A STUDY OF DRO-PWiseE COHDENSAYION Thesis for the Degree of Ph.D. MICHIGAN STATE UNWERSITY Ronald Luther Reisbig 1966 E585 ' JAL!PP.€"V l i I x ‘ e6 This is to certify that the thesis entitled A Study of Dropwise Condensation presented by Ronald Luther Reisbig has been accepted towards fulfillment of the requirements for Ph.D. degree inMechanical Engineering @54wa fl Major professor Date All S t 9 1966 0469 I‘vliclxigan State University ‘ 2" «200? ABSTRACT A STUDY OF DROPWISE CONDENSATION by Ronald L. Reisbig DrOpwise condensation of water vapor was studied on a verticle 1 foot high c0pper surface having an area of 1 ft.2. Dropwise condensation was promoted by coat- ing the surface with a 0.0017 inch thick film of poly- tetrafluoroethylene (teflon). Two experiments were per- formed to study the phenomenon. A heat transfer experi- ment was made to determine the heat flux and the heat transfer coefficient as a function of condenser surface temperature. The mechanism of dr0pwise condensation was studied experimentally by taking a series of high speed motion pictures. The pictures were taken at high magni- fication by using a microscOpe, and at low magnification without the microsc0pe. The heat transfer conditions were carefully determined while the pictures were being taken. Dropwise condensation heat transfer coefficients varied from 26,400 BTU/hrft°F to 6,650 BTU/hrft°F over a (Tsv-Ts) range of 0.5°F to 7.4°F. Heat flux values were determined up to 49,500 BTU/hrft2. The motion pictures were taken at film speeds in Ronald L. Reisbig ) the range 720 to 2500 pictures per second over a (TSV-TS range of 1.0°F to 5.4°F. The magnification in the pictures ranged from 0.124X to 18.5X. As a result of the photographic experiment as well as theoretical analysis, the following mechanism is pro- posed for dropwise condensation. Droplets obtain a cer- tain critical radius which is determined by the conden- ser surface temperature. These drOps then nucleate at random and preferred condensation sites located on active bare condenser surface. Random sites (with re- spect to both time and location) number as many as 1010 per in.2 per second. Preferred sites are wetted pits in the teflon film as well as nonwetted cavities. The wetted pits number about 105 per in.2 and the nonwetted 6 per in.2. Most of the latent heat pits number about 10 is transferred through nucleation sized drOps that grow by capturing vapor molecules. After the first collision of the nucleation sized drOps, the new dr0p field grows primarily by coalescence with other drOps. The drops continue to grow in this fashion until they roll off from the surface. Drop coalescence and roll-off clean the surface of condensate and create active area on which nucleation again occurs. This mechanism was used as the basis for the deri- Ronald L. Reisbig vation of equations for the heat flux and the heat transfer coefficient. These equations, which were de- rived using a kinetic theory approach, are shown to correlate very well with the experimental data. A STUDY OF DROPWISE CONDENSATION By Ronald Luther Reisbig A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Mechanical Engineering 1966 ACKNOWLEDGEMENTS The author wishes to express gratitude to Professor J. Lay for his advice and guidance during this program. Dr. St. Clair is thanked for finding the needed funds to support portions of the research. To my wife, Barbara, I wish to express the deepest gratitude for her devotion and understanding. She de- serves credit not only for typing and helping proofread this theSis, but also for providing a major portion of our family income during this program. The National Aeronautics and Space Administration, as well as The Ford Foundation is acknowledged for grants and fellowships which gave me the Opportunity to study for a Ph.D. ii TABLE OF CONTENTS Section 1.0 INTRODUCTION............... ..... t ...... .... 1 2.0 HEAT TRANSFER EXPERIMENT.................. 6 2.1 THE EXPERIMENTAL HEAT TRANSFER.APPARATUS.. 10 2.2 HEAT TRANSFER EXPERIMENTAL PROCEDURE...... 18 3.0 RESULTS OF THE HEAT TRANSFER EXPERIMENT... 23 4.0 THE PHOTOGRAPHIC EXPERIMENT............... 30 4.1 PHOTOGRAPHIC APPARATUS.................... 30 4.2 PHOTOGRAPHIC EXPERIMENTAL PROCEDURE....... 53 5.0 RESULTS OF THE PHOTOGRAPHIC EXPERIMENT.... 57 6.0 THE PROMOTER 0F DROPWISE CONDENSATION..... 45 7.0 HEAT TRANSFER THEORIES FOR CONDENSING VAPORS.00.0.0.0...OOOQOOCOOOOOCOOOOIOOOOOO 61 7.1 THEORY OF FILMWISE CONDENSATION........... 61 7.2 THEORY OF DROPWISE CONDENSATION........... 62 7.3 SURFACE PHYSICS OF DROPWISE CONDENSATION.. 65 7.4 SUREACE ABSORPTION PHENOMENON....... ..... . 73 7.5 ANALYSIS OF VAPOR MOLECULE CAPTURE BY'A SURFACEIOOO OOOOOOOOOOOOOOOOOOOOOOOOOO .0... 77 7.6 EFFECT OF CONDENSING CONDITIONS ON DROP FORMATIONAND GROVTHOOOOOO0.00.00.00.00... 82 7.7 REVIEW OF PAST MECHANISM THEORIES......... 86 8.0 PROPOSED MECHANISM OF DROPWISE CONDENSA-.. TIONOOIIOOOOO0.0.COCOOOOOOOOO00.00.0000... 95 9.0 MATHEMATICAL CORRELATION OF THEORY AND WEIMmTALDATAOOOOCOOOOOOCOO0.000...... 112 iii TABLE OF CONTENTS (CONT.) Section 10.0 CONCLUSIONS............................... 120 10.1 RECOMMENDATIONS........... ...... .......... 122 11.0 BIBLIOGRAPHY. ........... . ..... ............ 124 iv Figure 2.1 2.2 2.3 2.4 2.5 3.1 5.2 5.3 5.2 5.5 5.4 5-5 6.1 6.2 7.4.1 7.6.1 LIST OF FIGURES Title The Experimental Apparatus................ The Test Section and Pumping System....... Drawing of The Teflon Coated Condenser surfaCOOOOOOO...OOOOOOOOOOOOOOOOOOOOOCOOOO Pictorial drawing of The Test Chamber..... Schematic of Experimental Apparatus....... Heat Flux Data Correlation................ Heat Transfer Coefficient Data Correlation The Dependence of Film Coefficient 0n Heat Flux During Drapwise Condensation......... Sequence of Pictures Showing DrOp Field Build uPOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO ROll-Off Drop VelOCitYeoeeeeeeoeeeeeeeeeoo Effect of TS 0n Dr0p Growth Rate.......... Effect of Surface Temperature 0n Maximum DrOp Size Along The Condenser Surface..... Effect of Surface Temperature 0n DrOp NUCleation Time.0......OOOOOOOOOOOOOOOOO_OO Critical Surface Tensions of Fluorocarbons Pictures of The Cold Finger Test Devices.. Adsorbed Vapor Film On A Capillary Pore In ASClid surfECQOOOOOOOOOOOOOOOOOOOOOOOO... Effect of Condenser Surface Temperature On The Critical Drop Radius.................. Heat Flux Theory Correction Curve......... Page 11 24 26 28 59 42 45 45 45 51 56 75 85 117 LIST OF TABLES Table No. Page I Chemical analysis of a raw 1602. sample 149 of water used by Michigan State Univer- sity power plants. II Chemical analysis of four samples of water used in the boilers. 150 vi LIST OF APPENDICES Appendix No. Page I Heat Transfer and Photographic Data..... 127 II Error Analysis of The Data.............. 141 III Sample Calculations..................... 146 IV Boiler Water Analysis................... 149 vii NOMENCLATURE area surface area of a drOp with n molecules surface area of a critical sized drop diameter distribution function energy distribution function inactive fraction of the condenser surface area gravitational constant heat transfer coefficient, BTU/hr/ft2/°F heat of vaporization, BTU/hrAbm' heat of vaporization per molecule nucleation rate, nucleations/sec./in? thermal conductivity, Boltzmann's constant thermal conductivity of the liquid, BTU/hr/ft/°F heighth of the condenser surface distribution function mass mass rate of vapor molecules to a surface mass of a drOp number of molecules striking a surface number of molecules viii VS SV number of molecules in a critical drop pressure internal pressure of a drOp of size r saturated vapor pressure at the surface tempera- mmeTS saturated vapor pressure at the vapor temp. T heat flux, BTU/hr/ft2 radius critical drop radius gas constant temperature condenser surface temperature saturated vapor temperature time SV overall heat transfer coefficient, BTU/hr/ft2/°F velocity specific volume of liquid specific volume of vapor work accomodation coefficient evaporation coefficient density surface tension solid-vapor surface tension ix sl solid-liquid surface tension OT“ liquid-vapor surface tension 6 contact angle 1.0 INTRODUCTION A vapor can condense on a surface in either of three ways: "filmwise", wherein the condensate forms a continuous liquid film on the surface; "dropwise", wherein the condensate forms discrete drOps on the sur- face; and "mixed", wherein filmwise and dropwise conden- sation occur simultaneously. As a mechanism, mixed con- densation is the least important of the above three. All three condensation mechanisms produce surface heat trans- fer coefficients that are large compared with coeffi- cients produced by forced convection processes. Dropwise condensation produces heat fluxes that are an order of magnitude larger than those associated with filmwise condensation for a given value of surface subcooling (Tsv'Ts)' While drOpwise condensation is the more desirable mechanism, it is the least exploited. This can be ex- plained by the following facts, 1. DrOpwise condensation requires a surface that is not wetted by the condensate. Since most common fluids, such as water, wet clean metal surfaces, a nonwetting agent or pro- moter must be placed between the condensate and the metalic surface. To date few, if any, practical schemes have been prOposed 2 for promoting drOpwise condensation. 2. The mechanics of the mechanism of drOpwise condensation has not been understood. This has made it impossible to develOp a meaning- ful mathematical analysis of the process. This research program was undertaken to study the above stated problems, with major emphasis placed on number two. The original systematic investigation of dropwise condensation was made in 1930 by Schmidt, Schurig and Sellscnopp(50)*. Between 1955 and 1955 Drew, et a1(7, 8) extended knowledge about the conditions under which either drOpwise or filmwise condensation can occur. There are two schools of thought on the mechanism of dropwise condensation. In 1956 Jakob(20), suggested that the initial drOps are formed by an unstable conden— sate film which fractures and rolls into drOps. In the same year Eucken(28) suggested that the drOps nucleate. In 1959, Emmons(29) also developed a theory for dropwise condensation that preposes drOp nucleation. In recent studies Beer and McKelvey(2l) as well as Welch(10) have supported the film fracture concept of Jakob, while *Numbers in parentheses refer to bibliography. McCormick and BaerCBB) as well as Umur and Griffith(13) have supported the drop nucleation concept of Eucken. By analyzing the conduction across macrOSCOpic drOps Fatica and Katz(9) made an initial attempt to develop a mathematical expression for dropwise condensation heat transfer coefficients. Their equation presents the con- densation heat transfer coefficient in terms of the over- all heat transfer coefficient, which is a major drawback. Sugawara and Michiyoski(27) later extended Fatica's analy- sis to include the sweeping cycle as well as the adhering period.. Previous methods used to promote dropwise condensa- tion involved using chemical additives in the vapor or oily materials applied directly to the condenser surface. Examples of such additives are stearic and oleic acid, mercaptans, waxes and oils. The common failing of all these techniques is that replenishment is required, that is, the effectiveness of the promoter diminishes with trme. Chemical promoters are also adversely effected by dirt and rust present in the steam. Another disadvantage is that these promoters do not work on all base materials commonly used in condenser design. The variation in pro- moter performance with time helps explain the past dis- agreement between different sets of drOpwise condensation heat transfer data. 4 The use of thin plastic films which are coated di- rectly onto a condenser surface presents a promising technique for promoting drOpwise condensation. Topper and Baer(2) suggested the use of teflon in a 1955 study in which they demonstrated teflons ability to promote drOpwise condensation of such organic vapors as ethyl- eneglycol, nitrobenzene and aniline. A 1958 study by Beer and McKelvey(2l) compared the time-life performance of a surface coated with silicone grease, and one coated with teflon. They report that the silicone grease deter- iorated after 4 hours, while the teflon surface was not effected after 7 hours of Operation. In a 1965 study by Depew and Reisbig(24), teflon was used as the promoter on a horizontal condenser tube. In that study a teflon coating was shown to provide a practical method for pro— moting dropwise condensation. That study also produced the first significant heat transfer data for dropwise condensation psing teflon as a promoter. This research program was undertaken to determine; 1. Quantitative data for heat transfer to a vertical flat plate condenser surface with- out the time dependent variables associated with chemical promoters. 2. To study the mechanism of drOpwise condensa- tion, and establish the significant paramet- ers. In accordance with Jakob's(20) original 5 suggestion, the high speed motion picture camera, and microscOpe were used in this effort. To study the Operational effects on teflon films caused by several thousand hours of Operation in a steam environment. TO improve existing mechanism theories, and develOp a mathematical expression for the heat flux and heat transfer coefficient for dropwise condensation. 6 2.0 HEAT TRANSFER EXPERIMENT Dropwise condensation tests of the heat transfer from saturated water vapor to a teflon coated vertical condenser surface were made. The tests evaluated the state of the steam, the temperature of the condenser sur- face and the rate of steam condensation. The experiment was designed so that the state of the steam could be held constant while the condenser surface temperature was changed. By measuring the temperature difference between the saturated steam and the condenser surface, and using measured heat flux data, it was possible to calculate the condensing heat transfer coefficient as a function of this temperature difference. The method is illustrated by the following equation: h (TSV_TS) (2.1) Dropwise condensation was promoted and maintained during the tests by a thin coating of teflon. A complete discussion of the drOpwise promotion method is presented in section 6.0. Detailed descriptions of the experimental apparatus are presented in section 2.1. The experimental procedure used during the heat transfer tests is presented in sec- tion 2.2. Figure 2.1 and figure 2.2 are photographs of of the research apparatus. Note that these pictures in— Figure 2.2 The Test Section and Pumping System Thermocouple . . II Posutuons 7% 0.0. 'Copeer Cylinder. Inn—Teflon Coated S urf o ce (0.0017") \-WOter Po ss 0 9e (India .) Figure 2.5 Drawing of teflon coated capper condenser surface 9 Water inlet Teflon” Pad / /—Btass End Plate 9 Condenser Surface H |65lb l5§9 ' meer outlet Teflon Insulation \-t i [2" t as +4 Figure 2.4 Pictorial Drawing of The Test Chamber lO clude the photographic and Optical equipment as well as the heat transfer apparatus. 2.1 THE EXPERIMENTAL HEAT TRANSFER APPARATUS The experimental system used in this research was a cOpper cylinder, 12 inches long and 4 inches outside diameter. The 1 inch inside diameter of the cylinder was used to allow cooling water to pass through the test sec- tion. The cOpper in the cylinder was classed as, "eleca trolytic tough pitch rod", which is rated by the manu- facturer as 99.9 percent pure capper with a maximum of 0.04 percent oxygen. A drawing of the condenser surface is shown in figure 2.5. The 1.5 inch thick copper walls of the test section allowed the condenser surface to be: at a uniform temperature regardless of the temperature variation of the cooling water as it passed through the test section. The outside surface of the cylinder was coated with a 0.0017 inch thick film Of teflon. Four thermocouples were placed in each end of the copper cyl- inder. The location of the thermocouples is shown in figure 2.5. The external surfaces Of the COpper cylinder were machined on a lathe to a grade 52 finish. The out- side surface Of the COpper cylinder wall was polished with Wetordry, Waterproof Silicon Carbide, grit number 520 A, soft-black sandpaper before it was coated with teflon. O. .203 300 W I‘ll 32:. >0 see» :2: 30¢ 9.5a trout N. 52.623. J.— lln @IJ— _l|.@ll 23> i cozoom Sch—llmrl ~25 53% .Ylmf a Val a ll 23> l'l £050 3.9.2.5 . 32:0: . Figure 2.5 Scnematic of Experimental Apparatus 12 A pictorial drawing of the test section assesmbly and steam chamber is shown in figure 2.4. The ends of the OOpper cylinder were insulated on the bottom by a 2.50 inch long cylinder of teflon and on the tOp by a 1.25 inch long cylinder of teflon. The outside diameter of these teflon insulation cylinders was the same as the outside diameter of the condenser surface. The end plates of the steam chambertfige made of 5/16 inch thick brass, and each was sandwiched with a 0.25 inch pad of teflon. The steam chamber wall was made from a 178mm (5.9 inch) outside diameter section of glass tubing. The walls of the glass tube were 0.15 inches thick and the length of the tube used in the steam chamber was 15.75 inches. Four one inch 0.D. holes were made in the glass tube wall to give access to the inSide Of the steam chamber. Using a glass walled steam chamber allowed a complete Observa- tion of the entire condenser surface at all times. Since dropwise condensation is strongly effected by surface contamination, the ability to Observe the condition on the condenser surface was most important. The entire condenser chamber assembly was held to- gether by four K inch brass tie-rods. All steam joints in the chamber were of a mechanical nature requiring force from the tie-rods to implement a good steam tight seal. To insure a steam tight seal Of all joints and to correct for the different thermal expansions Of the different materials, a soft rubber gasket was placed at the tOp and bottom of the glass tube wall. Soft rubber gasket material was also used as spacer material between the teflon insulation block and the teflon pad on the upper end plate. All important joints were further seal— ed with "Plastic Rubber Cement" which is an elastic rub- ber in putty form and is sold by Sears Roebuck and Company. When this material dries it has the prOperties of soft rubber. Condensate from the condenser surface was col- 1ected at the bottom Of the steam chamber. The conden- sate exited the steam chamber by means of a % inch pipe which was threaded through the bottom end plate of the steam chamber. With this valve Open the condensed steam vapor was forced by chamber pressure into a 1000 m1 se- paration funnel where the condensate rate was measured. Steam entered the chamber through the center access hole in the glass chamber wall. The holes (see figure 2.4) were used to vent steam from the chamber. The second hole from the tOp of the glass tube was used to insert a pressure probe into the steam chamber. The access holes were sealed by rubber stOppers. Each steam chamber probe was sealed into a hole drilled through a rubber stOpper. The stopper was then forced into one of the holes in the glass wall of the steam chamber. This method for gaining access to the inside of the steam chamber provided a steam tight seal. 14 Water entered at the tOp Of the test section and exited at the bottom. A 1 inch 0.D., 6 inch long OOpper tube was soldered into a brass fitting which had external one inch pipe threads (see figure 2.5). This assembly was then screwed into the water passage of the condenser surface which had been taped for a 1 inch pipe thread on both ends. The test assembly was connected to the main water lines with flexible rubber hose. Water was pumped through the test section by a closed loop system. Figure 2.5 shows a schematic of the water loop. No data was taken from the water loop since its only function was to provide a controlled temperature heat sink. The water loop was designed to provide high and very steady flow rates without causing mechanical vibra- tion of the test section. The only instrumentation in the water lOOp was a Fisher-Porter Rotometer flow meter and a pressure gage to indicate the magnitude of the pump head. The centrifigal pump was driven by a 7% horse- power General Electric variable speed direct current motor. The direct current was supplied to the motor by a motor-D.C. generator set. The pump unit was equipped with a separate control panel with a variac dial to con- trol the pump motor speed. The pump speed was varied to give minimal temperature variation of the cooling water while it passed through the test section. Water was pumped from and returned to an Open galvanized tank which 15 had a 50 gallon capacity. The large capacity of this tank reduced the effect of temperature and pressure vari- ation in the water loop to a minimum. The water tempera- ture in the tank was allowed to increase by passing it through the test section where it absorbed heat from the condensing steam. When the tank water reached a desired temperature, cold tap water was introduced into the tank. The cold water stabilized the tank water temperature. The tank was equipped with an overflow drain which allowed the excess water to leave, keeping the volume of water in the water loOp constant. The cooling water was taken directly from the tap as it was supplied by the City of East Lansing. The steam used in this research was taken directly from the steam lines supplied by the Michigan State University power plant. Since the teflon film used to promote drOpwise condensation is not effected by small traces of impurities in the steam, no attempt was made to purify the steam before it entered the test section. Before entering the test section, the steam was passed through a small moisture separating tank that also acted as a heat exchanger to remove any superheat. The steam entered the test chamber in approximately a saturated state. Both the temperature and the pressure of the steam mag-measured in the test chamber. A special diffuser manifold allowed the steam to distribute to all parts Of 16 the chamber without causing undesirable vapor velocities over the condenser surface. The steam was experimentally stagnant at the condenser surface. A chemical analysis of the boiler feed water used to produce the steam is presented in tables I and II in appendix IV. Tables I and II are the results of tests made by the Allis-Chalmers Manufacturing Company of Milwaukee, Wisconsin on May 11, 1965. The feed water used to produce the steam used in this research had a total of 1.8 mineral parts per million parts of water. There were less than five parts per million of dissolved oxygen in the feed water. All temperature measurements were made with thermo— couples. The thermocouples were made from 24 gage (GG-24-DT) fiberglass covered c0pper constantan wire. This wire was supplied by The Thermo Electric Company of Saddle Brook, New Jersey. The thermocouple beads were made by placing twisted ends into a gas flame until the two wires fused into a small metalic ball. The thermo- couples made in this manner were calibrated at the ice point and at the steam point. The primary temperature recording instrument was a model 8686 millivolt potentio- meter made by the Leeds and Northrup Company. The error in temperature measurement introduced by the recording instrument was less than :0.046°F at 200°F. A complete 17 analysis Of the errors involved in the test section is presented in appendix II. An 8 point Brown Electric Automatic Temperature Recorder manufactured by the Minneapolis Honeywell Com- pany was also used. This instrument was used to deter- mine when the system reached a steady state condition. No recorded data was measured with this device. The thermocouples which were imbedded in the OOpper test section were constructed as follows. The thermo- couple leads were drawn through a 5/52 inch 0.D by 9/16 inch long piece Of stainless steel tubing. The bead Of the thermocouple was allowed to extend out Of the end of the tube a distance equivalent to the diameter of the bead. The tube was then filled with an epoxy that was allowed to harden. 'The excess epoxy was then cleaned from the thermocouple bead and the entire assembly was forced into the % inch deep holes drilled in the ends of the OOpper cylinder (see figure 2.5). Since the stainless tubes had a slightly larger outside diameter than the holes in the COpper cylinder, the probes had to be insert- ed with force until the thermocouple bead was forced against the OOpper. Care was taken during each step to insure that the thermocouple had not been broken during in~ sertion. With the thermocouple firmly in place the out- side interface between the cOpper and the stainless steel 18 tube was cleaned with sandpaper and covered with a small quantity of epoxy. With all eight thermocouples so plac- ed the c0pper cylinder was heated with forced hot air. The thermocouple positions were then checked to insure that they were giving prOper readings. With the thermo- couples thus placed the COpper cylinder condenser sec- tion was assembled with the teflon guard insulations to allow the lead wires Of the thermocouples to pass inward to the 1 inch OOpper water passage tube and then out of the test section. The thermocouple leads were connected to a selector switch on the test console. This switch allowed the potentiometer to be connected with any there mocouple circuit in the system. All thermocouple circuits were carefully labeled to establish their location in the system. 2.2 HEAT TRANSFER EXPERIMENTAL PROCEDURE The heat transfer experiment was designed to measure the following quantities; l. Condenser surface temperature at four locations. 2. Temperature at four locations in the cOpper test cylinder one inch behind the condenser surface. 5. Temperature of the steam in the test chamber. l9 4. Pressure of the steam in the test chamber. 5. Condensing rate of the steam. Figure 2.5 shows a schematic drawing Of the entire test apparatus. The following discussion will make frequent reference to the information presented in figure 2.5. Before the steam chamber was assembled the teflon condenser surface was washed with a mild detergent to re- move any grease and finger prints that may have been on it. The surface was then rinsed with distilled water and allowed to dry in the room air. The condenser test cham- ber was then assembled and no further cleaning of the con- denser surface was made during the experiment. The fol- lowing procedures were followed during each experiment. 1. Valve number 1 was Opened to allow steam to enter the system from the main steam line. 2. Valves 5, 4, 5, 6, 7 and 15 were fully Open- ed to allow steam vapor to vent from the test section. 5. Valve 2 was then Opened slowly to allow steam to enter the test section. Enough steam was let in to create a small positive pressure (1 inch of Hg or less) in the steam chamber. 4. Steam was allowed to vent through values 5, 4, 5, 6, 7, and 15 for at least 1 hour before taking data to insure that all the entrap- 2O ped air had been removed from the test chamber. Valves 8 and 9 were then fully Opened in the water loop and the pump was started. Water was circulated (at about 55 GPM) through the test section while valve 2 was regulated to insure that the steam chamber pressure re- mained positive. The water was allowed to circulate and be heated by the condensing steam vapor until a desired condenser surw face temperature was reached. Upon reaching the required temperature, cold tap water was introduced into the reservoir tank by Opening valve 11 enough to stabilize the cooling loop temperature. Vent valves 5 and 15 were then closed and the rate of venting from valves 6 and 7 was reduced to minimize the effect of vapor ve- locity in the test chamber. Valve 2 was also adjusted at this point to stabilize the steam chamber pressure. The steam chamber pressure was always maintained at between 2 and 5 inches of Hg above atmospheric pressure. The temperatures in the test cylinder were then monitored on the automatic temperature 21 recorder until the system reached a thermal steady state condition. 9. When a study state had been established valve 5 was closed and the time required to collect 1000 millileters Of condensate was measured. 10. While collecting condensate the various thermocouple circuits were switched into the Leeds and Northrup Potentiometer and the temperature data was recorded. 11. After the data had been recorded valve 5 was reopened to allow the condensate col- lector to empty. 12. Steps 9, 10 and 11 were always carried out at least twice to insure that the data was not changing with respect to time. 15. Valve 11 was adjusted to establish a new condenser surface temperature and steps 6 through 12 were repeated for the new data point. It should be noted that minor adjustments were sometimes made in the cooling water flow rate to reduce the temper- ature variation as it traversed the test section. As a rule the flow was kept as high as possible without causing undesirable vibrations of the test section. 22 A test was made to establish the rate of condensate from the inside of the glass wall of the steam chamber. During this test the steam chamber was not connected to the water loop. By forcing hot air through the cooling passage the condenser surface was raised to a temperature above the steam saturation temperature. Condensate was then collected Off the glass wall Of the steam chamber. Assuming that this rate of condensation represents a con~ stant, one could subtract it from the condensate rates measured during a heat transfer test. It was found that the rate of condensation from the walls of the steam chamber was less than 1.0 percent of any condensate rate measured during a heat transfer test. Since this effect was small, no correction was made in the condensate data. 25 5.0 RESULTS OF THE HEAT TRANSFER EXPERIMENT. The original data for the heat transfer during drOp- wise condensation are presented in appendix I. Figures 5.1, 5.2, and 5.5 present the data graphically. The heat transfer coefficient for drOpwise conden- sation on a teflon surface was determined over a range of (Tsv-Ts) of 0.5°F to 7.4°F. An analysis of the experi- mental error that is inherent in the data is presented in appendix II. Sample calculations indicating the proced- ure used to reduce the data are presented in appendix III. The heat flux data is graphed as a function Of (Tsv-TS) in figure 5.1. The data from this study is com- pared with data by Welch(10). The data are shown to be in rather good agreement. Welch used two different condenser surfaces. One was a % inch vertical OOpper slab and the other was 7 7/8 inch vertical cepper slab, on which cu- pric oleate was used as the promoter. The wide variation of condenser surface height used to produce these data indicates that drOpwise condensation is not influenced by this parameter, at least up to the one foot high sur- faces used during this program. The heat transfer coefficient data is presented in figure 5.2 where it is compared with data by Welch(10) and Reisbig(l). The agreement between the three sets of we FLUX 91165, BTU/hrft2 24 Figure 5.1, Heat Flux Data Correlation 9m 80" 70' a 50" A A .‘A A 50F 3 A .‘e '0 4GP AAAeg‘ae. CO A .. ’ 30, $3.61.. A t A AA .. g& 20" A .1' oo ‘ A 3. 00 0 0 fi Theor ,eqn.9.l5 it 0 O . : ‘o y . A l0 gt A A 79 6r- 5l‘ O-‘This Study 4L A— Watch (l0) 3L 2t- | l l J 1 l 1 J I l J l l 1 L1 .4 .5 .6.7.8.9l 2 3 4 5 6789l0 SURFACE SUBCOOLING (Tsv-TB), °F 25 data is again quite good. Welch°s data is higher in the range Of (Tsv-TS) from 1°F to 5°F. This is most likely due to the experimental method used by Welch to determine the heat flux. His heat flux values were based exclu~ sively on temperature measurements. His % inch high con- denser surface, which was used to obtain most of the data in the range mentioned, had a wall thickness of several inches. Any heat leak from the edge of the condenser sur- face would result in a higher measured AiT and thus a higher flux caused by this experimental error. The data derived from the present research is be- lieved to be more reliable since the condenser surface was much larger, thus reducing the effect of heat leakage from the system. Also, two independent sets of data were taken for the heat flux to insure reliable results. The data from reference (1) is shown to extend the range of the present data and to have a good linear re- lationship to the data from this program. Reisbig(l) used a % inch 0.D. horizontal tube which was coated with a thin film of teflon. The effect of condenser geometry again seems minimal since the data taken from a horizontal tube correlates with the data from the One foot high verti~ ca1.condenser surface used during this program. The theoretical curves shown in figures 5.1 and 5.2 are the result of equations whose complete derivations 26 cm on 0*. on a. .Amauemav eaooomam moeampm «a». -m ‘5. «9 “l0 —:¢. ON 9mm 5 w n .v n N _ _ _ q _ 1 a q j _ a . 4 _ a 1 . n. w 4 / l N 144 4 . ‘h‘ I, 1m "Al‘ \II'I“ 0 to Q 0 G A I AV 1 Infivm o I lb 16 rm 1...... 35232.: no. 2.23.5IO. low 8.7.2.3 I4 32... .2» IO ion to... soapaflonuoo anon pnoaoauuooo sameness poem I on Tm 933a .8 on beam/magma INHIOIJJHOO HHJSHVHEL man 27 are presented in section 9.0. A complete discussion of the correlation between the data and the theoretical equations is also referred to section 9.0. ‘Figure 5.5 shows the heat transfer coefficient plot- ted as a function of heat flux. A number of authors (55, 59, 40) have indicated that the heat transfer coef- ficient is independent of heat flux. Shea and Krase(l4) show that there is some variation of h with Q . The data from this program is compared with data by Fatica and Katz(9), Reisbig(l) and Welch(10). The data from this program as well as references (9, 1) indicate a strong downward trend for h as Q gets larger. Figure 5.5 shows that the scatter in the data for this type of cor- relation is quite large. Welch's data shows a reasonable agreement with the data from this program, but it has a larger degree of scatter. The data of Fatica and Katz(9) shows no trend by itself, however, it groups into the data from this program. The data by Reisbig(l) follows the trend of the data from this program but it is located in the lower portion of the data envelOpe. Due to consider- able data scatter the exact location of the data curve is ¢ifficu1t to determine. The solid line represents a imeasonable correlation if most of Welch's data is ignored. T11e two dotted lines represent the general shape of the luxper and lower bounds Of the data envelOpe. The general 90°, non wetting For €< 90°, wetting (n; UN 6 6 ‘ >9 4 - ~ b-O-s'v 0;; USU Addition of the vectors in the above diagram results in the following relationship, 02v: O'EI + 07v COSO (7.5.5) By combining equations 7.5.4 and 7.5.5 the equation de- velOped by Young(22) is Obtained. W51" 0'“ l 4" Cos 9) (7.5.6) This equation is a more useful relation than equations 7-3-4 or 70505 since Ogv and 031 can't be measured easily or accurately. Wetting of a solid surface implies that the contact angle is less than 90°. In general, surfaces with con- tact angles greater than 90° tend to be strong non-wet- ers. From equations 7.5.4 and 7.5.6 the cosine of the contact angle can be written as follows. 72 _ 0:7 " 9:7 (7.3.7) 0039- 0;, Thus, the following conditiOns can be stated for wetting and non-wetting, Wetting 0;, —- 02’, > 0 (7.3.881) Non-wetting 0:, " (If: < O (7.3.813) As an example, water has a liquid-vapor surface tension of about 60 dynes/cm at 212°F. A water droplet in con- tact with its vapor and a horizontal teflon surface has a contact angle of about 115°. The above discussion, thus, shows that the contact angle depends on the relative magnitude of the adhesional energy of the solid and liquid, and the cohesional energy Of the liquid. Or, from a microscopic view point, the relative attraction between molecules of the solid and liquid and between the liquid molecules themselves. It should be noted that a drop sitting on a vertical surface has a different contact angle at the top and bottom due to the distortion caused by the weight of the drOp. Such variations in contact angle have the greatest effect on a drop that is heavy enough to roll down the 73 surface. It was noted in section 5.0 that this type of phenomenon becomes more important as the height of the condenser surface is increased. 7.4 SURFACE.ADSORPTION PHENOMENON. Adsorption is another surface phenomenon that may be important to dropwise condensation. Adsorption is the term used to describe the existence of a higher con- centration of a vapor at the surface of a liquid or solid than is generally present in the bulk of the vapor. A solid or liquid surface possesses a residual force field. Adsorption results from the tendency of the free energy of a surface to decrease. Langmuir(12) showed that be- cause Of the rapid drOp of intermolecular forces with dis- tance the adsorbed layers are most likely no more than a single molecule in thickness. This view is presently accepted for adsorption at low pressures or at moderately high temperatures. However, at or near their saturation point the adsorbed molecules can hold other vapor mole- cules by means of van der Waals forces. Thus, it is possible to have an adsorption layer with a multimole- cular thickness. Van der Waals adsorption is character- ized by heats of adsorption that are the same order of magnitude as the heat of vaporization for a given sub- stance. Water has all the characteristics to allow it to have a van der Waal type adsorption. However, much 74 depends on the type of water vapor-solid surface being considered. Another important feature Of adsorbed films is that they establish an equilibrium with a solid sur- face very rapidly after a fluctuation in either temper— ature or pressure. This fact helps explain the rapid growth rate of liquid drOplets since the condensing Of adsorbed vapor films may help in the feeding process for a droplet. Once a film is cleared from the surface, it is instantaneOusly replaced. Thus, one might conclude that this feeding process is essentially a constant rate process. It is likely that the film feeding process is most important when the droplets of liquid are very small. Umur and Griffith(l5) report that from experimental observations, they were not able to measure a liquid film of water between drops greater than a monolayer of mole- cules in thickness. The steam was condensed onto a polished gold surface and the condensate films were meas- ured by a reflected light Optical system. The existence or nonexistence of a liquid film on the condenser surface is an important consideration,as was noted above. It is concluded that an adsorbed film no thicker than a moncmolecular layer exists between drOp- lets while steam condenses on a teflon surface. It may be possible, however, for multimolecular adsorbed films to exist in capillary cavities, as will be noted in the 75 following discussion. The existence of an adsorbed monolayer film or a con- densed monolayer film may be important to the nucleation of a drOplet. This is illustrated by considering the solid surface profile shown in figure 7.4.1. FIGURE 7.4.1 Adsorbed Vapor Film On A Capillary Pore In A Solid Surface. It is a well known fact of capillary physics that the pressure on the convex side of a curved fluid surface is less than the pressure on a concave side of the sur- face. Consider the Spherical shaped cavity Of radius r2 with a circular rim of radius r1. Point 0 represents the condition of the vapor in the neighborhood Of the cavity. Point 1 represents the condition Of the adsorbed film on the rim of the cavity and point 2 represents the condition of the film in the bottom of the cavity. Since the film is curved at point 1 and 2 we conclude; £3”? , 8-3.3.931. (7.4.1) 76 3 8, (7.4.4) and (F: - F; ) = 20}:(l/r.+l/tz) (7-4-5) Thus, the adsorbed film which acts like a membrane under tension trys to assume the smallest possible area per a given enclosed volume. Equation 7.4.4 leads to the con- clusion that any molecules adsorbed at point 1 will flow to point 2 under the pressure differential (Pl-P2) as given by equation 7.4.5. Note that for this development to be valid the adsorbed molecules in the film must be close enough to each other to be attracted by van der Waals forces of cohesion. It is significant to note that it is not necessary for the adsorbed film to cover the entire surface for the above arguments to be valid. The above discussion has not assumed any type of condensation. .For example, the discussions would be true even if the .solid surface was at or above the saturation temperature (if the vapor. If the surface temperature is below the Exaturation temperature of the vapor, condensation would take place. We, thus, see that the most probable conden— 77 sation site is at the bottom Of the cavity where the temperature is lowest and where there exists a more abun- dant supply of low energy molecules. This point will be discussed further in section 8.0. 7.5 ANALYSIS OF VAPOR MOLECULE CAPTURE BY.A SURFACE. In order to understand the vapor condensation pro- cess it is desirable to know the number of vapor mole- cules that strike the condenser surface per unit area and per unit time. If one was to Observe a surface, the following types of molecular collisions would be observed, 1. Molecules strike the surface and are adsorb- ed, that is, adhere permanently (are condens- ed). 2. Molecules strike the surface and bounce off immediately. 5. Molecules strike the surface and adhere but as a result of thermal agitation some mole- cules evaporate and return to the vapor a— gain. The net result is that molecules are continually coming to and leaving the surface. If the surface and the vapor are at the same temperature, thermal equilibrium is (established and the number of molecules entering and leaving are equal. However, if the surface is at a lower 78 temperature than the vapor the average number of mole- cules that are adsorbed exceeds the average number that evaporate. So, the latent heat released by the adsorption of molecules exceeds the latent heat absorbed by the eva- porating molecules resulting in a net heat transfer to the surface. If N is the number of molecules striking the surface per unit area and per unit time, and if CK is the fraction of the total number of molecules which strike the surface that are condensed, then 0( N is the number of molecules that condense per unit area and time. Also, if Pi is the fraction of the total surface covered with adsorbed molecules at any instant, then (l-Fh) is the fraction of the surface that is able to receive mole- cules, assuming that only a single layer of vapor mole- cules can form on the surface at any instant. Thus, the condensation rate is (l-Fm) C( N’ molecules per unit area )f the total surface per unit time. The rate that mole- cules evaporate will be assumed prOportional to the num- ber of molecules on the surface, which is indicated by the fraction Fm. Evaporation can, thus, be represented by 6 Fl, where e is a constant for a given vapor and surface. Thus, if T8v is the temperature of the satu- :rated vapor and T8 is the surface temperature, then at equilibrium, - _ . .1 (l-Fm)0( N-E Fm when TS-Tsv (7 5 ) n1 79 and (l-Fm) o( N > E Fm when TS”exp-§£5 TSC1-1I-—)] (9.9) In section 7.5 it was shown that, [RTSV Q=(1'Fm)°(hfg 1”,, T (9.10) A comparison of equations 9.10 and 9.9 shows that the fraction of active condensing surface (l-Fm) can be writ- ten as, T I h T (l-FI.) = [1-(T’fl5‘éxp-fiBO-fie] ‘ (9.11) 8 S SV 115 It is possible to simplify equation 9.11 by observing that (Tsv/Ts)% will always be a number close to unity. Also, since the absolute value of the exponent of the ex- ponential term is a number smaller than one, it is possi- ble to make the following approximation, - z 3 I_e’=z_§7+%-.... 37¢ ) 7(<