100,750 197027154 7481 74,800 78,13 0 10,6 197026A 56243 74,780 78,490 100,770 197027B 7452 74,800 78,070 0,3 19702.6 6, 6404 74.~770 78. 300 l 0. 800.197027B 7567 _74.8tJ10 _ 77. 940. 0 0 197026A4 6365 74. 750' 58' 6-'5o) 0.810 1970278 B 7500 74. 810 77. 7701 0. 5 197026A s6466 74. 740 78. 000 tO00:790 197027B 87618 74.~810 77. 70 0 Q. 3 1 97026A 6404 74'7 1~ —7-,0-60 -('76-0' 197027B8 7546 74. 810 77. 760 0. 0,RUN NO. TUBE NO. W WATER T WATER iN T — 41ATER —OU T T"'STEAM- RUN NO. TUBE NO. W WATER...T WAYE-R —N' T WA4TER IU~''-A LB/HR F F F LB/HR F F. 197026B 16540 74. 660 79. 360 100. 780 19 7027(;1 7735 _ 74._840 _ 7_9. 180 0. 19702638 6282 74.6'40 7 8. 54 100.-830 197027C 27416 74. 840 78. 460 0. 3 1970268 36336 74. 630 78. 580 100.870 197027C 37477 74. 850 78. 34010.93 1970'26B5 6572 74.610- 7 8.'0 70 1o'002'91I0 197027C 7484 74.850) 78.130 6.1 i 97026o t 6282 74.600 78.280 100.900 197027C 57481 74.860 78.100 0.8 1970268 66444 74.600- 78.150...i00.900) 197027C 67571 7 4.8-60 77.84 0 0;80 ] 97G266 6404 74. 590 77.8~80 100. 870 197027C 7. 513 74. 860 77. 86010. 5 1970,,66 8' 6502 74.580 77 8b() -i0b;8s6 197027C 87618 74.860'7.800.70 197026il 90448 74. 570 77. 920 100. 820 1 97027C 7560 74. 860 77. 86010. 0

TABLE XIII (Continued) RUN NO., TUBE NO. W WATER T WATER IN T WATER OUT T STEAM LB/HR F F F 197028A 1 9840 74.990 78.700 100.850 1_'7028A 2 9454 75.020 78.030 100.900 197028A 3 9500 75.030 77.960 100.940 197028A _4. _ 9570 75.040 77.800 100.980 197028A 5 9545 75.030 77.810 100.970 197028A 6' 9680 75.020 77.700 100.950 197028A 7 9555 75.020 77.470 100.940 197028A 8 9710 75.020 77.480 100.940 197028A 9 9625 75.020 77.500 100.940 RUN NO. TUBE NO. W WATER T WATER IN r WATER OUT Tr STEAM LB/HR F F F 197028B _ 1 9840 75.040 78.760 100.910 1970288 2 9454 75.040 78.080 100.920 197028B 3 9500 75.050 77.970 100.930 1970288 4 9580 75.050 77.750 100.920 1970286 5 9545 75.050 77.750 100.880 1970288 6 9680 75.040 17.650 100.850 1970286 7 9555 75.040 77.540 100.840 1970288 8 9710 75.050 77.500 100.860 1970288 9 9610 75.050 77.540 100.880 RUN NO. TUBE NO. W WATER T WATER IN T WATER OUT T STEAM (J LB/HR F F F. 197028C 1 9825 75.040 78.750 100.880 197028C 2 9440'5.040 78.080 100.880 197028C 3 9500 75.040 77.990 100.880 197028C 4 9610 75.050 77.840 100.930 197028C 5 9550 75.050 77.830 100.970 197028C 6 9615 75.060 77.660 101.010 197028C 7 9555 75.060 77.580 101.050 197028C 8 9700 75.060 77.530 101.040 197028C 9 9620 75.050 77.560 101.030

TABLE XIV Condensing Heat Transfer Data for Condensation of Steam at RUN NO. TUBE NO. W WATER..... T__.WATER__!.N.............T_.._WATER OUT T.STEAM RUN NO. TUBE NO. W ~ATER T.._W.ATER IN r WATER OUT T STEAM LB/HR F F F LB/HR F F F 197039B 2656............................................81-Z8~'0..........1'0"1~".'240 /97040C [ 3'/'63' 7~4"'930.................-8"C)'~650............. 101.320 74.980 1970398 75. 050 81. 260 101. 220 197040C 2 338~ 74. 950 80. 020................101_:_27___0 2365............................. - 197039B 2594 75.080 81.100' 101.200 197040C'5 3527 74.950 79.820 101.220 197039B 2526 75..080...................80.. 680 101.160 197040C 4 3590. 74.9_80.........._79.660.....1___0!... 180. 197039B 2z~40 " 75.040 80.800 101.130 197040C 5 3499 75.010 79.700 101.200 1970'398 2465 75.010 80.640 101.110 i97040C 6 3569 75.Otto 79.630..........!01.220 197o39~.................... -i~o,,'566.................1-6 ]]", 0? 0' 7'3380 Z4. 970 79.440 101.070 z 36~ 7,,. 940 t 97o4oc 197039B 2548 _.'74.9tO' 80.480 101.050' 197040C 8;3569 74.870 79.300...... [0.0..8_ 80 1970396 2510 74. 880 80.400 101. 040 19'7040C 9 361'3 74. 770 79. 070 100. 710 RUN NO. TUBE NO. W WATER T WATER IN..... T'WATER'OUT F'STEAM RUN NO. TUBE NO. N WATER T WATER IN T WATER OUT T STEAM LB/HR. F...............................F............................ F... LB/HR F F F 197039C 2634 74. 760........................8.!? 6. 6_..Q....................[ O_ t.,. 310 19704 IA i 5387 75. [ 70 19 ~ 680 100. 950 197039C 23555 74.800 81.020 101.300 1 97041A 2 4908 75.190 78.970 100.960 1970 J9C 2583 74. 820 80. 930 10 i. 290 197041A 3 5035 75. 200 78. 800 100. 980 1970'59C 2482 74.860........ 80.710..........101.280 197041A 4 5145 75.230 78.630 100.980 197059C 2402 74. 870..............8....0_,. 780............!..01. 270 19704 IA 5 5030'75.260 78. 690 ZOO. 970 197039C 2420?4. 890 80. 560 101. 270 197041A 6 5145 75.280 78. 650 100. 960 -'-1 197039C 2327 74.900 80.680 101.240 ~97041A 7 ~880?5.300 78.610.....1.00..:740. t 970 39C z zt 5? 74.900................~6"' 680...........i 6'i-~ 2 t 0 19704 t A 8 5 z 35? 5. 300 78.650 100.930 ~7039C 2,,78 74. RiO 80.5aO ZOZ. 190 ~970,,ZA 9 ~l~'~ 75.300?8.at 0 too. 9zO..... RUN NO. TUBE NO. W WATER T WATER IN..... T....Nfi.?.E.R OUT............._T STEAM.'RUN NO. TUBE NO. W WATER T WATER IN T W4TER OUT......_T__STEAM LB/HR F F F LB/HR F F F 197040A 3818 74.950 86.5'60.............1-0'i'. 200 197041B I 5368- 75.310 79.890 100.990 19 7040A 3424 74.9 70 79. 920 101.190 19?04lB 2 4908 75. 240 79.100.............IQQ, 940 197040A 3560?4.990.....79.840.... 10~. 186'.... I97041B..-3 50'58 75.210 78.840 100.880 197040A 3600 74.880..?9,420.. 1..Ol..ellO 197041B 4 5132 75.1'70 78.600 100.840 197040A'3521 74.760 79.260 101.050 19'70416 5 5042 75.160' 78.670...........IO()" 850 197040A 3590 74. 650 79.180 100.980 197041B 6 5145 75.150 78. 510 100. 860 191040A 3400 74.560........7g.'l/+O...........'[00'98'0 I97041B 7 4870 75o170 78.570 [00.910 197040A 3604 74.600 79. 100 101.050 197041B 8 5120 75.200'18.600 ~ 100.950 191040A.3638?4.640.................:f'9 76'~6-........-['617iY6 [9704[B...... 9' 5145 75.230 78.600 100.980.......... RUN NO. TUBE NO. W WATER T WATER IN........T"i~'ATER OUT T STEAJq" RuN'-"NO'.... TUBI5 NO.' W WATER T WATER IN T W/~TER OUt'"'' (STEAM L~,/HR F F F LB/HR F F............... F..... 197040B'3761 74. 860 80. 630'101. 250 1970Z, 3A I 8420 74.680'18.180 100. 940 1970409 3361 74.900............~0-.-()20 101.270 1970Z~3A.................. 2 7643 74.680 77.470 101.000 [ 97040B 35 34 74.9 [ 0 19.740 101. 280 L 9'70~3 A 3 7885 74. 690 r7,340 JO 1. 070 I97040B 3588 z4.950............'79.'5'~6...............'76'[%"2'i6....['970'4]A............. 4 8045 7'4.680 77.210 101.130 i 97040B 3499 74. 960 79. 600 lO 1. Z30 197043A 5'7834 74.670 7?. ]90 101.. lZO 197040B 3620 74. ~80 79.560 101.200 - 19'70'~'3'A —......... 6 8091 74.660 77.280 101.110 197040B ~ 7 7609 74. 640 T7. tO0 101. 090 3358 75.0.30 79.600 101.150....!?__7_0_~3.A........ 1970405 3555 75. 060...... 79. 560 101.150 197043A 8 8010 74. 620 T7 ~ 080 lO 1.0 70 197040B 3568 75. 090 79. 590 tO 1. I40 [ 97043A 9 8 tO2 74. 600 77. OZO [Ol ~ 050

TABLE XIV.(Continued) RUN NO. TUBE NU. W WATER T WATER [N T WATEROUT T STEAM RUN NO. TUBE NO. W W4A0L T WATEk IN T WATER OUr ITA LB/HR F F F L3/HR F FF 1970438 1 8458 74.680 78.20 101.110 191047A 1 3855 75.300 70. 82010.0 1970438 2 7660 74..660 77.600 101.020 197047A 2.3451 75.3340 80.2101010 197043B 3 7900 74.650 17.440 100.9.30 i19047A.3 3591 (15.350 80.06010.0 1970433 4 8078 74.620 77.080. 100.880 19(f04 74 4 3645 75.340 79.7101000 197043B 5 7884 74.610 77.190 100.930 197047A 5 35 35 75.310 79.980 0.7 1970430 6 7557 74.590 77.170 100.970 197047A 6 1616 75.280 79.74010.0 1970438 7 7641 74.590 76.880 101.000 197047A 7 3460 75.260 79.7401008 1970431 8 8008 74.600 76.870 100.990 1970478 0 61648 75.280 19.63010.0 1970438 9 61138 74.610 16.800 100.980 197047A 9 3680 75.300 79.6.301012 RUN NO. TUBE NO. W WATER T WATER IN T WATER OUT T STEAM RUN NO. TUBE NOir. 8 WATE-'R T WATER IN I WATER OUT 7STA LB/HR F F F LR/HR F FF 1970444 1 10110 74.860 77.970 101.110 197047C 1 3873 74.730 80.41010.8 197044A 2 9048 74.910 77.480 101.070 19(0470 2 3457 74.720 79.7501010 1.970448 3 9352 14.930 77.360 101.030 197C47C 3 3581 74.710 79.47010.4 197044A 4 9585 74.950 77.270 100.980 197047C 4.365 7 74.680 79.13010.7 19704448 9328 74.950 (1.320 100.980 1970470 5 3~567 74.660 79.14010.8 197044A 6 9545 74.940 77.240 100.970 197047C 3645 74.630 79.09010.9 1970444 7 9048 74.940 177.240 101.010 1970470 7 3444 74.610 f9. 0901103 197044A 8 9515 74.940 77.160 101.060 197047C 8 3680 74.b20 79.0601000 197044A 9690 74.950 77.100 101.010 1910J470 9 3615 74.640 79.07010.8 RUN NO. TU81 NO. W WATER T WATER IN T WATER OLT T STEAM RUN NO. TUBE W4. WATER T WATER IN T WATER OUT SEA'dl ~~~~~~~ ~ ~~~~~~~~~~~ ~ ~~LB/HR F F F LB/HR F FF 1970443 1.0 112 75.000 78.080 101.080 197049A 6550 75.200 79.3201002 1970440 2 9040 74.990 77.530 101.080 1970494 2 1595 0 75.220 78.64010.5 19(0446 3 935.3 74.990 77.350 101.090 191049A 3 6100 75.220 78.4001089 191(0448 4 9600 74.990 77. 320 101.070 1970494 4 5250 75.260 78. 1601080 19(0445 5 9316 74.990 77.370 101. 050 197049A 5 6 12:) 75.300 78.45010.0 i190446 6 9550 14.990 77.260 101.020 1970498 6 6280F 75.330 (8.19010.6 19704403 7 9047 74.990 77.220 101.020 1970498 7 8 9 2 75.350 78.19010.0 197044b 8 9543 (4.990 77.200 101.030 1970498 8 6215 75.340 78.1901000 19704-41 9685 75.000 77.170 101.040 1970498 9 6300 75.320 78.48010.0 RUN NO. 108'3I0-4~1. W8AC~ WATER IN T WATER OUT' T STEAM RUN NO. TUdE NO. 8 WATER T WATER IN T AATERP OUT TSEA L 14, / H kF F F LB/HR F F 1970440, 1 I1C0112 74.990 78.100 100.9%0 1970496 _ 1 6540'75.350 79.38010.5 197044C 2 3(C-41 74.990 77.520 100.970 1970493 2 5950 75.350 78.61010.0 1970440 3 9, )074.990 77.450 100.990 1910498 3 61258 75.340 78.58011.6 197044C /4 9591 (5.000 77.330 101.030 1 9 7 04 96 4 6 2 50 75.360 78.32010.8 19710440 i 93 2 (" 75.020 77.390 101.060 19 70496, 8 6 100 L 75.390'78.58011.4 1970440 6 955' 75.040 77.320 101.090 1970493 6 6261~ 75. 4 10 78.33010.9 197044C 7 9h50 ( 5.06 0 77.340 101. 120 1970498 7 594q 75.460 78. 300 1.3 197044L 8 9553i 75.070 7 7. 270 101.120 1970498 102 4 0' 75.490 78.3c011.1 1970440 93 9695 15.070 77.260 101.120 1 9 70,4 9 Ll 03 00 75.520 18.370 1099

TAB LE XIV (Continued) RUN NO. TUBE NO. W WATER T WATER IN T WATER OUT T- STEAM RUN NO. TUBE NO. WAT R F FAE N TWTE U TA LB/HR F F FLP, H FFF 197049C 16540 75.240..79.28g6....0"060 197051B I L0105 74.820 77.87010.0 197049C 25950 75. 250 78. 570......101. 020. 197051B 2 9030 74. 830 17. 490 O. 00 197049C 36115 75'.260 78.o430 100o 990 1970 518 3 9:345 74. 830 77.o340 11 4 1970~9 C 626 0 ~~~~~ ~ ~ ~~~75.270 78.290 100.990 197051B 4 9550 14.850 77.09010.0 197049C 56100 75.280 78. 360 101. Ol 197?051B 5 730 7.8 0?? 70 0 t.190 197049C 66290 75. 290 78. 220 101.030 197051lB 6 9630 74. 890 7 9 0 8 19 7049C 75945 75.310 78. 080 101.100 197051B 7 9000 74. 930 76. 96010.00 197049C 86250? 7.320 78.200 101.15 0 1970 51B 8 9510 74. 960 77.180 1 8 197049C 96280 75.~320 78.280 101.~200 197051B[ 9 9655 74.970 77.16010.00 RUN NO. TUBE NO. W WATER T WATER IN''T W-ATR'E-b6]T........T- ST RUN NO. TUBE NO. W WATER T WATER IN T WATER oUT.....TSEM LLB/HR F F F LB/HR A F F 197050A 18460 75.110.....78._520.......101.070 197051C I10130 74.900 77.97010.0 197050A 7680 75.120 77.930 101.0.50 197051C 29000 74.950 77'50010.0 197050A 37920 75.130 77. 880 101.030 197051C 39355 74. 980 77. 36010.10 197050A 48090 75.160 77.570 101.000 197051LC 9540 75.010 77.16010.6 197050A 57890 75.190 77.770 100.990 197051lC 591300 75. 020 77. 37010.00 197050A 68100 75.21 tO77,.600 tOO0,990 197051lC 69530 75.~030 77. ZO O,00! 97050A 7 65 0 7 5.2 J O ~~~~~~~~~~~~77. 540 101.010! 197051C 79035 75. 020 77. 000 11 0 197050A 70650.75,230......'77.590 101,040 197051C 9530 75.000 J7....7,230.......10.3 197050A 98 155 75.200 77.610 10 1. 060 197051IC 9966U 74. 990 7. 0 0 11 6 RUN NO. TUt3E NO. w WATER T WATER IN T WATER OUT T STEAM RUN NO. TUBE NO. W WATER T WATER IN T WATER OUT TA ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~LB/HR F F'FL / R F..... F... F.. 197050F~ 1 500 75.0'00' 78.380.....100.720 197~0528 66o07,5.........7;3 b.5 1 97050B5 7655 75. 000 77. 770 100. 840 197052Ai 25990 75.280 78. 550 109, 1970506 7900 74,990 77, 700 100,960 197052B 36155 75,300 78-,4A2010,0 197050B, 8090 75.030 77.510 101.llO 1970526 46305 75.350 78.38010.0 197050B 289 0 75.07 0 7 7. 700 tO1,150 ~~~~~~ ~ ~ ~~~ ~ ~ ~~~~~1970528 56185 75.370 78.470'[0,5 197050B 5 1890 75.1070 77.7040 101. 19 0 175 2 0 75.400 78. 330 10 7 197050O 7 100 75.107750 11 90902B 620 197OjOB 7 7650 75~~~~~~l.12 7!30....01"',200 19/0526, 5990 75,45'0..78.410'i',(0 1970506 8050 75. 100 17.630 101.180 1970528 62 70 75.460 78.28010.0 197050B 95 75. 090 177560 11001,150 1970528 6355 75.470 78. 320i0,0',RUN NO. TUBE NO..,W WATER T WATER IN [ WATER. out T STE~AM RUN NO. TUBE NO. W WATER T WATER IN T WATER OUT'lAM.. LR/HR F F -F LBR/HKR F FF 197051A I lO I I G 74. 740 77. 780 101. 060 197052C 1 6590 75.200 79.2401090 197051A 2 1-401I0 74.730 77.320 L01.070 197052C 2 5990 75.180 18.600...0.1 1 970.5 1A 3 9J50 74.720 77.260 101.080 197052C 3 6145 75. 160 78.44010.5 197051A 4 9550 74,750 77.060' 101,090 197052C 4 6 300 75,170 78,00........-['-9'' c6 19 7051 ~ 5 93l0 74.~780 77. 650 101.~090 1 97052C 5 6155 75 ~180 78.240 1 0.90 197051A 6 9530 74.810 ~ ~~~ ~~~~~~~~77.060 101.080 197052C 6 6308 75.200 78.05......10.2 197051A 7 9050 74.~840 77. 030 101.~030 197052C 7 5970 S2 0 782 0 10~95 i 9 0 ~11 3 35.50 74.840 76.990 100.970 197052C 8 6265 75.~3Z0 78.13010-96 197C 51 A 9 9665 74.840 77.010 100.920 197052C 9 6330 75.~370 78.18010.98

TABLE XIV (Continued) RUN NO. TUBE NO. W WATER..T _WATER IN T WATER OUT T T STEAM LB/HR F F F 197053A 1 8530 75.070 78.530 101.040 197053A 2 7705 _ __._ 75.120 77.940 101.070_ 197053A 3 7945 75.150 77.820 101.100 197053A 4 8100, 75.200 77.600 101.090 197053A 5 7935 75.220 77.820 101.060 197053A 6 8125 75.240 77.570 101.020 197053A 7 7690 75.260 77.630 101.090 197053A 8 8095 __ 75.260 77.610 101.090 197053A 9 8180 75.270 77.660 101.100 RUN NO. TUBE NO. W WATER T WATER IN T WATER OUT T STEAM LB/HR F F F 1970538 1 8530 75.360 78.720 101.050 1970538 2 7690 75.390 78.080 101.070 1970538 3 7935 75.410 78.090 101.090 1970538 4 8100 75.450 77.860 101.080 1970538 5 _ 7920 75.470 78.060 101.050 1970538 6 8125 75.480 77.900 101.020 1970538 7 7660 75.500 77.840 100.990 197053B 8 8080 75.500 77.790 100.970 1970538 9 8015 75.490 77.800 100.960 RUN NO. TUBE NO. W WATER T WATER IN T WATER OUT T STEAM LB/HR F F F F 1970548 1 iQ100 74.780 77.880 101.060 1970548 2 9005 74.790 77.320 101.030 1970548 3 9350 74.790' 77.130 101.000 197054B 4 9580 74.810 76.990 100.960 197054B 5 9325 74.820 77.190 100.960 197054B 6 9555 74.830 77.050 100.960 1970546 7 9045 74.820 77.070 100.970 197054B 8 9520 74.800 77.030 100.980 1970548 9 9655 74.790 76.980 100.990 RUN NO. TUBE NO. W WATER T WATER IN T WATER OUT T STEAM LB/HR __ F F F 197054C 1 10100 74.760 77.830 101.030 197054C 2 9020 74.790 77.250 101.070 197054C 3 9345 74.790 - 77.140 101.100 197054C 4 9560 74.810 77.010 101. i40 197054C 5 9310 74.810 77.070 101.130 197054C 6 9560 74.820 77.060 101.130 197054C 7 9050 74.820 77.100 10lL.00 197054C 8 9520 74.830 77.020 101.070 197054C 9 9655 74.840 77.020 101.040

APPENDIX D. COMPUTER PROGRAM FOR ANALYSIS OF MULTIPLE TUBE CONDENSING DATA AND TYPICAL COMPUTER CALCULATED RESULTS 61

TABLE XV Computer Program Written in the Michigan Algorithm Decoder for the Analysis of Multiple Tube Condensing Data $COMPILE MAD, EXECUTE, DUMP, PUNCH OBJECT C-AN C01 i G{3)*TAVG{I).P-. + GCI4ITAVG(I).P.4 + G(5! TAVG(I)I.Po5 PRtI) CPT(!)CVIUISCIII/KTII RE_ B'I} = ID*TWTUDE I I /iA'Lw*V ISC ( I)_ AII[) =: E +C) + Ei}*VAPORTI(i I + tL(ZI)AU PURT(II.P.2 + R MULTIPLE TUBE ANALYSIS PROGRAU! (I-A PTIII.. L (4)*VAPORT(II.P.4 + E()VAPURTIII.P. L;.rUT Ii (TTUL'.~(I) I TTLEI I ii/(E'LJU. ( " IAPuR T ii 1 TTUBEI(I) )/VAPCRT{I) - UTUbEO(I)))) INTEGER I, RUININO, RBNNUo, IUtBENBO,'EiALIU L' E'IIALU2O TU VICW(I): FXP.IIIDO)+ U( i)/TIALLAIi( ) + (2I)/TALLAL(" I-P2 + DIMENSION WTUBE(i50U TTuEEIT50). TTU:BEU(tC), VA ORIT(50), 1 U33I/TBULLLAII..3 TUUI U,.P ALAi P.4 LI TALSAI).I 1 1 TEGINU ( CP0)5/I. f T( I, 0TINT)' LMT11 ). 5;0 ITv [, T T -HI () = CI*KT( T)*RE(II.'OT.U.*P)(I) P;0.33 3 3-*"IUSC- / 2 DEN(5O-T KTI50). PRI5)., EkF(5O, VL(T5C), TVALLAt50I, 1 VISC(I PI.. C.14/I I...' - TWALL(II = I'aVG(~~~~~~~~~~~~~~~~~1) + G(!)/(A[T*H1tl) 3 V1SCN(50U) TWALL(5S), TBALLD(U50, DULIFF(U iL-TFI TULLII = TUVG() U )/ITIT..i. ) B KCiNDINU5C, DCOND(NU),MVCJUIND5'0) PIBU I'-' HUI50 TWHFNFV FR A;` (TWAUI LL(I) - TALLII)) G. 0o._ 5 DELTF U(50), QA)5C)I, CONbT(ST'), ST{)', UBENOi50T.... TULLS{I) = I /,LLt 6 CN(50T) CONSTAI(50I), RJTNNOIA(50), RUNNO:U)(53,, H.?C NLO t T._,__SF:~ TO RFT2 D(. 8), E(U), G(8),,T6), ) (BI), L(-), I F(I O, ITIFIBI TT _____ START READ TFORAT DAT A, IU, U, TL, T.UAL LI I WAI U'- ) Ir/UA ET READ FORMAT DATAB METALL1, MIZALZ:,LTF(I I) = ALLI, I) DIJNVT = 0 P.;)3 U-~i! 1 VAP; LTF(I) /2o0 SUMHVEL =! 0.C.(1) = C i H(O) FiLt1() + r, (Z)I 2 FiL; iTI P- 2 + ~~STIK,~ = 0C..]~~...... i ~ ~ I). P ~.+)*FILN~M~T(~. PIU + U, )*TFIMT(IIP P.4 T I k _1'))~'"TUT) 1 TBUUI )UE1F ILRT(I T.P. I.M......... S'H' B L R 1 -iI-P,~'A, N-'CR I = l, 1,)K()*F1LT( ) + K(2)/)FLN ) i-'T'.P2 ALPHA READ FCR;,AT DATAU,;hA; RUNNOb, TUbENO(II), i TUbEL!),. (3)*FiLT(I KI) P4 L KT.5)UFILMTI P, P U TTU EI(I1I'THBEO(I), VAPOR.I(II VCOND() = EXP. IL{ C) + L(I)/ FIL'T (I) U L(2OIFIL TLIT ).P2 + PRINT FORMAT TITL), RUNNOA., RUNNOB I Lt)/FILMT,) I.. U LI4)/F) I' I P.4 U LITI)UIL)I 1i).P.-P. PRINT COMM'ENT T8U.... I: (. KCOND( )* KCLUN I )*<CO ( I )U*OCO ND( I )CON( I/ PRINT FORMAT OUTI, OD, ID, TL. TK. M'RA! ETAL) 2 I (VCONEI i i*ULTT( I)))P i. _0- 25 U.....OD T o/12..T H C U.. I CI):15 TI )UPIii I 4R( I).( l C;1. 0 PPT LAL(TI ()/ OD) ID = II/12.0 iP.n..25 TL ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~OI =L1~ ~31.lJ/(1.O;/HiCUNU(vi}r q' AO3T*R/A M'Ef + Aj''~,0iT/~i(AI I*I()}. L = TL/O12.0 UBI I../II./C....)II.. U TUBk./BR.I AO BUT/IB I T *III R = (OD-ID)I/TK*2.0) DEtLiA(II OC(I )ULTD II)/r CONIT I I) DM =(CD-ID)/ELOG.(OD/ID).......... R, (,). L.F A.....L TF I /DELTFA ( I.6- 0. 001 AOT = 3.]416w*ODTL.....[).LTF(I) = ULTF'A() UE I.AIT.= 3.1416*ID*TiL -T'UN"A UFE T. UUT3 AMET =3.1416*DM*TL..S)F -...NDITIO BAL_ AFLOW =.1416*ID*ID/T. OAUI UT) L uO(IL TC(I*AUOT PRINT FORTAT OUT2, AOT, AIT, AFLOW'q Ci..'....U-R.BU A IU.) - I IH I) I. O I..0 __ THROUGH BETA, FOR I =, 1, I'G. 9 (I) = A l TAVGB i) = TTUMEIII) + TTUUc.(I))/2.0 _ ___ T.UUF.''T..._RANFE.R TO RCT4 LAT(I) = E(O) + E(1)*VAPORI'i I) Ei2*B'VAUPUR (I).P.2 + FNU OF CONDITION AL 1 E(')*VAPORT(I)oP.3 + E(4)*VAPORT(I).P.4 + EIB)*VAPORT(I).P.,5 UCU NTINSP. CPT(I) = A(B ) + A(1)*TAVG(I) + A(2i*TAVGUIII.P.4 U PRINT1-UiBT TI1LE 1 A(3I*TIVG(I).P.3 + A(4)*TAVG(I).Po4 + A(5)*TAVG(I).P.5 PRINT CTOtIUENT $8$ I.VC( ) EXP.( D() + D(1)i/TAVBI) ii (2)/TAVG()I P.. + PRINT FTOROAT HEADI 1 D(3)/TA/G(I).P.q + LB(4)/TAVG(II).P.4 T+ D(5IU/I VGI _IL:P.._:.... I.;;G PC.5, FBCR IU I G. 9 DEN(I) = I 0) + F(I)*UTA','(I) U F(2)'/,AV3I' P'.P P;5 PRIO; FORlAT Rl'LT, I, vTUc(i T BU.Cl)I i F(3)*TAVG(I)P. 3.F(4)TAVG'IioP.4 + FIDU*T A VT II *U.5 (I TAVB(I) PT) I D). ii VC{ )1I) KT(I) =' -) I G(I)UTVG ii' + G(Z))UTAVGOIITPP.. + PRTI)T FUOr5'VU I f-BT2 1 G(3)*T AVG(I).P.3 t'J(4*IU4VG((),P.E4 + U(5)UUAVG(I).Po 5 I'HRUNGH P:U6, FC'R I, i, i G. 9 U(I) = WTLfEI) CPT(i) I TTu3I (i -TTU ) TTLUbEI(I)) P/iT;ITT i'",,AT.', I PR(Il T.IALL"I) LC' = IUU BBL. BIBU I)_ - I... I.... 1] I UqI, i:I(V, ReIk, I h_ _ I(I.... = I AJT*L DI) IUOH I?, I UN U1, 1, i G. 9 PR() 7I( UNV;_C I) / KT1:I k','A RE, L. T3,1, VAPOIRT71). LAT(I), TWAL LOII). RE(!) = TL,.L::.Ci I/(AF/I,*UVI CIII) I DFLi-( }, il',i( ),'NCTCOND(U, C)COND(I).... VEL(I) =`WT Ub~: (I/ I(AFF LOB*C LN(I ) 360C0 PRIBN; Oi h.AD4 SUMVEL = SU-/VEL + VEL(1)....... 1;8 FUR I = i, 1 I ioG. 9 TI...sf = STINI + TTUBEI(I) P-Z/INT FU U','A UI 1-, I4 VCTND('B T )T PHYGRIl)l UMVTT = SUU VT + VAPOFRT{I) l I), LIT,'),!( ))~ HI (I) ), ON( I)I BWALLA I) = TAVG(I) Q = ~,RETI VI1CW(1) U XP.(D(O) + D( )/TWALLA(I) + D0(2)/TwALLAI. P.z + U 1 Dii)/TBALLA(Ii.P.3 + (14)/T L ALLAEI).P..4 +b {5)/TWALL_......'$c =... HI1) = CIUUTi'I)R E(1). P.T.8PRU)I).F,.3333.)UI(V'iC(II/ iUB UBUL) 1-Cl 1 1, 1' 1,B. H HI(1) T~~~~~~~~~~~~~~~k~' n,:<;uG, UF~LI, ECR I =1, 1, I,.6. 9 1 VISCW([I).P.,'B D ) = I -(i) TALL( I) = ITVG(1) + Q(I)/(AII*H!(I)) UEN = SUEN + B _());'ENEVER.AU.(TWALLA(I, — TAALL(i)).G. 3 b'N(I) -DEN/I -'ALLLAI) = TWALL(I SCPT = CPT U CPT(I) TRANSFER TO RET CPT(I) = SCPT/I... END OF CONDITIONA L WTUf( I ='EN( I )*AVGVL*3600./UAB-LSW*I HCOND(I) 1 l0/(!./OitU I) -UAOT*RU/AE - UA2T//(ATiITII)I I ITI/FO() = TTUHEI +.I U G )/(T II/ J-UP I )l*PT(])) DELTF(I) -'O(1)*LIU 1);/U. N ( 1 TUBS))) I TTSUT 111 U TTUOi)( I))/C DELTF(I -JO I I I *L`4 I D I r —!~~~~~ONO ( I T4VL, I) = (TTu'dIE(I) + TT,;hP0(I))/2.0 TWAfLLO( 1) = VAPOR T( 1) -:,;(1) i/ (AOT ahCOND(1) )() =G()i~1)1V(l iZ)TV (I~. TU AULSLI, G(0) + G(T11)*I(V(I) + k,(2)*TAVG(I ).Po2 + FLMT(I) = VAPOT RT())- DFL)IF I)/2. 1,(3)UTAVG(I).P.3 + uI4)*TUV(II).P.4 U+ )(5)*TA VG(I-).'P 5 ON I H(C) + I 11,7 1 LiV T + Fi ( 2 ) k F L t DL' )N ( I F(0) + I-(I)*TAV(?(I) + F(2)*TAVG( I,,P.2 + COND(I) = HBI) +U (i)tu5 IL'I))U B+H(i)T FLTTI1),T.2 U lIEN) ) UIT)UE iUTAU) U F.I..T..G.I).........I.I... U 3t3*FILUTI(i 1.P1.3 + ~II(4)*UF IL"' 1.P.4 U. r(5)U iL;;T(I1).P.5 1 II'(3U*AVG( 1).P.3 + F(,+)*TAVG(I). P.4 + F(5*ITAVG((I).P.5 DCCN(,F) K(I) +U (1)-FILF TI ) IU iLi2LiiT(11).P.2+ U,,C)I) = OTXP.( IT(O) U S1)/ )1)+ U(2)I/TAVG(I.P.+2 U. i(3)-*FILT(II)..3 + K(~-):FFiL-LT(TI )-,14 + U (t) IILIMTT(I).P.5 I 0i(3)/TAVG(;),.P.3 + UI()/TAVG(I) P.4 U Di( /TAVG(I).P.b)VCOND(I) = EXP. ( LS), L(U I)/FIL'(I1 U L 2 )/rILN[1 I).P.2 + CPT(I1) = UA(') + A(I)*TAVG(1) + A(2)rT AVo(I).P.2 + 1 L(3)/FILM TII 1P. 3 + LI4)/ FILF I IM..T,4 UI IUI/-IL,(I) L.1.5) " At 3U)*TA'VC,()..3 + A(4)UTAVU(1)oP.4 + A(5I TBAVG(I1).P.5 PHYGR() = (KCONT( II)U*KC LTND(I)I KCON(II)*DC/ONC; i *UCotUl) __Ii/ -.. LAI))() (0) + F(I)*VAPOU T() )+ U(2)*VAPURT(I)oP.2 +. (VCOND( I)*DFlLTF (I 1). ).P10.2.i3)*V APU RT( I)oP.3 +U (4)UVAPORT ( I ).P.4' U E(5TiTVABPORT( II.P.5 BETA CONST (I) = HCCN4(I )*(OD/i4.17*1).U.UP. *LAT(I)))..o.O25 / TIBALLA(I) = TWSLL(I) I PHYGR(I)' 1VI SCU( )- = -IXP.(D(u) + I(1I)/TvALLA 1) T+ (2)/TWALLA ()I.P.2 + ATiN = STIN/9.0 i )(3)/i WI..(L 1I).'. + U14)/TwALLA (1i).P.4 +(5)/TWALLA(I).P.5) AVGVT - SUMVT/9.C HI(!) U ()UI*U(!)U P:). ).bUPii( P).,333T3,3*(VUISCIII/ AVGVEL ='UMVEL/9.0 1 VIsCW(II ))U).P.0. _14/iD_ PRINT FORMAT TI1LL1 TWALL(] ) - (I)/(HI II )*AIII) + IAVC( I PRINT COM'UENT 8 Wri38 NFVUR.AF-.I(I LLA U ) - IwALL(I)).G. 0_.3 __ _ PRhINT FORvAT HEAD1 WALLA(I ) = TwALL(I) THROUGH P01, FOR I = 1B', I G. 9 FRANSkER TO RETI P01 PRINT FORMAT RESLT1 I B i,/1 )I ilUb/Ill), NID OF CON'CI Ii NAL 1 TTUBEO(I), TAVG(I), CPT(), DEN(I), VISC( I) - L4TO(1 i = (TTU 6EO(1) - TI/bEI(I))Y(/ELUG.( IVAPOT(i) - PRINT FORMAT HE4D2 I1 ITTuEi)(I)) /{VaPIRT(I) - F ITU/BO(O)))) THROUGH PO2, FOR I =1 1, I.G. 9 U()(1)) = /(I/(L-ITF)( I )AOT* I PO2 PRINT FORMAT REU LT2, I, KT)l). PB(I), A TIULL(), hC:N,(I) T.0/ IO/ UO/ (II) -ABTU / ET -/ AOT/(A'ITI(II)I 1 VISCW(l). VFL(I). RF(1), H (I) I)ELTF(II) UO() I*L'4Ti( I)/nUI T()..... PRINT FORuAT HEAU3 ILMUT() = I VAPCRT(I)- utL[F(i)/2.0 UhROUSR POT, EBB I =1, 1. 1.G. U9S/+I I)UUlUIUIII UUOUIIRI., 1hROUGH P03, FOR I = 1, 1, I G.GF 9'COND(1) = H(3) +3i11)*F1LMl(I) + i(2)*FILMT(1).P.2 + P(3 PRINT FCR'AT RESLT3, I, VAPORT(I), LAiCU-'-T LL''. 1 UH(3)5IL;T(;)./P. U si43 *UIL4T(" ),P.4 + Ui')'FILD.T(H).P.5 1 IELTF(I), FILNT(1), KCONU(I), DCOND(I) TCONII) II KIT ) U) )-Li II K(2)E FILMT)I I.P.2 U _ PRINT iORU4AT HEAD4 1 K(3)';,F[L'T(1).P ~ J i 4)',FiL:,!r(F1).P.4 + r()F II)P.5 TIR'3UUH P04, FOR I = 1, 1, 1 r 9.Vc..... = XP. ( L(D)...i.T L(....I...ILMTI P.P 2 PO4~~~~~~~~~~~~~~~~~~~~~~~~STII UURINTI1 FO)/IRMAT) UELTI,2/FILMT(II)P.O_U PUB PHINT FORMAT B'ESLT4, I, VCOND(I), PHYGR(B ),.... 1 L(')/F'IL'T I).P.)3 + L{I4)/FILI-. I).P.BIN4 + Li(5-)/FiLMTIM T P. ) 1 (III) L"TD(1) UI () STIll hBi( I, UCN) _. PY0UR(I) = (ICSND (I) K I IUS)* KC/ND ( ) I *DCO ND(I) IDCC)NDI1/ THROUGH GAMMA, FOR I = 1, 1, I.G. 9 I (VIIIPI) UUl )iUf))L ~ P.'2 TTLUFI(I) = ATIN CI)) C= CONTD( I )/ (.72*PiYT*R) I (L AU TII7(I*.1 710.0.P.8/ (OD* VEL(I) = AVGVFL 1 I)).-.).25)VAPORT(I) = AVGVT {,ONSTA(1) = FONST(I)/ O.12b TET4 UTUB6EI)= D LEN(1)*UAVVBLU36D0.0*AFLO W PRINT EORu'-T TITLF3 TTUBE/(I) = I(I)/(ITdbLE( II CPT(1) + AIiN U TI)-UU) CC NT R_ _ _ TAVG(I) = (TTUBEI(I) U TTDISEO(I})/2.0 P5I1T FOP"AI HFADI CPT(1) = A(l) + A(1)*TAVG(I) + A(UI*TAVG(I)I.P.2 U TUOSGU PIg, FUR I = 1. 1 1.G. 9 I A(3)*TATVG (I)iI...3i A(4)*TAVG(1)BB,.P4 + A()*TATVG(II)*PN- PUT. PRINB U"H"BT RETLT, i ATUbE(I)I ITUBEIII)-. VISC(I[ = EXP. ( 0) i O(1)/TBVG(/) i I(D)/TAVG(IT)PO + 1 TTUO.UEII}, 1AV (UI),S PT(),T DEN(I)B VISC(I) 1 D(3)/TAVG([)TPI 3.+ B(4)/BAVO(I).P.4 U T(5)/TAVG(I),,P.'5) — ED. PRINI FORPAT HEA)2...ENI([ = F(P) U P0lIUTUTT~i) U +(2)*TAVGB)II P.2 U TUB/IT) POlO, FTR I 1. 1, 1.0.9 1 F(3)*TTVG(I).PI. + F()BTBBBIII.P. U FI5IUTAVG(III.4,5 P010 ERIT FOR+RT HEOLT?. I. Tii), PR'5II)*TUALLVII(.. KT(I) =.G(') + B(i)iU TAGI' I G(2)U TBAVG(I).P.2 U I VISCW(RI} VEL(), RE1) I. hI(U ) 62

TABLE XV (Continued) PRINT FORMAT HFAD3,__................... THROUGH POll. FORI I 1., I! G. 9 P011 PRINT FORMAT RESLT3, It VAPORT(I), LAT(I), TWALLOiI)o 1 DELTFII FILMT(II. KCONDI')'. DCOND(I' PRINT FORMAT HEAD4 THROUGH P012, FOR I 1. 1. 1.G. 9 P012 PRINT FORMAT RESLT4, It VCOND(I), PHYGR(I), 1 OIM, LMTD(I). UO(I)I, HI(I)" HCOND(l) PRINT FORMAT HEAD5 THROUGH P0E13, O.1 G P013 PRINT FORMAT RESLT5t I, CONST(I), CONSTA(R ), CN(I) VECTOR VALUES TITLE = 8A0Hil I CALCULATLD RESULTS FAO RUN NUM6Ek 12, C6 *$ VECTOR VALUES TITLEI = $ 83Hi I' CALCULATED RESULTS' FOR RAW DATA *$ VECTOR VALUES TITLE= $ 125Il CALCULATED RESUL ITS FOR DATA ADJUSTED TO CO-N —ANT INLET WATER TEMPERATURE AND 2CONSTANT VAPOR TEMPERATURE *$ VECTOR VAUSTTE 9=SMH 2 CALCULATED RESULTS ARE FOR AVERAGE CONDITIONS FOR TOP I 2 TUBES *$ VECTOR VALUES DATA = $ 5F1O.4 *1$ ___ ________ VECTOR VALUES DATAl A 5F14, CA, ITO, FID.S, 3FID,3 AFLOW TUBESIDE FLOW AREA, SQ.FT_ VECTOR VALUES DATA1 1 4', C'6, 110, FIOO, 3F10,3 *$.. VECTOR VALUES DATA2 N 2C6 1A________________S$y - rT0TEL tTN3COEEATTIED-sFERE-A:ESU0FT. VECTOR VALUES OU'ffi = S 3DM TUAE OUTSIDE DIAMETER INCHES AMET TOTAL MEAN METAL AREA, S$,F-T, 1 SOD. 104'OT-.T OT- TITATL-OUTSrTDE"HEAT'T VAS'FE-AR —AEI SO.-F. 131H TURE INSIDE DIAMTETER - INCHES 531. F10.4 AVGVEL AVERAGE WATER VELOCITY, FT./SEC. 12DM TUAE LENGTH - INCHES SD T, SE VRU TA EPRTR.F 14DM TORE THERMAL- CONDUCTH VITYES RTO/MR-TT-F 521, F4094F10-4511 CONSTANTS FOR HEAT CAPACITY OF WATER 141H TURF MHETMAL S43,60 2CY BTU/HR 521. F10 c-T ~ ASSUMED VALUE OF INSIDE HE'ATT-R-A FER COEFFICIENT CONSTANT 112H TUBE METAL - S43, 2C6 *$ CNT ODESGC' ~ ETCNTN VECTOR VALUES OUT2 =$ 43H TUBE OUTSIDE HEAT TRANSFER AREA -OEFFIC 1SOFT/FT S19. F10.4 /CF f — CONDENSING COEFFICIENT CORRECTION FACTOR CPT SPECIFIC HEAT FOR WATER. b/U/LB-F 14DM TUBE INSIDE HEAT TRANSFER AREA - SOFT/FT S20, F10.4 /..T/R 122H TUBE FLOW AREA - SOFT S40, F13.7 / DCOND DENSITY OF CONDENSATE, LB/CU.FT. 133H METAL RESISTANCE - MTU/HR-SOFT-F~7 — 5DM. F13.7 /DELTF TEMPERATURE DROP ACROSS CONDENSATE FILM. *F. 12AM INSIDE C0EFFIC-?ENT'CONSTANT 535. F1S.5 EL CALCOLATED VALUE OF AT DRPRACROSS CONDENSING FILM, F. DEN DENSITY OF WATER, LA./CU.FT.,VECTOR VALUES RESLTI = $ S9, 16, F15.0, 6FISO lD M MEAN METAL DIAMETER OF TORE, IN. OR FT. VECTOR VALUES RESLT2 ='$ 59. 14, F15.4.. F15.3, 2F15.2, D.(.I....CONSTANTS FOR.VISCOSI.TY..OF WATER (~, VECTOR VALUES RESLT3-= 59, 16 vF15.3s, F15.2. 31ID.34D DII) CONSTANTS FOR LATFNT HEAT OF STEAM 1 F1S,3 *$ FILMT CONOFNSATE FILM.TEMPERATURE!._~. —..... VECTOR VALUESAESLT4 69A SM, 16, DFlS.3* F15.2t F15.O3 F{Il CONSTANTS FOR DENSITY OF WATER 1 SF19.3 1.~ DG(I) CONSTANTS FOR THERMAL CONDUCTIVITY OF WATER VECTOR VALUES RESLT5 = $11G, SF15.4 * - HCOND CONDENSING COEFFICIENT. *TUMR,-SO.FT.-F.-____ __________ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~MCN C O -..-T NSDENMA TASFER COEFFICIENT, RT U/M R.-SQ.FT.-F.,VECTOR VALUE'S'MEATO =$1DDM2 TUR NO B TOE __________O ________ VECTOR VALUES HEAD1 =$12OH2 TUBE NO W TUBEHI INSIDE. HEAT.TRANSFER,COEFFI!CIENT, BTU/HR.-SQ,.FT.-F. TU1 E IN T TURE,0UT T-AVG' CMI F TH ONDUCTIVITY OF CONDENSATE — 2~~~~~~~~~~~~~ ~~~~~~~~~~~~TLDESIT'...... T-VISCOSITYE / 1 TTURF IN T TURF-OUTVl T-YG' I-CF ID TUbE INSIDE DIAMETER, IN. OR FT. hLB TYH T-VSCOSFT FYT1DMKCOND THERMAL CONDUCTIVITY OF CONDENSATE FILM, bTU/HR.-SU.FT.-F,/FT, -SLA/MA __F'''''' / F F__ RTU/ D KIII CONSTANTS FOR DENSITY OF CONDENSATE __________ VECTOR VALUES MERODF S LBDM T-H TURDR NO T-K KT THERMAL CONDUCTIVITY OF WATER-. ~,-BUTHR,-S.$FT.-F./FT. VECTOR VALUES HEAD2 =$ 120H2. TUbE NO T-K PR. WALL IN lW-VISCOSITY -T-YELULIALAYT LATENT HEAT OF STEAM, RTU/Lb. T WALL'i~~~~ T —T~o~'f- -VELOCITY RE HI.12DM.MT. LOGARITHMIC TEMPERAEURE DIFFERENCE, F.'FTRFT F LA/FT-HR F LII) CONSTANTS FOR VISCOSITY OF CONDENSATE 4T/SEQ. TU/HR-SQFT-F //////*i O TUBE OUTSIDE DIAMETER. IN. OR FT. VE"T-R"VALUES HEAD3 = N-12'H' TMEN''- — VAPOR TEMP PHYGR - PHYSICAL PROPERTCY GRO'UP 1 LAT HEAT T WALL OUT DT FILM T FILM PR PRANDTL NUMBER OF WATER O C-K C-ENS5IT / 12DM 0 Fl —_ EAS' DUTY,. TO/H'R.. _ _ 3 F BTU/LA F F OA CALCULATED VALUE OF MEAT DUTY RBTU/HR. 4 F BTU/HR-FT LB/CUFT //////*$ kA SYNOULDb NUMBER ATEEcTbR'VALCUES-iHEAD4 $ NODHO~12Tf ____________E NO'-. AISCOSITY RM METAL RESISTANCE, MR.-SQ.FT.IOUTSIDE AREAI-F./bTU 1 PHYGR H EATDUTY LMTD _. UO SC'T T SUM OF HEAT CAPACITYfOR WATER 1 HI M COND / 120H LA/F SUEN SUM OF DENSITIES OF WATER 3T-MR BTU/MR F BTU/HR-SQF. S TIN - "SUM OFI-NLET WATER TEMPERATURES -- — 4T-F BTU/HR-SOFT-F oTU/HR-SUFT-F //7/// $ SUELAT SUM OF LATENT HEATS FOR ALL RUNS VECTOR VALUES HEAD5 = A'6OH2 TUBE NO COND CONST -SUVE-L - SUM OF'WATER'tELOCI.IES 1CONST/0.725 CN ////// $... SUMVT SUM OF VAPOR TEMPERATURES VECTOR VALUES A = 0.10124896E Dl, -0,4667M063E-03, -"YAVO AVERAGE TiUBESIDE TEMPERATURE. F. I0.58540MM7C-05, -0.S2722l41E-DT, 0.7DM40616E-10# D.DEI IDK THERMAL CONDUCTIVIITY OF TUOE METAL, TU/HR.-SQo.FT.-F./FT. VECTOR VALUES D = -0.21968738E01, n.T4722744ED3,.L. T UB.ELENGTH, IN."OR FT. 1 -0.).3M63282E05, 0.1614] 324ED7, -0.24764542E8D O'.0EO TTUBEI.INLET WATER TEMPERATURE, F. ~ VECTOR VALUES =..1095,2 -0.5800, S.o. 0,09 0.0 TTU-E- OUTLET WATER TEMPERATURE, F..ECTOR VALUES F = 0.6313DDDOE02, -D.1170DDDDE-DI, D.DDD, - TUBENO " UBE NUMBER IN A VERTICAL ROW FROM TOP 1 O.OEOD.T, DDO.OEO'TwALLA ESTIMATED'VALUE OF INSIDE WALL TEMPERATURE. F. VECTOR VALUES D = 0.30DSTD27EDDD D.2527360E-03,.TWALL __ CALCULATED VALUE OF INSIDE WALL TEMPERATURE, F. 1 0.9205052M E-05,'-0,75847219E-07T, 0.17507457E-09, O.OEO.. TWALLO OUTSIDE WALL TEMPERATURE. F. VECTOR VALUES H = D,3037372E0D, O.25267360E-03, - U -00 OVERALL HEAT TRANSFER COEFFICIENT, BTU/HR,-SQFT.-F. 1 0.9205052DE-05, -0.75847219E-07, 0.17507457E-09! O.OEO VAPORT STEAM vAPOR.TEPPERTUTRE, F. VECTOR VALUEIC-Z'=" 0'.063i30000E02'D' -0 il7-D'DE-D1. 0.0E0 vCOND VISCOSITY OF CONDENSATEt.LB./F'T,-HR. VECTOR VALUES L -0.21968738E013,D.G472DD4Eo, v DEL WATER V'LOlTYY FT./SE C. 1 - 6 ~'46A82DEO", D 1 DD7 -47'-542EoDR, D.DEO VISC VISCOSITY OF WATER, LbM'/FT.-HR. TRANSFER TO START VISCW VISCOSITY OF WATER ATjWALL TEMPERATURE. LB./FT.-HR......EN-D- OF -'PROYGRAM... -TUBE TUBESIDE FLOW RATE, LB./HR.

TABLE XVI Typical Multiple Tube Analysis Computer Calculated Results CALCULATED RESULTS FOR RUN NUMBER 197044C TUBE CUTSIDE DIAPETER - INCHES.6271 TUBE INSIDE DIAMLTER - INCHES.5581 T~dE LENGTH - INCHES 72.1560 TUBE THERMAL CCNCUCTIVITY - bTU/HR-FTf-F I0.C.CUo TUBE METAL TITANIUM TUBE CUTSIGE HEAT TRANSFLR AREA - SCFT/FT.9872 TUBE INSIDE HEAT TRANSFER AREA - SQFT/FT.8786 TUBE FLCW AREA - SQFT.0016988 MET-AL RESISTANCE - 8TU/hR-S9FT-F.0002875 INSIDE COEFFICIENT CONSTANT.02468 CALCULATED RESULTS FOR RAW DATA TUBE NC N [UBE T TUBE IN T TUBE OUT T-AVG T-CP'T-DENSITY T-VISCOSITY LP/F-R F F F BTU/LB-F LB/CUFT LB/FT-HR 1 10112 74.990 78.100 76.545.999 62.234 2.160 2 9048 74.990 77.520 16.255.999 62.238 2.168 3 9390 74.990 77.450 76.220.999 62.238 2.169 4 9591 75.000 77.330 76.165.999 62.239 2.171. 9328 75.020 7 7. 390 76.2G5.999 62.238 2.169 6 9555 7 5.040 77.320 76.180.999 62.239 2.170 7 9C50 75.C60 77.340 76.200.999 62.238 2.170 8 9550 7 5.0170'17.270 76.170.999 62.239 2.170 19 q969 75.070 77.260 76.165.999 62.239 2.171

TABLE XVI (Continued) TUBE NC 1-K PR T WALL IN TW-VISCOSITY T-VELCCJIY RE Hi BTU/HR-FT F LB/FT-HR FT/SEC BTU/HR-SQFT-F 1.3490 6.182 85.05 1.95 26.568 >128140.818 4205.14 2.3489 6.208 83.05 2.00 23.771 114248.812 3828.78 3.3488 6.211 82.88 2.00 24.669 118516.046 3942.28 4.3488 6.216 82.51 2.01 25.197 120970.830 4006.00 5.3488 6.212 8'2.62 2.01 24.506 111711.722 3919.41 6 ~~~.3488 62482.38 2.01 25.102 120539.0B0 3993.44 7.3488 6.213 82.34 2.-C1 23.776 114196.544 3823.78 B.3488 6.215 82.16 2.02 25.089 120461.128 3990.05 9.3488 6.216 82.14 2.02 25.457 122219.510 4036.58 TUBE NO VAPCR TEMP LAT HEAT T WALL OUT CT FILM T FILM C-K C-UENSITY F 870/LB F F ~~ ~~~~~~~~~F BTU/HR-F LB/CUFT 1 ICO.960 1036.64 94.773 6.187 97.866.3616 61.985 2 1OC.970 1036.64 90.129 10.841 95.550.3604 62.012 3 100.990 1036.63 90.021 10.969 95.506.3604 62.013 4 101.030 1036.60 89.413 11.617 95.221.3602 62.016 5 101.060 1036.59 89.450 11.610 95.255.3602 62.016 6 101.090 1036.57 89.114 11.976 95.10'2.3601 62.017 7 101.120 1036.55 88i.712 12.408 94.916..3600 62.019 8 10-1. 120 1036.55 88.648 12.472 94.884.3600 62.020 9 101.120 1036.55 88.698 12.422 94..909.3600 62.020

TABLE XVI (Continued) TUBE NC C-VISCOSITY PI-YGR H-EAT DUTY LMTD U 0 Hi H COND Le/FT-HR BTU/HR F BTU/HR-SQFT-F BTU/HR-SQFT-F BTU/HR-SQFT-F 1 1.696 2.040 31413.04 24.382 1305.100 4205.136 5143.039 2 1.738 1.758 22865.86 24.693 938.013 3828.780 2136.613 3 1.739 1.753 23073.60 24.750 944.385 3942.284 2130.892 4 1.744 1.726 22322.09 24.847 910.054 4005.996 1946.410 5 1.744 1.726 22082.68 24.836 900.6-78 3919.414 1926.752 6 1.747 1.712 21761.08 24.893 885.549 3993.441 1840.634 7 1.750 1.696 2C610.96 24.903 838.409 3823.779 1682.654 8 1.751 1.693 20986.55 24.934 852.618 3990.055 1704.543 9 1.750 1.695 21197.42 24.939 861.001 4036.578 1728.651 CALCULATEL RESULTS FCR CATA ADJUSTED TO CONSTANT INLET WATER TEMPERATURE AND CCNSTANT VAPOR TEMPERATURE TUBE NC IA TUBE T TUBE IN T TUBE OUT T-AVG T-CP T-DENSITY T-VISCOSITY. LB/FR F F F BTU/LB-F LB/CUFT 18/FT-HR 1 9479 75.026 78.287 76.656.999 62.233 2.157 2 9479 75.02,6 77.470 76.248.999 62.238 2.168 3 9479 75.026 77.470 76.248.999 62.238 2.168 4 9479 75.026 77.377 76.201.999 62.238 2.170 5 9479 75.026 77.364 76.195.999 62.239 2.170 6 9479 75.026 77.318 76.172.999 62.239 2.170 7 9480) 75.026 77.219 76.122.999 62.239 2.172 B 9480 75.026 77.236 76.131.999 62.239 2.171 9'9479 75.026 77.252 76.139.999 62.239 2.171

TABLE XVI (Continued) TUBE NO T-K PR T WALL IN TW-V ISCOSI TY T-VELCCITY RE H OIL/HR-FT F LB/FT-HR FT/SEC BTU/HR-.SQFT-F 1.3491 6.173 8 5.45 1.94 24.904 120278.457 3998.34 2.3489 6.208 82.88 2.01 24.904 119684.846 3971.71 3 __.3489 6.208 82.88 2.00 24.904 119684.333 3972.83 4.3488 6.213 82.59 2.01 24.904 119616.596 3969.41 5 __.3488 6.213 82.54 2.01 24.904 119607.618 3970.0.2 6.3488 6.215 82.40 2.01 24.904 119573.656 3967.99 7.3488 6.220 82.09 2.02 24.904 119502.302 3964.27 B.3488 6.219 82.14 2.02 24.904 119514.472 3965.66 9- -.3488 6.218 82.19 2.02 24.904 119525.91 1 3965.73 ~~~~Ni ~~~~~~TUBE NO VAPCR TEMP LAT HEAT T WALL OUT OT FILM T FILM C-K C-DENSITY F BTU/LB F F F BTU/HR-FT LB/CUFT 1 101.051 CO03 6.5 9 94.973 6.049 98.027.3617 61.983 2 101.051 1036.59 90.024 11.016 95.543.3604 62.012 3 101.051 1036.59 90.020 11.014 95.544.3604 62.012 4 101.051 1036.59 89.455 11.579 95.262.3602 62.015 5 _ 101.051 1036.59 89.377 11.658 95.222.3602 62.016 6 101.051 1036.59 89.095 11.940 95.081.3601 62.018 7 101.051 1036.59 88.496 12.555 94.774.3600 62.021 8 101.051 1036.59 88'.599 12.437 94.832.3600 62.020 9 101.051 1036.59 88.696 12.340 94.881.3600 62.020

TABLE XVI (Continue d) TUBE NO C-VISCOSITY PHYGR HEAT DUTY LMTD uu Hi H COND LB/FT-HR BTU/HR F BTU/HR-SQFT-F BTU/HR-SQFT-F BTU/HR-SQFT-F 1 1.69 3 2.053 30878.12 24.359 1283.962 3998.338 5175.129 2.1.738 1.751 23148.49 24.783 945.706 3971.712 2128.020 3 1.738 1.751 23144.96 24.783 945.963 3972.834 2128.961 4 1.744 1.727 22264.84 24.831 908.327 3969.415 1948.293 5 1.744 1.724 22146.09 24.838 903.158 3910.018 1924.507 6 1.747 1.713 21705.49 24.862 884.423 3967.985 1841.879 7 1.753 1.690 20772.92 24.913 844.318 3964.266 1676.827 8 1.752 1.694 20934.71 24.904 851.577 3965.664 1705.412 9 1.751 1.698 21084.60 24.896 858.000 3965.727 1731.353 CALCULATED RESULTS ARE FOR AVERAGE CONDITIUNS FOR TOP I TUBE TUBE NC 6 TUBE T TUBE IN T TUBE OUT T-AVG T-CP T-OENSITY T-VISCOSITY LB/HR F F F BTU/LB-F LB/CUFT LB/FT-HR 1 9479 75.026 78.287 76.656.999 62.233 2.157 2 18958 75.026 77.879 76.452.999 62.236 2.163 3 28437 75.026 77.742 76.384.999 62.236 2.165 4 3179 17 75.026 77.651 716.338.999 62.237 2.166 5 47396 75.026 77.594 76.310.999 62.237' 2.167 6 5687i) 75.026 77.548 76.287.999 62.237 2.167 1 66355 75.026 77.501 76.263.999 62.238 2.168 8 ~ 75835 75.026 77.468 716.247.999 62.238 2.168 9 85314 75.026 77.444 76.235.999 62.238 2.169

TABLE XVI (Continued) TUBE NC T-K PR T WALL IN TW-VISCOSITY T-VELCCITY RE HI 3TL/HR-FT F LB/FT-HR FT/SEC BTU/HR-SQFT-F 1.3491 6.173 85.45 1.94 24.904 120278.457 3997.15 2.3490 6.208 84.18 1.97 24.904 119684.846 3980.91 3.3489 6.208 83.74 1.98 24.904 119684.333 3978.05 4.3489 J6.213 83.46 1.99 24.904 119616.596 3975.24 5.3489 6.213 83.27 1.99 24.904 119607.618 3973.92 6.3489 6.215 83.13 2.CO 24.904 119573.656 3972.51 7.3489 6.220 82.98 2.C0 24.904 119502.302 3970.58 8.3489 6.219 82.88 2.00 24.904 119514.472 3970.04 9.3488 6.218 82.80 2.00 24.904 119525.911 3969.69 as ND9~~~~~ ~TUBE NO VAPCR TEMP LAT HEAT T WALL COUT CT FILM T FILM C-K C-DENSITY F 8TU/LB F F F BTU/HR-FT LB/CUFT I lC1.051 1036.59 94.973 6.039 98.032.3617 61.983 2 IC1.051 1036.59 90.024 8.513 96.795.3611 61.998 3 [C1.051 1036.59 90.020 9.345 96.379.3608 62.002 4 101.051 1036.59 89.455 9.902 96.100.3607 62.006 5 101.051 1036.59 89.377 10.252 95.925.3606 62.008 6 1C 1.051 1036.59 89.095 10.532 95.785.3605 62.009 7 IC1.051 1036.59 88.496 10.817 95.642.3604 62.011 8 101.051 1036.59 88.599 11.020 95.541.3604 62.012 9 lCI.051 1036.59 88.696 11.167 95.468.3603 62.013

TABLE XVI (Continued) TUBE NO C-VISCOSITY PHYGR HEAT DUTY LMTD UD l H COND LB/FT-HR BTU/HR F BTU/HR-SCFT-F BTU/tHR-SQFT-F BTU/HR-SQFT-F 1 1.693 2.054 30878.12 24.359 1284.111 3997.151 5179.789 2 1.715 1.876 54026.61 24.571 1113.652 3980.910 3214.304 _____3 __ 1.723 1.830 77171.56 24.642 1057.448 3978.050 2788.369 4 1.7!28 1.802 99436.41 24.690 1019.939 3975.242 2543.165 __ 5 __ 1.731 1.785 121582.50 24.719 996.478 3973.922 2402.690 6 1.734 1.772 143287.99 24.743 977.704.3972.507 2296.899 7 1.737 1.760 164060.91 24.767 958.584 3970.583 2194.141 - ~ 8 1.738 1.751 184995.61 24.784 945.138 3970.044 2125.686 __ 9 1.740 1.145 206080.21 * 24.797 935.408 3969.690 2077.200 __TUBE NG _CUNO CCNST CCNST/0.725 CN 1 -. -1.4866 2.0504 2.0514 2.7166.9885 1.6571 -.. ~~~.7169.9889 1.6309 4.6651.9173 1.6233 5.6582.9078 1.6369 -.6.6340.8745 1.6497 7.5852.8071 1.6501 8.5936.8188 1.6608 9.6013.8294 1.6774

UNIVERSITY OF MICHIGAN I 1111 5 i 026561111111 72511111111 1111111 3 9015 02656 7225