T H E U N I V E R S I T Y OF M I C H I GA N COLLEGE OF ENGINEERING Department of Mechanical Engineering Technical Report No. 6 FILM BOILING ON VERTICAL SURFACES IN TURBULENT REGIME Narasipur V. Suryanarayana Herman Merte, Jr. Project Supervisor ORA Project 07461 under contract with: NATIONAL AERONAUTICS AND SPACE ADMINISTRATION GEORGE C. MARSHALL SPACE FLIGHT CENTER CONTRACT' NO. NAS-8-20228 HUNTSVILLE, ALABAMA administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR September 1970

TABLE OF CONTENTS Page LIST OF TABLES vi LIST OF FIGURES vii NOMENC IATURE xi ABSTRACT xiv Chapter I. INTRODUCTION 1 A. Purpose and Scope 1 B. Literature Survey 4 II. EXPERIMENTAL APPARATUS 16 A. Heating Surfaces 17 1. Heat flux measuring test surfaces 18 a. Method of attaching thermocouples 21 b. Thermal insulation of test sections 23 c. Test piece dimensions 24 2. Test surface for photographic studies 26 B. Dewars 28 1. Pyrex glass dewar 28 2. Drop package dewar 33 3. Dewar for photographic studies 35 C. Assembly of Test Surfaces 37 D. Photographic Apparatus 38 III. INSTRUMENTATION 40 A. Thermocouples 40 B. Potentiometer 41 C. Sanborn Recorder 41 D. Pressure 42 IV. EXPERIMENTAL PROCEDURES AND DATA REDUCTION 43 A. Filling Dewars 43 B. Calibration of Recorder and Thermocouples 44 C. Drop Package Operation 47 D. Photographic Studies 50 E. Data Reduction 51 F. Measurement of Vapor Film Thickness from Photographic Films 56 iii

TABLE OF CONTENTS (Continued) Page V. MODEL AND ANALYSIS 57 VI. RESULTS AND DISCUSSION 76 A. Validity of Experimental Technique 76 1. Simulation of a plane surface by a cylindrical surface 76 2. Use of transient technique to obtain steady state data 78 3. Heat transfer by radiation 82 B. Results 83 C. Discussion 93 1. Validity of laminar analysis 93 2. Effect of turbulence 94 3. Effect of interfacial oscillations 99 4. Effect of interfacial vaporization on velocity profile and friction velocity 112 5. Effect of reducing gravity 117 6. Effect of subcooling 118 7. Effect of height on heat transfer coefficient 119 8. Effect of AT on heat flux 123 9. Nu-Ra correlation 126 10. Effect of height on heat transfer enhancement coefficient 126 D. Summary, Conclusions, and Recommendations 139 1. Summary 139 2. Conclusions 140 3. Recommendations 141 Appendix A. DROP PACKAGE 142 B. EFFECT OF INSULATION 150 C. EFFECT OF CONTAINER SIZE 153 D. JUSTIFICATION FOR LUMPED ANALYSIS 155 E. ERROR ANALYSIS 159 1. Heat Flux 159 2. Temperature 163 iv

TABLE OF CONTENTS (Concluded Page 3. Uncertainty in the Measurement of the Distance of Test Sections from the Leading Edge 164 4. Uncertainties in the Measurement of Vapor Film Thickness by Photographic Methods 165 5. Specific Heat of Copper 165 F. PROPERTIES OF NITROGEN AND HYDROGEN 169 1. Nitrogen 170 2. Hydrogen 171 G. DATA 172 BIBLIOGRAPHY 188 v

LIST OF TABLES Table Page I. Details of Test Surfaces: a/g = 1 25 II. Details of Test Surfaces: a/g a 0.008 26 III. Test Conditions for Data Under Normal Gravity: a/g = 1 45 IV. Test Conditions for Data Under Reduced Gravity and Subcooled Conditions 49 VT. Conditions for Motion Pictures 51 VI. Transient Technique-Rate of Change of Dimensionless Temperature 81 VII. Comparison of Heat Flux Values Obtained Under Steady State Conditions and Transient Conditions-Liquid Nitrogen 82 VIII. Values of Eddy Diffusivities 98 IX. Deviations of Experimental Values from Predictions — Liquid Nitrogen 110 X. Deviations of Experimental Values from Predictions — Liquid Hydrogen 111 XI. Error in Heat Flux Calculations and Surface Temperature Determination Due to Lumped Analysis 158 XII. Specific Heat of OFHC Copper 166 XIII. Specific Heat of Copper-Comparison of Data from Different Sources 167 vi

LIST OF FIGURES Figure Paae 1. 2-1/4 in. diameter test surface. 19 2. Test section build up. 20 3. Different methods of attaching thermocouples. 21 4. Test surface for photographic studies. 27 5. Schematic of Pyrex dewar and associated equipment. 29 6. Device for raising and lowering test surface. 32 7. Drop tower test package. 34 8. Stainless steel dewar for photographic studies. 36 9. Arrangement for photographic studies. 39 10. Typical cooling curve —recorder output a/g = 1. Liquid nitrogen. 46 11. Typical cooling curve —recorder output a/g o 0.008. Li quid hydrogen. 48 12. Film boiling model. 59 13. Comparison of Spalding's universal velocity profile and Karman's three-layer model. 62 14. Velocity and temperature profiles in vapor film. 68 15. Control volume —film boiling. 69 16. Comparison of heat flux —1 in. dia and 2-1/4 in. dia heating surfaces. 79 17. Effect of height on heat flux-film boiling. ~N2. AT = 31%~R. 84 18. Effect of height on heat flux —film boiling. IN2. AT = 251~R. 85 vii

LIST OF FIGURES (Continued) Figure Page 19. Effect of height on heat flux-film boiling. LN2. AT = 2040R. 86 20. Effect of height on heat flux —film boiling. LN2. AT = 1000R. 87 21. Effect of height on heat flux —film boiling. LH2. AT = 400~R. 88 22. Effect of height of heat flux-film boiling. LH2. AT = 3000R. 88 23. Effect of height on heat flux-film boiling. LH2. AT = 2000R. 89 24. Effect of height on heat flux —film boiling. LH2. 89 AT = 1000R. 89 25. Effect of height, gravity, and subcooling on heat flux. LN2. 90 26. Effect of height, gravity, and subcooling on heat flux. LH2. 91 27. Relation between y, Re, and (EH/v) for universal velocity profile Eq. (5.1). 97 28. Film boiling: LN2; AT = 315~R; x = 0-1 in.; 105 frames/sec. 101 29. Film boiling: LN2; AT = 315~R; x = 1.5-2.25 in.; 103 frames/sec. 101 30. Film boiling: 1142; AT = 315~R; x = 4-5 in.; 110 frames/sec. 102 31. Film boiling: LN2; AT = 204CR; x = 0-1 in.; 106 frames/sec. 103 32. Film boiling: LN2; AT = 204~R; x = 2-3 in.; 110 frames/sec. 103 viii

LIST OF FIGURES (Continued) Figure Page 33. Film boiling: LN2; AT = 1000R; x = 0-1 in.; 104 frames/sec. 104 34. Film boiling: LN2; AT = 100~R; x = 1.5-2.5 in.; 109 frames/sec. 104 35. Model for predicting instability of interface. 106 36. Critical velocity vs. height for interfacial instability: a/g = 1. 107 37. Critical velocity vs. height for interfacial velocity: a/g - 0.008. 109 38. Effect of interfacial vaporization on velocity profile. 116 39. Effect of height on heat transfer coefficient. L12. 120 40. Effect of height on heat transfer coefficient. LH2. 121 41. Effect of AT on heat flux. LN2. 124 42. Effect of AT on heat flux. LH2. 125 43. Nu-Ra correlation. 127 44. Variation of vapor film thickness with time. LN2. AT = 100~R. 129 45. Variation of vapor film thickness with time. LN2. AT = 315~R. 130 46. Variation of vapor film thickness with height. L12. AT = 100CR. 131 47. Variation of film thickness with height. LN2. AT = 204~R. 131 48. Variation of film thickness with height. LN2. AT = 315 R. 131 49. Variation of heat transfer enrhancement coefficient C with dimensionless amplitude b. 133 50. Variation of C with x. LN2. AT = 315~R. 135 ix

LIST OF FIGURES (Concluded) Figure Page 51. Variation of C with x. LN2. AT = 100~R. 135 52. Variation of Cmax with Re. LN2. AT = 3150R. 136 53. Effect of varying C with x. LN2. AT = 315~R. 138 54. Drop package. 143 55. Release mechanism. 144 56. Drop tower —elevation. 145 57. Drop tower-plan on third floor. 146 58. Drop package deceleration —inner cylinder; oscilloscope trace. 149 59. Drop package acceleration-free fall. 149 60. Effect of Teflon insulation thickness. LN2. AT = 3150R. 151 61. Effect of container size. LN2. AT = 315~R. 154 62. Model for lumped analysis. 156

NOMENCLATURE Normal units used are indicated; when other units are used, they are indicated as such in the text. A area, ft2 a. amplitude of interfacial oscillations, ft b amplitude of interfacial oscillations = a/b(s), dimensionless C heat transfer enhancement coefficient Eq. (5.5a) Cp specific heat, Btu/lbm ~R gravitational acceleration, ft/sec2 hfg enthalpy of vaporization, Btu/lbm h' modified enthalpy of vaporization, Btu/lbm fg h heat transfer coefficient, Btu/hr ft ~R 2 h local heat transfer coefficient at height x, Btu/hr ft RP. x~ hL average heat transfer coefficient over height L, Btu/hr ft ~R L k thermal conductivity, Btu/hr ft OR k wave number L height of heating surface, ft m mass, lbm Nu local Nusselt number, dimensionless x NuL average Nusselt number, dimensionless P pressure, psi Pr Prandtl number,dimensionless xi

NOMENCLATURE (Continued) q heat transfer rate, Btu/hr q' heat flux = q/A, Btu/hr ft2 Re Reynolds number, dimensionless T vapor temperature, ~R T heater surface temperature, 0R w Y T liquid saturation temperature, 0R s t time, hr u velocity, ft/hr friction velocity = <!pD, ft/hr u velocity = u/u* dimensionless v velocity, ft/hr x height along heater surface, ft y distance perpendicular to heater surface, ft y+ distance = yu*/v, dimensionless thermal diffusivity, ft /hr r mass rate of flow, lbm/hr vapor film thickness, ft AT surface superheat = T -T, ~R w s vapor film thickness = y/, dimensionless t0 emperature = T/AT, dimensionless pcu*(Tw-T ) 90 pcua*(Tw-T), dimensionless q X wavelength, ft viscosity, lbm/hr ft xii

NOMENCLATURE (Concluded) v kinematic viscosity [t/p, ft2/hr p density, lbm/ft3 a surface tension, lbf/ft 7 shear stress, lbf/ft2 velocity u/u maxdimensionless iy U/max temperature (T -T)/AT, dimensionless In general the following subscripts are used. When there is no subscript, the quantities refer to the vapor. liquid s saturat ion v vapor heater surface xiii

ABSTRACT The purpose of this study was to (1) determine the local heat flux values in film boiling in a saturated liquid on a plane vertical surface in the turbulent regime, (ii) extend the region of laminar vapor flow through the use of a drop tower, (iii) gain an understanding of the nature and influence of liquid-vapor interfacial oscillations on heat transfer rates, and (iv) model and analyze the phenomenon of film boiling on a vertical surface to predict -eat transfer rates as a function of height and surface superheat. The variables studied in the determination of the local heat flux values were the height of the heating surface and heater surface superheat in two cryogenic liquids, nitrogen, and hydrogen. To avoid edge effects in a finite plane vertical surface, cylindrical heating surfaces were used. Heat flux values at 11 locations over a total height of 6 in. at four values of surface superheat were determined, employing a transient technique. A warm cylindri-al heating surface with thermally insulated instrumented sections was immersed in the cryogenic fluid, inducing film boiling, and the rate of cooling ~ras recorded. From this rate of cooling and properties of the test sections,.:eat transfer rates were computed. The region of laminar vapor film was extended by reducing gravity forces in a drop tower. Local heat flux values at six locations in a height of 4 in. wiere determined for one value of surface superheat each in liquid nitrogen and liquid hydrogen at a/g 0.00oo8. Additional heat flux values were obtained 2-ider subcooled conditions. xiv

Motion pictures of film boiling on a vertical cylindrical surface in liquid nitrogen were taken at four different heights of the surface and three values of surface superheat. Analyses of these motion pictures indicating the variation of vapor film thickness as a function of time, and the extent of interfacial oscillations, are presented. Film boiling was modelled on the assumption that the universal velocity profile of Spalding is valid everywhere in the vapor region. It is shown that interfacial oscillations increase heat transfer rates and the effect of such increase is taken into account in the solution of the resulting equations. Solutions are presented based on the effect of such oscillations being constant at all heights and also considering the variation of the extent of interfacial oscillations. The data presented show an initial decrease in the heat flux with height and a gradual increase after reaching a minimum value. These experimental values show considerable deviation, both quantitatively and qualitatively, from the laminar analysis predictions of heat transfer rates, These departures are explained on the basis of onset of turbulence and interfacial oscillations. The solution to the set of equations taking these effects into account are shown to predict heat transfer rates within + 15% in the turbulent regime. The heat transfer rates under reduced gravity forces show the same behavior as laminar predictions but are consistently higher. xv

CHAPTER I INTRODUCTION A. Purpose and Scope Boiling has been known for centuries, but it is only in the past few decades that serious studies are being made to understand this phenomenon. Surface boiling is generally classified as nucleate boiling where the liquid surrounding the heating surface makes repeated contact with the surface. This is characterized by vapor bubbles emanating from the surface. In film boiling the heating surface is blanketed by a vapor film and, in general, no bubbles emanate from the surface. In the third regime —the transition regimethere is partial nucleate boiling and partial film boiling, both taking place alternately or simultaneously at different parts in the surface. This transition boiling is unstable for an imposed heat flux and either nucleate or film boiling is established. Nucleate boiling is the more attractive mode of heat transfer in boiling as it is characterized by large rates of heat transfer (relative to film boiling) at low degrees of superheat of the heating surface. There exists an immense amount of literature on different aspects of nucleate boiling, both analytic and experimental. While in the majority of applications, nucleate boiling is the desired mode, there are important applications, particularly with the increasing use of cryogenic fluids in space applications, where film boiling occurs. It occurs during cool down of cryogenic containers and in quenching of metals.

2 Failure of nuclear reactor fuel elements may also lead to film boiling. Thus there are some technically important areas where film boiling occurs but relatively little work has been done on this aspect of boiling. Most of the experimental data reported on film boiling are for small diameter horizontal tubes or spheres. The purpose of the present study is to determine experimentally the local heat transfer rates in film boiling on a vertical surface. A transient technique is employed and local heat transfer rates are determined as a function of height and AT = (T ll-T ) in liquid nitrogen and liquid hydrogen. It was wa~ll sat observed that most available correlations based on a, laminar vapor film with a smooth interface predicted heat transfer rates which were much too low, particularly with increasing height. Visual observation of film boiling indicated that the interface was far from being steady and had oscillations of considerable amplitude. To obtain data on the nature of the interface and the vapor film thickness, motion pictures are taken with a high-speed camera. Although predictions based on a laminar vapor film are found to be too low, it may be expected that there is some region near the leading edge where the conditions of laminar vapor film with a: steady interface are satisfied. In order to examine the validity of such an expectation, the region of validity of laminar flow is extended by reducing gravity forces in a drop tower and local heat transfer rates determined. Additional limited data are obtained on heat transfer rates in film boiling in subcooled liquid nitrogen and liquid hydrogen.

3 There are two aspects of film boiling which render modelling of the phenomenon difficult —the possible onset of turbulence in the vapor film and the oscillations at the liquid-vapor interface, both of which tend to increase the heat transfer rates compared with film boiling in laminar flow with a steady interface. Some researchers have attempted to define a parameter to characterize the transition from laminar to turbulent flow. However, there is no evidence to support the value of the parameter so used. Moreover, it is to be expected that such a transition is gradual and not sudden. In the present analysis, no attempt is made to define, in precise terms, the extent of the laminar region and any parameter to indicate transition to turbulence. Instead, the velocity field throughout the region is approximated by Spalding's universal velocity profile which gives a, linear velocity distribution for thin films and a logarithmic velocity profile for thick films when it can be expected to be turbulent. With the assumption of unchanging temperature profile, it will be shown that any oscillations in the vapor-liquid interface will increase the average heat flux. From the motion pictures, it is established that considerable oscillations do exist and hence the heat transfer rates are higher than is expected for the case with a smooth, steady interface. The extent of such increase in heat transfer will be shown to be dependent on the ratio of the amplitude of oscillation to the mean vapor film thickness. No known method exists to predict the extent of such oscillations. However, two different approaches will be taken to find the value of the ratio of the heat transfer with interfacial oscillations so that with a steady interface, (1) an empirical one wherein the value of this ratio which best fits the experimental

data is used in the solution of equations obtained in the present analysis, and (2) a semi-empirical one whereby the value of this ratio is assumed to vary with the local Reynolds number and an attempt made to find this variation from the results of the photographic studies. B. LITERATURE SURVEY The phenomenon of film boiling on vertical surfaces is, in many respects, similar to that of film condensation and hence references to some of the works on condensation relevant to the present study are included. Nusselt (1)* developed an expression for heat transfer in film condensation on vertical surfaces, assuming laminar flow of the condensate film. Neglecting the acceleration terms in the momentum equation and assuming zero shear stress at the condensate-vapor interface, he obtained a, parabolic velocity distribution for the condensate film. Again neglecting the convective terms and conduction parallel to the surface in the energy equation, a, linear temperature distribution was obtained; with these assumptions the following expressions for the local and average heat transfer coefficients were obtained. r 3 h = 4 (T-T) I(1.1) x x 1 X Tw s w hL2 k~!/4 h = o.94 L (s-') (1.2) Numbers in parentheses refer to references in the Bibiography.

5 L _i _ __fg _ Nu 0.4 1 (1.5) L k RL kI -~ (T -T (13 Rohsenow (2) improved Nusselt's model by considering the nonlinearity of temperature distribution but retaining the same flow model. The calculation is based on an iterative process and the expressions for the heat transfer coefficient differs from that given by Nusselt only in that the enthalpy of vaporization is corrected to h / C AT 4 h =fg 8g hin the first iteration and to 1 C AT C AT \2 fg fg 10 hfTfg h " = hf' lo in' 0.8fg / (1 in the second iteration process. Sparrow and Gregg (3) further improved the solution by considering the acceleration and convective terms in the momentum and energy equations; the boundary layer equations are numerically solved after first reducing them to ordinary differential equations through similarity transformations; zero int.erfacial shear was assumed. Their results are in agreement with those of Rohsenow (2) and show that for Pr > 1, the effect of neglecting the acceleration terms is very small~ However, the departure from Nusselt's solution becomes significant for Pr~ < 0.003 and values of the parameter C AT/hf > 0.001. Koh (4) has given a solution to the condensate problem using integral methods; it is shown that this solution is within 5% of that obtained by solving the boundary layer

6 equations. Koh, Sparrow, and Hartnett (5) further improved the solutions by -t:r l.ving the boundary layer equations f,)r both the condensate and the vapor w-ith appropriate boundary conditions at, the interface, viz., compatibility of u, v, and au/ay for both the liquid and the vapor at the interface. SimiLarity techniques reduce tvhe set of nonlinear partial differential equations to ordinary differential. equations, which are solved numerically. Results of T.he solution for the local Nusselt number are tabulated as a function of the parameters Pr [p).l/(pq)]2, and C Al/h. It is shown that (i) interp fg aefia! shear has almost no effect on heat transfer for Pr~ > 10, (ii) interTac ial shear i.s importa.nt for liquid metals which have very low Pr < 0.01., and (iii) the heat transfer is relatively unaffected by the magnitude of the parameter [/ 2(p) /2' Bromley (6) assumed a model for laminar film boiling on vertical surfaces similar to that of Nusselt for condensation and obtained the following expressions for the average heat transfer coefficient h = constJ1 orv. hfg C i.6) kLv <.on.L L(T -T ) Pr h, L Ii P g h. C L'C L p const-, (1177) v' w s Tte value of the constant depends on -w7hether zero int-erfacial velocity or zero't, ertfacial shear. s assumed. Experiment al data obtained from horizcontal tubes were given in suppor+t of the hypothesized model.. Agreement between the predi::ti:c

7 and experimental results is reasonably good for small diameters. Allowance for radiation effects were made. In a subsequent work Bromley (7) has given a derivation for the use of modified enthalpy of vaporization in the above equation. The modified enthalpy of vaporization is given as r C AT 2 hf g = h +.4 h. (1.8) fg fg h hfg Following the pattern of development of the film condensation problem, McFadden and Grosh (8) improved this solution by solving the boundary layer equations for the vapor, with the approximation of zero interfacial velocity. Koh (9) has shown that this approximation is satisfactory, for values of the parameter ] (K>< I, which is satisfied under most conditions. Cess (10) solved the same problem by employing integral methods. Koh (9) treated it as a two-domain problem, applying the boundary layer equations to both the vapor film and the adjacent saturated liquid. The boundary conditions for velocity and shear stress for tne two domains were matched at the liquid-vapor interface. Using similarity transformation, a set of ordinary differential equations were obtained and these were solved numerically to obtain the dimensionless velocity pv and dimensionless temperature (T-T )/(T -T) for various values of the parameters [(p~) /( ) 1 1/ 2 C AT/h, and Pr. From the results of these calculations, it is concluded that (i) a decrease in the value of the parameter [(pa)v/(p2)l]1/ decreases the heat transfer rate. (ii) The assumption of zero interfacial ve-!locity is valid for a fluid with small [(pI)./(Ps)1] /. (iii) The effect of

8 vapor Prandtl number on heat transfer is small for thin vapor films but significant for thick films. Vapor film thickness is denoted by the parameter Cp AT/hfg. (iv) The heat transfer drops gradually to a minimum value and then rises again as Cp AT/hfg increases. (v) The temperature profile is quite linear for a thin vapor film and the nonlinearity increases as the vapors film thickness increases. The effect of a subcooled liquid with film boiling has been studied by several workers. Sparrow and Cess (11) employed the same techniques as Koh (9) in the solution of the boundary layer equations. However, they assumed zero interfacial velocity. This was subsequently improved by Nishikawa and Ito (12) who dropped the assumption of zero interfacial velocity and used matching boundary conditions at the interface. This solution and that given by Koh (9) are essentially similar, and the main difference is in the addition of one more energy equation for the subcooled liquid. The results show that with an increase in the degree of subcooling, the rate of heat transfer rises; the percentage increase of heat flux is greater for a lower degree of heater surface superheat. Frederking (13) approximates vapor and liquid velocity profiles and the vapor temperature profile with polynomials, employing integral methods to obtain the heat transfer rate. Similar methods have been employed by Frederking and Hopenfield (14) for the subcooled case. The effect of variable properties has been included in the analysis of McFadden and Grosh (15), who solved the boundary layer equation through similarity transformations. Tachibana and Fukui (16) have given a solution to film boiling in subcooled liquids using integral methods. Lubin (17) includes effects of radiation in his analysis.

9 It has been recognized (13) that laminar film boiling occurs rather infrequently as compared with turbulent film boiling. It occurs' at leading edges, stagnation points and on small objects under normal conditions. The experimental data of Bromley (6) and others, obtained mainly for small horizontal diameter tubes, are sometimes used in support of analytical solutions. Where experimental data are available, these solutions do not show any significant improvement in the predictions over the solution of Bromley (6); where these solutions show noticeable departure from that of Bromley (6) no experimental data are available. Merte and Clark (18) obtained experimental data for both the film and nucleate boiling in liquid nitrogen at standard and fractional gravity using 1 in. and 1/2 in. dia copper spheres. Rhea and Nevins (19) studied the effects of oscillations of a sphere in film boiling. Hendricks and Baumeister (20) have given an analytical solution for film boiling on submerged spheres. Chang (21,22) has attempted to use the wave theory, to predict heat transfer rates in film boiling on horizontal and vertical surfaces. The concept of Taylor-Helmholtz instabilities has been applied to film boiling on a horizontal surface by Berenson (23). The effect of the diameter of horizontal tubes on film boiling heat transfer was studied by Breen and Westwater (24). From their experimental data they show that for a given AT, heat transfer rates rapidly decrease with increase in diameter, reach a minimum, then slowly increase with diameter. They also infer that this critical diameter (having the minimum heat flux) is independent of the AT. Hosler and Westwater (24) have applied Taylor instability approach to film boiling on horizontal plates.

10 Experimental studies of the effects of increasing gravity on film boiling on a horizontal tube have been reported by Pomerantz (26) who concludes that the film boiling mechanism for a horizontal tube is dependent on the ratio of the diameter to the critical wavelength, and reports nominal 1/3 power dependency of heat flux on local gravity. An analysis of laminar flow of film boiling from a horizontal wire has been given by Baumeister and Hamill (27). They conclude that the heat transfer coefficient is a function of gravitational acceleration to the 0.375 power for large wires and to the zero power for very small wires. A number of other studies deal with particular aspects of film boiling, such as film boiling in a forced convection boundary layer flow by Cess and Sparrow (28), film boiling of liquid nitrogen from porous surfaces with vapor suction by Pai and Bankoff (29), film boiling of saturated nitrogen flowing in a vertical tube by Laverty and Rohsenow (30), slug flow and film boiling of hydrogen by Chi (31), effects of interfacial instability on film boiling of saturated liquid helium I. above a horizontal surface by Frederking, Wu and Clement (32), radiation effects by Sparrow (33) and Yeh and Yang (34), stability of film boiling two-phase flow in cryogenic systems by Frederking From the above references, it is seen that there are a number of analyses for film boiling from vertical surfaces. However, there is very little or no data in support of such analyses. As has already been pointed out earlier, the phenomena of laminar film boiling with a smooth interface is rarely observed, and in the majority of cases the interface is oscillating and the

II flow apparently not laminar. Considerable deviation has been observed between such predictions and experimental results. However, to date there appears to be very little reported work which takes into account the effects of turbulence and interfacial oscillations. Rohsenow, Weber, and Ling (36) made a study of heat transfer coefficients for film condensation in the turbulent regime, hypothesizing that the onset of turbulence would occur at a, given value of 4r/4. McAdams (37) gives a critical Reynolds number of 1800 for the onset of turbulence, but much lower values of 200-300 have been reported. Using the following model, similar to the threelayer model of Karman-Martinelli-Boelter, u y < yO + < 5 u+ -3.05 + 5.0 in y+ < y+ < 30 - ((-9) u = 5.5 + 2.5 in y 30 7 <y Y with u = u/, y = liquid film thickness and a transition criterion of 4F/1 =- 1800 and assuming that the eddy diffusivities for momentum and heat are equal, Rohsenow (36) obtained /) (1-. 0) Here I pi M 2 Here F2 is defined as,

L2 For Yo < 07 F - Pr + 5 n ( + 5 Pr ) + + 1OM 1' Pr + 2 M -i,_ i0 In~~~~~~~~~~~~~........ (1.11) l OM 60M lOM 2M- 1 1. + p + - + + t Pry y Pry ro ao o For y < Yo 5Pr< t 5Ln + Pr2 ( o j and M = I/ go Tv/g(Pp-v +. (1.12) Lee (38) took a s:lightly different approach. Using Diessler s expression:for eddy viscosity (53), he assumed that the eddy thermal diffusivity is a, jcnstant mul.tiple of eddy kinematic viscosityl Bradfield, BarkdolL, and Byrne (4?) report some data on natural convection film boiling in liquid nitrogen on the surface of forpedo shaped body at a height of 2.69 in. These results are shoc.'wr to agree within 1 32% of the prediction of Hsu and Westwater (39). However, no details are given as to how the local heat flux measurements were m, ade, nor on the manner of isola.ting that sectfi.on from adjoining parts of the body. iHsu (39) reported analyti.cal and experimental studies on turbulent film boiling on a vertical. surface, He postulated a two-layer model which was essentia.-y.:y a, simplified version of Karman's three-:layer model referred to above with a viscous subl.ayer where u+ = y for y+ < 10 and beyond this a uniform velocity in the turbulent core. The temperature profile was linear in the

13 viscous sublayer and uniform in the turbulent core. For the two-layer model it was assumed that u = y for y = 10. Because of the relationship between u+ and y+ at the transition from viscous sublayer to turbulent core we have (y+)2 = (y+u) = uy/v; then (y+)2 evaluated at y+ = 10 is the local Reynolds number based on the maximum velocity and the sublayer thickness. It was hypothesized that, since the Reynolds number based on the sublayer thickness determines the boundary between the viscous sublayer and the turbulent core, using an arbitrary critical Reynolds number of 100, the flow would become turbulent when the Reynolds number formed by taking the maximum velocity and the film thickness in the laminar region, near the leading edge, became 100. With this assumption, a force balance was made on an element of turbulent core, taking into account the gravity forces, the shear forces on the sublayer and approximating the shear force at the interface by the use of a friction factor.- As adequate data on such friction factors are not available values of friction factors for vapor-liquid interface for water and air given by Henratty and Engen (40) were used. Solution to the resulting momentum and energy equations give 2 2 1 2 5A 12 (y) - 3 —B) (x-Lo) + () (113) Y 3 3B+l o y* ~g(P- ) - 2 g(P -Pv ) ( P14) Pv \ Re* k f v + _ ____ ( h )(1.15) vvv — vfg hfg

14 k AT =q' V (1.16) YS I k h q _ V (1.17) x AT y The average heat transfer coefficient over the entire height of the heating surface is then obtained by integrating the local heat transfer coefficient, using Bromley's results for the laminar region. The resulting expression is h L 2h?g Re*v 1 / hLL 2 hfg v Re B + 1/3 2A (L-L ) + ( ) ) kv 3k v A AL(Bl + 1/) o Y* Y* V V L (1.18) Here L is the height over which laminar vapor film prevails. Experimental data were obtained using tubes of length from 2 in. to 6-1/4 in. and 1/2 in. O.D. to,/4 in. O.D. in methenol, benzene, carbon tetrachloride, nitrogen, and argon. The data so obtained are shown +o agree within ~ ",2% of the predicted values. Borishansky and Fokin (41) arrived at the following expressions based on dimensional reasoning: Film Thickness: 6 = const. FF q - C (1.19) P~ Pv Lhfg Pv using experimental results from other sources, a value of 31 was assigned to the constant in the above equation and the form of the function F as -~ I 0.53)

15 Nusselt Number based on film thickness: The following empirical expressions were given for the Nusselt number: P-PV 0 33 Nu = 0.28 %Ga, (1.21) 2 P0-PV 6 for 2 x 10 < Ga. < 1.6 x 10 Pv and Nu = 0.0094 Ga V (1.22) 6 Pl-ov 7 for 1.4 x o106 <l.5 x 107 6 pv where PI -Pv g6 P~-Pv Ga v = (1.23) P: v Pv This parameter corresponds to Grashoff number in natural convection.

CHAPTER II EXPERIMENTAL APPARATUS The data to be obtained for the present study were local heat flux values at different values of surface superheat both under normal and reduced gravity conditions, and values of vapor film thickness as a function of time for an understanding of the nature of the vapor film. To obtain local heat transfer rates, it was decided to employ a transient technique. The general nature of the technique adopted was to immerse a warm body in a relatively cold liquid so that film boiling was induced, and measure the time rate of change of temperature of the immersed body. If the temperature distribution of the body is known as a function of time, the rate of change of enthalpy gives the heat transfer rates. This transient technique has several advantages, as compared with steady state techniques. The main advantage of the transient technique is its simplicity. By installing thermocouples as needed in the test pieces, the rate of cooling can be recorded as a function of time. Steady state techniques to determine the local heat flux values would require, in addition to thermocouples to monitor the temperatures, comparatively elaborate set up of individual heating elements in every section of the test piece. The transient technique would enable data to be obtained even in the transition regime from film to nucleate boiling where steady state techniques have proved difficult because of the unstable nature of the transition regime. To obtain data under 16

17 reduced gravity conditions in a drop tower, where the drop usually takes a few seconds, transient techniques are preferred as steady states can be achieved only with test surfaces of negligibly small heat capacity. This transient technique has been successfully employed for obtaining boiling data under different conditions of gravity forces, pressures and subcooling in liquid nitrogen and liquid hydrogen (18,54). To determine the local heat flux values as a function of temperature, in film boiling in cryogenic liquids, a. suitably instrumented test surface with thermally isolated test sections was used, along with appropriate dewars for the cryogenic liquids. For measuring the vapor film thickness as a function of time, it was decided to adopt photographic methods which would produce motion pictures at a high speed. A test surface with a, constant, and uniform controlled surface temperature was used for experimental simplification. For this it was necessary to have a high-speed camera with associated auxiliaries and a dewar with plane transparent windows. The test surfaces, the dewars, and photographic equipment used for the present study are described in the succeeding paragraphs. A. Heating Surfaces To obtain heat flux versus wall superheat data, test surfaces were constructed of oxygen-free high-conductivity copper. The choice of this material was based on its high thermal diffusivity which would permit using lumped analysis (Appendix D) in the calculation of heat flux, thus permitting the use of

jus'lt one ttermocouple in eachL test section, and its well documented properties at low temperatures. For, photographic studies, it was necessary to have a steady state test surface; tellurium copper was chosen for this test surface bec:ause of its easy machinability. 1, HEAT FLUX MEASURING TEST SURFACES Ln order to avoid edge effects, cyli.,indrical test surfaces were used to simu;lafte p lae vertical slurfaces. A test piece assembly i.s shown in Figure 1, a.nd tr.e detai.ls are showy i.L:r Figure 2. Th.e test piece, Figure 1, consisted of tohree t est secticns, each 1/4 inr. thick with a hole'in the center to pass the thermucouple wires. Each. test section was insulated from the adjoining spacer pieces with- 0005'in, thic.k Teflon washers. Heat leakage to the adjoining sect:Lro-is was further reduced by cutting a 7recess such that only a circular sect ica'. of 1/16 in, radial width would bear in between. the sections. The sections were held together by twc 3/32 in, diameter stainless steel through bolts, L.'isulated from th.e copper'by wi'nd-ing a OoOil:i, Tefl.on tape around the bolts. B.. fl.i g from tht.,e top an.d thse bottom of th.e test piece was prevented by mounting additlo'.r:al cn.ylndri. c.al pieove cornstzucted of 0o001 ir, stainless steel shim sto k, TThe t.hermloco.uple wires from the test secti.cons were passed through the ce-t'ral' es, through a 1/4 in. dl.ameter stainless steel tube soldered to tce top sectli.on and oult of the tube through a Conax bare wire thermocouple glald, The stainless steel bolts holdinl'g th.e test pieces together also served: tfact t;he est piee t te cbles wnich ralsed and lowered the test surfaces in- the dewar.

'9 T.C. WIRES BOLTS d- 7 TOP PIECE I I I I'I I END PIECES OF 0.00I" I - - — SPACER ST. STEEL x 6" I PIECES SHIM STOCK I ], I| ] I I - T.C. WIRES T. C. PLUG, L _ __2PIECE T — 1/2"1.D-.2 1/4" O.D. Figure 1. 2-1/4 in. diameter test surface.

T.C. JUNCTION''_'- 3EINTEST SOLDERED ECTION;i ii I l/f A I ~ ~A I \COPPER PLUG. |SPACER THERMOCOUPLEC PIECE I 1/2.4 II.D. 2 1/4 "O.D. 1/8 DIA. BOLT HOLES 0 ~ I t+11,-'C —- C OPPER BOTTOM PIECE.005 ST. STEEL SHIM STOCK.001 ST. STEEL SHIM STOCK SEALED WITH RTV ST. STEEL INSULATING END PIECE 2 1//4 D/A. TEST SECT/ON / "D/A. TEST SECT/ON Figure 2. Test section build up.

21 The sections of the test piece were assembled to check the alignment of the different sections. The heating surfaces were then sandpapered with 400grit emery tape and smoothened with crocus cloth. The surfaces were finally polished with jeweler's polish to obtain a smooth mirror-like finish. No attempt was made to quantitatively measure the surface roughness, as it has seen established that film boiling is relatively insensitive to surface finish. a. Method of Attaching Thermocouples In previous work with spheres, thermocouples were attached to the sphere by drilling a 0.040 in. diameter hole in the sphere to the required depth and soldering the welded thermocouple junction at the bottom of this hole. In the present study this method of attaching thermocouples proved inconvenient as it requlired drilling a small diameter hole from the inside of the ring shaped test section. In order to find the most convenient way of attaching thermocouples consistent with acceptable response, six thermocouples of copper constantan were installed in different ways in a test block of OFHC copper measuring 2-1/4 in. wide x 1-1/2 in. high x 3/4 in. thick as shown in Figure 3. Thermocouples 1 and 2 were made by welding 30-gauge copper and constantan wires. These were Cu- CONSTi2 T.e. WIRES OFHC COPP. BLOCK;2 62 #65 #4#3 ~ c —- 2 1' _ Figure 3. Different methods of attaching thermocouples.

22 then inserted in a hole of 0.055 in, diameter x 1 in. deep in the copper block and attached to the block with 50-50 soft solder. Thermocouples 3 and 4 were identical and were made by welding the junctions and soldering these to similar copper plugs of 1/16 in. diameter x 3/8 in. long. Thermocouple 5 was made by welding the junction, slitting the edge of a 1/16 in. diameter plug, sandwiching the thermocouple junction between the slit ends and mechanically pressing them. Thermocouple 6 was made by electrically welding the wires to one end of an OFHC plug. It was found that this was mechanically weak; to provide the necessary mechanical strength, a thin coating of soft solder was applied to the junction after welding. These plugs were driven into hole at the bottom of the copper block, the wires coming out of the top through corresponding holes as shown. The responses of the various thermocouples were compared by immersing the.opper block in liquid nitrogen and recording the output of the thermocouples on a Sanborn Recorder. The temperature level at whnich these runs were made was 255 ~ (-205 ~F), It was found that Thermocouple 4 had the best response and the responses of all other thermocouples were compared with that of Thermo~oupiLe 4: Thermocouples 1 and 6 lagged by 5Sv (0.35~R), Thermocouple 2 by 2~v (0.1,~R), and Thermocouples 3 and 5'by l10ov (0.7~R), The time rate of Change of temperature as measured by Thermocouple 1 was lower by 0.5-1l compared with that of Thermocouple 2. There were no differences in the measured time rate of change of temperatures as recorded by Thermocouples 2, 3, 4, and 6, Thermocouple 5 measured 4% too low. These results indicate that there was an uncertainty of about 0.70F in the measurement of the temperature and less than 0,5% in the heat flux measurement due to thermocouple responses. In the test pieces the thermocouple junctions were made by welding the thermocouple wires, soldering the junction to a tapered copper plug of approximately 1/16 in. diameter and driving the plugs into holes in the test section.

23 Excess length of the plug was filed off and the plug end peened over and polished. b. Thermal Insulation of Test Sections The local heat transfer rates from the test surfaces to the surrounding liquid was determined by equating them to the rates of enthalpy change of the test sections in the test surfaces. For this technique to be satisfactory, test sections had to be thermally insulated from the adjoining spacer pieces. Before deciding to use cylindrical heating surfaces, attempts were made to use rectangular copper blocks as plane vertical heating surfaces. With some of the methods of insulating the sides of rectangular block to reduce end effects, interesting results were observed. With Teflon strips as insulation on the sides of blocks, higher heat flux values were observed than without the insulation strips. To avoid such edge effects, cylindrical heating surfaces were used instead of plane vertical surfaces. To insulate the test sections from the spacer pieces, attempts were made to introduce an air gap of 0.005 in. between them but this was not practicable because of difficulty in properly aligning the different sections. It was established that no adverse effects were introduced by using a 0.005 in. Teflon washer between the sections (Appendix B). To minimize the area of heat leakage from the test section to the adjoining sections due to temperature differential in the various sections during the cool down period, a recess was cut in the spacer pieces so that only a circular section of 1/16 in. radial thickness was in contact with the test section.

24 c, Test Piece Dimensions As has been mentioned earlier, to avoid possible edge effects, it was decided to use cylindrical test surfaces to simulate plane vertical surfaces, Th.is would thenn require establishliing that using a cylindrical test surface would give the same results as plane surfaces. It was proposed to establish thi.s fact by usin.g test surfaces of differen.t diameters so that if the results obta.aced from these surfaces agreed within themselves, it could be concluded tc'at the curvature had no effect. For th.e smaller test surface, it was arbitrarJily decided to use a 1 io diameter test surface. The selection of the largest diameter depended on the size of dewars available, To find the largest diameter test suroface that c ould be used in+- the available dewar without introduci.ng an.y effects due to the container size several tests were conducted and the results showed (Appendix C) that with the 4 inr diameter dewar, a maximum diameter of 3 in, for the test surface could be used, To be sure that the con-:taeliner size had no effect on the results obtained, it was decided to limit the d~ amet'er of test surfaces to 2-1/4 in. Hence, test pieces of 1 ino diameter a-.d 2-1/4 in, diameter wer3e constructed. Earlier reported results (24,39) i.dicated t-hat tu;bule:rice effects would become apparent at relatively short. eights from the leading edge-of tthe order of a fraction of an inch, It was, t:erle:fore, decided to co-nst ruct test surfaces of 6 in, height to obtain data.inder'normal gravity conr.ditio;.n so However, because of dimensional limitations irnmp.-sed'by ttrie dewar in the drop package, th-e Fheight of test pieces to be used i'L tne drop package was limited to 4 i'.o, a:d a diameter of 1 in,

25 To obtain local heat flux data under normal gravity conditions, five test surfaces were constructed as shown in Table I. It might be noted that each of the five test surfaces constructed contains one section located at the same height of 3 in. from the leading edge, for purposes of comparison of data obtained with the different test surfaces. TABLE I DETAILS OF TEST SURFACE: a/g=l Test Surface Diameter of Test Section Locations Identification Test Surface, Above Leading Edge, in. Number i.n 2 1 3/8, 3, 4-1/2 4 15/8, 3, 5-5/8 5 1 1/4, 1-1/2, 3 6 2-1/4 7/8, 3, 3-1/2 7 2-1/4 2, 3, 4 Because of the shorter heights of test surfaces that could be accommodated in the drop package for studies under reduced gravity conditions, it was decided to limit the number of test sections to two in each surface. Details of test surface dimension and test section locations for reduced gravity studies are given in Table II.

26 TABLE II DETAILS OF TEST SURFACES: a/g 0.008 Test Surface Diameter of Test Section Locations Identification Test Surface, Above Leading Edge, in. Number in. 8 1 3/8, 2 9 1 5/8, 3 10 11-1/8, 3-1/2 2. TEST SURFACE FOR PHOTOGRAPHIC STUDIES While all heat flux measurements were made by employing a transient technique, it was desirable to have steady state conditions available for photographic measurements of vapor film thickness. For this purpose a test surface as shown in Figure 4 was constructed of free machining telurium copper. A 1/2 in. hole was drilled in a. 1 in. diameter cylinder x 6-1/2 in. height to receive a 1/2 in. diameter cartridge heater of 1000 watts capacity. To avoid the possibility of noise pick up by thermocouples, D.C. power supply was used for the cartridge heater. Two thermocouples were installed in drilled holes at the top to measure the temperature of the test piece. The ends of the surface were closed by threaded copper end pieces. To prevent boiling from top and bottom ends of the test surfaces, end pieces of 0.001 in. stainless steel shimstock, similar to those used for the other pieces, were attached to the test surface. For photographic studies only a part of the cylinder was seen and hence a reference was necessary for quantitative measurements for film

27 END PIECES OF ST. STEEL SHIM STOCK 0.5" DIA. CARTRIDGE HEATER HEATER WIRE THERMOCOUPLE WIRES TELLURIUM COPPER HEATING SURFACE -- I"DIA.i Figure 4. Test surface for photographic studies.

28 thickness. For this purpose, an 18-gauge wire (0.040 in. diameter) was stretched parallel to the test surface at a distance of 1/2 in. from the cylinder. Pinch marks were made at intervals of 1 in., the first one approximately to coincide with the leading edge of the test surface. In the photographic films only about 3/4 in. along the axis was visible and these pinch marks served to identify the distance from the leading edge at which photographs were taken. B. Dewars Three different dewars were used-a deep Pyrex glass dewar for obtaining local heat flux values under normal gravity conditions, a cylindrical stainless steel dewar for local heat flux measurements under reduced gravity conditions, and a rectangular stainless steel dewar with Pyrex glass windows for photographic studies. In the glass dewar and the drop package dewar, the instrumented test surfaces were immersed in a pool of liquid nitrogen or liquid hydrogen and the temperatures of the test section monitored by the thermocouples attached to them and recorded on an eight-channel Sanborn Recorder. The test piece for photographic studies was heated by a cartridge-type electric heater. Pressures in the dewars were held constant by the use of pressure relief valves. 1. PYREX GLASS DEWAR To obtain the local heat flux values a Pyrex glass dewar as shown in Figure 5 was used. This dewar was double walled, vacuum insulated with an upper part

TEST SURFACE RAISING AND LOWERING MECHANISM' POP w w X VACUUM PUMP Fz Il UPRESSURE GAUGE INNER DEWAR INNER DEWAR WELL MANOMETER OUTER DEWAR Figure 5. Schematic of Pyrex dewar and associated equipment.

30 made of sinLrgle walled sec t:lon whi~ch termi nated with a metal flange'via a Kovar intermediate metal flange~ The dewar was s'ilvered except for -two 1 in. wide diametrically cpposi.te strips whiJch permitted visual observation of boiling. The dewar had an IoDo of 10 cm, a height of 65 cm, and had a capacity of 5 lit er s o The dewar itself was surrounded by a second double walled, vacuum insulated dewar whi]ch was used to surround the inn-er dewar with liquid nitrogen. T Ihis liqui.d nitrogen acted as a heat, shield for the test liquid contai. ired in t'he il: ner dewar, In previous works with spheres, thLLe test object was attached to a stainless steel tube which passed through a gland on the flange mounted on top of thle dewar, The sphere was introduced into the test liquid by sliding the tube'rV the g.lan.d. It was observed that small quartities of moisture adhering to t-.li s sltid g -i:g tube found its way into the glass dewar where it was vaporized. When the sphere was with-drawn from the test liquid, this moisture condensed.rl the sphere and if the sphere was immersed with this coating of condensed mC- istnre or Ltt, heat flux values highL.lgrer thtan that with a clean sphere were b.tai.r`ed, The proiblem was solved by raising the temperature of the sphere to levels above the dew poi.lIt and then:it.roduoring it'in the test liquid. i'owewv'er, t'he same procedure could not be adopted with'the present cylindrical test surfaces tc obtain data at temperature levels lower than 32 F; in such'-'ases starting with a temperature above 32~F and cooling the test surfaces to mch rn.er~ temperatu-res would resulIt iLn considerable temperature differentials ibeing establLshed betweenl the diffenent setJion.s that make up a test surface, tr;.us produ1cing a noV.i.sothermal surface~ O t was desired to maiLntain an

31 isothermal surface. This was accomplished by precooling the test surface to the vicinity of the desired temperature level by immersion in the liquid, removing the test surface, suitably warming it up to establish an isothermal surface and introducing it in the test liquid. For this technique to be successful, it was necessary to prevent the ingress of moisture, and hence a lifting and lowering device with a rotary seal instead of a sliding seal was designed and used. A manifold flange mounted on the top of the glass dewar provided all permanent connections such as vent lines, pressurization lines, etc., and also served as a base for the upper chamber assembly which supported the test piece. Figure 6 shows details of this assembly. The upper chamber contained a shaft one end of which was supported on a bearing on the inside of the chamber and the other end came out of the chamber through a gland. This shaft had two pulleys which housed sufficient lengths of stainless steel cables. The test piece was suspended from these cables. The shaft extension had a handle and an automatic stop to prevent the lowering of the test surface by its own weight. To the top flange of the chamber, a smaller flange with a bare wire thermocouple gland was attached. All the thermocouple wires from the test sections passed through this gland. The top flange also carried two 1/2 in. relief valves set to open at 1/2 psig, and a fitting for filling the dewar with liquid hydrogen. A dump tube extending to the bottom of the dewar was used to evacuate the liquid by pressurizing the dewar. The dump tube was connected to a heat exchanger made of copper tubing, whose outlet was led into

32 Io0 RING BEARING SUPPORT FOR GUIDE SHAFT GUIDE SHAFT t32 PULLEY SHAFT PULLEY Figure 6. Device for raising and lowering test surface.

33 the intake of an exhaust fan. This arrangement permitted the safe evacuation of liquid hydrogen. 2. DROP PACKAGE DEWAR (Figure 7) The stainless steel cylindrical dewar for the drop package is a double walled -vessel with super insulation. The inner vessel is 8 in. diameter x 12 in. deep with a neck opening of 4 in. diameter. To the top of the dewar is attached a heating chamber into which the test piece can be drawn and heated by an electrical heating coil. A reservoir for liquid nitrogen is provided at the top of the dewar; the liquid nitrogen in this reservoir precools the dewar before filling it with liquid hydrogen. A double walled fill line, a vent line, three thermocouples-two at different heights in the test liquid and one in the vapor space-a tube carrying two liquid level indicating sensors-one high level and one low levelpass through the lower flange of the heating chamber. Two more thermocouples and the electrical leads for the heater pass through the top flange of the heating chamber. A gland through which the tube carrying the test piece slides is mounted on this top flange. By raising or lowering this tube the test piece is removed or immersed from the test liquid. Two liquid level indicating sensors are mounted in the reservoir on the top of the dewar. The dewar itself is suspended from the cover plate of the drop package by stainless steel rods. Appropriate fittings for the fill lines, vent line, pressure release, etc., are mounted on the cover plate. After filling the dewar with the test liquid, two pressure relief valves were attached to the

34 TEST VESSEL SUPPORT ROD LIQUID LEVEL INDICATION FOR LIQUID NITROGEN LIQUID NITROGEN FILL LINE TEST OBJECT INSERTION ROD HEATING CHAMBER THERMOCOUPLE T EST OBJECT HEATING CHAMBER LIQUID NITROGEN COOLING COILS TEST OBJECT C - CRYOSTAT SUPPORT ROD RADIANT HEATER FOR TEST OBJECT VACUUM INSULATED LIQUID HYDROGEN FILL LINE RADIATION SHIELDS HYDROGEN VENT LINE (2 reg'd) -LIQUID NITROGEN VACUUM FITTING CRYOSTAT 1l t ~ ] I Zr ~ ~ ~~ SUPER INSULATION LIQUID LEVEL DETECTORS._ j__ J INERT GAS SPACE _.._-BULK LIQUID THERMOCOUPLE PROBES / / t ILIQUID HYDROGEN 0/'-" -" -_. —-TEST OBJECT IN IMMERSED POSITION Figure Drop tower test package. Figure 7. Drop tower test package.

35 fill line, to regulate the pressure in the dewar. A small lecture bottle mounted on the drop package provides helium for pressurizing the system for studies in subcooled liquids. The thermocouple wires from the test pieces pass through the 1/4 in. diameter supporting tube. The thermocouple outputs are connected to a recorder via a drop cable, consisting of eight 24-gauge copper wires and 24-gauge constantan wires, Double shielding of this cable was necessary to minimize noise pick up, particularly when operating at high sensitivities, The constantan wires served to make the reference junctions in ice. Details of drop tower, package construction, deceleration device, etc., are given in Appendix A. 3. DEWAR FOR PHOTOGRAPHIC STUDIES (Figure 8) A stainless steel rectangular dewar of inside dimensions 5 in. x 8 in, x 14 inr was fabricated for the purpose of obtaining motion pictures of film boiling. The dewar was double walled permitting the evacua.ti cf the space between them. For obtaining photographic films, four window glasses of 3 inr diameter Pyrex were installed, two on each side. To provide a seal between the window glasses and the frame, "O" rings generally available were nlot effective as they hardened at the low temperatures of liquid nitrogen. "O" rings of Rulon (made by Dixon Corporation) and of Compound 6317 (made by Precision Rubber Co.) were found to be satisfactory. Frequent chipping of the edges of the window glasses initially observed was eliminated by grinding the edges of the glasses~ Cont:raction of the t"0T'

TEST RING SURFACE 4 1/2" DIA. x 1/4" THICK SS RETAINING RING VIEWING A t I I I I I I WINDOW 31/2" DIA. x 1/4" THICK A — ~P GLASS WINDOW VACUUM SPACE OUTER VESSEL Figure 8. Stainless steel dewar for photographic studies

37 rings at low temperatures resulted in slackening of the bolts holding the windows with a loss of vacuum. This was corrected by the use of spring washers. With a vacuum pump running continuously, a vacuum of approximately 1/4 in. less than the barometric pressure was possible, with liquid nitrogen in the dewar. C. Assembly of Test Surfaces Before final assembly of the test surfaces, the copper pieces were temporarily assembled and polished so that a smooth alignrment was obtained. This was then disassembled. Three thermocouples of copper constantan of the required length were made by welding one junction. The thermocouple wire was then passed through the hole in the test section, and soldered to an OFHC copper plug which was then driven into the test section. Excess length of the plug was filed off and peened in place. This was then lightly filed, smoothed with emery cloth and finally polished with jeweler's polish till a smooth surface was obtained. After polishing it was not possible to locate the plug by normal visual inspection. The test piece dimensions were measured with a vernier calipers and recorded. The weight of the test section with the thermocouple was determined in a chemical balance. Subtracting the weight of the thermocouple gave the net weight of the test section. The thermocouple wires were insulated by slipping a 24-gauge Teflon or polyethelene tubing up to the bare wire thermocouple gland at the top. The test piece was then assembled with end pieces of stainless steel shim stock and 0.005 in, Teflon insulators

38;-,etween the test. sections and spa~~er pieces, The s'tainless steel bolts holding the sections together were insulated from the test piece with Teflon tape. After assemibling the test piece toe bolts were slightly tightened, the ex..ess Teflon trimmed, and the pieces properly aligned by pressing between two V-blo-kso The bolts were then tightened an>d t'he edges smoothed with crocus cloth, and finally polistL.hed, Thle stainless steel end pieces were sealed with a 0O,005 in, stainless steel disck us-ing RTV to seal the edges. The thermocouple wices from the gland on thle test surface to the glanrd on the hlisting device were also ins.sula.ted witr Teflon tubing~ The thermocouple wires leading from trhe gla.nd or the test piece to the gla..d on thie h.oisting dev'ice required greater flexlbilibtLy, Since Teflo:.rl has greater felxibility than polyethelene, particula'rly at low temperatures, it.; was used i'n'.'t.hi-s section, The thermocouple wil.'es were th.en passed through thde gland on the hoisting deviceo The test piece was attachled to the stanless steel h.ist.lng cable, and adjusted, so that the test piece remained vertical. The hoisting device with the test piece was t -etl: installed co::_ the glass dewar, DPo Phot.o:gr.ap-hic Appara'tus Tow measure to'<e vapor f1ilm t'"rliLKL ess an.r.'de the extent of inlterfacial oscillat.i-,ons, mottor. pictures were taKen' wmt,1 a high-speed drum camera, Dynafax Mo.<del 326 (manufactured'by BecDkman and Whitliey) A 35 mm film strip of 33-7/8 ir.!o lengtr is used a?!d the max.imum:umber of frames exposed was 224.'The film.i?.g rate could be varied from 180 frames/second to a maximum of 26,000

frames/second. Backlighting was provided by a 500-watt projector with a 3-1/2 in. diameter condensing lens. The speed at which the camera drum rotated (and hence the filming rate) was monitored by a magnetic tachometer mounted on the camera and read on an electronic counter. Kodak Pan-X film (ASA 125) was used. The arrangement of the equipment used to obtain motion pictures is shown in Figure 9. EL. COUNTER CI Tt"~:'% _ j s URF — TEST SURFACE CA M ER A-v 4'F LIGHT SOURCE DEWARFigure 9. Arrangement for photographic studies.

C HAPTER III INSTRUMENTATI ONI To calculate the local. heat flux values at different temperature levels, the t-rmoc ouple outputs from the test sections ian the heating surfaces were reco).rdeod. on a Sanborn Recorder~ The Sanborn Recorder itself was calibrated by cmparison with a potentiometer, The potert.iometer was also used for measur:ig the thermocuple output int. liquid. n.itr,-ogenl and liquid hydrogen for purpcses rof c-alibrating the thermocouples. A. Thermoco uples All thermocouple outputs were measured relative to the ice point. The thermocosuples we:re made of 30-gauge copper-constantan wires. The precise loca'tiL.,n sf'the thermocouples in the test section was unimportant as a lumped aa:l.aysis was employed in the calculat-ion of heat flux (Chapter IV) which gave aa:,oeptable accuir:acy (Appe:!.dix D)o Copper-c>nstan.tar. thermocouples have relat',izey'1,cw thermal po.wer at the low temperatures at which data were obtained idi the present experiments and it was necessay to roperate the recorder at high sensitivvities of up to 2,v/div, To minimize noise pickup when operating at this high sensitivity all thermcc)uple lead wires were covered by a double e*c.trotwcistatic: shield. The lead wires were ledd to a switch box which permitted: (i ) the thermocI ouple cuitputs to be fed into the recorder; 40

41 (2) the thermocouple outputs to be measured by the potentiometer for purposes of calibrating the thermocouples; and (3) the potentiometer output to be fed into the recorder for calibrating the recorder. B. Potentiometer To calibrate the thermocouples installed in the test surface, the outputs from the thermocouples in the test liquid (liquid nitrogen or liquid hydrogen) were read on a Leeds and Northrup Model K3 potentiometer; the unbalance in the potentiometer was amplified and detected with a Rubicon Model 3550 photoelectric galvanometer and amplifier system. The potentiometer has an accuracy of ~ (0.015'% + 0.5 Tv). The maximum output measured in liquid hydrogen was -6190 gv and the maximum error was ~ 1.43 4Tv corresponding to ~ 0.50R. To reduce the effect of building vibration, the amplifier for the null detection system was located on a platform suspended from the ceiling with soft springs in the supports. A Honeywell series 3100 spotlight galvanometer indicated the unbalance in the circuit. C. Sanborn Recorder Model 7708 A Sanborn Recorder was used to record the thermocouple output from the test section, as a function of time. The recorder had eight channels, and appropriate preamplifiers could be used for each channel depending on the input signal. For recording the

42 the:rm.noaouple outputs, Model 8803 high gain DC amplifier was used. The maximum usable deflection of the recorder stylus was 4 cm divided into 50 divisions on the recor.ding chart paper. The recording chart could be run at speeds varying from 0025 mm/sec to 100 mm/sec in nine steps. Generally, a chart speed of 25 mm/sec was used. A time marker recorded 1 see (or 1 min) timing pulses. The preamplifier could be operated at sensitivities from 10)00 v/div to 1 nv/div, with the usual operation. at 2 nv/div or 5 iv/div. The nonlinearity of the recordenr.is specified by the manufacturer to be - 0. 25 div, which corresponds to I: (0O5 v and ~+ 1.25 Tv at sensitivities of 2 4v/div and. 5 tv/div, respectively. The minimum temperature at which the recorder was operated at 2 kv/div was 136~R, and at this temperature, the recorder nonlincarity contributes an uncertainty corresponding to ~- 0. 05~R. The cor:responding values at 5 gv/div are 4.)O0R an.d.. 067FR. D. Pressure The pressure in the glass dewar and. in the drop package dewar was obseirved on a calibrated 12 ino Heise pressure gauge with a range of 0-25 psig with a c alibrated accuracy off ~ 0. 025 psi:. The gauge was divided into 0. 1 psi steps.

CHAPTER IV EXPERIMENTAL PROCEDURES AND DATA REDUCTION A. Filling Dewars To obtain local heat flux values in liquid nitrogen, the upper chamber with the test piece was assembled on the glass dewar. The dewar was evacuated of air with the vacuum pump and then filled with nitrogen gas to atmospheric pressure. The dewar was then filled with liquid nitrogen by pressurizing the liquid nitrogen container with nitrogen gas. When the proper quantity of liquid nitrogen was filled in the dewar, venting took place through two relief valves mounted on the hoisting device which were set to open at 1/2 psig. These relief valves maintained a constant pressure in the dewar during the experiments. Before obtaining the data, the atmospheric pressure was measured with a mercury barometer. For operation in liquid hydrogen a more elaborate purging sequence was followed to reduce the possibilities of contamination. The system was evacuated of all air, the vacuum broken with nitrogen gas, and pressurized to a positive pressure of 6-8 psig. This sequence was repeated three times with nitrogen gas and then three times with hydrogen gas before filling the dewar with liquid hydrogen. In all cases the outer dewar was filled with liquid nitrogen before filling the inner dewar with the test liquid.

44 B. Calibration of Recorder and Thermocouples Before proceeding to obtain the cooling curves at different temperatures, the thermocouples in the test surfaces and the recorder were calibrated and the recorder accuracy checked by the following procedure. The test surface was lowered into the test li-cuid ar:ic allowed to come to thermal equilibrium. The output of the thermocouples in the test sections was measured with the potentiometer. This was used to find the deviation of the thermocouple output from the standard tables. The output of the thermocouple corresponding to the temperature at which heat flux data were to be obtained was determined by using the standard tables (35) and assuming the deviation of the thermocouple outputs to vary linearly from the liquid temperature to the reference temperature (ice bath). The appropriate zero suppression was applied to the recorder using the potentiometer as the signal source. The recorder gain was also calibrated by changing the input from the potentiometer by a known value and observing the corresponding deflection on the recorder. The same procedure was adopted for all the channels on which the output from the test sections were to be recorded. The test surface was then raised from the test liquid and allowed to warm up to the desired temperature level. During this warming up a 650-watt movie lamp was used with appropriate masking on the glass dewar to locally heat the test surface to obtain an isothermal surface while recording the data. When the test surface temperature was just a few degrees higher than the temrperature at which the data were to be obtained, the recorder chart speed was set at

45 25 mm/sec and the test surface lowered into the test liquid. In general, cooling to the desired temperature took place within a few seconds-l0-15 sec. Figure 10 shows a typical recorder output. As soon as the test surface cooled down a few degrees past the desired temperature the test surface was raised, warmed, and the sequence repeated. The test conditions under which data were thus obtained are given in Table III. TABLE III TEST CO]NDITIONS FOR DATA UNDER NORMAL GRAVITY: a/g = 1 Test Surface Identi- Test Section m fication Number Location Aboveest Tw-Ti ( Liquid (Nominal) (and dia in.) Leading Edge, in. 2 (1) 3/8, 3, 4-1/2 LN2 315, 251, 204, 99.7 LI12 400, 300, 200, 100 4 (1) 5/8 3 5-5/8 LN2 315, 251, 204, 99.7 LH2 400, 300, 200, 100 5 (1) 1/4, 1-1/2, 3 LN2 315, 251, 204, 99'7 LH2 4I, 500, 3 200, -)D1 6 (2-1/4) 7/8, 3, 3-1/2 LN2 315, 251., 204, 99.7 7 (2-1/4) 2, 3 4 LN2 315, 251, 204, 99-7 In liquid nitrogen, five sets of data were obtained under each one of these conditions, and in liquid hydrogen, three sets of data were usually obtained.

T-2 T'l Test T -TIT Fj 4 -1 It4 Ai —-i St. Steel tit~~~~~~~~~~~~~~~~~~~t G_ _ ~~~~~~~~~~~~~End Piece DATE: 12/25/69 LIQUID NITROGEN 0.psig. st. TEST SURFACE # 7 RUN # 7004 Zero Suppression = 2O5O/,; SENS. 2/,sv/Div Chart Speed = 25mm/sec Figure 10. Typical cooling curve —recorder output a/g =1. Liquid. nitrogen. ~t-1~~~~~~~~~~~~~~~~4 Jff i~~~~~~~~~~~ Test 4 1 _:I~~t 4 S. %t ii tT~~~~~~~~~~~~~~~~~~~7t 4- -tift~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~F: -ii t~ 4-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~tt it + _F T~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~r~ ___rS. See DATE: 12/25/69 LIOUID NITROGEN 0.5psig. sat. TEST SURFACE RUN * 7004 Zero Suppression = -2050,~&,; SUN W''%" ez 2."/Div Chart Speed a 25mm/sec Figure 10. Typical cooling curve —recorder output a/g = 1. Liquid nitrogen.

2i7 C. Drop Package Operation The filling sequence for the metallic dewar in the drop package, used for obtaining local heat flux dataurnler reduced gravity and subcooled conditions was similar to that with the glass dewar. The dewar was filled with the package resting on a platform. When the dewar was filled with the test liquid, the test surface was immersed and allowed to cool down to the saturation temperature. The thermocouple outputs were measured with the potentiometer. The test surface was raised into the heating chamber where it was heated with an electrical heater lining the chamber. The heater was operated intermittently for short durations of approximately 15 sec at about 30 watts to avoid over heating. The package was then raised and held suspended in the release mechanism. The recorder was adjusted as described previously and the chart speed brought up to 25 mm/sec. The test surface was then immersed in. the test liquid, and the package released at the appropriate time. The instanrt of release was marked on the recorder chart by a signal provided by a dry cell in the package release circuit. The package was then hoisted back into position. Figure 11 shows the recorder output dur:ing one such drop. The method of inserting the test surface limited the data to bonly one value of AT, corresponding to room temperature. In some of the earlier experiments with spheres it was observed that when the sphere at a temperature much lower than the room temperature, was immersed in the test liquid, very high heat flux values were obtained. The cause of these high heat fluxes was found to be the ingress of moisture into the dewar; the moisture adhering to

:i~~~~~~~~~l:~~~E c:~~~~~~~~~~~~b!iiii I i II I' i I i i 40 4+_~~~~~~~~~~~~~~~~~~~~~ t',, oq,:~~~~~ 44,4r TJ! ~',! i:{i', I!!,;, ij Thi 0~l i l l l l i?"':T At~~~~~~~~~~~~~~i 14~~~~~~~~~~~4 0 1~~~~~~~T ~~~~~Fiji 4 -i ~~~~~~~~~~~~~~~~~~~~~~~~~~~FI ~~~~~~~ H~~~~~~~~4P ~rd ji~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4 rir i f L ij I /l''i i i i I.1_*~I I I I. 44{I II~ 41T r - I T-1 C~-~ifff~~ HCd;i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i i $9~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i ~' I iii II iiiii i ~ ~ ~ 4 J i Ijjj H4+ _14~~~~~~~~~~~~~~~~~~~~4!44 %4L22 ii! I~lj l ~-i~i~~i~ r~~~~-S —tl~;~~T i~tff -tjff?-rf-tt~mt~ttttt~:Y,7#; t~~l-ti.' a, i +Ti4i -- -44 -AA _ 14- k

49 the supporting tube in its raised position found its way into the dewar when the sphere was lowered. This moisture on the warm tube vaporized and remained in the dewar. When the cold sphere was raised, part of this moisture condensed on the sphere and remained until its temperature was above approximately 32~F. Thus, in order to avoid this condensation, it was necessary to raise the temperature of the test surface to at least 32~F. Starting with the test surface at this high temperature, it was impossible to obtain an isothermal surface at low temperatures. For obtaining subcooled data, two relief valves, one set at 1/2 psig and the other to a higher pressure were used. Just before introducing the test surface, the 1/2 psig relief valve was isolated and the dewar pressurized to a high pressure with corresponding gas; the test surface was then introduced into the subcooled liquid and the data obtained. The conditions under which the data were obtained are given in Table IV. TABLE IV TEST CONDITIONS FOR DATA UNDER REDUCED GRAVITY AND SUBCOOLED CONDITIONS Test Test Surface Test Conditions Test Surface Section Identification Location Test P, Subcooling Above Liquid psig (Nominal) a/g AT, oR Base, in. OR OR 8 3/8, 2 LN2 1/2 0 1.0, O. 008 354 LN2 34 21 1.0 333 9 5/8, 3 LH2 1/2 0 1. 0, 0. 008 451 10 1-1/8, 3-1/2 LH 2 32.5 8 1.0 443

50 D. Photographic Studies For photographic studies a test surface (Figure 4) which could be maintai.r)ed in steady condition was used.. The rectangular dewar was filled with LN2. The camera was loaded with Kodak Par X film. The test surface was introduced into the dewar, initiating film boiling, which was maintained by the cnlectrical cartridge heater. The temperature of the test surface was determin(ed by measuring the output of the two thermocouples Ln the test surface with the potentio-meter. The camera was then brought up to the desired speed, the lght source was switched on and the exposure made. When the first film was made, it was discovered that the test surface was indistinguishable from t.hr? vapor film. T-o determine the location of the test surface, the power supply to the heater was shut off, allowing the test piece to cool. down to the liquid tempe-sature. When all boiling ceased, a second exposure was made at'the same filming speed, as before but for a much shorter duration to give d-ulble expcsu-ires on 4-5 frames, which provid'nd the reference surface. Condit~ionbs undeer which motion pictures were obtained are givrern in Table V.

51 TABLE V CONDITIONS FOR MOTION PICTURES Nominal Height 0 in., 2 in., 4 in., 6 in. Height Covered 3/4 in. Speed/Writing Time 200 frames/sec/l sec 500 frames/sec/O. 5 sec Nominal Height 1 in., 4-1/2 in. Height Covered 1-1/2 in. Speed/Writing Time 200 frames/sec/l sec 500 frames/sec/5 sec (T -T ) OR 30C, 220, 100 w S E. Data Reduction With liquid nitrogen as the test fluid, the range of thermJcouuple output recorded on the recorder chart was determined from the zero-sLuppressicon applied to the recorder and the sensitivity at which it was Operated. The value of the zero-suppression applied was determined from the output of the thermocouple at approximately the desired temperature at which the data were to be obtained; the sensitivity at which the recorder was operated was such as to give a reasonable slope on the recorder. It was found that when the recorder was run at a chart speed at 25 rnr/sec, a writing time of approximately 2-6

52 sec provided a reasonable slope by operating at a sensitivity of 5 iv/division at higher AT and 2 iv/division at lower AT. The heat flux was determined from the relation: rate of change of enthalpy = heat transfer to test section. In calculating the rate of change of enthalpy, a lumped analysis was employed, i. e., it was assumed that the error due to assuming the temperature profile in the section to be independent of time was negligibly small. The justification for this is given in Appendix D, where it is shown that the error in assuming lumped analysis for computing rate of enthalpy change is less than O.050/o. The assumption of lumped analysis is equivalent to saying that the time rate of change of temperature determined at any one location in the test section can be assumed to be valid at all points in the section. In Appendix D one of the assumptions made in justifying this assumption is that the value of the heat transfer coefficient is constant at a given section. Experimental values show that this is approximately the case for film boiling in the range of temperature employed in the present study. We therefore have mO C (T) d - (4.1) or = m C(T) dAT A A dt and

55 h = (4 3) AT To compute the value of q' and h, m, Cp, A, AT, andedAT/dt mu'st be determined. The mass of the test section was determined by weighing the thermocouple after it was made and then weighing the test section-thermocouple combination after attaching the thermocouple to the test section. The area of heat transfer from the test section was determined by measuring the diameter of the test section along two perpendicular diameters and taking the arithmetic average of the two. The thickness of the test sections was measured at four locations. These measurements were made with a vernier calipers reading to 0. 001 in. The value of C at the appropriate temperature was taken from Reference 58, tabup lated values of which are given in Appendix E. The time rate of change of thermocouple output was measured directly from the recorder chart by measuring the local slope and then converted to time rate of change of temperature. The following sample calculation illustrates the method adopted for reducing heat flux data: Test Surface 7 Nominal diameter of test piece, 2.25 in. Test Section, 2 Location of test section, 3 in. above leading edge Weight of thermocouple, 2. 067 gm Weight of section + thermocouple = 80. 619 gm Weight of test section = 78.552 gm = O. 17317 lb

54 Thickness of section at four locations = 0.247 in, 0.250 in., 0.254 in., 0. 249 in. Average thickness = 0. 250 in. Diameter at two locations, 2. 249 in., 2.250 in Average diameter = 2. 2495 in. Area of heat transfer = 3. 14159 x 2.2495 x 0.250 2 = 1. 7668 in. = 0.012269 ft2 (m) 17317 - 14.114 lb/ft2 A 0.012269 Date: 12/25/69 Run #7004: liquid nitrogen 1/2 psig, saturated Zero suppression measured with potentiometer = -2050 pv Sensitivity, 2 wv/div Speed of chart drive: 25 mm/sec Reading obtained = 25 div from zero suppression base Thermocouple output at which data obtained (reference to ice point) 24v = -2050 v + x 25 div = -2000 Av Div Calibration of Thermocouple and Recorder Thermocouple output in liquid nitrogen from potentiometer,-5521 sv Barometric pressure, 29.24 in.Hg = 14.4 psi Liquid nitrogen pressure = 1/2 psig = 14.9 psia Saturation temperature of LN2 corresponding to 14.9 psia = 139.4~R

55 Thermocouple output from standard tables at 159.40R = -5526 Ctv Deviation at - 5526 pev = -5 piv Standard table thermocouple output at -2000 iv = -2000 + -20 x 5 5521 = -2001.8 4v Temperature corresponding to -2001.8 jv Cfrom standard table) 390. 2R Tv AT = T -T 390.2 - 139.4 = 250.8~R w s Thermopower at this temperature = 33 25 = 18. 47 8 OK OR Time Rate of Change of Temperature Thermocouple output change corresponding to 40 divisions on chart paper at 2 gv/div = 80 Wv Temperature change corresponding to 80 v = 4.33R Time for this change = 3.2 sec 4. 3 Time rate of change of temperature = x 3600 3..2 4871.2 OR Hr. C (390. 2~R) = O. 0865/lb ~R (q/A) = C dT A p dt = 14.114 x 0.0865 x 4871.2 = 5466. 1 Btu/hr ft2 Data for subcooled and reduced gravity conditions were similary reduced.

56 F. Measurement of Vapor Film Thickness from Photographic Films The films were projected on a ground glass with an enlargement of approximately ten times. The film gave a, field on the test surface corresponding to a height of approximately 3/4 in. The diameter of the reference wire was 0.040 in. and established the scale of the projected image. The film was positioned to project the double exposed image defining the boundary of the test piece heating surface. The pinch marks on the reference wire established the location of the test section in terms of its height from the leading edge. The distance between the reference wire and the edge of the vapor film on the other images was similarly measured and from these measurements the film thickness was computed. In some of the images, it was difficult to define the vapor film boundary precisely, and in such cases the boundary was averaged over the entire image and the thickness measured. The film thickness was computed at a filming rate of approximately 200 frames/sec after studying the film thickness at 500 frames/sec and 200 frames/ sec under identical conditions and establishing that study of films at 200 frames/sec gave all the desired information. The filming rate was established by counting the number of images in the strip and from the fact that these were exposed in a writing time of 1 sec giving approximately 200 frames/sec or 1/2 sec giving approximately 500 frames/sec.

CHAPTER V MODEL AND ANALYSIS Several analyses are available for the solution of laminar film boiling with a steady interface and have been described earlier in Chapter I, "Literature Survey" (6, 8-16). Little experimental data are available to support the analyses. The region of validity of such analyses has not been defined and from existing experimental evidence, laminar film boiling with a steady interface is unlikely to be encountered except under unusual circumstances such as very near the leading edge, stagnation points, reduced gravity conditions, etco The modelling of film boiling on a vertical surface to predict heat transfer rates is complicated by two main factors: (a) The probable onset of turbulence and insufficient knowledge to define transition from laminar to turbulent flow regime0 (b) Onset of interfacial oscillations of considerable amplitude. At present there is no way of predicting the amplltudes of i-iterfacial oscillations. It will be shown, later, that these interfacial waves play an importalnt role in enhancing heat transfer rates, Recognizing these difficulties, an attempt will be made to predict heat transfer rates in film boiling on vertical surfaces usinrg some of the well known and experimentally proven concepts in single phase turbulent flows, taking into consideration the effect of interfacial waveso 57

58 A vertical surface, immersed in a liquid at its saturation temperature T is maintained at a uniform temperature T > T, inducing film boiling, S W S Figure 12. To find the heat transfer rates, the following assumptions will be made: (i) The liquid is incompressible; within the range of pressure used the density of the vapor is evaluated at the film temperature, and is assumed constant over the entire vapor film. (ii) The vapor has constant properties evaluated at the mean vapor film temperature. (iii) The liquid is uniformly at its saturation temperature and the variation of saturation temperature with height is negligible. (iv) The increase in enthalpy of the vapor as it flows is negligible compared with the heat transfer to the liquid resulting in vaporization. In other words, the heat transfer rate is constant across the vapor film. It is recognized that this is not strictly true. The effect of increase of enthalpy of vapor, is to reduce heat transfer to the liquid leading to a decrease in the rate of vaporization at the interface. This is usually accounted for by applying a, correction factor to the enthalpy of vaporization. Bromley (7) used the correction factor [1 + 0.4 C AT/hfg. Frederking and Clark (57) and Dougal and Rohsenow (56) ha:ve used the factor rl + 0.5 C AT/hfg. In turbulent flows, the major part of the vapor can be expected to be at the mean film temperature and hence, for this application the factor (i + 0.5 C AT/hf ) seems to be more appropriate and will be used.

59 VAPOR LIQUID TWT_ Tx I ( re 12 Flm bong model Figure 12. Film boiling model.

60 (v) Velocity profile and shear stress distribution are not affected by vaporization at the liquid-vapor interface. (vi) The eddy diffusivities for heat and momentum are equal. (vii) Steady state prevails and time averaged values can be used for all parameters. (viii) Heat transfer from the test surface by radiation is negligible and the vapor and liquid are transparent to radiation. (ix) The interfacial velocity is zero. For laminar vapor flow with a smooth interface, Koh (9) has shown that this is a reasonable assumption if the ratio l (0) /(p ) ]l/2 is less than 1.0. For most common fluids this condition is satisfied, e.g., for liquid nitrogen and hydrogen these ratios are 0.014 and 0.067, respectively, and hence the interfacial velocity can be neglected in the laminar region. On a qualitative basis, it can be expected that a similar behavior would persist in the turbulent regime also. (x) Other researchers (39,50) have attempted to seek a parameter to define transition from laminar to turbulent flow. It will be assumed that transition takes place gradually. The universal velocity profile (44) proposed by Spalding is an accepted approximation for single-phase turbulent flows. This will be assumed to be valid for half the vapor film thickness from the heating surface. Coury and Dukler (50) consider the liquid-vapor interface to be rough and have used different velocity profiles for the two halves of the vapor film. However, in the present analysis, from assumption (v), its mirror image will be assumed to be applicable to the other half of the vapor film adjacent to the interface. The velocity profile is expressed as

+ + 1 ku + (ku (ku (ku y = u + 1[e - 1- ku - -] E - 3'4: Fl(U ) (5.1) with k = 0.407, and 1/E = 0.0991. For small values of u, this may be approx+ + + imated to y = u implying a linear velocity profile. For large'values of u, Eq. (5.1) can be approximated to + 1 ku y - e or - E + + u _ 5.7 + 2.5 In y which is the well known logarithmic velocity profile. Figure 13 shows the close correspondence between this velocity profile and Von Karman's threelayer model (48). The main difference lies in the fact that very close to the wall, Von Karman's profile assumes a total absence of turbulent effects. Diessler (53) proposed that this assumption of turbulence effects disappearing at an arbitrary distance from the wall is unrealistic and proposed his velocity profile valid for y < 26 which rendered cM + 0 as y + O; beyond y+ 26, Diessler used the logarithmic velocity profile. Spalding combined these concepts of Diessler and proposed his velocity profile given by Eq. (5.1). The assumption that this expression is valid for all values of film thickness thus yields an approximately linear velocity profile for thin filmsnear the leading edge or close to the heating surface, where viscous effects may be expected to be dominant and hence the flow more nearly laminar, and a logarithmic velocity profile for large values of film thickness away from the leading edge and heating surface.

30 25 20 115 U+ 5.5+2.5 Iny+ (Ref 48) Spalding (Ref 44) Eq.(5.1) 100 101 102 103 104 Figure 13. Comparison of Spalding's universal velocity profile and Karmants three-layer model.

63 (xi) It has been observed that, ingeneral, the interface is not steady but that it oscillates with considerable amplitude —of the order of vapor film thickness. It may be anticipated that the influence of these oscillations on the heat transfer rates is considerable and must be taken into account. As little is known about the effect of such oscillations on the temperature and velocity profiles, the following simple approach will be adopted in an attempt to take into consideration the interfacial oscillations. It will be assumed that the dimensionless temperature profile is unaffected by the oscillations, This can be expressed as T -T $ = w = f(r.); -= T -T w s with 71 = O = o f(O) = O = 1 = 1 f(l) = 1 and q = q k d = k AT f'(0) d (5,2) A dy y dy y=O Consider the case with a steady interface where & is not a function of time, denoted by b(s) and the corresponding heat flux by q'(s). Then q'(s) = k AT f'(O) ) It may be noted that f(q) is independent of time and hence f'(O) is a constant.

64 Let t now be a function of time denoted by 6(t). Since the nature of the oscillation is not known, it is assumed to oscillate sinusoidally about the above mean value b(s) so that 6(t) = b(s) + a sin wt = b(s) [1 + b sin cut] Here a = amplitude of oscillations b = dimensionless amplitude a() --- f = frequency of oscillations 2Tr Then, q'(t), the instantaneous heat transfer is given by q'(t) = k AT f'(O) -t) _ k AT f'(O) 1 (5 6(s) 1 + b sin ut Replacing k T f(o) by q'(s), q'(s) q'(t) = q'(s) (5.4) q(t) 1 + b sin wt The time averaged value of the heat flux is then obtained by t 2T/f q( s)/ d q'(t) = - 2 1 + b sin c t = c q'(s) (5.5)

with J1 b2 The coefficient C is an indication of the extent of increase in heat transfer due to interfacial oscillations and may be termed the heat transfer enhancement coefficient. The maximum limiting value of "b" is unity, when the liquid comes in contact with the heating surface(at which point the "film boiling" model breaks down). Its minimum value is zero, giving a steady interface. In general, 0 < b < land the value of the coefficient C > 1. Thus the effect of interfacial oscillations is to increase the heat flux as compared with a steady interface. This is also confirmed by Coury and Dukler (50) who measured the instantaneous heat transfer rates. There is, as yet, no way to predict the amplitude of oscillations from first principles and the value of "C" must be found by some other means. One possibility is to compute it from measurements of vapor film thickness, and another is to determine it empirically from measurements of heat flux. This is discussed in detail under Chapter VI, "Results and Discussions." (xii) For the vapor film, boundary layer equations are applicable and p = p(x). In particular, p f p(y). With these assumptions we have, from the velocity profile + + 1 +ku (ku) (k)_ _ (ku y u +- 1 - ku (1) From the expression for shear stress we h:e From the expression for shear stress we have

66 _ 0 M du IP _v dy or E + M 1 V + du k k+ ku ku+)2 ku+ +~ E L l- ku - ()2 (ku ) F(u) (5.6) E 2: 3 2 From assumption (vi) we have _H _ _M + _H =M F (u ) (5-7) V V 2 From assumption (iv) the differential form of energy equation takes the form C,' q' _ w dT pC C (EH + ) dy -H 1 dT -v Pr+ dy (5.8) Letting p C u (T -T) 9 =- ( ) (5 9) q'(s) and, for T = T s p+ C u (T -T) (5.9a) w q'(s) and substituting Eq. (5.9) in Eq. (5.8) we get de l ~dy9 ~~ _eH/v~~~ 1+~ ~ l(5.10) dy + EH/V+l Pr

67 Noting, from Eq. (5.1) + k ku+ (ku+)2 (ku+3 F(u) (5.) dy = 1 + - 1- (ku) - F (u. we get.... F.(u ) + (5.12) du F (u)+ Pr It has been assumed that the velocity profile and shear stress distribution are not influenced by conditions at the interface and this leads to a symmetric velocity distribution, with the velocity distribution in 6/2 < y < 6 being the mirror image of that in 0 < y < F/2. Similarly, for the temperature we expect the temperature profile for + in 6/2 < y < F to be the inverted mirror image of that in 0 < y < 6/2. These profiles are indicated in Figure 14. From a consideration of these profiles we expect -te temperature at y 6 F/2 to be (Tw +T)/2. Denoting the corresponding dimensionless temperature by 9 /2, Eq. (5.12) can be integrated to yield u F(u) + M 3 + W =2 1 du (5.13) W 0 F (u+) + - F(t2 Pr + + + + where uM is the value of u at y = 6/2. It may be noted that since F3(u) =F2(u ) + 1, for Pr = 1, the temperature profile is identical with the velocity profile in O < y < 6/2 and is the inverted image of it in 6/2 < y < 6. From conservation of mass, for the control volume with its boundaries in the vapor, Figure 15A we have d 6 -f pudy = m (5.14) dx 0

68 VAPOR LIQUID Tw VELOCITY PROFILE TEMPERATURE PROFILE dx ~*~* x\ Ts Fie 14 Velocity a erature profiles in por filmy Figure 14. Velocity and temperature profiles in vapor film.

69 VAPOR LIQUID SURFACE —-*, udy + udy Ts TW, o dorh _ 1 A. CONTINUITY fpudy LIQUID -VAPOR v8 d8 INTERFACE pucp Tdy + d ucpTdy, - dx 8 qI B ENERGY fpucp Tdy udy+dx f dy -d. - " - - dx frli I i Iti C. MOMEN UM x, Fg e15 u2dy

70 where mi = rate of mass crossing from the liquid-vapor interface into the control volume in the vapor space. To evaluate mi we have from conservation of energy for a steady flow process, control volume-Figure 15B, ~H +q. = ZH -W in in out s where H. = enthalpy flow into the control volume in H = enthalpy flow out from the C.V. out q. = heat transfer into the C.V. lln all enthalpy terms are referenced above the saturation temperature of vapor. W shaft work Applying this to the control volume (and noting that W = 0) we get per unit width in the z-direction f pu C T dy + q' dx - q' dx o0 p w i 5 d d 0 pu C T dy + - J pu C T dy dx (5.15) 0 P dx 0 p Here q' = heat flux from the heating surface and w q' - heat flux from the vapor to the liquid at the interface 1 causing mass flux rn to crcss into the vapor space by evaporation of the liquid. Replacing q by m h we obtain I = fg = ihh +-f u C T dy (5.16)

71 The last term in Eq. (5.16) represents the increase in enthalpy of the vapor that enters the C.V. at x which for fully developed temperature profile is zero, and the increase in enthalpy of the mass m in crossing the C.V. at the liquid-vapor interface. A correction to take the latter into account has been made by using the modified value h' in place of hfg so that Eq. (5.16) fg takes the form q?....t= (5.17) ht, htfh fg fg The L.H.S. of (5.14), after changing the variables, yields dx 0 pudy =2 pv /2u dy d M~ + + =2 d pv JO u F( u) du I+ l + kuj + +2 =2 pv! u +- kuM e - ku - (ku) M E M M M (kuM) (kuM) duM 2' 3' dx du + M 2 pv F (u ) (5.18) 4 M dx with kf (ku+)3 4 3 +ku (ku ) ++$ M 2 M M F (u) - u + -ku e - (ku) - (ku ) - 4M M E M M M 2 3. (5.18a) Substituting Eqs. (5.17) and (5.18) into (5.14), we get du dx F4 (u+) 2h'g pv

72 Momentum equation applied to the control volume, Figure 15C consistant with assumption (xii) gives 2d S0/2 2 dp E Pg (5.20) 2-f pu dy = - T -T - dx O dx i w a /2 2 L.H.S. of Eq. (5.20) - 2 x So pu dy dx 0 d N +2 + + = d - f pu* v u F (u ) du dx 0 3 d* du 2 pv F (u (5.21) SM dx 6M dx where F (uM = u F(u ) du 03 ku ku +5+ + _ M _1 + k -ku+)2e M 2 ku e + 2 e 2 M M k E (kuM)3 (kuM)4 (ku)5 (ku M) 5 14~- 210(5. 22) 3 4 10 36 and F (u) uM F (u) (5.23) 6M M 5 M From assumption (xii) we have!d' p (5.24) dx/vapor dx/liquid (5.24) From assumption (v) we have -- -- = * (5.25) P P

73 From Eq. (5o1) and definition of 5, we obtain + - v - = v ~F(uF ) (5.26) 2 u* 2 u* 1 M Combining Eqs. ( 520), (5.21), (5.24), (5.25), and (5.26), we obtain du F M) dx + u* F6(uM) M 5\ M dx 6 M dx PQ P) 1(U M u* (U5*227) Q g F u (5.27) = U* W We thus end up with a system of equations to be solved, given by Eqs. (5.5), (5.9a), (5.13), (5.19), and (5.27) repeated below in sequence for convenience, and redesignated as Eqs. (5.28), q'(t) = C q'(s) p C u*(T -T ) -I ) = - p + w u+ F (u+) + = 2 J du (5.28) w 0 F (u) + __ 2 Pr du M 1 gqj(t) dx + 2h' pv 4( M) du (P -p) F (u) 2 ~F (U du* + M u* F (u ) - + u* F6(U ) g-*M dx 6u dx P U v Here the forms of the functions F1, F2, F3, F4, F5, and F6 are given by Eqs. (5o1), (5.6), (5011), (5.18a), (5o22), and (5.I13) For the solution of the above system of equations, it is necessary to have the value of the heat transfer enhancement coefficient C and the values of uM and u* at some location x = x (say).

74 The value of the coefficient can be expected to be a function of both AT and the height x for a given liquid. It may be expected that the dimensionless amplitude of oscillations is relatively small near the leading edge where interfacial instabilities begin to appear, increasing with height thereafter, There are no known ways of determining its value and recourse will have to be taken- to find its value by some semi-empirical relationship between C and another kiowrn parameter based on experimental results, A more detailed discussionla o'n the value of C and its variatior with height is contained in Chapter VI. For the present it is assumed that the function C = C(x) is known. To initialize the values of u* and uM, Bromley's correlations (6) were used, From his solution we have 2 AS 2 u = (n-n ) (5.29) p -p with A - - p v S A62 u (5.50) max 8(5.3) (5031) du ~ -.. F du ___ - (5,32) w dy jy=0 p v 2 Recastiv-g these we obtain l* L PjP P g (5533)

75 u 2! 2 1 + max AS p 2 2 M u* 8 -p g8 PIP _ 5 16 k AT x 8 0177 LP~ g v 8 (5~34) From Eqs. (5.31), (5.33), and (5,34), the values of u+ can be calculated for any given value of x and the numerical integration of the system of Eqs. (5.28) can proceed. These nonlinear equations were numerically solved on an IBM 360 computer using Runga Kutta procedure. In the actual solution the numerical procedure was started with uM = 2 and the corresponding values of x and u* computed.

CHAPTER VI RESULTS AND DISCUSSIONS A. Validity of Experimental Technique The objective of the present work was to obtain local heat transfer rates in film boiling on a plane vertical surface. To eliminate the edge effects in finite plane surfaces, cylindrical surfaces were used; to obtain local heat flux values, the time rate of change of enthalpy of the test surface was computed. Neglecting heat transfer by radiatioin, it was assumed that this change in enthalpy was due solely to heat transfer to the surrounding saturated liquid. The validity of the use of a cylindrical surface under transient conditions to give data for plane surface under steady state conditions and the assumption of negligible radiation from the surface will now be examined. lc SIMULATION OF A PLANE SURFACE BY A CYLINDRICAL SURFACE The principal differences between a cylindrical surface and a plane surface arise from two sources: effect of surface tension and the change in area with radius. Within the vapor film, surface tension is of no consideration. At the interface, however, its effects on the pressure within the vapor film should be considered as cylindrical test surfaces were used. One of the assumptions in the analysis is that the pressure in the vapor film is a function of the height x only and does not vary in a horizontal plane. But at the interface, because i76

77 of the curvature of the test surface, surface tension introduces a pressure difference between the liquid and the vapor, whose magnitude is given by 1A1 (6.1) H V where RH and RV are the principal radii of curvature. One of the principal radii of curvature will be taken to be the minimum radius of the test surface equal to 0.5 in. in the present experiments. The curvature in the vertical plane is caused by the thickening of the vapor film and interfacial waves. There is some difficulty in estimating the value of RV but for simplicity it will be arbitrarily set equal to RF so that AP = 2a/RH. For nitrogen C = 8.8 dynes/cm = 63. 4 x 10 lbf/ft so that AP = 3. Q4 x 10-2 lbf/ft For hydrogen o = 8.8 dynes/cm = 14.4 x 10-5 lbf/ft so that AP 0.692 x 10-2 lbf/ft2 The lowest pressure at which the experiments were run was - 14. 7 psia (2140 lbf/ft ) so that in comparison with this pressure, the change in pressure at the interface due to surface tension is, indeed, negligible. It is possible that at the leading edge RH is small and AP is of some significance. But such effects at the leading edge are ignored as, in any case, they are confined to a very small height from the leading edge. The change in area with radius can be ignored if the ratio of the vapor film thickness to the radius of the heating surface 6/r is much less than unity. From the solution to the system of Eqs. (5.28) resulting from the present analysis, the value of this ratio 6/r lies between O. 1 and. () 05. From the results of the photographic studies it has a value between ). 1 and 0. 2.

78 To show that the geometrical effects of using a cylindrical test surface as compared with a plane surface are negligible, reference is made to Figure 16 where heat flux values obtained from 1 in. dia. cylindrical test surfaces and those obtained from 2-1/4 in. dia test surfaces at the common location of 3 in. above the leading edge are represented. Each data point in Figure 16 represents the mean of a number of runs made with a test surface, the number of such runs being indicated next to each data point. The range of values obtained with each surface is indicated by a vertical line, passing through the pont, the extremities of which represent the maximum and minimum values obtaihned with the test surface, If the geometry of the test surface had any appreciable effect on heat transfer rates, heat flux values obtained with 2-1/4 in. dia test surfaces would have been considerably different from those obtained. with 1 in. dia test surfaces. Within the scatter of experimental data, heat flux values obtained with 2-1/4 in. dia test surface agree with these obtained with 1 in. dia test surfaces and it is concluded that for the present applications, the use of cylindrical surfaces of 1 in. dia and above dc anoct introduce any significant errors due to effects of geometry and surface tensio1n as compared with a plane surface. 2. USE OF TRANSIENT TECHNIQUE TO OBTAIN STEADY STATE DATA To, estimate the effect of employing atransient technique to obtain data u~nd.er steady state conditions, consider the energy equation in its simplified form consistent with the assumptions made in Chapter V, t'odel and Analysis." The oiff:erential form of the energy equation for the transient case (as

79 8000 7000 K5 x5!5 5 13 AT =315~R 6000 5 Y5 -5 13,3 AT =2510R 5000 ILL 1E~~3 5 5 x5 3 3 AT =204~R 4000 3!3 T 2000 +3 3 T = MOO~R 2000 2 4 5 6 7 Test Surface Identification |,1" 1" 1" 21,, 21" Test Surface ~I I I3 234 Diameter Figure 16. Comparison of heat flux-1 in. dia and 2-1/4 in. dia heating surfaces.

80 opposed to the steady case resulting in. Eqo (5.8) takes the form aT q1y (6~ 2) Ot - pC ay p If, in the nondimensional form of Eq. (6.2), the time rate of change of temperature is shown to be small compared to unity, the transient technique can be expected to give results close to that under steady state conditions. For nondimensionalizing the different variables, the characteristic temperature will be taken to be AT, the difference between the heater surface temperature and the saturation temperature of the boiling liquid. The characteristic time will be based on a representative length and a representative velocity. The choice of a representative length will be the height of the test piece L. In the turbulent regime, the average velocity is close to the max-velocity and hence an. arbitrary value of 0O 75 U will be taken to be the characteristic max velocity. With these nondimensional parameters, we have T t AT L/u (6.3) q Q&~ __Y y/L pC uAT a aQ(6 (6.4) %7._ %r

If 6e/aT << 1, aQ/6Y can be assumed to be zero, which is the steady state condition. To find the value of ae/6T, we note that at Y = 0, the vapor undergoes the greatest time rate of change of temperature (equal to that of the test surface) since the temperature of the other boundary-the liquid-remains constant at its saturation value. Computed values of 0e/6T are given in Table VI. TABLE VI TRANSIENT TECHNIQUE-RATE OF CHANGE OF DIMENSIONLESS TEMPERATURE aT ~R Liquid AT(~R) u (ft/hr) L(ft) at (hr LN2 515 66,000 0. 9,000 0. 00022 LN2 100 45,000 0.5 5,700 0.00055 LH2 400 90, 000 0.5 24, 000 0.00033 LH2 100 45,000 o. 5 10, 000 0. 0011 In Table VI,u is taken as 0. 75 u, with u obtained from the solutions of max max Eqs. (5.28). aT/6t values are experimental values. From these computations it is seen that the nondimensional time rate of change of temperature is insdeed small and hence the transient technique employed in the present experiments can be expected to give acceptable equivalent steady state results. To further test the validity of the transient technique employed in the present work to give data under steady conditions, comparison will be made between heat flux values obtained under these two conditions.

82 Column "A'" in Table VII gives average heat flux values obtained with the steady state test surface used for photographic studies described in Section A-2, Chapter II. This test surface was one continuous piece and hence it is possible to measure only the overall mean heat transfer rate. Column "B" gives the integrated heat flux values computed by using the local heat transfer rates obtained with the transient technique. These two are seen to agree quite well, thus indicating that employing the transient technique to obtain steady state values is acceptable. TABLE VII COMPARISON OF HEAT FLUX VALUES OBTAINED UNDER STEADY STATE CONDITIONS AND TRANSIENT CONDITIONS LIQUID NITROGEN AT, (Steady Stat B OBtu/hr ft2) (Transient Btu/hr ft2) 315 7050-7350 7011 200 4690 4692 100 3400 3543 3. HEAT TRANSFER BY RADIATION It is assumed that the vapor is transparent to radiant heat flux from the ambient or the heater surface. In order to assess the heat transfer by radiation from the test surface, several conservative assumptions will be made. In the present series of experiments relatively low heater surface temperatures

of the order of 500~R were used. The heater surface was immersed in liquid nitrogen or liquid hydrogen, and to obtain the upper limit of heat transfer by radiation an ambient temperature of O0R will be assumed. For copper, values of 0.01-0.07 Btu/hr ft2 R are given for the emissivity (37), the lower value being for polished surface and the higher value for "commercial, scraped shiny but not mirror-like" surface. The test surfaces used were given "mirror-like" finish but again, to find the upper limit, the higher value for emissivity will be used. With these values, for a test surface temperature of 5000R, we have -8 4 q' = 0.072 x 0.1713 x 10 x 500 Radiation 2 - 7.7 Btu/hr ft For lower temperatures, these are much lower and for all surface temperatures used, this forms less than 0. 1% of the computed heat flux and therefore ignored. B. Results Figures 17-26 are plots of experimental values of heat flux q' vs. height of the test surface. Each of Figures 17-24 includes: (i) Experimental data for one value of ATo The data point is the mean of several runs under identical conditions, the vertical line through each point showing the maximum and minimum of experimertal values obtained.

1 0,000 9000 ~~~~9000 L ~SU(Ref 39) 8000O - C= 1.78 C= 1.5 5000 m 4000- C= 1.0l 3000 romley (Ref 6) 2000 1 I I 1 2 3 4 5 6 -Fu X (Inches) Figure 17. Effect of height on heat flux —film boiling. N2. AT - 315~R.

85 10,000 9000h UU(Ref 39) 8000 7000 2 6000 C= 1.7 U.T 5000 = 1[ - C=:1.65 z 4000 2000 Bromley (Ref. 6) 2000 1 2 3 4 5 6 X (Inches) Figure 18. Effect of height on heat flux-film boiling. LN2. AT = 2510R.

86 10,000 9000 8000 HSU(Ref39) 7000 6000 5000k C= I.7 IA C= 1.6 M 4000 3000 2000 Bromley (Ref 6) 1500 I, I I I 2 3 4 5 6 - X (Inches) Figure 19. Effect of height on heat flux-film boiling. LN2. AT = 204R.

87 7000. 6000 ~ 5000 m 3000 C-2.0 C= 1.78 2000 - Bromley(Ref 6) I000 1000 1 2 3 4 5 6 -- X (Inches) Figure 20. Effect of height on heat flux —film boiling. LN2. AT 100'

88 30,000ooo C= 2.0 C:2.3 20HSU(Ref 39) 20,000 -,. =1.7 C=1.9 lo,ooo lt ~~ _8Q00~~ ~Bromley (Ref 6) 6000 I I L I _ _ 2 3 4 5 6 - X (Inches) Figure 21. Effect of height on heat flux —film boiling. LHE2. AT = 400oR. 20,000 8000\. C=I.8 Bromley (Ref 6) 4000-,I I I I I 4 I 2 3 4 5 6 - X (Inches) Figure 22. Effect of height on heat flux —film boiling. IJH2. AT = 3(00~R.

89 20,000 I HSU (Ref 39) 4000 2 3 4 5 6 - X (Inches) Figure 23. Effect of height on heat flux-film boiling. LH2. AT = 200R. I0,000 I I I 8000I 6000t C=2. L 4000 ir I \ ~/ C= 1..7 DF -\ ~~C= 1.9 C= 1.8 - 2000 tI I 1000I 2 3 4 5 6 -- HX (Inches) Figure 24. Effect of height on heat flux —film boiling. LH2. AT = 200~R.

9o AT a Subcooling Pressure ~R 9 ~R Psig o 337 I 21.1 34 & 357 I 0 0.5 o 354 0.008 0 0.5 * 357 I 0 0.5 (Data Obtained Just Prior to Drops) 20,000 AT - 337oR 00 ~Subcooled 21. 1~R 034 Psig AT =350~R (Ref 54) 10,000 I"Dia Sphere AT=357~R 3ATM (SAT) 0.5 Psig (Sat.) "- 8000 Present Analysis - CtU_- _ _ L C =1.8:I 6000 t AT = 3500R (Ref 54) 0 I"0Dia Sphere a I ATM (SAT) 4000 | =0.008.oo AT = 354~R Experimental Data = o.ooe Bromley (Ref 6) \, —------- a/g= 0.016 a /g =0.008 I000 I 2 3 4 5 -e X (Inches) Figure 2~. Effect of heightj gravity, and subcooling on hea-t flux. t~2.

91 I I II AT a Subcooling Pressure ~R 9 ~R Psig o 449.3 1 8.1 32.5 * 457.4 1 0 0.5 o 453.6 0.008 0 0.5 40,000 Subcooled 8.1~R 32.5 psig,* * AT = 4570R (Sat.) 20,000~ t Present Analysis C = 2.4 10,000 a-=008 AT = 453~R 6000 -. o o o Experimental Data 4000 Bromley (Ref 6) 2000 2000 1 2 3 4 5 o X (Inches) Figure 26. Effect of height) gravity, and subcooling on heat flux. LH2.

92 (ii) Several curves showing variation of heat flux with height as predicted from the present analysis-Eqs. (. 28) for different values of the heat transfer enhancement coefficient, C, which indicates the influence of interfacial oscillations. The corresponding value of C for each curve, assumed constant over the entire height, is indicated in the plots. (iii) Predictions from the laminar analysis of Bromley (6) and from the turbulent model of Hsu (39). Figures 17-20 are for liquid nitrogen at nominal AT values of 315~R, 2510R, 204~R, and 100~R at 0.5 psig and a/g = 1 and Figures 21-24 are for liquid hydrogen at nominal AT values of 400~R, 3000R, 2000R, and 100~R at 0.5 psig and a/g = 1. Five sets of data were taken in liquid nitrogen at each test condition. The plots in Figures 17-20 include data obtained from both 1 in. dia and 2-1/4 in. dia test surfaces. Figures 21-24 for liquid hydrogen represent the mean of experimental values from three runs with 1 in. dia test surfaces. Figures 25 and 26 show: (i) Experimental values of heat flux vs. height for a/g = 1, a/g 0. ~08 for one value of AT at 0.5 psig. (ii) Experimental values of heat flux vs. height for subcooled liquid for one value of AT at a/g = 1, at a pressure higher than 0.5 psig. (iii) Bromley's (6) predictions of q' - x for a/g = 0.008 and a/g = 0.016 for liquid nitrogen and a/g = O. 008 for liquid hydrogen.

93 (iv) Predictions of q' vs. x from present analysis with a constant heat transfer enhancement coefficient C = 1.8 for liquid nitrogen and 2.4 for liquid hydrogen. Figure 25 shows the above q' vs. x values for liquid nitrogen; a subcooling of 21. 1~R at 34 psig was obtained. Figure 26 is a similar plot for liquid hydrogen; a subcooling of 8. 1~R at a pressure of 32.5 psig was obtained. In computing the predictions from the present analysis, properties of nitrogen and hydrogen were evaluated at the film temperature-the arithmetic mean of the surface and liquid temperatures. Appendix E gives the values used in the analysis for nitrogen and hydrogen and their sources. C. Discussion 1. VALIDITY OF LAMINAR ANALYSIS In Figures 17-24, it is clearly seen that the laminar analysis of Bromley (6) with a steady interface predicts much lower values than cobtained, the departure of predictions from experimental values being greater for higher values of x. For liquid nitrogen, for example, at a AT 315~R experimental values are 18.2% higher at a height of 1/4 in. and 212% higher at a height of 5-5/8 in. than predicted by laminar analysis. For liquid hydrogen, at a AT = 4000R, the corresponding figures are 4.25% and 171%. This trend shows that the assumptions under which Bromley derived his correlations are probably valid only near the leading edge.

Of greater importance than the deviation from experimental values is the qualitative difference between the predictions and actual values. Laminar analysis (6) predicts a heat flux which is a continuously decreasing function of height. But experimental values clearly establish that there is a reduction in heat flux with height for small values of the height x, though the reduction is not as high as predicted in the laminar analysis, the heat flux reaches a minimum value and reversing the trend, begins to increase with height; the rate of increase is much smaller than the rate of reduction observed close to the leading edge. 2. EFFECT OF TURBULENCE The first attempt to explain this departure of experimental values from those predicted by laminar analysis was made by Hsu (39). He used a two-layer model in the turbulent region, a laminar sublayer adjacent to the heating surface where both the velocity and temperature distributions are linear, and a turbulent core where both velocity and temperature are uniform; the interface was assumed to be steady and smooth. The predictions using his analysis are al soc shown in Figures 17-24. His assumption that the temperature in the turbulerL core is the saturati.on temperature and all the temperature drop takes place in the laminar sublayer appears unrealistic and has been questioned by Dougall and Rohsenow (56). In liquid nitrogen, experimental values are lower than predictions from Hsu's theory-about 5Co lower at AT = 315~R and height x =_ 5-5/8 in. The predictions are high for other values of AT in liquid nitr.oge~J.; the extent of deviation varies with height, being low for low values

95 of x and then progressively increasing with x. For liquid hydrogen, the predictions are high for low values of aT but this deviation decreases with an increase in AT, till at AT = 400~R, Hsu's predictions are almost a perfect fit for the experimental data. Considering the simplifications made in his model, this fit is indeed remarkable. So far, no definite study has been made to determine the onset of turbulence in film boiling. Generally, attempts have been made to apply the traditionally accepted views on transition to film boiling with some modifications. In condensation, values of transition Reynolds number based on equivalent hydraulic diameter, 4r/4L = 1800 to 400 (36) have been used. For film boiling Hsu (39) used a value of Re = 100 to signify transition to turbulence, the Reynolds number being evaluated at the maximum vapor velocity. In a recent work Coury and Dukler (5C) have used a value of 35 for the transition Reynolds number in film boiling. There are several complications that must be considered in specifying the transition of the laminar vapor flow to turbulent flow. In general, vaporization at an interface, which is physically equivalent to blowing, and heat transfer from a surface have destabilizing effects (48). It has also been remarked (48) that there is a possibility that the decrease in the viscosityof liquid at higher temperatures may have a stabilizing effect. Frederking (35) has given a linearized analysis of the onset of instability in film boiling but, as he has also remarked, -the onset of instability does not necessarily indicate that transition to turbulence will take place. He has

96 reported values of transition Reynolds number ranging from 15 to 200 for falling liquid films. In the present approximate analysis, no critical Reynolds number has been used to signify transition to turbulence. As indicated in Chapter V, "Model and Analysis," the universal velocity profile (Eq. (5.1)) used is assumed valid in the entire flow field. This gives a straight line velocity distribution and a very small value of CH/V (compared with 1/Pr) for small values of dimensionless film thickness y+. The flow can be expected to be laminar for small values cf y+ when molecular diffusion predominates over any turbulent effects. The values of eH/v as a function of y+,Eqs. (5.6) and (5.7), for the profile employed are given in detail for values of y+ up to 10 in Table VIl,o Figure 27 shows a plot of y+, Re (= 2F/i) and C H/V. From Table VIII and Figure 27 it is seen that ce/v is quite small for small values of y+. The heat transfer across the vapor film is given by Eq. (5. 13) reproduced below: u F (U 0 -2 F e S / I).Fu du (5. 13) w+2 where F2(u ) = em/ H/V. For 1/Pr - 1 0O then IH/v is less than 0. 46 x -l + 10 for y < 5 and begins to increase until it is of the same order as 1/Pr at around y 10; thereafter it begins to increase rapidly and for y -40 1/Pr becomes insignificant in comparison with EH/V, indicating that in this region molecular diffusion is of little importance compared with eddy diffusivityo This implies that, so far as eddyr diffusivity or the effects of turbulence Cn heat transfer is concerned, it begins to be of significance at

10,000 I I I I I i i 140 9000 -120 7000- -100 z Re 5000- - 80 3000- E 60 VH 1000 - - 40 500 - 20 SCALE CHANGE 10 20 30 40 50 100 150 200 250 300.-. y Figure 27. Relation between y, Re, and (EH/v) for universal velocity profile Eq. (5.1).

98 TABLE Vi:II VALUES OF EDDY DIFFUSIVITIES + + Y tH/V| Y EH/v 0. 2 0. 68 x 10 7.3 0. 22 0. 4 0.12 x 10- 8.6 o. 43 0. 6 0.62 x 10o 10. 1 0.78 1.0 0.5 x 10 12.2 1.37 2. ( 0. 88 x 1o-3 19.1 3.83 3. o 0.49 x o10 339 9.86 4. 0.17 x lo10 67.9 24.13 5.0 0.46 x 101 146.7 57.22 6.1 0.11 328.6 132.97 y - 10. If Re is defined oin the basis of mass flow rate, Re = 2r/g, y. 10) ccrresponds to a Re; 100. It is interesting to note that Hsu (39) als, usd a Re - 10 to signify transition o-f laminar vapor film to turbulence in his analysis, though based on a somewhat different reasoning. The profile used implies a Reynolds number based on mass rate of flow wh~ich depends on the value of y. If one used Von Karman's three-layer model in stead, then yi 30 for the turbulent core, and implies a transition Re 60). Considering the destabilizing effects of vaporization at the liquidvapor intuterface and heat transfer from the surface in film boiling, it seems mo~re appropriate to consider that turbulent effects begin to appear at values

99 of Re lower than that implicit in the three-layer model. Therefore, as an alternative, portions of the three-layer model may be used as appropriate, depending on the value of Ymax The universal velocity profile employed here has the advantage that it is a reasonably good approximation for all values of + + u+ (and y ). As has been remarked earlier, eH/v becomes significant max max around y = 10 and Re - 100 for 1/Pr I. Also above y = 10, the velocity distribution begins to show logarithmic behavior. Hence it may be considered that a critical transition Re - 100 is implied in the present analysis, above which turbulence effects begin to dominate over molecular diffusion. Using the velocity profile Eq. (5. 1) and the implied values of eddy diffusivities, and ignoring the effects of interfacial oscillations, predictions from the present analysis are shown in Figure 17, with C = 1. O. This predicts higher heat flux values than predicted by laminar analysis (6), the heat flux reaches a minimum and begins to increase gradually. Qualitatively the predictions show the same trend as experimental values but the departure from the experimental values is significant-the prediction being about 50& lower than the actual value at a height of 5-5/8 in. for liquid nitrogen at a AT = 315 R. The height at which the minimum heat flux is predicted is also considerably greater than obtained in experiments. It is, therefore, clear that the onset of turbulence alone will not explain all the departures from laminar analyses. 3. EFFECT OF INTERFACIAL OSCILLATIONS In the previous section, it was concluded that the onset of turbulence alone is not sufficient to explain the departure of predictions from

100 experimental values. In Chapter V, under assumption (ix) it was shown that interfacial oscillations will increase heat transfer rates as compared with a smooth steady interface. Figures 28-34 show photographs of film boiling in liquid nitrogen for AT values of 315~R, 204~)R, and 100~R at three different heights. The scale of the photographs, position and AT are indicated in each set of photographs. These were taken with a high-speed camera and the effective filming speed for each set is indicated in terms of frames per second. As can be seen from the photographs, the vapor is opaque to the light from the source and in order to determine the location of the heating surface a few frames were double exposed when there was no boiling. Such a double exposed frame is also shown in each set. To establish the location, x, of the heating surface and the scale for the photographs a.040 in. dia wire with pinch marks at regular intervals was stretched parallel to the heating surface and can be seen in the photographs. Photographs in Figures 28, 31, and 33 show that even very close to the leading edge, the interface begins to oscillate and the assumption of a steady interface, except, possibly, very close to the leading edge is unrealistic, particularly with the large amplitudes of oscillations observed at some distance away from the leading edge which tends to enhance heat transfer rates c onsiderably. Frederking (35) has given an analytical solution to the problem of interfacial instability in film boiling assuming a parabolic velocity profile for the vapor film. He concludes that for all values of Re6, there is a finite range of unstable wave numbers such that the flow never is completely stable.

DOUBLE~~~~~~ DOUBLE DOUBLE EXPOSEDEXPOSED — FRAME 5 10 5 10 INN,~~~~~~~~~~ 4~~~~~~~~ ": 4 9't:: ~~~~~~~~~~~~~.:::':,: 0,040 in. L,:~ 8 dia. wire 3~~~~~~~~~~~~~~~~~ 3 2~ 2 It.i:i...!.!?:!::: ~~ ~~~ ~~ ~~~~~ ~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:j:: 6 6 -,:~:::~ 0.0:: 4 08 i n. "..... i~~~~~~~~~~~~~~~~~~~~~~~B~ ~~~~~~''':ii~~ D: ~~~~~~~~~~~~~~~~~~~~~~~ii::i:::: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~::::::::::::::::: Figure 28. Film boiling: LN2; AT = 315R; Figure 29. Film boiling: LN2; AT = 315 R; x = 0-1 in.; 105 frames/sec. x = 1.5-2.25 in.; 103 frames/sec.

102 5 10 i ~~ l.g. l _..E,,.,..,':': I0 3..... 0.040in. d ia. wi.re 2 l: E..: 6 I -16 Figure 30. Film boiling: LN2; AT 315 I~R; x = 4-5 in.; 110 frames/see.

5 10 5 10 4 9 499 3 ~1 i _ ]0.040 in- ~~~~~~~~~~~~~~~~dia.~~~~~~~~~~~~~~~ wire.,, 0 22 il77 2 Figure 31. Film boiling,: LN2; AT = 204R; Figure 32. Film boiling: LN2; AT = x = 0-1 in.; 106 frames/sec. x = 2-3 in.; 110 frames/sec.

5 010 5 10 99~ 4:] E 9 0.040 in. die. wire 8 3 8 Leading Edge -Leading Edge l6 61l; 6 Figure 33. Film boiling: LN2; AT = 100R; Figure 34. Film boiling: LN2; AT = 100~R; x = 0-1 in.; 104 frames/sec. x = 1.5-2.5 in.; 109 frames/sec.

105 This analysis is based on a plane interface. In film boiling there is a thickening of the vapor film because of vaporization of the liquid, giving rise to a finite curvature of the interface. This is particularly significant near the leading edge as can be observed from Figures 28, 31 and 33, showing photographs of film boiling in liquid nitrogen near the leading edge and is also indicated in Figure 35 showing the model for predicting the instability of the interface. Analysis for two fluids of different densities flowing with some relative velocity u (52) shows that the critical wavelengths for small velocities are large. Hence the onset of instability is indicated by the appearance of waves of long wavelengths. Near the leading edge, velocities are small, being zero at the leading edge itself, and hence the critical wavelengths are large in this region. The question then is, does the finite curvature of- the interface at the leading edge inhibit the appearance of waves of wavelength larger than a certain multiple of the height? As indicated in Figure 35 showing the model for instability, as an approximation one can visualize the curved interface near the leading edge to be a part of a wave, of wavelength nx, where n is an integer and x is the distance from the leading edge. At any height, the vapor film thickness 6 is increasing with the height x because of the vaporization of the liquid and hence d5/dx is positive at every x so that n cannot take a value less than 4. Thus the longest wavelength of any disturbance that can be superimposed on the interface is X < 4x. At a given height x = x, the vapor velocity is u. We may now hypothesize that for instabilities to occur at x, the critical wavelength X < 4x; if x > 4x it is a

106 stable configuration. From Reference 52, we have for parallel flows in a vertical plane with one fluid (liquid in the present case) stationary, the condition for the stability of the interface given by VAPOR;VAPOR |LIQUID 2 _k__ 1 2 u < + (6.5) 1 2 p+p Ts where - = _ _p,6. c p+p 2 pF+ p k = wave number X = wavelength Figure 35. Model for predicting a = surface tension instability of interface. From Eq. (6.5), the critical wave number is given by pp 2 ~P u k = (6.6) c p+p C Thus every height x is associated with a critical wavelength and wave number X and k and a critical velocity u given by Eq. (6.6). Also, from the lamc c c inar solution (6), at a given x the vapor has a maximum velocity u. It is hypothesized that if at any given value of x, uv(X) > u (x) then instabilities are possible; if u (x) < u (x) then it is a stable configuration. v c Figure 36 is a plot of u and u vs. x for liquid nitrogen and liquid v c hydrogen at different values of AT. At some x = x^, u (x) = u (x) and

154 LH2 T= 4000R 15 LN2 17 =3/5"R Uv (Ref 6),, 1010 0 I 0 U 0 Uv(Ref 6) Ucr (X= Ox) (X=4x) 0L..... I_......____ 10 I 20 30 40 0 10 20 30 40 15 L H2 A1 /000PR 1 L/V2 z3T =/0001? X0 I10 Uv (Ref 6) 5 r Uv(Ref 6 Ucr " (X= 4x) (X.17'= 4x) 10 20 30 40 0 10 20 30 40 WX x 103(Ft) -— X x 103(Ft) Figure 36. Critical velocity vs. height for interfacial instability: a/g = 1.

108 interfacial instabilities appear. To the left of x, it is hypothesized that the interface is stable. Figure 37 is a similar plot for liquid nitrogen for a/g = 0.008. From these plots it can be seen that the greatest height over which the interface can be expected to be stable is 14 x 10lOft (0. 17 in. ) for liquid nitrogen at AT = 100~R, a very small region. Thus from these approximate calculations, supported by linearized analyses and photographic studies, it can be concluded that a steady interface, if it exists, will be limited to an extremely small region under normal gravity conditions. For liquid nitrogen at a/g = 0. 008, however, instabilities appear at a height of approximately 0.23 ft (2.8 in. ). This will be discussed in greater detail under Section 5, "Effect of Reducing Gravity." From the above discussion it is clear that interfacial oscillations appear quite close to the leading edge, and under assumption (ix) Chapter V it has been shown that the effect of such oscillations is to increase the heat transfer rates. This is also confirmed in a recent paper by Coury and Dukler (50). Analyses of photographs such as reproduced in Figures 28-34 discussed in greater detail in Section 7, "Effect of Height on Heat Transfer Coefficient," clearly establish that the amplitude of interfacial oscillations are of the same order as the vapor film thickness. Recalling from Eq. (5.5a) that the increase in heat transfer due to interfacial oscillations is given by ~~~~~~C = ~~~~~~~~~(5.5a) 1-b2

109 15 LN2 AT=3150R =0.008. \Ucr t 5~ \ Stable = Unstable 2.8" —-~ Uv (Ref 6) ~ 10 20 30 40 50 - X x 102 Ft Figure 37. Critical velocity vs. height for interfacial velocity: a/g = o.0o8.

110 with such oscillations b takes a value not very different fcom 1 and hence the value of C can be quite high. Equations (5 28) were solved numerically for several values of the heat transfer elnhancement coefficient for both liquid nitrogen and liquid hydrogen for the values of AT for which experimental data were obtained. Curves showing these predictions are plotted in Figures 17-24. It may be observed that the present analysis, even with a C-value independent of the height x, comes closer to the exerimental values both quantitatively and qualitatively for both liquid nitrogen and hydrogen thanl either of the two predictions considered so far (6,539) if an appropriate value of C is used. This analysis shows the greatest deviation near the leading edge, particularly in liquid nitrogen. In liquid nitr-egen the extent of deviation is given in Table IX. I. gene-ral the greatest departure from the predictions is observed within 1 in. fro)m the leading edge, and if this is omitted, the limits on deviatioCn are ct-n. nsiderably reduced, as can be seen from the last colum-i of Tables IX. TABLE I:X DEVIATIONS OF EXPE:IMENTAL VALUES FROM PREDICTIONS-LIQUID NITROGEN AT (R) C Deviation Deviation Excluding AT (~R) C o Deviation 1 in.o frocm Leadi: ng Edge 315 178 +2l17 - 1.8 ~7.07 - -7.9 251. 1.6 -9.5 - -14.i -I0.25 - +7.8 2,0{)4 1.7 -19.5 - +18.4 t53. 05 - +1~5 10)0 2.4 -50 - +7 -5.82 - t7.O

111 The deviations of experimental values from predictions for liquid hydrogen are shown in Table X. TABLE X DEVIATIONS OF EXPERIMENTAL VALUES FROM PREDICTIONS —LIQUID HYDROGEN % Deviation Excluding 5/8 in. from Leading Edge 400 2.3 -6.6 - +21.6 -6.6 - +3.22 300 2.3 -3.68 - +22.6 -3.68 - +5.7 200 1. 9 -8.7 - +18.9 -8.7 - +8.7 100 1.9 -8.8 - +10.4 -1.67 - +10.4 Here also it can be observed that the deviations are greatest near the leading edge and predictions are much better away from it. The analyses is essentially for the turbulent region, and on this basis it can be said that the experimental values are within -8.7% - +13.5% of the prediction. In these predictions, the values of the heat transfer enhancement coefficient C range from 1.7 to 2.4, and for the set of conditions for which results are obtained, these can be said to be the extreme limits for the value of C. For liquid hydrogen, using any value within these limits, the experimental values would be within -38.7% to +27% of the predictions over the entire height of the heating surface covered in the present series of experiments.

112 4. EFFECT O)F INTERFACIAL VAPORIZATION ON VELOCITY PROFILE AND FRICTION VELOC ITY In the model employed to predict the heat transfer rates, Chapter V, one of the significant assumptions (v) is that the vaporization.) at the interface has no appreciable effect on the velocity profile and shear velocity. Marxman and Gilbert (45), Marxman (46), and Woolridge and Muzzy (47) have reported the results of their experimental studies regarding the effect of vaporization on. flat plates, on the velocity and shear stress distribution in turbulent boundary layers. Defining the blowing parameter "B" as B 2(pv)wall (6.7) p uC(67) e e f where p - density of the vapor at the wall v - blowing velocity at the plate p = density i-n the free stream e au - velocity in -the free stream 2 C = friction factor- 2T /p U f w e e T - wall shear stress they show that the dimen:lsionless veloc-ty Q = u/u is given. by 1 1 h7 = r + B7i)/ (1 + 1 B) (6.8) wheere q dimenlsionless distance y/s K = boundary layer thickness.

113 For the case of B = 0, indicating no blowing, this reduces to the well known 1/7 power law distribution. It was also shown (46) that the friction factor can be expressed in the form ln(l + B) Cf = g(Re) + B) (6.9) where g(Res) is a function of Reynolds number which gives the friction factor for B = 0. To evaluate this use is made of the expression given by Schlichting (48) -o. 25 = 0.0225 Re- (6.10) f Denoting the friction factor for no blowing by Cfo, for the same free stream velocity, the friction factor with blowing is then given by 0 -0.25 ln(l + B) =. 0225 Re 2C B - 0.0225 ~ 7 )-0.25 ln(lB+ B) (6.11) 0.25 0.23 0.25 1 o( o n( + B) 2 fo ), o B The ratio ( /) 5 indicates the effect of boundary layer thickening due to blowing. Ignoring this effect, we obtain

i14 Cf ln(l + B) (612) C B fo which is identical to the expression obtained earlier by Lees (49). We now assume, for the purpose of estimating the effect of vaporization at the interface on the velocity distribution and shear stress at the interface, that the above expressions for flow on a flat plate are valid for flow between parallel plates, with free stream velocity u being replaced by the maximum velocity u. To obtain a numerical value for B we proceed as max follows: For a flat plate, B = (pv)w (6.13) _ 2 2 Pue f where 2T'W f pu e e For flow between parallel plates, u in Eq. (6. 1) is replaced by u interface B = interface (6.14) 2U max pu 2 max u Tw _J- 2 max + But — u* = *2and u p u* max

115 Hence (pv). u (PV)i max B = - (6.15) P u max It is now possible to estimate a numerical value for B. (pv)i is the rate at which vaporization is taking place at the interface and is given by o:/hf. With the assumption (iv-Chapter V) that q' = I' q? _ w (vi h' fg Experimental values of;/hfg for liquid nitrogen at AT = 315~R are, q = 7000 Btu/hr ft 2F and h' = 126. 4 Btu/lbm so that q;/h = 55. 5 lb/ft hr. u fg C fg max and u are found from the solution to Eqs. (5.28) and are of the order of max 10 and 8, 000 ft/hr, respectively, for the above conditions. Using these values, B = 0.52 For this value of B the velocity profile P is compared with that for B = 0 in Figure 38. It is seen that the velocity profile is not significantly affected by the vaporization at the liquid-vapor interface, in the present experiments. The friction velocity u* is reduced in the ratio Cf/Cf = Jln 1.5/C.5 = 0.9 due to the effect of vaporization. Although one may argue that a reduction of 10o in the friction velocity is not insignificant, this decrease in friction velocity due to vaporization is neglected in the present analysis.

116 1.0 o 0.80.6A 0.4 o B=O A B = 0.52 0.0 0 LI I I I 0.2 0.4 0.6 0.8 1.0 Figure 38. Effect of interfacial vaporization on velocity profile.

117 5. EFFECT OF REDUCING GRAVITY Figures 25 and 26 show plots of heat flux vs. height for film boiling in liquid nitrogen and liquid hydrogen for a/g = 1, a/g = O. 008 and subcooled liquids. Also plotted on these figures are predictions from the present analyses for a/g = 1 with a heat flux enhancement coefficient C = 1.8 for liquid nitrogen and C = 2.4 for liquid hydrogen assumed constant for all heights x, Bromley's predictions (6) for a/g = 0.008 and a/g = 0.016 for liquid nitrogen and a/g - 0. 008 for liquid hydrogen. The a/g = 1 curves are for AT = 3570R for liquid nitrogen and AT = 4570R for liquid hydrogen; values of C = 1.78 for liquid nitrogen at a AT = 315~R and C = 2. 4 for liquid hydrogen at AT = 400~R were used for predicting the heat transfer rates Figures 17 and 21 and on the basis that the AT values of 3570R and 4535R are not very different from 315'R and 400'R the same values for C were tried. It is seen that experimental values are within -2.4% - +12.7% of the predicted value. As can be expected, heat transfer rates are reduced. at lower gravity levels. Even up to a height of 3-1/2 in., the heat flux is decreasing with height, indicating the probability that the onset of interfacial oscillations or turbulence, or both, have been delayed. Predictions from laminar analysis of Bromley (6) for two values of a/g = 0. 008 and 0. 016 havp also beerplotted in Figure 25. From Appendix A, it can be seen that the maximum value of a/g attained in the drop tower was 0. 008. However for comparison purposes, q' - x plot obtained from laminar analysis (6) for a/g = O. 016 has also been

118 included in Figure 25. Even these predictions with a/g = 0.016 are observed to be significantly lower than experimental values. The experimental values for liquid nitrogen are uniformly 100l higher, but qualitatively show the same behavior as predicted. The heat flux decreases with height, a characteristic of laminar flow with a steady liquid-vapor interface. In Figure 37, showing the plot of critical velocity vs. height for a/g = 0.008, it is noted that the onset of interfacial waves is delayed by the reduction of gravity to a height of 0.23 ft (2. 8 in. ) as opposed to 0,014 ft (0, 17 in. ) at a/g = 1. This is consistent with experimental values of heat flux which decreases with height up to a height of 3.5 in. for both liquid nitrogen and liquid hydrogen as can be seen from Figures 25 and 26. This supports the hypothesis that heat transfer enhancement is caused by interfacial waves. The results in liquid hydrogen are similar to those in liquid nitrogen in all respects. Insofar as can be inferred from the experimental values of heat flux under reduced gravity, it may be said that the qualitative variation of the heat flux with height is consistent with those predicted by laminar analysis up to a height of 3-1/2 in. Hence the region of validity of laminar analysis was physically extended by the use of the drop tower. 6. EFFECT OF SUBCOOLING Figures 25 and 26 give experimental values of heat flux vs. height for liquid nitrogen with a AT =T -T = 337~R at 34 psig giving a subcooling of w s 21. 1R; for liquid hydrogen the corresponding values are AT - 449.35R at 32.5 psig giving a subcooling of 8. 1~R In order to determine the effect of

119 subcooling it is necessary to know the effects of pressure as the subcooled data is available only at higher pressures than those without subcooling. From Lewis' experimental results on 1 in. dia sphere in liquid nitrogen (54), at AT = 357~R, p = 1 atm, q' = 7000 Btu/hr ft2 and at p = 3 atmospheres (corresponding to 29 psig), q' = 9000 Btu/hr ft. These are indicated in Figure 25 with horizontal lines labelled 1 in. dia sphere. On the assumption that the effect of increasing the pressure is constant all along the height of a vertical surface, and is of the same order as that for a sphere, it can be seen that, for the same heating surface temperature and liquid temperature, subcooling reduced the value of AT, defined as the surface superheat above the saturation temperature; but even with a decrease in the value of AT so defined, there is a substantial increase in the heat transfer rates through subcooling the liquid via pressurization. 7. EFFECT OF HEIGHT ON HEAT TRANSFER COEFFICIENT Figures 39 and 40 show heat transfer coefficient h plotted against height x for liquid nitrogen and liquid hydrogen, respectively, for 4 values of AT each. It is interesting to observe from Figure 39 that for x > 1 in., h is substantially constant within approximately + % for the range of AT between 204~R and 3150R. For heights less than 1 in. there is considerably greater variation in the value of h. From Figure 39 for AT = 315~R, 251~R, and 204~R the following conclusions can be drawn: (i) Initially up to a height of about 1 in., the heat transfer coefficient rapidly decreases with height.

50 35 l/,. 215 0 2 FI~igre ~~9. E ect of helgla% -oQ heat % ser eo ef ~.. /1~~~~~ Inches bb ~. ~1

121 60 55 0 N 400*R \ / 300*R 45 ~m 45 200~R 40 35 30 0 1 2 3 4 5 6 -- X (Inches) Figure 40. Effect of height on heat transfer coefficient. LH2.

122 (ii) For all three levels of Li, approximately tne same minimrul vaLue of h is reached. (iii) For all three levels of AT, the minimum value of h is reached approximately at the same height of about 1 in. It is significant that the minimum is reached at about 1 in., for AT = 315~R. It was already pointed out in Section 2 that it may be said, from values of c H/V, that turbulence effects begin to be significant at Re = 100. From the results of the present analysis, Re(x = 1 in.) = 104 for AT = 315~R. (iv) Above this height at which h reaches its minimum value, h begins to increase gradually. (v) At a given height x, the value of h is higher for lower AT. Trends similar to each of the above were also observed by Breen and Westwater (24) in experiments with horizontal tubes in isopropanol, where the tube diameter was varied. On the basis of observations similar to (iii) above, they concluded that the "critical diameter" is independent of AT. It may also be noted that for AT = 100~R, while the general behavior of the h-x plot is similar to those of h at other AT values, h is consistently higher. The minimum value of h seems to occur at a greater height x = 2 in. It should be noted that this AT = 10C~R is quite close to ATmin (AT corresponding to minimum heat flux-Reference 54) which is of the order of 45g-50'R for liquid nitrogen. It is possible that transition effects are beginning to show at this AT.

123 A similar h-x plot for liquid hydrogen in Figure 40 presents some interesting departures. For every value of AT, h reaches a minimum at a height varying from 3/8 in. to 2 in depending on the value of AT Here the similarity with the general trends observed with liquid nitrogen ends. The height at which hmin is reached progressively increases from approximately 3/8 in. at AT = 400~R to about 2 in. at AT = 100~R. h is different for each AT min varying from a maximum of 42.5 Btu/hr ft 2F at AT = 400~R to a minimum of about 35.75 Btu/hr ft ~F at AT = 1000R. Also at heights x < 1.5in, h increases with AT, in contradiction to the trend observed in liquid nitrogen. One feature of the variation of heat transfer coefficient with height is that near the leading edge, for AT = 315~R, 250~R, and 204~R in LN2 it actually increases initially. This is contrary to the trend predicted by laminar analysis. 8. EFFECT OF AT ON HEAT FLUX Figures 41 and 42 show plots of q'vs. AT at different heights for liquid nitrogen and liquid hydrogen, respectively. These curves also show an initial reduction of q' with x up to a height of approximately 7/8 in. and thereafter q' begins to increase. Data for 1 in. sphere for liquid nitrogen (54) and liquid hydrogen (64) are also shown for purposes of conparison. lIt may be observed that these plots show that for small values of x the reduction in q' with AT is much smaller than for larger values of x and that they show a trend of higher q' for low values of x. Breen and Westwater (24) also observed similar trends in their experiments with horizontal tubes.

124 10000 9000 "I DIA. SPHERE::/8 4000 7000 2 r>I'~~, "; 13000 3 2000 - 100 200 300 400 -- of AT(oR) Figure 41. Effect of AT on heat flux. IN2.

125 30,000 I" Sphere 8000- 4- 8:6000 - 4000 3 / 100 200 400 600 800 1000 - AT(~R) Figure 42. Effect of AT on heat flux. LH2.

126 9. Nu-Ra CORRELATION Figure 43 shows the local Nusselt number plotted against Rayleigh number. These are defined as h x x Nu = Local Nusselt Number = x k where h = local heat transfer coefficient and x p(P -p) C': h Ra x g+ 0.5i x 2 k C AT P All the data for both liquid nitrogen and liquid hydrogen have been represented in this plot. All the properties were evaluated at the film temperature, the arithmetic mean of the extreme temperatures of the vapor film. From this plot, it can be seen that the empirical correlation proposed by Thederking and Clark (57) for spheres Nu = 0.14 Ra 1/3 predicts the heat transfer values reasonably well with Nu and Ra conmputed on the basis of x. The Nu for liquid hydrogen are generally higher than this x correlation particularly at low Ra. The prediction for liquid nitrogen is much better. 10. EFFECT OF HEIGHT CN HEAT TRANSFER ENHANCEMENT COEFFICIENT Thus far, in the solution to Eqs. (5 28) a constant value of the heat transfer enhancement coefficient C was used. From an examination of Eq. (6.6)

io4 10 4 -1,-I I I I I I I A I I I11,, I I o LN2 DATA A LH2 DATA Nux=0.14 (Rax )1/3 (Ref.57) 103 \ o' A 0O f l o2; A ~ -- < 1 0 0 ho~~~R x3Pv(P2-PV)g C (CL + 0.5) 1022K A K 0107 108 109 101 1011 1012 >- Rox Figure 435. Nu-Ra correlation.

128 giving the relation between the critical wave number, velocity of the vapor, and fluid properties, it may be expected that the growth of the interfacial instabilities would also depend on these parameters. Therefore, for a given fluid, the dimensionless amplitude of the oscillations may be expected to depend on the velocity of the vapor and the vapor film thickness; these vary with height x, and as C is directly related to the dimensionless amplitude one may expect this to vary with height. To obtain a better understanding of the variation of C with height as it relates to film thickness given by Eq. (5.5a) the motion pictures of film boiling in liquid nitrogen were analyzed. Figures 44 and 45 show representative plots of vapor film thicknessframe number taken from such photographs as are reproduced in Figures 28-34. As the filming speed was constant (indicated as frames/sec in the plot), the frame numbers also represent time. Figure 44 shows variation of film thickness with time at heights of 0. 146 in., 0.39 in, and 0.78 in. from the leading edge at a AT = 100~R in liquid nitrogen. All the data shown on this plot were obtained from a single film strip. Similarly, Figure 45 shows the variation of vapor film thickness at heights of 4.02 in., 4.4 in. and 4.77 in at AT - 315~R in liquid nitrogen Similar plots were made for all films taken at different heights (four heights) and AT = 315~R, 2040R, and 100~R — a total of 12 films. Figures 46, 47, and 48 are plots of film thickness against height for different AT, recast with data obtained from plots such as Figures 44 and 45. It may be observed from Figures 44 and 45 that the maximum and minimum vapor film thicknesses are functions of time. To

3- X 0.78" A_ x X=0.39" 3 -'2 o 0 X =0.146" 3- -I I — 0.05 sec 2 q-V O L II-I I I I I, I I 10 20 30 40 50 60 70 80 90 100 - FRAME # (208 fps) Figure 44. Variation of vapor film thickness with time. LN2. AT = 1000R.

8 X 4.77"t N 4 c 2 X) L X 4.4" LL. L X =4.02 8 d -- 0.05 sec 610 20 30 40 50 60 70 80 90 100 110 --- FRAME # (220fps) Figure 45. Variation of vapor film thickness with time. LUN2. AT = 3150R.

131 Un z. MAX. FILM THICKNESS HEIGHT (Inches) Figure 46. Variation of vapor film thickness with height. LN2. AT = 100~R. 6- * MAX. FILM THICKNESS o MIN. FILM THICKNESS 0 5~f40 I 2 3 4 5 6 -'HEIGHT (Inches) Figure 47. Variation of film thickness with height. LN2. AT = 204~R. Cn O3 o 8 z 7- * MAX. FILM THICKNESS 0 o MIN. FILM THICKNESS -1O 1 2 3 4 5 6 7, HEIGHT (Inches) Figure 48. Variation of film thickness with height. LN2. AT = 315~R. zr 43- I 2-b i U

represent all the relevant data from plots such as Figures 44 and 45, Figures 46-48 were constructed in the following manner. Each darkened circle represents the "mean maximum vapor film thickness" at a given location for one value of AT. A vertical line is drawn through this point to indicate the range of variation in the maximum vapor film thickness. Similarly, each blank circle represents the "mean minimum vapor film thickness," with a vertical, line through it to represent the range of this "minimum thickness." A calculation of C directly from measured values of film thickness becomes difficult because of the following: (i) It can be observed from Figures 44 and 45 showing the variation of vapor film thickness with time, that the amplitude of oscillations is a function of time, and the heat transfer enhancement coefficient C related to the dimensionless amplitude through Eq. (5.5a) is also a function of time (ii) The value of C = 1/(1-b2) where b is the dimensionless amplitude-ratio of the amplitude of oscillations to the mean vapor film thickness —is shown plotted against b in Figure 49. From Figures 46-48 showing the minimum and maximum vapor film thickness as a function of time, it is established that the oscillations are of the same order as the vapor film thickness, so that b is close to 1. At such high values of b, from Figure 49, the value of C is seen to be very sensitive to changes in values of b. A measurement to the degree of precision necessary is not possible, as indicated in Appendix E "Error Analysis."

133 10 t en e Dimensionless Amplitude p 2; C= EQN (5.5a) -b2 0.4 0.6 0.8 1.0 b-lob Figure 49. Variation of heat transfer enhancement coefficient'ith dimensionless amplitude b. coefficient C

134 (iii) It is also doubtful if the assumption of constant temperature profile is valid when the vapor film thickness becomes very small. In such a situation it is likely that due to the high heat transfer rates possible under such circumstances local quenching may take place leading to local suppression of surface superheat, which in turn causes a reduction in the heat transfer rates. Keeping these factors in mind, instead of attempting to determine one value of C at a given location, three possible values were determined at each location for AT = 3150R and 100'R-a maximum value obtained from the upper limit of maximum vapor film thickness and the lower limit of minimum vapor film thickness, a mean value obtained from the mean maximum and mean minimum values and a minimum value obtained from the lower limit of the maximum vapor film thickness and the upper limit of the minimum vapor film thickness. The plots of such values of C as a function of height for AT=315'R and AT=100'R are shown in Figures 50 and 51. We may now attempt to specify a function giving the variation of C with height or another parameter associated with height, either directly or indirectly. As has been indicated earlier in this section, the value of C may be expected to be dependent on the vapor velocity, vapor and liquid density, vapor film thickness and other parameters such as surface tension and gravity. The mechanism of such oscillations is not completely understood and the precise definition of the interfacial oscillations is not possible at the present time. As a simplification, it will be hypothesized that the local Reynolds number is an indication of such oscillations. Figure 52 was constructed by replotting C from Figure 50, on a log-log scale replacing x max with the corresponding Reynolds number at that location. The Reynolds number

135 3 t NCM ax 2 C=0.69 Re (Eq. 6.18) 0 I I I I I I I 0 I 2 3 4 5 6 7 - o-X (Inches) Figure 50. Variation of C with x. LN2. AT = 315~R. 3 a 1 o C(Mean Il~~~ F_>,. ~~~~~~~~CMin. 0o. I i i I! I 0 1 2 3 4 5 6 7 X (Inches) Figure 51. Variation of C with x. LN2. AT = 100~R.

5.I............. i...........r'-'-T — I- I... I I.. 3.5k K2.5- C= 0.23 Re' C) C = 0.373 Re 1.01 I 10 102 103 10 I02 I03 2. Variation of CRe. T = 5 Figure 52. Variation of Cmax with Re. LN2. AT = 315~R.

137 was obtained from computations of turbulent film boiling using constant value of 1.78 for C. Two lines represented by C = 0.373Re (6.16) and C = 0. 23Re 75 (6. 17) are also shown on the same plot and these can be said to encompass the values of C for AT = 3150R. From Figure 50 it can be seen that the minimum value max of C is very close to 1. 0, being less than 1. 1 to a height of 5 in. and thereafter increasing to 1. 15 at 6 in. Because of these very low values, the minimum value of C was set equal to 1. Using Eqs. (6.16) and (6.17) each to represent C and C = 1 as C, Eqs. (5.28) were solved and the resulting max min' values of q'vs. x are shown in Figure 53. In each case, if the functional representation of C, Eqs. (6. 16) and (6. 17) gave a value C < 1.0, it was taken as C = 1, as C cannot admit a value of less than 1. 0. Equation (6.16) predicts a slightly higher value for C at low Re than Eq. (6.17) and. the effect of this is clearly seen in predictions close to the leading edge where Eq. (6.17) gives lower q' values. For higher values of Re, the differences in C values given by these two expressions gradually decrease, which is reflected in the similarity of q' - x behavior. q' - x plot for C = 1 is also shown in Figure 53.

138 10000 9000 C 0.373 Re307 C80000.23 ReO.376 8000 C=0.69 Re000 6000 0 5000 C= 1.0 4000 *EXPERIMENTAL VALUES I I I I I 0 1 2 3 4 5 6 -— X (Inches) Figure 53. Effect of varying C with x. LN2. AT = 3150R.

i39 From these curves, it can be seen that the experimental values lie between the two extreme approximations in the value of C, with Cmin = 1.0. Recognizing that the actual variation of C would probably lie between these two extremes, several different approximations were tried and the one giving the best fit for experimental data is shown plotted in Figure 53 with C given by O. 161 C = C.69Re (6.18) This curve follows all the essential trends observed in the experimental data, the decrease in heat flux at low values of x, reaching a minimum at about 1 in. from the leading edge and then increasing with height. With this representation of C, the effects of interfacial oscillations begin to show at heights of around 0.2 in. (indicated by values of C obtained in the solution of Eqs. (5.28)) and this is consistent with the approximations in Figure 36 which indicates that the interfacial oscillations begin to appear at around 0. 12 in. from the leading edge. Equation (6. 18) is also shown plotted on Figure 50 showing variation of C with x. D. Summary, Conclusions and Recommendations 1. SUMMARY The purpose of this study was to experimentally determine the local heat transfer rates in film boiling on a vertical surface and predict such heat

140 transfer rates with a suitable model. Vertical cylindrical test surfaces were used to simulate vertical plane surfaces, and heat transfer rates were determined at 11 locations up to a height of 6 in. for four different values of AT in two cryogenic fluids-liquid nitrogen and liquid hydrogen. Supporting data were obtained with motion pictures in order to understand the nature of the vapor film. The laminar vapor regime was extended by the use of the drop tower. 2. CCNCLUSIONS From the results obtained over the range of height, AT and liquids covered, the following conclusion can be drawn: (i) Under normal conditions, a/g = 1, laminar region with a smooth interface is confined to a very short region near the leading edge. (ii) Initially, heat transfer rates decrease with height, reach a minimum and begin to increase gradually. (iii) Interfacial oscillations of large amplitudes are established within a very short distance from the leading edge. (iv) Within a short distance from the leading edge, heat transfer rates are enhanced due to the effects of interfacial oscillations and turbulence effects. (v) The model adopted using a universal velocity profile, predicts the heat transfer rates reasonably well.

141 (vi) The empirical correlation suggested by Frederking and Clark (57) for spheres predict heat transfer rates reasonably well. (vii) Even in the laminar regime, the heat transfer rates are considerably higher than predicted by laminar analysis (6). (viii) Minimum heat flux increases with a decrease in height. R. RECOMMENDATIONS For further work on this problem the following suggestions are made. (i) Extend the scope of experimental work to cover other liquids and higher AT and x using a flat vertical surface. (ii) Experimentally determine the temperature and velocity profiles in the vapor film and the relation between c and c H (iii) Improve the analysis by considering the effect of vaporization at the interface, both on the velocity profile and shear stress distribution and the relation between C and c m H

APPENDIX A DROP PACKAGE Figure 54 shows details of the drop package. This consisted of an inner cylinder, acting as a piston, which moved in an outer cylinder. A metering pin, appropriately shaped, was attached to the bottom of the inner cylinder and passed through an orifice plate attached to the bottom of the outer cylinder. A tube with a conical wooden piece at its lower end, fixed to the outer cylinder acted as a guide for the metering pin. The dewar itself was suspended from the cover plate of the inner cylinder. A tube screwed into the cover plate acted as the guide for the tube carrying the test piece in the dewar and had a lifting pin at the top, which could be held in a release mechanism (Figure 55). The lifting pin had a circular groove, in which balls in a cage registered. They were retained in place by a sliding ring, which had a tapered part as shown. When the ring was lowered, the balls moved out, releasing the drop package. The outer sleeve was remotely controlled by an air-cylinder piston arrangement. The drop tower (Figures 56 and 57) consisted of an enclosed chute extending from the third floor to the first floor of the laboratory, giving a free drop distance of approximately 32 ft. and a free fall drop time of approximately 1.34 sec. After the drop the package was hoisted by an air winch placed on the third floor. Tne package was brought to rest by a sand box at the bottom; the conical wooden piece at the end of the tube on the outer cylinder of the drop package penetrated 142

VACUUM INSULATION CYLINDER ASS'M S ALING RING /1 ~ SPIKE SUPPORT FIN RELEASE ROD,! ORIFICE CRYOSTAT CONE FOR PENETRATION JL SPIKE TO INTO SAND DECELERATE PISTON ASS'M CYLINDER METERING PIN GUIDE BUSHING GUIDE BUSHING AIR ESCAPE PASSAGES

SLIDING RING -er -1 I, L- li LIFTING PIN Figure 55. Release mechanism.

145 EXHAUST FAN ELEVATOR r /r TEST PACKAGE TOWER CO2JETS SHEET ALUMINUM { X SHAF1 /ELINING SHEET ALUMINUM SHAFT C02 JETS BUFFER / CHAMBER SAND BOX SHEET ALUMINUM Figure 56. Drop tower-elevation.

WIRE CAGE BLOWOUT TO ELEVATOR I_ DOOR PNEL SHAFT HEAD PARTS AIR LOCK CHAMBER 0 DRAWERS ROOM J LU L I HOIST UNIT 0t z~~~~~a. I CONIROL AND z (UN. RECORDING AREA WORKSHOP | AREA o -___- 0~s I, l T.I _j Fi 3. ro 24 0'- Figure 57. Drop tower-plan on third floor.

147 the sand approximately 17 in. under free fall conditions before the package was brought to rest. As liquid hydrogen was used in the drop tower the following safety precautions were taken. (i) An explosion proof ventilating fan giving two air changes per minute to remove hydrogen vapor, was continuously running. (ii) A gas analyzer sampled the air sequentially from four stations in the drop tower and sounded an alarm whenever the hydrogen concentration in the area where a sampling station was located exceeded a preset limit. (iii) Provision of nonsparking lead sheathed floors, grounding of all equipment, nonsparking beryllium tools and grounding leg straps for personnel in the area to prevent sparking due to discharge of static charges. (iv) Provision for flooding the drop tower with C02 in case of rupture of cryostat containing liquid hydrogen, or small fires. Before releasing the package the innerer vessel was fully exte.Lded and held in that position by the release mechanism. In this position., there was very little clearance between the metering pin and the orifice plate. When the outer cylinder, after release, hit the sand and came to rest, the inner cylinder continued its motion, the air trapped in the outer cylinder built up pressure tilt the clearance between the orifice plate and the metering pin increased'venting the air until the inner'vessel was within a few inLches of coming to rest. The clearance between the meterinrg p>,' and the orifice plate

148 decreased at this point allowing the trapped air in the outer cylinder to provide a cushion for the inner vessel carrying the dewar and test surface till it came to a, complete rest. The deceleration was measured by a piezoelectric crystal mounted on the top of the test package. The signal from the crystal was fed to a charge amplifier and then measured in an oscilloscope. A pressure transducer mounted on the test package monitored the air pressure in the outer cylinder. A typical oscilloscope trace is reproduced in Figure 58. The maximum deceleration was approximately 25 g and the maximum air pressure 17 psig. The acceleration of the inner cylinder carrying the dewar and test surface was measured during free fall by a Kister model 303 accelerometer. The output was recorded on the Sanborn Recorder. The accelerometer was calibrated before use by a device which gave variable acceleration from a/g = 1 to a/g = -1. The a/g under free fall conditions is given in Figure 59. From this plot it is seen that the body force increased as the package fell, due to increasing air drag. This increase reached a maximum value of approximately 0.008. The lapsed time in free fall was approximately 1.345 sec.

149 DECELERATION og AIR PRESSURE 5 psi - TI ME Figure 58. Drop package deceleration —l rnier cylinder; oscilloscope trace. z I I I I I I 15LUO I 0 - LLJ o0 LLJ cr 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 TIME (Seconds) Figure 59. Drop package acceleration-free fall.

APPENDIX B EFFECT OF INSULATION Local heat flux measurements were made by recording the temperature of a test section as a function of time and equating the time rate of change of enthalpy of the test section to the heat transfer from the section. For this method to be valid, the test section must'be thermally insulated from the adjoining spacer pieces, Attempts were made to introduce an air gap (of around 0.005 in,) between the test section and adjoining pieces but this was not practicable mainly because of difficulty in properly aligning the several pieces in the test piece. Satisfactory results were obtained by using Teflon washers between the different sections. To minimize the area of heat leakage from the'test section to the adjoining sections due to the temperature differential in the'various sections during the cool down period, a recess was cut in the spacer pieces so that only a circular section of 1/16 in, radial thickiness was pressed against the adjoining section, separated by a Teflon washer, In order to study the effects of introducing an insulating material, test piece 1 was co"i.structed using different thicknesses of Teflon insulation washers (0o005 iLo,, 0o010 in,, 0.015 in,, and 0.060 in.) in sequence and comparing the resulting heat flux data observed. A plot of the heat flux data from the different sections for different thicknesses of the insulating material is given in Figure 60O From this plot it is observed that heat flux values are constant, within the limits of experimental scatter for various thicknesses of Teflon from 150

o Bottom Test Section, Middle Test Section o Top Test Section 2x104 NOTE: Each set of data point represents a different test. 0 0 t00 0 0 F 00000 10 I l H Z r 20 L 0 _0 0o( i03 Figure 60. Effect of Teflon insulation thickness. LN2. AT = 3150R.

152 0.005 in, to 0,015 in. but there is a considerable increase in measured heat flux when the thickness is increased to 0.060 in, It is believed that this increase is due to increased heat transfer to the liquid via the larger thicknesses of Teflo,.o, The surface temperature of the Teflon is depressed but because of the lower diffusivity of Teflon, there is no enthalpy flow to sustain the temperature at a high'value, and hence nucleate boiling is quickly established with a subsequent considerable increase in the heat transfer rate. The 1/4 in, copper section is now placed between two Teflon pieces whose surface temperature is much lower than that of the section itself, Hence, in addition to the heat transfer directly to the adjacent fluid, there is a secondary heat transfer path through the Teflon pieces, This leads to an increase in the heat transfer rate from the section, But with lower thicknesses, the Teflon is blanketed by a'vapor film and there is no direct liquid surface contact, It was concluded that 0,005 in, thick Teflon would pro'vide a satisfactory insulation and was used in the test surfaces,

APPENDIX C EFFECT OF CONTAINER SIZE The available glass dewar had an inside diameter of 10 cm (4 in,), To find the maximum diameter of the test piece that could be used in this container without the walls of the container affecting the results, heat flux'values were obtained with a 1 ino diameter test piece, first in a 6 in. diameter container, then with tubes of 2-1/2 in,, 2 in,, and 1-1/2 in, diameter tubes placed in the 6 in. diameter dewar. The heat flux data obtained with this test piece at three different locations —5/8 in,, 3 in,, and 5-5/8 ino from the leading edge at a mean temperature of 4[55~R —are plotted in Figure 61, This was the highest temperature of the surface used and consequently vapor generation rate was highest. From the plot it can be observed that a radial clearance of 1/2 in, is adequate to reduce the effects of the container walls to acceptable limits. Hence, test pieces were made of 1 in, and 2-1/4 in. diameter cylindrical pieces, giving a mi-nimum radial clearance of 3/4 in, between the test surface and container walls. 153

o Bottom Section Middle Section o Top Section TEST NOTE: Each set of 3 data points represents one test SURFACE 104 TTUBE TEST 03 o 0 o0 0 0o 0 o o0 SECTIONS I" DIA. TUBEI DIA D 03 Figure 61. Effect of container size. LN2. AT = 3150R.

APPENDIX D JUSTIFICATION FOR LUMPED ANALYSIS In the experiments, the heat flux to the surrounding liquid from the test surface was calculated by measuring the rate enthalpy change of the test section. The rate enthalpy change of the test section was determined through a time-temperature chart obtained from one thermocouple installed in the test section. The validity of this procedure is dependent on the assumption that the time rate of change of temperature at every point in the test section is the same. To test the validity of this assumption consider a semi-infinite slab of thickness 2d (Figure 62), suddenly immersed in a cryogenic fluid at its saturation temperature T with a heat transfer coefficient h assumed to be cons stant. From Figure 39 showing variation of h with AT, it can be seen that h is substantially constant for different values of AT. The initial uniform temperature of the block is T and is high enough to induce film boiling. o The applicable equation is 1 at 2 a (D.1) at x2 with t = O T = T r O x = O-O = o (D.2) X = d d x = d k + h(Tw-T) = 0 135

156 VAPOR LIQUID -,. ~9 I Ts F 2d - Figure 62. Model for lumped analysis.

157 Substituting 0 = T - T and using the appropriate transformed boundary conditions, the solution to this is 00 2 = A e -n t cos x (Do3) n n The eigenvalues x are given by hd. d tan d - Biot Modulus (D.4) n n k and the coefficients A by 2 go sin A d n = d + sin A d cos X d n n n The exact heat flux is then given by =A k axx=d The experimental procedure can be simulated by finding the time rate of change of temperature at a given location, say X = X, from Eq. (DPo) and assuming this to be valid at every X, the time rate of change of enrthalpy can be found~ Thus the heat flux obtained by this simulated experiment is given by m C qAat (X = X) (D7 If qT and q' agree well, lumped analysis can be said to be valid. ex A Twelve eigenxvalues were determined (using a computer) for typical values of h and d = 3/8 in~ for liquid hydrogen and liquid nitrogeno The percent error due to the use of lumped analysis is then given by

158 o q - q error =, (D.8) The maximum error in assuming the temperature at X = O to be the surface temperature I s then given by 9(X = O) - O(X = d). Representative values of percent error in heat flux calculations and determination of surface temperature due to the use of lumped analysis are given in Table IX. TABLE XI ERROR IN HEAT FLUX CALCULATIONS AND SURFACE TEMPERATURE DETERMINATION DUE TO LUMPED ANALYSIS Liquid AT(0R) h, Bi h= % Error in (X = O)Btu/hr ft2 ~R k q' Eq. (D.8) e(X = d) LN2 291 25.0 0.003397 0.057 O. 5G LN2 195 22.5 0.003057 0.051. 300 LN2 97 27.0 0. 00375 0.057 0.16 LH 377 37.5 O. 005095 o.o86 0.96 LH2 282 40. 0 0.00543 5 0.092 0.76 LTH2 189 355.0 0.004557 0.077. 43 LH2 88 55.0 0.003125 0.058 0.14.~~~~~~~~~~~~~~~~~~O.1..4

APPENDIX E ERROR ANALYSIS In the experiments possible errors are associated with the determination of heat flux from the test surface, the test surface temperature, height along the test surface at which the test sections were located and the measurement of vapor film thickness from motion pictures. 1. Heat Flux The uncertaintities in heat flux determination arise from (a) the uncertainty associated with its determination from the relation q' C (E.1) and (b) the heat loss from the test section. (a) The uncertainties associated with the computation of the heat flux will be estimated following the procedure proposed by Kline and McClintock (62). According to this procedure, the uncertainty is given by' yY 7 2x Ay =Ax + Ax + + Ax (E.2) ~Dx 1 % xbr 22 __x n x 2 J in i where Ay is the uncertainty associated with computing y = Y(X1, x2,...Xn) and Axl, Ax2,...Ax are the uncertainties associated with each of the xi. Applying this to the determination of heat flux q', Eq. (E.1), A7 2 ()2 (c>2 A(dT/dt)) (E ) p (dw/dt) 159

160 The mass of the test section was determined in a chemical balarnce having an accuracy of + 0.0005 gmo To find if the polishing of the test surface after final assembly made any significant difference in the mass determined, one of the test surfaces was dismantled and the mass of the test sections before and after such polishing compared, It was found that they were within - 0.01 gm, Using this value Am/m is estimated to be within 0.01/28 = o.ooo65. The area was computed by measuring the thickness and the diameter of the test surface sections with a vernier calipers measuring within + 0.0005 in, The uncertainty in computing the area is given by AA At Ad2 hA [( t + ( d) 1 (El4) where t = th-lckness of section and d = diameter of section. For th e test surfaces used, t 0,25 in, and d = 1.0 in, and 2,25 in. Ai E Eo ioos + (o ~ 0.002 A 0.25 ), 10 ThIe unicertainty associated with the'value of C arises f rom two sources (i) the un:rcertainty in reading the values of C from Refo 58 wh:i.uh were used in computing threse values, and (ii) the uncertainty iTn the data of Ref. 58 as applied to the material used for the present experimerts, which is.o 01, and is considered in greater detail under Section 5, "Specific Heat of Copper," The uncertainty in reading the'values from Refo 58 is estimated to be 0.002/0.2 = 0o01. The time rate of temperature was measured on the recorder chart, and in film boling the trace of thermocouple output-time has a very small curvature,

161 and the slope can be measured with reasonable accuracy. The uncertainty in the slope is estimated to be 0.02/2 = 0. 01. Combining all these, we obtain the uncertainty in computing q' to be Aq'/q' = [0.00065 + 0.002 + 0.02 +.012]1/2 =0.016 or 1.6%. (b) Heat loss from the test surface section arise from (i) loss through thermocouple wires, and (ii) leakage to adjacent sections through the Teflon insulating washer. (i) To compute heat loss through thermocouple wires assume thermocouple junction to be at the test surface temperature and the other end coming out of the gland at the top of the test surface to be at the liquid saturation temperature. For computing heat loss the constantan wire is replaced by a copper wire. The minimum length of wire from the test surface to the gland was 4 in.; AT = 4OC~R in LH2. Thirty gauge wires having a diameter of O.010 in. were max 2 used for the thermocouples. Assuming an average thermal conductivity of 300 Btu/hr ft ~R (58) we get AT q = 2KAwire AX 0.7854x10 4o00 =2 x 300 x /12 -2 = 9.8 x 10 Btu/hr On the basis of the heat transfer area from a 1 in. diameter test surface section this corresponds to q, 9.8 x 10 = 2 Btu/hr ft wires -2

162 which is negligibly small compared even with the lowest flux measured-2900 Btu/hr ft. (ii) Heat loss to adjacent sections: it may be expected that the heat loss from a given test surface section to an adjacent section is compensated by the heat gain from the other adjacent section and the net loss or gain is neglibible. However, to obtain an estimate of the maximum possible error due to this heat loss (or gain), consider one adjacent section to be at a lower temperature than the test section with 0.005 in. Teflon insulating washer separating the two sections each having perfect thermal contact with the Teflon washer. The temperature differential over the different pieces of the test surfaces was a maximum of 1,5'R between the bottom piece and the top piece. There were a total of five pieces between them and hence a temperature differential of 0.5~R between two adjacent pieces may be assumed. The area of heat transfer, because of the recess in the section, was limited to a radial thickness of 1/16 in. For Teflon K = C. 1 Btu/hr OR ft (58). With these values, for 1 in. diameter test surface AT Tr x 1 x 1/16 0.5 qs = KA - = 0.1 x X ins AX l4 0.005/12 = 0 1875 Btu/hr Based on the area of heat transfer of the test section this is equivalent to 37.5 Btu/hr ft and is 1.3% of the lowest computed value. Combining all the sources of uncertainties it is estimated that the uncertainty in the computed heat flux values are within + 2.7%.

2, Temperature The temperature of the surface was determined from the thermocouple in the sections of the test surface. The errors in its determination are due to (i) errors in measuring the output, and (ii) error due to assumption of lumped analysis. (i) The error in reading the output is due to nonlinearity in the recorder output and the error in the potentiometer which was used to calibrate the recorder. The potentiometer had an accuracy of + 1.3 4Tv in the range of values used in the experiments. The nonlinearity in the recorder output is specified at + 0.25 div. corresponding to + 0.5 Tv at a sensitivity of 2 4v/div. Therefore, the maximum error in reading the output is estimated at + 1.8 Tpv corresponding to 1.8 _xv 1.80R x = + 0.2~ R - 16.4 p4v/ok - at 156.50R-the lowest surface temperature at which data were obtained. (ii) Error due to assumption of lumped analysis is estimated at 0.50R at AT = 3000R for LN2 and 1~R for LH2 at AT = 400~R (see Appendix D). Hence, the uncertainty in the determination of surface superheat is + 0.50R in 315~R or 0.2%o for LN2 and + 1.2~R in 4000R or 0.3% in LH2.

164 3. Uncertainty in the Measurement of the Distance of Test Sections from the Leading Edge The sources of uncertainties arise from two factors (i) the finite height of the test section leads to uncertainty in the precise location at which the heat flux was determined. The height of the test section was 0.25 in. and the heat flux was assumed to have been measured at the midheight of the test section, being the average over the height of 0.25 in. It may be assumed that the heat flux computed represents the heat flux at some point in the middle third of the test section leading to an estimated uncertainty of + 0.041 in. in the location at which the heat flux was measured. (ii) Because of the introduction of the stainless steel end pieces at the bottom, boiling is induced in the end piece through heat transfer by conduction from the test piece, thus shifting the leading edge from the bottom of the test surface. To estimate this shift in the leading edge, the end piece was treated as a fin with a constant heat transfer coefficient corresponding to the lowest measured in the experiments (which would give the greatest shift). The base of the fin was assumed to be at the maximum surface temperature and boiling was assumed to have ceased at a point in the fin which had the temperature corresponding to q' he distance over which this mi n temperature drop took place was computed as the shift in the leading edge. For liquid nitrogen Tm at which q' i was assumed, was 40~R above saturation temperature and h=20 Btu/hr ft2~R (54); the corresponding values for liquid hydrogen were ATi =20~R and h=30Btu/hr ft ~R(64) obtained in experiments with mm

1 in. sphere. With these values, it is estimated that the shift in leading edge is 0. 037 in. for liquid nitrogen and 0. 068 in. for liquid hydrogen. Combining the two, the uncertainty in the measurement of the location of the test section is within + 0.110 in., - 0.026 in. 4. Uncertainties in the Measurement of Vapor Film Thickness by Photographic Methods The motion pictures were projected on a ground glass sheet to give a magnification of 10 times the original size, the distances were measured by the use of a 0.040 in. diameter reference wire which established the scale of the image. The distances on the image were measured with a vernier calipers having an accuracy of + 0.0005 in. It is estimated that the error in the measurement of the reference wire diameter on the image was within + 0.010 in. and the uncertainty in the measurement of the vapor film thickness as + [0.010 x 5/10] or + 0.005 in. 5. Specific Heat of Copper To evaluate the rate of enthalpy change of the test surface to compute the heat flux'values, values for specific heat capacity of copper were taken from Ref. 58. Discrete values used from this are given in Table XII.

166 TABLE XII SPECIFIC HEAT OF OFHC COPPER (Ref. 58) Temperature C ** Temperature C ** P P ~K ~R J/gm~K* to 0 ~K ~R J/gmoK* Btu 1b R IlbOR 70 126.173.0415 180 324.346.0826 80 144.205.04896 200 360.356.0850 90 162.232.0554 220 396.364.0869 100 180.254.0607 240 452.371.0886 120 216.288.0o688 260 468.376.0898 1 40 252.313.0748 280 504.381.0910 160 288.332.0793 300 540.386.0922 *Joule/gm ~K = 0.23885 Btu/lb ~R. **C values at intermediate temperatures were found by interpolation. To evaluate the reliability of the values of specific heats used in the computation of rate of enthalpy change, these values were compared with those of Dockerty (60), Martin (59), and Farukawa, et al. (63). The values from these csources and from Ref. 58 (which is itself based on Ref. 60) are given in Table XIII, which also gives values of specific heats of commerically pure copper and from a comparison of these values, it can be seen that the maximum variation in the values of specific heat given by different workers is within l% below 12C00K and less than 0.5% between 12G0 and 35G0K. It may

167 TABLE XIII SPECIFIC HEAT OF COPPER-COMPARISON OF DATA FROM DIFFERENT SOURCES Temperature C (Btu/lbm ~R) OK OR Ref. 59 Ref. 60 Ref. 61 Ref. 63 Ref. 60* 102 x 102 x 102 2 2 xlO xlO x 10 x 10xl 70 126 4.13 4.10 4.07 4.09 4.08 80 144 4.896 4.86 4.84 4.83 4.84 90 162 5.54 5.51 5.49 5.48 5.48 100 180 6.07 6.02 6.02 6.02 5.995 120 216 6.88 6.87 6.85 6.86 6.84 140 252 7.47 7.47 7.47 7.47 16o 288 7.93 7.91 7.91 7.92 7.91 180 324 8.26 8.25 8.24 8.25 8.25 200 360 8.50 8.49 8.49 8.51 8.496 220 396 8.69 8.69 8.69 8.71 8.71 240 432 8.86 8.84 8.85 8.88 8.88 260 468 8.98 8.99 8.99 9.01 9.00 280 504 9.10 9.11 9.11 9.11 9.12 300 540 9.22 9.21 9.196 9.199 9.21 *Commercially pure copper. All other 99.99%o pure copper.

168 also be seen that the specific heat is relatively insensitive to small amounts of impurities in copper as observed from values given in the last column of Table XIII for commerically pure copper. Martin (59) also concludes that heavily cold worked copper has a specific heat of about 0.15% higher than that of annealed copper. From these values it may be concluded that the maximum uncertainty in the value of specific heat for the machined OFHC copper used in the experiments is within + C.6/%.

APPENDIX F PROPERTIES OF NITROGEN AND HYDROGEN 169

1 J Nitrogen T (OR) Film Temp. p(61) i(58) C (61) (. -h )(6i) k(58) 1+T +T w s (OR) Ibm/3) ( lbm/ft hr) (Btu/lbm ~R) (Btu/lbm) (Btu/hr ft'. ~R) 494,1 316,8 0,1217 0.04356 0 249, 13305 0. 00971 454,3 296.9 0.1323 0o0363 0.253 126,14 O.009298 390~ 2 264 8 0 o 1 481 0.0242 0. 2541 117.83 0.007907 3 43 04 241 4 0,1633 0.02226 0O 2568 112 e2 0.007619 2359 1 189.3 0o 2108 0,0176 0 2628 98,70 0.005781 0 Saturation pressure 14,9 psi; T (61) = 139.4 ~R p (61) = 50.578 lbm/ft3 hf (61) = 85.64 Btu/lbm gNumbe *Numbers in parentheses refer to referenuces in bibliography.

2. Hydrogen T (OR) Film Tempo p(65) ) C (65) (h -h )(65) k(58) T +5 Tw__ s (lbm/ft ) (lbm/ft hr) (Btu/lbm ~R) (Btu/lbm) (Btu/hr ft ~R) 2 (~R) 490 3 263.6 0.010 0.01331 2.99 798 5 O. 052 436, 9 236.9 o.o0118 0.01226 2,89 718 47 0.050 336.9 186.9 o0,149 0.01113 2.65 578.27 0.039 236,9 136,9 0,0205 0,00847 2,54 447,22 0.031 136.9 86 9 0. 0325 o. oo00605 2, 517 321 48 0020 Saturation pressure 14,9 psi; T (65) = 36.9 OR p (65) 4.43o6 lbm/ft3 hfg (65) = 191.78 Btu/lbm *Numbers in parerntheses refer to references in bibliography.

APPENDIX G DATA Data were reduced following the procedure outlined under Chapter IV, Section E, "Data Reduction." No datum was discarded. During a run the pressure increased by up to 0.25 psi due to vapor generation. 172

173 P = 0.5 psig: Saturated Liquid: a/g = 1 Run Dia Height Above Test TT q Leading Edge L stat~ @ NO. in. Leding Edge, Liquid OR Btu/hr ft2 Btu/hr ft2 OR in. 2001 1 3/8 LN2 314.9 7378.5 23.43 3 314.9 6624.8 21.04 4-1/2 314.9 6880.7 21.85 2002 1 3/8 LN2 314.9 7378.5 23.43 3 314.9 6535.6 20.75 4-1/2 314.9 6880.7 21.85 2003 1 3/8 LN2 314.9 7378.5 23.43 3 314.9 6506.5 20.66 4-1/2 314.9 6815.9 21.64 2004 1 3/8 LN2 314.9 7530.7 23.91 3 314.9 6506.5 20.66 4-1/2 314.9 6880.7 21.85 2005 1 3/8 LN2 314.9 7304.8 23.2 3 314.9 6565.0 20.8 4-1/2 314.9 6880.7 21.85 2006 1 3/8 LN2 250.8 6969.3 27.8 3 250.8 5303.3 21.15 4-1/2 250.8 5639.6 22.49 2007 1 3/8 LN2 250.8 6969.3 27.8 3 250.8 53035.53 21.15 4-1/2 250.8 5588.6 22.8 2008 1 3/8 LN2 250.8 6969.3 27.8 3 250.8 5258.0 20.96 4-1/2 250.8 5538.5 22.o8 2009 1 3/8 LN2 250.8 6969.3 27.79 3 250.8 5303.3 21.15 4-1/2 250.8 5588.6 22.28 2010 1 3/8 LT2 250.8 6892.6 27.48 3 250.8 5258.0 20.96 4-1/2 250.8 5538.5 22.08 2011 1 3/8 TIN2 204.0 6525.6 31.98 3 x204.0 4297.2 21.06 4-1/2 204.0 4526.6 22.18

174 P = 0.5 psig: Saturated Liquid: a/g = 1 Run Dia Height Above Test Tw-Tsat gq' h, Leading Edge, No. in. inLiquid R Btu/hr ft2 Btu/hr ft' o, 2012 1 3/8 LN2 204.0 6525.6 51.98 3 2041.0 4297.2 21.06 4 —1/2 204.0 4526.6 22.19 2013 1 3/8 LN2 204.0 6691.4 32.79 3 204.o 4383.1 21.48 4-1/2 204.0 4590.3 22.50 2014 1 3/8 LN2 204.0 6691.4 52.79 3 204.0 4268.9 20.92 4-1/2 204.0 4557.9 22.3L1 2015 1 3/8 LW2 204.o 6525.53 31.98 3 204.o 4311.3 22.13 4-1/2 204.0 4574.1 22. 42 2016 1 3/8 LN2 99.7 5796.0 58.13 3 99.7 2891.0 28.99 4-1/2 99.7 3176.0 31.85 2017 1 3/8 LN2 99.7 5707.0 57.24 3 99.7 2914.0 29.22 4-1/2 99 7 3163.0 31.73 2018 1 3/8 LN2 99.7 5664.0 56.81 3 99.7 3052.0 30.61 14-1/2 99.7 3218.0 32.27 2019 1 3/8 LN2 99.7 5796.o 58.14 3 99.7 2961.0o 29.69 4-1/2 99.7 3218.0 32.28 2020 1 3/8 LN2 99.7 5888.0o 59.09 3 99.7 2984.0 29.92 4-1/2 99.7 3163.0 31.72 4001 1 5/8 LN2 314.9 6676.5 21.20 3 314.9 6419.6 20.39 5-5/8 314.9 7774.0 2)4.69 4002 1 5/8 LN2 314.9 6617.8 2 002 3 314.9 6475.4 20.56 5 -5/8 314.9 7734.2 2) —. 5 6

175 P = 0.5 psig: Saturated Liquid: a/g = 1 Run Dia, Height Above Test TTsat q h No. in. Leading Edge, Liquid 0R Btu/hr ft2 Btu/hr ft2 oR in. 4003 1 5/8 LN2 314.9 6502.3 20.65 3 314.9 6419.6 20.39 5-5/8 314.9 7616.7 24.18 4004 1 5/8 LN2 314.9 6502.3 20.65 3 314.9 6419.6 20.39 5 -5/8 314.9 7616.7 24.19 4005 1 5/8 LN2 314.9 6559.1 20.83 3 314.9 6475.4 20.56 5-5/8 314.9 7648.0 24.29 4006 1 5/8 LN2 350.8 5632.9 22.46 3 250.8 5327.9 21.24 5-5/8 250.8 6226.3 24.83 4007 1 5/8 LN2 250.8 5632.9 22.46 3 250.8 5241.3 20.90 5 -5/8 250.8 6226.3 24.82 4008 1 5/8 LN2 250.8 5733.3 22.86 3 250.8 5241.3 20.89 5-5/8 250.8 6348.4 25.31 4009 1 5/8 LN2 250.8 5632.9 22.46 3 250.8 5241.3 20.90 5-5/8 250.8 6348.4 25.31 4010 1 5/8 LN2 250.8 5632.9 22.46 3 250.8 5284.6 21.07 5-5/8 250.8 6286.4 25.06 4011 1 5/8 LN2 204.0 5035.0 24.67 3 204.0 4306.3 21.10 5-5/8 204.o 5345.9 26.o6 4012 1 5/8 LN2 204.0 4997.6 24.49 3 204.0 4306.3 21.11 5-5/8 204.0 5077.4 24.88 4013 1 5/8 LN2 204.0 4961.2 22.99 3 204.0 4306.3 21.10 5-5/8 204.0 5077.4 24.88

P = 0.5 psig: Saturated Liquid: a/g = 1 Run Dia, eight Above Test Tw-Tsat, q', h No. in Leading Edge, sat R No. in. i.Liquid Btu/hr ft2 Btu/hr ft2 ~R 4014 1 5/8 LN2 204.0 4819.7 23.62 3 204.0 4251.7 20.84 5-5/8 204.0 5002.6 24.52 4015 1 5/8 LN2 204.0 4889.4 23.96 3 20440 4251.7 20.84 5-5/8 204.0 5077.4 24.88 4016 1 5/8 LN2 99.7 4747.0 47.61 3 99.7 2921.0 29.29 5-5/8 99.7 3481.0 34.91 4017 1 5/8 LN2 99.7 4932.0 49.46 3 99.7 2966.0 29.75 5-5/8 99.7 3613.0 36.26 4018 1 5/8 LN2 99.7 4631.0 46.45 3 99.7 2921.0 29.29 5-5/8 99.7 3545.7 35.56 4019 1 5/8 LN2 99.7 4747.0 47.61 3 99.7 2954.0 29.63 5-5/8 99.7 3481.0 34.91 4020 1 5/8 LN2 99.7 4575.0 45.88 3 99.7 2822.0 28.30 5-5/8 99.7 3579.0 35.89 5001 1 1/4 LN2 314.9 6189.6 19.65 1-1/2 314.9 6268.3 19.90 3 314.9 6609.3 20.99 5002 1 1/4 LN2 314.9 7191.5 22.84 1-1/2 314.9 6401.7 20.33 5 314.9 6609.3 20.99 5003 1 1/4 LN2 314.9 6292.2 21.98 1-1/2 314.9 6294.2 19.98 3 314.9 6496.3 20.63 5004 1 1/4 LN2 314.9 6398.7 20.32 1-1/2 314.9 6268.3 19.91 3 314.9 6726.4 21.36

177 P = 0.5 psig: Saturated Liquid: a/g = 1 Run Dia, Height Above Test Tw-Tsat,', h Leading Edge, saty 2 2 OR o. in. Leadin LiquidR Btu/hrft Btu/hr ft2 R 5005 1 1/4 LN2 314.9 6509.3 20.67 1-1/2 314.9 6294.2 19.99 3 314.9 6726.4 21.36 5006 1 1/4 LN2 250.8 5896.3 23.50 1-1/2 250.8 5126.1 20.44 3 250.8 5349.5 21.33 5007 1 1/4 LN2 250.8 5589.4 22.28 1-1/2 250.8 5126.1 20.44 3 250.8 5306.0 21.56 5008 1 1/4 LN2 250.8 5894.3 23.50 1-1/2 250.8 5046.0 20.11 3 250.8 5349.5 21.33 5009 1 1/4 LN2 250.8 5894.3 23.5 1-1/2 250.8 5046.0 20.12 3 250.8 5349.5 21.33 5010 1 1/4 LN2 250.8 5789.0 23.08 1-1/2 250.8 5004.0 19.95 3 250.8 5306.0 21.16 5011 1 1/4 LW2 204.0 5200.6 25.49 1-1/2 204.0 4112.5 20.16 3 204.0 4340.3 21.27 5012 1 1/4 LN2 204.0 5450.0 26.71 1-1/2 204.0 4138.2 20.28 3 204.0 4340.3 21.27 5013 1 1/4 LN2 204.0 5450.0 26.71 1-1/2 204.0 4396.1 21.54 3 204.0 4340.3 21.27 5014 1 1/4 LN2 204.0 5009.2 24.55 1-1/2 204.0 4112.5 20.16 3 204.0 4340.3 21.27 5015 1 1/4 LN2 204.0 5240.5 25.73 1-1/2 204.0 4138.2 20.28 3 204.0 4340.3 21.27

178 P = 0.5 psig: Saturated Liquid: a/g = 1 Run Dia, Height Above Test Tw-Tsat, q' h, No. in Leadin.g Edge Liquid ~R Btu/hr ft2 Btu/hr ft2 ~R in. 5016 1 1/4 LN2 99.7 5810.0 58.27 1-1/2 99.7 3441.3 34.1 3 99.7 3190.0 31.99 5017 1 1/4 LN2 99-7 5899.3 59-.1 1-1/2 99.7 3553 4 35.64 3 99.7 3299.1 33.09 5018 1 1/4 LN2 99.7 5899.3 59.17 1-1/2 99.7 3441.3 34.52 3 99.7 3112.8 31.22 5019 1 1/4 LN2 99.7 5945.1 59.62 1-1/2 99.7 3520.7 35.31 3 99.7 3216.6 32.26 5020 1 1/4 LN2 99.7 6184.8 62.32 1-1/2 99.7 3536.9 35.47 3 99.7 3216.6 32.26 6001 2-1/4 7/8 LN2 314.9 6391.4 20.29 3 314.9 6930.5 22.0 3-1/2 314.9 7404.2 23.51 6002 2-1/4 7/8 LN2 314.9 6311.9 20.04 3 314.9 6954.5 22 08 3-1/2 314.9 7194.1 22.82 6003 2-1/4 7/8 LN2 314.9 6067.0 19.26l 3 314.9 6722.6 21.35 3-1/2 314.9 6995.7 2 6004 2-1/4 7/8 LN2 314.9 6048.9 19.20 3 314.9 6722.6 21.34 3-1/2 314.9 6807.9 21.62 6005 2-1/4 7/8 LN2 314.9 6048.9 19.20 3 314.9 6722..6 21.34 3-1/2 314.9 6947.6 22.0 6006 2-1/4 7/8 LN2 250.8 5015.0 19.99 3 250.8 5445.6 21.72 3-1/2 250.8 5443.6 21.70

179 P = 0.5 psig: Saturated Liquid: a/g = 1 Run Dia, Height Above Test Tw-Tsat, q'_ h, No. in. Ieading Edge. Liquid OR Btu/hr ft2 Btu/hr ft2 OR in. 6007 2-1/4 7/8 LN2 250.8 5015.0 19.99 3 250.8 5411.6 21.57 3-1/2 250.8 5443.6 21.70 6008 2-1/4 7/8 LN2 250.8 5015.0 19.99 3 250.8 5445.6 21.72 3-1/2 250.8 5512.5 21.97 6009 2-1/4 7/8 LN2 204.0 4111.5 17.12 3 204.0 4598.1 19.15 3-1/2 204.0 4492.0 18.71 6010 2-1/4 7/8 LN2 204.0 4093.3 17.05 3 204.0 4598.1 19.15 3-1/2 204.0 4628.2 19.28 6011 2-1/4 7/8 LN2 204.0 4093.3 17.05 3 204.0 4598.1 19.15 35-1/2 204.0 4536.5 18.89 6012 2-1/4 7/8 LN2 99.7 3739.8 37.51 3 99.7 3161.0o 31.70 3-51/2 99.7 3012.4 30.21 6013 2-1/4 7/8 LN2 99.7 3440.5 34.50 3 99.7 3368.9 33.79 3-1/2 99.7 3323.3 33.33 6014 2-1/4 7/8 LN2 99.7 3583.9 35.94 3 99.7 3325.2 33.35 3-1/2 99.7 3302.1 33.12 7001 2-1/4 2 LN2 314.9 6509.6 20.67 3 314.9 6767.4 21.49 4 314.9 6951.9 22.07 7002 2-1/4 2 LN2 314.9 6468.4 20.54 3 314.9 6835.6 21.70 4 314.9 7072.9 22.46 7003 2-1/4 2 LN2 314.9 6593.5 20.93 3 314.9 6789.9 21.56 4 314.9 6905.0 21.93

180 P = 0.5 psig: Saturated Liquid: a/g = 1 Run Dia, Height Above Test TwTsat,' hq No. Leading d.ge, Liquid OR Btu/hr ft2 Btu/hr ft2 ~R in. 7004 2-1/4 2 LN2 250.8 5223.8 20.82 3 250.8 5466.1 21,79 4 250.8 5365.3 21.39 7005 2-1/4 2 LN2, 250.8 5223.8 20.83 3 250.8 5332.7 21.26 4 250.8 5466.0 21.79 7006 2-1/4 2 LN2 250.8 6223.8 20.82 3 250.8 5398.6 21.52 4 250.8 5466.0 21.79 7007 2-1/4 2 LN2 204.0 4433.2 21.72 3 204.0 4460.8 21.86 4 204,0 4594.7 22.49 7008 2-1/4 2 LN2 204. 0 4269.0 20.92 3 204.0 4334.7 21.24 4 204.0 4549.2 22.29 7009 2-1/4 2 LN2 204.0 4269.0 20.92 3 204.0 4334.7 21.24 4 204.0 4596.7 22.57 7010 2-1/4 2 LN2 99.7 3107.8 31.17 3 99.7 3097.1 31.06 4 99.7 3078.7 30.87 7011 2-1/4 2 LN2 99.7 3053.0 30.62 3 99.7 3273.5 32.83 4 99.7 3173.1 31.82 7012 2-1/4 2 LN2 99.7 3145.6 31.55 3 99.7 3232.7 32.43 4 99.7 3173.1 31.83 4021 1 5/8 LH2 400 16354.7 40.9 3 400 19625.8 49. 7 5-5/8 400 20398. 0 50.99 4022 1 5/8 LH2 300 11045.7 36,8 3 300 12373.7 41.2 5-5/8 300 14201.6 47.3

P = 0.5 psig: Saturated Liquid: a/g = 1 Run Dia, Height Above Test Tw-Tsat, q' h Leo.ing Edge, No. in. Leading Edge, Liquid R Btu/hr ft2 Btu/hr ft2 OR in. 4023 1 5/8 LH2 200 6991.7 34.96 3 200 7658.1 38.3 5-5/8 200 8914.3 44.6 4024 1 5/8 LH2 100 4601.8 46.o 3 100 3504.1 35.o 5-5/8 100 4334.7 43.3 4026 1 Runs made in nucleate boiling 4027 1 5/8 LH2 100 4754.2 47.5 3 100 3486.9 34.9 5-5/8 100 4308.9 43.1 4028 1 5/8 LH2 200 7466.8 37.8 3 200 7658.1 38.3 5-5/8 200 8914.3 44.6 2021 1 3/8 LH2 100 5795.4 57.95 3 100 3606.1 36.1 4-1/2 100 3852.2 38.5 2022 1 3/8 LH2 100 5233.2 52.3 3 100 36o6.1 36.1 4-1/2 100 3728.9 37.3 2023 1 3/8 LH2 200 7666.0 38.3 3 200 7807.1 39.04 4-1/2 200 8845.6 44.3 2024 1 3/8 LH2 200 7666.0 38.3 3 200 7807.1 39.04 4-1/2 200 8540.5 42.7 2025 1 3/8 LH2 300 12319.9 41.1 3 300 13281.8 44.2 4-1/2 300 13493.9 45.0 2026 1 3/8 LH2 300 11625.8 38.8 3 300 12668.7 42.2 4-1/2 300 13274.5 44.2

182 P = 0.5 psig: Saturated Liquid: a/g = 1 Run Dia, Height Above Test Tw-Tsat, g' h, No. in. Leading Edge, Liquid ~R Btu/hr ft2 Btu/hr ft~ 0R in. 2027 ] Runs made in nucleate boiling 2029 1 3/8 LE2 400 17261.4 43.2 3 400 19456.9 48.6 4-1/2 400 20207.8 50.6 2030 1 3/8 LH2 400 17065.2 42.7 3 400 19712.9 49.3 4-1/2 400 20071.2 50.2 2031 1 3/8 LH2 300 11625. 8 38.8 3 300 12866.7 42 2 4-1/2 300 13167.5 43.9 2032 1 3/8 LH2 200 7365.4 36.8 3 200 7973.2 39.4 4-1/2 200 8845.6 44.2 2033 1 3/8 LH2 100 5156.3 51.6 3 100 3606.1 36.1 4-1/2 100 3853.2 38.5 5023 1 1/4 LH2 100 5176.1 51.8 1-1/2 100 3684.2 36.8 3 100 3780.6 37.8 5024 1 1/4 LH2 100 5251.2 52.5 1-1/2 100 3703.1 37.0 3 100 3840.3 38.4 5025 1 1/4 LH2 200 7842.0 39.2 1-1/2 200 7438.5 37.2 3 200 8142.6 40.7 5026 1 1/4 LH2 200 7611.4 38. 1 1-1/2 200 7163.0 35.8 3 200 7237.9 36.6 5027 1 1/4 LH2 300 12544.0 41.8 1-1/2 300 12142.5 40.4 3 300 13213.2 44.0

P = 0.5 psig: Saturated Liquid: a/g = 1 Height Above Run Dia, Test Tw-Tsat,'v h, No. in. Leading Edge, Liquid ~R Btu/hr ft2 Btu/hr ft2 ~R in. 5028 1.1/4 TM2 300 12452.5 41.1 1-1/2 300 12499.6 41.3 3 300 13315.7 44.3 5029 1 1/4 LH2 400 16868.3 42.1 1-1/2 400 17572.6 43.9 3 400 19055.5 47.6 5030 1 1/4 LH2 400 17635.0 44.1 1-1/2 400 18192.8 45.5 3 400 19290.7 48.2 5031 1 1/4 LH2 400 17243.1 43.1 1-1/2 400 17981.3 44.9 3 400 19290.7 48.2 5032 1 1/4 LH2 300 12185.7 40o.6 1-1/2 300 12384.4 41.3 3 300 13013.0 43.4 5033 1 1/4 LH2 200 8531.4 42.6 1-1/2 200 7438.5 37.2 3 200 8142.6 40.7

Run Test Tw, Pressure TW-T Subcooling, Height Above h No. Liquid OR psig OR a/g OR Leading Edge, Btu/hr ft2 Btu/hr ft2 R in. 8003 LN2 494.1 0.5 354.7 0 0 3/8 2818 7.94 2 2122 5.99 8003 LN2 497.5 0.5 358.1 1 0 3/8 8385 23.4 2 8133 22.7 8004 LN2 497.5 0.5 337.0 1 21.1 3/8 16844 50.1 2 14719 42.5 8004 LN2 494.1 0.5 333.6 1 21.1 3/8 19250 57.2 2 14680 43.6 8005 LN2 494.1 0.5 533.6 1 21.1 3/8 16365 48.7 2 15855 46.6 8005 LN2 497.5 0. 5 337.0 1 21.1 3/8 16421 48.7 2 15906 47.4 8006 LN2 494.1 0.5 354.7 1 0 3/8 8110 22.87 2 8940 25.19 H 8006 LN2 497.5 0.5 358.1 1 0 3/8 8143 22.75 - 2 8358 23.39 8007 LN2 494.1 0.5 356.7 0 0 3/8 3385 9.55 2 2180 6.15 8007 LN2 497.5 0.5 358.1 1 0 3/8 8279 23.15 2 8150 22.8 8010 LH2 490.3 0.5 453,6 1 0 3/8 23390 51.6 2 24800 54.6 8010 LH2 494.1 0.5 451.4 1 0 3/8 23350 51.0 2 25080 56.4 8011 LH2 490.3 32.5 445.5 1 8.1 3/8 27990 62.9 2 32000 72.0 8011 1H2 494.1 32.5 449.3 1 8.1 3/8 27890 62.1 2 30990 69.o 8012 LH2 490.3 0.5 453.6 0 0 3/8 7707.8 16.99 2 5975.0 13.17

Run Test Tw. Pressure Tw-Tst Subcooling, Height Above h, o. Liquid OR psig OR a/g R Leading Edge, Btu/hr ft2 Btu/hr ft2 OR in. 8012 LH2 494.1 0.5 457.4 1 0 3/8 23980 52.6 9001 2 22500 49.4 9001 L2 494.0 O. 5 354.7 1 0 5/8 8842 24.9 3 7928 22.4 9001 LN2 497.5 0.5 358.1 1 0 5/8 8367 23.4 3 7950 22.2 9002 LT2 494.0 0.5 354.7 1 0 5/8 8350 23.5 9002 Ln'2 497.5 0.5 358.1 1 0 5/8 7991 22.3 3 7880 22.0 9003 L2 494.1 2.5 333.6 1 21.1 5/8 14200 42.6 3 11850 37.6 90035 L42 497.5 2.5 3371 1 21.1 5/8 13990 41.5 3 11250 33.4 9004 LN2 494.1 5. 333.6 1 21.1 5/8 14261 42.7 3 11600 34 9004 LN2 497.0 52.5 337.0 1 21.1 5/8 14211 42.2 3 11600 34.o 9005 LNT2 494.0 0.5 356.7 0 0 5/8 2060 5.86 3 1455 3.64 9005 LN2 497.5 0.5 358.1 1 0 5/8 8158 22.8 3 7367 20.6 9005 LN2 494.0 0.5 354.7 1 0 5/8 8187 23.1 3 7807 22.0 goo9006 2 494.0 0.5 3554.7 0 0 5/8 2120 5.95 3 2040 5.75 oo006 1{2 497.5 0.5 358.1 1 0 5/8 8074 22.5 3 7240 20.1 9010!l2 494.1 0. 5 457.4 1 0 5/8 22432 49.1 3 24208 53.0

Run Test Tw, Pressure Tw-TS, Subcooling Height Above cg, h, No. Liquida R psig OR a/g OR eading Edge, Btu/hr ft2 Btu/hr ft2 ~R in. 9010 LH2 490.3 0.5 453.6 1 0 5/8 23275 51.4 3 25325 55.9 9011 LH2 490.3 34 445.5 1 8.1 5/8 27556 61.5 3 31309 69.9 9011 LH2 494.1 34 449.3 1 8.1 5/8 27495 61.4 3 30588 68.3 9012 LH2 494.1 0.5 451.4 1 0 5/8 22432 49.1 3 23677 51.8 9012 LH2 488.9 0.5 452.2 0 0 5/8 5910 13.1 3 5150 11.5 10001 LN2 497.5 0.5 358.1 1 0 1-1/8 7710 21.5 3-1/2 8150 22.8 10001 LN2 494.1 0.5 354.7 1 0 1-1/8 7861 22.2 H 3-1/2 8150 22.8 10002 LN2 497.5 0.5 358.1 1 0 1-1/8 7672 21.42 3-1/2 8170 22.8 10002 LN2 494.1 0.5 354.7 1 0 1-1/8 7641 21.5 3-1/2 8550 24.1 10003 LN2 494.1 34 333.6 1 21.1 1-1/8 13550 40.5 3-1/2 13872 41.5 10003 LN2 497.5 34 337.0 1 21.1 1-1/8 12802 38.1 3-1/2 12012 35.7 10004 LN2 494.1 0. 5 354.7 0 0 1-1/8 2320 6.6 3-1/2 2090 5.9 10004 LN2 497.5 0.5 358.1 1 0 1-1/8 7549 21.1 3-1/2 7811 21.8 10010 LH2 490.3 0.5 453.6 1 0 1-1/8 22809 50.5 3-1/2 26825 59.1 10010 lI2 494.1 0.5 457.4 1 0 1-1/8 22007 48,1 3-1/2 27350 59.8

Run Test Tw, Pressure TW-T Subcooling, Height Above h KTo. Liquid OR psig OR a/g "R Leading Edge, Btu/hr ft2 Btu/hr ft2 OR in. 10011 LH2 490.3 32.5 445.5 1 8.1 1-1/8 29189 65.3 3-1/2 34715 77.6 10011 LH2 494.1 32.5 449.3 1 8.1 1-1/8 28282 63.0 3-1/2 33602 74.9 10012 LH2 490.3 0.5 453.6 0 0 1-1/8 9518 21.0 3-1/2 4260 9.4 10012 LH2 494.1 0.5 457.4 10 1-1/8 23569 51.5 3-1/2 23443 51.3 co

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