THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING THE CONDENSATION OF SUPERHEATED FREON-114 AND STEAM VAPORS OUTSIDE A HORIZONTAL TUBE Garen Balekjian This dissertation was submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan. September, 1956 IP-181

We wish to express our appreciation to the author for permission to distribute this thesis under the Industry Program of the College of Engineering. ii

TE PROBLEM The mechanism of heat removal from a superheated vapor as it approaches a surface below the dew point of the vapor is not entirely understood. Experimental studies reported in the literature on the condensation of superheated vapors outside horizontal tubes are meager. A theoretical approach to the condensation of superheated vapors is needed to predict the behavior of superheated vapors at extreme conditions of low pressures and high superheats. Determination of the conditions under which the condensing surface is no longer wetted with a film of condensate is of special importance for the proper design of superheated vapor condensers. The condensation of superheated vapors is studied on the outside of a horizontal tube. Experimental heat fluxes are presented in a form useful in engineering design. The general theory for the interphase transfer of mass and energy is applied to the analyzed results to correlate experimental condensing loads and calculated interfacial vapor film coefficients. The behavior of superheated vapors is interpreted satisfactorily by interphase transfer theory. iii

ACKNOWLEDGMENTS The author wishes to express his sincere appreciation to a number of individuals for their assistance during the course of this study and in particular to the following: Professor Donald L. Katz for his continuous interest, encouragement, suggestions, and advice. Professors Julius T. Banchero, Stuart W. Churchill, Joseph J. Martin, and Gordon J. Van Wylen for their interest and suggestions during various phases of this work. Secretaries of the Chemical and Metallurgical Engineering Department for their help in material purchasing. Messrs. Cleatis Bolen and George Foster of the Chemical and Metallurgical Engineering Department for their valuable help during construction of the experimental apparatus. Continental Oil Company for their generous financial support which made possible the experimental work completed during 1955. iv

SUMMARY A review of the literature on the condensation of superheated vapors indicated meager information for superheated vapors condensing on the outside of a horizontal tube and a general lack of understanding of the behavior of superheated vapors under widely different conditions. The condensation of superheated Freon-114 and steam was investigated on the outside of a plain 0.750-inch-diameter horizontal copper tube housed in a 6-inch-diameter shell. Experimental data with measured wall temperatures were obtained for superheated Freon-114 condensing at pressures of 43.7 and 77.0 lb per sq in. absolute and for superheated steam condensing at 9.16, 23.35, 23.87, and 44.09 lb per sq in. absolute. It was observed that superheat in the vapor caused a lowering of the tube surface temperature. Studies indicated that this was related to a lowering of the condensate surface temperature as well. A general lowering of the heat flux as much as 23.4 per cent below that of the saturated vapor was obtained with increasing superheat. This lowering of the heat flux was explained and correlated with the condensing load. The overall performance obtained with the condensation of superheated vapors under various conditions of pressures, superheats, and tube surface temperatures was explained by the relative importance of interphase, and intraphase processes of mass and energy transfer. The general theory of interphase mass and energy transfer was applied to explain the condensation of superheated vapors by a mechanism of mass and heat transfer through the vapor-liquid interface. The behavior of superheated vapors under widely different conditions was predicted by in

terphase transfer theory. The theoretical equation was modified and used to correlate satisfactorily the experimental condensing load and the calculated temperature and pressure conditions at the interface with the degree of superheat. The applicability of the correlating equation to predict condensing loads and interfacial film conditions for fluids other than Freon-114 and steam was discussed. The calculated condensate surface temperatures were used to determine the temperature drop through the interfacial film. Interfacial film coefficients were calculated and correlated with the temperature drop through the interfacial film and the temperature and pressure conditions at the vapor-liquid interface. The variation of the interfacial film coefficient and heat flux in the region close to the "dry point" was obtained by extrapolation of the calculated interfacial film coefficients. The prediction of the "dry point" for a given application was presented and illustrated in a method correlating the interfacial film coefficient with the free convection and radiation film coefficients at the "dry point." Condensate film coefficients calculated by the conventional method used for the design of superheated vapor condensers were evaluated by comparison with the experimental results. The limitations of this procedure were pointed out. The equation correlating the results from the filmwise condensation of superheated Freon-114 and steam was used in the outline and illustration of a basic procedure for the design of condensers involving the filmwise condensation of superheated vapors outside horizontal tubes. The applicability of this method for peculiar conditions of low pressures, high superheats, and high condensate surface temperatures was discussed. vi

TABLE OF CONTENTS Page THE PROBLEM iii ACKNOWLEDGMENTS iv SUMMARY v LIST OF TABLES viii LIST OF ILLUSTRATIONS ix INTRODUCTION 1 LITERATURE AND INTRODUCTORY THEORY 4 Saturated Vapors 4 Superheated Vapors 6 The Mechanism of Mass and Energy Transfer 9 Theory of Interphase Mass and Energy Transfer 15 EXPERIMENTAL APPARATUS AND MATERIALS 22 EXPERIMENTAL PROCEDURE AND DATA 28 Cleaning and Assembly of Condenser Shell and Tube 28 Charging and Operating the Equipment 30 Experimental Data 32 CALCULATION AND CORRELATION OF RESULTS 37 Overall Performance of Condenser with Superheated Vapors 38 Theory of Filmwise Condensation of Superheated Vapors 54 Correlation of Results 69 Design Procedure 83 CONCLUSIONS AND RECOMMENDATIONS 89 APPENDICES 92 Appendix A. Details of Experimental Apparatus 93 Appendix B. Experimental Studies on Tube-Side Water Film Coefficient 102 Appendix C. Sample Calculations 124 Appendix D. Calculation of a Typical Value of 0g 133 Appendix E. Example Design of a Superheated Freon-114 Vapor Condenser 135 Appendix F. Property Charts 143 NOMENCLATURE 154 BIBLIOGRAPHY 158 vii

LIST OF TABLES No. Page I Condenser Shell and Experimental Tube Characteristics 26 II Experimental Data and Calculated Results for Superheated Freon-114 (Film Condensation) 33 III Experimental Data and Calculated Results for Superheated Steam 34 IV Experimental Data and Calculated Results for Superheated Steam (Mixed Condensation - Dry-Point Runs) 36 V Correlation of Calculated Condensing Rates and Interphase Film Coefficients (Based on Results in Figure 18) 39 VI Experimental Data and Calculated Results for Tube-Side Water Film Coefficients 107 VII Determination of Exponent by the Method of Least Mean Squares 111 VIII Temperature Distribution Along Condensing Tube 120 IX Original Data Sheet 124 viii

LIST OF ILLUSTRATIONS No. Page 1 Experimental apparatus. 23 2 Flow diagram of equipment. 24 5 Details of condenser shell and tube. 25 4 Details of wall thermocouple installation. 25 5 Film condensation of superheated Freon-114. 29 6 Dropwise condensation of superheated steam. 29 7 Effect of superheat on heat flux for condensation of Freon114. 41 8 Effect of superheat on heat flux for condensation of steam. 42 9 Effect of superheat on condensing load for condensation of Freon-114 and steam. 44 9a Correlation of the effect of superheat on the heat flux with the condensing load. 45 10 Heat flux and condensing load for condensation of superheated steam while approaching dry tube conditions. 49 11 Overall outside film coefficient for condensation of superheated steam while approaching dry tube conditions. 51 12 Effect of superheat on overall outside film coefficient for condensation of superheated Freon-114 and steam. 53 12a Decrease of tube surface temperature with superheat. 56 13 Effect of superheat on interphase vapor film coefficient (hi) for condensation of Freon-114 and steam. 60 14 Effect of superheat on condensate and interfacial film resistances for Freon-114. 62 15 Effect of superheat on condensate film and interfacial film resistances for Freon-114. 63 16 Effect of vapor temperature level on overall outside film coefficient of superheated Freon-114. 65 ix

LIST OF ILLUSTRATIONS (continued) No. Page 17 Temperature profile for a condensing superheated vapor. 67 18 Correlation of calculated condensate surface temperature with superheat for condensation of Freon-114 and steam. 70 19 Correlation of calculated condensate surface temperature lowering with superheat for condensation of Freon-114 and steam. 72 20 Correlation of condensing load with superheat as a function of condensation coefficient (f). 78 21 Correlation of interfacial film coefficient (hi) with interfacial film temperature drop as a function of condensation coefficient (f). 82 22 Comparison of conventional design and experimental condensate film coefficients for superheated Freon-114. 85 23 Wilson plot with water flow rate exponent of o.80. 108 24 Determination of water flow rate exponent by the method of least mean squares. 112 25 Equal area curve for determination of water flow rate exponent. 113 26 Wilson plot with water flow rate exponent of 0.91. 115 27 Comparison of predicted and experimental tube-side film coefficient for water. 116 28 Temperature distribution along condensing tube. 121 29 Effect of water flow rate on water film coefficient and temperature distribution along condensing tube. 122 29a Trial-and-error method for determination of condensate surface temperature, Ts, ~F. 140 30 Correlation of condensing load with superheat as a function of condensation coefficient (f). r and Ts/Tg assumed = 1.0. 144 31 Dry tube condition for condensing superheated steam. 145 32 Vapor pressure of Freon-114. 146 33 Density of liquid Freon-114. 147

LIST OF ILLUSTRATIONS (concluded) No. Page 34 Thermal conductivity of liquid Freon-114. 148 35 Viscosity of liquid Freon-114. 149 36 Enthalpy of superheated Freon-114 vapor. 150 37 Thermal conductivity of water. 151 38 Nusselt physical property group for Freon-114. 152 39 Nusselt physical property group for water. 153 xi

INTRODUCTION The condensation of superheated vapors is an important process encountered frequently in industry. Compounds prepared by gas or vaporphase reactions yield the product in the form of a superheated vapor which is subsequently condensed into the liquid or solid state. The manufacture of titanium tetrachloride is a typical example. Superheated refrigerant vapors are condensed in refrigeration units. Superheated steam used extensively in power plants may sometimes be condensed in the superheated state. A superheated vapor in contact with a surface at temperatures below the dew point of the vapor will form a film of liquid condensate on the surface. The heat extracted from the vapor passes through the liquid film much as in the condensation of saturated vapors. The differences in the condensation of superheated vapors from the process for saturated vapors lies in the removal of the superheat from the vapor at a short distance from the surface of the liquid film and the effect which this process has on the temperature of the liquid at the vapor-liquid interface. The proper design of a superheated vapor condenser requires a knowledge of the effect of superheat on important variables such as the condensing load, condensate surface temperature, and the corresponding temperature drop at the vapor-liquid interface. A generalized correlation of these variables for all fluids is necessary as a fundamental method for the design of a superheated vapor condenser. This requires also the

formulation of a theory whereby the behavior of superheated vapors may be predicted for a wide range of pressures and superheats in order to anticipate the peculiar condenser condition when the tube surface is no longer wetted with a liquid film or the "dry point." At present a theoretical approach to the condensation of superheated vapors is available for the special case of vapors condensing inside a vertical tube. Experimental study of this theory is reported in the literature at one superheat for steam. 23 Experimental work on the more common case of condensation on the outside of horizontal tubes is limited to generalized statements concerning the overall heat flux for superheated steam'55 and heat flux and condensing coefficient studies for Freon-12.26 The design of superheated vapor condensers is based on the condensate film coefficient calculated from Nusselt's equation 1 discussed in the next section. The latent heat for a saturated vapor is replaced by the heat removed in desuperheating and condensing the superheated vapors. Although this procedure is found useful in many engineering applications its validity for conditions of low pressure or high superheats is very questionable. In some applications where the superheat is of the order of 10000F the necessary condensing capacity is obtained by increasing the condenser area determined by the conventional design method. A systematic study of the important variables is made in this work for the condensation of superheated Freon-114 and superheated steam on the outside of a horizontal tube. Two fluids with widely different physical properties enable a more thorough approach to the desired generalized correlation. The studies include the condensation of superheated Freon-114 at two pressures of 43.7 and 77.0 lb per sq in. absolute, with a maximum superheat of 1800F and superheated steam at 9.16, 23535, 23.87,

and 44.09 lb per sq in. absolute with a maximum superheat of 184VF. The effect of superheat on the overall heat flux and condensing load is presented. The results are further analyzed to obtain the calculated condensate surface temperature, the temperature drop across the condensate film, the temperature drop across the vapor-liquid interface, and the corresponding condensate film and interfacial coefficients. The general theory of interphase mass and energy transfer is applied to the condensation of superheated vapors and used for the interpretation of results. The condensation coefficient (f) derived from the kinetic theory of gases is used to correlate the experimental condensing load and the calculated interfacial temperature and pressure conditions with the degree of superheat. The results are also correlated as a function of the interfacial heat transfer coefficient, the interfacial temperature and pressure conditions, and the temperature drop through the interfacial film. A comparison is made between the heat transfer film coefficient calculated according to the conventional design procedure and the experimental film coefficient evaluated on the same basis. A more fundamental procedure for the design of superheated vapor condensers is outlined and illustrated for superheated Freon-114 in Appendix E.

LITERATURE AND INTRODUCTORY THEORY The condensation of superheated vapors is a special case of the process of condensation and the general operation of interphase mass and energy transfer. For a thorough understanding of this special problem a brief survey of the literature and the theory concerning condensation of saturated and superheated vapors is presented in this section. In addition, the theory which has been developed for interphase mass and energy transfer is discussed. SATURATED VAPORS Nusselt's classical work37 presents theoretical equations for the condensation of vapors on different surfaces. The derivation of these equations and a detailed discussion of experimental data on this subject is available in several references. The following is the equation derived by Nusselt for the prediction of the condensate film coefficient for saturated vapors condensing on the outside of a horizontal tube:14 4k 3 p 2 g (-AH) hc = 0.72 f (1) [f Do Atc where he = condensate film coefficient, Btu per (hr)(~F)(sq ft outside) (-AH) = total heat removed, latent heat for saturated vapors, Btu per lb {Subscript f = condensate properties at the mean film temperature, Tf, ~F k = thermal conductivity, Btu per (hr)(~F)(ft) p = density, lb per cu ft

= viscosity, lb per (ft)(hr) g = gravitational acceleration, 4.17 x 108 ft per hr per hr Do = outside tube diameter, ft Atc = temperature difference through condensate film, (Tsv - to), ~F Tsv = saturation temperature, OF to = outside tube surface temperature, OF. Based on the assumption of a linear temperature gradient through the film and a linear variation of the fluidity (1/p) with temperature the following equation is derived by Drew33 for the mean condensate film temperature: Tf = Tsv - 3/4 Atc (2) where Tf = mean condensate film temperature, ~F. The following equation shows better agreement with experimental data and is recommended for the evaluation of the mean film temperature: Tf = Tsv - 1/2 Atc (3) The simplifying assumptions used by Nusselt in deriving equation 1 consist of the following:35 1. Linear temperature gradient through the condensate film. 2. Heat transfer only by conduction through the condensate film. 3. Linear variation of condensate film properties with temperature. 4. Clean and smooth surface. 5. Laminar flow of condensate film. 6. No effect due to condensate film curvature. 7. Constant tube wall temperature. The validity of these assumptions is shown by the fact that experimentally determined condensate film coefficients are generally found to

be about 10 to 20 per cent above those predicted from equation 1. 4 Bromleyl3 points out that correct evaluation of the integral 4 A sin l/3 0 d0 3 sin in Nusselt's derivation gives a value of 0.728 for the coefficient in equation 1. Equation 1 becomes complicated when the temperature profile through the film is not assumed to be linear and the effect of cross flow within the film is considered. The following correction factor to equation 1 is recommended by Rohsenow as an improvement over an earlier 12 contribution by Bromley: 4 Cp Atc 1 + 0.60 (4) where Cp = specific heat of condensate, Btu per (lb)(~F). This correction factor is recommended as a satisfactory approximation to the more complex equation for the range of 0 < Cp At < 1.0 -AH The effect of condensate film turbulence on the condensate film coeffi28 cient is observed by Kirkbride. Other factors such as vapor velocity and its effect on turbulence of the condensate film and literature related to them are reviewed in reference 44. SUPERHEATED VAPORS The condensation of superheated vapors is discussed in the original work of Nusselt.37 In a manner similar to the derivation of equation 1, the differential equation representing the overall heat balance is integrated for the height of a vertical condensing surface to give the following 2equation:4

pfg(AH) H + +RYH + YH6 (5) Hfkf 5 6 where H = height of the vertical surface, ft YH = thickness of the condensate film at lower end of surface, ft R h(Tg Tsv) ftkf (Tsv - t)' hv = convection coefficient from the superheated vapor to the condensate surface, Btu per (hr)(~F)(sq ft outside) Tg = superheated vapor temperature, OF. The condensate film thickness YH determined from equation 5 by trial and error is substituted in equation 6 to calculate the condensing rate on the vertical surface of height H: Pf2g yH3 m = H (6) where m = condensing load, lb per (hr)(ft of surface width). Stender 7 and Merkel use an approximation for equation 5 to predict the effect of superheat on the heat flux of vapors condensing on a vertical surface. The ratio of the heat flux for a superheated vapor to that of the saturated vapor is related graphically to the function hv(Tg - Tsv ) hc(Tsv - to) This relationship predicts an increase of up to 57 per cent in the heat flux due to superheat. A discussion of Nusselt's equation for the condensation of superheated vapors inside a vertical tube considering the effect of vapors at constant velocity and an improved equation allowing for the variation of

23,24 vapor velocity along the condensing length is given by Jakob. Studies with steam at one atmosphere pressure and 4050F superheat indicate a small increase in the heat flux due to superheat at low heat fluxes. This effect is reversed at higher heat fluxes. A survey of the literature on condensation of superheated steam ij presented by McAdams.35 Generally with steam at one atmosphere pressure, a small increase of heat flux is reported due to superheat. Further discussions on this effect are included in references 15, 16, 19, and 29. Patents are available for devices which may be used to desuperheat steam. o,36 Experimental data reported in the literature on the condensation of superheated vapors on the outside of a horizontal tube are meager. Katz 26 et al. report the results of their studies for superheated Freon-12 condensing on the outside of plain and finned tubes. No effect of superheat as compared to saturated vapors is observed for the range of pressures 103 to 172 lb per sq in. absolute and the maximum superheat of 122.5 F. Nusselt's derivation of equation 1 applied to superheated vapors gives a similar equation where the factor (-AH) represents the total heat removed in condensing the superheated vapors rather than the latent heat of condensation. This equation predicts a small increase in heat flux due to superheat. It is assumed that the vapor at the condensate surface is in equilibrium with the liquid and is at its saturation temperature. This implies there is no resistance to mass and energy transfer at the vapor-liquid interface. Conventional design of superheated vapor condensers is based on the condensate film coefficient predicted by this method. Equation 1 is useful in many engineering applications where vapors with 100~F to 200~F superheat are condensed at normal pressures of

one to five atmospheres. The validity of this method is doubtful for applications where peculiar conditions of high superheat, high wall temperatures, and low pressures prevail. THE MECHANISM OF MASS AND ENERGY TRANSFER The mechanism which controls the condensation of molecules moving toward a cold surface involves the effect of superheat on the condensate surface temperature. The importance of the liquid surface temperature at the vapor-liquid interface has been recognized for some time. In 1928 23 Jakob has suggested that a condensate-surface temperature lower than the saturation temperature may prevail during the condensation of superheated steam in order to account for the lower heat flux obtained in evaporators using superheated steam as compared to the performance of saturated steam. A theoretical attempt to prove this hypothesis is made by Bosnjakovic. 3 Starting with the kinetic theory of gases and using several simplifying assumptions he derives an equation relating the condensing load for superheated steam with the lowering of the condensate surface temperature below that at saturation. A discussion of this study is given in the section presenting the interpretation and correlation of experimental results. The calculations of Bosnjakovic indicate that the condensation of steam at one atmosphere pressure and a superheat of 4n5~F requires a condensate surface temperature 12.6~F below the saturation temperature of 2120F. Subcooling of the condensate surface desuperheats partially the adjacent vapor molecules and gives a density of vapor molecules at the liquid surface comparable to that with saturated steam. Bosnjakovic considers the subcooling as necessary to condense high-velocity superheated steam molecules as they penetrate into the liquid surface. This discussion does not differentiate between intraphase film temperature

10 difference in the vapor and interphase film temperature difference at the vapor-liquid interface. The condensation of superheated vapors belongs to those operations which involve the transfer of momentum, mass, and energy across a phase boundary. The mechanism of such processes has not been analyzed adequately because of the equilibrium conditions usually assumed. In contrast with studies concerning the diffusional transfer processes, for an interphase transfer operation the velocity of one phase relative to that of the other is assumed to be zero, the temperature of the two phases at the interface is assumed to be the same, and in the case of a multi-component system the composition of the two phases is assumed to be that at thermodynamic equilibrium. The kinetic theory of gases has useful applications in studying interphase transfer processes because it describes the behavior and the bulk properties of a group of molecules at a given temperature and pressure. The following equation is referred to frequently in the literature concerning interphase mass transfer: ms = f(Ps - Pg) 2 RT (7) where ms = net mass of molecules transferred, lb (mass) per (hr)(sq ft interfacial area) M = molecular weight of fluid, lb (mass) per lb mole R = gas constant, 1544 (ft)(lb force) per (lb mole)(~R) Ts = temperature of liquid or solid surface, ~R Pg = pressure of gas phase at vapor-liquid interface, lb (force) per sq ft absolute

11 Ps = equilibrium pressure corresponding to Ts, lb (force) per sq ft absolute gc = conversion factor, 4.17 x 108 (lb mass)(ft) per (lb force) (sq hr). The condensation coefficient f is defined as the following ratio: Number of molecules condensed f = Total number of molecules striking the surface (8) Equation 7 is derived by combining the number of collisions predicted by the kinetic theory of gases with the molecular density in the gas phase 18 calculated for an ideal gas.l8 This simple derivation involves the following assumptions: 1. Ideal gas behavior. 2. Molecular velocity distribution identical to that of a uniform gas described by Maxwell's probability distribution function.l8 3. Equilibrium at the phase boundary. Assumptions (1) and (2) are valid for many applications. The behavior of molecules of a non-uniform gas involving intraphase transfer of energy is expected to show deviations from these assumptions. The molecular behavior of a condensing vapor is uniform within the vapor phase and non-uniform only through the short distance represented by the thickness of the interfacial film across which heat transfer and cooling of molecules occur. In most instances where the use of equation 7 is encountered in the literature the third assumption of the equilibrium of the two phases is overlooked. Equation 7 is applied frequently to correlate experimental data on condensation and evaporation and to estimate the temperature difference across the vapor-liquid interface, whereas its derivation implies that the vapor and liquid are at the same temperature

12 at the phase boundary. This confusion is partly due to the fact that most interphase transfer studies involve also intraphase transfer. This is shown for the condensation of superheated steam inside vertical tubes by measurement of the temperature gradient in a direction normal to the 23 condensing surface. Roecke and Jakob report independently a zone about one millimeter thick in which extensive cooling of superheated steam occurs. This distance is many times thicker than the interfacial film which is of the order of magnitude of one mean free path of the condensing molecules. A theoretical equation for the temperature gradient in the vapor phase of a superheated vapor is derived by Cornell.17 Except for the theoretical work of Bosnjakovic 2 the application of theoretical equations based on the kinetic theory of gases is limited to studies of interphase mass transfer in which no superheated vapor phase exists. A thorough survey of this literature is presented in the recent work of Schrage. Early studies in this field are aimed at the determination of the value of the condensation coefficient (f) for various substances. During evaporation the coefficient (f) represents the relative number of molecules which leave the liquid phase and move away from the surface, and (l-f) represents the relative number of molecules which move away from the liquid surface by reflection after striking the surface. For a substance at steady-state conditions of temperature and pressure the evaporation and condensation coefficients are equal. For the special case of evaporation or condensation at zero pressure in the vapor phase equation 7 assumes the simpler form:2 me = f Ps (9) where

13 me = maximum rate of evaporation or condensation of a substance = mass evaporating into a perfect vacuum = (mass of saturated vapor which strikes unit area of the surface per unit time) times (fraction f of incident molecules which are able to remain on the surface. Early attempts to determine the condensation coefficient for various solids and liquids are reviewed in reference 45. In an early paper 1 Altyl reports a value of about 0.01 for water at low pressures. In another paper5 Alty and Nicoll describe the method used to determine this value. Experimental data obtained for the rate of evaporation of water at various pressures are extrapolated to zero pressure. Equation 9 is then solved for the unknown (f). Alty2 recognizes the uncertainty of the final value of f determined by extrapolation and uses a more reliable method in which the temperature of the drop surface is calculated from the measured drop geometry. The value of f calculated from equation 7 is 0.036 for water and unity for carbon tetrachloride. Alty3 also reports experimental values of f for benzene (1.0), alcohol (small), iodine (1.0), naphthalene (1.0), synthetic camphor (0.172), and benzoic acid (0.29). These values of the condensation coefficient are related to the electrical structure of the compound and it is concluded that the condensation coefficient of polar compounds is relatively small, whereas that of non-polar compounds is very close to unity. Priiger39 has determined the condensation coefficient of water and carbon tetrachloride at atmospheric pressure. The values of f of 0.04 and unity for water and carbon tetrachloride, respectively, agree with those reported by Alty and co-workers. A recent study on the rate of condensation of -water vapor under vacuum presents a correlation based on equation 9.

14 Using the value of 0.036 determined by Alty for the condensation coefficient (f) of water, and assuming the slope of the vapor-pressure 46 curve of water to be a constant for reasonably small increments, Silver combines the Clapeyron equation with equation 7 to obtain the following relationship: ms = 778 f ( L (T - Tsv) (10) 2'ABTs T where PL = density of liquid, lb per cu ft T = average temperature between Ts and Tsv, OR. Defining an interfacial vapor film coefficient of heat transfer (hi) as ms (-AH) hi (Ts - Tsv) (11) and combining it with equation 10 the following equation is derived for the interfacial film coefficient:' hi = 778 f c (AH) PL (12) where hi = interfacial vapor film coefficient, Btu per (hr)(~F)(sq ft outside) f = 0.036. Silver recommends the use of equation 12 to calculate the interfacial vapor film coefficient and the interfacial film resistance for saturated steam condensing at low pressures. The fraction of the total temperature drop across the liquid film and across the interfacial vapor film is determined by the fraction of the total resistance to heat transfer due to the respective films:

15 1 1 1 1 + (13) where ho = overall outside film coefficient, Btu per (hr)(~F(sq ft outside). Equation 12 is used by Cornell17 in a method recommended for the evaluation of the condensate surface temperature (Ts), the interfacial film coefficient (hi), and the temperature drop across the interfacial vapor film for the condensation of superheated steam. It is assumed that the vapor at the interface is at the saturation temperature, and the temperature drop through the interfacial film is of the same order as that for a saturated vapor. It will be shown in a subsequent section that the use of equation 12 derived from equation 7 is not valid because the interfacial temperature drop is assumed to be zero. This discussion indicates that in all these investigations the experimental results are interpreted in terms of a transfer mechanism across the vapor-liquid interface. However, the equations used to calculate these results assume thermodynamic equilibrium across the interface and are not valid for the non-equilibrium cases to which they are applied. The proper mathematical relations describing the interphase transfer of mass and energy are derived by Schrage and are presented in the next section. THEORY OF INTERPHASE MASS AND ENERGY TRANSFER The process of interphase mass and energy transfer may be described by the statistical behavior of the molecules at the vapor-liquid interphase. The rate of evaporation and condensation of molecules may be determined if the velocity distribution of the molecules is known as a

16 function of the absolute temperature. Usually the mean velocity of the molecules in the liquid or solid surface is assumed to be zero. In most practical applications this assumption is justified because of the large difference in the density of the vapor and liquid or solid phases. Therefore the absolute rate of evaporation (me) defined by equation 9 is assumed to depend on the thermodynamic properties of the surface, for instance, the pressure Ps* and temperature Ts. During studies of the condensation coefficient (f) of water vapor Alty and co-workers4 observed that although only a fraction of the vapor molecules striking the liquid surface condense, all molecules attain the liquid surface temperature after colliding with the surface. The molecular density within a given volume of velocity space is defined by the following equation: dn = sdC (14) where dn = the number density of molecules with velocity C in the velocity space dC s = velocity distribution function. The extent of the rigorous mathematical approach used to analyze interphase transfer operations depends on the selection of the particular velocity distribution function(s) in equation 14. A function of the velocity distribution obtained from statistical mechanics is used by Lennard-Jones and Devonshire31 to describe exactly the behavior of simple molecules held by Van der Waal's forces. This study is useful for the prediction of the behavior of simple gases (hydrogen, helium) striking a surface. For a uniform gas at steady-state conditions the form of the velocity

17 distribution function(s) predicted by statistical mechanics is the Maxwell velocity distribution defined as: = n B3 B2[(U-U) + (V V)2 + (w-2 () s = n 2e (1) where n = number density of molecules U,V,W = molecular velocities in the x, y, and z directions, respectively of the Cartesian coordinates drawn at the liquid surface (U and x are positive in a perpendicular direction away from the liquid surface) U,VW = mean absolute velocity of the molecules in the x, y, and z directions, respectively B = c During evaporation or condensation the behavior of gas molecules During evaporation or condensation the behavior of gas molecules deviates from that of a uniform gas because of the disturbing effect of the liquid surface. Additional deviations from uniform gas behavior may be due to the fact that at the vapor-liquid interface there is intraphase heat transfer among the gas molecules. In general these deviations from the Maxwell velocity distribution will be small and will be indicated by the agreement between theory and experimental results. Thermodynamic equilibrium at the vapor-liquid interface implies that U = V = W = O and the vapor and liquid temperatures are equal at the interface (Tg = Ts). Substituting for the velocity distribution function(s) from equation 15 in equation 14 and integrating over all velocity space, Schrage45 derives equation 9 for the absolute rate of evaporation at equilibrium. This is equal to the absolute rate of condensation and

there is no net interphase mass or energy transfer. The Absolute Rate of Condensation under non-equilibrium conditions can be predicted from the Maxwell velocity distribution if uniform gas behavior is assumed very close to the vapor-liquid interface. In this case the mass rate of flow of molecules moving toward the interface is negative (U < 0). Using Ug instead of U as the term corresponding to the rate of mass transfer in equation 15, and with V = W - O corresponding to the mass transfer conditions, Schrage45 derives the following equation for the absolute rate of condensation under non-equilibrium conditions: mc Pg r (16) 2Bg7l /2 where subscript g refers to vapor properties at the vapor-liquid interface. mc = absolute rate of condensation,lb per (hr)(sq ft interfacial area) = a correction factor involving the error integral ( (BgUg) and defined as r = BgUg B [1 - BgUg )]. (17) Substituting for the gas density and Bg and comparing equation 16 with equation 9, the absolute rate of condensation is expressed by the following equation: mc = ()(T)/[T (18) When the two phases are at equilibrium the absolute rate of condensation and evaporation are equal since in equation 18 at Ug = O, r = 1.0,

19 and (s) = = 1.0. The Rate of Mass Transfer for a pure substance at the vapor-liquid interface is obtained by adding equations 9 and 18: gi M [Ps -~ g 1T (19) 2 whereTs where ms = condensing load, lb per (hr)(sq ft interfacial area) Tg = vapor temperature at the vapor-liquid interface, OR. The following assumptions are implied in the derivation of equation 19: 1. Vapor behaves ideally. 2. Vapor molecules behave similar to those of a uniform gas. 3. No intraphase mass and energy transfer in the vapor. 4. Condensation coefficient (f) is constant and independent of the molecular vector velocity. It is a function of the state of the surface and the kind of molecules involved.45 5. Behavior of molecules described by the Maxwell velocity distribution. 6. Non-equilibrium conditions at the vapor-liquid interface. When the two phases are at equilibrium and both (Ts/Tg) and rare unity equation 19 becomes similar to equation 7 presented earlier and discussed frequently in the literature. Use of equation 19 requires the evaluation of the correction factor F. Equation 17 presents Fas a function of BgUg or ~g (BgUg = 0g). The quantity ~g is expressed by the following equation:'

20 1/2 Ms PS. (20) Calculated values of (F-1) are presented graphically as a function of |Igl for the range 1 > Igl > 10-3.45 The use of equation 19 to predict the deviation from equilibrium for actual cases is made difficult by the functional interdependence of ms} me, f, r, and y. Schrage applies equation 19 to predict the deviation from equilibrium (Pg/Ps*) during evaporation and condensation at different values of the ratio (ms/me). Although equilibrium conditions are not assumed at the interface, a value of unity is used for (Ts/Tg) and f in order to simplify the evaluation and use of F in equation 19. A relationship equivalent to equation 19 with the assumption of F equal to unity is presented by Bosnjakovic in connection with discussion 2314 of the condensation of superheated steam. 5 This theoretical attempt seems to be the only one reported in the literature on superheated vapors and does not distinguish between the interphase film and intraphase film temperature differences. There is no evidence of the application of the theory of interphase mass and energy transfer presented by Schrage for the interpretation of experimental results with superheated vapors condensing on the outside of a horizontal tube. Application of this theory and the resulting equation 19 is made in the next section to correlate the experimental condensing load and superheat with the calculated interfacial temperature and pressure conditions for superheated Freon-114 and steam. The calculated results are also correlated as a function of the interfacial vapor film coefficient, the interfacial film temperature difference, and the interfacial temperature and pressure conditions. A method is outlined for the design of superheated vapor condensers using

21 these correlations. The use of equation 19 is simplified by expressing (F-i) as a simple function of I0gl and combining the resulting equation with equations 19 and 20 to eliminate F from equation 19. The relative importance and effects of interphase film and intraphase film temperature differences are also discussed in the next section.

EXPERIMENTAL APPARATUS AND MATERIALS The experimental apparatus consists of a closed system for generating vapor, superheating it, condensing the superheated vapor and returning condensate to the vapor generator. Figure 1 shows the entire experimental unit and Figure 2 is the flow diagram describing the various units. Details of the apparatus are given in Appendix A and Figures 3 and 4. The essential feature of the apparatus is the horizontal condenser tube, 3/4-inch outside diameter and 3 feet long housed in a 6-inch shell. Table I gives the condenser shell and experimental tube characteristics. Four thermocouples are installed in the tube wall to measure the temperature. Water at a controlled temperature is circulated through the tube to extract the heat from the condensing vapor. The heat transfer rate is determined by the temperature rise of the water measured with mercury-inglass thermometers and by the flow rate of water indicated by a calibrated rotnmeter. Thermocouples in the vapor space of the condenser indicate the temperature of the vapor. A pressure gage or manometer gives the pressure in the condenser. The degree of superheat in the vapor is automatically controlled by an electric superheater. Water and Freon-114 are selected for this study as two fluids with widely different properties. Freon-114 is chosen as the organic fluid because generally it gives stable film condensation, it has a suitable vapor pressure, and its cost is not prohibitive. The condensation of superheated Freon-114 vapor is encountered in industrial refrigeration units. 22

23 cn FLU 1.. 11.... | I LU I I,* --- ---- -I —-.......

WATER T4 2 PSI 1 G H STEAM 1 4 TER S3 7 ~~~~~~~~~~~~~~~~~~~'T'I C C OTO REAl 9~~~~~ T. ~,_ I Le MC. iv~~~r I WN-S 8 =' ~I THERMO3WA~s~ ROP ST'AT 133 R CONDENSER I THERMOCOUPLE SWITCH AP 2 SUPERHEATER 9 FLOWRA 125_CU POW E R 3 REBOILER- IO WATER PUMP AND MOTOR STEAW4 AUXILIARY CONDENSER I I STEAM TRAP 5 VACUUN PUMP 12 WATER HEATER 6 JERGUSON SIGHT GAUGE 13 WATER COOLER 7 PRESSURE GAUGE 14 STIRRERI AND MANOMETER FIGURE 2-FLOW DIAGRAM OF EQUIPMENT

"- 1 z2l 1~1C-~- - VDs. --- FIGURE 3-DETAILS OF CONDENSER SHELL AND TUBE A / -0- 30 GAUGE /- WELL: If 1 s O PPER0.055" DIA. - CONSTANTAN /16" DEEP.072" O.D. INSULATED WIRE / ~~4 j.\t~ _ ~|.009" WALL THICKNESS SEJUNCTION A TUBE SOLDER 3-GROOVE| /f'i 0.076"XO0.076"XO.50"LONG 3 F II SECTIONAL VIEW A-A FRONT V/EW FIGURE 4- DETAILS OF WALL THERMOCOUPLE INSTALLATION

TABLE I CONDENSER SHELL AND EXPERIMENTAL TUBE CHARACTERISTICS Condenser Shell F Experimental Tube Material - Galvanized Plain Carbon Steel Pipe Material - Plain Copper Tube Outside diameter, inches 6.648 Outside diameter, inch 0.750 Inside diameter, inches 6.066 Inside diameter, inch 0.531 Wall thickness, inch 0.291 Wall thickness, inch 0.1095 Header spacing, inches 36.5625 Exposed length of tube in condenser, inches 34.4375 Overall length, inches 39.0625 Outside area, Ao, sq ft/ft 0.1962 Inside area, Ai, sq ft/ft 0.1390 Right-end removable header Area ratio, Ao/Ai 1.41 Outside diameter, inches 8.5 Total outside heat-transfer area, sq ft 0.565 Inside diameter, inches 6.0 Inside cross-sectional area, sq ft 0.001533 Bolt circle diameter, inches 7.5 Logarithmic mean diameter, inch 0.636 Eight 0.5-inch bolts Gasket: Garlock No. 7022, 0.125 inch thick Metal resistance at 212F, km = 218hr-F-ft End packings hr-~F-sq ft outside Chevron type 530 Btu Outside diameter, inches 2.0 For Runs 56 to 72: Inside diameter, inches 1.5 Exposed length of tube in condenser, inches 35.4375 Depth, inch 1.0 Exposed length of brass collar at each end in condenser, inch 0.5625 Sight windows Outside diameter of brass collar, inches 1.50 Number of windows 6 Outside heat-transfer area of collars, sq ft 0.0552 Diameter, inches 2.0 Outside heat-transfer area of tube, sq ft 0.582 Glass thickness, inch 0.50 Total outside heat-transfer area, sq ft 0.6372 Inner gasket: Teflon, 0.125 inch thick Total inside heat-transfer area, sq ft 0.424 Outer gasket: Crainite, 0.0625 inch thick Area ratio, Ao/Ai 1.504.~~~~~~~~~~~~~~~~~~~~~~~~~~~Ae raio A o A 1.5

27 A study of superheated steam is particularly interesting because of its frequent use and the possibility of condensing superheated steam in industrial power plants. At the time steam was selected, it was expected that it could be made to condense filmwise. However, for most of the data on steam, the condensation was a mixture of dropwise and film condensat ion.

EXPERIMENTAL PROCEDURE AND DATA The cleaning and assembling of the condenser shell and tube is important, particularly with steam since dropwise condensation occurs under certain conditions. The charging of the apparatus with water or Freon-114 is described as the second step in the procedure. The measurements made on condensing superheated Freon-114 and superheated steam are presented along with tabulations of the data. CLEANING AND ASSEMBLY OF CONDENSER SHELL AND TUBE The experimental tube is cleaned thoroughly by first treating with hydrochloric acid, then rinsing with water, and finally rubbing the outside with an acetone-wet pad to remove grease. The condition of the outside surface is important with regard to the type of condensation which is obtained. Low-surface tension fluids in general form a smooth film upon condensation. Stable film condensation is obtained during the condensation of superheated Freon-114. This is illustrated in Figure 5. The actual tube surface can be seen beneath the clear condensate film. The clean experimental tube does not offer a stable surface for the film condensation of superheated steam. Apparently, small specks of grease or dirt are sufficient to cause the formation of active centers of dropwise condensation. The nature of the surface and its effect on the type of condensation has been studied extensively.33 An interesting 23 description of the two types of condensation is given by Jakob. Fatica 20 and Katz present a fundamental study and a method of predicting dropwise condensation of steam. A more recent study by Hampson gives also 28

FIGURE 5- FILM CONDENSATION OF SUPERHEATED FREON-114 FIGURE 6- DROPWISE CONDENSATION OF SUPERHEATED STEAM

30 many references in this field. Several attempts made during this investigation to obtain stable film condensation with superheated steam include various degrees of polishing of the surface, and the use of very small amounts of organic polar compounds (e.g., alcohols) as wetting agents. No appreciable variation in the transition period from initial film to eventual mixed condensation of steam is observed by such technics. Figure 6 illustrates dropwise condensation of superheated steam. The clean tube is placed in the condenser in such a manner that the brass collars protrude at the two ends as shown in Figure 3. The tube is secured tightly with Chevron packing and the packing glands. Tube assembly is completed by connecting the tube to the water line with the rubber hose connections (No. 15 in Figure 2) and joining the four thermocouples to the main thermocouple circuit through Cinch-Jones connectors. CHARGING AND OPERATING THE EQUIPMENT The experimental apparatus is evacuated prior to charging. A DuoSeal vacuum pump is used for about one hour to reduce the pressure in the apparatus to about 0.1 inch Hg absolute, as shown in Figure 2. At the end of this period valve A is shut off and the vacuum pump is stopped and separated from the condenser vent. The system is charged with Freon114 by placing the cylinder in a horizontal position and connecting it to vent A. Valves J, K, and N are shut off and cold water is run through the condenser tube by turning on valve L. Valve A is opened and the system charged by condensing Freon-114. The reboiler level is sufficiently high when about 50 lb of Freon-114 are introduced. To charge the system with distilled water, vent A is shut off after

31 evacuating the apparatus, and a 3-gallon bottle of distilled water connected to the reboiler vent b. The reboiler level is sufficiently high when about 2.75 gallons of water are introduced. No cold water is run through the condenser tube during this period. The auxiliary equipment is arranged to provide hot water at a constant temperature and flow rate. Valves G, K, L, M, and 0 are shut off and the reservoir is filled with water up to a level 10 inches from the top. Valve N is turned on, the stirrer and the centrifugal pump are started,and the water is circulated through the water heater and raised to the desired temperature level. Valve M is then turned on completely and the desired water flow rate is maintained with control valve E. The selected condenser pressure is obtained by controlling the steam flow rate into the reboiler. To superheat the vapor the thermostat is set at the desired temperature and the power switched on. The average tube-side water temperature is maintained constant by a combination of the following methods: by controlling the steam pressure of the water heater, by varying the amount of cooling in the water cooler, and by draining some hot water from the reservoir through valve O and introducing some cold water through valve I. The system is purged from non-condensables by bleeding vapor through vent A and the manometer vent. The system is free of all non-condensables when no variation is obtained for the tube-side temperature rise under steady operating conditions. During the condensation of steam under vacuum the vacuum pump is used to apply a continuous suction through vent A. This avoids the accumulation of non-condensables due to leakage. The experimental data consist of the following measurements: condenser

32 temperatures, condenser tube-wall temperatures, tube-side water flow rate, inlet and outlet water temperatures, room temperature, and barometric pressure. EXPERIMENTAL DATA Experimental data are presented for Freon-114 at two pressures, steam at four pressures, and for "dry point" studies for steam under vacuum. The procedure consisted of condensing saturated vapor followed by various degrees of superheat up to 180~F for Freon-114 and 184~F for steam. A sample of the original data is shown in Table IX of Appendix C along with the calculation of results. Condensation of Freon-114 is studied at two pressures of 77.0 and 43.7 lb per sq in. absolute and different vapor superheats ranging from O0F to 179.670F. These experimental data and the calculated results are given in Table II as run numbers 1 through 26. The condensation of superheated steam involves several studies. Four sets of data are taken comparable to those of Freon-114 at constant pressures of 9.16, 23.87, 23.35, and 44.09 lb per sq in. absolute with maximum superheats varying from 109.12~F to 184.25~F. These runs are presented in Table III. The wall temperature is measured for run numbers 40 through 55. Run numbers 56 through 72 are made without measurement of the experimental wall temperatures and are taken on the original tube without the four thermocouples and with characteristic given at the end of Table I. These runs are interesting because they constitute the only data obtained in this study with relatively stable film condensation of steam. Wall temperatures for runs 56 through 72 are calculated from the experimentally determined equation for the prediction of the tubeside heat transfer coefficient, as shown in Appendix B.

~,,z n (1Pt lm Cranemini J. on ) 1' —.o. 170.o ~9.~ l~5.1 ~.~ 7~-~9 170.0 -- 133.50 0.00~ O.00~S --- 170.0 17~.8 2'~.T~ 1~.~ l~.~& 0 ~8~ 1~.72 *.~ 71~0 12,(~JO 8k.~ 1~0.1 ~8.~ Tl~.~ lO.~ 1+9.01 119.8 ~.0'l'k. ~ ['(0. [.... 1~.~ 0.00~6 0.00~ --- 170.} -~ -- 1~.~ -. 0.~ t~o ~0.72 ~.~ 71~0 12,6~0 0~.7, l~.~ ~.,0 ~,.s, 10~.~ ~.~1 ~.0 ~.~ 70.~ ~-;a.a ~.7~ ~ 1~.70 0.009~0 0.00~ 0.0~0~0 170.~ 17~.~ i~ -- l~.m -- 1.91 ~ 1~.~ 2.$}?o~o 1~,~oo $.19 lkg-O ~0.~?k.~ 167.2 k9.78 lkl.8 251.0 69.~0 l'tg.0 k.~ ~ 1~0. ~'~ 0.00~ O. 00~ 0.000~ 171.8 1~.0 -- 1~.~ -- ~.r~ *,~0 ~.m ~.~ ~ l~,teo ~1.~ 1~.o ~.9~ ~.~ ~.o ~o.o~ ~7.8,,~.~ ~.~o 18~.7 n.,e ~ 1~.~? o.ooo,~ o.oo~ o.oo~ 1~.~ 17~.~ & -- 11~0.~0 --?.o~ z799 k9.~o 2.8~ ~ 12,z8o 91.oo 1~9.o 6O.~9 79.81 198.o Do.6~ 1~7.o ~2.9 67.90 181.8 12.~1 99v 127.89 0.00690 o.oo99o o.coloo 168.7? --- 1~).~ -- [~,~ 1~; 21~9 i~.~ 2.~ ~o 12,~o lO~. 61~ 11~.8 99.~1 ~,81 12~.8 5~.81 l~o o 2~o.1 (~.6o l~.k 55.~1 57# 1~.81 0.00~ 0.00~1,0 0. ofl~9 1~7.1 1~.8 --- 1,0.~ - z,:o ~.~ zsz, ~ ~o mteo 1~1.~ 1Ol.O ~.~ lm.l~ lo~.~ 99.ee ~.2 m~.8 0,2o ~.~ ~7.~ ~-~.~ ~.~ o.oo~1~ o.oo~ o.oo~ ~o.o ~11.~ lO -- l~.]~ - ~.1~ ~.~ ii~.l~ ~.~ ~ 1~,9oo 1~9.89 ~0.1, ~.~ 1~o.~ ~.9 ~3.1~6 11~.~ 211.o 69.00 19~.# 69.96 18~.9 125.~9 O.OlO1~ o. oo'j~:ao o.oo~8 lJ~7.1 185.7 11 -- 1~.~ -- 6}.~ ~1~ ~.1~ p.~?o(ao 1~, ~OO lkT.~ ~-7 ~.07 1~8.~ ~0.0 60.6~ 116.~ ~-7 61'.6o 19~.9 7~-~ 168.~ 1~.67 o.o1111 o.00~16 0.00~ 1~.~ 18'j.~ kja 1~ --- ~.7'~ - 95.~ [al~ i~.1~ ~.~ ~ 12,~jo lW.~?l.~ ~?.11 1~.~1?~.2 6~.oo 1o~.~ 19}.9 61~.~ 1~.8 1o5.21 1~1.o 1~1.91 o. Ol~O o.oo9~ o.oo~ 1~?.8 1~.o a --- ~.19 - lm.~ m~ ~.~o }.oo},~o 1~,~o 1~.~ ~-~ ~.~ 1~.~1 ~.~ ~.~ ~o~.o 18~.~ ~9.~o ~.~ ~.m ~c,.o ~81.~ o.m~ o.oo~m o.0o~1 1~o.~ 1~1.~ 19 --- ~.~} -- uo.~ ~ ~.~0 ~.o~ ~1o 15,~o 819.~ ~-~ ~.~8 a,.~ ~.~ v~.~ lo9.e 1~.~ ~.~o ~o}.~ ~9.~ ~.~ 11~.~ o.o1~ o.oo~ O.OlO~ 1~ 1~}.~ ^,1. ~,1, ~.~s 1~.~ t~ ~.~ ~,...~ ~o,.~,~t - i,~ ~-~o~ 17 -- 10~.t~ - ~.~ ~,o,a.~ Zl~'l ~ lOOOO 97.~7 17~.o ~.~8 ~.~7 9~.o6 1o~.~ 181.~ ~9.09 t~.o lO.~ ~7~ ~.~7 o.oo~, o.oo~1 o.oolO~ ~ m8.6 18 --- 122.90 -- ~6.1~ 297o 1,8.118 ~.21# 9(~37 10,070 7k.lR 1~9.8 97.1~ 69.79 19,~.o.57.79 9~.9 17k.2 ~9.09 ~57.1, Z6.66 577 96.21, 0.006~. 0.00~89 0.00~69 Z~ ~:Ol ~ --- 1~.~1 -- ~e.O~ ~0,m.*S ~.~1~ ~, 10,070 ~.7~ ~lZ.1 ~.~ ee.~ ira.7 6o.~0 ~.~ 1~.a ~.0~ ~7.~ ~2.~ ~ ~.~ o.00e~ o.00~ o.00,t,7. ~'~ ~,~ ffi --- 197.?'f -- 61.~ ~ I~.T~ 2.~1~ ~ lO,070 10~.0~ ~.} 59.~2 1~. ~'j ~.} 6~.76 ~).} 1~.0 ~.o9 ~57.# 69.~6 159 9~.91 0.01018 0.00~ 0.o~ ~9.6 ~o7 ~ ~-~ 9~.~ ~.m ~.~ 71~ ~.0 t~.8 ~1.00 2~.9 Io~.m 8~.~ ~.99 0.0~97 0.00~ 0 0011~7 z~ ~.~ oo --- ~09.~ -- 10~. 11~ ~0 ld~.~o 2.07 ~0 9,#~0 60.0 i~6.~ ~0.67 l~k.~ 6o.9 72.11'F~.9 150.7 ko.~o 2~.~ 11t*.69 8~.2 90.8~ 0.01~} O. o01~6 ~0~ ~k --- ~0.~ -- 1~.17 ~0 ~S~ 1.~ ~ ~,000 181.~ ~~.9 91,~ 1,0.~ ~0.~ *~.~1 ~.~ 117.~ ~oo ~ m.~e 6~.9 ~.67' 001~ O OiW8 ~0~ ~.6 --- e~7.~1 -_ 1~1.1~ t~7o ~o.6o 1.~ ~ ~,ooo eo~.ol ~.o ~o.w a~.~ ~.~ 81.9~ ~.~ 11o.9 ~.~o ~.o 17o.o, ~.7 ~.~7 o.o~o o.oo~ o.o1~ ~ --- zr't6. O~ -- I'F). 67 2970 Idt.k~ 1.91~;,9~0 8,89O Z27.61 ~,~.9 1*9.#k ~6.65 ~.0 87.~ ~.65 101*.o 57.7o g:.r~. ~. 191.99 1,6.0 8k.lk 0.08569 0.00]~95 ~

TABLE III ~?ED RZSULTS FO~ SUe~HZ~TED STEA, i I i....... c.... to, ~F Ato, ~F f~ hc, T,,'F I............. mxed Condensation ~0 9.149 192.46 189. O~ 3.42 2666 177.60' 3.26 8,700 15,40o 14.~6 1057 188.76 3.70 4160 986.37 8.82 19.6 0.28 55,000 5.~2 4~O9 189.04 41 9.16~ ~)0.69 189.14 11.55 2666 177.2o 3.31 8,840 15,620 23.49 665.o 188.70 11.~ l~Y2 990.17 8.93 15.8 0.285 9~,900 11.705 139 188.985' 42 9.098 223-33 188.78 3A.55 2666 177.60 2.9~ 7,740 13, ~'00 45.73 229.6 187. U2 ~6.31 377.0 1501.43 7.72 13.68 0.298 57,600 ~6.07 ~80 187.26 43 9.218 269.69 189.39 8o.3o 2666 178.00 2.8~ 7,690 13,600 91.69 148.2 181.85 87.8~ 15~.8 lO23.o3 7.50 13.28 O.2~ 98,100 87.61 155.2 182.08 44 9.16~ 288.45 189.14 99.29 ~o66 177.20 2.824 7,550 13.~0 111.23 119.8 183.96 tc~.47 127.8 1032.25 7.31 12.92 0.228 ~8,6oO 10~.24 1~ 18~. 19 45 9.168 298.26 189.14 lO9.12 2666 177.6o 2.52 6,72o 11,9oo 120.66 98.6 178.97 119-29 99.6 1037.o9 6.49 11.49 0.195 61,00o 119.1o 99.9 179.16 Avg. Value 9.16 189.10 2666 177.53 Nixed Condensation %6 23.8~7 237.28 237.28 0 6050 177.40 11.08 67,000 118,900 59.88 1978 2o9.9O 27.58 433O 995-97 70.3 124.2 27.98 4,3.)O.... 237.28 47 --- 253.96 --- 16.68 6090 178.0 lO.4 63,000 111,4oo 75.96 1~68 2G9.55 h4.41 251o 962.98 65.5 116.0 25.10 4,~J~O 19.31 5760 2~-65 48.., 26O.89 --- 23.61 6090 178.25 10.30 62,%0O 110,2OO 82.64 13~ 209.~8 51.41 2145 965.89 6~.5 114.1 2~.80 4,49O 26.61 419O 2~.28 %9 --- 268.10 --- 9O. 8.2 6o9o 178.40 10.4 62,90o 111,200 89.'~0 1240 2o9.42,98.68 1892 5'69.57 6~.9 11%.8 29.0O 4,49O 35.68 3300 2~.42 9o --- 304.70 --- 67.42 609o 178.20 9.99 60,900 107,000 126.5 6%6 207.18 97.52 1098 987.39 61.3 108.4 23.5 4,490 74.02 1447 29O.68 51 --- 56o.00 --- 122.72 6o5o 177.75 9.5o 57,5oo 101,800 182.25 558 199.10 16o.90 652.1013.97 96.6 100.2 21.9 4,69o 139.o 7~2 221.00 52 --- 370.%9 --- 155.21 6050 180.72 9.45 57,100 101, ~0 18~. 77 5~4 203.94 166.55 60~ ~ 1018.97 96.1. 99.4 21.7 4,660 144.8~ 699 ~.6~ 53 --- 590.10 --- 152.82 605O 176.95 9.5o 57,9OO lol,800 213.15 %77 197.1o 195.oo 526 1ce8.47 96.0 99.0 21.75 4,68o 171.29 59~ 218.89 --- 408.00 --- 170.72 6090 178.00 9.41 57,000 101,000 29O.0 ~39 202.91 205. o~ 4~2 10~6.57 5~..0 97-3 21.5 4,700 183.99 590 224.41 95 --- 421.93 --- 184.25 609o 176.82 9.24.55,900 99,000 244.71 40~ 19~.70 226.83 ~3~.5 1043.37 53-5 94.6 20.8 4,7.9o 206.03 ~ 215.5..~ AvE. Value 23.87 237.28 609O 178.09 Film Condensation (to calculated from predicted tube-side water coefficient -- Appendix ~ ) 23.441 2~.52 2~6.52 0 ~55 177.40 7.20 3%O00 ~,900 ~.12 928 212.03 24.~9 22%0 9~.26 ~.7 57.6'm,..49 2,2'8.... 2~.~ 57 23.299 2~6.19 2~6.19 0 %855 177.~6 7.13 ~,6~O 9,400 98.83 929 211.664 2~.53 2220 9~+.68 ~6.32 57.0 24.53 2,215.... 2~6.19..58 2.5.312 2~6.22 236.22 0 ~895 177.39 7.10 34,4~0 ~, 000 ~.87 919 211.42 24.8o 2180 994.66 ~6.10.56.6 2~.80 ~,~.... 236.22 9~ --- 2~6.98 --- lO.O7 %859 178.2o 6.79 33, o00 51,69O 6~.18 798 210.77 35.61, 1~9o 99~. 74 ~+. ~0 9~.0 23.0 2,2~6 12.61 4100 233.77 60 --- 265.96 --- 2~.65 4855 177.32 665 32,39o 9o,69o 88.6~ 571 209.~9 ~6.61 895 969.52 33.40 ~.4 ~.4 2,262 ~+.21 1480 231.75 61 --- 283.6o --- 47.29 %855 1~7.56 6.71 32,6o0 51,100 lO6.0~ ~ 209.86 73.74 69~ 978.18 33-35 52.3 22.6 2,263 91.14 1000 232.~6 62 --- 288.83 --- 52.52 %855 177.12 6.65 32,5OO 9O,600 111.71 49~ 209.1~ 79.68 635 98o.78 32.99 51.6 22.2 2,~80 57.48 881 231.35 63 --- 335.29 --- 9B.98 4815 177.22 6.%3 31,ooo ~8,900 1~3.07 5O7 2O7.9O 127.39 ~O 1003.10 5O.85 %8-5 20.9O 2,318 106.49 455 228.80 6~ —. ~66.9O --- 19O. 19 4855 177.09 6.18 9O,000 47,090 18~.41 248.2 206.82 159.68 29~ 1018.10 29.5 ~6.5.20.16 2, ~+0 1~9-92 398 226.98 65 --- 399.07 --- 198.76 4855 176.76 5.92 28,8oo 45,100 218.31 206.4 205.32 189.75 238 1031.60 27.9 43.7 18.92 2,~80 170.8~ 26% 22~.24 66 --- 402.77 --- 166.46 4855 177.75 6.50 ~0,600 48,000 22%O2 213 20~. to 19~.67 246.5 1035.90 29.6 %6.4 20.9O 2,~83 174.17 275.5 228.6O Avg. Value 23.351 2~6.31 4851 177.98 Film Condensation (to calculated frOm predicted tube-side water film coefficient -- Appendix ~ 67 44.O88 273.17 273.17 4855 178.79 11.98 ~,200 88,2OO 9~.~8 935 2~.21 ~8.96 ~ 929.9~ 6O.5 9~.9 ~8.96 1,963.... 27~. 17 68 --- 5O~.48 --- 29.31 %855 176.96 9-93 48,150 75,6OO 125.52 6O2 224.66 77.82 972 944.~- 51.o 80.0 ~6.9 2,0~ 4O.92 18~ 261.96 69 --- 372.83 --- 99.66 4855 177.75 9.5O 46,100 72,400 195.08 370.5 223.39 149.~ lu~ 980.14 47.05 7~.9 ~ —5 2,097 114.9A' 630 297.89 70 --- 578.32 --- 10415 4855 177.o2 9.635 %6,8oo 73,400 2Ol.3,0 ~,-5 223.32 155.00 473 983.04 47.55 74.6 35.2 2,082 119.80 612 2~..'~ 71 --- 416.5 --- 143.33 4855 177.46 9.51 45,2oo 71,00o 2~9.o~ 297 222.29 194.21 ~65 1001.6~ 45.19 70.9 55.6 2,115 160.61 %81 295.89 72 --- 418.91 --- 145.74 4855 177.98 9.36 45,~OO 71,4OO 241.53 296 222.43 1~6.48 ~63 1002.6~ 45.3 71.1 33.8 2,106 16~.68 4.59 2~.2} Avg. Value ~.A. o88 273.17 4855 177.56

35 Buns 27 through 39 are made with superheated steam under vacuum to study the wall temperature and heat flux under conditions where a superheated vapor might not condense and wet the surface. These runs are sum marized in Table IV. Runs 7 through 105 are made with saturated steam at 22576F to 248.59OF to study the tube-side heat transfer coefficient for water. Runs 75 through 84 are made prior to the installation of wall thermocouples whereas runs o85 through 105 are made with measured wall temperatures. The conditions for all runs are controlled-to give Wilson-plot 49 type data. Appendix B presents the calculation and discussion of these results and those on the longitudinal temperature gradient in the tube wall based on runs 101 through 105. Experimental data and calculated results for runs 75 through 105 are given in Tables VI, VII, and VIII in Appendix B.

TABLE IV EXPERIMENTAL DATA AND CALCULATED RESULTS FOR SUPERBEATED STEAM (Mixed Condensation - Dry-Point Runs ) i 2 3 4 5 6 7 8 9 10l1 12 13 14 15 16 177 18 |Cond e cdne auai|Slrea ae ly|Ag ae ae ep |Ut1Ba etTse vrl ep oefcet |usd ue|Otiei offcet |Ts.Dieec odnig| C Ru o rssr ep, epA ~ ae Tmp, Rs raserd Rae Dfeece C t o ufaeTm.ndm-DferneBu (TVt) F od se | S ei g F|TvFIX t bh y F |At~,Buh A h-qI ~a Oh-Fs tot| tF | Ao r -qi vt||Wzl/r|M.....s.... ~~~~~~~~~~~~~~~~~~~~~rTm. Toa Hea 29 ~ ~ ~ ~ ~ ~ ~ ~ ~~ ~~~~~~~~~~~~~~ ~etTase Coffcin Outside Tube1 Outsid Film Coeffc ien Tem.77 2056 39 17D i feec C ondns i n 51.6 123.373-4g 30 8 261 8.8 43.2 Trasfere Rate0 Difere c e Surf a c Temp0 T em.1 D ife r nc (Tsv.47 48.6 Load9 5.9.66.9 31 7.8 psia8 18.6 T g.1 ~ 21 T s v, 0.28 121 2t 504.6 l 5817.54.5 / 724.4120 r.3 32 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~w 7-7 220.3 ~8.1 39.2 4215h Q/A.7 Btu/r-2 ft6 AlaO 44.6 42.1 17.04.3 t 3 u 40.06l 27 9.0 23.0188.2 8 179.9 72 4215 176.20 10.62 448 0 1210 41.7 7 1 29.0 179.65.941440.33 50.02 3.03 o71.202 Avg 8.6 2Value17 439 4215 176.1 0.7 9305 6 39 0 7 0 1 8 8 1 3 1 2 37. 457 30 9-55 2266-35 182.86 76.31 266621 176.00 0. 9 1670> 296l ) 7-50. r S:12 191.08 17.( 48.6 6S= ll ) 1.604 -2Dry 36 9-27 222.66 189.64 81.11 2666 17589. 281 2 1 0 --- 9 --- 8 -17.26 188.64 Low2 ----- 1.20 7 2. 1 t 327 9.11 220.77 188.11 78.22 4215573022106 18894.60 --- 1 1 -— 78.57__18.0 Low 2 --- --- 0 1.036 1.86ngDr 33 7.68 218.89 180.52 78.67 42715 7.0 01 9889.210 --- 1 --- -— 77.00 ___18.8 9 ___3 ___ 2 0. 801.70 r 369 8.29 2690.42 1879.64 81.02 2666 1889.10 -----— 81.12-6 188.60 Lih -- ow.g r

CALCULATION AND CORRELATION OF RESULTS This section presents the experimental results obtained from the original data, the discussion of the mechanism and theory of filmwise condensation of superheated vapors, the correlation of experimental and calculated results, and an outline for the design of superheated vapor condensers. The experimental results are presented in a manner which shows the effect of superheat on the overall heat flux, the condensing load and the overall outside film coefficient. These results are given in Table II for Freon-114 and Table III for steam. The variation of these results for the case where the degree of superheat of the vapor does not vary apreciably whie' the saturation temperature of the vapor approaches that of the outside tube surface is discussed and summarized in Table IV. The concept of the vapor-liquid interf acial f ilm is applied to the condensation of superheated vapors. The calculated condensate surface temperature is used to obtain the temperature difference across the condensate film and the interfacial vapor film. The temperature difference through the interfacial film is used to determine the interfacial film coefficient. The results of these calculations are shown in Tables IIand III for Freon-1114 and steamr4respectively., The assumptions involved in the application of this mechanism is discussed. The experimental results are correlated on the basis of the'Interphase mass and energy transfer theory presented and discussed in the liter -- +IIatur rev17iew.6 The feto suiginefca qiiru

38 Ts T = 1.0 Tg is discussed and illustrated in the correlation of results. The experimental condensing load is correlated with the degree of superheat and the interfacial temperatures and pressures as a function of the condensation coefficient (f). The calculated interfacial film coefficients are correlated with the temperature drop through the interfacial film and the interfacial temperatures and pressures as a function of the-condensation coefficient. Table V presents the results of these calculations. A comparison is made between the condensate film coefficient obtainedby the conventional design method presented previously and the experimental coefficients calculated on the same basis. The recommended correlations are used to outline a method for the design of superheated vapor condensers. OVERALL PERFORMANCE OF CONDENSER WITH SUIPERHEATED VAPORS The experimental heat transfer rates and condensing loads are presented in this section. The rate of heat transfer in the condenser is determined from the tube-side water flow rate and the temperature rise of the water by the following equation: Q- WtCp (T2-Tl) (21) A A where Q=total heat transferred,, Btu per hr Wt= water flow rate, lb per hr =2 outlet water temperature, OF

TABLE V CORRELATIONOF CALCUAE Co ONESIGRATES ADINEFHAE FILMCOEFFICIET (RBasd oi Results in Figur 18) 1 2 3 4 5 6 7 8 9 10. 11 12 13 1841 FunctioniofCorltnFuci. Codnae Coideisate Squar Roo of OItiphasi Condensation Depressionof IntrhseFl lIterha Fi1m CFunc~tiong InFrphtioPessuF CifereelCodens Run o. Srfae Tep., Surfac Absolutte Temp., FPressF Coefficient Superheat, Condensate ITemp. ifBfierec Coeficiient Femp.RatioFroup psi Coficdlito 2 T N. S,02 Ti Presur, Differencei ATs, F SuraceTi Tem. itip DFi hi, Btu TiiFiti b8p \p17 C ME~ii~ Ps (P (0)2tPE)F h0,F(si -T(s), [ T,)i/ _-HF8] Gs(f) =[h F s iaE 8 (8.F,,Oi (Tsv Tihr 0- F-sq ft out (.)FgF,') F 0 F k P G(iiB-, ()=0[F ~J/ i Froin-114 FilE Condensation it ATF = 0 Ts Ts.iv 28.00'F Fi PgF = 71.43 piii 1 128.00 71.43 24.32 0 --- 0 0 0 2 128.00 71.43 24.32 0 --- 0 0 0 --- ------ 3 127.58 70.998 24.28 0.832 18,820 5.88 0.82 5.86 2160 2860 0.9901 0.077 81,000 3,2 8 127.86 70.872 28.28 0.558.10,920 7.07 0.58 7.61 1680 1833 0.9872 0.098 62,200C,6 5 127.31 70.70 28.28 0.71 8,350 8.89 0.69 9.58 1272 870 0.9839 0.150 39,835802 6 127.06 70.462 28.23 0.968 6,090 12.20 0.98 13.18 938 862 0.9782 0.078 33,1002,1 7 125.63 68.997 28.20 2.833 2,500 31.02 2.37 33.39 570 68.5 0.9860 0.883 11,530C8 8 125.15 68.51 28.19 2.9 1,880 37.37 2.85 80.22 309 46.5 0,9357 0.590 9,300 3 9 128.78 68.096 28.18 3.338 1,592 82.88 3.26 86.18 266 34.6 0.9268 0.668 8,000 7 10 123.36 66.718 28.15 8.712 1,080 61.35 8.68 65.99 189.2 16.32 0.8988 0.982 5,190 7. 11 122.79 66.152 28.13 5.278 939 69.02 5.21 78.23 168.2 12.68 0.8871 1.128 8,390 5. 12 121.96 65.33 28.12 6.10 796 80.17 6.08 86.21 186.8 9.26 0.8710 1.330 3,660o2. 13 120.61 68.029 28.09 7.801 630 98.72 7.39 106.11 120.2 5.92 o.8455 1.651 2,820 2. 18 119.20 62.682 28.07 8.788 517 118.15 8.80 126.95 102.8 8.06 0.8202 2.008 2,250 1. 15 117.972 61.523 28.08 9.907 883 135.83 10.03 185.86 91.5 3.06 0.7990 2.327 i,888 1. Friii-114 FOi Ciidensitlio it ATs 0 Ts = T,., 98.00'F F, g F8 448.89 Rsu, 16 8.00 48.89 23.62 0 --- 0 0 0 —-------- 17 97.805 88.858 23.61 0.832 9,910 8.25 0.595 8.6845 1132 1122 0.9818 0.80 53,6006,6 l8 96.21 43.592 23.58 1.298 3,170 28.90 1.79 26.69 377 118.3 0.9542 0.258 15,90059 19 95.104 82.805 2-3.56 2.085 1,880 80.51 2.896 83.806 232 83.8 0.9275 0.825 9,28021 20 93.756 81.852 23.53 3.038 1,1228 59.77 8.288 68.01 157.2 19.1 0.8964 o.688 5,780 8. 21 90.69 39.755 23.86 5.135 609 168.67 7.31 111.98 684.9 5.88 0.8310 1.165 2,680o3. 22 90.896 39.625 23.86 5.265 581 107.56 7.568 115.06 82.0 5.06 0.8270 1.205 2,585 23 9.126 39.375 23.85 5.515 55 113.09 7.874 120.96 78. 8.56 0.8197 1.265 2,810 1. 28 88.838 38.520 23.82 6.37 831 132.59 9.166 181.76 63.5 3.05 0.7917 1.500 1,835 1. 25 87.074 37.38 23.39 7.51. 383 159.61 l0.926 170.38 52.7, 2.01 0.7628 1.815 1,822 83. 26 85.89 36.62 23.36 8.27 293 178.09 12.11 190.20 86.5 1.582 0.7116 2.08 1,190 62 Sieam NIixed Condinsitiin at 87s = 0 7s = 7,sv 189.10OF FS = g 9.1608 siii 80 188.87 9.1158 25.87 0.650 8,880 3.36 0.23 3.59 8290 2860 0.9985 0.0196 20,300 6o 81 188.30 9.0085 25.86 0.1653 2,580 11.59 0.80 12.39 1260 207 0.9812 0.0699 5,760o6 82 186.73 8.7082 25.83 0.8566 761 38.23 2.37 36.60 378 20.8 0.9868 0.2076 1,680o5. 83 183.57 8.1258 25.37 1.0338 325 80.59 5.53 86.12 158 3.77 o.8820 0.4778 7084.1 88 182.31 7.904 25.38 1.2568 260 99.33 6.79 106.12 125.8 2.85 o.8582 O. 5826 561 52 85 181.65 7.790 25.33 1.3710 212 109.16 7.85 116.61 102.0 1.815 o.8862 0.6370 856 39 Steam, Mixid Coidiisatioi at 8TE = 0 7, = T7,, 238.00OF F, = 8 28.080 poia 86 238.00 28.080 26.82 0 0 0 0 —--- 47 236.20 23.303 26.38 0.777 3,930 15.96 1.80 17.76 6280 221 0.9751 0.875 6,88036 88 235.83 22.978 26.37 1.102 2,720 22.89 2.57 25.86 8320 106.8 0.9646 0.672 8,860o7. 89 238.63 22.683 26.35 1.837 2,100 30.10 3.37 33.87 3320 62.9 0.9510O 0.877 3,88510. 50 230.59 21.012 26.28 3.068 930 66.70 7.81 78.11 1882 12.5 0.9031 1.872 1,522 2. 51 228.62 18.779 26.16 5.301 898 122.00 13.'38 135.38 751 3.68 b.83819 3.228 812 60 52 223.50 18.382 26.18 5.699 855 132.89 18.50 1846.99 690 3.10 0.8230 3.468 789 51 53 221.83 17.668 26.11 6.812 803 152.10 16.57 168.67 668 2.38 0.8016 3.892 6684.9 54 219.56 17.68 26.07 7.038 361 170.00 18.88 188.88 535 1.9120 0.7829 8.265. 5984.1 55 218.15 16.582 26.08 7.898 329 183.53 19.85 203.38 886 1.622 0.7693 8.538 3542.6 Steami Film CoideniitLio it 87, = 0 7, = 7s,,.= 234.50'F Fr = F = 22.589 psii 56 238.50 22.589 26.35 0 -- 0 0 0 —-------- 57 238.50 22.589 26.35 0 -- 0 0 0 —---- 58 238.50 22.589 26.35 0 0 0 0 —------ 59 233.71 22.262 26.38 0.327 8,350 11.88 0.79 12.67 8090 383 0.9821 0.121 11,860o2 60 032.82 21.738 26.31 0.851 1,617 51.86 2.08 33.38 1512 88.2 0.-9538 0.322 8,280o2. 61 031.26 21.276 06.29 1.313 1,683 89.10 3.28 52.38 978 20.02 0.9296 0.508 2,730 5. 60 230.92 21.182 26.28 1.887 380 58.33 3.58 57.91 876 16.26 0.9227 0.556 2,880 8. 63 207.90 19.980 26.23 2.609 889 102,79 6.60 107.39 451 8.53 o.865o 1.029 1,238 1. 68 025.89 19.236 26.19 3.353 362 132.00 8.61 180.61 335 2.57 0.8099 1.383 901 68 65 228.07 1.8.580 26.15 8.007 2684 160.57 10.83 171.00 268 1.66 0.8000 1.622 7084.1 66 223.58 18.811 26.15 8.178 289 168.27 10.92 179.19 266 1.618 0.7923 1.696 715 39 Stieam Til Condiniition, it ATs = 0 7, = Ti-i 265.00'F FS = 2 38.539 piLE 67 265.00 38.539 26.93 0 -- 0 0 0 —-- 68 262.63 37.080 26.88 1.495 1,880 37.88 2.37 39.85 1898. 36.1 0.9477 0.878 4.5oo13. 69 * 258.22 34.375 26.80 8.168 475 107.83 6.78 118.61 631 4.15 0.8624 1.115 1,80012. 70 257.88 38.175 26.79 4.364 857 113.32 7.12 * 120.88 609 3.80 o.8563 1.888 1,382 1. 71 255.52 32.828 26.75 5.715 332 151.5 9.88 160.98 4481 2.06 0.8163 1.996 950 59 72 255.38 32.787 26.75 5.79 328 153.91 9.62 163.53 836 2.00 o.8180 2.023 940 57

40 Detailed sample calculations are given for run 21 inAppendix C. The condensing load is obtained from the rate of heat transfer and the enthalpy change of the condensing superheated vapor. Becase of the temperature drop through the condensate film, the condensate leaving the condenser is normally assumed to be subcooled. Measurement of the condensate temperature in the liquid return line to the reboiler (Figure 2) indicates that the liquid leaving the condenser is essentially at its saturation temperature. This is due to the intimate contact of the condensate with the superheated vapor in the lower half of the condenser. The proper enthalpy change of the vapor is that corresponding to the condensation of the superheated vapor to the saturated liquid. The condensing load is calculated from the following equation: = Q. ~~~~~~~(22) m - Q As (- AH) The degree of superheat is defined as the difference between the temperature of the superheated vapor and the saturation temperature corresponding to the condenser pressure. The experimental heat fluxes calculated from equation 21 are presentedi in Figure 7 for Freon-ll1f and in Figure 8 for steam. The general trend indicated is a gradual decrease in the'heat flux due to superheat. The effect of superheat on the heat flux varies for the various pres sures. At 17400F superheat the reduction in heat flux compared to the heat flux at saturation varies from 6.4 per cent for superheated Freon-ll4 condensing at 45.7 lb per sq in. absolute to 25.4 per cent-for superheated steam condensing at 9.2 lb per sq in. absolute. An increase in heat flux with superheat is indicated only by

14,00 I T T I I I'-I T T T! ~ 1 ] | FREON-II4 Ts F t F LL _ _V' W 0 0 1-15 I316 49.23 e 13,000 I)~~~~~~~~~~ito- * 16-26 96.42 48.66 cr' w I-I <'12,000 cr w Fco <10,000 e- p- I X P"4,:3 7 ps,, w m9 8 000 0 20 40 60 80 00 120 140 160 180 200 DEGREE OF SUPERHEAT ATS, ~F FIGURE 7- EFFECT OF SUPERHEAT ON HEAT FLUX FOR CONDENSATION OF FREON-114

STEAM Tsv, ~F tw, F -0- 40-45 189.1 177.5 II_4)000 _ _ 46-55 237.3 178.0 % 56-66 236.3 177.4 - - - 67-72 273.2 177.6 MIXED P=23'87 PSIA CONDENS.ATION P= 44.O9 PSIA FILM Ca~_ __ _ _ P=44.09 PSIA -CONDENSATION - 86)000 LUA 12 )0 0 0. - _ _ - - _ _ _ _ _ _ - _ _ _ _ - T.,I

43 It is interesting to observe the trend indicated for the effect of superheat on the condensing load in order to interpret the overall performance of superheated vapors. The condensing loads calculated from equation.22 are presented in Figure 9 on a semilogarithmic plot of the condensing load versus the degree of superheat. In all cases for both Freon-114 and steam the condensing load decreases gradually with the superheat. A comparison of Figures 7 and 8 with Figure 9 indicates that at the lowest condensing loads represented by the steam data at 9.2 lb per sq in. absolute the reduction in heat transfer for a 140'F superheat 3is a maximum of 2.4 per cent. For intermediate condensing loads this reduction is 14.1 to 19.0 per cent. For the higher condensing loads represented by the Freon-114 data at 43.7 lb per sq in. absolute the reduction in the heat transfer rate is a minimum of 6.4 per cent for the same degree of superheat. At the highest condensing loads with Freon-114 condensing at 77.0 lb per sq in. absolute the trend in the heat transfer rate is reversed and there is an increase of 5.8 per cent in the heat flux. These results indicate that the trend obtained for the effect of superheat on the heat flux curve depends on the condensing load, Figure 9a. This is due to the fact that an uncertain amount of desuperheating of. the vapor, occurs in the condenser because of the intimate contact of the subcooled condensate flowing from the tube surface with the vapor zone surrounding it. During this process of desuperheating of the vapor and heating of the condensate some vaporization of the condensate may occur specially at high superheats. This process of heat transfer and that due to

LL 100 I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ z 3 WL 20 RUN NO P SATF F Z Q~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1-15 770 336 492F-4 0 ___ 16-26 43. 64 86 -0-40-45 91 8. 7. TA _n- ~ ~ ~ ~~~~~:46- 55 23h 3. 7. 56-666 23.5 26 7.'067- 72 440 27. 176 I 0 _ 0 20 40 60 80 tOO 120 140 108 DEGREE OF SUPERHEAT,) AT.0F FIGURE 9- EFFECT OF SUPERHEAT ON CONDENSING LOAD FOR CONDENSATION OF FREON-114 AND STEAM

45. I0 RUN NO FLUID P. PSIA o I - 15 FREON-I114 77.0 * 16-26 " 43.7 0 5.'-40-45 STEAM 9.2 046-55 " 23.9 o' 56-66 " 23.4 o b 67-72 " 44. 1 0 __.8 -1016 0 4 0.. %.-~~ 4ODNIGLA gi2 LIJ C -5_ N. X z w w a-15 0 -0I w~~~~~~~~ 0 -0 o n~ -25 0 40 80 120 160 200 CONDENSING LOAD) Ms, LB/(HR)(SQ FT) FIGURE 9A- CORRELATION OF THE EFFECT OF SUPERHEAT ON THE HEAT FLUX WITH THE CONDENSING LOAD

vapor-liquid interface between the superheated vapor and the condensate surface. The latter will be referred to as the primary process of heat transfer. For the ideal case when all desuperheating and condensation of the vapor occurs at the vapor-liquid interface the theory of interphase transfer predicts a lowering of the heat flux with increase in superheat. When heat transfer occurs by both primary and secondary processes then only a portion of the expected lowering in heat flux is actually observed since the effective temperature of the vapors at the vapor-liquid interface is lower than the superheated vapor temperature. This results in a lower temperature difference through the interfacial film and a higher interfacial vapor film coefficient. It follows from this reasoning that at appreciably high condensing loads an increase in the heat flux is possible if the extent of cooling of the superheated vapor by the secondary process is appreciable. This subject is discussed further in the next section concerning the mechanism of mass and energy transfer. The only disagreement of the experimental results with this explanation is the 19.0 per cent lowering in the heat flux at 140'F superheat given by steam condensing at 44.1 lb per sq in. absolute. The present interpretation of results predicts a lower reduction in the heat flux for steam at 44.1 lb per sq in. absolute than the 14.1 per cent decrease indicated by steam condensing essentially filmwise at 23.4 lb per sq in. absolute. This discrepancy may be due to the unstable pattern of condensation which steam exhibits. The apparently constant lowering of the heat transfer rate for steam condensing at 23.4 and 23.9 lb per sq in. absolute corresponding to appreciably different condensing loads is due primarily to the difference in the tube-side water flow rates and the type of condensation obtained..

47 Heat transfer rates and condensing loads obtained for a constant tube-side water temperature vary according to the condensing pressure, the tTube-side water flow rate, and the extent of fouling on the tube side. For steam an additional factor is the type of condensation obtained. The experimental data with measured tube-wall temperatures indicate a gradual fouling. Experimental data, runs 56 through 72, obtained on the original tube (Table I) prior to wall thermocouple installation indicate some fouling on the tube side. The extent of fouling is determined by comparing the performance of the tube at any time with that of the clean tube. The results of the studies on the water-film coefficient inside the experimental tube are discussed and presented as Wilson plots49 in Appendix B. The equation used to predict the water-film coefficient and enable the calculation of the outside tube surface temperature for runs 56 through 72 is given in Appendix B. The calculated fouling factor is found to be 0.00023 (hr)(~F)(sq ft inside) per Btu. The conditions under which a superheated vapor does not form a wet film of condensate on the tube surface is important because convection coefficients from a gas to a solid usually give heat transfer rates which are much lower than that obtained during condensation. In the previous section the effect of superheat at reasonable condensing loads is found to be a gradual decrease in the heat flux as compared to the heat flux obtained with the saturated vapor. In the next section this effect is related to the lowering of the condensate surface temperature below that of the saturation temperature. It is important to know the degree of superheat at which the condensate surface temperature decreases sufficiently to attain the limiting value corresponding to the outside tube surface temperature. Under these conditions condensation ceases and the

48 tube surface becomes dry. At a given pressure and tube-wall temperature the superheated vapor temperature corresponding to the degree of superheat required to attain the dry tube condition represents the "dry point." During the present studies the degree of superheat required to attain the "dry point" is found to be extremely high. "Dry points" estimated in the next section for Freon-114 are found to be between 625~F and 925~F. Thus, a direct investigation of this problem is presently impossible. A similar problem which can be investigated experimentally is the condensation of superheated vapors at constant superheat and different values of (Tsv-to). This group represents the difference between the saturation temperature of the vapor and the measured outside tube-surface temperature. Heat flux data obtained while (Tsv-to) approaches zero describe the manner in which the heat transfer rate, the condensing load and the overall outside coefficient vary in the region where the tube surface temperature approaches the saturation temperature. Table IV gives the results of these experiments (runs 27 through 34) made with superheated steam condensing under vacuum. The group (Tsv-to) is varied conveniently by maintaining the superheat and the tube surface temperature constant and reducing the condenser pressure until the saturation pressure approaches the tube surface temperature. Beyond a certain degree of approach the experimental heat fluxes are found to be inaccurate because of the very small temperature rise obtained on the tube side. Figure 10 presents variation of the heat flux and the condensing load obtained for the condensation of steam at pressures varying from 7.5 to 9.0 lb per sq in. absolute and superheats varying from 37.300F to 46.72~F. The experimental results indicate a gradual decrease in the heat flux and the condensing load as (Tsv-to) approaches zero. The trend

49 10,000 0, 10,L RUNS 27-34 e al Pe 7.5-9.0 PSIA Tsv 179.94- 188.28' F - 6,000 6 LLJ37.30- 46.7 4,000 __ _ _ 6-' 4)000 4 8 crr C Z 2)000 _2 W HEAT TRANSFER O By Z FREE CONVECT IO 0 0 2 4 6 8 10 APPROACH TO WALL TEMPERATURETs-tolF FIGURE 10- HEAT FLUX AND CONDENSING LOAD FOR CONDENSATION OF SUPERHEATED STEAM WHILE APPROACHING DRY TUBE CONDITIONS

of the curve shows a minimum value for the heat flux cwhen the tube surface is at the saturation temperature. The overall outside film coefficient is calculated from the heat flux and the measured temperatures by the following equation; ho = Q (23) A(Tg-to) where ho = overall outside film coefficient, Btu per (hr)(~F)(sq ft outside) Tg = temperature of superheated vapor, OF. Figure 11 presents the variation of the overall outside film coefficient with the temperature difference through the film. The experimental results do not extend to values of (Tsv-to) where the tube surface is dry, but Figures 10 and 11 indicate that this condition is reached when the tube surface is at the saturation temperature. This is proved by visual observation of the tube surface and the temperature measurements made while (Tsv-to) becomes zero and negative. These results are tabulated as runs 35 through 39 in Table IV. Small discrepancies in the measured saturation, tube wall, and water temperatures are indicated in column 13. These are due to the difficulty of attaining satisfactory steadystate conditions at the very low heat fluxes involved. Columns 17 and 18 describe the physical condition of the tube. These results substantiate the fact that below the "dry point" a superheated vapor will condense and wet the tube so long as the tube surface temperature is below the dew point of the superheated vapor. The degree of superheat and the tube surface temperature varies somewhat for runs 27 through 34. In order to determine the overall outside

51 RUNS 27-34 E) w~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ a 140 PC 7.5-9.0 PSIA -O TsT 179.94 - 188.28~F 0 sv e Ai Ts 37.30- 46.72~F U.a~ t 175.93~F 120 ----- U. O* 100 of 0 IZ i c z w 80 Uw 0 0 60 LL 40!-. w > d / 00 20 30 40 50 60 OVERALL OUTSIDE FIL M TEMPERATURE DIFFERENCE, Ato, F FIGURE II- OVERALL OUTSIDE FILM COEFFICIENT FOR CONDENSATION OF SUPERHEATED STEAM WHILE APPROACHING DRY TUBE CONDITIONS

film coefficient at (Tsv-to) equals zero the experimental superheats and tuibe surface temperatures are graphically extrapolated to (Tsv-to) equals zero. Figure 31 of Appendix F indicates that when (Tsv-to) is zero, the saturation and tube surface temperatures are 176.0~F and the degree of superheat is 33.0~F- The outside film coefficient can be estimated at these conditions by the following equation recommended for the evaluation of the natural convection coefficient on the outside of a horizontal 33 tubei: ho = o.53 [k3 pf g pf p to]/4(24) f Do where ho = natural convection coefficient for a horizontal tube, Btu per (hr)(~F)(sq ft outside) Subscript f refers to vapor or gas properties evaluated at the mean vapor film temperature Tf, ~F Tg + to Tf = Tgt OF 2 f: = coefficient of cubical expansion of vapor or gas, ~R At0 = vapor or gas film temperature difference, (Tg-to), F..The outside film coefficient calculated from equation 24 is found to be o.86 Btu per.(hr)(~F)(sq ft outside) and is represented by the square point in Figure 11. The corresponding heat flux and condensing load are calculated from equations 23 and 22, respectively, These values are found to be 28.4 Btu per (hr)(sq ft) and 0.0282 lb per (hr)(sq ft outside) and are presented in Figure 10 by the square point. Figure 12 presents in a conventional way the overall outside film coefficients for superheated Freon-114 and steam calculated from the ex

4 10 RUN NO FLUID P, PSIA 0 I- 15 FREON-114 77. O0 - - _ 0 16-26 " 43.7 - -F - - - -0-40-45 STEAM 39. 1 6.- I =- _ 1 46-55 23. 87 - = = _ _ s _-2 3.35 w 2:0 ra mLL O O T T F_ _P_ 10 100 1000 OVERALL OUTSIDE FILM TEMPERATURE DIFFERENCE, At., F FIGURE 12- EFFECT OF SUPERHEAT ON OVERALL OUTSIDE FILM COEFFICIENT FOR CONDENSATION OF SUPERHEATED FREON-114 AND STEAM

perimental data by equation 23. The lines representing the data at various pressures have a negative slope of unity. The overall outside film coefficient increases consistently with pressure for both Freon-114 and steam. The apparent discrepancy indicated by the steam data for a condensing pressure of 23.9 lb per sq in. absolute (runs 46 through 55) is due to appreciable dropwise condensation obtained during these runs. These results are further analyzed in the next section to calculate the interfacial coefficient at the vapor-liquid interface. THEORY OF FILMWISE CONDENSATION OF SUPERHEATED VAPORS The mechanism of the condensation of superheated vapors is discussed in this section. The applicability of the theory of interphase mass and energy transfer and its limitations are presented for the interpretation of the experimental and calculated results and for an understanding of the condensation of superheated vapors. The process of condensation of vapors involves the transfer of mass and energy from a vapor phase to a liquid surface. For a saturated vapor the vapor moves onto the liquid surface and condenses. The primary barrier to energy transfer is the layer of condensate through which heat is essentially carried by conduction from the condensate surface to the tube surface. This process attains steady state at constant pressure and tube surface temperature by the build-up of the condensate thickness and with it the resistance to heat transfer. The deviation from equilibrium, if any, is very small at the vapor-liquid phase boundary and the vapor-liquid interface can be assumed to provide no barrier for mass and energy transfer. Both vapor and liquid at the interphase are at the saturation temperature. These assumptions are implied in the derivation of equation 1 discussed in an earlier section and are justified by good agreement between'experimental and theoretical results.

The transfer of mass and energy during the condensation of a superheated vapor proceeds much in the same way as that of a saturated vapor. However, the assumption of thermodynamic equilibrium at the vapor-liquid interface seems to be questionable because of the conflicting evidence indicated by experimental results. The temperature and pressure conditions which prevail at the interface are uncertain because of the difficulty of the necessary measurements and the lack of effort evidenced from a review of the literature in this field. Experimental and theoretical studies reported in the literature indicate conflicting opinions and results on the effect of superheat on the heat flux obtained during condensation. The results vary from a large or small increase in the heat 33,34,35,47 flux due to superheat, no effect of superheat on the heat 26 flux, an increase in the heat flux at low heat transfer rates with a 24 subsequent decrease at high heat transfer rates, to a decrease in the heat flux due to superheat. 3 These results tend to indicate that in general the process of condensation of superheated vapors is not adequately understood, and in particular, the nature and importance of the vaporliquid interface is overlooked. A thorough understanding of the condensation of superheated vapors requires a theoretical approach to the interphase transfer of mass and energy because the vapor-liquid interface is definitely present. However, an understanding of all processes involving mass and heat transfer is necessary in addition to that which occurs at the phase boundary. Evidence of the effect of superheat on the process of condensation is the general lack of agreement among the results of different investigators, and the difficulties encountered with superheated vapor condensers designed by conventional methods discussed previously. The heat

transfer rates obtained in condensers designed to handle vapors with excessively high superheats or superheated vapors at pressures considerably below atmospheric are usually below their design capacity. This indicates that in some applications the vapor-liquid interface offers an appreciable barrier to the transfer of mass and energy, whereas in others the assumption of equilibrium at the interface is valid. In the present investigation an attempt is- made to observe the various processes which enable the transfer of mass and heat in order to determine the conditions under which the effect of superheat becomes important. The experimental data cover a wide range of condensing loads which evidently influence the effect of superheat on the heat flux by the secondary process of heat transfer discussed in the previous section. The experimental results indicate a gradual but definite decrease in the tube surface temperature with increase in the superheat of the condensed vapors (Tables II and III, Figure 12a). It is also shown in Figure 9 58 i~ ~ ~ > -RUN NO FLUID P, PSIA tl > 56- 1 I 16- 26 FREON-114 43.7 0 w 54 4I"Jo. m-P 50 48 0 20 40 60 80 00 120 140 160 180 200 DEGREE OF SUPERHEAT,AT,F 5' FIGURE 12A- DECREASE OF TUBE SURFACE TEMPERATURE WITH SUPERHEAT

that in all cases with superheated Freon-114 and steam the condensing load decreases with increase in the superheat of the vapor. It follows from these observations that for the heat flux curves (Figures 7 and 8) which indicate a reduction in the rate of heat transfer with increase in the degree of superheat, the condensate surface temperature definitely decreases with increasing superheat. That this is true also for those Freon-114 results which indicate a slight increase in heat flux is shown later (Figure 17). This conclusion results from the fact that the slope of the temperature profile through the condensate film is proportional to the heat flux through the film. If the condensate surface is assumed to be at the saturation temperature during the condensation of the saturated vapor, then it must be at a lower temperature during the condensation of the superheated vapor which gives a lower heat flux (smaller slope) and a lower tube surface temperature. It is concluded from this discussion that superheat in the condensing vapors affects the temperature and pressure conditions at the vapor-liquid interface. This implies the presence of a phase boundary where the vapor is not in equilibrium with the liquid and the vapor film interface becomes a barrier to the condensation of superheated vapor molecules. The temperature of the liquid and the vapor at the interface is not measured experimentally. A comparison of the experimental condensate film coefficient for the saturated vapor with that calculated from equation 1 shows good agreement for those cases which give stable film condensation. For saturated Freon-114 the calculated condensate film coefficient is 4.1 per cent higher than the experimental value of 170 Btu per (hr)(~F)(sq ft outside) obtained at a pressure of 77.0 lb per sq in. absolute and 17.5 per cent lower than the experimental value of 251 Btu per (hr)(~F)(sq ft outside) obtained at a pressure of 43.7 lb per sq in. absolute.

Since the temperature drop through the condensate film is unknown for condensing superheated vapors, it is more convenient to calculate the condensate film coefficient from the equation using the condensing load which is obtained experimentally. The following is the equation recom33 mended for this calculation and it is equivalent to equation 1: pf2 1/3 f he = 1.2 f (,,' (25) where r' = condensing load, lb per (hr)(ft of tube length). The use of this equation is simplified by the calculation of the physical property group (kf3 Pf2 g/3 i Of as a function of the mean condensate film temperature (Tf). These calculations are illustrated in Appendix C. The experimental condensate film coefficients obtained during mixed condensation of steam at 9.2 and 23.9 lb per sq in. absolute (runs 40 through 55) are considerably higher than those calculated for film condensation from equations 1 and 25. For these runs the condensate film coefficient for a run with superheated steam is estimated from the experimental film coefficient at saturation by multiplying the latter with the ratio of the condensing loads raised to the one-third power. It is important to note that any error in the prediction of the condensate film coefficient does not introduce any appreciable error in the interfacial temperature difference finally evaluated. This is shown in Tables II and III by the relative magnitude of Atc and Ati at various superheats. Above superheats of 10~F the error in the calculated value of the temperature drop at the interface (Ati) is negligible. The cal

culation of the condensate film coefficient by equation 25 involves the determination of the temperature drop through the condensate film (Ate) as shown in the sample calculations of Appendix C. The condensate surface temperature is evaluated from the experimental tube surface temperature and the calculated Atc by the following equation: Ts = to + Atc (26) The temperature drop through the interfacial film is obtained from the following equation: Ati = Tg - Ts (27) where Ati = temperature drop through the interfacial film, OF. Equation 27 gives the maximum temperature drop available at the interface and implies that this temperature drop occurs at the vapor-liquid interface. The validity of this assumption is shown by the extent to which experimental results agree with the present theory. Possible deviations from this assumption are discussed later in this section. The interfacial vapor film coefficient is defined as follows: hi A(Tg TS) (28) where hi = interfacial vapor film coefficient, Btu per (hr)(~F)(sq ft outside). Since the exact location and area of the interface is unknown, a good approximation is the use of the outside tube area. This assumption is implied in equation 28. The overall outside film, condensate film, and interfacial film coefficients are related by equation 13 presented earlier with the introductory theory. The calculated interfacial film coefficients are given in Tables II and III. Figure 13 presents the relationship between the calculated inter

60 I0 ( _ = =n =-_ _ _ _ | || | | | | | |RUN NO FLUID P, PSIA:Oi)~~~~~~ ~ ( = ~~ = —__ == - __0 I-I 5 FREON-114 77.0 I'-o~ ~ ~ ~ ~ ~~~~' == =.- v- It 23.35 (~~lo2~~~~ L,67-72 44.09 I — m -0 - 00 U- I 10 1I LLJ _ DEGREE OF SUPERHEAT- 1,,4., FIGURE 13- EFFECT OF SUPERHEAT ON INTERPHASE VAPOR FILM COEFFICIENT (H) FOR CONDENSATION OF FREON-114 AND STEAM

61 facial film coefficients and the degree of superheat for Freon-114 and steam. For the range of low superheats the spread of the Freon-114 results is reduced in comparison with the trend indicated in Figure 12. The relative spread of the steam results is the same for the experimental outside film coefficients (Figure 12) and the calculated interfacial film coefficients (Figure 13). The effect of superheat on the overall film resistance, the condensate film resistance, and the interfacial film resistance is shown in Figures 14 and 15. These resistances are defined as the reciprocal of the corresponding film coefficients. Figure 14 presents the individual film and total film resistances for the Freon-114 data. Figure 15 gives the results for Freon-114 at the condensing pressure of 77.0 lb per sq in. absolute on rectangular coordinates. The concept of the individual film resistances is indicated clearly in Figure 15 for the range of experimental results. At saturation the interfacial film resistance is assumed to be zero. As the degree of superheat is increased the condensing load and the condensate film resistance decrease gradually, whereas the resistance of the film at the vapor-liquid interface increases rather sharply. This corresponds to the rapid decrease in the interfacial film coefficient which is infinite at saturation (Figure 13). Up to a superheat of about 30~F the interfacial coefficient of Freon-114 seems to be independent of the pressure. Figure 13 is useful in predicting conditions of superheat in the region close to the "dry point" defined previously. At the "dry point" the tube surface is dry and the outside film resistance is represented by the interfacial film resistance. The corresponding condensate film resistance is zero. It is also reasonable to assume that at this point the

0.2 RUN NO rO rc P, PSIA I 15 0 77.0 7 CA LCU LATED 16- 26 0 + 43.7 "DRY POINT 0.1 w V/ / II z / _ _ - _ _ -i LLJ -Ji c I I0.01 o0 10 -- OF S, A11. ~F -J. \ 0.001 10 t00 I000 DEGREE OF SUPERHEAT, T ~F FIGURE 14- EFFECT OF SUPERHEAT ON CONDENSATE AND INTERFACIAL FILM RESISTANCES FOR FREON-II4

63 0.016 RUNNO Tr0 Yc P, PSIA 1-15 S 0 77.0 0.014 rC) z 0.012 4 I.I, on oo Q~ co w._ w o 0.010 _____ ~0 5cn U) D Ua0 0.006 I Cl zicn zx 0.006 _ ______ cr -J -j w 0.004 _ 0 0.002 0 0 20 40 60 80 100 120 140 DEGREE OF SUPERHEAT ATs,~F FIGURE 15- EFFECT OF SUPERHEAT ON CONDENSATE FILM AND INTERFACIAL FILM RESISTANCES FOR FREON-I114

64 interfacial film coefficient is approximately equal to the natural convection coefficient evaluated from equation 24. Lines representing the calculated natural convection coefficients are shown in Figure 13 for Freon-114 condensing at 43.7 and 77.0 lb per sq in. absolute. Intersection of these lines with the extrapolated interfacial film coefficients gives the calculated "dry points" for superheated Freon-114 condensing at a constant pressure and a constant tube surface temperature. The "dry points" shown by the square points in Figure 13 represent a superheated vapor temperature of 10580F and a superheat of 9250F at a pressure of 77.0 lb per sq in. absolute. The corresponding values at a pressure of 43.7 lb per sq in. absolute are 721~F and 625~F. It follows from the trend obtained in Figure 13 that as the superheat is increased past the value corresponding to the "dry point," the latter marks a sudden reversal in the variation of the outside film coefficient. However, it is likely that this reversal in trend occurs smoothly and not abruptly as obtained in Figure 13. This is suggested by the experimental results described previously and presented in Figures 10 and 11. The trend of the heat flux curves may be followed beyond the "dry point" by considering the slope of the line in Figure 13 beyond the "drypoint." For the range in which radiation effects are not appreciable the heat flux curves would decrease gradually. When heat transfer by radiation becomes controlling the heat flux curve would indicate a reversal in trend and a gradual increase. In Figure 14 the interfacial film resistance curves are extrapolated to the "dry point" values shown by the square points. Figure 16 describes the variation of the overall outside film coefficient as the superheated vapor temperature attains the "dry point,"

65 200 - RUN NO P, PSIA 0 I- 15 77.0 o41 -- I I I I I I I I I - z o 100 _ wo 20 10 __ 200 400 00 1000 2000 SUPERHEATED VAPOR TEMPERATURE, TG,'F FIGURE'16- EFFECT OF VAPOR TEMPERATURE LEVEL ON OVERALL OUTSIDE FILM COEFFICIENT OF SUPERHEATED FREON-114

for the Freon-114 data obtained at a pressure of 77.0 lb per sq in. absolute. The general trend is the same as that obtained in Figure 13 because near the "dry point" the value of the interfacial film coefficient approaches that of the overall film coefficient. At a constant condensing pressure increase in the tube surface temperature reduces the "dry point" of the superheated vapor. For applications involving the condensation of superheated vapors at high superheats and high tube surface temperatures or low values of (Tsv-to), it is important to evaluate the dry point of the condensing vapors. This requires a knowledge of the interfacial film coefficient as a function of the degree of superheat. The correlation of the calculated interfacial film coefficients on a generalized basis enables this calculation. Such a correlation is presented in the next section. The calculated interfacial film temperature difference and the corresponding interfacial film coefficient discussed in this section assume that condensation of the superheated vapors occurs entirely by the mechanism of interphase mass and energy transfer. There is evidence that this is true to an uncertain extent. Figure 17 presents the temperature profile for a condensing superheated vapor. The profiles presented qualitatively correspond to runs 6 and 14 for Freon-114 condensing at a pressure of 77.0 lb per sq in. absolute. The degree of superheat is 7.0~F for run 6 and 113.0~F for run 14. The reductions in the tube surface temperature, the condensate film thickness, and the calculated condensate surface temperature with increase in ithe degree of superheat are shown. The increase in the interfacial film thickness with increasing superheat is shown for the case of interphase mass and energy transfer. The effect of superheat on interphase transfer is lowering of the condensate surface

67 CONDENSATE FILM I'I THICKNESS, I NTRAPHASE Yc I A T ENERGY'I AT'S/IH TRANSFER J SH INTERFACIAL UNIFORM // G U EVAPOR FILM VAPOR REGION -~0 I / / ITHICKN ESS, I -..RUN 6-,,.T L PROFILE FOR A CONDENSING SUPERHEATED VAPOR

temperature. The general theory of interphase transfer discussed previously predicts this lowering of the condensate surface temperature below the saturation temperature. This assumes that a temperature drop of (Tg-Ts) occurs at the vapor-liquid interface. The order of magnitude of the interface is somewhat less'than the mean free path of the superheated vapor molecules. This thickness is exaggerated in Figure 17 in order to clarify the concept of the vapor-liquid interface. Condensation of superheated vapors involves secondary processes of heat transfer other than interface transfer of mass and energy. Deviations of the behavior of superheated vapors from that predicted by interphase transfer theory are due to heat transfer from the superheated vapor to the subcooled condensate and heat transfer between the vapor molecules adjacent to the interface. The latter is known as intraphase energy transfer. Usually intraphase and interphase transfer operations occur simultaneously and complicate the proper treatment of interphase transfer data. The effect of intraphase energy transfer on the temperature profile is shown by the dashed line in Figure 17. The resulting film temperature drop across the vapor-liquid interface is only a portion of the total temperature drop (Tg-Ts) available. This results in a lowering of the condensate surface temperature which is less than that predicted from interphase transfer theory. The higher condensate surface temperature results in a higher temperature drop and a higher heat flux across the condensate film. It is seen from this discussion that both intraphase energy transfer and contact of the superheated vapor with the condensate tend to counteract the effect of superheat which tends to lower the rate of interphase mass and energy transfer. Therefore the effect of superheat on the heat

flux depends on the relative importance of these opposing trends. At low tube surface temperatures, high values of (Tsv-to), moderate superheats, and high condensing loads the secondary process of heat transfer tends to become appreciable because of the large quantity of subcooled condensate which contacts the superheated vapor. Conversely at high tube surface temperatures, low values of (Tsv-to), high superheats, and low condensing loads interphase mass and energy transfer becomes controlling. It may be concluded from this discussion that condensation of superheated vapors may indicate a higher, the same, or a lower heat transfer rate than the corresponding saturated vapor. The correlation, of the experimental and calculated results on the basis of interphase transfer theory will show the validity of this theory as applied to the condensation of superheated vapors. This attempt is made in the next section. CORRELATION OF RESULTS The theory of interphase mass and energy transfer is used for the correlation of experimental and calculated results. The actual heat transfer through the vapor-liquid interface cannot be determined from the experimental results, because of the uncertain amount of heat transfer occurring by secondary processes discussed earlier. This introduces a certain amount of uncertainty in the temperature of the superheated vapor at the vapor-liquid interface. It is assumed that the vapor at the interface is at the condenser temperature. The uncertainty introduced by this assumption is of the same order as that of the calculated condensate surface temperature. The temperature of the condensate surface calculated by the method outlined in the previous section is presented as a function of the degree of superheat in Figure 18. The semilogarithmic plot indi

RUN NO FLUID P,PSIA EQUATION OF LINE RUN NO FLUID P,PSIA EQUATION OF LINE 0 1-15 FREON-114 77.0 L N TS/128.0 o -0.0006026 AT8 ) 46-55 STEAM 23.87 LN TS/238.0-0.0004745 ATS * 16-26 " 43.7 LN TS/98.0 —0.007408ATS d 56-66 " 23.35 LNTS/234.5 -0.0002833 AT -0-40-45 STEAM 9.16 LN TS/8I.1 -0.00036A81ATS AT 67-72 " 44.09 LNTS/265.0 — 0.0002405 AT8 0.6 w 220 ---- -- w I0 180.140 DEGREE OF SUPERHEAT, ATs ImF FIGURE 18- CORRELATION OF CALCULATED CONDENSATE SURFACE TEMPERATURE WITH SUPERHEAT FOR CONDENSATION OF FREON-114 AND STEAM cn~~~ -0 ~~~~-o —. — u) OF FREON-II4 AND STEAM

71 cates a straight-line relationship for Freon-114 and steam. Lines are drawn to represent the best trend indicated by the individual calculated points. The equations of these lines given in Figure 18 show the mean saturation temperature for all the runs in a given set corresponding to the mean condenser pressure. Saturation and condensate surface temperatures used for the correlation of experimental heat transfer rates and condensing loads are obtained from the lines shown in Figure 18. This is justified because of the uncertainty inherent in the calculation of the condensate surface temperature and the unavoidable variation of the saturation pressure and temperature for the runs corresponding to the different degrees of superheat at a given pressure. The lowering or depression of the condensate surface temperature below the saturation temperature (Tsv-Ts) is calculated and shown in Figure 19 as a function of the superheat. These and other calculated results used for the correlation of heat flux and condensing load with superheat are given in Table V. The line shown in Figure 19 represents the best fit for Freon-114 results. The calculated results for superheated steam fall slightly below those for Freon-114. Superheated steam corresponding to a pressure of 24.08 lb per sq in. absolute shows a depression of condensate surface\ temperature (Tsv-Ts) which is about 50 per cent higher than those of Freon-114 and steam at other pressures. This may be due to the pronounced dropwise condensation obtained during these runs (46 through 55) and the greater uncertainty in the calculation of the condensate surface temperature. The condensation of superheated Freon-114 and steam is studied under conditions which tend to reduce the extent to which processes other than that of interphase mass and energy transfer prevail. The effects of va

72 30 RUNNO FLUID P,PSIA Tsv,,F o 0 1-15 FREON -114 71.43 128.0 20 * 16-26 " 44.89 98.0 -0- 40-45 STEAM 9. 1608 189.1 ( 0 46-55 " 24.080 238.0 45 _ - 56-66 " 225 89 234.5 0 67-72 38.539 265.0 U 10 w:[ I T I I - I - I 1 - = - Q. J C') w 0L2 0 I (I) 0 - 10 100 200 LLJ FIGURE 19- CORRELATION OF CALCULATED CONDENSATE; 0.6 FIGURE 19- CORRELATION OF CALCULATED CONDENSATE SURFACE TEMPERATURE LOWERING WITH SUPERHEAT FOR CONDENSATION OF FREON-114 AND STEAM

73 por velocity and intimate contact of the condensate with the superheated vapor are minimized by the experimental condenser shell and tube selected. The small tube provides a low heat transfer area and reduces the condensing load per unit length.. The relatively large shell with two inlets reduces the velocity of the vapors moving toward the cooler condensing surface. Previous discussion of the experimental results indicates a distinct effect of superheat on the temperature and pressure conditions at the interface. The mechanism of condensation of superheated vapors involves the transfer of mass and energy through the vapor-liquid interface. The temperature and pressure conditions are not determined experimentally because of the nature of this study. Based on evidence from the experimental results the validity of the assumed and calculated interfacial conditions is tested by direct application of the equations derived from the theory of interphase mass and energy transfer.. At a given temperature and pressure the net mass transfer rate is related to the interfacial conditions of temperature and pressure by equation l9presented earlier. This equation is based on the theory of interphase mass and energy transfer discussed earlier in the literature review and is valid for the general case where the vapor and liquid are not in equilibrium (Ts/Tg ~ 1) at the interface. In deriving equation 19 the condensation coefficient (f) is assumed to be a function of the state of the surface and'the kind -of molecules involved. For a given substance the condensation coefficient decreases with increase in the superheat of the vapor. This observation is explained in this section. The molecular velocity of the vapor and the rate of collision of the molecules with the condensate surface increases with in

74 crease of the vapor temperature. The condensation of superheated vapor molecules requires a condensate surface which has a greater potential to absorb molecules than that necessary for the condensation of saturated vapor molecules. This is due to the higher average energy content of a superheated vapor molecule as compared to that of a saturated vapor molecule. Thus, during the condensation of a pure substance the rate of mass transfer or the condensing load is controlled by the rate at which energy or heat is extracted from the superheated vapor and conducted through the liquid film. To increase the probability of condensation of the higher velocity superheated vapor molecules the condensate surface temperature must be lower than that necessary to condense lower-velocity saturated vapor molecules. The lowering of the condensate surface temperature is limited, however, by the mechanism of conduction whereby the heat extracted from the condensed molecule must be transferred to the tube surface. Therefore, the overall rate at which superheated vapor molecules are condensed is less than that of saturated vapor molecules. The increase in the rate of collisions on the one hand and the decrease in the rate of molecules condensed on the other tend to reduce the value of the condensation coefficient (equation 8). Figure 19 indicates that the effect of superheat on the condensate surface temperature is comparable for different fluids and different pressures. Experimental and calculated results obtained for the film condensation of a pure substance or different substances with similar molecules can be correlated as a function of the condensation coefficient (f) if the latter represents the characteristic variable describing the temperature and pressure conditions at the vapor-liquid interface. Direct application of equation 19 is complicated because of the cor

75 rection factor F as indicated earlier. This relationship is simplified by expressing [ as a simple function of the variable 0g defined by equation 20. Values of ([ -1) are presented graphically for condensation (Og < O) and evaporation (Og > O) in reference 45 for the range 1 10Ig > 10-3. The major portion of this graph corresponding to the range of IOgl of 0.1 > I0gl > 0.001 is represented satisfactorily by a straight line with a slope of unity. The following equation approximates the cal. culated values of F for condensation with a maximum deviation of + 4 per cent within the specified range: r = 1 + 1.85 1glI for 0.1 > I gl I 0.001. (29) Substituting for the absolute rate of evaporation (me) from equation 9 in equation 20 Og is expressed as: m0 2S BT5 1/2- (30) 2il/2 f Pg gcM Ts Equation 30 is used subsequently to calculate the range of values of Og corresponding to the experimental and calculated results obtained in this investigation. Values of I0gl lying within the specified range justify the use of equation 29 for the elimination of F in equation 19. Substituting for r in equation 19 the linear function given by equation 29 and solving for 0g the following equation is obtained: 11/21/2 RTs 1 (31) OS\ 5 Pg T -.85fPg T/ g-M..5 Combining equations 30 and 31 to eliminate 0g the following equation is derived for the condensation coefficient (f):

76 i27x RTs 1.52 ms gcM Pg gS1/2 (32) Equation 32 is equivalent to equation 19 discussed earlier. The correction factor d is eliminated in equation 32 and the condensation coefficient is presented as a function of the condensing load and the temperature and pressure conditions at the vapor-liquid interface. A relationship similar to equation 32 is presented by Bosnjakovicll45 without the correction factor r and its equivalent constant coefficient 1.52. He does not define the temperature drop through the interface and the expected deviations from equation 32 because of intraphase film temperature drop. A temperature gradient extending beyond the vapor-liquid interface (shown in Figure 17) indicates intraphase heat transfer. This secondary process of heat transfer affects the predictions made from equation 32 in two ways. Firstly, it reduces the effect of superheat on the condensate surface temperature and results in a higher condensate surface temperature. Secondly, it lowers the superheated vapor temperature at the interface. The overall effect of intraphase heat transfer is a higher value for the ratio (Ts/Tg), a lower value for the terms [Ps* - Pg Ts and a higher value for the condensation coefficient (f) in equation 32, as compared to the assumption of interphase mass and heat transfer alone. Substituting for l2iR/gc equation 32 is simplified to: ms g(s

77 where Ps* and Pg are expressed in lb (force) per sq in. absolute. The experimental and calculated results are used to calculate f from equation 33 and 0g from equation 31. These calculations indicate values of oIgl of about 0.007 and justify the use of equation 29 to eliminate r in equation 19. Og may be calculated also from equation 30. Substituting for the molecular weight in equation 33 the following equations are obtained for Freon-114 (M = 170.9) and steam (M = 18.02): ms Ts (34) f~ 6P _p Ts)1/2i for Freon-114; (34) f0 [s Pg (T /23 for steam (35) G(f3 ) = [P () s/ (56) is used for the correlation of the experimental condensing load and the calculated temperature and pressure conditions at the interface with the degree of superheat. The effect of molecular weight is not included in order to differentiate easily between the Freon-114 and steam results. Table V gives the results of these calculations. The correlating group is plotted against the superheat in Figure 20. Of the two fluids, Freon114 indicates stable film condensation and is expected to give results which agree better with predictions of interphase theory. This is shown by the satisfactory grouping of the Freon-114 results about the line ciable scatter which indicates that the results of more stable film conbyw orersn the satsfatoygupn ofit.he steam11 results abouct te linape

78 105 RUN NO FLUID P, PSIA 0 I - I 5 FREON-I 14 71.43 ~ 16-26 44.89 E__I___ T___3 -0-40-45 STEAM 9.1608' 46-55 24.080 4 56-66 22.589 colb b, 67-72 38.539 S"k0' o A N xo uI o4 = I__ w \O' I, I I I \ ^ 02 o0 FIGURE 20- CORRELATION OF CONDENSING LOAD WITH SUPERHEAT AS A FUNCTION OF CONDENSATION COEFFICIENT (f)

79 densation data (runs 56 through 72) lie above those of the mixed condensation data (runs 40 through 55). Assuming that the condensation coefficient is equal for superheated Freon-114 and steam vapors at the same superheat, the correlating line for the steam results is obtained from the correlating line for Freon-114 and the square root of the molecular weight ratio. The scatter of the steam results from this line is to be accounted for by the mixed condensation obtained with steam. The present theory assumes the existence of a uniform condensate film whereas the pattern obtained with dropwise condensation is widely different from this. It is interesting to note that the present correlation predicts conservative condensing loads for superheated steam condensing filmwise. The maximum deviation of the results is +12 per cent and -20 per cent for Freon-114 and + 50 per cent for the steam results. The equation of the correlating line in Figure 20 including the effect of molecular weight is found to be sV M 46,700 () Ts 1/2 ATs1.16 Pg gg) Ps* where ATs = (Tg-Tsv), ~F. Equation 33 is combined with equation 37 to give the following relation between the condensation coefficient (f) and the degree of superheat: =f ~2.38 5 — 1.1~6 (38) The values of the condensation coefficient (f) calculated from equation 38 are not necessarily correct because of the nature of the preceding calculations. However, the condensation coefficient is found to be the important correlating factor for the prediction of the effect of su

8o perheat on the filmwise condensation of' superheated vapors. Equation 38 may be used to estimate the value of (f) at saturation or zero superheat by calculating the degree of superheat corresponding to f - 1.0. This is found to be 2.11~F. Since the value of f cannot exceed unity by definition, it may be deduced that the value of the condensation coefficient is close to unity for the filmwise condensation of saturated Freon-114 and steam. For quantitative determination of (f) the interfacial conditions must be known accurately by direct or indirect experimental measurement. The approximate-equation 7 discussed earlier is used extensively for the correlation of mass and heat transfer data without clarification of the underlying assumptions. A comparison of equation 7 with equation 32 indicates that in the former the group T)1/2 Ts is assumed to be unity. A function of the condensation- coefficient defined as E(f) = ms (39) (Pg-Ps *3) is calculated and shown in Figure 30 given in Appendix F. These results are given in Table V. Figure 30 indicates a satisfactory correlation for the Freon-114 results. Steam results with both dropwise and filmwise condensation are spread above the correlating line drawn for steam. This inconsistency is accounted for by the assumption of (Ts/Tg) = 1.0 which invalidates the use of equation 7 for applications involving a temperature drop through-the interfacial film. Equation 35 is modified to correlate the calculated interfacial film coefficient with the temperature drop through the interface (Tg-Ts) and

81 the interfacial conditions. The condensing load (ms) in the correlating group defined by equation 36 is replaced by the representative variables which are the interfacial film coefficient (hi) and the enthalpy change for the condensed superheated vapor. The resulting group is defined as H(f) = (A) g (40) These calculated results are given in Table V and presented in Figure 21 as a function of the temperature drop through the interfacial film. In general the calculated results indicate a pattern similar to that observed in Figure 20. Following the previous assumption of equal condensation coefficients for Freon-114 and steam at the sane superheat the correlating line is drawn for the steam results. The use of this line for the prediction of interfacial film coefficients gives conservative results for superheated steam condensing filmwise. The group of variables defined in equation 40 is a direct function of the condensation coefficient (f) and correlates the calculated results satisfactorily for the filmwise condensation of superheated Freon-114 and steam. The correlating lines drawn in Figure 21 are represented by the following equation: hi'~jr -60,500 (-AH) [g -g Ps Equations 37 and 41 and the correlating lines in Figures 20 and 21 are recommended alternately for the prediction of the condensing load and the interfacial film coefficient for the filmwise condensation of Freon-114 and steam. The use of these relationships requires determination of the condensate surface temperature for the specific conditions of superheat

82 2X10 RUN NO FLUID P, PSIA o0 I -15 FREON-114 71.43 ~~\, k~ C~ \ 16 -26 " 44.89 ~~~~~4'~~-0- 40-45 STEAM ~ 9.1608 - ____10 I 46-s55 " 24.080 56-66 " 22.589 " 67-72 38.639 744-1 8<z103 X 1 I Al - CD - i r> 10 10 100 1000 TEMPERATURE DIFFERENCE THROUGH I NTERFACIAL FILM, AtL (TG-TS ),F FIGURE 21- CORRELATION OF INTERFACIAL FILM COEFFICIENT(h,) WITH INTERFACIAL FILM TEMPERATURE DROP AS A FUNCTION OF CONDENSATION COEFFICIENT(O)

83 and outside tube surface temperature. For tube surface temperatures corresponding to the values given in Tables II and III and the condensing pressures used the degree of lowering of the condensate surface temperature can be obtained from the respective position of the results in Figure 19. The general procedure recommended for the evaluation of the condensate surface temperature is given in the next section. The correlations derived in this discussion are used in the next section to outline a general procedure for the design of superheated vapor condensers under widely different conditions of superheat, pressure, and outside tube surface temperature. DESIGN PROCEDURE The correlation of the experimental and calculated results based on the theory of interphase mass and energy transfer is satisfactory for the experimental results which correspond to the filmwise condensation of superheated Freon-114 and steam. These correlations are recommended for the prediction of variables necessary for the design of superheated Freon114 and steam condensers. For most applications encountered in industry where vapors with as much as 2000F superheat are condensed filmwise at pressures ranging from one to five atmospheres and the mean tube-side water temperature is about 100~F these correlations may be used for the design of condensers handling fluids with properties similar to those of Freon-114 and steam. The conventional design procedure based on the condensate film coefficient calculated from equation 1 is discussed earlier. To determine the validity of this method for the range of variables studied in this investigation condensate film coefficients are' calculated for comparison with the experimental results for Freon-114. The conventional film co

84 efficients (hc") are calculated fromi equation 1 by using a (-AH) value corresponding to that of the actual run and a constant (Tsv-to) value obtained for the saturated run of each of the two condensing pressures. The film coefficient obtained from the experimental heat transfer rates is calculated on a comparable basis from the following equation: hc' = A(Tsv-to) where hc' = condensate film coefficient comparable to hc", Btu per (hr) (~F)(sq ft outside). The calculated results are given in Table II and presented in Figure 22. For Freon-114 condensing at a pressure of 43.7 lb per sq in. absolute the conventional film coefficients are conservative up to a superheat of 90~F but become steadily greater than the corresponding coefficient calculated from the experimental results. For Freon114 condensing at a pressure of 77.0 lb per sq in. absolute conventional film coefficientsare higher than the condensate film coefficients calculated from equation 42. The trend shown by the curves in Figure 22 indicates that conventional film coefficients calculated for design purposes may be 15 to 25 per cent higher than the corresponding actual film coefficients at normal superheats of 100 to 200~F. Even at normal condensing pressures these deviations may be more pronounced at higher superheats. This discussion shows that at best the use of equation 1 is limited to the estimate of design film coefficients for applications involving normal pressures and superheats. Under peculiar conditions of low pressures, high superheats, and high tube surface temperatures a more fundamental approach is necessary. The general design procedure outlined below is based on the correlations derasived in the previoutios thsection from considerations of interphase transfer theory. It involves the trial-and

280RUN NO P PSIA 0 1-15 77.0 00 260jjI 6 26 43.7 260 ~pC 240 P=-43.7 PsIA z 220 LL. w - _ 200 - VT O J O, y~~~~~~~~~~~=077. 0 f(Tsy'0 ot = 0 w I I i 7l0"'A0 1 80 z Q /A w P= 770 PSA 1;C7 ( a 0 SV- U- z__ o 160 0 20 40 60 80 100 120'.140 160 180 DEGREE OF SUPERHEAT, AT8, F FIGURE 22- COMPARISON OF CONVENTIONAL DESIGN AND EXPERIMENTAL CONDENSATE FILM COEFFICIENTS FOR SUPERHEATED FREON- 114

86 error determination of the condensate surface temperature for the specified conditions of condensing pressure, superheat, and tube surface temperature. The following procedure is recommended for the evaluation of the condensing load: 1. As a first approximation a reasonable condensate surface temperature (Ts) is assumed, and the corresponding equilibrium pressure (Ps*) is obtained from the vapor pressure of the fluid. 2. The given superheat and condenser pressure, and the assumed variables are substituted in equation 37 and the condensing load is calculated. 3. The heat transfer rate through the interface is calculated from the condensing load and (-AH). 4. The condensate film coefficient is calculated from equation 1 using (-AH) and the temperature difference (Ts-to) corresponding to the assumed Ts. 5. The heat transfer rate through the condensate film is calculated from the evaluated condensate film coefficient and the value of (Ts-to) corresponding to it. 6. The calculated heat flux through the vapor-liquid interface is compared with the calculated heat flux through the condensate film. If the two values deviate appreciably a second trial is made for another assumed value of Ts. Equation 41 can be used alternately for the design of a superheated vapor condenser. The calculations involved in using equation 41 are more tedious in general and the method outlined above is preferable. The recommended procedure is illustrated for the design of a superheated Freon114 condenser in Appendix E. It is important to note that the present

87 method is recommended for the design of superheated vapor condensers in which the vapors condense filmwise on the outside of horizontal tubes. This procedure gives results which are conservative for most normal applications. In general the extent of secondary processes of heat transfer is appreciable in most industrial applications. The intimate contact of the superheated vapor with the condensate lowers the temperature drop through the interfacial film and gives an actual interfacial film coefficient higher than that calculated directly from equation 41 or corresponding to the condensing load determined from equation 37. The present method is useful for the prediction of interfacial film coefficients and condensing loads under unusual conditions of low pressures, high superheats, and high tube surface temperatures. During the condensation of a superheated vapor at low pressures of 0.1 to 1 inch mercury molecular effects and interfacial film resistances become appreciable. At high superheats and high tube surface temperatures the possibility of the superheated vapor not forming a wet film on the tube can be predicted. This is obtained by evaluating the interfacial film coefficient corresponding to the specified condensing pressure and tube surface temperature for a series of superheats from equation 41. For the same application heat transfer film coefficients for natural convection and radiation are calculated for a series of superheats. The two sets of film coefficients are plotted against the superheat in a manner similar to the results presented in Figure 13. The intersection of the two curves gives the estimated "dry point." A comparison of the specified superheat with that corresponding to the calculated "dry point" indicates the relative severity of the specified conditions. The design procedure discussed in this section is a fundamental method

88 of wide applicability. The somewhat tedious calculations inherent to the basic approach are justified by the predictions which these equations enable under varied conditions encountered in the filmwise condensation of superheated vapors outside horizontal tubes.

CONCLUSIONS AND RECOMMENDATIONS A survey of the literature reveals that the condensation of superheated vapors is not entirely understood. The present study reveals and explains some important phenomena occurring during the condensation of superheated vapors. The various steps used and the conclusions derived from the results of this investigation are outlined as follows. 1. The necessary apparatus including the horizontal tube condenser was constructed and experimental data were obtained for the condensation of superheated Freon-114 at pressures of 43.7 and 77.0 lb per sq in. absolute and superheated steam at pressures of 9.16, 23.35, 23.87, and 44.09 lb per sq in. absolute. 2. A lowering of the tube surface temperature was observed with increase in the superheat of the condensing vapor. Studies showed that superheat causes a lowering of the condensate surface temperature as well. The indicated effect of superheat was a general decrease in the heat flux of as much as 23.4 per cent in comparison to the heat flux of the saturated vapor. 3. The lowering of the heat flux for the different pressures was correlated with the condensing load. The overall performance obtained from the condensation of superheated vapors was explained in terms of the interphase and intraphase mass and heat transfer processes which occurred. 4. The general theory of interphase mass and energy transfer was applied to the condensation of superheated vapors. A mechanism of mass and heat transfer through the vapor-liquid interface based on this theory was introduced to explain satisfactorily the condensation of superheated 89

90 vapors. Deviations from the theory were analyzed and explained by intraphase and other mass and heat transfer processes which occur simultaneously with interphase mass and energy transfer. The condensate surface temperature was calculated from the experimental condensing load by the modified Nusselt equation. The interfacial film coefficient was calculated from the experimental results and the calculated condensate surface temperature. 6. The relationship derived from the theory of interphase mass and energy transfer was modified to enable the theoretical analysis of the results. The experimental condensing loads obtained during filmwise condensation were correlated satisfactorily with the degree of superheat and the calculated temperature and pressure conditions at the vapor-liquid interface. 7. The calculated interfacial film coefficients were correlated with the temperature and pressure conditions at the interface as a function of the temperature drop through the vapor-liquid interface. 8. The behavior of superheated vapors in the region close to the "dry point" was explained. The calculated interfacial film coefficients were correlated with the calculated free convection and radiation film coefficients at the "dry point." A method was proposed to estimate the "dry point" of a superheated vapor condensing at a specified pressure, degree of superheat, and tube surface temperature. It was verified experimentally that a superheated vapor below its "dry point" will condense on a surface so long as the latter is at a temperature below the dew point of the superheated vapor. 9. The experimental results were compared with results calculated by the conventional method used for the design of superheated vapor con

91 densers. A basic procedure was outlined and illustrated to design condensers for the filmwise condensation of superheated vapors outside horizontal tubes. The use of this method was discussed for applications presenting peculiar conditions of pressures, superheats, and tube surface temperatures. Further study of the condensation of superheated vapors is necessary to determine the precise nature and importance of the vapor-liquid interface. For a thorough understanding the interfacial temperature and pressure conditions.must be obtained accurately from-direct or indirect experimental measurements. Difficult as it may be progress in this field indicates the necessity of the measurement of the vapor and liquid temperatures at the interface and the temperature gradient through the superheated vapor region beyond the phase boundary. The applicability of electrical resistivity measurements is suggested for the accurate determination of these temperatures.

APPENDICES

APPENDIX A DETAILS OF EXPERIMENTAL APPARATUS The three components of the experimental equipment are the vapor generation and superheating units, the condenser shell and tube, and the water circulating system. The vapors are generated in a reboiler with steam as the source of heat and are superheated in a Chromalox electric heater. The condenser shell has condenser temperature and pressure measurement devices, and six sight glasses for visual observation of the experimental tube. The condenser tube has thermocouples installed in the wall to measure the temperature at four points. The reboiler, superheater, and condenser shell are welded together and heavily insulated with several layers of magnesia and glass-wool insulation. This resulted in a negligible heat loss from the condenser to the surroundings. The water circulating system consists of the mixing reservoir, the water heater, and the pump for the controlled heating and circulation of water through the experimental tube. VAPOR GENERATION AND SUPERHEATING The vapors are generated in a reboiler made from a section of 6-inch galvanized pipe 24 inches long as shown in Figure 2. The source of heat is steam at 125 lb per sq in. gage which is condensed inside two parallel U-shaped coils. The coils are made from two 30-inch lengths of 0.750-inch outside diameter copper tubes. The connection at the top of the reboiler with valve B is used to charge the system with distilled water. Valve C 93

is used to empty the unit. The condensate line is equipped with a steam trap and a by-pass. A Chromalox electric superheater is used to superheat the vapors. The unit used is GCH - 330, 240 volts, with a capacity of 3 kilowatts, and equipped with a K-3150 three-pole magnetic contactor. The magnetic contactor coupled iiith a thermostat enables automatic control of the superheater outlet vapor temperature. The temperature of the superheated vapor leaving the superheater varies as much as 50F -with the off-on operation of the heating coil. However, the loss of heat in the connecting lines and the volume of the condenser shell level the temperature fluctuations to about 1~F at the highest superheats used. CONDENSER SHELL AND EXPERIMENTAL TUBE Figure 3 indicates the condenser shell and tube details, and Table I summarizes the shell and tube characteristics. The condenser shell is made from a 38-inch length of 6-inch galvanized pipe. The 6-inch pipe is selected to give a very low vapor velocity inside the shell. Two headers with 6 inches diameter are machined for a 2-inch diameter and one-inch deep packing section and packing gland. The left-end header is inserted and welded to the shell whereas the right-end header is removable by the flanged connection shown in Figure 3. Three sight glasses at the top and three at the front enable visual observation of the process of condensation and the external tube condition. The vapor enters the condenser through a manifold which is designed to give a uniform flow and temperature distribution inside the condenser shell. At the top of the condenser are located the pressure tap, two connections for thermocouples used to measure the condenser temperature, and a

vent A used to evacuate the system with the Duo-Seal vacuum pump prior to charging the system, charge the unit with Freon-114, and purge the system of non-condensables. A one-inch pipe at the center of the shell returns the condensate to the reboiler. Condensate flow is observed through the Jerguson gage in the return line. The Condenser Temperature is measured with two thermocouples, TLC located close to the left end and TMC located close to the middle. These thermocouples are made from 30 AWG gage iron-Constantan wire with glass wool insulation. The insulated wire is inserted through a length of 15 BWG type 304 stainless-steel tubing, bare lengths of the two wires about 0.0625 inch long are twisted together at the protruding end, and the hot junction is completed by silver soldering the twisted ends to the stainless-steel tubing and filing the solder down to a small point. The hot junction is located 1.25 inches above the condenser tube, i.e. half way between the condenser wall and the tube. Thermocouples TLC and TMC were calibrated at the low range in a constant temperature bath against Bureau of Standards thermometers, and at two points at the high range corresponding to the boiling point of water at barometric pressure and the melting point of tin (231.90C). The cooling curve method is used to determine the actual thermocouple reading at the melting point of tin. A similar iron-Constantan thermocouple is installed in the condenser wall at the middle and is calibrated in an identical manner. Thermocouple measurements are made with a Leeds and Northrup portable precision potentiometer graduated in 0.01 millivolt. Potentiometer readings are accurate to + 0.002 millivolt. The ice point of water is used as the cold junction. All thermocouple calibration corrections are made to the Leeds and Northrup Tables.50

The Condenser Pressure is measured with a mercury manometer 30 inches long at pressures below one atmosphere and up to 25/lb per sq in. absolute. A Bourdon type gage graduated at 2 psi intervals up to 100 lb per sq in. gage is used to measure condenser pressures above 25 lb per sq in. absolute. This gage is calibrated against a mercury column at the low range and against a dead-weight tester at the high range. Corrections for liquid leg in the line are shown in Appendix C. The auxiliary condenser is used to prevent vapor stagnation and damage to the heating coils of the superheater. Vapors are allowed to flow from the two ends of the main condenser and condense on the outside of five 12-inch long finned tubes of 0.50-inch outside diameter. Valve D controls the water flow rate through the auxiliary condenser. The Selection of the Experimental Tube involved consideration of the following factors. The tube wall temperature is to be measured accurately with thermocouples. Easy installation of thermocouples favors a thick wall whereas reduction of the temperature drop across the tube wall favors a tube with a thin wall and high thermal conductivity metal. The inside diameter is to be such, that for a reasonable tube-side water flow rate the temperature rise and the convection film coefficient are sufficiently high. A small outside diameter tends to reduce circumferential tube wall temperature gradients due to the gradual build-up of the condensate thickness. On the basis of these considerations a plain copper tube of 0.750inch outside diameter, 0.1095-inch wall thickness is selected. The length of the tube is 35.4375 inches long with a 4-inch long brass collar silver soldered to the left end and a 3-inch-long brass collar silver soldered to the right end. When placed in the condenser the brass collars protrude 0.5625 inch into the condensing chamber at each end. This corresponds to

97 a total outside heat transfer area of 0.6372 sq ft used for the preliminary run numbers 56 to 72 summarized in Table III. For all subsequent runs with measured tube-wall temperatures the brass collar ends protruding into the condenser are thermally insulated with Teflon sleeves and washers thus exposing a 34.4375-inch length of tube to heat transfer. The corresponding outside heat transfer area is o.565 sq ft. The tube wall temperature is measured at four points by copper-Constantan thermocouples which are described in detail in this section. The experimental tube is placed symmetrically in the condenser as shown in Figure 3, Chevron type 530 packing is used to seal the ends and the whole unit is made leak proof by tightening gently on the packing glands. To minimize longitudinal heat conduction a 4-inch length of oneinch rubber hose and clamps (No. 15 in Figure 2) are used to connect the condenser tube with the circulated water line. The Measurement of Tube-Wall Temperatures is a convenient way of determining the individual resistances to heat transfer offered by the shellside and tube-side fluid and fouling films. Thermocouples installed properly in the tube wall enable this type of measurement. It is desirable to have a sturdy hot junction the location of which is known exactly. The selection of materials and method must be such that the conduction of heat along the leads is minimized and the temperature distribution at the hot junction is essentially the same as that in other geometrically similar locations. The temperature at the hot junction may be in error because of an abrupt change in the thermal conductivity of the metal at that point. In applications where a vapor condenses on the outside of a horizontal tube a slight hump or depression would also introduce errors in the measured wall temperature.

98 Various methods of installing -wall thermocouples are available in the literature. 8,33,4 Baker and Mueller7 suggest a convenient groove design, but the method of installation is erroneous since the hot junction well is filled with solder. They also discuss the circumferential variation of wall temperature with various fluids condensing at high and low temperature differences. Considering the condensate flow pattern around a horizontal tube the highest wall temperature is expected to be at the top and the lowest temperature at the bottom. The results of Baker and Mueller7 and of Katz et al.25 on the condensation of steam and nhexane indicate this trend. A discussion of the wall temperature variation is given by Bromley.l3 The thick-walled tube with a small diameter minimizes variation of the tube wall temperature specially at small temperature differences. Copper-Constantan wire of 30 AWJG gage is used for the thermocouples to minimize the errors due to conduction along the leads. This error esti41 mated by the method of Rizika and Rohsenow is found to be very small. Figure 4 indicates details of thermocouple installation used in this investigation. A longitudinal groove is cut in the wall 0.076-inch wide, 0.076-inch deep, and 0.50-inch long. Beginning at the end of the groove and perpendicular to it a hole is drilled such that its bottom is at the desired hot junction at the middle of the wall. This hole is 0.055 inch in diameter and 0.1875 inch deep. The 30 AWG insulated duplex thermocouple wire is inserted through the desired length of 15 BWG type 304 stainlesssteel tubing 0.072 inch in outside diameter so that it extends about 0.5 inch at the other end. The hot junction is prepared by removing all insulation from the protruding insulated wire in excess of 0.3125 inch, twisting the two bare wires together and cutting the length of twisted

99 junction in excess of 0.0625 inch. The twisted junction is soldered, then placed in the hole, and -the stainless-steel tube placed in the groove. The groove and the top of the hole is sealed with solder and all excess solder filed off -to obtain a smooth surface. The hot junction is thus free from solder and condensate flow is uniform. The steel tube is taken out of the condenser through holes drilled through the 3-inch-long brass collar at the right end and soldered to the collar. This prevents leakage of vapor or liquid through the thermocouple assembly. Four thermocouples are installed in the tube wall with locations as shown in Figure 3. The two thermocouples at 0~ (top) and at 900 at the left end do not indicate an appreciable wall temperature variation. These thermocouples were calibrated in place, and the correction is applied to the 38 calibration in reference 30. WATER HEATING AND CIRCULATING SYSTEM The water heating and circulating section of the apparatus is designed to heat city water to any desired temperature up to 200~F and circulate the hot water through the experimental condenser tube at velocities up to 20 feet per second in order to maintain the condenser tube wall at any desired temperature. A 55-gallon-capacity drum equipped with a stirrer is used for hot-water storage. The water is withdrawn from the storage tank (Figure 2) by a centrifugal pump and is circulated through the test section. The water heater 12 consists of a single-tube and single-shell pass condenser with steam condensing inside the tubes. It has a 3-feetlong bundle with 40 finned tubes of 0.870 inch in outside diameter and 16 fins per inch, and a total outside area of 65.6 sq ft.

100 Figure 2 indicates the piping used to obtain flexibility and control of operation. During normal operation valves G, K, L, and 0 are closed. Valve E is used to control the water flow rate through the test section and Valve J is used to vary the flow of by-passed water in order to maintain a steady water temperature in the storage tank. The water heater capacity is varied by the quantity of by-passed water and the steam flowing through the two valves. Small adjustments necessary to maintain a constant reservoir water temperature are enabled by valve F which controls the capacity of the water cooler 13 by varying the quantity of the city water flowing through the tube side. Water cooler 13 is assembled from a 1.5-inch pipe shell and four 12-inch-long finned tubes of 0.5-inch outside diameter. The Water Flow Rate through the experimental tube is measured by a Fischer-Porter flowrator located upstream to the test section. The flowrator has a maximum capacity of 21.1 gallons per minute and is calibrated by measuring the length of time necessary to collect a desired quantity of water for a constant flowrator reading. During this operation valves H. J, K, and N are turned off, valves G and M are fully open, and valve E is used to control the flow of water coming from the main line through valve L. The temperature of the water is recorded as read on thermometers T1 and T2. For water temperatures different than that used for the flow14 rator calibration a correction is made by use of the following equation: [P(Pf P)]a Wt(actual) = Wt(calibration) (A-1) [P(Pf - P)Ic where p = density of water Pf = density of stainless-steel float subscript a refers to properties at the actual temperature subscript c refers to properties at the calibration temperature.

101 The flowrator calibration is checked several times throughout the duration of the experimental work.'The Ambient Room and Water Temperatures are- measured with mercuryin-glass thermometers. The inlet and outlet water temperatures are measured with thermometers T1 and T2, respectively, shown in Figure 2. Thermometers T1 and T2 are graduated in 0.10, from O0C to 1000C and calibrated to + 0.010C against a platinum resistance thermometer used with a Mueller bridge. The accuracy of the readings made during the experimental runs with the help of a magnifying glass is + 0.020C.

APPENDIX B EXPERIMENTAL STUDIES ON TUBE-SIDE WATER FILM COEFFICIENT The inside and outside film coefficients of heat transfer between the tube-side fluid and the inner tube surface and between the outer tube surface and the shell-side fluid, respectively, can be determined directly from the experimental heat flux if the mean tube wall temperature is measured. For the preliminary data (runs 56 through 72) obtained during this investigation the wall temperature is not measured. The possibility of determining the individual film coefficients by a method presented by 49 Wilson, is examined in this section. A procedure is outlined and illustrated for the calculation of the inside and outside film coefficients from Wilson-plot type data. The validity of this procedure is proved by good agreement between the calculated water film coefficient and that determined directly from experimental data obtained with measured tube wall temperatures after installation of tube wall thermocouples. A brief discussion of the observed temperature gradient along the tube is given at the end of this section. DETERMINATION OF TUBE-SIDE WATER FILM COEFFICIENT The convection coefficient for water flowing through a tube is correlated with the tube diameter, water flow rate, and the fluid properties by the Dittus-Boelter equation. Over the range of temperatures from 40~F to 220~F the following simplified equation is recommended by McAdams: hw = 150 (1 + 0.011 tw) Vt00 (B-l) 0.20 di 102

103 where hw = convection coefficient for water, Btu per (hr)(~F)(sq ft ins.) = average water temperature, OF Vt = water velocity through the tube, ft per sec di = inside diameter of tube, inches. Equation B-1 predicts reliable film coefficients of water for applications in which the following conditions prevail: 1. The temperature and velocity proviles of the flowing stream are established and flow is fully developed. 2. The degree of turbulence in the flowing stream is not increased due to an excessive roughness of the tube wall or various pipe fittings located upstream within a distance less than about fifty tube diameters. Assumptions 1 and 2 presented above are not valid for most applications in which the experimental apparatus is relatively small and heat transfer to water occurs in a short length of tube. Deviations from assumptionl referred to as "end effects" and additional turbulence in the flowing stream tend to increase the coefficient (c) and the exponent (n) of the water velocity term in equation B-l. Such effects are reported in 42 the literature. For a given experimental tube equation B-1 may be written as: hw = c (1 + 0.011 tw) Vt di(l-n) where the simple expression (1 + 0.011 tw) presenting the variation of the fluid properties with temperature is assumed to be valid for conditions in which n is different from 0.80. The overall resistance to heat transfer consists of the various film

104 resistances between the shell-side and tube-side fluids. Using equation B-2 to express the water-film coefficient and assuming no fouling of the outer tube surface the overall resistance is defined by the the following equation: 1 1 A0 di (ln)Ao Uo = h + rm + fi A + c(l + o.01 tw)Vtn Ai (B-3) where U0 = overall coefficient of heat transfer, Btu per (hr)(~F)(sq ft outside) rm = tube wall resistance, (hr)(~F)(sq ft outside) per Btu fi = inside fouling factor, (hr)(~F)(sq ft inside) per Btu Ao = outside tube surface area, sq ft per ft Ai = inside tube surface area, sq ft per ft. The metal resistance (rm) is defined as follows: r _ _ km Am m km En where -Ym = tube wall thickness, ft km = thermal conductivity of tube metal, Btu per (hr)(~F)(ft) Am = mean metal heat transfer area, sq ft per ft, Am = idm/12 dm = mean metal diameter, inches do - di dm 0 - i do ~n di do = tube outside diameter, inches. During the conensation of a saturated vapor the overall coefficient is defined by the following equation:

UO. (B-4) It follows from equations B-3 and B-4 that the overall coefficient calculated from data obtained in a manner in which the water flow rate is varied whereas the other three terms on the right side of equation B-3 are maintained individually constant presents the effect of the water film coefficient on the overall coefficient. In actual practice the metal and fouling resistances under stable tube surface conditions are approximately constant. Wilson49 presents a method in which it is assumed that the outside film resistance is constant if the saturated vapors are condensed at a constant pressure while the average water temperature is maintained constant and the flow rate varied. On the basis of this assumption a plot of 1/Uo against 1 (1 + 0.011 tw) Vt080 is expected to give a straight line. The intercept of this line on the ordinate corresponds to an infinite water velocity and film coefficient and gives the sum of the other three resistances. The outside film coefficient can be evaluated from the value of this intercept and the known metal resistance if the tube is clean or the extent of fouling is known. In practice even if the condenser temperature is maintained constant the condensing load and the corresponding outside film temperature drop vary with varying water flow rates. The best approximation to a constant outside film resistance is obtained when the overall temperature difference and the condensing load are maintained constant. However, the main objection to the use of the Wilson method in many applications is the fact that the value of n = 0.80 is not valid and the results obtained from the

o06 Wilson plot with the assumed value of 0.80 are erroneous. If Wilson-plot type data are obtained in which all resistances other than that of the water film are approximately constant, the calculated results for a Wilson plot can be used to determine the exponent n for the particular apparatus used for the studies. This method is presented and illustrated in this section for the derivation of equation B-2 valid for the calculation of the tube surface temperature for runs 56 through 72 with filmwise condensation of steam. Runs 73 through 84 in Table VI present the Wilson plot type data obtained with saturated steam condensing at a temperature of 248.590F with a mean water temperature of 86.490F. The Wilson plot ordinate and abscissa are calculated for these runs with the assumed value n = 0.80. The calculated results are given in Table VI and presented in Figure 23. The trend indicated by the calculated results deviates appreciably from a straight line and presents a curve concave upwards. This trend depends on the value of the exponent n used in the calculations and shows that the actual exponent must be greater than the assumed value of 0.80. Since the mean water temperature is maintained very closely constant at about 86.490F, the effect of temperature on fluid properties may be omitted and the equation of the straight line desirable for the correlation of Wilson-plot type data presented by the following equation: y = a + bx (B-5) where 104 y = Uw (hr)(OF)(sq ft outside) per Btu 104 Wt a = Wilson plot intercept b = slope of the corresponding straight line.

1 2 3 4 5 6 7 8 9 88 11 12 184 14 19 16 17 88 19 -Sid' H-84444484888844f88 _ 4 O,, 4 44 4 4 9 -44.8 C-d-.-Wt- FlT.L.1H-t4 —1 T,___H-t_ 85W 8 858A.i..G i qt. 858O 458 8)' 858 858 88thod8f8448t4S498.C. T.848T,4888f 88- 48 8 4 8 4 88 4 8 88 44440 844448~.74 38I88,4 848-84f 888448.8488 (4888.)98t8 88.88,84884i48448.44=89,7T4889,.84.,.484... 84 C488.,84 84 8 448. T,!.p., WtR~~~~~~~~~~~~~~~~~~t~~~,,,, _~~~~~~~~~~F Q, Bt./h~~~~~~~~~~~~~~~- Btu, -F Bt U. S-f~ ~ ~ ~ ~ ~ ~~~~~~~~~4 8 484 4 73 448.84 8,868 88.44 89.49 88,768 887,688, 468.88 684.8 85.868 9.58 4.85 22.331 3894.8.8.5 74 848.88 84,848 8.54 28.47 78,838 488,488 868.88 7(86.4 88.7823 84.98 3.308 884.6849 10.458 6.969 4.664 34.888 754848.664 4,88448 6.84849.84 7(6,788 1845,888 868.84 8848.84 48.584 6.654 2.88 813.8845 8.621 5.692 84.7588 2.481 76 848.68 5,3808 86.58 484.485 88,900 848,888 468.84 985.8 88.088 5.848 2.8754 88.868 6.7434 4.3488 2.8846 18.884 77 848.628,5888 8.848284.848 86,9848 45,888 868.848 948.84 18.545 4.8458 8.7848 8.985 5.741 84.70 4.3884 8.5848 78 848.447,230 86.8888 2.245 88,4848 6848,888 864.8484 964.7 88.8466 4.8848 8.588 8.177 5.244 3.8464 2.1574 1.384 79 848.78 7,8478 86.44 48.484 96,998 468,888 162.844 88884 9.970 4.8484 1.8488 7.888 5.0843 3.226 2.864 1.8448 88 848.59 8,8848 86.89 88.87 95,588 889,888 1664.78 88845 9.8469 84.588 1.8488 6.9849 4.417 2.804 1.780 1.8848 88 848.86 8,988 86.848 88.44 98,988 864,888 968.86 4886 9.8484 3.55 1.302 6.9254 4.3496 2.789 1.771 1.884 88 848.78 9,788 86.846 9.684 984,888 866,888 464.44 88884 9.775 84.848 1.8884 6.45 4.08. 8.577 8.628 1.029 884 848.78 88,6848 86.88 8.98 94,780 467,888, 868.96 88847 9.6434.'484.8.8 4798888848.,8 84 848.47 48,848. 86.848 7.988 94,688, 867,8408 866.94 48845 9.668 8.88 1.012 5.5884 84.448 2.8847 1.8484 08.446 8848. 84888 848.59 86.49 884 848.84 8,0888 884.98 849.78 88,688 846,888 864.884 984 88.48 88.848 4.850 884.484 484.68o4 94848848848 86 847.77 84,878 85.98 844.88 887,888. 889,888 868.87 4878 8.584 8.844 84.468 88484.9 848.88488848.6.678 87 848.87 4,8484 884.85 89.77 888,488 848,688 868.48 88488 7.684 6.654 2.685 1888.48 64.5498487.887244,4 848 448.46 584,58 87.88484.9845 38,888844, 468c 864.46 88445 6.68 54.32 2.o88 888.77 67.698868848.3,4842 89 448.87 6,648 86.88 244.5 8684,888 498,888 468.87 18888 84.84 4.494 8.784 898.846 784.71 48 98 447.58 7,888 86.78 23.415 488,888 8448,488 868.44 8988.04 84.9884 8.8478089 878.842 77.442 84 9 84,4 984 244.48 9,8484 86.88 48.88 858,888 43,8488 498.848 44684 4.64 84.4884 8.8848 164.29 80.8 4 4.881638 8, 98 4384876 88,8848 88.88 86.98 484,888 8464,8488 458.76 24488 4.87 4.840.984 i64 23 48484. 884848 446.44 86.48 984 4484.76 4,768 87.88.18048 87,848 4848,8488 4848.684 8488 8.94 9.8 34.7754 888.88 434.934858844 78 ~8 58 4448,7 8.8 4.8 86,488 488,888 4849.76 8478 6.88 6.44 8.44 497 8 8844.474 4 984 4484.79 6,488 88.88 44.44 1349,800 847,8488 4849.69 4778 5.64 4.665 8.7,98 868.84 648488816.468.3, 96 8484.69 7,678 87.48 19.434 849,888, 484,888 4848.89 8988 84.84 84.96 8.488687 7948884 4.4,7 97 4225.634 8,848 87.88 87.98 458,888 288,8 858.684 4888 4.95 3.558 1.8444 8848465 69.94848485.8 484 98 22448.58 9,478 87.88 87.44 8 684, 888898, 8888848.5 844880 4.754 34.364 8.858 1524.75 7.88188 88 4.447 99 4884.89 88,488 88.68 86.68 74,888 8487,8488 8849.49 48884 4.58 84.44 8.81.674.18885834.64 888 445.98 44,8488 86.68 484.8484 888,888 8488,888 4849.844 4488. 4.86 4.785 8.978 848.54 77.44 484484 8.48971 484.88 7748, 4848. 98484 4484.76 86.74 48484 27.848 2,083 488.4 44.87 49,788 54,8488 45.58 4458 8.78 7.345 84.20 2884.28 12.188 84 64.4 488 227.831 34,245 484.2 48.98 847,688, 66,5484 46.44 88442 6.58 84.86 2.13 8.8444848 8.8 88.8 48 8884 847.84 4,484 484.8 9.88 44,888 784,888 484.44 4644 6.48 4.884 8.684 489.84 88.4448848.528.4 888 447.84 84,488 484.4 8.254 44,5504 78,988 84.84 8768 84.89 84.48 1.3324 486.88 80.23 449 4.8 4 4884 447.58 6,888 484.8 7.88 46,85o 84,90 484.58 4848 84.88 84.49 1.19680-9 19 Avg. V.8488 427.44 488.7

10o8 20 — - RUNNO Tsv,F tW)F 73-84 248.59 86.49 0 8592 246.44 86.48 -0- 93-100 225.76 86.74 _l 101105 227.24 181.7 - I0.~ FIUR 2- ILONPLT IT WAE LO AEEXOET F08

109 Equation B-5 is used for the determination of the correct exponent n for this application by the method of least mean squares. Values of x and y calculated for runs 73 through 84 corresponding to assumed values of n of 8o 085'0.90, 0.95, and 1.00 are given in Table V. The least mean square deviation of all the runs is determined for each assumed value of n and the correct value of n is selected as that which gives theminimum least mean square deviation for the experimental results. Derivation of the equation expressing the least mean square deviation as a function of x and y is given in this section. The deviation of a run from the best line obtained by the determination of a and b in equation B-5 is defined as e = y - a - bx (B-6) where e deviation of a run from best line. The least mean square deviation is defined by the following equation: je2 (y-a bx).(B-7) 72. It f ollows from equation B-7 that z~e is a minimum f or the best straight-line fit when je2.and are zero. Differentiating ie2 in equation B-7 with respect to a and b, equaing+n the resultinga two equations to, zero and solving for a and b the

110 y b x a = / (B-8)'N 3xy- xy N 2 (B-9) x jx2i. b = 5 2 where N number of runs in the set, twelve for runs 73 through 8. Substituting for b from equation B-9 into equation B-8 y _ x xy x N a = N N j2-(jx)2 (-a X2 N Substituting for a and b from equations B-10 and B-9 into equation B-7: jxj ZxY - N ~je2 = - N N jx2 - j 2 N N N - X ~x2 - (Zx)2 N~~~ ~3imlifingthe relationship given in equation B-ll thfolwn the~ caclae expeiena reut x ady i / /~~x y / xy - x~~~~ N2 x2_ N

111 jje2 box - x( (B =~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - N Equation B-2 isusedtodetermine the least mean square deviation fo tevalues of x and y given in Table VI f or five values of the exponent rying from 0.80 to 1.00. The calculated deviations are given in T e VII. TABLE VII -DETERMINATION OF EXPONENT BY T'E METHOD OF LEAST MEAN SQUARES (Runs 73 through 84) N~~ x Assumed B2Least Mean Squarea e Assumed A e2 Value of n Deviation, e2 An var~~~- Dn rm08 o10.Te cluae eiations ar gien in'Ao.8o 0.23905 - o.2762 o.85 0.22524 - 0.1162 0.90 0.21943 + 0.0734 0. 95 0.22310 + 0.2582 1.00 0.23601 Figure 24 presents the variation of the deviation with the assumed value for the exponent n. In order to determine the value of n where 12 is a minimum the average slope of the curve is obtained between consecutive

112 0.2 ________. 0.235 - _ __ z 0 w 025 0.230 - 0.22.5 w~~~~~~~~~~~~ I- ~' 0.80 0.85 0.90 0.95 1.00 EXPONENT FIGDURE 24-~DETERMINATIO OF WAT E R F LOWV RATE EXPONENT BY T HE- METHO[D OF LEAS3T MEAN~ SUARES

IN3NOdXB 31V MO1 A 831VM -O0 ~NOUVNI83i3 804 3A;nfo V38V VfnlO3 -Z 3lid U LN3NOdX3 00 g6'0 060 S80 080 V0Ot,.o 7ITT

114 the area of the curve below the zero line is equal to the area above it. This curve intersects the zero line where the least mean square deviation is aminimum at n = 0.91. This point is also shown in Figure The actual value of n = 0.91 obtained by this analytical procedure is used to prepare the Wilson plot presented in Figure 26. It is interesting to note that the curved trend indicated previously by runs 73 through 8 (Figure 2) is eliminated by using the proper value of n. In order to prove the validity of this procedure additional Wilsonplot type data were obtained with saturated steam condensing at 246.44"F (runs 85 through 92) and 225.760F-(runs 93 through 100) after installation of tube-wall thermocouples. The calculated results for these data with a clean tube are tabulated in Table VI. Wilson-plot results are computed for the assumed value of n = 0.80 and the calculated value of n 0.91 and presented in Table VI, and Figures 25 and 2-6. In both figures no appreciable effect of condensing pressure on the overall coefficient is observed. This is due to the mixed condensation of steam discussed further in a later section. The experimental water film coefficient is calculated from the heat flux and the measured temperature drop through the water film by the following equation: h = Ao(B-l3) A(ti-tw) Ai where ti inside tube surface temperature,'F. The calculated water film.coefficients are given in Table VI and presented in Figure 27 as a function of the water flow rate. Water film coefficients calculated from-the DittusBoelter equation simplified for water (equation B-l) are indicated in Fig

115 1 6 0 0 RUN NO Tsv F tW, F i- 84 248.59 86.49 85- 92 246.44 86.48 / 4- 100 225.76 86.74 0 C_'"".101- 105 227.4 18,1.7 C?""/~~~~~cpd 10 ~0' /'\ o A~~~~~~~o co 0~~~~~~~~~~~000 I.-~~~~~B 0 4~~~~~~~~~ 0~ ~~~~~~I FIGURE 26- WILSON PLOT WITH WATER FLOW RATE EXPONENT OF 0.91

116 10,000 -- I 8,000 - qE 700 II. 5,000 _ _ _ _ _ _ _ _ 3,000- --- - _ _ _ -r~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-l zV UJ 0 ~2,000 RUN NO TSV,&F, t, 085-92 246. 44 86.48 — 93-100 225. 76 86.74 4)101-lOS 227. 24 181.7 PREDICTED FROM Tnu0.91 tW= 86.49PF,002,000 3,000 4,000 6,000 8,000 10,000 20,00 WATER FLOW RATE,.~ t LB/HR FIGURE 27 - COMPARISON OF PREDICTED'AND EXPERIMENTAL TUBE-SIDE FILM COEFFICIENT FOR WATER

117 er cent at a water flow rate of 2000 lb per hr per cent at 12,000 lb per hr. This deviation is due to the excess turbulence caused by fittings in the flow conduit and the end effects in the condenser and accounts for the abnormal temperature gradient observed along the tube. This subject is discussed in a later section in Appendix B. The intercept of the Wilson plot for runs 85 through 100 is shown in Figure 26 to be 0.00027 (hr)(~F)(sq ft outside) per Btu. t follows from equation B-3 that the outside film resistance can be evaluated by subtracting that portion of the resistance due to the metal wall [0000049 (hr)(F)(sq ft outside) per Btu from Table I] since these results were obtained with a clean tube. The resulting film resistance for the saturated steam is 0.000221 (hr)(~F)(sq ft outside) per Btu and the corresponding condensate film coefficient (he) is 4530 Btu per (hr)(F)(sq ft outside). Comparison of this value with the experimental values (runs 8~ through 100) given in Table VI for the range of water flow rates used indicates an increase of 28.3 to 41.5 per cent in the value of the condensate film coefficient. In general with increasing water flow rate and heat flux the condensate film coefficient is expected to decrease. Thi's discrepancy is due to the mixed condensation of steam and the gradual increase in the extent of dropwise condensation with increasing heat flux. This explanation is proved by the order of magnitude of these coefficients which are about twice the value of the coefficients predicted from equation 1 for filmwise condensation. It'is interesting to note that the values of. these film coefficients agree with those of runs 40 and 46 (Table III) obtained'under similar conditions of mixed condensation. beusdtoealae h cntant' c neutinB2 TevldiyoZh

118 resulting equation based on the exponent of 0.91 calculated by the method of least mean squares is checked by comparing the film coefficients calculated from this equation with the experimental coefficients obtained for runs 85 through 100 and presented in Figure 27. The relative location of the lines in Figure 26 indicates a certain amount of fouling for the results from runs 75 through 84. Using the condensate film resistance obtained previously by extrapolation of the clean-tube data and the intercept from the line for runs 73 through 84 (Figure 26) the extent of fouling is determined as follows from equation B-3: 1 (o.oo80 - 0.000049 - 0.000221) 1.41 0.000376 or 0.00038 (hr)(~F)(sq ft inside) o.ooo37 or o~oBtu The slope of the line for runs 73 through 84 is found to be 1.452 in Figure 26. The resulting water film coefficient equation is: 0.7 (1 + 0.011 tw) Wt0~~.(-k Values of hbW calculated from equation B-14 are indicated in Figure 27 by the dashed line identified with a slope of 0.91. It-is seen that the equation derived by the outlined procedure for the determination of n predicts water film coefficients which-agree satisfactorily with experimentally determined values. The deviations of the calculated results from the experimental are within the range of the experimental errors involved,in the measurements and vary from +4.4 per cent at the low range to -5.2 per cent at the high range. Introducing the water velocity and tube diame_L_ hw 185.2 (1. I + 0.1 1 t- ) 0.09 (B1)

119 Results predicted by equation B-15 deviate from those of equation B- about as much as the experimental film coefficients shown in Figure 27 and discussed earlier. Runs 101 through 105 are made to find out the possible effect of the water circulating pump and stirrer (Nos. 10 and 14 in Figure 2) on the water film coefficient. The experimental results are given in Table VI and are shown as Wilson plots in Figures 23 and 26. Film coefficients presented in Figure 27 are compared with the clean-tube data. No effect of pump and stirrer is observed due to the various straightening sections between the pump and the experimental tube (Figures 1 and 2). Comparison of the waterfilm coefficients with values predicted from equation B-t indicates a slight fouling of o.oooo6 (hr)(0F)(sq ft ins.) per Btu. The validity of equation B-14 for the prediction of water film coefficients follows from the foregoing discussion. Equation B-lit is used to calculate the water film coefficient for runs 56 through 72 shown in Table EITI. These results constitute the only data on the filmwise condensation of superheated steam and are obtained prior to wall thermocouple installation. Equation 1 is used to calculate the condensate film coefficient for the saturated runs (runs 56, 57, 58, and 67). The water film coefficient determined from -equation B-lit is' combined with the condensate film coefficient and the experimental overall coefficient to calculate the extent of tube-side fouling. The indide fouling factor evaluated by this method is found to be 0.00023 (hr)(0F)(sq ft ins.) per Btu and is used along with equation B-lit to determine the tube surface temperature for runs 59 through 66 and 68 through 72 obtained with f ilmwise condensa

120 TEMPEATUE DISTRIBUTION ALONG CONDENSING TUBE The importance of end effects on the water film coefficient is observed from the experimental results and is discussed in the previous section. Figure 27 indicates that the average water film coefficient may be as much as 755 per cent higher than the normal value predicted from euation B-. It is important to note that this increase is due primarily to the very high water film coefficients which prevail in the region extending from the right end of the tube where the water inlet is located. The effect of this phenomenon is an apparently abnormal temperature gradient along the tube. f the entrance effect is neglected the wall temperature is expected to indicate an almost linear variation along the tube being lowest at the water inlet end and highest at the water outlet end. The experimental wall temperatures for runs 101 through 105 are shown in Table VIII and presented in Figure 28. For all water flow ratesthe wall temperature is lowest at the water inlet, higher at the water outlet, and highest at the middle of the tube. The difference between the wall temperature (tM-tL) at the middle of the tube and at the water outlet is also shown in Table VIII and presented in Figure 29 as a function of the water TABLE VIII TEM~PERATURE DISTRIBUTION ALONG CONDENSING TUBE Measured Wall Temperature Temperature Run No. Water Outlet Middle Water Inlet Dif ference, End,9 tLP OF tM,0 F End,. tRp \OF (tM-tL),,'F 101 215.53 215.59 210.82 0.26 102 212.00 212.7 206.407 105 208.67 2~~~~09.74 20.91070

121 ~23C - ____TSVI1 220 L TIIv 22 UN Wt =2083 LB/ 0T 101 102 104 105, MIDDLEt WATER t MIWATER OUT, T2 INT DISTANCE ALONG TUBE INCHES ALONG CONDENSING TUBE

122 0~~~~~~~~~~~~~~~ RU 0N Tsv OF tW FI_ 6000~101- 05 227.24 181.7 _ 2 5000 1o6 U-~~~~~~~~~~~~~~ 5 v I-~~~~~~~~~~~~~~~~V2z 000 _____ w~~~~~~~~~~~~~~ 5 1 000 0.24 w w 20010 00 30 40 00 60 WATE'FOW RTEWt, B PR H FIGRE29 EFECTOFWATER FLOW RATE) BPRH ON WATER FILM COEFFICIENT AND TEMPERATURE DISTRIBUTION ALONG CONDENSING TUBE

123 flow rate. Figures 28 and 29 indicate that the temperature rise at the middle above that at the water outlet varies with the water flow rate and the mean water film coefficient. It may be concluded from these observations that the peculiar temperature distribution is due to entrance ef fects which are more pronounced at high than at low Reynolds numbers or water flow rates. The (tbrtL) curve in Figure 29 is extrapolated to the origin to show that theoretically the middle. and water outlet temperatures wi'll be equal when there is no heat flux and therefore no entrance effects.

APPENDIX C SAMPLE CALCULATIONS A sample of the original data and calculations are presented in this section for run 21 with superheated Freon-114 condensing at a pressure of 43.74 lb per sq in. absolute. Table IX presents the original data. TABLE IX ORIGINAL DATA SHEET Run No. 21 Condensing fluid: Freon-114 Cooling fluid: Water Temperatures: Room 78.0 ~F Inlet water, T1 8.64~C Outlet water, T2 9.80oC Condenser, middle, TMC 5.038 mvolts left end, TLC 5.000 mvolts Tube wall, left end, 0~ tLO 0.460 mvolts left end, 90~ tL9O 0.418 mvolts middle, 00~ tM 0.462 mvolts right end, 0~ tR 0.418 mvolts Pressures: Condenser 29.7 psig Barometric at 29.5~C 29.52 in. Hg Rotameter reading 23.5 per cent 124

125 (1) Condenser Pressure, Pg: P P(barometer) + P(gage) + calibration (17.5) (p fluid) (12) (144) P(gage) 29.7 lb per sq in. gage Calibration= -0.21 lb per sq in. (29.52) (13.53) (62.4) = 14 4 0 lb P(barometer) -(95) (15.5)(6.47 14.40 lb per sq in. (12) (14) Assume vapor in gage line is saturated at Pg. 44lb per sq in. absolute p fluid = 1.58 lb cu ft (175) (1.38) 0.014 lb per sq in. (12) (144) P 14.40 + 29.7 - 0.21 - 0.01 = 43.88 lb per sq in. absolute From tables of thermodynamic properties9 The saturation temperature is assumed to be that for run 16 because of its proximity to the more reliable saturation temperature measured by thermocouples for run 16. =96.420F and Pg 45.7 lbprsq in. absolute (2) Ove rall Performance: From the rotameter calibration at 25.5 per. ce'nt,. Wt =2570 lb per hr. The correction to the thermometer readings T1 and T2 is negligible f or this range. The f ollowing a-re a f ew values f rom the thermometer calibration chart: Observed Temperature Correction 50 0.4 0.56

126 Inlet water temperature = 8.64~C Water temperature rise, Att = 9.80 - 8.64 =.60 - (1.16) (1.8) =.o86F Mean water temperature = 8.64 + 0.58 = 9.220C = (9.22) (1.8) + 32 =48.60F Total heat transferred = W C At Wt Cp tt (2570) (1.0) (2.086) = 5360 Btu per hr Q5360 Bt Heat transfer rate, 51560 Bt r rate, = 0.565= 9500(hr)(sqft) () Condenser Temperature: The correction to all potentiometer readings is 0.002 mvolts. uncorrected TLC = 5.000 + 0.002 = 5.002 mvolts and uncorrected TMC = 5.038 + 0.002 = 5.040 mvolts. Mean uncorrected temperature= 5.002 + 5.040 2 ~ 501mvolts Correction to condenser thermocouples =-0.020 mvolts Corrected thermocouple reading= 5.021 - 0.020 =5.001 mvolts From Leeds and Northrup Tables5 Condenser temperature, Tg 202.670F Degrees superheat in -vapor =Tg- -202.67 - 96.42 =106.250F Overall temperature difference ATa= (Tgtw) =202.67 -48.60o 154.070F =a 950 1. t

127 Condensing Load, ms: 3From Figre 6 in Appendix F or reference 9 at Pg 43.74 psia and Tg - 202.67OF Enthalpy of superheated Freon-114 H 103.16 Btu per lb at P 43.74 psia Enthalpy of saturated liquid h 31.60 Btu per lb Heat removed, (-AH) = 103.16 - 31.60 = 71 Btu/lb Total vapors condensed, Ws = Q/-AH 5360 71560 = 75.0 lb per hr Condensing load, ms = WS/A 75.0 12.8 lb per (hr)(sq ft) (5) Tube Wall Temperature, tin Uncorrected t = 0.418 + 0.002 = 0.4620 mvolts L9 Uncorrected tM 0.462 + 0.002 =0.464 mvolts Uncorrected tR =o.418 + 0.002 =0.420 mvolts 0.462 + 0.420 Mean uncorrected tL -2 =0.441 mvolts tL calibration correction =0.020 mvolts Corrected tL =0.441 + 0.020 =0.461 mvolts tm calibration correction =0.019 mvolts Corrected tM =o.464 + 0.019 =o.483 mvolts

128 Mean tube wall temperature, 0.461 + o.483 + 0.434 = 0.459 volts From Leeds and Northrup Tables for 38 Calibration30 tm = 53.32~F (6) Metal Resistance, rm: At tm = 53.32~F km3 = 222.7 Btu per (hr)(~F)(ft) From Table I Log-mean diameter, dm = o.636 inch Outside diameter, do = 0.750 inch Wall thickness, Ym = 0.1095 ft 12 metal resistance rm = Ym do km Am rm = j(01095)j(0.750) (12)(222.7) (o.636) =.000048 (hr)(~F)(sq ft outside) Btu Temperature drop through metal wall Q Atm = rm = (9500) (0.000048) = 0.46~F (7) Outside Tube Surface Temperature, to: to = tm + Atm 2 to = 53.32 + 0.46 = 53.55 F 2 (8) Overall Outside Film Coefficient, ho: Overall outside film temperature drop Ato = Tg- to = 202.67- 53.55 = 149.12~F

129 = 9500 = 65.7 Btu vA(Tgt) 149.12 (hr)(~F)(sq ft outside) (9) Condensate Surface Temperature, Ts: The following equations are obtained from equations and 25 by substituting for the tube characteristics. k3 p 1/4 /V/4 hc = 1.45 ) y- (c-i) 1.552 gkf/ p f 3 g/3 hc777 ) (c-2)/3in - \- ~/3 For steam runs 56 through 72 the following equation is used instead of C-2: 1.41 3 2 + 1/3 1.41 (k f Of hc = (Ws)'/3 ( f Assume Atc 41.o00F..The mean condensate film temperature, Tf =to tc 53 5 + i.2 74.050F 2 From Figure 38 in Appendix F at Tf =74.050F (k3 -2g2/ 721-.0 V!5 (7s5o)'1 =4.21 From equation C-2 hc (1.352) (721.0), Bt hc ~(4.21) - 251. 5 (hr)(0F)(s q ft, out side

130 which checks the assumed value of 41.0~F. to + Ato = 53.55 + 41.0 = 94.55~F (10) Interfacial Vapor-Film Coefficient, hi: Temperature drop through the vapor-liquid interface Tg - T s T = 202.67 - 94.55 = o108.12F g h - Q = 9500 = 87.9Btu A(Tg-Ts) 108.12 (hr) (F)q ftoutsie) Items 1 through 10 are given in Tables II and III. (11) Saturation and Condensate Surface Temperatures Obtained fro Correlating Line Drawn in Figure 18 Derivation of Equation of In Ts versus ATs - The slope of the line is determined from two sets of coordinates: at AT5 =O0F Ts Tsv= 98.00F ATS 115.00F Ts 90.00F in ~. in 98.0 slope = TS2 = 90.0 AT51-ATS2 0-115.0 log 98.0 = 1.99123 log 90.0 = 1.95424 log 98.0 - log 90.0 =0.05699 log (log 98.0 -log 90.0) =8.56808 lo1 log 2.5053 0.36229 =98905 -1

131 log 115.0 2.06070 / 98.0\ log 90.0 )= 8.93037 - 10 - 2.06070 \115.0/ = 6.86967 -10 n 98.0 slope 90.0 = - 0.00074075 - 115 The equation expressing Ts as a function of ATs is 9 8 0.00074075 A (-4Ts AtT = 98.0F, P = 44.89 lb per sq in. absolute.:v g Corresponding degrees of superheat 202.67- 98.o = 104.67~F From equation c-4. the calculated condensate surface temperature is = g0.690F.The equilibrium vapor pressure is obtained from refe rence 9 at Ts = 90690FI, PS 3 9.755 psia Lowering of the condensate -surface temperature due to superheat, T5v - Ts 98.0 - 90.69 =7.51 (12) Interfacial Film Coefficient Based on Cor related Condensate Surface Temperature:, Ati =T - Ts 202.67 - 90.,69 111l.980F

132 () Calculation of Correlating Group ms T ~~~~G(f)~ - * In Table V: \Tg - Ps 0.69 + 460 = 550.69~R T = 202.67 + 460 = 662.67~R 5 69 = 0.8310 (T)/ =(0.8310)1/2 = 0.9116 Pg T)/ = (44.89)(0.9116) = 40.92 psia Pg - = 40.92 59*755 =1.165 psi = 55 = 25.46 From-Item 4', m5 152.8 l (hr)(sq ft) G~f) -(132.8) (23.46) (1.165) =28 (14) Calculation of Correlating Group hi 4fS R(f) -(A)[g()1/2 -P* From Item 4, -ARH 71.56 Btu/lb H H(f) 25.9

APPENDIX D CALCULATION OF A TYPICAL VALUE OF 0 g The value of 0g is calculated for run 15 to check the validity of the specified range of O.1-> Igl >0.001 necessary for the elimination of from equation 19. The following equations may be used: r = 1 + 1.85 10gl for 0.1 I 0.gl 001 (29)>.oo 0 l X 1/2 = mg iRTs T) (50) 2ir1/2 f P g11 \L'~~9 = 1 ( s (T 1/2 mTg\1/2 2 T - 1 g TT P5 g \T 1.85 f Pg kTs} gM(1) 1.5 m52g, RT5 = 61.521552psia g ~ ~ ~ ~~~~ j~Pg (#) f = 2527ps For run 15 ~15

134 (1) Calculation of 0g from equations 31 and 32: Substituting for f from equation 32 into equation is defined as L _Pg (T1/2]11 * (.5231) (-2.*327.) _ (.43) (o.899) - (1.85) (.52) (7.43) (o.81 = 0.521 + 0.013 - o.541\ = - o.007 (2) Calculation of Og from equations 50 and 52: Substituting for f from equation 52 into equation 50 Og is de-' fined as: (2rc/2)(.52(Pg)\2 5 Solving or th Pvlu ofTg1/ (-2.527) ~ ~ ~ ~ ~ ~~(D2 = (2~1/2)(l2)1.52)(7l4) g.95) — 006 (5) Calculation of F From equation 29, at IgI =.0068 F'=1 + (l.85)(o.oo68) =1.0126

APPENDIX E EXAMPLE DESIGN OF A SUPERHEATED FREON-114 VAPOR CONDENSER The design procedure outlined previously is illustrated in this sec tion for the design of a condenser involving filmwise condensation of superheated Freon-1l14 outside horizontal tubes. Problem: 1000 lb per hr of superheated Freon-114 vapors are to be condensed on the shell side of a horizontal tube condenser with water flowing inside the tubes. The superheated vapors enter the condenser at 400F and condense at a pressure of 60.0 lb per sq in. absolute. The wa ter flow rate and temperature are such that the mean outside tube surface temperature is 85.0~F. The required total outside heat transfer area is to be determined. The following conditions are specified: a. Tubes with 1-inch outside diameter are to be used. b. No fouling occurs on the shell side. C. Condensate leaving the unit is saturated. (1) Overall Heat Duty: From reference 9 the enthalpy of the vapor at 60 psia and 4000F'is H =140.59 Btu per lb Ts =116.300F Enthalpy of saturated liquid is h 3 6.42 Btu per lb. Heat removed, -AH = 140.59 - 36.42 =105.97 Btu/lb. Overall hea duty Q- =- W T(AH

136 (2) Degree of Superheat, ATs: ATs = Tg - Tsv Tg = 400F, ATs = 400 - 116.30 = 283.70~F (3) Film Coefficient Equations: The condensate film coefficient is calculated from equa h = 0.725 4kf3 pf g (-AH) Do kf Atc To simplify the use of equation 1 define (fPf29 z1/4 = / Values of z/4 are presented in Figure 58 in Appendix F as a function of the mean condensate film temperature, Tf. For the 1-inch outside diameter tubes used in this application equation 1 becomes: (0~725)(103'97)1/A l_~_1/4 hc (1.0/12)1/4 At hc 4 (.3 (E-) Equation 37 is used to determine the Tcondensing load (m) and the condensate surface temperature (TS) by trial and error. The calculated \1 (~/'2 - 16s]37

137 For Freon-114, M = 170.9, 4= 13.073. For this application equation 57 becomes ms 70.9- 46,700 L 1/2 1.16t>70 Tsg (~.)1/2 - ~sj (283'70)1'6 T51/2 g * ~~~~ s ms= 8y6 PgS. (-2 r(4) Trial-and-Error Determination of Condensate Surface Temperature a. First trial - Assumes = 100.0~F AsumedAtc T - to = 100.0 - 85.0 = 15.(F * From reference 9, P5 46.59 psia =s 100.0 46o =560.0O1R =_~ v7= 07 25.66 T =400.0 + 46o =860.0 g (\: = __ 0.651 (T)1/ 860.60 )/.0 (T1/2 Pg =~(6o.65)(08o). 4.40pi 1/2 [Pg (60.))-(08]7= 48.44 -465 ps205ps (876)(2.o 4 lb3.0 s 9 T =7. (r(s t

138 A- = (75?9)(103.97) = 7890 Btu 7890 (hr)(sq ft) The assumed value of Ts and the corresponding assumed value of Atc is checked by calculating the condensate film coefficient from equation E- and the calculated Atc. Mean condensate film temperature Tf + Atc = 85.0 +15.0 _ 92.50F 2.2 3From Figure 8 in Appendix F, at Tf 92.5~F, Z/ = 135.2 Atc1/ = (l5.0)/4 = 1.968 Substituting these values in equation E-1: _ _ _ _ _ _ _ _ _ Btu hc =(.)(52 295.5 (r(F(qftotie (1.968) (r(6F sqtotie Calculated Atc= Ac Ac = 80 26.660F 295.5 The calculated value of Atc is higher than the assumed value of 15'C. A value of;Atc hi'gher than l5'C is assumed in the second trial. b. Second trialAssume T5 102.O0F P5 47.92 psia As sumed Atc 102.0 - 85.o =1.0 = 0. +17o =5620F

139 Substituting in equation E-2, (876) [6o.0 (). - 47.92 s (23.77) ms = 21.4 lb per (hr)(sq ft) Q/A = (21.4)(103.97) = 2222 Btu per (hr)(sq ft) Tf = 85 + 170 = 93.5~F Z/4 = 135.0 2 1,/4 3./4 Atc/ = (17.0) = 2.03 From equation E-1 h =(4.3) (135.0) B 286 c (2.03)) 286 (hr)(~F)(sq ft outside) 2222 o Calculated At = 286 7.79F The calculated value of Ate is lower than the assumed value Of 17.0F The assumed and calculated values of Atc and Ts are indicated in Figure 29a. These results indicate that the condensate surface temperature and the corresponding Atc may be approximated by the values obtained from the intersection of the two lines in Figure 29a. This is shown by the third. trial. c. Third trialFrom the intersection of the assumed and calculated values shown in Figure 29a, Ts= 101.120F =S 47.25 psia Atc =101.12 - 85.0 =16.120F T = 101.12 + 46o= 561.120F NJ 5T 57

140........ l0 CALCULATED AtC 26___ * ASSUMED AtC ii. LU ow 0 18__ __ oz U. U.. 431 4 LU I(0 698 100 12104 CONDENSATE SURFACE TEMPERATURE, T OF TS FIGURE 29A TRIAL-AND-ERROR METHOD FOR DETERMINATION OF CONDENSATE S-URFACE TEMPERATURE, T8 OF

141 (876) [60.0 (:2)/ - 47.23] (23.74) 46. lb per (hr)(sq ft) )(103.97) = 4800 Btu per (hr)(sq ft) A 16.12 5 + 2 = 93.06~F Z1/4 = 135.1 =(16.12)1/4 = 2.oo008 From equation E-1 (4.3)(135.1) Btu h~ 200' = 289.5 (hr)'(F)(sq ft outside) Calculated Atc = 48 16.60F - th9.5 Comparison of these results with the trend shown in Figure 29a indicates that the correct condensate surface temperature i's very close to the assumed value at the intersection. The correct value of Atc indicated is slightly higher than 16.120F, and it may be taken to be Atc =16.150F T =85.0 + 16.15 1 01.150F (3) Total Outside Area Required, A: Heat flux, =hc Atc A=(289.5)(16.15) =4670 Btu per (hr) (sq f t) =s (4670) =45.0 lb per (hr)(sq ft) (103.97) Requre utside area, A quirw

142 The temperature drop through the interfacial film (At) and the corresponding interfacial film coefficient (hi) are Ati = T - Ts = 400.0 - 101.15 = 298.85~F Q hi = 7 -TS g A(Tg-Ts ) = (4670) h (298870 ) = 15.6 Btu per (hr)(~F)(sq ft) =(298.85), The correlating groups used in Figures 20 and 21 are calculated for this application: G(f) - (45.0)(25374) = 855 at ATs = 283. (1.25) 8 H(f) = 159)l2)-2.845 at At1. 298.850F These values agree with the correlating lines corresponding to Freon114 and presented in Figures 20 and 21.

APPENDIX F Ioons~wroTrm

.RUN NO FLUID P, PSIA 0- I-15 -FREON- 114 71.43 16- 26 44.89 X0'40'45 STEAM 9.1608 - 46-55 "24.080 == =5-66 ~ ~,=:E22.589 *:67-72 38.539 4w~, I-. w 10 ___ 10 ASSUMED =I.0

145 RUN NO 27-34 e to Vs (Tv -to) AT vs (1v-to) P, PSIA 7.5 9.0 -,, T s, OF 179. 94-188.28,, ~OF 175.93 L,,J.,. 2..9L..... - - _ 44 180 4OC _,. w178 _ 38ct APPRACHTO TBE ALLTEMPRATRE,(Tsv-to, 0

8 80 m~~~~~~~~~ z -J ___ ~ ~ ~ U; 6 (I) U) w W. 0 20 0~ 40 60 80 100 120 140 160 TEMPERATURE) 0 F FI GURE 32- VAPOR PRESSURE OF FREON- 114

147 94__ 92 90 CD 0. -j 884_ __10 6 I- ~ TMERTR

148 0.054 t~0.042__ 0.0420_ H~4 010 2 4 6 5: ___ __TEM ERATUR OF__ H~FGR 4~TERA CNUTVT 0~~~~~FLQI RO 1

149 0.680 0.600 0.40 0.36 I. 028 0.520 -j.40 4 01 1020 ___ ___ T___ ER_ _O o~ 0.360 0~~~~~~~~~~~~~~~~~~~~~~~ii~i Co ~..... l

150 P, PSIA Tsv, -F SAT'D LIQUID ENTHALPY hLBTU/LB 118 43.7 96.42,31.60 77.0 133.16 40.59 114 - - - -- _ --- -- _ - 10 a~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~... 0 34 9 z 0aI 94 - - - _SUPERHEAT- VAO -EPRAUE -G - w~~~~IUE3 NHLYO UEHAE SUPERHEATED VAPOR TMEAUE G2

0.40 I.-.,.,0.38 I-U E 7 - E A C N C I T O A E (RF4 IL.. 0.36 0O.3 9- 0.32 00 150 200 250 300 350 400 TEMPERATURE OF FIGURE 37 — THERMAL CONDUCTIVITY OF WATER (REF.4e)

152 -~~ ~ ~ ~~ ~~ ~~ ~ m - - - 7 148 ~~~~~~~~750 148~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~' 144 ___ ~~~~~~730.140 ___ ______ 710 136 690 1 32 -670 1 28 ___650 -v~~~~ / 124 630 120 m 610 60 80 100 120 140 TF )CONDENSATE FILM. TEMPERATURE, F FIGRE 8-'NUSEL PHSIAL ROPRT GROUP FOR FREON-114

153 680 -.5800 660 - ___ 5600640 __5400 o/~~ 620 - 5200 600 5000 580 - _ __ __ __ __ _- 4800 560 _ _ _ _ _ __ _ _ _ _ __ _ 4600 160 180 200.220.240 260 280 300 TF OF CONDENSATE FILM TEMPERATURE FIGURE 39- NUSSELT PHYSICAL PROPERTY GROUP FOR WATER

NOMENCLATURE a intercept of Wilson-plot line A total1 outside area, sq ft inside tube surface area, sq ft per ft Am mean metal heat transfer area, sq ft per ft A~ outside tube surface area, sq ft per ft b slope of Wilson-plot line B equivalent to the group 4f V2RT Bg value of B at T = Tg coefficient in equation for hw specific heat, Btu per (lb)(~F) di inside diameter of tube, inches dm mean metal diameter, inches d ~~outside diameter of tube, inches Do ~outside tube diameter, ft 1e2 least mean square deviation E(f) correlating group involving inm T, P5 and Pg f condensation coefficient f. ~inside fouling factor, (hr)(0F)(sq ft ins.) per Btu g gravitational constant, 4.17 x 1.08 ft per kr per hr 9c covri- ato,417 x 108 (lb mnass)(ft) per (lb force)(sq hr) G(f) correlating group involving m, T, Tg P5_ and Pg h enthalpy of saturated liquid,. Btu per lb hc coP-ndensate film coe~ffic-ient,_ Btu -per (h)(F(sit outider)

155 NOMENCLATURE (continued) ho overall outside film coefficient, Btu per (hr)(~F)(sq ft outside) hv convection coefficient for a gas or vapor, Btu per (hr)(~F)(sq ft) hw water film coefficient, Btu per (hr)(~F)(sq ft ins.) H height of vertical surface, ft; enthalpy of vapor, Btu per lb (-AH) total heat removed, latent heat for saturated vapor, Btu per lb H(f) correlating group involving hi, Ts, Tg, Pc* Pg, and (-AH) kf thermal conductivity of condensate film, Btu per (hr)(~F)(ft) km thermal conductivity of metal, Btu per (hr)(~F)(ft) m condensing load, lb per (hr)(ft of surface width) mC absolute rate of condensation, lb per (hr)(~F)(sq ft) me absolute rate of evaporation, lb per (hr)(sq ft) ms condensing load, lb per (hr)(sq ft) M molecular weight lb mass per lb mole n number density of molecules; exponent of water velocity dn number density of molecules with velocity C in velocity space dC N number of observations for least mean square deviation Pg pressure of gas phase lb (force) per sq ft absolute, lb (force) per sq in. absolute in equations 33 through 41. P5 equilibrium vapor pressure at Ts, lb (force) per sq ft absolute, lb (force) per sq in. absolute in equations 33 through 41. ~Q total heat transferred, Btu per hr Q/A heat flux, Btu per (hr)(sq ft outside) rc condensate film resistance, (hr)(~F)(sq ft outside) per Btu ~ri interfacial film resistance, (hr)(~F)(sq ft outside) per Btu rm metal resistahce, (hr)(~F)(sq ft outside) per Btu rn overall outside film resistance, (hr)(~F)(sq ft outside) per Btu

156 NOMENCLATURE (continued) ~R gas constant, 1544 (ft)(lb force) per (lb mass)(~R) s velocity distribution function Atc temperature drop through condensate film, (Ts-t0), ~F Ati temperature drop through interfacial film, (Tg-Ts), ~F Atm temperature drop through metal wall, (to-ti), ~F At0 overall outside film temperature difference, (Tg-to), ~F Att temperature rise of water, (T2-T1), ~F Atw temperature drop through water film, (ti-tw), ~F ti inside tube surface temperature, ~F tL wall temperature at water outlet end, OF tm mean tube wall temperature, ~F tM wall temperature at the middle of tube, ~F to outside tube surface temperature, ~F tR wall temperature at water inlet end, ~F tw average water temperature, ~F T average temperature between Ts and Tsv, ~R Tf mean condensate film temperature, ~F Tg superheated vapor temperature, ~F TLC condenser temperature at left end, ~F TMC condenser temperature at the middle, ~F T condensate surface temperature, ~F Tsv saturation temperature, ~F T1 inlet water temperature, ~F Ta outlet water temperature, ~F AToa overall temperature difference, (Tg-tw), ~F ATs degree of superheat, (Tg-Tsv), ~F

157 NOMENCLATURE (concluded) Ua absolute mean molecular velocity representing rate of mass transfer Uo overall heat transfer coefficient, Btu per (hr)(~F)(sq ft outside) Vt water velocity, ft per sec Ws rate of condensation, lb per hr Wt water flow rate, lb per hr x abscissa of Wilson plot, lO Wtn 1O4 y ordinate of Wilson plot, lU Uo Ycondensate film thickness at position H, ft YrM tube wall thickness, ft Z physical property group, ( ff g) Other Symbols f subscript refers to (1) condensate properties at the mean film temperature and (2) gas or vapor properties at the mean gas or vapor temperature coefficient of cubical expansion of vapor or gas, BR p density, lb per cu ft Pg gas density, lb per cu ft liquid density, lb per cu ft Ps saturated liquid density at Ts, lb per cu ft viscosity, lb per (ft)(hr)'r correction factor, function of error integral O(BgUg) r' condensing load, lb per (hr)(ft of tube length) D(BgUg) error integral function 0g equivalent to BgUg, variable defining r

BIBLIOGRAPHY 1. Alty, T., Proc. Roy. Soc. (London), A131, 554-64 (1931). 2. Alty, T., Phil. Mag., 15, 82-103 (1933). 3. Alty, T., Proc. Roy. Soc. (London), A161, 68-79 (1937). 4. Alty, T., and Mackay, C. A., Proc. Roy. Soc. (London), A149, 104-16 (1935). 5. Alty, T., and Nicoll, F. H., Can. J. Research, 4, 547-58 (1931). 6. Am. Soc. Ref. Eng., The Refrigerating Handbook, 6th Ed., New York, 1949. 7. Baker, E. M., and Mueller, A. C., Trans. AIChE, 33, 534-7, 542 (1937). 8. Baker, H. D., Ryder, E. A., and Baker N. H., Temperature Measurement in Engineering, John Wiley and Sons, New York, 1953. 9. Benning, A. F., and McHarness, R. C., Thermodynamic Properties of Freon-114, Kinetic Chemicals, Inc., Wilmington, 1944. 10. Bowman, R. A., U. S. Patent 2,279,552. 11. Bosnjakovic, F., Forsch. Gebiete Ing., 3, 135 (1932). 12. Bromley, L. A., Ind. Eng. Chem., 44, 2966-9 (1952). 13. Bromley, L. A., Brodkey, R. S., and Fishman, N., Ind. Eng. Chem., 44 2962-6 (1952). 14. Brown, G. G., et al., Unit Operations, John Wiley and Sons, New York, 1950. 15. Claassen, H., Centr. Zukerind., 35, 129 (1927). 16. Claassen, H., Wgrme, 61, 403 (1938). 17. Cornell, D., "Condensation of Superheated Vapors," Heat and Mass Transfer Seminar Report, Univ. of Michigan, 1952. 158

159 BIBLIOGRAPHY (continued) 18. Daniels, F., Outlines of Physical Chemistry, John Wiley and Sons, New York, 1948. 19. Dobkin, G. I., Teplosilovoe Khoz., 1, 21 (1941); see Chem. Abs., 37, 4278. 20. Fatica, N., and Katz, D. L., Chem. Eng. Progress, 45, 661-74 (1949). 21. Gibson, L. C., "Rate of Condensation of Water Vapor Under Vacuum," Ph.D. thesis in chemical engineering, Univ. of Wisconsin (1952). 22. Hampson, H., General Discussion on Heat Transfer (London), 58-61 (1951). 23. Jakob, M., Mech. Eng., 58, 729-39 (1936). 24. Jakob, M., Heat Transfer, Vol. I, John Wiley and Sons, New York, 1953. 25. Katz, D. L., Hanson, G. H., et al., Petroleum Refiner, 25, 419 (1946). 26. Katz, D. L., Hope, R. E., Datsko, S. C., and Robinson, D. B., JASRE, 53, 315 (1947). 27. Keenan, J. H., and Keyes, F. G., Thermodynamic Properties of Steam, John Wiley and Sons, New York, 1948. 28. Kirkbride, C. G., Trans. AIChE, 30, 170-86 (1933-34); Ind. Eng. Chem., 26, 425-8 (1934). 29. Lang, M., Forsch. Gebiete Ing., B5, 212 (1934). 30. Leeds and Northrup Co., Standard Conversion Tables, Philadelphia. 31. Lennard-Jones, J. E., and Devonshire, A. F., Proc. Roy. Soc. (London), A156, 6-44 (1936). 32. Markwood, W. H., and Benning, A. F., Thermal Conductances and Heat Transmission Coefficients of Freon Refrigerants, Kinetic Chemicals, Inc., Wilmington, 1942. 33. McAdamhs, W. H., Heat Transmission, 2nd Ed., McGraw-Hill Book Co., New York, 1942.

160 BIBLIOGRAPHY (concluded) 34. Merkel, F., Die Grundlagen der WVtrmeUibertragung, Leipzig, Steinkopff, 192735. Monrad, C. C., and Badger, W. L., Trans. AIChE, 24, 84-119 (1930). 36. Nelson, M. A., U. S. Patent 2,306,895. 37. Nusselt, W., Z. Ver. deut. Ing., 60, 541-6 and 569-75 (1916). 38. Perry, J. H., Chemical Engineers' Handbook, 3rd Ed., McGraw-Hill Book Co., New York, 1950. 39. Pruiger, W., Z. Physik, 115, 202-44 (1940). 40. Ramey, H. J., Henderson, J. B., and Smith, J. M., AIChE Heat Transfer Symposium Series No. 9, 50, 21-8 (1953). 41. Rizika, J. W., and Rohsenow, W. M., Ind. Eng. Chem., 44, 1168-71 (1952). 42. Robinson, D. B., "Effect of Vapor Agitation on Boiling Coefficients at Low Temperature Differences," Ph.D. thesis in chemical engineering, Univ. of Michigan, 1949. 43. Rohsenow, W. M., ASME Annual Meeting, Preprint No. 54-A-144, 1954. 44. Rohsenow, W. M., Webber, J. H., and Ling, A. T., ASME Annual Meet.ing, Preprint No. 54-A-145, 1954. 45. Schrage, R. W., Interphase Mass Transfer, Columbia Univ. Press, New York, 1953. 46. Silver, R. S., Engineering, 161, 505-6 (1946). 47. Stender, W., Z. Ver deut. Ing., 69, 905 (1925). 48. Timroth, J., and Vargaftik, N., J. Tech. Phys., 10, 1063-73 (1940). 49. Wilson, E. E., Trans. ASME, 37, 47 (1915).

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