THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING HEAT TRANSFER IN FALLING-FILM LTV EVAPORATORS Joachim R Sinek A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan Department of Chemical and Metallurgical Engineering 1961 September, 1961 IP-534

ACKNOWLEDGEMENTS The author wishes to express his acknowledgements to: the late W. L. Badger, prime mover behind the Wrightsville Beach pilot plant, who suggested the thesis topic, and to whose memory we respectfully dedicate this work; the engineers and operators of W. L. Badger Associates, Inc,, for their unfailing encouragement, friendship and assistance; the U. S. Department of the Interior, Office of Saline Water, for permission to use the experimental data in this dissertation; the members of the author's doctoral committee Professor Edwin H. Young, Chairman Professor John A. Clark Associate Professor Kenneth F. Gordon Mr. Ferris C. Standiford Professor Brymer Williams ii

TABLE OF CONTENTS Page ACKNOWLEDGEMENTS.o o o o o o o o o... o o o o o o o o o o.. o. o ii ABSTRACTOOO,..O.OOOOOO.OOOOOOO. 0 0000 0vii LIST OF SYMBOLS AND ABBREVIATIONS... oO OO.O O O 0o4 o.oo.O o... O Viii SECTIONS I EXPERIMENTAL WORK....................................... 1 EQUIPMENTa.o o c o a a 0 a0 0 0o a a 0 o o 0 o 0 a o 0 a a 4 INSTRUMENTATION....................................... 4 TUBES.. oooo o 000000 o0000.eoo 0 000000000.0o o ooooooooooo o o0 6 FEED DISTRIBUTION.... o...................o....... o..o o 7 NATURE OF HEATING SURFACE.o o.................... oo o 7 READINGS, OBSERVATIONS AND RECORDS o............ o o.. 8 CHEMICAL ANALYSIS OF BRINE CONCENTRATION.,........o o 8 PHYSICAL PROPERTIES OF SEA WATER BRINES................ o 9 CALCULATIONS, o,.o..o...o o.......oooo..Oo o.o O.. 4 o 9 Calculation Procedureo.....a.............................. 9 Steam............................................. 0. 9 Heat Transfer and Pressure Drop...................... 12 Condenser Water,. e o o, a o e oooo o.o o o o o o 13 Blowdowns........................................... 15 B10WdOwn. a < o o o e o o o o o o oa o ea a a a 0 a a o a a a a o a o o a a o s a o 0 o a 15 Feed....,.0. 0 o 00 -0 a 0 e00 a e0 o a 0 16 Mass Balance o...................................... 17 Energy Balance......Ooo Oooooaooo...............oooo 17 SUMMARY OF CALCULATION PROCEDURE, o..,,......,,, o. o.. 18 a) Calculation of Mass Balance., o,. oo o o......... 18 b) Calculation of Steam Enthalpy and Heat Load...... 18 c) Calculation of Feed, Blowdown and Vapor Enthalpies.................................. 19 d) Calculation of Enthalpy Balance.............. 19 e) Calculation of Overall Heat Transfer Coefficients00 o 000.00.0000000..00000 0..........0 0 0a 20 f) Calculation of Pressure Drop..oo.... o.... o o o 20 RANGE OF PROCESS VARIABLES.. a........00000000000 o o 0 21 OPERATING PROCEDURE o o o.o o....................... 21 II THEORY OF FALLING-FILM FLOW.o. o... o o o. o o. o o o. o o. oa 23 A. FU2DAMENTALSo0 o o o.................................. 23 B. LITERATURE RESEARCH: FLUID MECHANICS..................0 26 C LITERATURE RESEARCH: HEAT TRANSFER (NON-BOILIN.G)...... 46 iii

TABLE OF CONTENTS (CONT'D.) Page III LITERATURE RESEARCH ON NUCLEATE BOILING FUNDAMENTALS...... 57 RATE OF HEAT TRANSFER IN NUCLEATE BOILING..... 57 BUBBLE FORMATION............ 61 BUBBLE GROWTH....................... e 65 BUBBLE BEHAVIOR..................... 67 SUGGESTED HEAT TRANSFER MECHANISMS IN NUCLEATE BOILING. 68 IV LITERATURE RESEARCH ON GAS-LIQUID FLOW............ 71 V LITERATURE RESEARCH ON PERTINENT EVAPORATOR STUDIES...... 77 A. CLIMBING-FILM LTV'S................. 77 B. WIPED-SURFACE EVAPORATORS................ 78 C. FALLING-FILM LTV'S.................... 78 VI DESIGN AND RESULTS OF EXPERIMENTS......... 82 A. RUNS LWCI-1 TO LWCI-32................... 83 Design of Experiment............... 83 Accuracy of Results................... 85 Experimental Results.................. 87 B. RUNS LWCJ-1 TO LWCJ-16 AND C. RUNS LWCK-10 TO LWCK-29................. 89 D. RUNS LWDA-2 TO LWDA-38.................. 92 VII THEORETICAL MODEL OF FALLING-FILM EVAPORATIVE HEAT TRANSFER MECHANISM............................ 96 FUNDAMENTAL MODEL..................... 96 BOILING POINT ELEVATION................... 98 LONGITUDINAL PRESSURE-DROP MODEL............. 102 CALCULATION OF TUBE-SIDE HEAT TRANSFER FILM COEFFICIENT FROM THEORETICAL MODEL.................. 108 iv

TABLE OF CONTENTS (CONT'Do) Page VIII PREDICTION OF OVERALL HEAT TRANSFER COEFFICIENTS FOR RUNS WITH ZERO FEED SUPERHEAT FROM THEORETICAL MODEL.o.......... 109e CALCULATION OF STEAM-SIDE TEMPERATURE DROPo........ 110 CALCULATION OF TUBE-WALL TEMPERATURE DROP........e..... 111 CALCULATION OF OVERALL HEAT TRANSFER COEFFICIENT...... 113 COMPARISON OF THEORETICAL MODEL WITH EXPERIMENTAL RESULTS............................................a oo a 113 IX THEORETICAL ANALYSIS OF RESULTS FOR TESTS WITH 20~F FEED SUPERHEAT.. o.. o... o o. o o o o... e.. o.... o.. 118 APPENDICES A. EXPERIMENTAL DATA AND CALCULATIONS RUNS LWCI-1 TO LWCI-32,,. o................o o o.......... 121 B, EXPERIMENTAL DATA AND CALCULATIONS RUNS LWCJ-1 TO LWCJ-16,.,........... oo o. o..... o o 124 C. EXPERIMENTAL DATA AND CALCULATIONS RUNS LWCK-10 TO LWCK-29..o...o..o... o.... o.....o.... 127 D. EXPERIMENTAL DATA AND CALCULATIONS RUNS LWDA-2 TO LWDA-38.. oo000000.00 o06, o0. 00. 0 o. 130 Eo GRAPHS USED TO CORRELATE EXPERIMENTAL DATA.....oo...... 133 F. DISCUSSION OF ACCURACY AND EVENTUAL MODIFICATION OF THEORETICAL CORRELATION OF HEAT TRANSFER COEFFICIENTS.......o...00 a 0 0 O a0 0 a 0 0 a 0 0 a o 0 0 0 0.. a 0 c a a a0 4 a. 143 a) Effect of Scatter in hstm...................... 1 44 b) Effect of Using Feed Chlorosity to Calculate UVH-.................... o o o a 0 a 145 c) Effect of Neglecting Bubble Superheat, o......... 147 BIBLIOGRAPHIES BIBLIOGRAPHY ON FALLING-FILM FLUID FLOW AND (NON-BOILING) HEAT TRANSFER.. o oooo0a................ o.oo o oo o o ooo 151 BIBLIOGRAPHY ON NUCLEATE BOILING FUNDAMENTALS.............. 154 Vx

TABLE OF CONTENTS (CONT'D) Page BIBLIOGRAPHY ON GAS-LIQUID FLOW.......... o.. o................... 157 BIBLIOGRAPHY ON EVAPORATOR STUDIES.............. o....... o o 160 ADDITIONAL BIBLIOGRAPHY USED IN DESIGN, RESULTS AND ANALYSIS, OF EXPERIMENTS. o o.o oo o.....o..... a. o. o o o..o o o e 0 o. C 162 vi

ABSTRACT A procedure is presented for predicting liquid-side and overall heat transfer coefficients in falling-film evaporators. A model is developed for the heat transfer mechanism in falling-film evaporation, according to which the temperature difference across the falling film obeys the same law during evaporation as in the transfer of sensible heat and as in condensation. The temperature difference across the falling film is therefore calculated as the quotient of the heat flux and a heat transfer coefficient. For this heat transfer coefficient the correlation by Dukler is used. It consists of numerical values obtained by directly computer-integrating the basic heat and momentum transfer equations, and has been shown to correlate successfully experimental data on falling-film heaters and falling-film condensers. In order to make a comparison with experimental data it is necessary to know the temperature difference between wall and vapor-head rather than the temperature drop across the falling film. The calculated temperature drop is therefore corrected for the longitudinal pressure drop, the boiling point rise due to solutes, and the boiling point rise due to the presence of bubbles. The latter is calculated by postulating bubbles of the same size as the film thickness, and by applying the Gibbs equation connecting bubble superheat with surface tension and bubble size. Overall heat transfer coefficients are calculated by using the theoretical model for the liquid-side heat transfer; steam-side coefficients are estimated as 1.28 times the Nusselt correlation, on basis of the experiments of Baker, Kazmark and Stroebe, and the recommendation of McAdams; it is shown that the overall coefficient is fairly insensitive to changes in the steam-side coefficient. The experimental work consisted of measuring overall heat transfer coefficients in a 7-tube falling-film LTV evaporator for a wide range of operating variables. The tubes employed were 1-in. and 2-in. tubes, 24 ft long. The test liquids were sea water and sea water concentrates. Boiling temperature ranged from 100 to 230~F, heat flux from 3,200 to 6,500 Btu/(hr)(sq ft), film Reynolds number from 1,000 to 11,000, film Prandtl number from 1.6 to 4.5. In roughly half the runs, the feed temperature was equal to the vapor-head saturation temperature; in the others, the feed temperature was 20~F higher. A total of 105 runs were made, each at a different combination of tube diameter, vapor-head saturation temperature, feed temperature, feed salinity, feed rate, and steam rate. For runs with feed temperature equal to the vapor-head temperature, the measured overall coefficients agreed within 10% with the calculated coefficients. For runs with feed temperature 20~F higher than the vapor-head temperature, overall coefficients were consistently 10% lower, apparently due to flashing at the tube entrance. It is shown that the correction for boiling-point rise due to bubbles is an essential part of the correlation. vii

LIST OF SYMBOLS AND ABBREVIATIONS A Heat transfer surface area; sq ft b Wetted perimeter; ft B Falling liquid film thickness; Bp at wave peak; Bt at wave trough; BL at tube length L; ft B Value of y at y = B (BPR) Boiling-point rise due to presence of solute; OF c Specific heat; cp at constant pressure; cl of liquid phase; Btu/(lb)(~F) C,Cb,Csf Dimensionless numerical constants (C1) Chlorosity; grams per liter D Diameter; ft.; De equivalent diameter, in. EM Momentum transfer eddy viscosity; EH heat transfer eddy viscosity; ft2/hr f Dimensionless friction factor f( ) Function of; more specifically, the steam saturation temperature as function of pressure; as in: 212~F f(29.922 in. Hg abs.) (Fr) Froude number g Acceleration of gravity; ft/(sec)2 or ft/(hr)2 viii

gc Unit conversion factor, equal to 32.17 poundals/lbf G Mass flowrate per unit cross-section; Gr at the terminal tube length; lb/(hr)(sq ft) h Local film heat transfer coefficient; Btu/(hr)(sq ft)(OF) hm Mean value of h with respect to entire heat transfer surface; hstm for steam-side heat transfer; hf for heat transferred through falling liquid film; hVH for heat transferred through falling liquid film, assuming film to be at the BPR-corrected VH saturation temperature; Btu/(hr)(sq ft)(OF) H Enthalpy flow; Btu/hr A Hvap Heat of vaporization; Btu/lb J Mechanical equivalent of heat; 778.16 ft-lbf/Btu k Conductivity; Btu/(hr)(sq ft)(~F/ft) KFKV Dimensionless variables in Brauer's correlation L Tube length; Lo reference tube length; LT terminal tube length; ft n Dimensionless numerical factor in Deissler's correlation (Nu) Nusselt number; (Nu)m mean value of (Nu) for entire heat transfer surface p Pressure; P1 in liquid phase; Pv in vapor phase; P pressure drop; lb /sq ft or in, Hg ix

(Pr) Prandtl number; (Pr)l liquid phase Prandtl number q Heat flux; Btu/(hr)(sq ft) Q Rate of heat transfer; Btu/hr r Bubble radius; rl, r2, principal bubble radii; ft rh Hydraulic radius; ft Rg Gas-phase holdup fraction; R1 liquid-phase hold-up fraction (Re) Reynolds number; (Re)crit critical Reynolds number; (Re)wl Reynolds number of first wave appearance; (Re)i, (Re)wi, (Re)c characteristic film Reynolds numbers in Brauer's correlation t Temperature; t1 in liquid phase; tv in vapor phase; tw at tube wall; tsat saturation temperature; tstm steam. condensation temperature; ttr transition temperature; OF t Dimensionless temperature in Deissler's correlation A t Finite temperature difference; A tsat between tw and tsat; L tsub between tsat and ti; A tstm across steam-side condensate layer; Atw across metal tube wall; A tf across falling liquid film; tapp between tw and the VH saturation temperature; tOAapp between tstm and the VH sat. temp.; A tOA between tstm and the BPR-corrected VH sat. temp.; A tcorr between tw and the BPR-corrected VH sat. temp.; OF u Local velocity; ui at interface; u' at y=- E; ft/sec x

u* Dimensionless friction velocity u- Dimensionless velocity UVH Overall heat transfer coefficient, assuming film to be at the BPR-corrected VH sat. temp. v Specific volume; cu ft/lb V Average velocity with respect to entire flow cross-section; ft/sec w Mass flowrate; lb/hr (We) Weber number x Distance parallel to flow direction; ft y Distance normal to flow direction; ft yT Dimensionless distance normal to flow direction Poe Dimensionless number expressing variation of kinetic energy with radius for fluid flow through a pipe P Dimensionless variable in Dukler's correlation /p Bubble contact angle Characteristic film thickness in Brauer's correlation; ft (b Angle of inclination with respect to horizontal bd Dimensionless constant in von Karman's correlation xi

,AC Viscosity; lb/ (hr) (ft) yV Kinematic viscosity; ft2/hr r/ Density; (g gas density; /1 liquid density; lb/cu ft or Surface tension; (IH20 surface tension of water; lbf/ft; ~Shear; ti interfacial shear; Zw wall shear; lbf/sq ft P ~Characteristic heat transfer coefficient in Nusselt's correlation; Btu/(hr)(sq ft)(tF) ~t ~ Dimensionless magnitude in Nusselt's correlation t ~Characteristic bubble superheat magnitude; in. Hg Mass flowrate per unit perimeter; lb/(hr)(ft) Adz X Dimensionless ratios in Lockhart-Martinelli correlation Abbreviations and Terminology app apparent; designates temperature drops when it is assumed that the evaporating liquid is at the vapor-head saturation temperature corr corrected; designates temperature drops when it is assumed that the evaporating liquid is at the vapor-head temperature corrected for BPR gpl grams per liter OA overall VH vapor-head xii

INTRODUCTION Falling-film long-tube vertical evaporators are finding increasing application in the evaporation of sea water and of heat-sensitive liquidso This is mainly because these evaporators have high heat transfer coefficients at low temperature differences, and because of their small hold-upo However, the technical literature is almost completely devoid of experimental data or theoretical analyses of falling-film evaporation, This dissertation is presented in the hope that it may contribute to engineering knowledge by filling this long-felt need. The author was fortunate in having at his disposal a well-equipped pilot plant, including a 24-ft falling-film LTV evaporator. This pilot plant was the sea water evaporator test station of the Uo So Department of the Interior, Office of Saline Water, located on the premises of the International Nickel Co, laboratory, Wrightsville 'Beach, No Co It was designed, erected and operated for the Government by the author's employers, Wo L. Badger Associates, Inc., Consulting Engineers, Ann Arbor; the author was in charge of the erection (1957) and subsequent operation (1957-60)o - The purpose of the test station was mainly to investigate and demonstrate the application of falling-film evaporators to sea water conversion, with particular emphasis on scale prevention. Part of the time was devoted to heat transfer work: a systematic series of experiments was performed to measure heat transfer coefficients for a wide range of operating conditions. The author secured permission to use these data for his dissertation. A model for falling-film evaporative heat transfer was developed by the author, Heat transfer coefficients calculated from this model were found to be in good agreement with the Wrightsville Beach test data, and should permit a more precise design of falling-film LTV evaporators, The model should also contribute to a better understanding of the physical nature of falling-film evaporation. xiii

SECTION I EXPERIMENTAL WORK INTRODUCTION The experimental work consisted of a series of runs in which a falling-film LTV evaporator was used to evaporate sea water brines, and in which the overall heat transfer coefficients were measured. These runs were performed over a wide range of operating conditions: feed rate, steam rate, vapor-head temperature, feed temperature, feed salinity, and tube diameter. Boiling temperature ranged from 100 to 230~F, heat flux from 3,200 to 6,500 Btu/(hr)(sq ft), film Reynolds number from 1,000 to 11,000, film Prandtl number from 1.6 to 4.5, feed superheat from 0 to 20 ~F The purpose of the experimental work was the accumulation of sufficient data to enable a reasonably accurate prediction of the heat transfer coefficient to be made for a given set of operating conditions. The experimental work was necessary because, to the best of our knowledge, no such information on falling-film LTV evaporators exists in the literature. The results of the experimental work were also used in order to compare them with those predicted from the theoretical model (Sections VIII and IX) -1 -

-2-.':.;:~...........,...... General View Looking Southeast General View Looking Southwest Control House, Left Foreground, LTV FC Evaporators, Center Evaporator, Right Center. FC Evaporators, Left Center.General View Looking North LTV Evaporator, Left Center FC | |,, 1 x r~Evaporators, Right ~~~~~~~~~~~~~ i: i::l::ii::::i-:::::::::::i~ ~ ~ ili?

-3 -N C ^y --- —— MI VAP-.'CONDENSER TRC 1, ~HEATING ELEMENT V D V D S C ~-fPRCL F BD C Steam cod VAPOR HEAD F Feed ____ BD Blowdown FTRC e Flowrate recorder-Sightglass on BD~~~~~~~V Vapor -controller volumetric Q Q+Q vr, I --- —-I ^7 ^drip tank Steam Ip-C I Pressure recorder-controller C Steam condensate ITRC ITemperature recorderV Vapor -controller ' D e Pressure gage or D Distillate manometer manometer CW Cooling water Thermometer N Non-condensibles Figure 1

EQUIPMENT The experimental equipment was part of the sea water evaporation pilot plant on Harbor Island, on the North Carolina coast. This plant is an open-air installation and is located a few feet from the ocean's edge, on the premises of the corrosion test station of the International Nickel Co., Inc., Wrightsville Beach, N.C. The test evaporator was a falling-film LTV (Figure 1 ), The heating element was essentially a 24-ft vertical single-pass heat exchanger. Feed entered the tubes at the top, and flowed down through the tubes while receiving heat from the steam, which condensed on the shell-side. A mixture of vapor and concentrate ("blowdown") came out of the bottom tube ends and into a wide separating tank ("vapor-head"). Vapor was led from the top of the vapor-head to a surface condenser; blowdown was pumped out of the bottom. Auxiliary equipment included a small steam-heated feed pre-heater; a surface condenser; a two-stage Nash vacuum pump with an additional steam-jet air ejector; two plant-size forced-circulation evaporators (FC's) operating independently of the LTV. Steam was supplied by two nearby boilers at ca. 105 psi, and reduced to 15-30 psi prior to entering the system. - The entire equipment was provided with heavy thermal insulation. INSTRUMENTATION Two sets of instrumentation were provided, for the following two purposes:

-5 -1) Process control, in order to maintain the operating variables at steady predetermined values. 2) Measurement, to calibrate the process control instruments, and for the accurate determination of all variables necessary for a mass balance, an enthalpy balance, and a calculation of the overall heat transfer coefficient. Process control of feed flowrate, feed temperature, steam flowrate, and vapor head pressure was carried&out by means of pneumatic recordercontrollers, panel-mounted in a separate control shack. It should be pointed out here that the heat load was controlled by an orifice-type steam flowrate controller in the steam line, not by a steam-pressure controller in the steam chest; steam-side pressure was, therefore, a dependent variable, not an operating variable. Measurement of blowdown flowrate, distillate flowrate and steam condensate flowrate was carried out in volumetric drip-pots provided with sight-glasses; the rate of rise in the tanks was timed with a stopwatch. These volumetric drip-pots were previously calibrated with weighed amounts of watero (The vapor-head acted as volumetric drip-pot for the blowdown rate.) All three drip-pots had calibrated thermometers. In addition, blowdown concentration was determined by chemical analysis, since the density of brines is a function of concentration as well as of temperature, - Measurement of feed temperature was carried out with a calibrated thermometer located close to the feed cone. - Measurement of steam temperature was similarly taken on a thermometer located close to the steam entrance cone. - Measurements of feed pressure, steam pressure

-6 -and vapor-head pressure were performed with mercury manometers (vacuum operation) or with sensitive Bourdon gages, previously calibrated against mercury manometers (pressure operation). An instrument that was used neither for control nor for measurement, but which gave an excellent picture of the steadiness of the process, was an automatic temperature-difference recorder. It showed the time-dependence of the temperature difference between the condensing steam and the vapor in the vapor-head. It consisted of a resistance bulb in the steam-chest and a similar resistance bulb in the top part of the vapor-head, electrically connected to a panel-mounted indicator. TUBES The test evaporator was a 7-tube LTV; one tube was mounted in the center of the circular tube-sheets, the other six around it on a triangular pitch. The LTV was built for 24-ft tubes. The tube sheets were fashioned in such a way that the tubes were not rolled in but grommetted in. Three neoprene grommets per tube end were used, and proved satisfactory. Tests were carried out with 24-ft tubes; 2-in. 12 ga. tubes were used for all operating conditions, and a similar series of runs was then repeated with 1-in. 16 ga. tubes. Mixed tube bundles were used, with respect to tube materials, since other tubes were not available. The 2-in. tube bundle consisted of 2 copper, 2 aluminum brass, 1 arsenical admiralty, 1 Ampco grade 8, and 1 90/10 cupronickel tube. The 1-in. tube bundle had 2 copper, 3 aluminum

brass, 1 arsenical admiralty and 1 90/10 cupronickel tube, Although mixed tube bundles are generally not desirable, the difference in conductivity of -the metals was not enough to cause an appreciable maldistribution of heat load. FEED DISTRIBUTION Even feed distribution among the 7 tubes presented a problem due to the absence or near-absence of a longitudinal pressure drop through the tubes. (This problem is not encountered in bottom-fed LTV's.) Careful levelling of the upper tube ends proved unsuccessful. The final solution was the use of inserts fitted on the upper tube ends. These inserts contained a horizontal orifice-plate or a nozzle, through which the feed had to flow to reach the tube itselff, and which caused a pressure drop high enough to equalize the feed distribution. A horizontal splash plate only a little smaller than the tube Io D and mounted under the orifice converted the jet into falling-film flow; this was visually verified on glass tubeso The performance of a feed distribution device was measured by timing the flowrate of each individual tube with beaker and stopwatch. The disadvantage of having to use inserts was the impossibility of measuring longitudinal pressure drops directly. This problem will be referred to in more detail. NATURE OF HEATING SURFACE The heating surface was inspected by opening up the LTV, removing

-8 -the inserts, and looking through each tube against a light, No fouling, salting or scaling was ever observed, Scale was prevented by controlling the feed pH with sulfuric acid; this was checked by hourly pH-meter readings. No time-dependence of heat transfer rate over a period of many weeks could be observed. READINGS., OBSERVATIONS AND RECORDS Test work was carried out on a 24-hour day basis. Each shift was manned by an engineer and an operator. Each hour all instrument readings were taken and written down on specially prepared data sheets. Every three hours, or whenever deemed necessary, the drip-pot readings were taken in addition to the other readings; also, samples of feed and blowdown were taken and the concentrations determined by chemical analysis. Hourly observation of a descriptive nature were also written on log sheets facing the data sheets, CHEMICAL ANALYSIS OF BRINE CONCENTRATION Analyses were carried out in a chemical laboratory close at hand. Brine chlorosity was determined directly by titration with standardized silver nitrate. Chlorosity is defined as the grams per liter (20~C) of total halide expressed as chloride. Concentration can also be expressed by concentration factor, which is the ratio of salinity to the salinity of "normal" sea water*; sea water generally has a concentration factor * A universal standard; see Sverdrup, Ho YV, et al, "The Oceans", Prentice-Hall, 1st Ed.,, 1942.

-9 -close to 1.0. Concentration factor is a unique function of chlorosity, and has been tabulated. PHYSICAL PROPERTIES OF SEA WATER BRINES Charts were used in which density, concentration factor, specific heat and boiling point rise are given as functions of chlorosity and temperature. These charts were compiled for the Office of Saline Water by W.L. Badger Associates, Inc. CALCULATIONS Calculations were performed on specially prepared calculation sheets (see sample calculation sheet). Calculation Procedure The calculation procedure used for these tests is described herein in considerable detail to help clarify any questions that might arise. A sample calculation form, numbered to correspond to the following description, is shown on page 10. Steam 1. Pressure measured by bourdon tube gage (if used) on heating element. 2. Correction as determined by gage calibration. 3. Corrected pressure, or actual vacuum reading if measured by mercury manometer. 4. Barometric pressure as obtained from aneroid barometer,

CALCULATION FORM FOR TEST L.T.V. EVAPORATOR Test No.(l) Start-up date, time: Op: _ Date, time: _____ LTV effect No. Flowsheet: Calculated by: Recorded in book:._____ Date, time: _____ air temp., "F... Steam: Distillate: cond. press., in. Hg read. latent heat. Btu/lb. 4 Corr. (2), corr'd. sensible ht. above feed T., Btu/lb 4 Corrected barom. press. j heat from evap., Btu/lb. 46) cond. press., in. Hg abs. drip temp(47)0F;Feed-drip,Btu/lb saturation temperature, F (6) heat to cond., Btu/lb. actual temperature, ~F.(7) drip pot interval, sec. (5) steam enthalpy, Btu/lb (8) drip pot combined factor 51 drip temperature, bF.) drip pot reading, mm. 5 drip enthalpy, Btu/lb (10) evaporation rate, lb/hr (53) heat input, Btu/lb (11) total heat from evap., Btu/hr. drip pot interval, sec. (;~) total heat to cond., Btu/hr 55 drip pot combined factor 3 Condenser ht. bal. error.((57)%) drip pot reading, mm. ( ] flow rate, lb/hr 5) Blowdown: Flowmeter reading (6) temp....., Corr., c'd. 6F (58) Flowmeter factor 17 sp. gr (59) at (Pr-0F, c'd T x total heat input, Btu/hr 8) chloride, gpl (6) heat to atmosphere, Btu/hr 19) concentration factor (63 heat to vapor side, Btu/hr 2 specific heat, Btu/lb. enthalpy above feed T. Btu/lb (65) Heat Transfer and Pressure Drop.: drip pot interval, sec. (6) heat transfer area, sq. ft. 21) drip pot combined factor 67) V.H. press., in. Hg read e) drip pot reading, m. w) Corr. (23), corrd. 24 flow rate, lb/hr (69) V.H. press., in. Hg abs. enthalpy flow, Btu/hr (70) V.H. satur. temp., (F 26) BPR(7l, corr. At(72),corr. coeff. PP overall At, 0F 27) PP overall heat tr. coeff. (2 Feed: V.H. temperature, OF read (9) temp.....Corr., c'd. bF (74) Corr., corr'd. 30) sp. gr(7) at 7) 0F, c'd. (77) PT overall At, aF (31) chloride, gpl (7 PT overall heat tr. coeff. (32) concentration factor7 Feed'press., in. Hg read (33) flowmeter reading 0 Corr. _, corr'd. (34) flowmeter factor 8i Feed press., in. Hg abs. 5) flow rate, lb/hr (82) Overall A P, in. Hg (36) flow based on conc'n. ratio, lb/hr (83) feed/evaporation ratio Condenser Water: rotameter reading37 Mass Balance: rotameter combined factor (3 Evaporation rate, lb/hr (85) flow rate, lb/hr (39) Blowdown rate, lb/hr ( temp. out....corr c'd, ~F (4) Total output, lb/hr 87) temp. in....corr c'd, 0F T Feed rate, meas. lb/hr temperature rise, -F Error ((90)%), lb/hr heat gain, Btu/hr (43) Feed rate, analyt, lb/hr 91 Error ((93)%), lb/hr 92 Energy Balance(enthalpies above feed temp.) Blowdown enthalpy, Btu/hr (94) Vapor enthalpy, Btu/hr (95) Loss to atmosphere, Btu/hr 6 Total output, Btu/hr 97) Heat to vapor side, Btu/hr (95) Error ((lO0)%), Btu/hr (99)

-11 -checked frequently with local airport. 5. Item (4) plus (if under pressure) or minus (if vacuum) item (3). 6. Saturation temperature from Keenan and Keyes' Steam Tables at absolute pressure indicated by item (5). 7. Actual steam temperature measured at inlet to heating element. This thermometer usually indicated some superheat. The piping was arranged to minimize the possibility of moisture entrainment in the steam. 8. From Steam Tables at pressure (5) and temperature (7). If temperature (7) was below 20CPF., enthalpy of saturated vapor at pressure (5) was used. 9. Actual temperature of steam condensate. This was usually close to item (6), but accuracy was doubtful. 10. Enthalpy of water at temperature (6), from Steam Tables. 11. Item (8) minus item (10) gives heat available per pound of steam. 12. Time, measured by stopwatch, for condensate level to rise a fixed distance (14) in the gage glass on the volumetric condensate measuring tank when the discharge pump was stopped and the discharge valve closed, 13. Calibration factor of volumetric tank —a function of the effect of temperature on the density of water and the measuring distance. Determined originally by adding known weights of water and measuring the rise in level. 14. Distance level rose in time (12) -- 5 inches in these tests.

-12 -15. Item (13) divided by item (12) gives pounds per hour of steam used. 16. Actual reading of recording flow controller. 17. Item (15) divided by item (16) —used only to aid in subsequent adjustments of flow controller to get desired steam flow rates. 18. Item (15) times item (11) gives total heat given up by steam in Btu per hour. 19. Heat loss from steam side of heating element —as determined by test as a function of item (6) minus the outside air temperature. 20. Item (18) minus item (19) gives the rate of heat transfer through the heating surface. Heat Transfer and Pressure Drop 21. Area based on inside diameter of the 7 tubes —78.3 square feet for 2-in. tubes, 38.3 square feet for 1-in. tubes. 22. Not used since all vacuum and pressure readings obtained by mercury manometer. 23. D ii;to, 24. Actual vacuum in vapor head, as measured by mercury manometer. 25. Item (4) minus item (24). 26. Saturation temperature at pressure (25), from Steam Tables. 27. Item (6) minus item (26) —the apparent temperature difference across the heating surface, assuming that the sea water had no boiling point elevation. 28. Item (20) divided by (item (21) times item (27)) —the overall heat transfer coefficient before correction for boiling point elevation.

-13 -29. Actual temperature read on thermometer in bottom vapor head. This thermometer should read approximate saturated vapor temperature. 30. Item (29), corrected for thermometer calibration error. This temperature was used primarily as rough check of item (26). 31., 32. Not used, except as rough or quick check, and as a guide in adjusting the vacuum controller. 33. Actual reading of pressure gage or mercury manometer connected to feed cone at inlet to evaporator tubes. 34) Item (33) corrected for gage calibration error, or actual manometer reading when such was used. 35. Item (4) minus item (34). 36. Item (35) minus item (25) —pressure drop from orifice to outlet of tubes, due to friction, hydrostatic head, acceleration effects, and orifice pressure-drop. Condenser Water 37. Actual reading of rotameter in sea water line to surface condenser used to condense distillate from LTVo 38. Combined factor equal to calibration factor determined by test of rotameter times the specific heat of sea water (0.955 Btu/lb.- F. ). 39. Item (37) times item (38)) = l:b/hl-. sea water times 0.955. 40. Temperature of sea water leaving condenser, corrected for calibration error. 41. Temperature of sea water entering condenser, corrected for calibration error. 42. Item (40) minus item (41).

-14 -43. Item (39) times item (42) —heat picked up by sea water in condensing distillate. Distillate 44. Latent heat of water at temperature (26), from Steam Tables. 45. Item (26) minus item (74) —heat required to raise one pound water from feed temperature to distillation temperature (specific heat — 1.0). 46. Item (45) plus item (44) —enthalpy of vapor above feed temperature. 47. Actual temperature of condensate in measuring tank. 48. Item (74) minus item (47) —heat given up in sub-cooling condensate. 49. Item (46) plus item (48) —heat given up in condensing one pound of distillate and subcooling it to temperature (47). 50. Time, measured by stopwatch, for distillate level to rise a fixed distance in calibrated measuring tank. 51. Calibration factor of volumetric tank —similar to item (13). 52. Distance level rose in time (50) —5 inches in these tests. 53. Item (51) divided by item (50) gives pounds per hour of distillate. 54. Item (53) times item (46) gives Btu per hour heat leaving the evaporator with the distillate (taking liquid at the feed temperature as 0). 55. Item (53) times item (49) gives Btu per hour given up to the condenser water in condensing and subcooling the distillate.

-15 - 56. Item (43) minus item (55) —heat actually picked up by condenser water less heat that should have been given up to the condenser water. 57. Item (56) divided by item (55). This is a secondary check of the overall heat balance. It is only used to indicate the probable source of error if item (100) is relatively large. Blowdown 58. Same as item (30). 59* Specific gravity measured by hydrometer. 60. Temperature of gravity measurement. 61. Specific gravity at flowing temperature (58). Obtained from physical property charts, either from items (59) and (60) or from item (62). 62. Chlorosity —established by titration. 63. Concentration factor based on standard sea water of 19.:.' chlorosity. Determined from physical property charts. 64. Specific heat at chlorosity (62) and temperature (58) — from physical property charts'. 65. Item (64) times (item (58) minus item (74)) —heat required to raise one pound of blowdown from feed to discharge temperature. 66. Similar to items (12) and (50). 67. Similar to items (13) and (51) —a function of measuring distance (68) and specific gravity (61). 68. Measuring distance —7 inches in these tests. 69. Item (67) divided by item (66). 70. Item (65) times item (69).

-16 -71. Boiling point rise from physical property charts at chlorosity (62) and temperature (58). 72. Item (27) minus item (71) —overall temperature difference corrected for boiling point rise. This is temperature difference used in correlating all data. 73. Overall heat transfer coefficient corrected for boiling point rise —as used in correlations. Feed 74. Actual feed temperature, as read corrected for thermometer calibration. 75. Similar to item (59), for a sample of LTV feed liquor. 76. Similar to item (60), for a sample of LTV feed liquor. 77. Similar to item (61), at temperature (74). 78. Similar to item (62). 79. Similar to item (63). 80. Actual reading of recording feed flow controller. 81. Calibration factor for flow controller obtained by comparing controller with volumetric measurements in blowdown tank. 82. Item (80) times item (81) —a function of flow rate and specific gravity (77). 83. Item (69) times item (63), divided by item (79) —due to high accuracy of chlorosity determinations, this is a more accurate measure of feed flow than item (82). 84. Item (83) divided by item (53).

Z17 -Mass Balance 85. Same as item (53). 86. Same as item (69). 87. Item (85) plus item (86). 88. Same as item (82). Theoretically equal to (87). 89. Item (87) minus item (88). 90. Item (89) divided by item (87), times 100. 91. Same as item (83). Theoretically equal to (87). 92. Item (87) minus item (91). 93. Item (92) divided by item (87), times 100. This is an accurate indication of errors in flow rate measurement. Errors of 10o would usually be considered satisfactory, but the error in these tests rarely exceeded 3%. Energy Balance 94. Same as item (70). 95. Same as item (54). 96. Heat loss from vapor side of LTV —as determined by test as a function of item (26) minus the outside air temperature. 97. Sum of items (94), (95), and (96). Total calculated heat transferred through the heating surface, on the basis of the heat carried away. 98. Same as item (20). Calculated heat transferred from the steam to the heating surface. Theoretically equal to (97). 99. Item (97) minus item (98). 100. Item (99) divided by item (97), times 100. This is a good

check of heat input and distillate production. Errors of 15% would usually be considered satisfactory. The error in these tests rarely exceeded 8%. SUMMARY OF CALCULATION PROCEDURE a) Calculation of Mass Balance The evaporation rate was determined by timing the distillate drippot, and determining the distillate density by its temperature. The blowdown rate was similarly determined, by timing, and from blowdown temperature and concentration. Both rates were added together to give a value for the feed flowrate. - This value was compared to the blowdown rate multiplied by the ratio of B owdownceoteot-ttonrftow^QM eooneentia tion. b) Calculation of Steam Enthalpy and Heat Load The steam flowrate was determined from the steam condensate drippot. The steam saturation temperature was determined by measuring the absolute pressure of steam condensation and using the steam tables. The steam superheat was calculated from the saturation temperature and the -Ltemperature reading of the incoming steam. This determined the enthalpy of the condensing steam, in Btu/hr. From this was subtracted the heat loss from steam chest to atmosphere. This heat loss was experimentally determined before the beginning of the heat transfer runs as function thethe temperature difference between steam chest and atmosphere, by filling the empty steam chest

with steam and measuring the rate of condensation for various temperature differences. This calibration was repeated after the heat transfer runs, and was found to be unchanged. The heat loss was of the order of 3,000 - 13,000 Btu/hr for the heat transfer runs. The steam-chest was continuously vented from the top of the condensate drip-pot; during vacuum operation, to the vacuum pump, and during pressure operation, to the atmosphere. Venting was always excessive to insure removal of non-condensibles. c) Calculation of Feed, Blowdown and Vapor Enthalpies For the purpose of this calculation, the feed was arbitrarily designed as having zero enthalpy. - The blowdown enthalpy was calculated by multiplying the blowdown rate by the blowdown specific heat and by the blowdown-minus-feed temperature difference. - The specific vapor enthalpy, Btu/lb, was calculated by adding the heat of vaporization to the vapor-minus-feed temperature difference; this was then multiplied by the vapor flowrate, lb/hr. d) Calculation of Enthalpy Balance Blowdown enthalpy and vapor enthalpy were added and compared to the heat load. A correction was added due to the heat losses from the vapor-side (vapor-head, vapor line) to the atmosphere. This heat loss was determined by measuring the cooling rate of circulating hot sea water in a -edparate heat-l s t.est, perforrred before the heat transfer runs were startedo

-20 -As a check, a heat balance was also calculated around the condenser, by use of cooling water flowrate and temperature rise. This balance was only approximate, but served to point out any gross deviations. e) Calculation of Overall Heat Transfer Coefficients Steam-side temperature was taken as the saturation temperature corresponding to steam-chest absolute pressure. - "Apparent" vaporside termerature was taken as the saturation temperature corresponding to vapor-head absolute pressure. - "Corrected" vapor-side temperature was taken as the "apparent" vapor-side temperature plus the boilingpoint rise corresponding to the particular blowdown concentration and temperature In calculating the overall heat transfer coefficients, the calculated steam-side heat load and the inner tube diameters were used.e* The apparent coefficient was calculated by using the apparent vaporside temperature to calculate the overall temperature difference; the corrected overall heat transfer coefficient was similarly calculated by using the corrected vapor-side temperature to obtain the overall temperature difference. f) Calculation of Pressure Drop Due to the presence of tube inserts, pressure drops could not be measured directly. Vapor-head pressure was subtracted from feed pressure to give the desired pressure drop plus the orifice pressure dropo After * 38.3 seq ft for 7 1-in, tubes, 78.3 sq ft for 7 2-in, tubes.

-21 -each run, the steam was turned off, all other operating variables remaining unchanged; the resulting pressure drop was then due to the inserts only, and was subtracted from the orifice-plus-vapor pressure drop to give the desired two-phase flow pressure drop, RANGE OF PROCESS VARIABLES The following is a list of the process variables and their explored range: Tube ID,, in,: 0.870, 1.782 Vapor-head sat. temp,, ~F: 100, 125, 150, 1759 200; 230 Feed concentration factor: 1, 2 Feed flowrate, lb/hr: 1-ino tubes: 1,500, 35000 2-ino tubes: 1.500, 35000, 6,000 Steam flowrate, lb/hr: 1-in. tubes: 150, 250 2-in, tubes: 250, 450 Feed superheat*, ~F: 0, 20 The test schedule consisted of the determination of heat transfer coefficients for all combinations of process variables, OPERATING PROCEDURE Since the equipment was run on a non-stop schedule, the beginning of a run generally coincided with the end of the previous run, The process variables were changed by setting the automatic control instruments to the desired values; this was subsequently checked from *Feed superheat = Feed temperature - V. H. saturation temperature.

-22 -the next set of readings of the measurement instruments, - After three or four hours a complete calculation was made from the last set of readings. This was repeated every hour; generally two or three such calculations were made each run, and the results compared. If there was a change in readings, the run was continued until perfectly constant conditions were reached. Usually, however, steady-state was reached after two hours of operation, but the run continued for three or four hours more to ensure non-transient behavior. The two FC's were generally idle and were used as feed storage tanks, one for feed of concentration factor 1.0, the other for 2.0. Blowdown and distillate were recombined and pumped back to the respective FC. For tests with concentration factor 1.0 and cold feed (100 or 125 ~F), sea water was used directly, and the blowdown and distillate pumped back to the ocean. - Feed of concentration factor 2.0 was directly prepared in one of the FC's. * FC ~ forced circulation evaporator

SECTION II TBEORY OF FALLING-FIIM FLOW A. FUNDAMENTALS For steady-state one-dimensional downward flow through a vertical round tube, a force balance on an element of downward length dL yields, for any flow regime, dp 1 d(V2) W g (1) dL a2gcv dL rh vgc The wall shear stress 'w is taken positive when opposed to the flow direction L. An energy balance on this same element yields: dH dQ wv [ 1 (v ) g (2) dL dL J 2gc dL vgc The dimensionless velocity distribution factor oC is due to radial variations in kinetic energy. It is 0.5 for parabolic velocity distribution, 1.0 for highly turbulent flow. Assume isenthalpic flow, with negligible longitudinal variation in kinetic energy. From equ. (1): d^p =~ -w _^ g ()(3) dL rh vgc Consider the effect of decreasing flowrate on a tube with initially highspeed full-pipe flow. For any type of flow to take place in the L-direction, i.e., downwards, the pressure drqp dp cannot be negative: dLL w T g(4) rh vgc -23 -

This is valid for any type of flow regime. Let wA be the unique wall shear stress such as to cause zero A --- pressure drop in full-pipe flow, It is, therefore, the lowest wall shear stress at which full-pipe flow can take place. For full-pipe flow, rh = tA g.. _c (5) D vgc From equ. (4) we have, for any flow regime, 0rw rA VW rh,or' t.D7T (6) rih D r w(6) For full-pipe flow, rh =, fw. >w> As we decrease the flowrate and Zw falls below TwA, it must necessarily follow from equ. (6) that rh becomes less than D If the tube wall remains wetted, annular flow must resulto In annular flow, then, the pressure drop is zero-; friction loss and eventual gain in kinetic energy occur at the expense of potential energyonly. The flowrates employed in our research never exceeded 7% of the minimum flowrate necessary to cause full-pipe flow, i.e., to cause a wal_.1 shear stress Tw - For the ure urs of this analysis, no interfacial shear was assumed.

-,25 -The hydraulic radius for a film of thickness B is~ [D2 (D:.. 2B )2. B' For very thin films this expression reduces too rh - B (8) The Reynolds number is defined as in full-pipe flowe 4rhV 4w 4r( (Re)- - = (9) It is, therefore9 not necessary to know the film thickness in order to calculate the Reynolds numbere For films thin enough so that equ. (8) holds, equ (9) becomes: (Re) 4 B (10)

-26 -B) LITERATURE RESEARCH: FLUID MECHANICS Consider a liquid flowing down a flat plate, at an angle with the horizontal. Assume no interfacial shear, and perfectly streamline flow (Figure 2). A force balance yields: Figure 2 eg(B-y)b dx sin _ du bdx (11) Postulating zero wall velocity, equ. (11) is integrated across the film: u = (By- 2 ) sin9 (12) The mass flowrate per unit breadth is calculated as: r- } ufdy ^ 3sin (13) 0 The results of this classical analysis by Nusselt(37) in 1916 can also be expressed in the following ways: B = (32/3 (Re)l/3 sinl1/3 I (14) V (g)/3 (Re)2/3 sinl/36 (15) rw g sin (16)

TABLE I List of Experimental Studies on Momentum Transfer and/or of Single-Phase Heat Transfer in Falling Films AUTHOR YEAR TEST LIQUID APPARATUS WIDTH OR LENGTH RANGE OF (Re) F3IM THICKNESS EEF. DIA. (i. (.) (.MEASUREENT Hopf 1910 water, glass trough 2.05 15.8 600 - 2,400 micrometer 31 molasses 0.5 - 3.5~ inclination Claasen 1918 water, aq. NaC1, outer wall vertical 1.97 53.1 28 - 120 holdup 14 molasses steel & brass tubes 1.57 77.1 Schoklitsch 1920 water glass trough 10.0 -- 88 -180,000 ---- 41 0.25 - 2.0~ inclination Chwang 1926 water, min. oil glass plate 9.84 -- 3.6 - 440 micrometer 13 0 - 13 inclination Cooper, 1930 dil. aq. H2S04 inner wall vertical 0.439 25.0 1.53 - 192 holdup 18 Willey glass tube Warden 1930 water inner wall vertical 2.43 28.8 278 - 7,320 holdup 44 glass & brass tubes 2.50 30.1 Kirkbride 1934 water, min. oil outer wall vert. - tube -- 29.9 0.16 - 8,000 micrometer 33 Fallah, 1934 water inner wall vertical 0.532 56.5 80 - 3,370 holdup 25 Hunter, Nash glass tubes 0.875 84.4 1.011 57.5 Bays, 1937 2 min. oils inner wall vertical 1.5 49 - 73 2 - 2,000 * only 5 McAdams 2.5 Sexauer 1939 water outer wall vertical 1.18 8 - 102 3,300 - 16,500 micrometer 43 steel & brass tubes 2.36 McAdams, 1940 water inner wall vertical 1.5 49 - 73 2,100 - 51,000 * only 35 Drew, Bays 2.5 Friedman, 1941 water, inner wall vertical 1.00 60 0.09 - 460 holdup 26 Miller 3 min. oils Pyrex tubes 0.62 Grixley 1945 water, CC14, C6C6, aq. ---- - - 8 - 4,300 ---- 30 glycerol, aq. EtOH Pennie, 1952 5% aq. Na2CO3 inner wall vertical 0.502 -- 50 - 13,000 micrometer 39 Belanger copper tube Dukler, 1952 water vert. flat 24 96 480 - 3,000 film 22 Bergelin brass plate capacitance Brotz 1954 water, C15H32, inside wall vertical 0.583 11.8 400 - 17,200 holdup 10 min. oil glass tubes 0.787 19.7 1.575 39.4 Also * Garwin, 1955 water flat brass plate 8 30 2,900 - 12,800 * only 27 Kelly 0 - 90~ inclination Brauer 1956 water, aq. glycol outer wall vertical 1.772 70.9 0 - 4,000 photographs, 6 brass tube holdup. Also * Anderson, 1960 water inside wall vertical 0.427 50 holdup 1 Mantzouranis glass tube * Heat transfer tests

-28 -TDwg~ 24 - f - rwgc C 24 (17) From equ () and () it can also be seen that the velocity at From equ. (12) and (15) it can also be seen that the velocity ui at the interface (free surface) is 1,5 times the average velocity. For vertically downward flow, of course, sin 0 is equal to one in all these equations. Hopf* (31)9 the earliest investigator (1910), used too narrow a trough for his data to be considered reliable except for very shallow depths because of ripple formation at the side walls, - Claasen(14) used very thin films, of the order of several mils, on pipes of varying degrees of roughness. Unfortunately, over half of his runs were made with molasses whose viscosity he did not record. - Schoklitsch(41) extended his tests to very high flowrates and observed the flow regimes with the classical color-band methodo Copper, Drew and McAdams(l7) correlated the results of the first six investigators of Table Io The results show fairly good agreement with Nusselt's theoretical analysis for low flowrates, The friction factors scatter ca. ~ 30% about the straight line of equ. (17) when plotted on a log-log graph, for (Re) of less than 1,000. In analogy with full-pipe flow, this was considered the streamline portion. Above a (Re) of ca. 2,000 the friction factors changed much less with (Re), and this was, therefore, considered to be the turbulent zone. Other *-See Table I.

-29 -manifestations of turbulence, such as eddies and waves, were observed in this range, This analogy between full-pipe and falling-film flow was contradicted by Kirkbride's observation(33) that the first appearance of waves or ripples occurred in falling water films at a (Re) as low as 8. He noticed that the wave peaks were as much as 3.7 times the average film thickness. The, (Re) of first wave appearance, (Re)w, decreased as more viscous liquids were used. His film thickness measurement data below (Re)wl, i.e. for smooth films, followed the Nusselt theory, but those above, i.e., for wavy flow, did not. The latter may have been due to Kirkbride's micrometer technique, which gave maximum rather than average film thickness readings. Fallah, Hunter and Nash(25) correlated data from the literature in a manner similar to Cooper, Drew and McAdamsO Their own data were in fairly good agreement with the Nusselt theory for the entire viscous region. - Sexauer(43) ran falling-film tests at very high flowrates. He used a retracting micrometer tip and took his film thickness readings as the tip freed itself from the liquid. His readings were in poor agreement with the Nusselt theory, Friedman and Miller(26) confirmed Kirkbride's observations regarding ripples for (Re) above 25; they also found the velocity at the interface to be much higher than predicted by Nusselt above a (Re) of 25. These velocities were measured with a dye technique. However, they found that the mean film thickness followed Nusselt's correlation up to (Re) of 1,000 - 2,000.

-30 -Grimley(30) also observed wave motion in falling-film flow at values of (Re) above 25. He obtained very clear spark photographs of these waves By studying the behavior of test liquids with a viscosity range of 0.7 - 26.4 cp and a surface tension range of 19 - 75 dyne/cm, he derived the following dimensionless relation for the Reynolds number of incipient wave formation: (Re)wl1 1.16 )1/8 (18) For water at room temperature this turns out to be 25- - Grimley further observed from his photographs that the waves propagated in an orderly fashion up to a (Re) of 1,000 for water, and that turbulence set in at a (Re) of cao 2,000, He found that the range of wave flow regime was not affected by moderate air velocities in either direction. - Grimley studied the velocity profile by adding a drop of dye to the surface, observing it with a modified ultramicroscope and timing the rate of fall; no further description of the method is given. The resulting velocity profile starts out from the wall at values of u that are slightly below Nusselt's theory; at a Y ratio of ca. 0.9, however, the velocity B rises to a sudden peak as much as 3 times the value of the theoretical maximum velocity. At the interface itself the profile converges with Nusselt 's Pennie and Belanger(39) in 1952 measured the film thickness in a falling-film heater, A sewing needle controlled by a micrometer traversed the entire tube. The needle was glyptal-coated except for the point, and was connected in series with an audio-oscillator. When passing through

-31 -the air space no sound was emitted until re-entry into the film at the opposite side. The whole needle was inclined 45~ to the horizontal in order to improve accuracy. - Their values tend to be too high since they had no way of determining mean rather than maximum film thicknesses. - This research was carried out in a single tube similar to those used in their falling film heater. It is interesting to note that in the description of their heater the authors showed tube entrance orifices for flow distribution very similar to those used by us; also, their observation of the flow pattern as a falling-film liquid emerges from the bottom tube ends coincides with ours. Dukler and Bergelin(22) in 1952 presented the first new theoretical treatment of falling-film flow since Nusselt. Nusselt had developed his equations for streamline flow only, since at that time little was known about turbulent flow. Dukler and Bergelin used the Nikuradze - von Karman universal velocity profile to integrate the flowrate equation through the laminar layer, the buffer layer and into the turbulent layer, thus presenting a universal correlation for any flow regime. With the usual dimensionless variables: y= 7syu^ (19) y" u _ (20) u the friction velocity u*- - (21) B u (22) and with B -r-= Y=B) (22)

-32 -one can integrate the flowrate equation for thin films: + (Re) 4 Ju dy(23) 0 with a given universal velocity profile correlation. Nikuradze's universal velocity profile and its substitution into equ. (23) are, respectively, u' -y,,. (Re) 2B+ (0 y+< 5) (O <(Re)< 60) (24) u- -3.05 + 5.00 ^,y+) < (Re) B (5 AB+- 8.05) + 12.05 (5 <y'<30) (60 <(Re)< 1,080) (25) u - 5.5 2- 2.5:e&y+ (Re)= B (2.5:rnB-B+ 3.0) - 64 (y +>30) ((Re) > 1,080) (26) Dukler and Bergelin extended their theory to include an interfacial shear stress Zi different from zero. In full-pipe flow (Figure 3a) the radial shear stress profile for a given hydraulic radius is given by the wall shear stress Tw alone. In falling-film flow (Figures 3b, c, d, e) the shear profile, and hence the velocity profile, depend on ji as well as on Tw and the hydraulic radius. If the film is thin enough so that the hydraulic radius is equal to the film thickness B, a force balance on an element of film gives: r= - ti - gs (27) gc Bggo (2) A u*= ic + Bg (28)

-33 -*B+ =- B gc + Bg (29) For a given Reynolds number, B is calculated from equ. (24) to (26) and substituted into equ. (29); for a known value of Ti one can then calculate the film thickness B. I(O (b) (c) Id) (e (o) (b) (c) (d) (e) No gas flow Concurrent Countercurrent gas flow gas flow ( All liquid flow in downward direction ) Figure 3 The interfacial shear stress Ti can be derived from the general pressure drop equation of the gas core: dp 1 d(V|) i gg (30) d-~ = 2~Pgc Pg dL ( 30 *' tit v (pg g _ d (31) if kinetic energy changes can be neglected and the film is very thin in relation to tube diameter - The e term in parentheses in equ (31) is the frictional gas-phase pressure drop.

-34 -Dukler and Bergelin presented experimental evidence only for the case of zero interfacial shearo Equ. (29) simplifies to: B B B+2/3 (g2)l/3 (1/3 B=)1 3 (32) which below y = 30, (Re) = 1,080, falls very close to the Nusselt correlation when applying equ. (24) and (25). The authors used a Reynolds number range of 480 - 3,000 and found fairly good agreement with their theory. Their experimental set-up was the flow of a thin water film down a vertical flat brass plate. The film thickness was measured indirectly by determining the electric capacitance of the film; this was done with small disc electrodes held close to the film, and gave the root-mean-square film thickness. The mean film thickness was calculated from the root-mean-square film thickness by means of a geometric correction. derived from the study of the actual wave profiles on high-speed flash photographs. - Brauer(6) has observed that the results of Dukler and Bergelin fell slightly above their theoretical film thickness curve, and attributed it to the size of their disc electrodes, which, although small (1/8 x 3/16 in ), were probably still too large. Dukler and Bergelin's theory depends on the Nikuradze velocity profile, which was obtained with full-pipe flow. Dukler and Bergelin justified its application to film flow by postulating that a given element of fluid does not "know" whether it is part of a liquid mass in full-pipe flow or in film flow. For zero interfacial shear, their experimental results seem to support their reasoning. For moderate values of Ti they reasoned that Nikuradze's correlation should still be applicable within the bulk of the film for the same reason as before, and that at

-35 -the interface itself the turbulence would be so high as to make little difference. Brotz(10) in 1954 determined film thicknesses for flow down the inner walls of vertical glass tubes. He found Nusselt's relationship to hold up to a (Re) of 2,360; above this point he found B to be proportional to (Re)l/3 but was unable to formulate a general'correlation. Perhaps the most painstaking experimental investigation on fallingfilm flow is due to Brauer(6) in 1956. He investigated flow down the outside wall of a long vertical brass tube at room temperature. Reynolds numbers ranged all the way up to a highly turbulent 4,000. To determine the effect of viscosity he used water and aqueous diethylene glycol solutions, the viscosity ranging from 0.90 to 14 cp. Specific gravity was 1.0 - 1.1. The effect of surface tension was evaluated by artificially depressing water with small amounts of dodecyl sodium sulfate; surface tension ranged from 62% to 100% of normal water (74.6 dyne/cm). Brauer determined the following variables at different Reynolds numbers: the wave peak film thickness, Bp; the wave trough thickness, Bt; the average film thickness, B; the velocity at the interface, ui; the average velocity, V; the friction factor, f Peak and trough film thicknesses were determined by using a micrometric needle-probe; an oscillograph coupled to an electronic counter was connected to the needle. The number of waves per unit time were counted for given wall-to-needle distances, and the statistical frequencies were thus determined. The frequency curves were symmetrical

-36 -about well-defined maxima which were characteristic of the flow regime, and which gave Bp and Bt The average film thickness was determined by taking shadow photographs of the tube without liquid and with liquid, and planimetering the difference in area. Hold-up measurements gave the flowrates, which yielded the average velocities via the average film thicknesses, Interfacial velocities were determined by floating tiny pieces of flat plastic down the tube; for low velocities the rate of fall was visually timed, and for higher velocities a piece of plastic was photographed for a given exposure time, and the length of the streak measured. Wall shear stress was measured indirectly. The heat transfer coefficient was experimentally determined by inserting a small, electrically heated copper surface flush into one spot on the tube, and measuring the heat input and the copper surface temperature. Brauer "calibrated" this instrument with smooth films to give Zw as function of the heat transfer coefficient h, since for smooth films Zw can be calculated from the film thickness via equ. (27). The instrument was then used to determine cw on wavy films by postulating that the analogy between heat transfer and momentum transfer was the same for wavy films as for smooth films. Brauer clearly distinguished a turbulent region above a critical Reynolds number (Re)crit. This is analogous to full-pipe flow. Below this critical point, however, he distinguished 5 more different flow

TABLE II PROPERTIES OF BRAUER'S FLOW REGIMES (Re) f B Bp/B V Ui/V <w1 I 1 1.5 24(Re)-1 l Wl-i 1 - 2.65 1.5 - 2.15 i-w2 1.22(Re)-1/3 / ( R)1/3 /3 (e )/3 w2-c 34(Re)-1 2.65 2.15 c-crit 72(Re)-17/5 2.15 - 1.5 l -------------.. --- —-- |.3 1/( R )2.65 - up >,rlt 72(Re)-3/5(Re)-8/'15 3( 1/et)e )i )8/15 (gA/31(R)/5(Re)7/15i

-38 -regimes, separated by 4 characteristic Reynolds numbers denominated (Re)wl (Re)i, (Re)w2 and (Re)c e The visual aspects of the different flow regimes were described as follows. Starting with a very low flow rate, the film was perfectly smooth up to (Re)wl, the point of first wave formation (16 for water). Above this point small sine waves flowed smoothly all the way down the tube in closed rings. These waves formed roughly 4 in, below the feed point. At (Re)i, the point of instability (36 for water), the waves broke up after 5 - 6 in. of travel. These partial waves then proceeded further down the tube at different velocities, overtaking one another to form new waves. The location below the feed point where waves first fo-rmed.alsoswandered.upc and\wdown,-/;but. &atayscabout sit, Oli.ginal.ameansposition. At (Re)w2 (60 for water) no further change ook. place with increasing flowrate. In the neighborhood of the critical point (Re)crit (1,600 for water), the wave surface changed from smooth to rough due to the formation of capillary waves. Turbulent spots formed on the interface, and at Reynolds numbers above 2,400 very large ring waves formed that seemed to fall rather than to flow down the tube. - No visual effects were seen to change as (Re)c was passed (320 for water). - See Table II for a quantitative description of Brauer's flow regimes. In full-pipe flow, the transition from laminar to turbulent flow' occurs at a Reynolds number having a fixed value independent of the fluid's physical properties. Brauer found that for film flow, all 5 characteristic Reynolds number depend on physical properties. Brauer expressed them in terms of the same dimensionless variable 3 3 (,4g

-39 -used by Grimley. This number, called KF by Brauer, is the only combination of the Reynolds, Froude and Weber numbers that does not include inertial forces, i.e., velocity and film thickness: ~ ' 3 =(Re)4(Fr) (33) <KF=e (33) KFM /ig, (We)3 It is, therefore, the dimensionless variable'that relates gravity forces, viscous forces and surface forces. See Table III. Table III Value for Water at General Value Room Temperature (Re)wl 1.224 KF1/10 16 (Re)i 2.88 KF1/10 36 (Re)w2 5.40 KF1/10 60 (Re)c 0.0724 KF1/3 320 (Re)crit 140 KF1/10 1,600 B For flow to be fully developed, i.e., constant - ratio, Brauer found experimentally that the entrance length was equal to 892 B, or 892 ( /) 3(R)1/3. In this expression, the non-turbulent value for B is used because the film, though fully developed, was found to observe a non-turbulent behavior for a short distance after constant BC was attained. B

The effect of a trip wire was studied by Brauer. He found that it only had local effect, and that the disturbance smoothed out quickly, - He also measured the interfacial surface area on his shadow photographs. He found that the increase in area due to waves was negligibly small even for turbulent flow. The only effect due toc'a change of surface tension, according to Brauer, is a shift in the values of the characteristic Reynolds numbers, expecially (Re)crit; no other effect could be detectedo On comparing Brauer's results for average film thickness with those of Dukler and Bergelin, the two correlations are seen to check very closely in the turbulent as well as in the sub-critical range, although the two correlations were derived in quite different ways. His results also check with those of Friedman and Miller. - Brauer's friction factor plot departs from Nusselt's above (Re)wl > but comes so close to it as to fall well within the scatter of the data summary of Cooper, Drew and McAdams. - His observations on wave formation and on the dependence of (Re)w1 on physical properties check with Kirkbride, Friedman and Miller, and Grimley. Brauer's results present two curious features. One is the value Ui~ of - i which even for highly turbulent flow was observed to be 1.5. The other is, that his friction factors do not satisfy the force balance from equ. (27), gwgc B"g, except for smooth films. Brauer mentioned these two points but only explained them as resulting from wave action,

-41 -Dukler(23) in 1960 questioned the existence of a laminar sublayer in turbulent falling-film flow. - It has long been known that for fullpipe flow the laminar sublayer is a useful approximation only. In 1932 Fage and Townend(24) had detected dampened radial pulsations very close to the tube wall; even at 0.5 i from the wall they were unable to find rectilinear motion if the core of the liquid flowing through the pipe was turbulent.* The increase of turbulence with distance from the wall is gradual, not stepwise; since for full-pipe flow the region near the wall is only a small part of the entire flow cross-section, the inaccuracy involved in assuming the existence of a purely laminar sublayer is negligibly small. - Dukler reasoned that for falling-film flow the inaccuracy would be excessive, and that both laminar and turbulent transfer mechanisms had to be considered at all pointsnof the film. The general shear stress equation, to be integrated across the entire film, is therefore: r= i; (~ + (OE) M (34) or, in dimensionless form: aE dul ^ [+ ) (35) Tw ( V) dy Dukler used the Deissler correlation (19), (20) for the eddy diffusivity EM near the wall: * They used an ultramicroscope to observe the flow of tap water through a horizontal glass tube. When intensely illuminated, the water was found to contain sufficient particles to act as bright points of light when viewed against a dark' background.

-42 -e <-~ (1 ~,2>(0 y <20) (36) EM == nuy - e ) (}y - e 1y+) ( y <2) (36) and the von Karman correlation for highly developed turbulent flow at a region further removed from the wall: EM K 2 (du/dy)3 2 (du /dy )3 )3 EM ~ fC2 wdy]3 - X2^ ^u^ 3, (y ~> 20) (37) (d2u/dy2)2 (d 2u/dy 2)2 The dimensionless shear stress equation, (35), thus becomes: r 1 (+ -:1 + n y2uyd- (1 e-nu y)] duu ((0 y <20) (38) and= 2 (du+/-dy)4 (y+ ) 20) (39) (d2u+/dy+2)2 The Deissler correlation is semi-empirical, and has been substantiated by full-pipe tests with air, water, glycol, and sodium hydroxide. Tests were run at wall-distance parameters as low as y A 2. The validity of this correlation extends up to y+ 26; however, Dukler only used it up to yKt 20. Dukler used a value of 0.10 for n as suggested by Deissler. - Von Karman's expression for the eddy diffusivity in highly developed turbulent flow is derived from his similarity theory, the suggested value for his universal constant C 'being 0,38.* Dukler included interfacial shears ~Z different from zero in his mathematical treatment. We already have equ. (29): * Dukler's paper does not explicitly state that he used this value of., but the result of his calculations indicate that he apparently did so.

-4f3 -BB ic.- Bg (29) which for zero interfacial shear simplifies to: B+ B3/2 () 1/2 To simplify the mathematical treatment, Dukler defined the dimensionless variable s, which is the ratio of the actual film thickness to the thickness the film would have if Ti were zero, all other magnitudes (B+, Vr, g ) being the same:* S ) /3 \/ (41) It can also be shown that: 3 s _ 1 - ' (42) Substituting equ. (41) into equ. (29): + s(B+)2/3(gyr)-1//3 ic s(B+)2/3(g)2/3 (43) Squaring both sides, dividing by (B+)2 and re-arranging, we obtain: s3 + s2 (- 1 = (44) (B+)2/3(g2V.3)1/3 Define T-ig (45) (g2P3)1/3 * In Dukler's paper the symbols a{,.m,, are used in place of our s, B B', respectively.

-44 -with 3> 0 for co-current < 0 for countercurrent gas flow; Zi is computed from the gas-phase frictional pressure drop, equ. (31). The final equation for s is then: s3 s2 -1=0 (46) Dukler solved this equation by means of a digital computer* for values of p/(B+)2/3 from 0 to 2,000. The force balance:;gc= Lwgc -;yg (47) can be reduced to the dimensionless formo r - 3 3, y+ (48) Ww B' Combining with equo (38) and (39), we obtain: s3 *+. F 2++, -n2u y+) du+ 1 - s, y - [1 - n u y - e-j (07 20) (49) y1- y ^U (y4 <20) (50) ( (d2u+/dy+2)2 These two equations were integrated!- on a computer for a wide range of -s3 and the results were plotted as a universal velocity profile on a B 3 graph of u vs y being a parameter. graph ofu vs, y,_ B+ The flowrate equation (Re) 4 dy(23) 0 was integrated on a computer using the above velocity profile. The * This could have been done quite easily without a computer.

-45 -results are given as B vs. (Re), the interfacial shear number being a parameter. For 3 > 30, B' is a function of (Re) only. The film thickness equation B s(Bt)2/3 /-2 ) / (51) obtained from equ. (41) was similarly computed, and-plotted as B vs. (Re), with 3 as parameter. 'For f3 0, B merges with the Nusselt equation for (Re) < 200. At a (Re) of 1,600, Nusselt's film thickness is only about 10% below that of Dukler. - Anderson and Mantzouranis(l) in 1960 presented a mathematical analysis based on the Nikuradze velocity profile. It is identical to the work of Dukler and Bergelin except that the authors considered a finite radius of curvature of the wall, i.e., a small-bore tube instead of a flat plate. They also considered the effect of gas velocity. It can be seen from their resulting curves that the tube bore would have to be very small for the curvature to have any noticeable effect on the film thickness; certainly much smaller than the tube sizes used in our work. Their experimental data were obtained with water flowing down a 0.427-in. I. D. glass tube and a moving air core, and scattered widely. The authors attempted to explain this scatter by entrainment, or by the formation of a "double profile", i.e., laminar flow at the interface as well as at the tube wall, with the two developing velocity profiles meeting at mid-film. - They found no influence of the ripples on the film thickness. They found that the surface tension affected the ripple regime but not the mean film thickness.

-46 -C) LITERATURE RESEARCH: HEAT TRANSFER (NON-BOILING) The main interest in the study of the whole field of falling-film flow has been its application to falling-film condensers and coolers. Nusselt( 37) (38) extended his fluid mechanics to the solution of the heat transfer problem. For his analysis he postulated pure saturated vapor, streamline flow, no interfacial shear, a flat condensing surface, and constant physical properties, kh ~ (52) From Nusselt's film thickness expression, equ. (14), h (3-C 9 /3 3Re) (53) Defining (541/3 ~ i' -k3 2 g (54) then Re) <3 (55) The heat transfer coefficient decreases wit;- the.onee-third powert of the flowrate. - Nusselt also solved the Graetz problem for a laminar film: hL 4.46 0.565 hc 4 4 _ ^35 ^t ^56 (& C 0.05) (56) rc' 2- 2.235 0. 565 hL r = 0o0942 + 5.65 ( > 0.05) (57) here (58) where 3 ( Re -4/3 g,/3 (pr)- L (58)

-47 -Equ. (38) and (39) can be approximated by the expression: hL _ 2.62 2/3 (59) CP Nusselt applied his analysis to the study of falling-film condensers. He found that for a constant steam-to-tube temperature difference t, hm hL = 1.47 (ReL)-/3 (60) L where hdL (61) and hL is the heat transfer coefficient at the bottom end of the condensing surface, i.e., at length L. - It we define a Nusselt number: (Nu) (62) then according to Nusselt's theory: (Nu): 1 (Pure conduction) (63) hmBL 4 and (Nu), k - (64) m k 3 Most industrial condensate films become so thick as they flow down the condensing surface that they reach turbulence. Values of hm are, therefore, generally higher than according to Nusselt's correlation, and increase rather than decrease with flowrate.* Falling-film condensation research since Nusselt has been oriented chiefly towards quantitative * Dropwise condensation will not be considered at this point.

48 -expressions that take turbulence into account. - Kirkbride(33) and Badger(2)9 (3) proposed an empirical correlation above a (Re)L of 1,800, expressing hm/' as function of (Re)L - Colburn(l5) suggested a semi-empirical relation based on the j-factor analogy, for (Re)L above 2,100; he expressed hm/b as a function of (Pr) as well as of (Re)L - Grigull(28) used the Prandtl analogy and the one-seventh-power law to derive an expression which was not explicit in hm and could only be represented graphically, using (Re)L and (Pr); the trends were similar to those of Colburn's correlation. Grigull decided on a critical Reynolds number by taking that which would best correlate all experimental heat transfer coefficient determinations. In a later paper(29) in 1952 he presented an empirical correlation of hm/9g as function of (Re)L only, for (Re)L > 1,600. - Seban(42) in 1954 applied the Prandtl analogy and the Nikuradze velocity profile for (Re)L> 1,600, and obtained hm/0 as a complicated function of (Re)L and (Pr) - Rohsenow, Webber and Ling(40) in 1956 extended this treatment to condensation with high vapor velocities, and concluded that the critical Reynolds number decreased with increasing values of ti to a lower limit of 70. This list of research studies on condensation heat transfer is by no means complete, but serves to illustrate the trends in condensation researcho Most of the correlations depend on some critical Reynolds number that varies from author to author; above this (Re)crit the authors postulate laws of momentum and heat transfer that do not necessarily apply to film flowo They also ignore departures from Nusselt's correlation in the subcritical range; even for zero vapor velocity and

-49 - no dropwise condensation, coefficients are usually reported between 12 and 35% higher than predicted by Nusselt's equ. (55) or (60). For design purposes, McAdams(34) recommends a value for the subcritical region 28o high than theoretical* and for turbulent flow the relation of Kirkbridge - Badger or that of Colburn. There have been several falling-film sensible-heat transfer studies since Nusselt, Bays and McAdams(5) used three steam-jacketed copper tubes to determine local heat transfer coefficients for two mineral oils in laminar flow down the inside wall. Temperature differences were obtained with wall thermocouples or by using dropwise condensation, Nusselt's equ. (59) was found to be valid when modified by a SiederTate-type viscosity ratio; Nusselt's postulate of constant physical properties was too unrealistic with regard to oil viscosity in these runs. As in equ. (59), h was found to be proportional to Fl/9 Turbulent flow was investigated by Sexauer(43). Water at room temperature flowed down the outside of vertical tubes that were heated from the inside by upflowing warm water. Flowrates were determined by weighing; film temperatures were measured with a thermometer, local wall temperatures with thermocouples. Temperature drops across the film were of the order of 1 - 2 OF. The results were correlated by the equation: L a(Re)O0.5(- )015 L 0.935 (65) k LF *x For the same (Re)T.

-50 -Here, Lo is a reference length, a a numerical factor. - This equation correlated results for all diameters and lengths, but the factor a varied according to tube material; for steel tubes it had 72.5% of the value for brass tubes. Tube length is shown to be immaterial in turbulent flow. McAdams, Drew and Bays(35) used the same equipment as Bays and McAdams to investigate water films in turbulent flow. For a mean water temperature of 190~ F they correlated their data by the equation: h= 120 r1/3 (66) with hm in Btu/(hr)(sq ft)(~F), r in lb/(hr)(ft). - Drew(21) tentatively suggested a more general correlation in dimensionless form: hm 1/31/3 4 =0.01 (Re)3Pr)1/3 (67) which at ca. 190~F would reduce to equ. (66). - This is the equation generally recommended by handbooks for the design of falling-film heaters at (Re) > 1,800. Garwin and Kelly(27) in 1955 measured the heat transfer coefficient across turbulent water films flowing over an inclined brass plate. A steam chest was flanged to the underside of the plate. Wall temperatures were measured to within ca. 0.5~F with thermocouples. The mean film temperature was ca. 93~F. The results were correlated by the equation: hm - 87 r1/3 sin0.2 9 (68)

-51 -with hm in Btu/(hr)(sq ft)(~F), F in lb/(hr)(ft). For the vertical plate, of course, sin ' reduces to one, and the resulting equation is similar to that of McAdams, Drew and Bays, equ. (66), - Equ. (67) for water at 93~F has a numerical coefficient of 65, instead of 87 as found by Garwin and Kelly. Brauer(7), 1957, (8), 1958, extended his results on falling-film momentum transfer to heat transfer by means of a theoretical study. In his mathematical model the entire resistance to heat transfer is concentrated into an equivalent thermal sublayer of thickness., in pure streamline motiono For smooth Nusselt-type film flow, c = B; in the presence of ripples and waves, - is smaller than the trough film thickness. Let u' be the (unknown) velocity at y = E X Then: '.wg.. C W (69) k kgc w ul. - u' (70) u T(Nu):.-f i u (71) Since both Zw and B. were expressed as functions of (Re) in his previous work on fluid mechanics, he was able to express h and (Nu) as functions of (Re); see Table IV. - Brauer postulated u' as solely dependent on physical properties, and defined a dimensionless viscosity number Kv Kv g (72) (u')3

-52 -Kv (or u') could be calculated from any one actual heat transfer measurement. - Brauer considered Ky rather than (Pr) as indicating the effect of viscosity on falling-film heat transfer. TABLE IV (Re) r ge h (Nu) c-crit 2 g73(g52.V )(Re)1/5 2.731/3(Re)/5 | 1.641t/3(Re)8/15 crit 2.73(g2? )(Re ):15(Re)2/5 |2.73Ky3(Re)^1/5(Re )2/5 1.64K 3(Re,:2/5(Re)14/15 Based on his heat transfer theory, Brauer developed equations for the critical tube length that would divide the tube into a laminar section and a turbulent section, and for overall heat transfer coefficients of condensate films extending into the turbulent section. He found his correlation satisfactory for the results of Badger(2) with diphenyl, of Badger(3) with diphenyl - diphenyl oxide, and of Baker, Kazmark and Stroebe(4) with steam. He used whatever value of u' gave the best correlation; for steam at atmospheric pressure, u' = 2.5 ft/sec. - Brauer also compared his correlation with those of Kirkbride, Colburn for (Pr) 5, Grigull, Seban, and Rohsenow, Webber and Ling. He showed that above a (Re) of 3,000 they all fell within a - 15o

-53 -scatter band-* Dukler(23) in 1960 extended his study of falling-film fluid flow to the heat transfer problem. As in fluid flow, he considered eddy transfer in superposition on molecular transfer at all points in the film. The basic heat transfer equation is, therefore: dy q (k+- VCpEH) (73) Supposing physical properties and heat flux to be radially constant, and defining a dimensionless temperature as: t' [- - u*(tw - t) ~ (74) ( q wall the basic heat transfer equation in dimensionless form is: EH dt+ (75) (Pr) j A - *x- Though of no direct bearing on our subject matter, it may be of interest to point out that Brauer9) in 1958 also extended his theory to mass transfer in falling liquid films. Replacing thermal conductivity with diffusivity, and the heat transfer coefficient with the liquid-film mass transfer coefficient, he obtained mass transfer Nusselt numbers as functions of (Re) and Kv analogous to his heat transfer w rk He successfully correlated the results of Kamei and Oishi 32) on absorption of carbon dioxide in water, and previous work on absorption and desorption of carbon dioxide. For all these results he used u' equal to 0.22 ft/sec. He used the same value of u' to correlate mass transfer test results on soluble-wall columns. Brauer explained the fact that u' had a lower value for mass transfer than for heat transfer by ascribing the physical transfer mechanism to radial motions of particles from interface into the bulk due to wave action; this should have more effect on mass transfer than on heat and momentum transfer, since the latter two rely on molecular collision in addition to bulk movement. - Since the liquid Schmidt number was not used at all, Brauer's theory established proportionality between the liquid-film mass transfer coefficient and the liquid diffusivity.

-54 -From the definition of t, equ. (74), the definition of B, equ. (22), and the definition of i3, equ. (41), it also follows that: h (Pr)(B)/3 (76) (s st' As in his fluid flow study, Dukler integrated the rate equation for 0 < y < 20 with the Deissler correlation, and for y ~ 20 with the von Karman correlation and the assumption that EH = EM: 1 )- + n2u+y+ (1 - e-n2u+y) dt( (Pr) -(0y 20) (77) (O< y. 20) _1_ __ - dt s3 + dub (yi 20) (78) 1 - s^ y The integration was carried out on a digital computer, using the velocity profile obtained in the fluid flow study. For each value of t so obtained, the value of h/c.? was calculated by means of equ. (76). The results were plotted as curves of h/]< vs. (Re), r and (Pr) being two independent parameters. For condensers, similar curves were obtained for hm/ vs. (Re)L, 3 and (Pr) being parameters. They were arrived at by integrating the local heat transfer coefficients along the entire tube: ~hm (Re)L e L( ('79) -(Re0L d(Re) h '

-55 -Dukler tested his theoretical development against experimental results. For zero interfacial shear, the heat transfer coefficients merge with Nusselt's straight line at a (Re) of ca. 50. For steam condensing at (Re)L between 150 and 1,000, we have found the Dukler correlation to fall within - 7% of McAdams' recommended use of 1.28 times hm from Nusselt's equ. (60) An extreme test for Dukler's work is the correlation of the results obtained by Misra and Bonilla(36) in 1956 on the condensation heat transfer coefficients of mercury and sodium vapors. These authors' values of hm were only 5 - 15% of the values predicted from the Nusselt theory; Reynolds numbers ranged up to 1,500.* Dukler found his theory to correlate these results in a satisfactory manner; all previous attempts of other authors had failed. For film flow under turbulent conditions, we have found Dukler's correlation to fall within t 6% of that of Bays, equ. (66), and within 5% of that of Garwin and Kelly, equ. (68), for the range of Reynolds and Prandtl numbers employed by these authors. It also falls close to the correlations of Kirkbride - Badger and of Colburn at high flow rates. In the case of significant interfacial shear stress, Dukler's correlation also proved satisfactory. Such tests were reported by Carpenter(ll), who condensed water, methanol, ethanol, trichloroethylene * Incidentally, ripples formed in the mercury at (Re), 66. **Despite the fact that these authors used the liquid bulk temperature, not the interface temperature as does Dukler.

-56 -and toluene inside vertical tubes at very high vapor velocities. His results had been correlated by Carpenter and Colburn(l2) and Colburn(16) who used a semi-empirical expression derived in part from Nikuradze's velocity profile. Dukler satisfactorily correlated Carpenter's test results by calculating i- via Ti and using the appropriate / parameter in his curves; Ti was calculated from the Martinelli-Lockhart correlation.

SECTION III LITERATURE RESEARCH ON NUCLEATE BOILING FUNDAMENTALS RATE OF HEAT TRANSFER IN NUCLEATE BOILING McAdams, Addoms et al.(30) used improved measurement techniques to repeat work by early investigators on the boiling of saturated water on submerged platinum wires. Pressures up to 1,200 psig were used, causing wire superheats from 2 to 2,500~F. For superheat"s up to 10~F, the heat transfer rates were roughly those q predicted from convective heat transfer correlations. From Burn-out 17~ F upwards, i.e., above the "knee" of the curve in Figure 4, ee the heat flux rose very steeply with increased superheat until 0 t sot a maximum ("burn-out point") Figure 4 was reached at a superheat of 420 F; film-boiling set in at higher superheats. Heat transfer coefficients are thus seen to be much higher in nucleate boiling than in non-boiling convective heat transfer. McAdams, Kennel et al.(31) observed the upward flow of degassed distilled water through an annulus, the inner surface being a cylindrical heating element composed of a copper and a stainless steel section. Heat transfer measurements were made for wide ranges of subcooling, water flowrates and equivalent diameters. For tw < tsat no boiling occurred, and the heat transfer rate were predictable from the SiederTate correlation. For tw ~ tsat the same applied up to a transition -57 -

-58 -wall temperature ttr c At this transition point, corresponding to the knee in Figure 4, vapor first appeared and surface boiling commenced. Below the knee, the driving potential was tw - tl; above, it was tw - teat' i.e., wall superheat L tsatg and tl was no longer a significant variable. For tw > ttr all their points followed the correlation: q = ( sat)386 (1) The constant C. was higher for tap water than for de-aerated water,* Kreith and Summerfield performed similar tests for a wider range of variables, with water(26) and with aniline and n-butanol(27). Similar results as those of McAdams, Kennel et alo were obtained. One of the practical interests of this field is the possibility of accurately predicting boiling heat transfer rates at high heat flux and high pressure in order to design smaller and more compact boilers. Rohsenow and Clark(40) performed tests up to pressures of 2,000 psia. They found results similar in form to those at lower pressures. The significant parameters in nucleate boiling were found to be, first, pressure (i.e. tsat), and in second place velocity, which ceases to be significant at high heat fluxeso For the nucleate boiling range, the heat transfer curve has generally been found to follow a correlation similar in form to equ, (l). The exponent of tsat is mostly reported to be between 3 and 4 (25) (28), (32), (38). The uncertainty lies in C, i.e., the location of * Extrapolating these results to zero subcooling (tl tsat) would place the transition point at a wall superheat of 220 Fo

-59 -the transition point. Bernath and Begell(7) have made a thorough study on the effect of velocity and subcooling. They plotted the results of hundreds of tests for de-ionized water flowing up a heated annulus, as wall superheat A tsat vs. degree of suDcooling tsub O tsat - tl (see Figure 5.). It was shown that the degree of subcooling had no effect ont 0 At b at,_t Ats Sat,. sub the rate of heat transfer at q = Const. unless a critical degree of V'> V2 subcooling Atsub was exceeded; for Atsub t' sub the curve in Figure 5 was a 0 At ^~~~sub straight line of slope m. The following are the empiri- Figure 5 cal correlations: tao 5 - V q - 3.24 x 105 bI 4.exlO(De )043 6tsub.2(30.0 -) 24 x Vo) (3) and for tsub > Atsub, m -- +. 2.54 x 10-7q - 1.297 * (4) with temperatures in 'F, velocity V in ft/sec, heat flux q in * Note interaction of velocity and subcooling for tsub >^tub; also, minimum value of V

-60 -Btu/(hr)(sq ft)(~F), equivalent diameter De in in, - These results were obtained on an aluminum surface at pressures between 25 and 125 psia. According to Averin(2), tsat for aluminum is 6.0 - 050~ C higher than that for copper, nickel, or stainless steel. If this correction is applied to the data of McAdams, Kennel et al., their data as well as the data of Bernath and Begell are reported to follow the above correlation within 4~ F. The role of additives on boiling heat transfer rates has not been correlated or completely explained. Lowery and Westwater(29) suggested that the determining variable might be a change in interfacial tension between the liquid and some solid nucleus, as well as in liquid-metal and liquid-air interfacial tension; the later two also have direct bearing on the wettability of the heating surface and the bubble contact angle. It is known that surface-tension depressants raise the boiling heat transfer rate of water(33)o The literature contains various correlations for the burn-out point. Rohsenow and Griffith(41) presented a theoretical correlation based on calculating the heat flux at which the bubbles would come so close to each other laterally as to touchy thus coalescing and producing film boiling.

-61 -BUBBLE FORMATION Let p be the pressure of a, small spherical gas bubble of principal radii rl and r2. Let the bubble be completely surrounded by a liquid phase at pressure Pi * If bubble and liquid are the same temperature, then(17): P - P- ( 1 + 1 (Gibbs equation) (5) If the gas is the pure vapor of the liquid, the liquid is, therefore, superheated; the superheat is easily calculated from equ. (5) by means of the Clapeyron equation. It we knew T to be constant down to molecular dimensions, p for a bubble consisting.of one molecule of water would be 7,500 atm, according to equ. (1). In order to form a bubble "de novo" inside a mass of liquid would require that a number of molecules must simultaneously obtain sufficient kinetic energy to overcome the forces of attraction between them. It has been calculated that the probability of this occurring is virtually nil except in the region of the critical points. To prove this experimentally, de-gassed and purified water has been heated to 520~ F without boiling; such water has also been saturated with gases at 100 atm and de-pressurized to atmospheric pressure without effervescence. Bubble formation cannot occur without the presence of available gas * Developed previously by Laplace, based on force balance; Gibbs is credited with its development based on thermodynamic energy considerations,

-62 -particles, contaminants, mechanical shock, etc. Bubble formation is not promoted by edges or points unless these contain absorbed gas on the surface or trapped gas in capillary spaces(ll) Equo (5), then, does not necessarily apply to commercial boiling systems, where the superheat needed to initiate boiling may be far less than calculated due to the nucleating influence of gas absorbed or occluded by foreign particles or by the heating surface itself. Besides, Gibbs' equation is based on a simplified model in which there is a unique surface between phases. In reality there seems to exist a transition layer several molecules thick between phases. For diameters 0 smaller than, say, 20 molecules (ca. 80 A) the theory cannot be applied(20). Also, Gibbs' theory assumes static equilibrium and therefore a reversible process of formation; the apparently instantaneous nature of bubble formation would appear to invalidate this assumption. Experimental evidence, however, indicates that the inaccuracies involved in Gibbs' simplified model are tolerable small. Jakob and Fritz(24) boiled water at atmospheric pressure on a copper surface having cubical cavities of 0.25 mm per side. The measured superheat, 10 C, corresponds to a Gibbs-equation bubble of 0.07 mm diameter, ca. 1/3 of what could be expected from the cavities. - Bankoff(3)s (4) discussed cavities and grooves in metal heating surfaces. He calculated the maximum width of a cavity into which the meniscus of a given liquid can advance at given values of temperature, pressure, surface tension and contact angle, he performed a similar calculation for the maximum radius of a semi-circular groove. He reviewed the data of Rinaldo(37)

-63 -Addoms(l), and Vos and van Stralen(42), who had measured the minimum superheat in saturated pool boiling of water at pressures from 14.7 to 1,985 psia. For each experimental determination he calculated the critical cavity or groove dimension; these fell amazingly close to the Gibbs-equation bubble diameters. - Griffith and Wallis(l9) used gramophone needles to punch cavities of known radius in the surface of their metal heating surface; the measured superheat corresponded to Gibbsequation bubble radii that fell very close to those of the needles. Corty and Foust(lO) made a detailed experimental study of the size and shape distributions of the microroughnesses in their heating surface, and correlated them qualitatively with the nucleation site density and the wall superheat for several liquids. - Clark, Strenge and Westwater(8) took photo micrographs and electron micrographs of nucleation sites on a single zinc crystal, on polycrystalline zinc, and on aluminum alloy 2024, using ether and n-pentane and applying extreme precautions against contamination. They found that grain boundaries had little or no effect on boiling nucleation and that nucleation sites were not regions of special atomic density in the metal (effect of anisotropy). Of the 20 sites studied, 13 were pits of 0.3 to 3 mils width, 4 were scratches of 0.1 to 0.8 mils width. The measured superheats in all cases corresponded to Gibbs-equation bubble sizes larger than the widths of the nucleation sites. - Averin(2) found no effect of surface roughness on boiling heat transfer at all, near the burn-out point. McAdams, Kennel et al(31), and later Pike, Miller and Beatty(34) investigated the influence of the presence of gas on nucleation.

De-aerated tap water initiated boiling at a much higher superheat (700 F) than tap water (20~ F) or water saturated with carbon dioxide, in pool boiling on a wire. Wire gage or wire position relative to the liquid surface had no influence on superheat. - Bankoff, Hajjar and McGlothin(5) measured superheats in the pool boiling of 7 organic liquids that had been allowed to stand exposed to the air, in order to prove that nucleation occurs on the wire and not in the liquid phase. The wire was annealed in air. They noted that with time the superheat increased, probably due to the desorption of air from the wire due to boiling. Also, the bulk of the nuclei were observed on the wire, not on the idust particles within the liquid phase.

-65 -BUBBLE GROWTH The expansion rate of bubbles is of interest because of the agitation effect on the liquid and the resulting acceleration of the rate of heat transfer. Plesset(35) combined the Gibbs equation with the Rayleigh equation and derived a differential equation in which figure the first and second derivatives of the bubble radius with time, (The Rayleigh equation is a more general fluid flow equation and applies to any bubble pressure, irrespective of its relationship to the radius via the surface tension.) The mathematical model on which it is based assumes a spherically symmetrical pressure field, a liquid of infinite extent, inviscid flow, and a spherical bubble. Foster and Zuber(l5) combined Plesset's equation with the Clapeyron equation and solved for the expansion rate in terms of the superheat, after.considerable simplifying assumptions. A similar mathematical analysis by Plesset and Zwick(36) yielded a much simpler expression for the bubble radius as function of time. Its validity was experimentally proved by Faneuff, McLean and Scherrer(l4), who sent periodic current pulses of very short duration (1 ftsec) through a nichrome wire submerged in 1800 F water; a stroboscopic light source actuated by the same timer allowed bubble growth to be photographed with a high-speed camera. Griffith(18) reasoned that the principal stirring action occurred during the visible life of the bubble, and that during this time the growth rate was essentially dependent on the heat transfer in the liquid to the bubble wall. Assuming laminar flow and constant physical properties,

-66 -he solved the heat diffusion equation for the velocity, and obtained an expression that successfully correlated the experimental results of Dergarabedian(l2) for the expansion rate of bubbles in boiling water (ca. 0.22 ft/sec).

-67 -BUBBLE BEHAVIOR Fritz(l6) has shown that the maximum diameter of a steam bubble is: 1 2gcr D sCb g(r- (6) where p is the contact angle, Cb an empirical constant, Jakob(23) showed furthermore that the bubble diameter was inversely proportional to the number of bubbles per hour, for the same heat flux; that the number of bubbles per square foot of heating surface at any moment was directly proportional to the heat flux; and that the velocity of bubble detachment was equal to the product of bubble diameter and number of bubbles per hour. Gunther and Kreith(22) and Gunther(21) made detailed photographic measurements of bubble behavior while heating a flow of subcooled water with a submerged electrically heated metal strip. For low velocity and subcooling, bubbles were observed to have a period of steep initial growth, followed by a rather long period of slow growth and a period of slow decay. As velocity and subcooling increased, the growth and collapse curves tended to steepen and to become mirror images of each other; both bubble size and bubble life span decreased, and changes in heat flux only caused a change in the bubble population. - While attached to the wall, the bubbles were roughly hemispherical in shape; with less subcooling they began to detach themselves, since the quenching boundary had moved further away from the wall.

-68 -SUGGESTED HEAT TRANSFER MECHANISMS IN NUCLEATE BOILING The following are some mechanisms that have been suggested: 1) Bubble activity excites microconvection in the normally laminar sublayer. According to this theory, though, heat flux should depend on subcooling, which it does notO Also, the translational motion of bubbles is of the order of 10 ft/sec; it does not seem logical that it should cause higher heat transfer rates than convection, which may well reach linear velocities of 20 - 30 ft/sec. Another reason against this theory is the fact that bubbles only occupy 25% of the heating surface(l3). 2) Bubbles act as surface roughness. However, in that case the heat flux should again depend on subcooling, and also on the "relative roughness" (ratio of bubble size to tube size); neither of the two apply. (13) 3) Latent heat transport: the bubble absorbs latent heat, which it transfers to the liquid upon collapsing. - Rohsenow and Clark(39) analyzed this possibility by making a rigorous thermodynamic calculation of the amount of heat thus transported by a bubble of given size, specific volume, and specific heat of vaporization. The heat per bubble was multiplied by the bubble density and bubble frequency from the highspeed motion pictures of McAdams, Kennel et al. It was found that, of the increase in heat transfer over convection due to boiling, at most 2% could be due to the bubbles acting as "carriers". - A similar conclusion can be drawn from the photographic analysis of Gunther and Kreith(22),

-69 -4) Bubble pumping action: the bubble leaves an empty space upon collapsing or detaching itself, which is filled up by cold liquid. This mechanical pumping action is far more effective than convective heat transfer, which is based on diffusion by eddies. - Yamagata, Hirano et al.(43) reported direct proportionality between the heat transfer Nusselt number and the cube root of the number of vapor columns formed in water boiling over a horizontal heating surface, - Rohsenow(38) calculated the bubble Reynolds number, which should characterize this agitation, and correlated the bubble Nusselt number as function of (Re) and (Pr); the final Rohsenow correlation is:.Hvap s l (7) Here, q is the heat flux in excess of the convective heat flux, Csf an empirical constant. Rohsenow found his correlation to be satisfactory for the experimental pool boiling results of previous investigatorso - Clark and Rohsenow(9), investigating boiling heat transfer to water at high pressures, also found the Rohsenow correlation to hold. - Other correlations based on heat transfer from heating surface to liquid with stimulation due to bubble agitation have been suggested by Bankoff and Mikesell(6), Engelberg-Foster and Greif(13), and others. 5) Film model, suggested by Bernath and Begell(7) and others; the film is defined as having the thickness which is the distance from the ioheating surface to the point where the average temperature of the mixed phases is the saturation temperature of the liquid: i.e., the region where

-70 -there is superheat. Bernath and Begell postulate that wall superheat is proportional to film thickness. Film thickness is a function of heat flux, subcooling, and free-stream turbulence. Qualitatively, the effect of heat flux is described as tending to increase film thickness (and hence superheat) because of greater bubble population; the effect of subcooling and/or convection, as tending to decrease film thickness because of the bubble-quenching zone moving closer to the wall; the effect of velocity is described as causing increased wall shear stress, hence a thinner film. The interaction of velocity and subcooling, as per equ. (4), is explained by the negligible quenching effect of subcooling on the thickness of a thick film (low velocity) as compared to the considerable effect of the same degree of subcooling on a thin film (high velocity). Photographic evidence for this concept was taken from the work of authors such as Gunther and Kreith(22), and Gunther(21).

SECTION IV LITERATURE RESEARCH ON GAS-LIQUID FLOW The practical interest in this field is mainly to be able to predict pressure drop with reasonable accuracy; preferably in the case of passage of mass from one phase to the other, as in evaporation or condensation. Due to the extreme complexity of the process, however, there is no unified general theoretical treatment. Experiment is still far ahead of theory, but as yet there is no general empirical correlation either. Boelter and Kepner(5), Martinelli, Boelter et al.(21), Martinelli, Putnam and Lockhart(23), Lockhart and Martinelli(l9), and Martinelli and Nelson(22) proposed a simplified model. Designed for isothermal airliquid flow through horizontal pipes, its basic assumptions are that pressure drop is only frictional, that gas pressure drop is equal to liquid pressure drop (i.e., no radial pressure gradients), and that the two phases are in thermodynamic equilibrium and fill the pipe completely. For the purposes of the Martinelli model, a phase is arbitrarily considered in laminar or turbulent motion, irrespective of its actual flow behavior, according to whether its superficial* Reynolds number is below 1,000 or above 2,000 respectively. Using these superficial Reynolds 16 numbers, friction factors are calculated for each phase: if 0,046 "laminar".. if "turbulent". From the friction factors, super(Re)0_2 ficial* pressure drops are calculated separately for gas and liquid, and are denominated f4 ) and.^^ L 1 ' respectively. It can then be shown that the actual two-phase pressure drop (-I)Tp is a unique * Superficial in the sense that for the purpose of this calculation the phase in question is fictitiously assumed to fill the whole crosssectional flow area in single-phase flow. -71 -

-72 -function of either one of the two superficial pressure drops and of the (unknown) actual hydraulic radii and cross-sectional surface forms of the two phases. By defining: -r _ / (P/ /L)Tp.......... -g i (APL L) (2) - g g (, p//AL) t/ = ifli~~~~~( 3) " - It (I P/ AL)g (3) the above can be stated more conveniently by saying that l and 0 g are unique functions of X. - Calling the liquid and the gas volumetric holdups R1 and Rg, respectively, it can also be shown that R1 and Rg should be unique functions of XJ. - Since the actual hydraulic radii and the cross-sectional surface forms of the two phases are unknown, the functions must be experimentally determined. This was done by the investigators for the horizontal flow of air-water mixtures, Due to the many simplifying assumptions contained in the Martinelli model, it correlates two-phase pressure-drop data within a scatter of ca. ~ 50%. Despite its drawbacks, it is much used because of its ease of manipulation. It has even been applied, with empirical modifications, to cases that directly contradict its initial assumptions, as in upward or downward flow with and without vaporization, where frictional pressure drop is far from being the total pressure drop, and in stratified or plug flow, where radial pressure gradients cannot be neglected. Analytical

-73 -modifications of the Martinelli model were proposed by Levy(l6) and Gazley(l3); neither correlation improves the predictions of pressure drop and liquid holdup. Far more numerous are the empirical modifications of the Martinelli model: Johnson and Abou-Sabe(l5) for horizontal nonisothermal air-water flow; Lieberson(l7) for isothermal vertical upflow; Van Wingen(31), Chenoweth and Martin(9) and Baker(l) for gas-oil flow in large-diameter pipe lines; Stein, Hoopes et al.(28) for downflow through concentric internally-heated annuli; Martinelli and Nelson(22) for horizontal forced-circulation evaporator tubes; Dengler(ll) and Untermeyer(30) for vertical upflow evaporator tubes. A different approach from the Martinelli model is the homogeneous flow model. Its basic assumptions are equal linear velocity for both phases ("fog" flow) and interphase thermodynamic equilibrium.* This model permits the use of friction factors. The pressure drop equation can thus be integrated along the tube. - The friction factors in all correlations are empirically determined. Several authors applying the homogeneous flow model correlated their friction factors against modified Reynolds numbers, without offering any theoretical justification: Shugaeff and Sorokin(27), Marcy(20), and Dittus and Hildebrand(l2) used the liquid-phase viscosity in their Reynolds number, and McAdams, Wood and Heroman(24) employed a weighted viscosity; Shugaeff and Sorokin for air-water flow, Marcy for the flow of flashing refrigerants, and the * The latter assumption is not axiomatic: Styrikovich and Miropolski(29) reported superheated steam in the upper part of a heated horizontal pipe carrying steam-water mixtures.

-74 -others for the flow of oil with vaporization. Bottomley(6) and Benjamin and Miller(2), (3) successfully applied the homogeneous flow model to watersteam flashing. Jakob, Leppert and Reynolds(l4) measured pressure drop for the forced-c onvection boiling of water in a horizontal heating tube, and recalculated their results according to the homogeneous flow model and the (separated-flow) Martinelli-Nelson model; their actual results fell between the two widely-spreading curves without showing preference for either model. In general, the homogeneous flow model is best applicable to high-speed flow, as in flashing. Davidson, Hardie, et al.(10), investigating forced-circulation boiler tubes, found that pressure drops calculated with friction factors were several times greater than the actual values except at high Reynolds numbers. Linning(l8) proposed a model for vaporization two-phase flow in which he postulated annular flow. This model has not had much application, due perhaps to the unwieldiness of the final equationo Other methods that have been used to analyze gas-liquid flow are dimensional analysis, suggested by Schmidt(26), and the approach of Calvert(7), who obtained velocity profiles by applying the principles of Prandtl and von Karman to two-phase annular vertical air-water upflow. Calvert calculated the gas-phase pressure drop from the interfacial shear; the latter was assumed to be a function of interfacial roughness, and was obtained by taking some fraction of the stagnation pressure times the area of drag caused by the roughness. Since the degree of roughness

-75 -at the interface is unknown, the final equation contained unknown constants which were calculated from empirical data obtained by Calvert and by Radford(25). There are hardly any data in the literature on two-phase pressure drop for liquid phase in downward falling-film flow through pipes of more than capillary size. Carpenter(8) measured pressure drops in a vertical-tube condenser for condensing vapors at high vapor velocities. The substances used were water, methanol, ethanol, trichloroethylene and toluene. Since for falling-film flow the film thicknesses were negligibly small as compared to tube size, superficial Reynolds numbers were used for gas-phase Reynolds numbers. Also, total pressure drop was equated to gas-phase pressure drop, and the gas friction factor plotted against the gas Reynolds number for varying liquid flowrates. For zero liquid flowrate, the friction factor plot was identically equal to that for pure gas flow. The shape of the friction factor curve for increasing liquid rates was closely akin in form to single-phase flow friction factor curves for increasing tube-wall roughness. - The parameter in these curves was taken as - rather than as (Re)l, since the viscosity did not vary sufficiently to warrant the use of a Reynolds number. For liquids other than Ho.r water, the parameter wa's furthermore divided Log fg by the ratio of surface tension to water surface tension (see Log (Re) Figure 6 ). It can be Figure 6

-76 -seen that the pressure drop was equal to the dry-wall pressure drop except at high gas and liquid flowrates. Bergelin, Kegel et al.(4) performed tests for co-current down-flow of air-water mixtures through 1-in. tubes. Their results followed Carpenter's correlation fairly closely, but deviated + 30% from the Lockhart-Martinelli correlation,

SECTION V LITERATURE RESEARCH ON PERTNENT EVAPORATOR STUDIES There is a large amount of published evaporator literature in existence. The following is an abstract of several studies that may contribute to a better understanding of falling-film evaporation. A, Climbing-Film LTV's Dengler(3) in 1952 made a fundamental study of heat transfer and pressure drop, evaporating water in a single-tube LTV. With regard to pressure drop, he found that the Lockhart-Martinelli model could be used if sufficiently modified; to do this he employed radioactive tracers. For heat transfer he used thermocouples to measure wall temperature, and found that for temperature drops of up to ca. 10 OF, heat transfer obeyed an essentially convective mechanism and could be predicted by using a Dittus-Boelter type of correlation. For higher temperature drops the heat transfer coefficients became higher than the corresponding convective coefficients would have been, and varied with powers of the temperature drop greater than unity, as in nucleate boiling. Guerrieri and Talty(4) in 1956 performed similar tests with 5 organic liquids over a wide range of operating variables. They essentially corroborated the findings of Dengler in all respects. Sonic choking at the tube ends was discussed by Schweppe and Foust(l8) and by Harvey and Foust(6) in 1953. They found that critical flow in their experimental evaporator was occasionally reached at flowrates lower than predicted. Their discussion was incomplete in that it tacitly assumed a homogeneous flow model, and because void fraction, i.e., linear velocity, was not measured. -77 -

-78 -B Wiped-Surface Evaporators Several studies have been published on evaporators in which the heating surface is mechanically wiped in order to produce a very thin film of liquor. This has special application in cases of heat-sensitive liquids where low hold-up and low temperature difference are desirable. Climbing-film evaporators of this type have been described by Hadley and Thomas(5), and falling-film wiped-surface evaporators by Hausschild(7) Schneider(l7) Billet(l), Poocza(l5), Kirschbaum and Dieter(l2), Kern and Karakas(9), and Lustenader, Richter and Neugebauer(l3) In most cases the experimental results apply only to the particular machine being studied, and consist of empirical correlations of hold-up and heat transfer in terms of wiper-blade velocity and feed rate. The theoretical studies assume streamline flow onlyo There is also a considerable number of patents in this field. C. Falling-Film LTV' s The literature on falling-film LTV's is practically non-existent. Chambers and Peterson(2) described a falling-film sulfuric acid concentrator, but did not present sufficient data to study the heat transfer characteristics. Kerry(lO) qualitatively described a falling-film machine used as a liquid-oxygen vaporizer in an air separation plant. Keville(ll) described the performance of a falling-film LTV iMled ftr concentrating milk; his published numerical data are not sufficient for the formulation of a sound heat transfer correlation

-79 -Karetnikov(8) in 1954 made a laboratory investigation of heat transfer through a falling film of de-aerated water at ca. 1400 F, under boiling and non-boiling conditions. The apparatus was a vertical l6mm OD x 600 mm copper tube, inside a glass shell. The tube was electrically heated from inside and had thermocouples caulked into the walls. The water flowed down the outer tube surface from a special feed distributor. The glass shell was provided with a manometer. Reynolds numbers ranged from 570 to 2,600, and the heat load from 1,800 to 12,500 Btu/(hr)(sq ft). - Boiling heat transfer experiments were carried out under a vacuum of ca. 24 in, Hg. Non-boiling tests were performed under identical conditions but at atmospheric pressure. - The following observations were made: 1) In non-boiling heat transfer the film was transparent and offered a visual appearance similar to that found by previous investigators, 2) When boiling, the film was never transparent, being full of bubbles all the time. 3) When the heat flux reached maximum values ranging from 3,500 Btu/(hr)(sq ft) at (Re) 570 to 12,500 Btu/(hr)(sq ft) at (Re) 2,600, the film was actually repelled from the wall and falling-film evaporation became impossible. 4) Boiling heat transfer coefficients varied little with heat load; if anything, they decreased with increasing heat load. 5) Boiling heat transfer coefficients increased with increasing flow rate. 6) Boiling heat transfer coefficients were lower than the non-boiling coefficients for the same flowrate and heat load. - At extremely

-80 -low flowrates, the boiling coefficients reached and even exceeded the non-boiling coefficients, However, this may be due to the fact that the author used the arithmetic mean. rather than the log-mean temperature difference to compute the non-boiling coefficient. This error, which causes coefficients to appear too low, becomes all the more severe as the flowrate decreases, and may thus account for this reversal of trend at extremely low flowrateso 7) The non-boiling heat transfer coefficients deviated considerably from any known falling-film heat transfer correlation. The author did not indicate his method of measuring temperature differences, and this deviation can therefore not be explained, This does not mean that his conclusions under heading 6) are necessarily untrue, since the relative relationship between boiling and non-boiling coefficients may be sound. despite the fact that their absolute magnitudes may be questionable. - The author did not mention the heat transfer work of any previous investigators, Richkov and Pospelov(16) in. 1959 studied the falling-film evaporation of preheated water and caustic soda solutions flowing down the o14t side wall of a 30 mm OD x 1,200 mm vertical nickel-plated copper tube, at atmospheric pressure. The tube was electrically heated from inside and was provided with wall thermocouples. - The range explored was (Re) 3,100 to 4,100, q from 4,800 to 52,000 Btu/(hr)(sq ft) - Feed and e.xit liquor temperatue eres were measured with mercury thermometers (to an accuracy of 0,10 C) and their average used as the boiling temperature of the liquid; although not expressly stated, this value was then apparerntl7y

-81 -subtracted from the wall temperature in order to compute the heat transfer coefficient. - The conclusions made were as follows: 1) The visual appearance of the boiling film was described at great length though not supplemented by sketches or photographs, For heat fluxes not in excess of 9,000 Btu/(hr)(sq ft), steam bubbles formed continuously, rapidly growing to the same size as the film thickness itself; they flowed down the tube in this manner until surfacing and bursting. The liquor film had the aspect of a descending deposit of large bubbles. 2) At high heat fluxes, of the order of 50,000 Btu/(hr)(sq ft), the film seemed to disintegrate with the formation of large falling droplets. This is similar to the observation of Karetnikov. 3) An empirical correlation for water was derived: h 2.12 q0O32(Re)0.435 All magnitudes are in British engineering units, Btu - hr - ft - ~F. 4) Similar correlations were derived for caustic solutions of different strengths. These correlations differ in the value of all three numerical factors; besides, for all caustic solutions the exponents of q were negative. The ease with wh-ii4h an excessive heat load destroys the typical fallingfilm flow regime was also commented on by Mueller(l1) in 19610 He cited the case of a falling-film vaporizer which under a temperature drop of 16~F still maintained a falling-film flow regime, but which under higher heat loads had a temperature drop of 45 - 55~F as in pool boiling. He explained this by assuming that in a falling-film evaporator the critical temperature drop was so low because of the absence of a force that would bring the fluid back to the tube walls once it had left them~

SECTION VI DESIGN AND RESULTS OF EXPERIMENTS INTRODUCTION Each run was characterized by a different set of magnitudes for the 6 independent variables. The object of each run was the measurement of the overall heat transfer coefficient. The 6 independent variables were: tube diameter, feed rate, steam rate, vapor-head temperature, feed temperature, and feed salinity. The experimental work was initiated with a 2-level experiment of 5 variables, for a constant tube diameter. The experiment, the LWCI runs, consisted of 32 randomized runs, and its results indicated the significance of each variable. Further experiments were designed on the basis of this information in order to explore the entire region, defined by the upper and lower levels of each one of the 6 variables, with as few runs as possible. A total of 105 runs was performed. Since the overall heat transfer coefficient is a function of all 6 variables, it was found impossible to make a clear representation of the results in graphical form. They are therefore presented as numerical tables. -82 -

SECTION VI DESIGN AND RESULTS OF EXPERIMENTS INTRODUCTION Each run was characterized by a different set of magnitudes for the 6 independent variableso The object of each run was the measurement of the overall heat transfer coefficient. The 6 independent variables were~ tube diameter, feed rate, steam rate, vapor-head temperature, feed temperature, and feed salinity, The experimental work was initiated with a 2-level experiment of 5 variables, for a constant tube diameter. The experiment, the LWCI runs, consisted of 32 randomized runs, and its results indicated the significance of each variable. - Further experiments were designed on the basis of this information, in order to explore the entire region, defined by the upper and lower levels of each one of the 6 variables, with as few runs as possibleo A total of 105 runs was performed. Since the overall heat transfer coefficient is a function of all 6 variables, it was found impossible to make a clear representation of the results in graphical form. They are therefore presented as numerical tables, -82a

SECTION VI DESIGN AND RESULTS OF EXPERIMENTS A. RUNS LWCI-1 TO LWCI-32 Design of Experiment Runs LWCI-1 to -32 constitute the initial study. Their object was to determine which of all possible variables had a significant effect on the heat transfer coefficient, and to determine the sign and magnitude of this effect, in 2-in. tubes. Table V gives the variables that were studied, together with their range of magnitude. Variable Lower Higher Level Level Vapor-head saturation temperature, OF 150 230 Feed concentration factor 1 2 Feed "superheat" *, F 0 20 Feed rate, lb/hr 1,500 6,000 Steam rate, lb/hr 250 450 TABLE V The low and high levels of the operating variables were set by practical considerations. 150~ F was the lowest vapor-head saturation temperature that could be reached with the existing condenser, cooling water and vacuum equipment. 230~ F was the highest because of possible scale formation at higher temperatures; the danger of scale also * i.e., feed temperature minus vapor-head saturation temperature -85 -

-84 -determined the choice of 2 for the highest feed concentration factor. The range of feed superheat, 0 to 200, covers the practical range of interest for falling-film LTV operation. The flowrates for feed and steam were limited by the equipment, but cover the practical range of interest; liquor Reynolds numbers vary from 1,400 to 10,300 and feed-to-evaporation ratios from 3.3 to 24. In order to run a completely balanced experiment(4), each level of each variable was tested at all the levels of all the other variables. Since each variable was run at 2 levels (low and high), and the number of variables was 5, the number of experimental runs was (2)5 32. The runs were assigned the letters LWCI, followed by consecutive numbers from 1 to 32, this being the order in which they were performed. They were arranged in a randomized fashion, shown in Table VI,in order to cancel out any time trends. Feed rate i 1,500 6,000 Steam rate 1 250 - 450 250 450 Conc. factor 1 2 1 2 1 2 VH sat. Feed temp. superh, 0 i 18 4 2 30 6 32 21 1 150. ---- - -.. —. i 20 15 20 22 7 13 11 27 31 0 5 23 24 14 i26 16 8 29 230 -—... 20 17 1O 9 19 3 28 25 12 TABLE VI

-85 -Accuracy of Results Errors may have originated from the following causes: 1) Malfunctioning of the test equipment. 2) Malfunctioning of the measuring instruments. 3) Random error. 4) Error in data on physical properties used in order to calculate heat transfer coefficients. 5) Personal error in reading the instruments. 6) Personal error in recording, transcribing, and calculating. Test equipment malfunctioning was mainly due to poor performance of the automatic control instrumentation. This was due to the fact that the range of operation was too wide for the existing instrumentation. A steady steam rate and good feed temperature regulation were often very hard to obtain. Results obtained under doubtful conditions were afterwards discarded. The instrument errors having the greatest effect on heat transfer coefficients are errors in steam-chest pressure and in vapor-head pressure. Since overall temperature differences were of the order of a few degrees only, even small errors in absolute pressure would cause large errors in heat transfer coefficient. - At 1500 F, mercury manometers were used to read both pressures. At 2300, however, the steam-side pressure was read on a Bourdon gage. A series of precision pressure gages were tried; none were satisfactory, since their calibration (against a mercury manometer) would often change after several days of operation. The vapor-head

-86 -pressure at 230~ was measured with a mercury manometer, vapor being prevented from entering the instrument piping by means of a small but positive hand-controlled purge of compressed air through the manometer pipe into the vapor-head. (A similar scheme for the steam-side pressure would have introduced air into the steam chest, thus inhibiting condensation,) A larger instrument error at 2300 than at 1500 F was therefore expected. The boiling-point rise data* were taken from Report No. 438, W. L. Badger and Associates, Inc., written for the U. S. Department of the Interior, Office of Saline Water(5). They are based on the correlation of the work of several investigators on sea water concentrates and on pure sodium chloride solutions, and involve a small degree of interpolation and extrapolation. They are presented as curves of (BPR) vs. concentration, with temperature as parameter. Any error due to the use of these data would be expected to be larger at 2300 than at 1500 F, first, because boiling-point rise at 230~is larger than at 1500 F, and secondly, because at 230 the heat transfer coefficients are higher, and (BPR) thus constitutes a larger percentage of the apparent temperature difference than at 1500 F. - The (BPR) was calculated for the average chlorosity in the tube, and for the film temperature (roughly, the average between steam temperature and vapor-head temperature). Personal error in instrument reading, and in recording, transcribing and calculating, was held down as much as possible. Instrument readings * Graph No. 1 of Appendix E. o

-87 -were generally performed by the engineers, not the operators; the steam tables of Keenan and Keyes(2) were used in the calculations; readings with poor mass or energy balances were discarded; and the written work was checked several times. Several runs were re-run at a later date, and the results were found to be practically the same. Experimental Results A summary of the experimental results is presented in Appendix A. These data represent the last 2 sets of readings for each run. In eases where there was evidence of equipment or instrument malfunctioning during one of the readings, only the more reliable set or sets of readings are presented in Appendix A. The average overall heat transfer coefficient for each run is presented in Table VII, expressed in Btu/(hr)(sq ft)(~F). Feed rate 1,500 6,000 Steam rate 250 450 250 450 Conc. factor 1 2 2 1 2 1 2 |7H sat. Feed temp. superh. 0 445 464 472 435 565 498 520 500 150 20 418 438 441 422 468 480 481 470 0 645 678 606 573 868 774 794 745 230 20 590 606 600 587 737 687 701 647 TABLE VT'I

-88 -From Table VII it can be seen that the temperature and the flow-rate are significant variables. This was expected, since it is similar to most cases of heat transfer to a moving fluid. - Feed salinity, as expected, is a variable of little or no significance. At these low concentrations, concentration has little influence on density, viscosity or Prandtl number, and it is quite probable that the discrepancy between runs that differ only in concentration factor is due to small errors in estimating the boiling point rise. Perhaps the most surprising result is the insensitivity of the overall heat transfer coefficient to the steam rate, i.e., the heat load. This is the kind of result one would expect from a sensible-heat transfer run, not a boiling run; in nucleate boiling, an increase in heat load of 80% normally causes an increase in heat transfer coefficient of 220 - 480%. * This is certainly not the case here. The effect of feed superheat is also surprising; it depresses the heat transfer coefficient by roughly 6%. With regard to the accuracy of the results, some of the results at 2300 F seem to be off; run 14 seems to be too low, whereas 26 and 8 are definitely too high. The error must be ascribed to the causes previously mentionedon page 85~ "See page 58.

-89 -B, RUNS LWCJ-1 TO LWCJ-16 AND C, RUNS LWCK-10 TO LWCK-29 The results of the LWCI runs permitted an intelligent planning of further research. In the LWCI runs, the variables had been tested only at their lowest and at their highest possible values; the runs had shown that temperature and feed rate might bring additional information if run at intermediate values, but obviously not so the steam rate and the feed concentration, The LWCJ series was designed essentially to complement the LWCI series by running tests at intermediate vapor-head saturation temperatures (175 and 2000 F); runs were also made at the intermediate feed rate of 3,000 lb/hr at all temperatures. These runs, 16 in all, were all run at a concentration factor of 1 and a steam rate of 450 lb/hr; 8 of them at a feed superheat of 0, the others at a superheat of 20~F. At a later date, the pilot plant was modified by adding a steam-jet air ejector to the Nash vacuum pump, and by substituting the steam shell of an idle FC evaporator for the old overhead condenser. This allowed operation at higher vacuum, and the range of vapor-head saturation temperature was extended down to 1000 F. These are runs LWCK-10 to LWCK-29, run at 100land 125~ F. - This concluded the work on 2-in. tubes. TableVIIIindicates the runs for the entire test program on 2-ino tubes (series LWCI, LWCJ, LWCK), constituting a total of 68 runs. The letters LWC have been omitted for brevity.

-90 -Feed rate 1,500 3,000 6,000 Steam rate 250 450 250 450 250 450 Conc. factor 1 2 1 2 1. 1 1 2 1 2 VH sat. Feed temp. sup. 0: K-18 K-19 K-15 K-12 K-16 K-10 100 --—.. 20 K-21 K-29 K-20 K-14 K-13 K-17 K-28 K-ll 0 ' K-22 K-24 K-26 125 20 ' K-23 K-25 K-27 0 I-18 i- 4 I- 2 1-301 J- 1 I- 6 1-32 1-21 I- 1 150 --—... 20 1-15 1-20 1-22 I-7 J- 2 1-13 I-11 1-27 1-31 I15.....T J- 2..... 0 J-ll J- 3 J- 7 175 20 J-12 J- 4 J- 8 0 i J'- J-15 J- 9 200 20 J- 6 J-16 J-10 0. I- 5 1-23 I-24 i-14 J-13 I-26 I-16 I- 8 1-29 230.... 1 20 I-17 1-101 I- 9 I-l19i J-14 I- 3 1-28 1-25 I-12 TABLE VIII The experimental data of the LWCJ and LWCK runs are summarized in Appendices B and C, respectively. The overall heat transfer coefficients for the entire test program on 2-in. tubes are presented in Table IX.expressed in Btu/(hr)sq ft)(OF). The conclusions that were reached after the LWCI runs regarding the effect of the different variables on the heat transfer coefficient are

-91 -shown to be valid for the entire region. It is because of this that 68 runs were sufficient to explore this region, which consisted of 144 possible combinations of the different levels of variables involved. Feed rate i 1,500 3,000 6,000 Steam rate i 250 450 250 450 250 450 Conc. factorn 1 2 1 2 1 1 1 2 1 2 VH sat. Feedi temp. sup.i! 0 j 314 305 327 315 329 327 100 |; 20: 331 325 304 293 290 291 299 254 0 i 373 404 i 428 125 ---: _ 20 380 391 388.-......'..... — ' ----......... 0 445 464 472 435 0 460 565 498 520 500 150 20 418 438 441 422 446 468 480 481 470,_..................................................................... t,....................................................................................... 0 491 527 574 175 20 469 495 528 0 530 576 556 200 - 20 553 557 591 0 6645 678 6o6 573 641 868 774 794 745 230 20 590 6 66 6 587 18 737 687 701 647 TABLE IX

-92 -Do RUNS LWDA-2 TO LWDA-38 These 37 runs comprise the test program using 1-in, tubes. They were performed after the runs with 2-in, tubes had been completed, and had a similar choice of variables. Vapor-head saturation temperatures were 100, 125, 150, 175, 200, and 230~F, as with the 2-in. tubesfeed superheats were also 0 and 20~ F. The feed rates were 1,500 and 3,000 lb/hr. (Flows higher than 4,000 lb/hr proved impossible for these narrow tubes: one of the 7 tubes would revert to full-pipe flow and starve the other 6 tubes of feed.) The steam rates were 150 and 250 lb/hr. The latter gave roughly the same heat flux of ca. 6,000 Btu/(hr)(sq ft) as 450 lb/hr of steam gave with the 2-in. tubes. The 150 lb/hr steam rate was really too low for adequate process control; it was used in 12 of the 37 runs, chiefly to test the assertion that steam rate had little significance on heat transfer coefficient. Only 1 run was made with a feed concentration factor higher than 1, to test the assertion that concentration had little or no significance.

-93 -Feed rate 1,500 3,000 Steam rate 150 250 150 250 Conc. factor 1 1 2 1 1 VH sat. Feed temp. superh.. 0 34 2 37 4 100 ------- 20 35 3 38 36 5 0 o 8 6 125, 20 7 9 7 i 0 33 10 30 12 150 20; 32 11. 31 13 0 i 14 16 175 i 1 20 15 17 0 19 18 200 - 20 i 20 21 0 23 22 25 24 230 1 20 28 27 29 26 TABLE X Table X: shows the run numbers of our work with 1-in. tubes. Appendix D) gives a summary of the experimental results of each run. Table XI. gives the measured overall heat transfer coefficients, in Btu/(hr)(sq ft)(OF).

-94 -Feed rate 1,500 3 3,000 Steam rate 150 250 150! 250 Conc. factor 1 1 2 1 1 t _ _ _ _.I__.._.!"- _.. _..... __ ^_..~ __.._ __ = _ VH sat. Feed temp. superh. 100 0 i 191 172 177 162 100 20 162 153 161 130 133 o 0 267 231 125 20 245 190 i 5O 0 391 381 350 319 150 20 368 364 284 280 j ____________ |j____ —!;,_ '__ __ - ___ _ _ _ _ 15 0 1 494 436 175 20! 484 405 0 i 626 529 200 20: 605 577 0; 652 773 599 643 230 20 656 687 631 674 TABLE XI The following conclusions may be drawn from the tests on 1-in. tubes: 1) The significance of the variables in 1-in. tubes is very similar to that in 2-in. tubes except that of feed rateo 2) At high temperatures (200 - 2300 F) the heat transfer coefficienuts are practically the same as in 2-in. tubes; they become increasingly lower than those in 2-in. tubes as temperature is lowered. This effect ' This figure is evidently too high.

-95 -of vapor-head saturation temperature appears to be the only difference between operation with 2-in. and 1-in. tubes,

SECTION VII THEORETICAL MODEL OF FALLING-FILM EVAPORATIVE HEAT TRANSFER MECHANISM FUNDAMENTAL MODEL Figure 7 serves to WALL FILM VAPOR * CORE illustrate the definition CO W of the heat transfer coefE ficient through the liquid film, hf. If tw is the temperature at the inner tube wall, tv the temperature of the film at or close Distonce to the vapor interface, then: Figure 7 Atf tw - tv (1) hf - (2) f tf Our experimental work shows conclusively that the heat transfer coefficient remains practically unchanged even when the heat load is increased by 80%, and that this is valid for all temperatures, flowrates, feed superheats, concentration factors and tube diameters employed. This indicates that the heat transfer mechanism should be convective. In view of the low temperature drops involved, this explanation is plausible, especially in view of the analogous results of Dengler and of Guerrieri and Talty with climbing-film LTV's. The available correlations for convective heat transfer through -96 -

-97 -falling liquid films are those of Drew, Brauer, and Dukler,* Drew's correlation is not supported by any experimental evidence except for water at 1900 F. - Brauer's correlation contains an empirical factor, namely, the velocity at the '"equivalent" film thickness; we have no way of predicting this factor, which seems to depend on the nature of the liquid and its temperature. Dukler's analysis is the direct computer solution of the basic differential equations for momentum and heat transfer. Except for the use of the Deissler and the von Karman universal velocity profiles, no simplifying assumptions or empirical factors of any kind are contained in this analysis. It successfully correlates experimental falling-film sensible-heat transfer and condensation data over an extremely wide range of variables; this shows that the two universal velocity profiles, though derived from tests with full-pipe flow, are valid for fallingfilm flow. We used this correlation as our theoretical model. The Dukler correlation for our range of variables is presented * in graphs 2 and 3. Graph 2 is a plot of the dimensionless film thickness 2\ 1/3 group B (2) 1/ versus Reynolds number, for negligible interfacial shear. Graph 3 is a plot of the dimensionless heat transfer coefficient hf as function of the Reynolds and Prandtl numbers, also for negligible shear. Graph 2 is taken directly from Dukler's papero Graph 3 resulted from a cross-plot of Dukler's curves of vs. (Re) for values of (Pr) of 1.0, 2,0, and 5.0. * See pages 50, 51 and 53 respectively. ** See Appendix Eo

-98 -Graph 4 is a plot of c, computed for sea water concnetrates as function of temperature and chlorosity. The heat transfer coefficients thus calculated are essentially local coefficients. The mean value of the coefficient.with respect to the entire tube length should, in all rigor, be calculated by integrating the local coefficients along the tube. This may be avoided, however, by considering that in our tests the vaporization rate was low compared to the feed rate; the average between feed rate and blow-down rate should be satisfactory for computing the mean Reynolds number, especially since the flowrate varies linearly due to the constant heat flux along the tube. The small change in salinity during vaporization has little effect on the physical constants of the liquor, and can be satisfactorily taken into account by using the mean salinity. Graphs 5 and 6 are plots of viscosity and Prandtl number, respectively, of sea water concentrates. They were calculated from data on physical properties contained in Report 438 of Wo L. Badger Associates, Inc,, for the Office of Saline. Water(5), BOILING POINT ELEVATION According to our theoretical model, Figure 7, a precise knowledge of tv as well as of the wall temperature is required in order to calculate A tf o However, tv would be extremely difficult to measure, and must therefore be calculated from the local vapor pressure, Pv' This pressure is equal to the measured vapor-head pressure plus any (usually very low) pressure drop A p caused by friction, acceleration

-99 -and elevation, and can be computed. Let the general function t. f(p) (3) be the equation of the temperature vs. vapor pressure of the volatile solvent; for aqueous solutions it is tabulated in the steam tables. If the vapor phase in falling-film evaporator tubes consisted of saturated steam, it would then follow that tv - f(Pv). For boiling liquids, however, the equilibrium vapor is not saturated but superheated: tv > f(pv) This superheat is due to two causes: the presence of bubbles, and the presence of solute. Let a spherical bubble of radius r be in equilibrium with the surrounding liquid phase. Let p' be the pressure of the gas inside the bubble. Let Pv be the pressure of the liquid, which is the same as the pressure of the extended equilibrium gas phase (no curvature). A balance on the tangential tensile forces acting on the bubble surface yields the well-known relation: cr. 2.7r = (p' - Pv) z-r2 (4) or': p (5) Pr: - Pv r The presence of solute lowers the vapor pressure of the solution below that of the pure solvento This causes the equilibrium vapor to be superheated by a temperature difference (BPR), the boiling-point rise. If tv and p" are the temperature and pressure, respectively, of the vapor in equilibrium with the liquid, then: (BPR) - tv - f(p) (6)

-100 -Consider now the case of both bubble and solute action occurring simultaneously, as in boiling sea watero The vapor in equilibrium with the boiling liquid is in bubble form; hence p' of the discussion on bubble action becomes identical with p" mentioned under solute action, Combining equ, (5) and (6), we arrive at the conclusion that in this case the boiling-point elevations due to bubbles and to solute are additive: tv f(Pv+ 2-) + (BPR) (7) r Using our symbols, f(Pv) is the "apparent" vapor temperature, and f(pv)?, — (BPR) the "corrected" vapor temperature, in the parlance of 2<industrial evaporator practice. The neglect'of the - term in industry is due to the fact that in most cases it is negligibly small except for very small bubbles, and because there is little information regarding the size and behavior of bubbles in commercial evaporators. In falling-film evaporation, both Karetnikov and. Richkov et alo` —<' report observations on bubble size, namely, that the bubbles become stable when they reach.the same proportions as the film thickness itself. This stands to reason, First, a stable bubble can certainly not be larger than the film. Second, suppose there exists an array of bubbles of different sizes, ranging from very small up to a maximum with diameter equal to the film thickness. B v These bubbles cannot all exist at equilibrium with each other, for the same reason:that small. crystals cannot exist in equilibrium with large crystals when suspended * See Appendix F for the effect of neglecting 2_ in falling-film evaporation, ~* See pages 79 and 80 respectively,

-101 -in a saturated solution: according to the second law of thermodynamics, the smaller bubbles (or crystals) shrink spontaneously until they disappear. The Dukler analysis offers the needed information on the thickness of falling films, and the surface tension of sea water concentrates can be found in the work of Sverdrup et al(3). The bubble boiling-point elevation -r may be calculated as follows: B B / f in. Hg (8) B where / is defined as: x 1/ 33.876 x~L~/ lg) 36 in. Hg, (9) r~ being expressed in dynes/cm, ( 9 /3 in ft 1 The convenience of this formulation is that A is a function of e 2g 1/3 temperature and chlorosity only, whereas B ( P )/ is a function of the Reynolds number only. Graph 7 shows; B 2) 1/3 can be read from Graph 2, the Dukler film thickness correlation. The film thicknesses for our experimental work range from 11 to 28 mils, when calculated with the Dukler correlation. Values of 4~ B range from 0.11 to 0.25 in. Hgo Neglect of the bubble boiling-point elevation*is unimportant at 2300 F, but at low temperatures it can cause considerable error due to the slope of the vapor-pressure curve of water at low temperatures. This may explain the reason why Karetnikov"^' * See Appenldix F **See page 79

-102 -found his boiling coefficients to be lower than his non-boiling coefficients, especially since he worked at very low Reynolds numbers (and hence low film thicknesses). Boiling-point elevations from bubble action and from solute action change little along the length of the tube*; the values for the average values of film temperature and chlorosity were always used in our calculations. LONGITUDINAL PRESSURE-DROP MODEL It is necessary to know the pressure-drop in order to be able to calculate Pv: Pv L=: PVH ^+ U (10) This pressure-drop is the friction, acceleration and elevation pressuredrop due to the downward two-phase flow through the tube, with eventual sonic choking. No sonic choking was encountered during the experimental work. It was calculated that the highest vapor exit velocity, ca. 950 ft/sec, was less than 70% of the speed of sound at that temperature. Vapor exit velocities were calculated from a separated-flow model, which of itself yields higher values than the homogeneous-flow model such as used by Harvey and Foust and by Schweppe and Fousto,Acceleration-pressure drops were calculated according to the * See Appendix F for a discussion of this point~ ** See page 77.

-103 -separated-flow model, which should be applied in falling-film flow. To do this, the film thickness was calculated from the Dukler correlation, and the liquid cross-sectional area subtracted from the total tube cross-sectional area to give the gas flow cross-section. Elevation heads were also calculated. A certain degree of conjecture had to be used in order to calculate frictional pressure-drop. A thorough search of the literature on twophase flow had failed to yield a satisfactory universal correlation for two-phase pressure-drop in falling-film flow. Bergelin, Kegel et alo reported that for gas flowrates below a critical value, the pressure-drop in falling-film two-phase flow was equal to the pressure-drop of the gas phase alone. Our highest calculated exit gas velocity in 2-in. tubes was 386 ft/sec, with a gas Reynolds number of 20,000. For the low liquor rates employed, this gas rate is lower than the critical gas rate for 1025 in. tubes as employed by the authors, Pressure-drop for 2-in. tubes was therefore calculated for dry-tube flow as follows: dp 2G2v (l) - -& ' f -i^ (11) Let th te l of ch d e y G Let GT be the terminal valubeof the gas f low density G Let LT be the terminal length of the tube (24 ft in our case)4

-104 -Basic assumption: uniform heat flux along the tube. lo G =uT L (13) LT L 2 '. pA f 2G \ vL dL (14) ( 2G2vL O gcDLT 2 L 2GT 2 2 -P =- 2 L fvL dL (15) gcDLT 0 T:his integral can be solved by dividing the tube into a laminar length 16 where the Reynolds number varies from zero to 2,100 and f - e),R9 and a turbulent length with f 0oo46 (Re)-0' It can be shown that the pressure-drop arising from the laminar section is negligibly small and that the laminar section is negligibly short. Hence: dp (0.046)(2)GT8 0S2vLl8 6) dL - 8 0 gcD LT (o-o46)(2)GT (- v L2' (g<, v const.) (i7) 2.h8gcD LT- The pressure-drop increases with the 2.8th power of the tube length. In fa:.c't, for the typical case of 2-in. t;ubes, with vapor-head temperature 100C- F, steam rate 450 lb/ihr, we have 90% of the pressure-drop conentrated in the bottom 3o7% of the tube length. It is practically an "exit pressure-drop". In order, therefore, to avoid an integration of pressure-drop with length, we simplified the pressure-drop model by calculating the whole pressure-drop as an exit pressure-dropo The error

-105 -involved,in this assumption is small because of the low magnitude of the pressure-drops involved, so low, in fact, that they could not be experimentally determined during the tests with 2-in. tubes. Table XI! presents the calculated values of the total pressure-drop, in ino Hg, this being the sum of friction, acceleration and elevation pressure-dropso Friction accounts for one-half to two-thirds of the total, and was calculated for dry-tube flow as described. Graph 8 reproduces Table XII for purposes of interpolation, for temperatures below 2000 F. Tube size, in. 1 2 Steam rate, lb/hr 150 250 250 450 Feed rate, lb/hr 1,500 3,000 1,500 3,000 1,500 6,000 1,500 6,000 Vapor. temp., OF 100 0.708 0.725 1.827 1.879 0o067 0.069 0.205 0.211 125 ~ 0.359 0.368 0.928 0.958 0033 0,: 0034 0.10 6 150 I 0o195 0O200 0.506 0o518 o016 0.017 005 0.05 5 175 o.01080 O.ll 0.288 0o295 0.005 O.006 0 0027 0o028 200 0059 0.061 0.168 0.173 -0o003 -3 - 3 0.010 0o011 230 0.024 0.024 0o085 0o088 -0o015 '-0.014 -0.006 -0.006 TABLE.XiT It can be seen from Table XII that for 2-in, tubes the vapor pressure-drops are extremely small; so small, in fact, that at the higher temperatures the pressure gains due to the weight of the 24-ft column of

-io6 -vapor is higher than the combined friction and acceleration pressure-drops, thus producing a total vapor pressure-drop that is negative, i.e,, a pressure gain. As mentioned earlier, the upper tube ends were provided with enrtrance.. orifices in order to equalize the feed distribution among the 7 tubl,,es The unavoidable disadvantage of this scheme was our resulting inability to measure feed pressure directly; feed pressure minus vapor-head presisure would then have given us the vapor pressure-drop. As it was9, the mea.sa,'2;red quantity was the sum of the vapor pressure-drop plus the orifice pressuredrop, the latter amounting to a major portion of this sum. This disadvantage was circumvented by the following procedure: after a sufficietnumber of hourly heat transfer readings for a given run, the steam was shut off but nothing else was changed. Under these conditions the pressure-drop was due only to the orifice pressure-drop, since the th'be did not contain any vapor. The orifice pressure-drop was measured., and subtracted from the measurements taken during the run itself; this should yield the vapor pressure-drop. The values thus obtained scattered considerably. This was n.re; unexpected, because: 1) the orifice pressure-drops amounted to several inches Hg, w-:hivle 1t:ie vapor pressure-drops were very small; 2) the orifice pressure-drops themselves fluctuated strongly dule t:o momentary pressure changes in the feed line; 3) any amount of flashing through the orifice, due to even a very c.lv feed superheat, raised the orifice pressure-drop,onsiderarblyo

-107 -The theoretical minimum for the two-phase pressure-drop is the dry-tube pressure-drop as per Table XII. The vapor pressure-drops observed in the 2-in. tubes were of the same order of magnitude; hence the values of Table XII were used in our calculations as the two-phase pressure-drops. For 1-in, tubes the problem was more complex because: 1) orifices were smaller*, hence orifice pressure-drops were higher; 2) the measured two-phase pressure-drops were higher than the dry-tube pressure-drops for runs at lower temperatures and at the high steam rate, The two-phase pressure-drops were approximated as follows: the dry-tube values of Table XII were corrected by adding the empirical corrections of Table XIII this roughly correlates the experimentally obtained twophase pressure-drops. Data are in in, Hg. Feed rate 1,500 3 000 Steam rate 150 250 150 250 Vapor temp. 100 - 175~ F 0o00 0o60 0.00 1.20 200 0.00 0.00 0.00 0.60 230 0Io0 0.00 0.00 0.00 TABLE iXIII * Preliminary work with the 1-ino tubes had shown a tendency for full-pipe flow to occur in any one tube, which then completely starved the other six of feed. This could only be avoided by installing smaller orifices. - For the same reason feed rates in excess of 4,000 Ib/hr could not be used.

-108 -CALCULATION OF TUBE-SIDE HEAT TRANSFER FILM COEF FICIENT FROM THEORETICAL MODEL This is best illustrated by taking- a typical example from the Appendix; say, the first of the two sets of data of run CI-1: ~ v the film viscosity, is found on Graph Noo 5: 1l17 lb/(hr)(ft). (Re), the film Reynolds number, is calculated as 4w/b L: 5,900. (Pr), the film Prandtl number, is found on Graph No, 60 2.88. hfA/, the dimensionless Nusselt heat transfer group, is:ound on Graph No. 3: 0o319 (Dukler's correlation)o {D, the Nusselt heat transfer coefficient group, is taken from Graph No, 4: 4,060 Btu/(hr)(sq ft)( OF) 4X the bubble superheat magnitude, is taken from Graph No. 7: 2.83 in. Hgo B!) / the dimensionless Nusselt film thickness group, is taken from Graph No. 2: 23.4 (Dukler's correlation)o tp, the tube exit pressure-drop, is taken from Graph Noo 8; for 1-in. tubes we correct for liquid effect by adding values from Table XIII. For the set of data of this example, the result is: 0.06 ino Hg o Pv, the actual pressure in the tube vapor core, is the VH sat. press, plus A p: 7.61 + 0o06 = 7.67 in. Hg the bubble superheat pressure, is calculated as X/B ) 2.83/23~4 -O.12 in. Hg f(pv + 4 )g the tube vapor core temperature corrected for bubble superheat, is found in the steam tables: f(7.67 + 0o12) f(7o79 ino H.g abs.) = 15lo16 OF

-109 -tv, the tube vapor core temperature (corrected for BPR as well as 4C bubble superheat): f(pV+ B-) - BPR = 151.16 + 2.03 = 153 190 F h-, the heat transfer coefficient for actual conduction-convection (DukLer) hf through the falling film itself, is calculated by multiplying h by (: (0.319)(4,060) - 1,295 Btu/(hr)(sq ft)( ~F). A tf, the temperature drop through the falling film (see Figure 7, page ' ) is calculated by dividing the heat load Q by the inner tube surface (78.3 sq ft) and by hf: 458,000/(78o3)(l,295) 4.52c F This solves the heat transfer problem, since it gives the wall temperature: tv - A tf 153o19 -, 4.52 = 157-710 Fo - Heat transfer occurs only across the film itself, over a temperature drop of Atf 4 4.520 F. However, in experimental work and for evaporator design the important temperature difference is between the wall temperature and the BPR-corrected vapor-head saturation temperature, A tcorr* It must be emphasized that in a falling-film evaporator A tcorr is not a temperature drop across a film, but simply the difference between two temperatures. Still, the BPR-corrected vapor-head saturation temperature has the advantage of being experimentally measurable*, and heat transfer coefficients based on it are the usual way of reporting heat transfer information. Atcobrris therefore calculated here from our theoretical model; A tcorr- 157.71 - (150.22 -f 2.03) - 5,460 F * The vapor-head saturation temperature is experimentally measurable, and BPR is added to it,

-109aCalculation of heat transfer coefficients as illustrated on the previous two pages may be summarized as follows: VH pressure p = 7.61 in.; f(7.61) = 150.22~ VH + Tube exit pressure drop + A p = 0,06 in. Vapor core pressure Pv = 7.67 ino; f(7.67) = 150o53~ + Bubble superheat + 4a/B = 0.12 in. 7079 in.; f(7o79) = 151.16~ + Boiling-point rise (solutes) + BPR = 2.03~ Vapor core temperature tv = 153519~ + Temp. drop across film (Dukler) + A tf = 4.52~ Wall temperature tw = 157,71~ Hence A t = 157 71 - 150o22 = 7.49~F app and A tcorr A tapp -BPR = 7.49 - 2.03 = 5.46F Figure 8 shows temperatures and pressures at different points according to the proposed model, WALL FILM VAPOR CORE 38 mils — tw 157.71 t - 15319 4/ t = 153.1967 Pv 7.67 P v/t 31\\ pv7.67 P ~-/' f tv^ = 153.19 p = 7.79 \\ (Equilibrium)/ = 7.67 / @ \ BUBBLE / TUBE END VAPOR HEAD / PVH = 7.61 Figure 8.

-109b - Adoption of the proposed model implies that several basic assumptions must be postulated: 1) The liquid contains bubbleso This is based on the observations of Richkov and Pospelov, and of Karetnikov; the films at Wrightsville Beach could not be observed due to the nature of the equipment, 2) There is not enough relative motion between bubbles and liquid to create turbulence. Heat transfer therefore follows the laws of convection for liquid films. - The assumption of little relative motion is also based on. the observations of Richkov and Pospelov and of Karetnikov, who report that the bubbles float downwards at the same velocity as the liquid, 3) There are not enough bubbles' to destroy the essentially liquid texture of the film; for heat transfer calculations, the physical properties of the film are those of the liquid phaseo 4) There are, however, sufficient bubbles so that the liquid temperature at the vapor core interface is determined by the bubble superheat. 5) The bubble diameters are of the same order of magnitude as the film thickness.. 6) The bubble surface is spherical in shape, at least near the vapor core interface The model does not contain any suggestions regarding the form, temperature and pressure of that part of the bubble that is close to the wallo Neither does it contain any assumption regarding what fraction of the vapor enters the core by evaporation of the plane interface, and what fraction enters the core due to the emergence and bursting of bubbles,

-109cTransfer of vapor does not necessarily have to occur solely by bubble bursting, because according to the model the liquid at the plane interface is superheated, and will spontaneously form superheated vapor of the same temperature and pressure. This constitutes a driving force that forces the liquid to lose enthalpy to the vapor coreo The thermodynamics of this statement are readily illustrated by the temperature-entropy diagram, Figure 9. The T-S curve is that of the (plane-surface) vapor-liquid equilibrium of a salt solution having a BPR of 2o03 ~F T p=7.7 Al/A B' B 155.19OF t 152.56~F p 7.7 S Figure 9o Point A represents the condition of the (superheated) liquid near the plane interface with the gas core; point B represents the condition of the (superheated) vapor in the core. We have the following relationships in terms of F, the free energy

-109dF - FA = (equilibrium) B' A' 7 67 F - F v dp (reversible isothermal B B' g single-phase expansion) 7~79 7o67 F - F v dp (reversible isothermal A A / single-phase expansion) 7 79 7067. A FF - F (vg v) dp <O (spontaneous B A process) 7o79 Hence superheated liquid (A) is spontaneously transformed into superheated vapor (B)o The proposed model is necessarily limited by assumptions 1) to 6) all of which are postulated without there being any experimental proof of their validityo It must be emphasized, therefore, that this is by no means the only possible model for falling-film evaporative heat transfer. However, the present model appears to be thermodynamically sound, and is shown in the next Section, to yield a satisfactory prediction of heat transfer coefficients under widely varying operating condition,

SECTION VIII PREDICTION OF OVERALL HEAT TRANSFER COEFFICIENTS FOR RUNS WITH ZERO FEED SUPERHEAT FROM THEORETICAL MODEL -109e

INTRODUCTION Overall heat transfer coefficients were predicted for all combinations of operating conditions that were actually tested in our experimental work for runs at zero feed superheat. In order to calculate the overall coefficients, the tube-side temperature drops were predicted from our theoretical model; the steamside temperature drops were predicted from the experimental results of Baker, Kazmark and Stroebe and from the recommendation of McAdams. It was found that overall heat transfer coefficients thus estimated agreed within 10% with those measured in our experimental worko -109f

CALCULATION OF STEAM-SIDE TEMPERATURE DROP In heat transfer studies it is usual to measure the wall temperature directly, chiefly by means of thermocouples. These give readings with a scatter of ~0.5%, say, for good operation. For our runs, however, this degree of scatter would have meant a scatter in liquor-side film coefficient of up to ~ 65%> not counting scatter from any other source. This is due to the unusually low temperature differences encountered in falling-film LTV evaporation. - In addition, the installation and operation of thermocouples would have presented problems of a practical nature for which the pilot plant was not equipped. Another possibility was the experimental determination of the steam-side film coefficient by means of a Wilson plot. Steam condensate Reynolds numbers ranged from ca. 200 to ca. 1,500. At these very low steam rates it proved impossible to determine the steam-side coefficient in this manner, since temperature drops at the hot end of the tube became immeasurably small. This was predicted by calculation and proved in an experimental attempt to make a Wilson-type determination. The only alternative was to estimate the temperature drop through the condensate and the tube wall. Little dropwise condensation of steam zould have taken place because the tubes had been in continuous operation for weeks or months before these tests took place; because no oily layer was ever observed in the steam-condensate drip tank; because the tube metals used do not tend to promote dropwise condensation as does, say, stainless steel; because the outside of the tubes before, -110 -

-111 -during and after the tests never showed any trace of oil; because no time trends in overall heat transfer coefficient were ever observed; because of the excessive continuous venting of the steam chest; and because the steam condensate passed through 2 vertical storage tanks before returning to the boiler, whose main consumer of steam was our pilot plant. For such cases, McAdams* recommends the use of a film coefficient 28% higher than that obtained from the Nusselt correlation with the same Reynolds number. - Dukler** has recently presented a correlation that we have found to fall within ~ 7% of that of McAdams. - The curves in Graph 9 were constructed according to the McAdams recommendation and were used to determine the steam-side temperature drop for each set of readings. This recommendation is particularly applicable to the LTV, as shown by Baker, Kazmark and Strobe(l) in 1939. Their tests were conducted on a single-tube LTV consisting of a 2-in. tube 20 ft long. Tube wall temperatures were determined with thermocouples embedded at intervals of 1 ft. In the particular region of interest, namely, (Re) -K 900, the steam-side heat transfer coefficients averaged 1.28 times the Nusselt correlation; see Appendix F for a discussion of the scatter in a tgtm* CALCULATION OF TUBE-WALL TEMPERATURE DROP The temperature drops through the tube walls were determined as follows: * See page 49. **See page 55.

-112 -a) 2-ino tubes: 7 2-ino 12 BWG x 24'-0" tubes: No. of tubes Material k, Btu/(hr)(ft)( OF) 2 Aluminum brass 58 2 Copper 200 1 Ampco grade 8 43 1 Admiralty 64 1 90-10 Cupronickel 26 Average conductivity (arithmetic mean): 92.7 Btu/(hr)(ft)( OF) Log-mean diameter: 1.895 in. Temperature drop, OF: 1.177 x 10-6 Q, where Q is the total LTV heat load, in Btu/hr (i.e., not the load per tube)o b) 1-in, tubes: 7 1-in. 16 BWG x 24'-0" tubes: No. of tubes Material k, Btu/(hr)(ft)( OF) 3 Aluminum brass 58 2 Copper 200 1 Admiralty 64 1 90-10 Cupronickel 26 Average conductivity: 9409 Btu/(hr)(ft)( ~F) Log-mean diameter: 0.932 ino Temperature drop, ~F: lo39 x 10-6 Q The tube-wall temperature drops turned out to be so small,.even when compared to the steam-side and liquor-side temperature drops, that the effect of using mixed tube bundles on the distribution of the heat load among the 7 tubes was insignificant,* * The purpose of installing mixed tube bundles was to make simultaneous corrosion studies on different tube metals.

-113 -CALCULATION OF OVERALL HEAT TRANSFER COEFFICIENT The overall heat transfer coefficient is calculated by dividing the heat flux Q/A by the overall temperature difference ( Atstm + tw + A tcorr). This is best illustrated by a typical calculation; again, take the first set of data of run CI-1, Appendix A, as example. hstm, the steam-side heat transfer coefficient, is read from Graph No. 9: 1,089 Btu/(hr)(sq ft)( OF) A tstm, the mean temperature drop through the condensate layer, is calculated by dividing the heat load Q, 458,000 Btu/hr, by hstm and the outer tube surface, 87.9 sq ft: 4.78 OF A tw, the temperature drop through the metal tube wall, is calculated as 1.177 x 10-6 Q: 0.54 OF UVH, the overall coefficientis calculated by dividing Q, 458,000 Btu/hr, by the inner tube surface, 78-3 sq ft, and by the overall temperature difference, 4,78 + 0.54- 5.46 = 10.78 OF: 542 Btu/(hr)(sq ft)( OF) COMPARISON OF THEORETICAL MODEL WITH EXPERIMENTAL RESULTS Table "XIV shows the comparison of the values for the experimentally obtained heat transfer coefficients and the values predicted from our theoretical model for UVH in the 2-in, tubes. It is interesting to -'observe: thait there is.'ag.reement with a maximum deviation of 10%, except for the two runs whose results are in parentheses. These two runs are the very same ones whose experimental values were considered to be definitely too high, from an analysis of the experimental data alone

-114 -(see page oI ). Our theoretical model corroborates this; the error in the two runs is probably due to experimental error, therefore, and cannot be ascribed to a defect in the theoretical model. Feed rate 1,500 3,000 6,000 Steam rate 250 450 25 450 250 450 Conc. factor 1 2 2 1 1 1 2 1 2 VH sat. temp. Experimental Values of UVH 100 314 305 327 315 329 327 125 373 404 428 150 445 464 472 435 460 565 498 520 500 175 491 527 574 200 530 576 656 230 645 702 621 573 641 (868) 774 (794) 745 Theoretical Values of UVH 100 291 297 326 317 363 362 125 392 431 469 150 471 471 470 465 513 571 529 551 548 175 530 566 607 200 578 615 656 230 650 650 623 629 659 759 749 694 698 % Deviation 100 -8 -3 -0 -1 +9 410 125 - 5 +6 +9 150 +6 42 -0 +7 +10 +1 -6 +6 -t9 175 +7 + 7 45 200 - 8 — 6 0 230 41 -8 +0 |.9 +-3 (-14) -3 (-14) -7 TABLE XIV

-115 -Table XV compares the experimental values of UVH in the 1-in. tubes with those derived from the theoretical model. For some runs, deviation between experiment and theory is higher than with the 2-in. tubes. This is because pressure-drop dominates the whole picture. Take, for example, the first set of readings of run LWDA-12. Here, / tcorr is 13.800 F., of which 8.70~ F are accounted for by pressuredrop alone (the rest is made up of A tf = 4.610 F, and a bubble superheat of 0.49~ F). For tubes as narrow as these, then, a good two-phase pressure-drop prediction is far more important than a good heat transfer prediction, and the % deviation of Table XV is a test of the pressuredrop accuracy rather than of our falling-film heat transfer model. The test enclosed in parentheses is the same one whose experimental value is evidently too high (see page 94 ). - Also, the runs with 150 lb/hr steam have little significance, since adequate control at this low steam rate was impossible in our experiments. Except for the runs mentioned in the previous paragraph, whose experimental values are unreliable, our theoretical model predicts UVH for the 1-in. tubes with a maximum deviation of 9%. Figure 8 shows the agreement between theory and experiment in graphical form, for both 2-in. and 1-in. tubes. It refers to all runs with saturated feed.

Feed rate 1,500 3,000 Steam rate 150 250 150 250 Conc. factor 1 1 1 1 VH sat. temp. Exptl. UVH 100 191 172 177 162 125 267 231 150 391 381 350 319 175 494 436 200 626 529 230 652 (773) 599 643 Theor. UVH 100 200 174 202 158 125 265 237 150 466 374 486 335 175 473 446 200 6o8 580 230 707 671 769 712 % Deviation 100 + 5 1 +12 -2 125 -1 3 150 1+6 -2 +28 +5 175 -4 t2 200 -3 - 9 230 +-8 (-13) +222 -10 TABLE XV

-117 -CORRELATION OF UVH /00 0/ 5 _ --- —--- -' _ / / y^ / J U 4tl~~'^ // /F / / IO0/, *. TUBES o^, / w /.+ i-/n. TUBES 0 '^/ Figure 10

-117aA more stringent test of the model is the prediction of the liquid-side heat transfer coefficient. The predicted value of h can. VH be compared with experimental values; although the latter were not measured directly, they can be computed by taking 1 - 1 ( Astm/f Af hvH UVH \ hstm w \\alll exptl. exptl Table XVI and XVII show the comparison for 2-in, and 1-in, tubes9 respectively; agreement is generally within 20%o Figure 11 illustrates the correlation of predicted with measured values of the experimental hVH

-117bFeed rate __^i! 1,500 3,000 6,ooo Stea..r..a.te _ _ 0.....,.v................,........................................ Steam rate 250 450 250 450 250 450 Conco factor 2 2 1 2 1 1 2 1 2 VII sat, temp. Experimental Values of hVH 100 438 447 462 470 482 492 125 583 665 738 150 683 690 824 719 777 1025 925 998 918 175 8 854 967 1148 200 928 1095, 1431 230 1147 1221 116 100o4 1289 (2100) 1591 (2125) 1813 Theoretical. Values of hVH 100 398 430 460 475 543 577 125 632 743 867 1.50 747 707 818 802 942 1047 1040 1124 1092 175 978 1110 1283 200 1088 1245 1431 230 1160 1151 1220 1170 1361 1524 1487 1529 1557 % Deviation 100 -10 -4 -o +1 +11 +15 125 +8 +10 +11 +15 150 +9 +2 -1 +18 +2 +11 + 11 +16 175 +13 +13 +11 200 +15 +12 0 230 +1 +6 +5 +14 +5 (-38) -7 (-39) -16 TABLE XVI

-1.1.7cFeed rate 1,500 3, 000 Steam rate 150 250 150 250 Conco factor 1 1 1 1 VH sat. tempo Exptl. hH ____________ [ ______VH 100 229 205 209 191 125 354 291 150 560 572 488 442 175 839 685 200 1246 904 230 11.35 (1821) 979 1258 Theor. hV 100 242 208 245 185 125 350 301 150 727 558 799 471 175 776 709 200. 1178.o060 230 1311 1.343 1529 1.549 % Deviation 1oo -1 100 I +5 1 1 +15 -3 125 -1 +5 150 +23 -3 +39 +6 175 -8.53 200 -6 +15 250 +13 (-36) +36 +19 TABLE XVII

-117dCORRELATION OF hVH 4 9 8 - X 1 - - - - X --- 7 6 - = ==A ---- - ----- - - 3 - - - - -- - -+ I — IN. TUBES- O2 --- - -- - - -- -------- ----- 00 +20%. * -20% o - ~~- ---- - - 2 3 4 Figure 11 5 ----- --- ----- --- ^ -?^ -^ ---- ----- - ' 2-IN. TUBES 4 _____ ___ _____ / /, / _ _ _ _ _ __ _ _ + I -IN. TUBES 102 2 3 4 5 6 7 8 9 103 2 3 4 5 6 7 8 9 4 EXPERIMENTAL Figure 11

SECTION IX THEORETICAL ANALYSIS OF RESULTS FOR TESTS WITH 20 F FEED SUPERHEAT The test results show that the overall heat transfer coefficients for runs with 200~ F feed superheat are always somewhat lower than the corresponding runs with zero feed superheat. The only possible explanation for this unforeseen result is, that flashing at the tube entrance produces such linear velocities that falling-film flow is only established a few feet further down. - The ease with which falling-film flow is destroyed due to high local vaporization rates is quoted by Karetnikov (page 79 ), Richkov and Pospelov (page 80 ), and Mueller (page 81 ); it is attributed to the absence of any force (except surface tension) that would bring the fluid back to the tube wall once it leaves it. The theoretical model for the runs with 20~F feed superheat is then as follows. The feed flashes, and falling-film flow is only established a few feet further down. At this point the feed has lost all its superheat, and proceeds downwards with evaporative heat transfer just as the corresponding runs with zero feed superheat. - Heat transfer occurs only where there is falling-film flow. Breaking down the overall heat transfer resistance into its steamside, wall, and falling-film components is out of place here, because we do not know the square footage of actual heat transfer surface. This latter quantity is the only unknown magnitude, and it determines the difference between the results of any run and the results of the corresponding run with zero feed superheat. -118 -

-119 -If the tube length taken up by the flashing could be calculatedY it could be subtracted from the total tube length to yield the actual heat transfer length. Unfortunately, too little is known concerning the exact mechanism of flashing. The problem is exceedingly complex; it involves inertial, viscous, and surface forces; a separate long-range research would be necessary to study it, In order to get an approximate idea of the flash lengths involved, we have divided the overall heat transfer coefficients by the theoretical values of UVH for the zero-superheat runs. The quotients, expressed as o, will then give the percentage of the total tube length where actual heat transfer takes place, i.e., where falling-film flow exists, These values are given in Table XVI for 2-ino tubes, and in Table XVII for 1-in. tubes. Feed rate 1,500 3,000 6,000 Steam rate 250 450 250 450 250 450 Conc. factor 1 2 1 2 1 1 1 2 1 2 VH sat. tempo 100 70 101 102 90 92 82 84 72 125 97 91 83 150 89 93 94 91 87 82 91 87 86 175 89 88 87 200 96 91 90 230 91 93 96 93 94 97 92 101 93 TABLE XVII I

-120 -Feed rate 1,500 3,000 Steam rate 150 250 150 250 Conc, factor 1 1 2 1 1 VH sat. temp. 100 81 88 92 64 i 87 125 92 80 150 79 97 58 84 175 102 91 200 100 99 230 93 '1102 82 95 TABLE XIX Control of the feed temperature, and hence superheat, was not always as accurate as might have been desired. Despite this, and despite the wide variations of tube diameter and all other variables between runs, the figures in Tables XVI and XVII are remarkably alike. With very few exceptions they amount to cao 90%. This means that flashing takes place in the top 2-3 ft., the rest of the tube being heat-transfer area. One can therefore predict UVH for the runs with 20~ F superheat by calculating UVH for saturated feed and considering the tube shorter by 2-3 ft. from its real length.

APPENDIX A EXPERIMENTAL DATA AND CALCULATIONS COLUMNS 1-14 THEORETICAL PREDICTIONS, COLUMNS 15-33 RUNS LWCI-1 TO LWCI-32 -12.1

-122 -2-in. Tubes, CI Series, Zero Feed Superheat Run No. VH sat. VH press. Feed rate Vapor rate Ave. flow BD Cl Feed Cl Ave. Cl Steam rate QxlO-3 Stm. sat. BPR EXPTL UVH (Re) (Pr) temp. ~F n. Hg 1,/hr lb/hr lb/hr gpl gpl gpl lb/hr Btu/hr temp. ~F ~F Btu/ft2-h-OF lb/hr-ft (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16 (17) CI- 1 150 6,ooo 40 450 150.22 7.61 5,857 457 5,628 44.77 40.97 42.87 447 458.0 163.83 2.03 505 1.17 5,900 2.88 150.22 7.60 6,251 444 6,029 37.29 34.60 35.95 445 451.1 163.55 1.69 495 1.14 6,485 2.83 CI- 2 150 l50 20 450 150.16 7.60 1,510 453 1,283 29.31 20.79 25.05 439 448.1 163.55 1.17 468 1.10 1,430 2.78 150.27 7.62 1,505 462 1,274 29.68 20.93 25.31 446 456.3 163.75 1.19 475 1.10 1,417 2.78 cI- 4 150 1,500 40 250 150.01 7.57 1,519 249 1,395 46.87 39.55 43.21 246 247.4 158.98 2.04 474 1.18 1,448 2.91 150.16 7.60 1,496 243 1,374 46.87 39.55 43.21 237 238.6 158.94 2.04 453 1.18 1,428 2.91 CI- 5 230 1,500 20 250 230.13 42.41 1,477 258 1,348 25.33 20.88 23.11 264 241.2 236.48 1.42 625 0.68 2,425 1.58 230.08 42.37 1,483 251 1,357 25.15 20.90 23.03 257 234.8 236.01 1.42 665 0.68 2,442 1.58 CI- 6 150 6,000 20 250 150.11 7.59 5,865 256 5,737 21.26 20.41 20.84 252 254.2 156.72 0.98 577 1.10 6,380 2.80 149.73 7.52 6,279 331 6,114 22.10 21.07 21.59 285 289.3 157.41 1.01 553 1.11 6,750 2.80 CI- 8 230 6,000 20 450 229.98 42.29 6,085 442 5,864 22.54 21.07 21.81 447 417.3 237.89 1.34 811 0.67 9,220 1.58 230.06 42.36 5,968 436 5,750 22.18 20.96 21.57 442 411.8 238.18 1.34 776 0.67 9,030 1.58 01-14 230 1,500 40 450 229.91 42.24 1,662 362 1,481 50.83 40.14 45.49 353 325.0 240.22 2.92 562 0.74 2,455 1.67 229.89 42.22 1,649 356 1,471 48.93 40.78 44.86 362 333.6 240.05 2.86 583 0.74 2,439 1.67 CI-16 230 6,000 40 250 229.92 42.25 6,212 236 6,094 40.02 38.76 39.39 245 222.9 236.04 2.47 780 0.73 10,220 1.68 230.03 42.36 6,244 229 6,129 41.05 39.71 40.38 245 222.8 236.27 2.53 768 0.73 10,290 1.68 0C-18 150 1,500 20 250 149.90 7.55 1,542 268 1,408 24.52 20.50 22.51 260 258.6 158.36 1.06 447 1.10 1,568 2.79 150.00 7.57 1,520 270 1,385 25.07 20.42 22.75 259 260.0 158.58 1.07 442 1.10 1,541 2.79 CI-21 150 o000 20 450 150.32 7.63 6,395 500 6,145 21.20 20.00 20.60 490 499.1 163.43 0.97 525 1.09 6,900 2.77 150.27 7.62 5,879 468 5,645 22.18 20.40 21.29 444 450.8 162.49 1.00 514 1.09 6,345 2.77 CI-23 230 1,500 40 250 230.08 42.37 1,527 238 1,408 34.52 29.58 32.05 251 227.9 236.25 2.00 697 o.69 2,500 1.62 230.14 42.42 1,523 236 1,405 34.12 29.62 31.87 252 228.7 236.25 1.98 707 o69 2,495 1.62 CI-24 230 1,500 20 450 229.94 42.26 1,540 439 1,320 28.03 21.17 24.60 445 412.8 239.95 1.53 622 0.66 2,450 1.57 229.77 42.13 1,545 440 1,325 27.95 20.96 24.46 443 411.0 239.75 1.52 620 0.66 2,460 157 CI-26 230 6,000 20 250 230.15 42.43 5,880 243 5,766 21.55 20.53 214 37 215.6 234.62 1.30 878 o67 10,540 1.58 230.11 42.40 5,950 245 5,827 21.55 20.57 21.06 244 222.2 234.72 1.30 858 0.67 10,650 1.58 CI-29 230 6,000 40450 230.23 42.49 6,107 438 5,888 31.52 29.44 30.48 457 424.7 239.46 l.90 740 0.70 10,300 1.62 230.24 42.50 6,015 443 5,793 31.55 29.36 30.46 456 423.7 239.35 1.90 750 0.70 10,120 1.62 CI-30 150 1,500 40 450 150.27 7.62 1,515 472 1,279 55.20 38.38 46.79 454 459.3 166.08 2.26 432 1.17 1,339 2.87 150.27 7.62 1,519 471 1,284 55.20 38.38 46.79 458 464.1 166.04 2.26 438 1.17 1,344 2.87 CI-32 150 6,000 40 250 150.06 7.58 6,244 258 6,115 34.57 33.36 33.97 256 256.5 158.22 1.60 500 1.15 6,510 2.88 149.95 7.56 6,180 256 6,052 34.58 33.20 33.89 256 256.3 158.18 1.60 495 1.15 6,450 2.88

-123 -2-i. Tubes, CI Series, Zero Feed Superheat (Cont'd.) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32) (33) hf/o Bufe/ 3 AP Pv 4i/B (pv+. tv hf r Atf Atgorr B tm Atstm Atw * - 3tu/ft2-hr-OF in. Hg P in. Hg in. Hg OF B F Btu/ft2-hr-OF OF Btu7ft-hr-OF OF OF Btu/f hr-F 0.319 4,060 2.83 23.4 0.06 7.67 0.12 151.16 153.19 1,295 4.52 5.146 1,089 4.78 0.54 542 0.323 4,130 2.84 24.6 0.05 7.65 0.12 151.06 152.75 1,332 4.33 5.17 1,090 4.71 0.53 554 0.252 4,220 2.88 11.7 0.06 7.66 0.25 151.78 152.95 1,062 5.38 7.00 1,090 4.67 0.53 469 0.252 4,210 2.88 11.7 0.06 7.68 0.25 151.89 153.08 1,060 5.50 7.12 1,097 4.75 0.54 470 0.257 3,980 2.82 11.8 0.02 7.59 0.24 151.37 153.41 1,022 3.09 4.45 1,312 2.14 0.29 478 0.257 3,980 2.82 11.7 0.02 7.62 0.24 151.52 153.56 1,022 2.98 4.34 1,377 1.96 0.28 464 0.207 6,260 3.53 14.9 -0.02 42.39 0.24 230.40 231.82 1,297 2.38 2.65 1,518 1.81 0.28 650 0.207 6,260 3.53 14.9 -0.02 42.35 0.24 230.35 231.77 1,297 2.32 2.59 1,530 1.75 0.28 650 0.321 4,180 2.85 24.4 0.02 7.61 0.12 150.85 151.83 1,340 2.42 3.16 1,293 2.24 0.30 570 0.325 4,180 2.85 25.2 0.03 7.55 0.11 150.48 151.49 1,359 2.72 3.47 1,243 2.64 0.34 572 0.254 6,250 3.52 30.0 -0.01 42.28 0.12 230.11 231.45 1,588 3.36 3.49 1,276 3.72 0.49 696 0.253 6,270 3.53 29.7 -0.01 42.35 0.12 230.20 231.54 1,587 3.32 3.46 1,280 3.66 0.48 692 0.213 5,980 3.45 15.0 -0.01 42.23 0.23 230.19 233.11 1,272 3.26 3.54 1,388 2.67 0.38 630 0.213 5,980 3.45 14.9 -0.01 42.21 0.23 230.18 233.04 1,272 3.35 3.64 1,373 2.76 0.39 627 0.269 5,980 3.44 31.9 -0.01 42.24 0.11 230.05 232.52 1,609 1.77 1.90 1,557 1.63 0.26 751 0.269 5,980 3.44 32.0 -0.01 42.35 0.11 230.19 232.72 1,609 1.77 1.93 1,558 1.63 0.26 746 0.255 4,200 2.86 12.2 0.02 7.57 0.23 151.21 152.27 1,070 3.09 4.40 1,287 2.29 0.30 472 0.255 4,200.86 12.1 0.02 7.59 0.211 151.37 152.44 1.070 3.10 4.47 1,287 2.30 0.31 469 0.325 4,240 2.87 25.6 0.07 7.70 0.11 151.26 152.23 1,379 4.62 5.56 1,056 5.38 0.59 552 0.318 4,230 2.87 24.3 0.06 7.68 0.12 151.21 152.21 1,344 4.29 5.23 1,088 4.72 0.53 550 0.210 6,130 3.47 15.0 -0.01 42.36 0.23 230.35 232.35 1,288 2.26 2.53 1,51 1.68 0.27 650 0.210 6,130 3.47 15.0 -.o01 42.41 0.23 230.41 232.39 1,288 2.27 2.54 1,541 1.69 0.27 650 0.207 6,310 3.54 15.0 -o.ol 42.25 0.24 230.23 231.76 1,308 4.03 4.32 1,280 3.67 0.49 622 0.207 6,310 3.54 15.0 -o.ol 42.12 0.24 230.06 231.58 1,308 4.01 4.30 1,283 3.65 0.48 623 0.261 6,260 3.52 33.2 -0.01 42.42 0.11 230.28 231.58 1,635 1.68 1.81 1,570 1.56 0.25 760 0.262 6,260 3.52 33.5 -0.01 42.39 0.11 230.24 231.54 1,641 1.73 1.86 1,557 1.63 0.26 757 0.264 6,120 3.47 32.0 -0.01 42.48 0.11 230.35 232.25 1,617 3.35 3.47 1,274 3.79 0.50 699 0.263 6,120 3.47 31.7 -0.01 42.19 0.11 230.36 232.26 1,610 3.36 3.48 1,274 3.78 0.50 697 0.253 4,o80 2.83 11.4 o.o6 7.68 0.25 151.89 154.15 1,032 5.67 7.29 1,092 4.78 0.54 464 0.253 4,080 2.83 11.4 0.06 7.68 0.25 151.89 154.15 1,032 5.74 7.36 1,092 4.83 0.55 465 0.326 4,o80 2.80 24.7 0.02 7.60 o.11 150.74 152.34 1,330 2.46 3.14 1,062 2.75 0.30 530 0.325 14,o8 2.80 24.5 0.02 7.58 0o.1 150.64 152.24 1,326 2.47 3.16 1,062 2.75 0.30 528

-124 -2-in. Tubes, CI Series, 206 F Feed Superheat Run No. VH sat. VH press. Feed rate Vapor rate BD Cl Feed C1 Ave. Cl;Feed super- Stm. rate Q x 10-3 Stm. sat. toAa BER ^ temp. 8 F in. Sg lb/hr lb/hr t heat bF lb/hr Btu/hr temp. F CF ~F corr Btu/ft2-hr-6F CI- 3 230 6,000 20 20 250 930.15 42.43 5,983 369 22.27 20220. 59 202 242 219.6 235.27 5.12 1.34 3.78 741 229.97 42.28 6,040 374 22.08 20.55 21.32 20.0 245 222*1 235.16 5.19 1.32 3.87 733 CI- 7 150 1,500 40 20 450 149.74 7.52 1,531 476 43.05 29.68 36.37 21.9 440 441.5 164.83 15.09 1.73 13.36 422 CI- 9 230 1,500 20 20 450 229.89 42.22 1,437 477 30.23 20.57 25.40 18.6 450 420.3 240.49 10.60 1.59 9,01 596 229.86 42.20 1,552 465 30.10 20.84 25.47 21.3 443 411.0 240.15 10.29 1.59 8.70 604 CI-10 230 1,500 40 20 250 230.40 42.63 1,460 240 39.83 33.80 36.82 16.0 '250 227.2 237.45 7.05 2.31 4.74 612 230.59 42.78 1,453 256 39.10 33.08 36.09 19.3 252 225.8 237.65 7.06 2.26 4-" 600 CI-11 150 6,000- 40 20 250 150.22 7.61 6,029 364 33.54 31.39 32.47 18.0 254 254.9 158.54 8.32 1.53 6.79 480 CI-12 230 6,00 40 20 450 229.80 42.15 5,763 589 35.42 31.83 33.63 22.6 455 423.3 240.30 10.50 2.12 8.38 645 229.91 42.24 5,725 565 35.17 31.88 33.53 18.2 463 430.7 240.51 10.60 2.11 8.49 649 CI-13 150 6,000 20 20 450 150.32 7.63 5,880 535 22.37 20.38 21.38 23.4 386 390.5 161.99 11.67 1.01 10.66 468 150.27 7.62 5,908 536 22.31 20.36 21.34 24.2 386 390.2 161.91 11.64 1.01 10.63 468 CI-15 150 1,500 20 20 -250 149.68 7.51 1,587 295 24.35 20.30 22.33 21.5 267 264.5 158.94 9.26 1.05 8.21 412 149.90 7.55 1,601 321 24.35 20.30 22.33 26.6 280 279.3 159.38 9.48 1.05 8.43 423 01-17 230 1,500 20 20 250 229.73 42.10 1,421 262 24.71 20.41 22.56 19.4 244 221.5 235.95 6.22 1.40 4.82 586 229.73 42.10 1,424 259 24.74 20.38 22.56 19.3 241 218.9 235.84 6.11 1.40 4.71 594 CI-19 230 1,500 40 20 450 229.96 42.28 1,518 485 40.50 27.56 34.03 19.2 457 423.5 241.29 11.33 2.15 9.18 589 229.90 42.23 1,528 493 39.31 26.50 32.92 19.2 459 426.1 241.30 11.40 2.09 9.31 585 CI-20 150 1,500 40 20 250 150.01 7.57 1,586 289 38.55 32.01 35.28 17.6 254 253.9 158.94 8.93 1.67 7.26 446 150.32 7.63 1,553 286 36.73 31.55 34.14 -17.9 254 253.7 159.47 9.15 1.61 7.54 430 CI-22 150 1,500 20 20 450 150.22 7.61 1,556 514 32.81 22.31 27.56 15.7 478 481.9 165.46 15.24 1.32 13.92 442 150.11 7.59 1,570 510 32.81 22.32 27.57 16.8 475 478.1 165.30 15.19 1.32 13.87 440 01-25 230 6,000 20 20 450 230.30 42.55 6,049 551 22.58 20.87 21.73 19.6 438 407.5 239.06 8.76 1.35 7.41 702 230.24 42.50 5,973 545 22.97 20.83 21.90 19.8 437 406.6 239.04 8.80 1.36 7.44 699 CI-27 150 6,000 20 20 250 149.73 7.52 6,265 418 22.10 20.36 21.23 20.9 282 283.8 158.31 8.58 1.00 7.58 478 149.41 7.46 6,257 395 22.10 20.36 21.23 21.5 257 257.9 157.22 7.8 l.0O 6.81 483 CI-28 230 6,000 40 20 250 230.48 42.69 6,022 352 34.07 32.47 33.27 19.9 244 222.4 236.74 6.26 2.08 4.18 680 230.49 42.70 5,995 346 34.00 31.96 32.98 19.0 243 220.3 236.60 6.11 2.06 4.05 695 CI-31 150 6,000 40 20 450 150.16 7.60 6,250 550 38.45 35.18 36.82 20.6 444 449.4 164.08 13.92 1.76 12.16 471 150.00 7.57 6,251 551 38.45 35.18 36.82 20.9 442 447.4 163.95 13.95 1.76 12.19 469

APPENDIX B EXPERIMENTAL DATA AND CALCULATIONS, COLUMNS 1-14 THEORETICAL PREDICTIONS, COLUMNS 15-33 RUNS LWCJ-1 TO LWCJ-16 -125 -

2-In. Tubes, CJ Series, Zero Peed Superheat (' (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20). 21) (22) (23) (24) ( (35) (26) (27) (28) (29) (30) (31) (32) (34) Run No. H Sat. VH press. Feedrate Vapor rate Ave.lov BD CI Feed ClAve. C Steam rate Qxlo-3 sto. tat. BPR Uy 4 e//B f0p^+) t ht-t At7tm At 100 0i.Hg 21/hr 1/11 11/12 315 11/12 Btu/321tem.0 07 B/72- /1-1t Btu/-hr- n.g \ in. Hg in..Hg in. B Btu/t2-hr- O CJ- 1 150 3,000 20.450 150.22 7.61 2,998 426 2,785 23.46 20.09 21.78 1404 407.4 162.65 1.03 456 1.08 3,160 2.75 0.280 420 2.88 16.8 o.05o 7.66 0.17 151.37 152.40 1,188 4.38 5.53 1,123 4.13 0.48 513 150.32 7.63 3,014 434 2,797 23.46 20.09 21.78 405 411.2 162.69 1.03 463 1.08 3,170 2.75 0.280 4,240 2.88 16.8 0.05 7.68 0.17 151.47 152.50 1,188 4.42 5.57 1,121 4.18 0.48 513 CJ- 3 175 3,000 20 450 174.90 13.64 3,017 467 8,783 23.83 20.17 22.00 453 625.2 186.78 1.14 530 0.92 3,710 2.27 0.262 4,840 3.12 18.2 0.03 13.67 0.17 175.54 176.68 1,268 4.49 5.13 1,153 4.39 0.52 566 175.07 13.69 2,986 460 2,756 23.83 20.17 22.00 451 443.5 187.01 1.14 524 0.92 3,670 2.27 0.262 4,840 3.12 18.1 0.03 13.72 0.17 175.70 176.84 1,268 4.47 5.10 1,154 4.37 0.52 566 CJ- 5 200 1,500 20 450 200.23 23.58 1,522 432 1,306 26.29 19.48 22.89 428 409.7 211.40 1.29 530 0-79 2,024 1.89 0.221 5,500 3.33 13.6 0.01 23.59 0.24 200.74 202.03 1,216 4.30 4.81 1,238 3.76 0.48 578 CJ- 7 175 6,000 20 450 174.67 13.57 5,894 475 5,656 22.03 20.27 21.15 457 451.2 185.80 1.09 574 0.92 7,540 2.28 0.298 4,840 3.11 26.8 0.03 13.60 0.12 175.16 176.25 1,442 4.00 4.49 1,147 4.48 0.53 607 CJ- 9 200 6,oo000o 20 450 199.69 23.32 6,014 457 5,786 21.86 20.20 21.04 446 427.1 209.18 1.18 656 0.80 8,850 1.91 0.281 5,460 3.31 29.4 0.01 23.33 0.11 199.94 201.12 1,534 3.56 3.81 1,216 4.00 0.50 656 cJ-11 175 1,500 20 450 175.03 13.68 1,509 457 1,281 27.32 19.31 23.32 452 445.7 187.84 1.21 491 0.91 1,726 2.27 0.236 4,860 3.13 12.8 0.03 13.71 0.24 175.89 177.10 1,148 4.96 5.82 1,155 4.40 0.53 530 CJ-13 230 3,000 20 450 230.08 42.37 2,982 435 2,765 22.99 19.54 21.27 435 403.8 239.36 1.32 647 0.67 5,050 1.57 0.228 6,3o00 3.54 21.4 -0.01 42.36 0.17- 230.28 231.60 1,437 3.58 3.78 1,289 3.56 0.48 659 230.05 42.35 2,950 430 2,735 22.99 19.54 21.27 434 403.5 239.48 1.32 635 0.67 5,000 1.57 0.228 6,300 3.54 21.3 -0.01 42.34 0.17 230.25 231.57 1,437 3.58 3.78 1,290 3.56 0.48 659 J-15 200 3,000 20 450 200.27 23.6 3,018 442 2,797 23.27 19.55 21.41 446 426.5 210.95 1.22 576 0.79 4,30 1.89 0.246 5,500 3.32 19.8 0.01 23.61 0.17 200.63 201.85 1,353.02 4.38 1,221 3.98 0.50 615

2-in. Tubes, CJ Series, 208 F Superheat Run No. VH sat. VH press. Feed rate Vapor rate BD C1 Feed C1 Ave. C1 Feed super- Stm. rate Q x 103 Stm. sat. tOApp BPB tOAo Ut r temp. ~F in. Hg lb/hr lb/hr heat F lb/hr Btu/hr temp. ~F F F F corr Btuft CJ- 2 150 3,000 20 20 450 150.16 7.60 2,992 476 23.66 20.08 21.87 20.9 405 410.3 162.94 12.78 1.04 11.74 446 J- 4 175 3,000 20 20450 174.83 13.62 2,986 510 24.45 20.06 22.26 20.4 451 445.9 187.48 12.65 1.15 11.50 495 CJ- 6 200 1,500 20 20 450 200.17 23.55 1,511 470 28.22 19.47 23.85 18.8 430 411.8 211.46 11.29 1.36 9.93 553 CJ- 8 175 6000 20 20 450 174.60 13.55 5,952 594 22.50 20.38 21.44 20.2 448 441.3 186.39 11.79 1.10 10.69 528 - CJ-10 20 2,000 620 20 450 199.61 23.28 6,104 547 22.42 20.47 21.45 14.6 433 414.8 209.80 10.19 1.22 8.97 591 CJ-12 175 1,500 20 20 450 174.70 13.58 1,523 474 27.52 19.25 23.39 16.8 438 430.9 187.66 12.96 1.21 11.75 469 CJ-14 230 3,000 20 220 450 230.05 42.35 2,939 494 23.14 19.62 21.38 19.6 434 402.8 239.70 9.65 1.33 8.32 618 CJ-16 200 3,000 20 20 450 200.25 23.59 2,969 491 23.55 19.65 21.60 15.9 442 424.0 211.21 10.96 1.23 9.73 557

APPENDIX C EXPERIMENTAL DATA AND CALCULATIONS, COLUMNS 1-14 THEORETICAL PREDICTIONS, COLUMNS 15-33 RUNS LWCK-10 TO LWCK-29 -128 -

2-i2. Tlbe., CK S-ccc-, Occo Z.= Ocd Sp-ol 2 (3 (4) (5) (6) (7) ( (9 (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20),)21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32) (33) f2)c Ic3c 11Ic 11h 11/c 071 cc,c c/c 0ccct(980 1 0c9(lo)clc-c (c )ch(1 '1c c cc 6-/12c79)c.. o(135.)c c fc(8 112 R-Xo. V -t. V3 ss. O e - VtVccc e A- floc D Cl Focdl C.1 A C C1 S — e 0.c. S 31 18 j 8 c, /. J..c c(.c 0 1-. 8 B(Qo3 tMIo28 wo ccrc cB l.c2cc' temp OF in Hg Ib/hr Ib/hr ~ ~ ~~~C~ reb/h.- 41,/h t-mp. 'F 'F B.R DP(t ()h Bt./ft2-h-QoP i.. H9 Y i..irg i.. Ng i.. Ng IF Bt./ft2-hI IF IF tO CK-10 306,ooo 20450 101.14 2.00 5,975 433 5,758 20.35 19.02 19.69 421 45.6 119.30 0.78 32 1.58 4,450 4.22 0.364 3,155 2.38 20.0 0.19 2.19 0.12 106.00 106.78 1,148 4.96 9.82 950 5-34 0.52 363 100.64 1.97 5,966 426 5,75 20.35 19 1969 19 442.7 118.77 0.78 326 1.59 4,440 4.24 0.364 3,145 2.37 20.0 0.19 2.16 0.12 105.55 106.33 1,145 4.94 9.85 953 5-29 0.52 361 CK-12 100 3,000 2 450 100.30 1.95 2,992 513 2,735 23.08 19.36 2122 446 474.2 120.66 0.85 310 1.58 2,120 4.22 0.315 3,155 2.38 14.0 0.26 2.21 0.17 107.02 107.87 994 6.05 12.1 935 5.77 0.56 6 100c81.98 3,027 519 2,772 23.24 19.59 21.42 447 474.8 120.66 0.85 319 1.58 2,150 4.22 0.315 3,155 2.38 14.0 0.26 2.24 0.17 107.45 108.30 994 6.10 12.76 935 5.78 0.56 318 CK-15 0 3,000 20 25 ccc.8c 1.92 3,007 235 2,879 2.63 19.80 20.72 242 256.9 111.08 0.82 320 1.64 2,150 4.40 0.322 3,060 2.33 14.0 0.07 2.05 0.17 104.65 105.47 986 3.33 7.17 1,107 2.64 0.30 324 101.31 2.01 3,013 5 2,886 21.73 19.64 20.51 243 258.0 112.01 0.81 333 1.64 2,l6 4.40 0.322 3,o6o 2.33 14.0 0.07 2.08 0.17 105.12 105.92 986 3.34 7.14 1,108 2.65 0. 327 CK-16 100 6,000 20 250 99.63 1.00 5,965 250 5,840 19.91 19.15 19.53 246 261.8 110.19 0.76 334 1.67 4,270 4.49 0.370 3,030 2.31 g.6 0.07 1.97 0.12 102.62 103.38 1,121 2.98 6.17 1,090 2.73 0.31 363 99.61 1.91 5,959 251 5,833 20.00 19.18 199 59 246 261.5 110.32 0.76 323 1.67 41270 4.49 0.370 3,030 2.32 19.6 0.07 1.98 0.12 102.78 103.54 1,121 2.98 6.15 1,090 2.73 0.31 63 CK-18 100 1,500 208 100.81 1.99 1,536 258 1,407 26.67 00.68 22.58 251 266.5 112.38 0.89 319 1.64 1,050 4.40 0.289 3,060 2.33 10.4 0.07 2.05 0.22 105.41 106.30 884 3.86 8.46 1,098 2.76 0.31 295 100.13 1.96 1,695 256 1,367 26.07 19.82 21.94 248 262.4 11.88 0.87 308 1.65 1,015 4.42 0.288 3,050 2.33 10.1 0.07 2.01 0.23 104.96 105.83 879 3.82 8.65 1,098 2.72 0.31 287 CK-19 100 1,500 20 450 122.47 9.96 1,583 679 1,063 28.05 19.35 23.72 450 476.9 121.38 0.96 306 1.59 973 4.25 0.282 3,140 2.38 9.9 0.23 2.19 0.24 107.73 108.69 887 6.87 14.13 938 5.79 0.6 297 2ool.3 1.94 1,523 473 1,286 2759 19.0 23.40 453 478.8 121.17 0.94 304 1.59 990 4.24 0.282 3,140 2.39 10.0 0.23 2.17 0.24 107.45 108.39 885 6.91 14.23 935 5.83 0.56 296 CK-22 125 1,500 206 50 126.69 3.92 1,499 478,26o 29.461 20.3 24.77 450 469.1 141.68 1.07 376 1.32 1,170 3.43 0.268 3,650 2.64 10.7 0.12 4.04 0.25 128.01 129.08 979 6.11 9.44 1,014 5.26 0.55 392 123.52 4.01 1,487 475 1,254 9.25 20.00 24.63 444 461.5 12.56 1.08 370 1.31 1,170 3.39 0.264 3,675 2.65 10.7 0.12 4.13 0.25 128.75 129.86 968 6.10 9.36 1,021 5.14 0.54 392 CK-24 125 3,000 20 450 126.31 3.88 3,833 468 2,799 83.78 20.11 21.95 651 670.8 140.45 8.95 393 1.32 2,600 3.63 0.298 3,640 2.63 15.4 0.11 3.09, 8.17 126.97 127.02 1,086 5,55 8.11 1,089 5.31 0.55 631 120. 3.09 97 466 2,065 23.06 20.12 21.99 454 474.1 140.12 8.95 410 1.32 2,66 3.45 0.299 3,635 2.62 15.5 03.1 4.00 0.17 126.96 127.91 1,08T 557 8.13 1,003 537 0.56 6 CK-26 125 6,08 20 450 124.77 3.93 5,928 464 5,606 01.37 19.76 20.66 651 671.2 139.66 0.90 463 1.31 5,328 3.44 0.341 3,640 2.62 20.1 8.11 4.04 0.12 126.97.27.77 1,21 4.85 6.95 1,007 5.34 0.55 69 126.68 3.92 5,935 468 5,781 21.75 20.99 20.92 653 673.1 139.79 8.91 625 1.31 5.331 3.44 0.341 3,668 2.62 22.1 0.12 4.03 0.12 126.78 127.69 1,261 4.07 6.97 1,085 5.35 0.56 669

2-in Tubes, CK Series, 200 F Feed Superheat - Experimental Data and Calculations Run No. VH sat. VH press. Feed rate Vapor rate BD C1 Feed C1 Ave. C1 Feed super- Stm. rate Q x 10-3 Stm. sat. toAaP BPR AcoA UV 2 temp. OF in. Hg lb/hr lb/hr heat OF lb/hr Btu/hr temp. oF OF OF OF Btu/hr-ft -OF CK-11 100 6,000 20 20 450 99.61 1.91 5,997 593 21.08 19.07 20.08 20.5 433 457.9 123.97 24.36 0.84 23.52 248 100.80 1.98 5,996 593 21.21 19.12 20.17 18.5 454 478.7 125.06 24.26 0.84 23.42 260 CK-13 100 3,000 20 20 450 99.96 1.93 2,997 489 23.57 19.62 21.60 22.5 409 435.6 120.35 20.39 0.88 19.51 285 99.43 1.90 2,981 482 23.70 19.88 21.79 22.1 414 441.0 119.52 20.09 0.89 19.20 294 CK-14 100 3,000 20 20 250 100.13 1.94 3,004 330 21.47 19.10 20.29 22.2 253 269.2 112.63 12.50 0.82 11.68 294 99.96 1.93 3,020 340 21.29 19.02 20.16 22.0 252 268.3 112.51 12.55 0.81 11.74 292 CK-17 100 6,000 20 20 250 99.96 1.93 6,015 355 20.64 19.43 20.04 19.3 246 260.2 112.13 12.17 0.80 11.37 292 99.78 1.92 6,091 368 20.40 19.23 19.82 20.7 244 257.7 111.88 12.10 0.79 11.31 290 CK-20 100 1,500 20 20 450 100.13 1.94 1,537 502 28.90 19.17 24.04 20.5 453 479.3 121.27 21.14 0.99 20.15 304 100.13 1.94 1,538 501 28.94 19.31 24.13 19.2 446 471.7 120.97 20.84 0.99 19.85 304 O0 CK-21 100 1,500 20 20 250 99.43 1.90 1,488 299 24.59 19.44 22.02 17.5 268 285.2 111.37 11.94 0.88 11.06 329 99.43 1.90 1,415 290 24.44 19.44 21.94 20.7 261 276.3 110.85 11.42 0.87 10.55 335 CK-23 125 1,500 20 20 450 125.61 4.02 1,498 492 29.86 20.03 24.95 18.6 455 473.4 142.56 16.95 1.10 15.85 381 125.52 4.01 1,482 498 30.92 20.61 25.77 18.2 447 464.6 142.37 16.85 1.15 15.70 378 CK-25 125 3,000 20 20 450 124.87 3.94 3,007 537 23.97 20.09 22.03 20.7 446 464.6 141.10 16.23 0.98 15.25 389 124.87 3.94 3,024 537 24.67 20.43 22.55 20.7 450 469.5 141.17 16.30 1.00 15.30 392 CK-27 125 6,000 20 20 450 124.49 3.90 5,941 585 21.60 19.48 20.54 21.1 449 468.4 140.91 16.42 0.92 15.50 386 124.59 3.91 6,043 584 20.77 18.71 19.74 21.0 448 467.4 140.78 16.19 0.88 15.31 390 CK-28 100 6,000 40 20 250 99.96 1.93 6,190 360 35.53 33.43 34.48 19.3 248 262.7 112.38 12.42 1.38 11.04 304 99.78 1.92 6,165 365 35.30 33.63 34.47 20.0 246 260.4 112.51 12.73 1.38 11.35 293 CK-29 100 1,500 40 20 250 100.64 1.97 1,532 279 38.50 31.34 34.92 18.9 245 260.2 112.26 11.62 1.40 10.22 325 101.14 2.00 1,523 271 38.47 32.05 35.26 18.2 241 255.6 112.65 11.51 1.42 10.09 324

APPENDIX D EXPERIMENTAL DATA AND CALCULATIONS, COLUMNS 1-14 THEORETICAL PREDICTIONS, COLUMNS 15-33 RUNS LWDA-2 TO LWDA-38 -1351 -

-132 -1-in. Tubes, Series DA, Zero Feed Superheat (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) () ( (13) (14) (15) (16) (17) Run No. VH sat. VH press. Feed rate Vapor rate Ave. flow BD Cl Feed C1 Ave. Cl Steam rate Qx-103 Stm. sat. BPR UVH 1 (Re) (Pr) temp.0 F in. Hg lb/hr lb/hr lb/hr L af I P # lb/hr Btu/hr temp. ~F OF Btu/ft2-hr-~F lb/hr-ft DA- 2 100 1,500 20 250 99.96 1.93 1,511 245 1,388 22.75 21.13 21.94 239 246.6 138.58 0.94 171 1.35 2,580 3.51 99.96 1.93 1,491 243 1,369 23.02 21.73 22.37 246 254.5 139.46 0.96 173 1.34 2,561 3.50 DA- 4 100 3,000 20 250 99.61 1.91 3,042 248 2,918 21.03 19.32 20.18 246 251.9 141.17 0.87 162 1.31 5,590 3.40 99.43 1.90 3,071 248 2,947 20.83 19.23 20.03 247 252.7 140.91 0.87 162 1.31 5,650 3.41 DA- 6 125 3,000 20 250 124.96 3.95 3,038 252 2,912 21.28 19.45 20.37 255 256.5 154.97 0.93 230 1.18 6,190 2.97 124.96 3.95 3,039 251 2,914 21.22 19.48 20.35 257 258.9 155.06 0.93 232 1.18 6,200 2.97 DA- 8 125 1,500 20 250 125.24 3.98 1,4a1 257 1,356 23.68 19.59 21.64 269 273.5 152.50 0.97 272 1.21 2,813 3.09 124.87 3.94 1,528 258 1,398 23.91 19.91 21.91 260 263.9 152.19 0.99 262 1.21 2,900 3.09 DA-10 150 1,500 20 250 149.90 7.55 1,573 252 1,447 21.92 18.41 20.17 261 257.4 168.23 0.97 387 1.05 3,459 2.65 149.95 7.56 1,535 252 1,409 22.26 18.66 20.46 252 248.6 168.33 0.99 374 1.05 3,362 2.65 DA-12 150 3,000 20 250 149.57 7.49 3,000 262 2,869 22.46 20.63 21.55 252 248.2 171.02 1.05 318 1.03 7,000 2.58 149.79 7.53 3,022 258 2,893 21.19 19.45 20.32 250 246.7 170.88 0.99 320 1.02 7,110 2.58 DA-14 175 1,500 20 250 175.67 13.83 1,508 232 1,392 24.52 20.47 22.50 249 241.2 189.27 1.17 506 0.91 3,840 2.24 175.29 13.76 1,550 235 1,434 24.83 20.74 22.79 243 234.6 189.17 1.19 483 0.91 3,960 2.24 DA-16 175 3,000 20 250 175.83 13.93 3,002 230 2,887 22.50 20.81 21.66 258 249.2 192.20 1.13 427 0.89 8,140 2.19 177.49 14.46 2,991 239 2,871 22.39 20.81 21.60 261 252.0 193.44 1.14 444 0.88 8,190 2.17 DA-18 200 3,000 20 250 200.92 23.92 2,965 227 2,846 22.60 20.99 21.80 237 222.2 212.99 1.25 535 0.78 9,160 1.87 200.17 23.55 2,942 216 2,824 23.14 21.71 22.43 236 219.2 212.38 1.28 523 0.78 9,090 1.87 DA-19 200 1,500 20 250 199.67 23.31 1,467 228 1,341 25.24 21.37 23.31 251 236.4 210.85 1.32 626 0.80 4,210 1.91 200.15 23.54 1,505 254 1,379 25.76 21.58 23.67 251 236.1 211.36 1.34 625 0.80 4,325 1.90 DA-22 230 1,500 20 250 DA-23 230 1500 20 150 229.77 42.13 1,4531 134 1, 386 22.39 20.34 21.37 151 133.2 236.32 1.32 665 0.67 5,195 1.57 1D 4.67 5,12~20 1.2505 22299 772 42 13 53 ~~4~ 2430 1,386 22395 199 0 53 639 230.03 42.33 1,431 125 1,368 23.25 21.31 22.28 144 126.6 23658 1.3820 DA-24 230 3,000 20 50 229.84 42.18 3,000 238 2,881 22.75 21.13 22.07 255 232.1 240.54 1.37 650 0.66 10,980 1.56 229.82 42.17 3,049 230 2,934 23.02 21.37 22.20 248 224.6 240.43 1.38 636 0.66 11,150 1.56 DA-25 230 3,000 20 150 229.89 42.22 3,039 128 2,974 22.48 21.53 22.01 146 127.5 236.87 1.36 592 0.67 11,120 1.57 229.93 42.25 2,995 128 2,931 22.80 21.71 22.26 145 126.5 236.76 1.38 606 0.67 10,990 1.57 DA-30 150 3,000 20 150 149.30 7.44 2,967 181 2,876 21.56 20.45 21.01 187 185.3 164.27 1.00 346 1.06 6,800 2.68 149.09 7.40 2,973 184 2,881 21.71 20.45 21.08 192 190.2 164.15 1.00 354 1.o6 6,820 2.68 DA-33 150 1,500 20 150 149.73 7.52 1,464 140 1,394 23.00 20.81 21.91 155 150.8 160.98 1.04 385 1.08 3,240 2.74 149.73 7.52 1,429 142 1,358 23.14 20.92 22.03 162 157.5 161.15 1.o4 396 1.08 3,155 2.74 DA-34 100 1,500 20 150 100.97 1.99 1,463 157 1,384 20.80 18.70 19.75 156 159.6 123.35 0.81 193 1.48 2,348 3.94 99.96 1.93 1,500 153 1,423 20.77 18.69 19.73 158 162.6 12316.8 189 1.48 2,418 3.94 DA-37 100 3,000 20 150 9.26 1,89 3,0o6 167 2,932 20.04 19.11 19.58 169 174.3 125.97 0.80 176 1.45 5,070 3.83 98.91 1.87 3,042.66 2,959 20.04 19.13 19.58 173 178.6 126.06 0.80 177 1.45 5,120 3.83

-133 -l-in. Tubes, Series DA, Zero Feed Superheat (Cont'd.) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32) (33) hf/ X)13 P Pv 40/B f(pv4) tv f f or hf tr hu Attm tw UVH Btu/ft2-hr-~F in. Hg in.Hg in. Hg in. F B F Btu/ft2-hr-HF ~F F tuft-hr-F F F Btu/ft2hr B'2/ HOF B OF Btu/ft2-hr OF 0.301 3,590 2.60 15.3 1.90 3.83 0.17 125.43 126.37 1,080 5.96 31.43 982 5.71 0.34 172 0.301 3,610 2.61 15.2 1.90 3.83 0.17 125.43 126.39 1,087 6.12 31.59 975 5.94 0.35 175 0.342 3,670 2.63 22.7 2.50 4.41 0.12 130.04 130.91 1,255 5.24 35.67 983 5.83 0.34 157 0.343 3,670 2.63 22.8 2.50 4.40 0.12 129.96 130.83 1,260 5.24 35.77 981 5.85 0.34 158 0.327 4,020 2.79 24.0 2.16 6.11 0.12 142.25 143.18 1,315 5.10 22.39 1,017 5.63 0.36 236 0.327 4,020 2.79 24.0 2.16 6.11 0.12 142.25 143.18 1,315 5.14 22.43 1,013 5.66 0.36 238 0.289 3,920 2.75 16.0 1.59 5.57 0.17 139.06 140.03 1,131 6.30 20.12 991 6.27 0.38 267 0.290 3,920 2.75 16.1 1.59 5.53 0.17 138.78 139.77 1,137 6.05 19.96 1,001 5.98 0.37 262 0.279 4,340 2.92 17.6 1.11 8.66 0.17 156.29 157.26 1,210 5.55 11.94 1,047 5.59 0.36 376 0.278 4,360 2.93 17.3 1.11 8.67 0.17 156.34 157.33 1,212 5.35 11.74 1,060 5.34 0.35 372 0.315 4,460 2.96 25.9 1.77 9.26 0.11 158.76 159.81 1,405 4.61 13.80 1,068 5.29 0.35 334 0.315 4,450 2.96 26.0 1.75 9.28 0.11 158.85 159.84 1,402 4.60 13.66 1,070 5.25 0.34 335 0.262 4,890 3.14 18.5 0.85 14.73 0.17 178.83 180.00 1,280 4.92 8.08 1,120 4.89 0.34 473 0.264 4,890 3.14 18.8 0.85 14.61 0.17 178.47 179.66 1,290 4.75 7.93 1,129 4.73 jJ 472 0.296 4,980 3.16 28.3 1.45 15.38 0.11 180.58 181.71 1,474 4.41 9.16 1,112 5.09 0.35 445 0.297 5,000 3.17 28.4 1.47 15.93 0.11 102.33 183.47 1,485 4.43 9.27 1,112 5.15 0.35 446 0.280 5,520 3.34 30.0 0.74 24.66 0.11 202.62 203.87 1,546 3.76 5.46 1,198 4.22 0.31 581 0.279 5,510 3.33 29.9 0.73 24.28 0.11 201.87 203.15 1,539 3.72 5.42 1,197 4.16 0.30 578 0.247 5,4 0 3.31 19.2 0.14 23.45 0.17 200.31 201.63 1,349 4.58 5.22 1,171 4.59 0.33 609 0.247 5,470 3.32 19.3 0.17 23.71 0.17 200.84 202.18 1,351 4.56 5.25 1,172 4.58 0.33 607 1,448 3.89 4.19 1,250 3.92 0.30 670 0.231 6,260 3.53 21.7 0.08 42.28 o.16 230.16 231.49 1,448 3.77 4.08 1,263 3.76 0.29 672 0.231 6,260 3.53 21.6 0.08 42.23 0.16 230.10 231.42 1,439 2.42 2.65 1,451 2.08 0.19 707 0.229 6,280 3.53 21.7 0.02 42.15 0.16 230.00 231.32 1,439 2.30 2.52 1,461 1.97 0.18 707 0.229 6,280 3.53 21.6 0.02 42.35 0.16 230.25 231.63 1,649 3.68 3.92 1,223 4.31 0.32 709 0.261 6,310 3.54 33.1 0.08 42.26 0.11 230.08 231.45 1,654 3.55 3.78 1,237 4.13 0.31 715 0.262 6,310 3.54 33.2 0.07 42.24 0.11 230.05 231.43 1,652 2.02 2.18 1,469 1.97 0.18 770 0.263 6,290 3.54 33.2 0.02 42.24 0.11 230.05 231.41 1,648 2.00 2.16 1,470 1.96 o.18 768 0.262 6,290 3.54 33.1 0.02 42.27 0.11 230.09 231.47 1,233 3.92 6.04 1,158 3.64 0.26 487 0.286 4,310 2.91 25.4 0.29 7.73 0.11 151.42 152.42 1,238 4.01 6.24.,148 3.77 0.26 484 0.287 4,310 2.91 25.4 0.31 7.71 0.11 151.32 152.32 1,083 3.63 5.42 1,220 2.81 0.21 467 0.255 4,250 2.89 17.0 0.17 7.69 0.17 151.52 152.56 1,080 3.80 5.65 1,205 2.97 0.22 465 0.254 4,250 2.89 17.0 0.18 7.70 0.17 151.58 152.62 1,036 4.02 17.28 1,070 3.39 0.22 199 0.312 3,320 2.46 14.7 0.77 2.76 0.17 114.23 115.04 1,036 4.09 17.51 1,064 3.46 0.23 200 0.313 3,310 2.46 14.8 0.76 2.69 0.17 113.38 114.19 1,200 3.80 18.77 1,048 3.78 0.24 200 0.356 3,370 2.49 21.5 0.92 2.81 0.12 1].4.23 115.03 1,203 3.87 18.83 1,041 3.90 0.25 203 0.357 3,370 2.49 21.6 0.91 2.78 0.12 113.87 114.67

-134 -1-in. Tubes, DA Series, 206 F Feed superheat Run No. VH Lat. VH press. Feed rate Vapor rate BD C1 Feed Cl Ave. C1 Feed super- Stm. rate Q x 103 Stm. sat..AtoA BFR AtoA. 7M temp. OF in. Hg lb/hr b/hr aPL. p heat eF lb/hr Btu/hr' temp. OF OF OF Or DA- 3 100 1,500 20 20 250 99.61 1.91 1,520 268 22.73 19.02 20.88 19.9 244 249.5 143.00 43.39 0.93 42.46 153 99.78 1.92 1,554 268 22.98 19.09 21.04 19.3 237 242.7 142.44 42.66 0.93 41.73 152 DA- 5 100 3,000 20 20 250 98.91 1.87 3,012 335 21.72 19.38 20.55 22.4 256 259.2 150.43 50.52 0.95 49.57 131. 99.43 1.90 3,000 316 21.53 19.46 20.50 20.7 250 253.5 149.57 50.14 0.95 49.19 135 DA- 7 125 3,000 20 20 250 124.96 3.95 3,099 306 21.62 19.48 20.55 17.4 256 255.0 161.15 36.19 0.98 35.21 189 124.96 3.95 3,064 309 21.69 19.54 20.62 18.2 260 259.1 161.40 36.44 0.98 35.46 191 DA- 9 125 1,500 20 20 250 124.96 3.95 1,549 280 24.08 19.72 21.90 19.3 256 258.3 154.24 29.28 1.02 28.26 239 125.06 3.96 1,481 280 23.77 19.73 21.75 20.2 268 270.6 154.33 29.27 1.01 28.26 250 DA-11 150 1,500 20 20 250 149.90 7.55 1,547 285 23.07 19.27 21.17 18.5 256 252.4,169.14 19.24 1.04 18.20.362 149.95 7.56 1,493 284 23.73 19.27 21.50 19.3 258 254.3 169.14 19.19 1.05 18.14 366 DA-13 150 3,000 20 20 250 149.79 7.53 3,002 323 21.49 19.11 20.30 20.8 267 262.9 175.13 25.34 1.00 24.34 282 149.79 7.53 3,003 324 21.42 19.07 20.25 21.6 258 255.0 174.73 24.94 1.00 23.94 278 DA-15 175 1,500 20 20 250 175.67 13.88 1,546 282 24.81 20.42 22.62 19.3 255 245.9 190.06 14.39 1.21 13.18 487 175.16 13.72 1,539 281 22.98 18.57 20.73 18.0 258 248.4 189.74 14.58 1.11 13.47 482 DA-17 175 3,000 20 20 250 176.27 14.07 3,118 306 23.14 20.95 22.05 18.0 243 232.9 192.18 15.91 1.19 14.72 413 175.09 13.70 3,065 292 23.16 20.95 22.06 19.2 244 234.5 191.71 16.62 1.19 15.43 397 DA-20 200 1,500 20 20 250 199.92 23.43 1,504 282 26.80 21.99 4.40 19.4 251 235.0 211.45 11.53 1.40 10.13 605 DA-21 200 3,000 20 20 250 202.34 24.63 2,904 286 22.78 20.67 21.73 16.7 250 233.7 214.10 11.76 1.26 10.50 579 202.28 24.60 2,910 274 22.89 20.74 21.82 15.9 248 231.7 214.05 11.77 1.27 10.50 575 20 250 DA-26 230 3,000 20 - 18.9 258 234.5 240.80 10.42 1.37 9.05 677 230.38 42.61 2,962 22.75 20.40 21.58 23.0 260 236.0 241.03 10.55 1.38 9.17 672 230.48 42.69 2,903 301 23.12 20.76 21.94 20 250 DA-27 230 1,500 20 17.9 252 229.0 240.27 10.18 1.44 8.74 685 230.09 42.38 1,518 258 25.69 19.70 22.70 17.2 253 231.1 240.58 10.23 1.48 8.75 689 230.35 42.59 1,502 262 25.76 20.99 23.38 20 150 DA-28 230 1,500 20 ---- 12.0 172 153.5 238.05 7.54 1.47 6.07 660 230.51 42.72 1,531 200 25.13 21.53 23.33 14.7 171 152.4 238.05 7.56 1.45 6.11 651 230.49 42.70 1,520 189 25.10 '20.86 22.98 20 150 DA-29 230 3,000 20 -- 21.4 177 157.4 238.03 7.89 1.35 6.54 629 230.14 42.42 2,994 239 22.23 20.58 21.41 20.8 175 155.7 238.04 7.84 1.42 6.42 633 230.20 42.47 2,989 244 23.32 21.71 22.52 20 150 DA-31 150 3,000 20 22.1 188 185.2 167.22 18.19 1.02 17.17 282 149.03 7.39 2,966 242 21.53 20.02 20.78 22.2 189 185.8 167.40 18.04 1.04 17.00 285 149.36 7.45 2,980 242 22.23 20.54 21.39 20 150 DA-32 150 1,500 20 22.5 189 186.9 163.75 14.50.l10 i3.4o 364 149.25 7.43 1,557 228 24.34 21.01 22.68 22.4 192 190.2 163.67 14.48 1.10 13.38 371 149.19 7.42 1,547 215 24.34 21.03 22.69 20 150 DA-35 100 1,500 20 20.5 160 164.5 127.75 27.45 0.86 26.59 162 100.30 1.95 1,502 191 21.73 18.98 20.36 21.7 163 168.3 128.01 27.88 0.85 27.03 163 100.13 1.94 1,494 189 21.56 18.80 20.18 20 150 DA-36 100 3,000 20 - 18.6 149 152.7 132.37 31.40 0.84 30.56 130 100.97 1.99 3,081 205 20.13 18.98 19.56 19.4 157 161.0 132.68 33.07 0.84 32.23 130 99.61 1.91 3,095 212 20.34 18.85 19.60 20 250 DA-38 100 1,500 40 16.1 217 223.2 139.79 37.99 1.48 36.51 160 101.80 2.04 1,609 233 38.68 32.11 35.40 14.8 212 2225 138.92 3745 1.47 3598 161 101.47 2.02 1,617 229 37.93 32.31 35.12

APPENDIX E GRAPHS USED TO CORRELATE EXPERIMENTAL DATA -135 -

-136 -BOILING POINT RISE OF SEA WATER CONCENTRATES 7 _ ___ oi 66 5 ____ I0 10 20 30 40 50 60 70 80 90 C'HLOROSITY - gpl |, __z_ _ _ _ _ _ _ _-z^^ ^~Graph 1 0 10 20 30 40 50 60 70 80 90 CHLOROSITY - gpl Graph 1

-137 -DUKLE 'S FILM 7HICKiESS CORRELATION 10 I I I I I I I I I I I 1 1/ 10 t Nusselt 4 0 E t I!0 t - - -— 9 a - -- - 9 104-. - - - - - - -- - -- - - - 4, —. - v — --------- -- --- -- (Re) Graph 2 10 10 10 (Re) Graph 2

-138 -DUKLER'S HEAT TRANSFER CORRELATION 1.0.. —.. _ __ 0.9 0.8 0.7 0.6 ~~~ ~~~~~~~~~~~~0.5 0.4 0.3 -- 0.200-0~~~~~~. 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 90 10.0 (Pr) Graph 3

-139 -NUSSELT'S HEAT TRANSFER GROUP FOR SEA WATER CONCENTRATES cl: 6500 20 5500 - _ X t — ---------- 1X --- S 4 0 -~ --- - -- - -- — ~ — — / / - 400 3500 -3000 ---- - 2500 100 120 140 160 180 200 220 240 F//' i t,,F Graph 4 - -~ ~ f l./ --- —_ __ __ _/, L/y ^ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 35 0 - - - 7 -^ - - - - - - - - - - - - Graph 4

-14oVISCOSITY OF SEA WATER CONCENTRATES 2.00 - 1.90 1.80 I. 70 1.60 1.50 1.40 1.30 1.20 - 1.10 1.00 0.90 - 0.8 0 -- -- -- - -- -- -- -- -- I I - C l: 50 0.70 40 24 20 0.60 20 100 120 140 160 180 200 220 240 t,~F Graph 5

PRANDTL NUMBER OF SEA WATER CONCENTRATES 5.5 - (Pr) 5.0 4.0 3.5 3.0 2.5 ~-~ 040 24 3.5 - 20 100 120 140 160 180 200 220 240 t, OF Graph 6 ^E^ EEEEEE\\EE, 30 ===,&^^k^ __________^^v________________ __ __ __ __ __ _ __ __ __ __ ^ s. __ __ _ __ __ __ __ _ __ __ __ __ _ I0012 - 1 4 - 1 0 1 0 0 0 2 0 24 _ _ _ _ _ _ _ _ _ _ _ _ _~~, _ _ __~FS ^ _ _^~~~~~~~~rp 6

-142 -FALLING-FILM BUBBLE SUPERHEAT MAGNITUDE X cl: 3.60 1 20 24 3.50 40 50 3.40 ___ __ 3.30 3.20 3.10, — 3.00. 2.90 -, 2.80 2.70 2.60 2.50 2.40 2.30 2.20 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 t,OF Graph 7

-l43 -DRY-TUBE VAPOR PRESSURE-DROP 1.0 we, 4I I. in. Tu be e I -"A" - LTV Vapor Rte: 250 Ib/hr c _______ ___~_ in._Tubes __ ____ _________ < ~3 LTV ----Feed — — Rates:LTV Feed Rates: Q.~'~~~~~~ ^^::!!;!!;,,5s^~ ^ 3000 Ib/hr O 2 ____ __ __1500 lb/hr __ __ _ =,_ 2 in. TueITube_ s | n C Z z "B LTV Vapor R ate: 150 lb/hr 0 > 8 l = = --- -S LTV Feed Rotes:,._I 7 _ 2 in Tubes _ 600 b/r _ o 9. LT V Feed Ratese ~- 6000 Ib/hr t,~F Graph 8

-144 -STEAM-SIDE HEAT TRANSFER COEFFICIENTS, PILOT PLANT 1600 -- 1500 1400 - >~ - - - - - - 1300 /oCo~ 1200 / J,ooo - -- - > ' -— 10 1000 9 00 800,, 100 120 140 160 180 200 220 240 t ~F stm Graph 9

APPENDIX F DISCUSSION OF ACCURACY AND EVENTUAL MODIFICATION OF THEORETICAL CORRELATION OF HEAT TRANSFER COEFFICIENTS -14,

-146 -Our correlation contains a degree of inaccuracy because steam-side film heat transfer coefficients were not measured but estimated. We have therefore calculated the effect on UVH of the maximum expected scatter in hstm. The result, as presented below, is that agreement between theory and experiment generally falls well within the+ 20% deviation boundaries despite the scatter in hstmo Two simplifications of our theoretical heat transfer model are also discussed below, One is the assumption that sea water physical properties should be taken at feed chlorosity instead of at average chlorosityo The use of the average chlorosity implies complete mixing; we have no proof of the presence or absence of mixing, nor do we postulate either. It turns out that it makes very little difference whether the feed or average chlorosity is used. - Another simplifying modification consists of neglecting - the bubble superheat. It is shown below that the resulting deviation between theory and experiment makes this simplification inadmissible. a) Effect of Scatter in hstm In order to predict UVH, we have used our theoretical model to calculate the liquor-side temperature drop, and McAdams' recommendation to estimate the steam-side temperature drop. The question arises as to how accurate this latter estimate is, and to what degree a scatter in hstm will cause UVH to scatter. Baker, Kazmark and Stroebe(l) used a single-tube LTV consisting of a 2-in. tube 20 ft long in their experimental work. They measured hstm by

-147 -means of thermocouples embedded in the tube at 1-ft intervals. Their results are thus seen to be particularly pertinent to our study. In our region of interest, namely, for steam-side Reynolds numbers below 900, their coefficients averaged roughly 1.28 times the Nusseltpredicted values; hence our use of McAdams' recommendation. Furthermore, practically all their points scattered between 1.00 and 1.56 times the Nusselt-predicted values. We have used this same degree of scatter in hstm in order to calculate the scatter in UVH. The result is graphically illustrated in Figure 9, which is identical to Figure 8 except that the region of scatter is indicated for each point by means of a vertical line joining the upper and lower limit. It can be seen that agreement between theory and experiment generally falls well within thet 20% deviation boundaries. In other words, the use of McAdams' recommendation is not essential to our theory; hstm does not have to be taken as 1.28 times, but at any value between 1.00 and 1.56 times, the Nusselt-predicted value. We used 1.28. b) Effect of Using Feed Chlorosity to Calculate UVH In our runs, the increase in chlorosity from feed to blowdown was relatively low. Run LWCI-14 is the run in which the value of UVH is most affected according to whether feed or average chlorosity is used in order to evaluate physical properties and hence UVH. On recalculating UVH using the feed chlorosity, the only noticeable change is in BPR, which for the average chlorosity is 2.89~F, but which for the feed chlorosity is 2.58~F. The net change in the overall heat transfer

-148 -CORRELATION OF UVH SHOWING OVERALL EFFECT OF UNCERTAINTY IN hstm I I I I I 9...______. 8 ___ ___ ZTi 6 _ 2 / 4 6!i 6 7 3! I 3/ / i..t.. //-. 2- / 10 2 3 4 5 / 7 8 9_ EXPER 2 BESAT Figure 11. // / / // I0 2$3 4 5 6 7 8 910 EXPERIMEmTAL Figure 11.

-149 -coefficient is 4% It can therefore be said that within the region of variables used in our work, it is for all practical purposes indifferent whether the feed or the average chlorosity is used. c) Effect of Neglecting Bubble Superheat We have recalculated all points neglecting bubble superheat, and plotted the results on Figure 12. The difference between Figures 12 and 10 is, therefore, the effect of neglecting bubble superheat; the.change is quite apparent when the figures are compared. The scatter is no longer uniform about the 450 ideal straight line but is biased toward the plus sideo Furthermore, correlation is quite poor for many points; the only runs that seem to correlate well are 1) runs at the high end of the temperature range, where the pressure difference 4- causes only a very small temperature B difference due to the slope of the steam pressure-temperature curve; 2) those runs with 1-in, tubes where the large longitudinal pressure-drop overshadows 4aB Neglect of bubble superheat is clearly inadmissible. * See page 117.

-150 -CORRELATION OF UVH NEGLECTING BUBBLE SUPERHEAT 8 ' 9 = = — -— ~~~~- r~'-I ----~ — ^ - -. --- —- -— I — - 8 - +- - /-^ -l -?____/........ __2 3 4 5 6 -7 84 9 10 -w^ ~ ~ ~ ~ EX PERIME ____ _AL_ o./// 2 __ /. / / e / <,,/ / / ^ / ///

BIBLIOGRAPHY ON FALLING-FILM FLUID FLOW AND (NON-BOILING) HEAT TRANSFER (1) Anderson, G.H., Mantzouranis, B. G., "Two-phase (gas-liquid) flow phenomena - I", Chem. Eng. Sci., 12, 109 (1960) (2) Badger, W. L., "Evaporation of caustic soda to high concentration by means of diphenyl vapor", Ind. Eng. Chem., 22, 700 (1930) (3) Badger, W. L., "Heat transfer coefficients for condensing Dowtherm films", Trans. AIChE, 33, 441 (1937), and Ind Eng. Chem., 29, 910 (1937) (4) Baker, E. M., Kazmark, E. W., Stroebe, G.W., "Steam heat transfer coefficients for vertical tubes", Ind. Eng. Chem., 31, 214 (1939) (5) Bays, G. S., McAdams, W.H., "Heat transfer coefficients in fallingfilm heaters - streamline flow", Ind. Eng. Chem., 29, 1240 (1937) (6) Brauer, H., "Stromung und WarmeUbergang bei Rieselfilmen", VDI Forsch. - Heft 457, 1956 (7) Brauer, H., "Warmeubergang bei der Filmkondensation", K9ltetechnik, 9, 274 (1957) (8) Brauer, H., "Warme'ubergang bei der Filmkondensation reiner Dampfe an lotrechten Wanden", Forsch. Ing.-Wes., 24, 105 (1958) (9) Brauer, H., "Stoffaustausch beim Rieselfilm, Chemo-Ing. Tech., 30, 75 (1958) (10) Brbtz, W., "Uber die Vorausberechnung der Absorptionsgeschiridigkeit von Gasen in stromenden Flussigkeitsschichten", Chem.-Ing. Tech., 26, 470 (1954) (11) Carpenter, F. G., "Heat transfer and pressure drop by condensing pure vapors inside vertical tubes at high vapor velocities", Ph.D. thesis, Univ. of Delaware, 1948. (12) Carpenter, F. G., Colburn, A. P., p. 20, Proceedings of General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and ASME, 1951. (13) Chwang, C. T., S. M. Thesis, Mass. Inst. of Tech., 1926

-152 -(14) Claassen, H., "Versuch zur Bestimmung der Dicke der fliessenden und anhaftenden Flussigkeitsteilchen bei der Berieselung an senkrechten Verdampferrohren", Zentr. Zuckerind., 26, (41), 497 (1918) (15) Colburn, A. P., "Calculation of condensation with a portion of condensate layer in turbulent motion", Trans. AIChE, 30, 187 (1934) and Ind. Eng. Chem., 26, 432 (1934 4) (16) Colburn, A.P., "Problems in design and research on condensers of vapors and vapor mixtures", Proco Inst. Mech. Engrs. (London), 164, 448 (1951) (17) Cooper, C. M., Drew, T. B., McAdams, W. H., "Isothermal flow of liquid layers", Ind. Eng. Chemo, 26, 428 (1934) (18) Cooper, C. M., Willey, G. S., unpublished memo. to Wo H. McAdams, 1930 (see ref. 17) (19) Deissler, R. G., "Analytical and experimental investigation of adiabatic turbulent flow in smooth tubes", NACA Tech. Note 2138 (1950) (20) Deissler, R. G., "Analysis of turbulent heat transfer, mass transfer, and friction in smooth tubes at high Prandtl and Schmidt numbers", NACA Tech. Note 3145 (1954) (21) Drew, T. B., personal communication to W. H. McAdams, 1938 (see McAdams, W. H., "Heat Transmission", McGraw-Hill, 3rd ed., 1954, p. 245) (22) Dukler, A. E., Bergelin, O. P., "Characteristics of flow in falling liquid films", Chem. Eng. Progr., 48, 557 (1952) (23) Dukler, A. E., "Fluid mechanics and heat transfer in vertical falling-film systems", Chem. Eng. Progr. Symp. Series, 56, (30), 1 (1960) (24) Fage, A., Townend, H. C. H., "An examination of turbulent flow with an ultramicroscope", Proc. Roy. Soc. (London), A 135, 656 (1932) (25) Fallah, R., Hunter, T. G., Nash, A. W., "The application of physico-chemical principles to the design of liquid-liquid contact equipment - III - Isothermal flow in liquid wetted-wall systems", J. Soc. Chem. Ind. (London), 53, 369 T (1934) (26) Friedman, S. J., Miller, Co 0., "Liquid films in the viscous flow region", Ind. Eng. Chem., 33, 885 (1941)

-153:(27) Garwin, L., Kelly, E. W., "Inclined falling films", Ind. Eng. Chem., 47, 392 (1955) (28) Grigull, U., "Warmeibergang bei der Kondensation mit turbulenter Wasserhaut", Forsch. Ing.-Wes., 13, 49 (1942) (29) Grigull, Uo, "WarmeUbergang bei Filmkondensation", Forsch. Ing.-Wes., 18, 10 (1952) (30) Grimley, S. S., "Liquid flow conditions in packed towers", Trans. Inst. Chem. Engrs. (London), 23, 228 (1945) (31) Hopf, L., Ann. Physik, 32, 777 (1910) (32) Kamei, S., Oishi, J., Mem. Fac. Engrg. Kyoto Univ., 18, 1 (1956) (33) Kirkbride, C. G., "Heat transfer by condensing vapor on vertical tubes", Trans. AIChE, 30, 170 (1933) and Ind. Eng. Chem., 26, 425 (1934) (34) McAdams, W. H., "Heat Transmission", McGraw-Hill, 3rd ed,, 1954, P- 337 (35) McAdams, W. H., Drew, To B., Bays, Go S., Jr., "Heat transfer to falling-water films", Trans. ASME, 62, 627 (1940) (36) Misra, B., Bonilla, C. F., "Heat transfer in the condensation of metal vapors: mercury and sodium up to atmospheric pressure", Chem. Eng. Progr. Symp. Series, 52, (18), 7 (1956) (37) Nusselt, W., "Die Oberflachenkondensation des Wasserdampfes", Z, VDI, 6o, 541 (1916) (38) Nusselt, W., "Der Warmeaustausch am Berieselungskuhler", Z. VDI, 67, 206 (1923) (39) Pennie, A. M., Belanger, J. Y., "A new method for liquid film thickness measurement", Can. J, Technol., 30, 9 (1952) (40) Rohsenow, W., Webber, JoHo, Ling, A. T., "Effect of vapor velocity on laminar and turbulent film condensation", Trans. ASME, 78, 1637 (1956) (41) Schoklitsch, A., "gUber die Bewegungsweise des Wassers in offenen Gerinnen", Akado Wiss. Wien, Math.-Naturw. Abt. IIa, 129 (1920) (42) Seban, R. A., "Remarks on film condensation with turbulent flow", Trans. ASME, 76, 299 (1954) (43) Sexauer, Th., "Der Warmeubergang am senkrechten berieselten Rohr", Forsch. Ing.-Wes., 10, 286 (1939) (44) Warden, C. Po, S. M. thesis, Masso Inst. Tech., 1930

BIBLIOGRAPHY ON NUCLEATE BOILING FUNDAMENTALS (1) Addoms, J. N., Sc. D. thesis, Mass. Inst. of Techn., 1948 (2) Averin, E. K., Otdel. Tekh. Nauk Izvestiia, Akad. Nauk SSSR, No. 3, P. 116 (1954) quoted by (7)@ (3) Bankoff, S. Go, AIChE Journ., 4, 1 (1958) (4) Bankoff, S. G., "The prediction of surface temperatures at incipient boiling". Chem. Eng. Progr. Symp. Series, 55, (29), 87 (1959) (5) Bankoff, S. G., Hajjar, A. J., McGlothin, Bo Bo, Jr., "On the nature and location of bubble nuclei in boiling from surfaces", J. Appl. Phys., 29, 1739 (1958) (6) Bankoff, S. G., Mikesell, R, D., "Bubble growth rates in highly subcooled nucleate boiling", Chem. Eng. Progr. Symp. Series, 55, (29), 95 (1959) (7) Bernath, L., Begell, W., "Forced-convection, local-boiling heat transfer in narrow annuli", Chem, Eng. Progr. Symp. Series, 55, (29), 59 (1959) (8) Clark, H. B., Strenge, P. S., Westwater, J. W., "Active sites for nucleate boiling", Chem. Eng. Progr. Symp. Series, 55, (29), 103 (1959) (9) Clark, J. A., Rohsenow, W. M., "Local boiling heat transfer to water at low Reynolds numbers and high pressures", Trans. ASME, 76, 553 (1954) (10) Corty, C., Foust, A. S., "Surface variables in nucleate boiling", Chem. Eng. Progr. Symp. Series, 51, (17), 1 (1955) (11) Dean, R. B., "The formation of bubbles", J. Appl. Phys., 15, 446 (1944) (12) Dergarabedian, P., "The rate of growth of vapor bubbles in superheated water", J. Appl. Mech., Trans. ASME, 7, 537 (1953) (13) Engelberg-Foster, K., Greif, R., "Heat transfer to a boiling liquid-mechanism and correlations", J. Heat Transfer, Trans. ASME, p. 43 (1959) (14) Faneuff, Co E., McLean, E. A., Scherrer, V. E., "Some aspects of surface boiling", J. Applo Phys., 29, 80 (1958) -15 -

(15) Forster, Ho K., Zuber, N., "Growth of a vapor bubble on a superheated liquid", J. Apple Phys., 259 474 (1954) (16) Fritz, W., "Berechnung des Maximalvolumens von Dampfblasen", Phys. Z., 36, 379 (1935) (17) Gibbs, J. W., "Collected Works", vol. I, p. 254, Yale Univ. Press, New Haven Conn., 1948 (18) Griffith, P., "Bubble growth rates in boiling", Trans. ASME, 80, 721 (1958) (19) Griffith, P., Wallis, Jo Do, "The role of surface conditions in nucleate boiling", Chem. Eng. Progr. Symp. Series, 56, (30), 49 (1960) (20) Grohse, E. W, Mueller, G. 0., Findlay, J. A., "Fundamental investigation of boiling heat transfer and two-phase flow", KAPL-M-Ei-1l 1958 (21) Gunther, F. C., "Photographic study of surface-boiling heat transfer to water with forced convection", Trans. ASME, 73, 115 (1951) (22) Gunther, Fo C., Kreith, F., "Photographic study of bubble formation in heat transfer to subcooled water". Heat Transf. & Fluid Mecho Inst., po 113 (1949) (23) Jakob, M., "Kondensation und Verdampfung: Neuere Anschauungen und Versuche", Z. VDI, 76, 1161 (1932) (24) Jakob, M., Fritz, W., Forscho Ing.-Wes., 2, 435 (1931) (25) Jens,, W. H., Lottes, P. Ao, Report ANL-4627 (1951) (26) Kreith, F., Summerfield, N., "Heat transfer to water at high flux densities with and without surface boiling", Trans, ASME, 71, 805 (1949) (27) Kreith, F., Summerfield, M., "Pressure drop and convective heat transfer with surface boiling at high heat flux; data for aniline and n-butyl alcohol"', Trans. ASME, 72, 869 (1950) (28) Levy, S., "Generalized correlation of boiling heat transfer", J. Heat Transfer, Trans. ASME, p 37 (1959) (29) Lowery, A. Jo,, eswater, J W., "Heat transfer to boiling methanol - effect of added agents", Ind. Engo Chem,, 49, 1445 (1957) (30) McAdams, W H o, Addoms, Jo No, Rinaldo, Po No., Day, R. S., "Heat transfer from single horizontal wires to boiling water", Chemo Eng. Progr,, 44, (8), 639 (1948)

(31) McAdams, Wo H., Kennel, W, E., Minden, C. So, Carl, R., Picornell, P. M., Dew, J. Eo, "Heat transfer at high rates to water with surface boiling,', Ind. Eng. Chem., 41, 1945 (1949) (32) McNelly, M, J., J. Imp. Coll, Chem. Eng. Soc., 7, 18 (1953) (33) Morgan, A I., Bromley, L. A., Wilke, C. R., "Effect of surface tension on heat transfer in boiling", Ind. Eng. Chem., 41, 2767 (1949) (34) Pike, F. P., Miller, P D.,, Jr., Beatty, K. O., Jr., "Effect of gas evolution on surface boiling at wire coils", Chem. Eng. Progr. Sympo Series, 51, (17), 13 (1955) (35) Plesset, M. S., "The dynamics of buibble cavitation", J. Appl. Mech., Trans. ASME, 16 277 (1949) (36) Plesset, M. S., Zwick, S. A., "The growth of vapor bubbles in superheated liquids", J. Appl. Phys., 25, 493 (1954) (37) Rinaldo, R. N., M. S, thesis, Mass. Inst. Techn., 1948 (38) Rohsenow, W. M., "A method of correlating heat transfer data for surface-boiling of liquids", Trans. ASME, 74, 969 (1952) (39) Rohsenow, W. M, Clark, J. A., "A study of the mechanism of boiling heat transfer'', Trans. ASME, 73, 609 (1951) (40) Rohsenow, W. M., Clark, J. A., "Heat transfer and pressure drop data for high heat flux densities to water at high sub-critical pressures". Heat Transf. & Fluid Mecho Inst., p. 193 (1951) (41) Rohsenow, W. M., Griffith, P., "Correlation of maximum-heat-flux data for boiling of saturated liquids", Chem. Eng. Progr, Symp. Series, 52, (18), 47 (1955) (42) Vos, A. S., van Stralen, So J. D., "Heat transfer to boiling water-methylethylketone mixtures", Chem. Eng. Sci., 5, 50 (1956) (43) Yamagata, K. Hirano, F., Nishikawa, Ko,, Matsuoka, H., "Nuclaeate boiling on a horizontal heating surface", Jap. Sci. Rev., 2, 409 (1952)

BIBLIOGRAPHY ON GAS-LIQ;)IDP FLOW (1) Baker, 0., "Design of pipe lines for the simultaneous flow of oil and gas", Oil & Gas J., July 26 (1954) (2) Benjamin, M. W., Miller, J. G., "The flow of saturated water through throttling orifices", Trans. ASME, 639 419 (1941) (3) Benjamin, M. W., Miller, JO G., "The flow of a flashing mixture of water and steam through pipes", Trans. ASME, 64, 657 (1942) (4) Bergelin, 0. P,, Kegel, P. K., Carpenter, F. G., Gazley, C., Jr., "Co-current gas-liquid. flow - II. Flow in. vertical tubes", Heat Trans. & Fluid Mech. Inst., p. 19 (1949) (5) Boelter, L. M. K,, Kepner, R. H., "Pres:sure drop accompanying two-component flow through pipes", Ind. Eng. Chem., 31, 426 (1939) (6) Bottomley, W. T.,, "The flow of saturated water through throttling orifices", Trans. North-East Coast Inst. Engrs. & Shipbuilders, 53, 65 (19375 (7) Calvert, S., "Vertical upward annular two-phase flow in smooth tubes". Ph. D. thesis, Univ. of Mich., 1952 (8) Carpenter, F. G., "Heat transfer and pressure drop for condensing pure vapors inside vertical tubes at high vapor velocities", Ph. D. thesis, Univ. of Del., 1948 (9) Chenoweth, J. M., Martin, H W.,, Petr. Ref., 34, 151 (1955) (10) Davidson, W. F., Hardie, P. H., Humphreys, C. G. R., Markson, Ao A., Mumford, A. R., Ravese, T., Trans. ASME, 65, 553 (1943) (11) Dengler, C. E., "Heat transfer and pressure drop for evaporation of water in a vertical tube", D. Sc. thesis, Mass. Inst. Techn., 1952 (12) Dittus F. W., Hildebrand, A., "A method of determining the pressure drop for oil-vapor mixtures flowing through furnace coils", Trans. ASME, 64, 185 (1942) (13) Gazley, C., Jr., "Co-current gas-liquid flow - III. Interfacial shear and stability", Heat Transf. & Fluid Mech. Inst., p. 29 (1949) (134) Jakob, M:., Leppert, G., Reynolds, J. B., "Pressure drop during forced-circulation boiling", Chemo Eng. Progr. Symp. Series, 52, (18), 29 (1956) — l57 -

-158 -(15) Johnson, H. Ao, Abou-Sabe, A. Ho, "Heat transfer and pressure drop for turbulent flow of air-water mixtures in a horizontal pipe", Trans. ASME, 74, 977 (1952) (16) Levy, So, "Theory of pressure drop and heat transfer for two-phase two-component annular flow in pipes", Ohio State Univ. Engrg. Exptl. Station Bull. No. 149, Proc. 2nd Midwestern Conf. Fluid Mech., P. 337, 1952 (17) Lieberson, N. G., "Two-phase flow in vertical pipes", M. S. thesis, Mass. Inst. Techn,, 1952 (18) Linning, D. L., "The adiabatic flow of evaporating fluids in pipes of uniform bore", Inst. Mech. Engrs. (London), Proc. (B), 1 B, 2 (1952) (19) Lockhart, R, W., Martinelli, R. C., "Proposed correlation of data for isothermal two-phase, two-component flow in pipes", Chem. Eng. Progr., 45, 39 (1948) (20) Marcy, G. P., "Pressure drop with change of phase in a capillary tube", Refrig. Eng., 57, 53' (1949) (21) Martinelli, R. C., Boelter, Lo Mo K,, Taylor, T. Ho Mo, Thomsen, E. G., Morrin, E. Ho, "Isothermal pressure drop for two-phase two-component flow in a horizontal pipe", Trans. ASME, 64, 275 (1942) (22) Martinelli, R. C., Nelson, D. Bo, "Prediction of pressure drop during forced-circulation boiling of water", Trans. ASME, 70, 695 (1948) (23) Martinelli, R. Co, Putnam, J. A., Lockhart, R. W., "Two-phase, two-component flow in the viscous region", Trans. AIChE, 42, 681 (1946) (24) McAdams, W. H., Woods, W. K., Heroman, L. C., Jr., "Vaporization inside horizontal tubes - II. Benzene-oil mixtures", Trans. ASME, 64, 193 (1942) (25) Radford, B. A., "Gas-liquid flow in vertical pipes - a preliminary investigation", M. S. thesis, Univ. of Alberta, 1949 (26) Schmidt, Eo, "Ahnlichkeitstheorie der Bewegung von Flussigkeitsgemischen", VDI Forsch. - Heft 365, 1934 (27) Shugaeff, V., Sorokin, S., "The hydraulic resistance of a two-phase mixture", Zhur. Tekhn. Fiziki, IX, (20), 1854 (1939)

-15)(28) Stein, R. P., Hoopes, J. W., Jr., Markels, M,, Jr., Selke, W. A., Bendler, A. J., Bonilla, C. F., "Pressure drop and heat transfer to nonboiling and boiling water in turbulent flow in an internally heated annulus", Chem. Eng. Progr. Symp. Series, 50, (11), 115 (1954) (29) Styrikovich, M. A., Miropolski, Z. L., "Flow lamination of a highpressure steam-water mixture in a heated horizontal pipe", Dokl. Akad. Nauk SSSR, 71, (2), (1950) (30) Untermeyer, S., "Boiling reactors: direct steam generation for power", Nucleonics, 12, 43 (1954) (31) Van Wingen, N., "Pressure drop for oil-gas mixtures in horizontal flow lines", World Oil, 129, (7), 156 (1949)

BIBLIOGRAPHY ON EVAPORATOR STUDIES (1) Billet, R., "Trennung von Flussigkeitsgemischen durch teilweise Destillation", Chem.-Ing.-Tech., 29, 733 (1957) (2) Chambers, F. S., Peterson, R. F., "Sulfuric acid concentration - DuPont Falling-Film Process", Chem, Eng. Progr., 43, (5), 219 (1947) (3) Dengler, C. E., "Heat transfer and pressure drop for evaporation of water in a vertical tube", Sc. D. thesis, Mass. Inst. Techn., 1952 (4) Guerrieri, S. A., Talty, R. D., "A study of heat transfer to organic liquids in single-tube, natural-circulation, vertical-tube boilers", Chemo Eng. Progr. Sympo Series, 52, (18), 69 (1956) (5) Hadley, G. F., Thomas, A. L., "A mathematical and experimental study of a climbing film evaporator",, Ind. Eng. Chem., 52, 71 (1960) (6) Harvey, B. F., Foust, A. S., "Two-phase one-dimensional flow equations and their application to flow in evaporator tubes", Chem. Eng. Progr. Symp. Series, 49, (5), 93 (1953) (7) Hausschild, W., "Leistung von Dunnschichtverdampfern mit zwangslaufig ausgebildeten Filmen", Chem.-Ing.-Tech., 25, 573 (1953) (8) Karetnikov, U. P., "Investigation of heat transfer in a boiling liquid film", Zhur. Tekhn. Fiziki, XXIV, (2), 193 (1954) (9) Kern, D. Q., Karakas, H. J., "Mechanically aided heat transfer", Chem. Eng. Progr. Symp. Series, 55, (29), 141 (1959) (10) Kerry, F. G., "Safe design and operation of low temperature air separation plants", Chem. Eng. Progr., 52, (11), 441 (1956) (11) Keville, J. K., "Heat transfer aspects of concentrated milk in a falling film evaporator", preprint 18, Second National Heat Transfer Conference AIChE-ASME, Chicago, Ill., Aug. 18-21, 1958 (12) Kirschbaum, E., Dieter, K., "Warmeibergang und Teildestillation in Dunnschichtverdampfern", Chem.-Ing.-Tech., 30, 715 (1958) (13) Lustenader, E. L., Richter, R., Neugebauer, F. J., "The use of thin films for increasing evaporation and condensation rates in process equipment", paper 59-SA-30, Semi-Annual Meeting ASME, St. Louis, Mo., June 14-18, 1959 (14) Mueller, A. C., "Discrepancies between theory and practice", Chem. Eng. Progr., 57, 76 (1961) -160 -

(15) Poocza, Ao, "Beitrag zur Theorie des Dunnschichtverdampfers", Chem.-Ing.-Techo, 30, 648 (1958) (16) Richkov, Ao I, Pospelov, V. Ko, "Study of heat transfer in the boiling of caustic sodasolutions in a thin film", Khimo Promo, (5), 426 (1959) (17) Schneider, Ro, "Ein neuer Dunnschichtverdampfer", Chem-Ingo-Tech., 27, 257 (1955) (18) Schweppe, J. Lo, Foust, Ao So, "Effect of forced circulation rate on boiling heat transfer and pressure drop in a short vertical tube", Chem. Eng. Progro Sympo Series, 49, (5), 77 (1953) For a recently published literature review on evaporation for 1959 and 1960, see also: Dedert, WO Go, "Evaporation", Ind Eng. Chemo, 53, 669 (Aug 1961) This article does not contain mention of any significant development on falling-film evaporation not quoted in our dissertationo

39015 03524 4519 ADDITIONAL BIBLIOGRAPHY USED IN DESIGN, RESULTS AND ANALYSIS OF EXPERIMENTS (1) Baker, Eo M,, Kazmark, Eo Wo, Stroebe, Go W., "Steam-film heat transfer coefficients for 7vertical tubes", Trans. AIChE., 35, 127 (1939); Ind. Eng. Chem., 31, 214 (1939) (2) Keenan, J. H., Keyes, F. G, "Thermodynamic Properties of Steam", John Wiley & Sons, 1st ed,, 1936 (3) Sverdrup, H. U., Johnson, Mo W., Fleming, Ro H., "The Oceans", Prentice-Hall, 1st ed., 1942, p. 70 (4) Volk, W., "Applied Statistics for Engineers", McGraw-Hill, 1st ed. 1958, p. 207 (5) W. L. Badger and Associates, Inc., Ann Arbor, Mich., Report No. 438, "Properties of Sea Water and Its Concentrates", 19579 and supplement, 1960, to Uo S. Department of Interior, Office of Saline Water -162 -