THE UNIVERSITY OF MICHIGAN COLLEGE OF ENGINEERING Department of Mechanical Engineering Heat Transfer and Thermodynamics Laboratory Final Report (including material for Quarterly Progress Report No. 3 for the period July through September 1960) PRESSURIZATION OF LIQUID OXYGEN CONTAINERS J... A. Clark H. Merte, Jr. V. S. -Arpaci M. Starr P. Fennema J. Beukema.S. Eshghy H. Law ORA Project 03583 under contract with: DEPARTMENT OF THE ARMY DETROIT ORDNANCE DISTRICT CONTRACT NO. DA-20-018-506-ORD-254 DETROIT, MICHIGAN administered through: OFFICE OF RESEARCH ADMINISTIRATION ANN ARBOR March 1961

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TABLE OF CONTENTS Page ABSTRACT iii I. OPTIMIZATION OF PRESSURIZED-DISCHARGE PROCESSES IN CRYOGENIC CONTAINERS 1 A. Experimental Program 1 B. Experimental Data 6 C. Analysis of Gas- and Wall-Temperature Response During the Discharge of a Cryogenic Liquid from a Container 10 1. Method of Analysis 13 2. Summary of Theoretical Results 20 3. Influence of System Parameters on Gas Temperature Response 22 4. Calculation Procedure 27 5. Determination of Mean Gas Density for use in the Theoretical Equations 28 D, Comparison of Theory with Experiment 29 1. Moving Ambient Case 30 2. Moving Heat Flux Case 31 II. BOILING OF A CRYOGENIC FLUID UNDER REDUCED GRAVITY 35 III. HEAT TRANSFER TO A CRYOGENIC FLUID IN AN ACCELIRATED SYSTEM 38 REFERENCES 42 ii

ABSTRACT This constitutes the final report on the subject contract. Material included herein is that which also describes the results of research effort during the third quarter, July to October, 1960. Owing to an increased rate of expenditure during the summer of 1960, funds for this research were expended by October, 1960. This increased rate of expenditure resulted from the addition of research personnel during the summer whose services became available then and who could and did contribute materially to the program. The increased rate of expenditure had the prior approval of the sponsoring agency. Owing to these circumstances, no fourth quarterly progress report will be issued on this contract. An orderly progress of research has been maintained, however, by the continuation of this work under the sponsorship of the NASA through the George C. Marshall Space Flight Center at Huntsville, Alabama, starting October 1, 1960. The following major topics are reported on herein: I, Optimization of pressurized-discharge processes in cryogenic containers. II. Boiling of a cryogenic fluid under reduced gravity. III. Heat transfer to a cryogenic fluid in an accelerating system. iii

I. OPTIMIZATION OF PRESSURIZED-DISCHARGE PROCESSES IN CRYOGENIC CONTAINERS Ao EXPERIMENTAL PROGRAM During the past quarter, the new system has been put into operation. Figure 1 represents schematically the flow diagram of the system and its component parts. The principal change from the previous system is the incorporation of an annular container around the main container, which is discussed later. Figures 2, 3, and 4 are photographs showing the general view of the experimental setup and its filling apparatus. The main control consul, Sanborn and Minneapolis-Honeywell oscillographic recorders, thermocouple switches, and nitrogen pressurization bottles are shown in Fig. 2. A view of the electrical heater controls for both the main container and the annular container as well as the insulated container assembly is shown in Fig. 3. Figure 4 is a photograph showing the insulated container assembly connected by means of an insulated transfer line and quick opening valves to a large, portable liquid nitrogen storage vessel. The pressurized-discharge container consists of two components, a cylindrical container (Fig. 5) and an annular container (Fig. 6). A sectional view of the two containers and the interior construction is shown in Fig. 7. Both containers are fabricated of 1/8-in. 5052 aluminum except for the end plates which are 1/2-in. aluminum. The cylindrical container has a diameter of 1.02 ft and the annular container has diameters of 1.25 and 1.67 ft. Both are 3 ft in length. The containers are connected hydrau1

lically at top and bottom by the inlet and discharge lines so that filling, pressurizing, and discharging is accomplished simultaneously in both containers and with equal liquid levels in each. The inside top of the main, or cylindrical, container is insulated with a l-in.-thick layer of styrofoam to reduce the heat-transfer interaction between the top and the pressurizing gas, and therefore reduce an "end effect" in the system. The outside of the annular container is wrapped with approximately two inches of Fiberglas to reduce heat-transfer interaction with the ambient. This may be seen in Figs. 3 and 4. The principal function of the annular container is to provide an automatically adjusting and matching thermal guard for the main container. This enables a reasonably accurate measurement of heat flux to be imposed on the main container. Chromel A heater ribbon is attached with Scotch thermo-setting tape to the outside of the main container and to the inside of the annular container, as is noted in Figs. 5 and 6. These are designed so that an identical heat flux is imposed on each container for the heat flux runs. Subsequent experience with this type of heating indicated an inadequacy except at low heat flux. At high heat flux (2000 Btu/hr-ft2 in this study) the heater ribbon appeared to expand and pull away from the main container, thus introducing an uncertainity in the imposed wall heat flux. This will be discussed in greater detail in later reports of this laboratory, and alternate methods of heating will be proposed. The heater circuit wiring diagram is shown in Fig. 8. For heat exchange with the ambient, it is necessary to remove the annular container from the assembly. 2

A total of 25 thermocouples is arranged at various locations throughtout the system as shown in Fig. 9. One thermocouple is used to measure the pressurizing gas temperature at the exit from the diffuser at the top of the tank, the point of which the gas enters the main container. Eight thermocouples are imbedded into the main container wall to measure its temperature. At four axial positions directly opposite four of the main container wall thermocouples, the temperature of the inside annular wall is measured. These measurements are taken to determine the effectiveness of the annular container in eliminating the temperature difference between its wall and that of the main container. At selected radial and axial locations in the main container, eight additional thermocouples, fixed in position, measure the temperature of the gas space. Since these are fixed position thermocouples, they are immersed in the liquid nitrogen until the liquid-gas interface passes. Because of their inherent heat capacity and the fact that gas condenses on them as they break the liquid surface, they do not measure the gas temperature reliably in the region of the interface. The measurement of temperatures in this region has been accomplished by four thermocouples which move with the interface and are always exposed to the gas. These thermocouples are mounted on the float of the level indicator and extend above the liquid-gas interface into the gas phase, This arrangement is shown in Fig. 10 and may also be seen in Fig. 7- In this way, a reliable monitoring of the gas temperature near the interface is obtained. Two different recording instruments are used in these studies. A 36channel Minneapolis-Honeywell oscillograph model 1012 "Visicorder" records 35

the temperatures of the walls of both containers and the temperature of the gas space in the main container. A 4-channel Sanborn (150 series) oscillograph records the weight of the liquid in the containers by means of a load cell, the level of the liquid nitrogen in the main container, the main container pressure by means of a pressure transducer, and the temperature of the pressurizing gas at the inlet to the main container. A typical Sanborn record for a run is shown in Fig. 11. The level indicator consists of what is essentially a potentiometer circuit with a moving contact attached to a float. A general view of the indicator is shown in Fig. 10o The float consists of two segments of an annular ring of HD2 styrofoam. Slide wipers are mounted on a framework which is attached to this float. The wiper arrangement is made of two directly opposed copper slides mounted on arms which are hinged about a common axis at the surface of the float. This arrangement maintains the wipers directly opposed at all times, even when the float pitches and rolls as it does when the liquid boils violently. Initially, one of the wires was made of chromel and the other copper, but excessive corrosion and subsequent unreliable contact between the slide and the wire made necessary a replacement of the copper wire with another of similar diameter but made of chromelo Figure 12 is the wiring diagram. Prior to filling the main container with liquid nitrogen, it was found necessary to purge the container with dry nitrogen gas. This eliminated water vapor from the tank space which would condense on the level-indicator voltage wires, insulating them from the wipers and reducing the efectiveness of the levelmeasuring system. 4

The purpose of the level-indicator has been three-fold. It is used to determine the velocity of the interface, as illustrated in Fig. 11, since it enables the determination of float location as a function of time. It can be used to determine the position of the liquid-gas interface, and thus the position of the floating thermocouples relative to the interface at any time throughout the run. Measurements indicate that the uncertainty of this indicator in determining liquid level is 1/16 in. The level indicator also has been used to determine bubble hold-up volume in the container, by measuring the drop in the level of the indicator upon the pressurization of the boiling liquid in the container. The bubble hold-up volume is then the product of the level drop and the cross-sectional area of the container. Figure 13 is a Sanborn oscillographic record showing the change in level of the float during pressurization and de-pressurization. From these data the total bubble volume in the liquid prior to pressurization can be found. It can also be noted from Fig. 13 that upon de-pressurization a greater vapor volume is formed that was initially present. This appears to result from flashing of the liquid which was heated somewhat during the time the liquid was pressurized as the vapor volume returned to essentially its original value following de-pressurizationo Bottled dry nitrogen gas was used as the pressurizing gas for all the experimental runs reported. To obtain the quantity of flow necessary to maintain a constant pressure during discharge, a surge tank is incorporated into the system (Fig. 1). Before starting discharge, the surge tank is pressurized to a high (100 psig) pressure, so that, when discharge begins, the 5

pressure rises in the main container very quickly to 35 psig. A regulator automatically maintains a constant discharge pressure of 35 psig throughout the run, as can be seen in Fig. 11. Two heat exchangers are utilized to obtain various values of inlet gas temperature. For the inlet gas temperatures between 0 and 1000F a boiling-water heat exchanger is used, and for the low temperatures, a liquid nitrogen heat exchanger is used. A variation in inlet gas temperature between the values +l00"F and -3000F is obtained by selectively wetting the surface of the heat exchangers with liquid nitrogen or boiling water and then allowing the ambient to heat or cool the pressurant to the desired inlet temperature. B. EXPERIMENTAL DATA The general purpose of the experimental system is to determine the variation of the mean density of the residual gas in the tank with a number of parameters which are imposed on the system. The gas space temperatures at the end of the run, as obtained from the various thermocouples in the system, are plotted versus distance in the tank for each run. This plot is then integrated with a planimeter and the (spatial) mean temperature is computed. From this and the pressure, the (spatial) mean gas density is obtained using an equation of state. The main parameters which are varied as the independent variables in the system are inlet gas temperatures and container wall heat flux. The inlet gas temperature is controlled over a range of from -300OF to +1000F by use of two heat exchangers as described above. Heat flux conditions have been adiabatic, heat exchange with the ambient, and imposed heat flux of 6

1000 Btu/hr-ft2 and 2000 Btu/hr-ft. Higher heat fluxes are expected to be used in the future. Another parameter which can be varied is the type of pressurant used. Nitrogen gas has been used primarily up to now, but it is expected that helium gas will be employed in the future. Time of discharge has been held constant at approximately 120 sec but may also be varied in future runs. Likewise, the discharge pressure has also been fixed at 50 psia in these runs. Future plans include changing the parameter to other levels. The following table catalogues all the experimental runs since August, 1959, listing the magnitude of the various parameters. For the runs from 44 to 49, not all the heat flux data were used for correlation. This resulted from uncertainty in the values of the heat flux imposed because, owing to expansion on heating, the heater wires altered their position on the tank wall. For these runs correlation was poor. This was the primary reason for re-wiring the tank, using heater ribbon having special mounting to prevent loss of alignment. Even this method does not appear to give results which are up to standard in reliability, as indicated above. 7

SUMMARY OF EXPERIENTAL DATA SINCE AUGUST, 1959 Run if No.n Date Tg P q" m n Remark No. 44A 8/25/59 + 36 48.4 76.5 Adb 87.5 1 Pressure fluctuated: disregarded 44B 8/25/59 + 43 39.4 58.4 Adb 70.0 1 Pressure fluctuated: disregarded 44C 8/26/59 + 40 49.4 105.6 Adb 95.0 1 Data used for correlation 44D No data collected 44E 8/27/59 - 3 48.8 104.0 1255 103.0 1 Data not used for correlation 44F 8/27/59 - 12 48.3 91.1 Adb 102.0 1 Data used for correlation 44G 8/27/59 - 2 49.3 107.2 1270 104.0 1 Data not used for correlation 44H 8/27/59 - 12 49-3 117.0 Adb 105.0 1 Data used for correlation 44i 8/27/59 - 4 49.3 125.2 1275 107.0 1 Data not used for correlation 44J 8/28/59 + 40 49.2 99.2 Adb 106.0 1 Data used for correlation 44K No data collected 44L No data collected 44M 9/14/59 + 7 48.8 100.4 1225 98.0 1 Data not used for correlation 44N 9/14/59 - 2 48.35 101.0 1250 99.0 1 Data not used for correlation 45A 9/2/59 + 76 44.17 102.1 Adb 105.0 1 Pressure too low: disregarded 45B 9/2/59 + 79 49.17 106.4 1260 100.0 1 Data not used for correlation 45C 9/2/59 + 63 45.17 108.4 Adb 102.0 1 Pressure too low: disregarded 45D 9/3/59 + go 48.56 115.6 Adb 102.0 1 Data used for correlation 45E 9/3/59 +103 48.56 130.3 1240 107.0 1 Data not used for correlation 45F 9/3/59 + 98 49. 36 110. Adb 975 1 Data used for correlation 45G 9/3/59 +103 48.46 119.3 1260 101.0 1 Data not used for correlation 45H 9/3/59 + 98 47.36 111. Adb 106.0 1 Pressure too low: disregarded 45I 9/14/59 + 81 49.35 122.1 1225 97.0 1 Data not used for correlation 45J 9/14/59 + 77 49.-35 104.1 1225 91.0 1 Data not used for correlation 46A 9/3/59 -299 47.36 98.8 Adb 97.5 1 Pressure too low: disregarded 46B 9/3/59 -125 48.36 100.7 Adb 98.0 1 Data used for correlation 46C 9/3/59 -269 50.36 97.4 1200 102.5 1 Tg fluctuated: disregarded 46D 9/3/59 - 32 46.36 99.7 1234 105.0 1 Pressure too low: disregarded 46E 9/3/59 - 77 47.36 90.5 1254 95.0 1 Pressure too low: disregarded 46F 9/3/59 - 50 47.36 79.2 Adb 87.0 1 Pressure too low: disregarded 46G 9/14/59 - 26 49.35 11.1 MAdb 108.0 1 Data used for correlation 46H 9/14/59 -256 44.36 125 Adb 107.5 1 Pressure too low: disregarded 46i 9/14/59 -103 48.85 108.4 Adb 110.0 1 Data used for correlation 46J 9/14/59 - 66 48.35 111.2 Adb 112.0 1 Data used for correlation 46K 9/14/59 -226 44.35 100 Mb 110.0 1 Data used for correlation 47A 10/22/59 -183 49.34 107.4 Adb 103.0 1 Data used for correlation 47B 10/22/59 -206 47.34 101 Adb 103.5 1 Pressure too low: disregarded 47C No data collected 47D 10/22/59 -228 49.34 106.6 1209 107.5 1 Data not used for correlation 47E No data collected 47F 10/29/59 -213 49.46 109.5 Adb 107 1 Data used for correlation 47G 10/29/59 -244. 48.46 109.9 Adb 111 1 Data used for correlation 47H 10/29/59 -173 48.96 107., Adb 112 1 Data used for correlation 47I 10/29/59 -159 48.46 107.6 Adb 110 1 Data used for correlation 47J 10/29/59 -123 40.46 120.8 1186 111 1 Pressure too low: disregarded 47K 10/29/59 -204 49.46 107.1 1200 106 1 Data not used for correlation 47L 10/29/59 -274 49.46 1ll.1 1216 107 1 Data not used for correlation 47M 10/29/59 -225 48.96 116.0 1209 112 1 Data not used for correlation 48A 11/12/59 + 22 48.4 118.2 3240 110 1 Data not used for correlation 48B 11/12/59 + 15 53.4 108.7 2100 108 1 Pressure too high: disregarded 48c 11/12/59 -244 48.4 19g.o 2240 108 1 Data not used for correlation 48D 11/12/59 -248 49.4 122.9 2248 112 1 Data not used for correlation 48E 11/12/59 + 94 53.4 102.7 2220 106 1 Pressure too high: disregarded 48F 11/12/59 + 59 54.4 109.0 2324 108 1 Pressure too high: disregarded 48G 11/12/59 + 81 34.4 147.0 2228 97 1 Pressure too low: disregarded 49A 11/12/59 + 22 52.9 98.3 3306 97 1 Pressure too high: disregarded 49B 11/12/59 + 12 52.4 114.3 3090 110 1 Data not used for correlation 49C 11/12/59 -212 47.4 116.9 3114 100 1 Pressure too low: disregarded 49D 11/12/59 -270 48.9 134.6 3134 113 1 Heaters off before discharge 49E 11/12/59 -266 54.9 107.2 2843 110 1 Pressure too high: disregarded 49F 11/12/59 + 94 54.9 118.5 3006 107 1 Pressure too low: disregarded 49G 11/12/59 + 94 54.9 109.4 3030 99 1 Pressure too high: disregarded 491 12/23/59 -220 51.50 103.7 2871 95 1 Data not used for correlation 49i 12/29/59 -270 49.o6 111.8 2695 105 1 Data not used for correlation 49J 12/29/59 -252 44.06 142.8 2651 104 1 Pressure too low: disregarded 49K 12/29/59 -102 49.06 164.5 2687 0 10 Data not used for correlation 47E No data collected8

SUMMARY OF EXPERIMENTAL DATA SINCE AUGUST, 1959 (Concluded) Run NO. Date Tg P ~ q mi n Remarks 49L 12/29/59 -102 49.06 119.9 2690 98 1 Data not used for correlation 49M 12/29/59 + 74 49.06 125.3 2691 103 1 Data not used for correlation 49N 12/29/59 + 94 49.06 106.2 2719 90 1 Data not used for correlation 490 12/29/59 + 94 48.06 133.2' 2727 100 1 Data not used for correlation 49P 12/29/59 + 98 99.06 166 2747 100 1 Data not used for correlation 50A 12/21/59 Exploratory long discharge time run; no data collected 50B 1/29/60 Exploratory long discharge time run; no data collected 51A 7/26/60 + 54 52.7 89.5 Amb 100 2 Data used for correlation 51B 7/27/60 + 94 46.7 98 Amb 78 2 Pressure too low: disregarded 51C 7/27/60 + 94 47.7 107 Amb 90 2 Data used for correlation 51D 7/27/60 + 36 47.7 114.5 Amb 91 2 Data used for correlation 51E 7/27/60 + 22 46.7 113 Amb 95 2 Data used for correlation 51F 7/27/60 + 52 42.7 112 Amb 104 2 Data used for correlation 52A 8/9/60 + 77 41.4 127.5 Adb 190 2A Data used for correlation 52B 8/9/60 + 98 44.4 109 Adb 182 2A Data used for correlation 52C 8/15/60 + 95 46.41 114 Adb 193 2A Data used for correlation 52D 8/15/60 -120 52.41 119 Adb 209 2A Data used for correlation 52E 8/16/60 + 74 49.41 117 Adb 203 2A Data used for correlation 52F 8/16/60 -102 50.41 121 Adb 203 2A Data used for correlation 52G 8/16/60 - 71 49.41 113 Adb 206 2A Data used for correlation 52H 8/16/60 - 48 49.41 117 Adb 202 2A Data used for correlation 52I 8/17/60 + 8 49.41 117 Adb 203 2A Data used for correlation 52J 9/1/60 -138 50.4 103 Adb 210 2A Data used for correlation 52K 9/1/60 -228 46.4 124 Adb 220 2A Data used for correlation 52L 9/7/60 -186 50.3 123 Adb 220 2A Data used for correlation 52M No data collected 52N 9/7/60 - 96 5p0 3 111 Adb 212 2A Data used for correlation 520 9/7/60 -168 49.3 123 Adb 220 2A Data used for correlation 52P 9/7/60 - 11 49.3 120 Adb 222 2A Pressure fluctuated: disregarded 52Q 9/7/60 + 31 49.3 122 Adb 230 2A Pressure fluctuated: disregarded 53A 8/10/60 + 82 49.41 118 542 198 2A Data used for correlation 53B 8/9/60 + 88 49.41 116 1083 185 2A Data used for correlation 53C 8/15/60 + 95 47.41 119 1083 203 2A Data used for correlation 53D 8/15/60 -144 53.41 107 1083 193 2A Pressure too high: disregarded 53E 8/16/60 + 86 49.41 119 1083 205 2A Data used for correlation 53F 8/16/60 - 98 50.41 113 1083 202 2A Data used for correlation 53G 8/16/60 - 52 49.41 115 1083 202 2A Data used for correlation 53H 8/16/60 - 48 49.41 120 1083 204 2A Data used for correlation 53I 8/17/60 + 4 48.41 117 1083 203 2A Data used for correlation 53J 9/1/60 -197 50.4 106 1083 219 2A Data used for correlation 53K 9/7/60 -132 49.3 124 1083 232 2A Data used for correlation 53L 9/7/60 -186 50.3 118 1083 221 2A Data used for correlation 53M 9/7/60 -154 50.3 119 1083 219 2A Data used for correlation 53N 9/7/60 -158 50.3 121 1083 218 2A Data used for correlation 530 9/7/60 + 17 50.3 119 1083 222 2A Data used for correlation 54A 8/15/60 + 98 52.4 124 2166 204 2A Data used for correlation 54B 8/15/60 -156 52.41 1ll 2166 186 2A Data used for correlation 54C 8/16/60 + 91 50.41 122 2166 206 2A Data used for correlation 54D 8/16/60 - 88 50.41 122 2166 199 2A Data used for correlation 54E 8/16/60 - 50 49.41 117 2166 204 2A Data used for correlation 54F 8/16/60 - 77 49.41 121 2166 204 2A Data used for correlation 54G 8/17/60 + 2 49.41 122 2166 289 2A Data used for correlation 54H 9/1/60 -190 49.9 110 2166 212 2A Data used for correlation 54I 9/7/60 -160 50.3 128 2166 218 2A Data used for correlation 54J 9/7/60 -183 50.3 124 2166 219 2A Data used for correlation 54K 9/7/60 -176 50.3 124 2166 219 2A Data used for correlation 54L 9/7/60 -183 49-3 126 2166 220 2A Data used for correlation 54M 9/7/60 + 26 50.3 122 2166 220 2A Data used for correlation 54N 9/7/60 + 31 49.3 122 2166 230 2A Data used for correlation g = Inlet gas temperature, ~F P = Discharging pressure, psia Q = Discharge time, second q" = Heat flux, Btu/hr-ft2 mi = Initial weight, lbm n = Tank model number 9

Tank Model Designations a. Tank number 1 refers to the tank as sketched in Fig. 2 of UMRI Report 2646-16-P, May, 1959. b. Tank number 2 refers to the same tank as (a) above, except that heater ribbon is used in place of heater wire, and Scotch thermosetting tape instead of asbestos. The tape is interwoven with the ribbon to help hold the ribbon in place. c. Tank number 2A refers to the same tank as (a) and (b) but with the annular guard tank mounted. Tank model assembly 2A is shown in Fig, 7C. ANALYSIS OF GAS- AND WALL-TEMPERATURE RESPONSE DURING TEE DISCHARGE OF A CRYOGENIC LIQUID FROM A CONTAINER The following analysis has been described and presented in Quarterly Progress Report No. 2, August, 1960, but owing to its bearing on experimental results obtained since and also to the character of this report, it is included here. The basic physical system analyzed is shown in Fig. 14. This consists of a cylindrical container from which the cryogenic liquid is discharged by means of a pressurizing gas. The first case considers the container exchanging heat with the ambient through a convection heat-transfer coefficient. The second case considers an arbitrary heat flux imposed on the outer surface of the container. The proper combination of the separate parts of the analysis, which is discussed below, provides the solution for simultaneous heat transfer with the ambient 10

and an imposed heat flux. This combination closely approximates the conditions imposed on cryogenic containers on space vehicles where both heat transfer with the ambient and external heat flux may be expected to occur. The following assumptions are made: (a) the velocity transient at the start of discharge of the liquid from the container is small compared to the thermal transients and therefore is neglected; (b) the axial conduction of heat is neglected in both the container wall and in the pressurizing gas; (c) the radial temperature distribution in both the container wall and the pressurizing gas are ignored, the temperature in each being lumped; (d) average convection heat-transfer coefficients are assumed to be constant; (e) physical properties of both container wall and pressurizing gas are constant; and (f) the dynamic response of the system is introduced by two sources: (i) change in the temperature of the pressurizing gas at the inlet of the container and/or (ii) the imposition of a heat-transfer interaction with the ambient. The heat-transfer interaction with the ambient consists of two separate modes: (a) heat transfer through a convection coefficient of heat transfer with an ambient at constant temperature and (b) an imposed heat flux on the outer wall of the container. It has been observed from experimental measurements that the liquid and wall temperatures below the liquid-gas interface had a negligibly small variation during the period of the discharge of the liquid from the container. This results from the fact that the liquid is at a saturated state corresponding to the initial pressure, and acts as a heat sink at constant temperature. Furthermore, it has a very large heat capacity and has a low 11

thermal resistance between it and the wall. Therefore, in the following analysis, heat transfer between the container and the ambient is assumed negligible for all regions below the liquid-gas interface. This is accomplished by assuming, in Case I, a constant ambient temperature equal to the liquid temperature below the liquid-gas interface, and in Case II, an imposed constant heat flux above the liquid-gas interface only. Thus, in Case I, the ambient moves with the liquid-gas interface, wetting only that part of the container wall above the interface, and in Case II, the imposed heat flux moves with the liquid-gas interface, affecting only that part of the container wall above the interface. In both these cases the difficulty arising from assuming the same convection coefficients of heat transfer above and below the liquid-gas interface is eliminated as had been previously done and reported. The differential equations from the First Law of Thermodynamics with associated initial-boundary conditions for this system are: For the gas: T + V 6T + bl(T - t) = 0 (1) For the container wall: at b2(T-t) (b3(Tat) (2) T(x,o) = T (3) t(x,o) = TQ (4) 12

T(o,G) = Tg (5) where T1 is the saturated liquid temperature and Tg is the temperature of the pressurizing gas at the inlet to the container. In Eq. (2), b3(Ta-t) corresponds to Case I, the moving ambient, where Ta, x Ve Ta = (6) T, x > VG and $ corresponds to Case II, the moving heat flux, where, x ve, = t (7) to, x > Ve The method of analysis for both cases is essentially the same and therefore only Case I will be carried out in detail. The results of Case II will be presented. 1. Method of Analysis a. Case I - Moving Ambient.-Upon scaling all temperatures to the saturation temperature of the liquid, the energy equations for Case I become: T* + V at- + bl(T* - t*) =O (8) t* b2(T* t*) + b3(t* - ) = 0 (9) 60 a T*(x,o) = O = T(x,o) - T1 (10) t*(x,o) = O = t(x,o)- T1 (1l) 13

T*(oG) = Tg (12) T a, x<VO a = o, x > VQ For mathematical convenience only, the above problem can be separated into the following two problems in which T- = T1+T2 and t* tl+t2, as follows, aT1 + vaT + bL(Tz - tt) = 0 (14 ) at- _ b2(T1 - tl) + b3(tl - o) = 0 (15) ao T1(x,o) = 0 (16) tl(x,o) = 0 (17) T1(o,G) = T* (18) aT2 + V T bz(T2 - t2) = (19) ao ax tz _ b2(T2 - t2) + b3(t2 - Ta) = 0 (20) aa T2 (x o) = 0 (21) t2(xo) = 0 (22) T2(o,G) = 0 (23) The solution of Eqs. (14)-(18) is obtained by the use of the Laplace Transformation in the timewise domain. The subsidary equation in terms of 14

the gas temperature T1, is, dTf 1 (; + b L r2T, O (24) dx V p+b with tIE transformed boundary condition, Th (o,p) =Tg/p (25) where b b3 + b2 (26) The solution of the above equation is obtained directly from the methods of treating ordinary differential equations. It is Xp blx blb2x = — e.e. e be (27) Tg P Combining Eq. (27) with the Laplace transformation of Eq. (15), the transformed wall temperature is found to be: blb2x _ blx V(p+b) = b2 e e V e (+b) (28) Tg p (p+b) The inverse transforms of Eqs. (27) and (28) can be obtained by the use of a table of Laplace Tralsforms;1 they are: -* e ~(08 ) + e ~ Io[2(s5) /, x~ VO(9 +,e5xK VG (29) 15

t- e t(is,-), x< V (30) g where (ns:,) e- - Io[2(s5b)1 ]/ (31) 0 blx (32) V 6- b2( - V) (33) T b2 (34) b2+b3 Io designates the modified Bessel function of the first kind zero order. The function V, defined by Eq. (31), has been obtained and calculated previously by Rizika,2 where it is presented in graphical form. The solution of Eqs. (19)-(23), which is the main concern of this analysis, is also obtained by the Laplace Transformation method. In this case it is convenient to use the Laplace transform in both the time and the space domains. Taking the Laplace transformation of Eqs. (19)-(23) in the x (space) domain results in the following two transformed equations with the appropriate initial conditions: dT2+VqT2 + b1(T2-t2) = 0 (535) dG *, /1 -VO dt2 _ b2(T2 - t) + b3a b -e = (6) 16

T2(qo) = 0 (37) 2(q, o) = 0 (38) Defining A(xG) = t2 - T2 (39) the container wall-gas temperature difference, the transformed container wall and gas temperatures can be found in terms of A where T is the Laplace transformed (in the x variable) temperature difference. They are: T2 = bl 1 e-V( )(q, *)d9* (40) -b\ b* b VqG~\ G 2= T l -e + bsa -b3 e} - b2 e. (q,* ) d* q ) q(b3-Vq) b2 (41) Taking the double Laplace transform of Eq. (39) with respect to x and 9, and the Laplace transform of Eqs. (40)-(41) with respect to 0, and combining produces, A = [v Tabv (42) p(p+b) I + p+b + q The inverse transformation of the foregoing equation with respect to x is (xb )V Vb3 ep] (43) p(p+b) On the other hand, the timewise Laplace transformation of the energy equation for the gas Eq. (19), in terms of A can be written as follows: 17

pT2 + V - T2 - bl = 0 (44) dT2(o,p) = O (45) Combining Eqs. (43) and (44) and solving for T2(x,p), and subjecting the solution to the boundary condition, Eq. (45), produces: * _ * p (Pb )x - Pp T2(x,p) T3 Tab3 (p+be V (46) p(p+b3) p(p+b3) p+b Using the timewise transform in Eqs. (39) and (46) results in the transformed temperature of the container wall, as follows: (x P) b3 - bx blx vb1pb = V b~bV 3 V ____ Ta p(p+b3) p(p+b3) (p+b) Using Laplace transform tables,l the inverse of Eqs. (46)-(47) are Ta = -s eX Gs ) - e l-e 4(s ] x V (48) Ta' where w hich is defined previously occurs with two diffe rent parameter systems (s,6) and (Ts,E)a Ihe solution of the problem as stated at the beginning is the linear combination of T1 and T2, Eqso (29) and (48 ), and tl and t2, Eqso (30) a~d (49). 18

b. Case II - Moving Heat Flux.-For the case of the moving heat flux, Eqs. (1)-(5) can be conveniently separated into the following two problems when the temperature is scaled to the saturation temperature of the liquid: 3T + V T + bl(T1 - tl) = (50) tl _- b2(T1 - tl) = 0 (51) a6G T1(x,o) = 0 (52) tl(x,o) = 0 (53) T1(o,G) = Tg (54) and aT2 + V aT + bl(T2 - t2) = 0 (55) at _ b2(T2 - t) - = 0 (56) T2(x,o) = 0 (57) t2(xo) = 0 (58) T2(o,0) = 0 (59) where B is defined in Eq. (7). Actually the solution of Eqs. (50)-(54) for T1 and tl is a special case of the solution of Eqs. (14)-(18) where b3 = 0 and hence i = 1. This special case has been solved. The second part, Eqs. (55)-(59) for T2 and t2, is solved in a manner similar to that used for solving Eqs. (19)-(23). The results are 19

T2(xG) - 5 + e- 3(s,5) - (l+b)V(sb5, x( VG (60) it2(xb = e+ eVA&(s5) )- a(s,61, x < V9 (61) where 5,s, and i have been defined previously and A(s,6) 5* e IO2(s ) d* (62) The function A(s,5) has been calculated and is presented in graphical form)3 The linear combination of Eqs. (29) and (30) with r = 1 and Eqs. (60) and (61) will yield the solution of the dynamic response of the gas and wall temperature of a pressurized container having an imposed wall heat flux. The combination of the solutions for the moving ambient case, Eqs. (29) and (48) and Eqs. (30) and (49), Case I, and the solutions of the second part of the moving heat flux case, Eq, (60) and Eq. (61), Case II, will provide the solution for the case in which both heat transfer with the ambient and an imposed heat flux occur. 2. Summary of Theoretical Results For convenience in using these results, they are presented in the following dimensionless form in which the various combinations indicated above have been performed. a. Case I - Moving Ambient. — (i) Pressurizing gas, x (< V@ T(x,')-T__ = e{i(Ris,) + e n Io [2(s)1 + ~TgT1-e l-e S(is,6s) - e [l-e si(s, l6) Tg-T J2 20

(ii) Container wall, x < VO i{1-) + [I-e-S9(T6 s,~]Tg-T2 Tg-T + (64) e 1 l-e t (s 5 + Te -S(Is, ) b. Case II - Moving Heat Flux. — (i) Pressurizing gas, x<: VG T(xO) GT e= e-s (s,6) + e I + Tg9T2- (6 5 0( 1I (65) Tg-TT T q"Po/ S agP + e (S16)-(S r (ii) Container wall, x< VG t(x,G)-Tje = @q"Po/hgP r + e-SFA(sb) - (sb]1 + e-S4(s, ) (66) Tg-TQ Tg-T L Two functions V(,s,~5) or 4f(s,b) and A(s,6) have been given in a previous progress report4 and are necessary for the calculations of T(x,G) and t(x,G) using Eqs. (63)-(66). The function (rjs,5) or 4(s,b) is presented here in Fig. 15. This function has been found and is tabulated by Rizika. The function A(s,5) has been found and is tabulated.3 This function is presented here in Fig. 16. At the moment both function 4 and A have been programmed on the IBM 704 for a numerical tabulation which makes their use more convenient and practical than the curves given. 21

In Eqs. (63)-(66) the quantities s, 6 and n are defined as: s = h (67) pCpA V 6 hP (= X) (68) 1n - (69) 1 + hoPo/hgP 3- Influence of System Parameters on Gas Temperature Response Equations (63)-(66) describe the response of both the wall and gas temperatures for the boundary conditions of an imposed ambient temperature (moving ambient) and an imposed heat flux (moving heat flux). In this section the influence of the system parameters on the response of the gas temperature for the case of a transient introduced by heat transfer with the ambient (moving ambient) is examined. Similar analyses can be done for the case of the moving heat flux and also including the influence of the system parameters on the wall temperature, but for the sake of brevity the analysis for the gas temperature alone will be presented. Sufficient detail will be given, however, so that the other cases could be carried out if desired. For the case of the moving ambient, the response of the gas temperature is given by Eq. (63), which may be written as T(x,o)-T = T (x, ) + T2(x, ) Tg-Tj Tg-Tj Tg-Tj (70) T1 (x,) + Ta-Tf T2(x,G) Tg-T~ Tg-Tj Ta-TI 22

in which Tl(x,G) = e -s {(s,6) + e T Io2(sb) /21 (71) Tg-T1 and T2- e () - e_'V(rIs,5) - (l-)1-es(s,b) (72) Tg-T= g-Tge_ Thus, it may be seen that the dimensionless gas temperature response may be written: T(x,G)-Tj f Ta-Tl (73) Tg-Tj Tg-Tj The term (Ta-Ti)/(Tg-Ti) may be imposed on the system arbitrarily and indicates the manner by which the influence of the ambient is introduced into the theoretical results. The parameters s, 5 and r are defined above in Eqs. (67), (68), and (69) in terms of the system parameters and time. The parameter s is made up of properties of the gas and V and may be considered a gas parameter; the parameter 6 is made up of wall properties, 0 and x, and may be considered a wall parameter. The parameter q introduces the effect of the relative convective heat transfer between the gas-and-wall and walland-ambient. A value of r = 0.5 indicates approximately equal convective coefficients ho and hg, whereas a value of j greater than 0.50 corresponds to conditions for which hg is greater than ho. The range of possible values for n is from 0 to 1o0, with the more probable range for these ea periments being from 0.50 to 10, i.e., for hg greater than ho. 23

To show the influence of s, 5, and r on the gas temperature, two plots have been prepared for two values of 1. Figure 17 is for rj = 0.75 and Fig. 18 is for j = 0.50. Each plot gives Tl(x,G)/(Tg-Te) and T2(x,A)/(Ta-TQ) as a function of s with 5 as the parameter. The dimensionless gas temperature (T(x,G)-T2)/(Tg-T2) is formed from Eq. (70) and thus requires the specification of the ratio (Ta-Tt)/(Tg-T2) in addition to the functions Tl(x,G)/(Tg-T~) and T2(x,BG)/(Ta-Tl) of Figs. 17 and 18 to complete its calculation. However, Ta-TA for a value of equal to 1.0, Figs. 17 and 18 may be employed directly Tg-Tl to obtain T(x, 0)-Ti which will be discussed later. Tg-Tj The absolute value of the gas temperature is written from Eq. (70) as T(x,@) = Tj4(Tg-TI) T(x@ + (Ta-TQ) 2(x@l (74) LTg-Tj. Ta-T j Hence, large values of T(x,G) and low gas density may be expected to correspond to large values of (Tg-T2), high inlet temperatures, and large values of (Ta-TI), high ambient temperatures. In pressurized discharge systems for cryogenic liquids T~ is usually fixed by the choice of liquid. Actually, it will be observed from Eq. (70), and also on physical grounds, that a high gas temperature and lower gas density results from the ratio (Ta-T2)/(Tg-Ti) being larger than 1.0, as this corresponds to Ta being greater than Tg, and heat is thus transferred to the wall and then to the pressurizing gas at least in the upper portions of the container. Large values of T(xG) also are associated with large values of the ratios Ti(X,@)/(Tg-Tj) and T2(x,G)/(Ta-Ti). These two important ratios are 24

given in Figs. 17 and 18 for rj equal to 0.75 and 0.50, respectively. The parameter is 6, the wall parameter and the abcissa is s, the gas parameter. For the conditions for which these curves are drawn Tj(xg)/(Tg-Te) is the significant quantity governing for the range of s from O to about 2 and 3, and for s greater than this quantity T2(x,@)/(Ta.-T) appears to be the significant quantity. What becomes evident from these results is that a high value of gas temperature (low gas density) is to be expected with low values of s, high values of 5 and low values of ry, Thus, this may be summarized by observing that for high values of T(x,Q), the following conditions should be obtained. a. Low Value of s: Since s =. x, this condition corresponds to ~CpAV a small value of gas space heat transfer coefficient, hg, and perimeter to A A flow area ratio, A. A small value of A is obtained with containers having a circular cross section of large diameter. In addition, a low value of s is obtained with high discharge rates (large interface velocity V) and employing a gas as a pressurant having a large heat capacity Cp and density p, although the latter is somewhat contradictory for those conditions for minimum mean gas density in the container. As is discussed later, it is desirable to select a pressurant and the conditions of pressurization conducive to small gas density. In regards to Cp, a large value of this is desired to achieve small values of s. It is important to note relative to this requirement the exceptionally large values of Cp for hydrogen and helium gas. At room temperature Cp for hydrogen is approximately 16 times that of oxygen, and helium about 6 times greater than oxygen. 25

hgP b. High Value of 5bo since 5 -- - (-X), this quantity is made large by large hg and P-o An increase in hg is contrary to that corresponding AO to small s and thus it is difficult to generalize on this quantity. The importance of the magnitude of this parameter will probably depend on the conditions of the discharge process and it seems better to decide each case separately. However, in a great many instances it probably will be desirable to have hg as small as possible, if this is a controllable variable. A large P- ratio is obtained by using container walls having small thickness. Ao For large S it is further desirable that the wall be of a material having a low product of p'C'. The condition on the use of these results is that 9 > V but within this a large interface velocity V will contribute to an increased 5. c. Low Value of rloj-Low values of T1 correspond to large values of the ratio hoPo/hgP. This condition is associated most practically with hO being greater than hg. Under these circumstances the heat transfer to the container from the ambient becomes very sig~Aificant and is reflected in the rem suits of T(x, ) o To indicate these influences directly, the dimensionless gas temperature (T(x,>)-Ti)/(Tg-Tl) is plotted in Figo 19 against s for values of 7 = 0o50, and 075 and 5 = 025 and loO and for the ratio = l, i, oeo for Ta = Tgo Tg-Tj A similar set of curves for other values of (Ta-Tl)/(Tg-TI) may be constructed from Figs. 17 and 18 for B = 0 50 and O 75 Minimum pressurizing gas density is a function of other variables as wello For most low pressure gases the density is written 26

P PM ~P RT RT Hence, the density is also minimized for conditions corresponding to lowest possible level of pressure and the use of a gas with small molecular weight. In this respect attention is drawn once again to helium and hydrogen as desirable pressurants. 4. Calculation Procedure The gas and wall temperature distributions over the length of the container are found from the equations derived from the theoretical analysis. In the analysis, hg, the inside heat-transfer coefficient, ho, the outside heat-transfer coefficient, 6'C', the heat capacity of the wall, and OCp, the p heat capacity of the gas, are treated as invariants. Since constancy of p'C' is a fair approximation an average value of O'C' for aluminum (6061-T6) P P at -2600F is used in all the calculations. Owing to the uncertainity in estimating the values of ho and hg, several values (in this case from 1 through 4 Btu/hr-ft2-_F) are chosen and the results of these calculations are compared with the experimental data. The heat transfer. In the experimental model, ho = 1 and hg = 2 Btu/hr-ft2-~F Btu appear to give the best results in the moving ambient case. Also hh - ft2F seems to be a proper value for moving heat flux case. These results are discussed later in this report. 27

5. Determination of Mean Gas Density for use in the Theoretical Equations Obtaining the correct value for p, the mean gas density is accompanied by a trial and error process. First a mean temperature Tm = l(TZ+Tg) is assumed. This provides a mean density to be used in gas temperature equations. Then the gas temperature distribution is calculated and a new mean temperature is obtained. The next step is to plot the computed mean temperature against the assumed mean temperature. Each trial will provide a point on such a plot. Another mean temperature is assumed and calculations are repeated. A straight line through two such points normally will suffice to define the locus of assumed vs. calculated mean temperatures. The intersection of this line and a 450 line passing through the origin will determine the true mean temperature. The true mean density then will be obtained using the equation of state. Figure 20 shows a number of points obtained for this process on a computed temperature-assumed temperature plot. For each inlet gas temperature, there are two points through which a straight line is drawn. The points on Fig. 20 are the calculation results for an adiabatic container having hg = 2 Btu/hr-ft2-OF. This trial and error process must be repeated for every inlet gas temperature to obtain the mean density as a function of the inlet gas temperature from the theory. Thus, for each inlet gas temperature, the true mean density is known, Using values of the mean density so determined, it is possible to calculate the wall temperature distribution without having to repeat any of the trial and error process. 28

D. COMPARISON OF THEORY WITH EXPERIMENT The use of these analytical results requires a knowledge of the system parameters. One of the most important of these but also one about which little is known is hg, the average gas-space heat-transfer coefficient. Owing to the relative uncertainity surrounding an a priori determination of hg, these theoretical results are computed for a range of values of hg of from 1 to 4 Bt2 and then compared with experimental data, the purpose hr-ft.OF being to establish an approximate magnitude for this quantity which will adequately represent the system. Figure 21 is a plot of mean density vs. inlet gas temperature for the above-mentioned range. This figure has been computed for an adiabatic container. The comparison with experimental data Btu shows that the analytical curve for hg = 2 hrft2_ oF closely approximates the data. The rest of the calculations have been carried out for hg = 2 and 3 Btu/hr-ft2-~F. It is important to note in regard to these results that a calculation of hg from established heat-transfer correlations for free convection5 corresponding to the conditions of the experiments (Figure 21) give a value between 2 and 3 Btu/hr-ft2-OF. Since this also is the range of values for which the theory and the experiments are in agreement, these results suggest that the convective heat-transfer processes within the gas space are governed largely by free convection. Whatever influence may be introduced by the axial flow resulting from discharge apparently is not large, at least for these experiments where the interfacial velocity was approxi - mately 0~025 ft/sec. As an estimate (yet unchecked), it might be anticipated. that these processes will remain to be controlled by free convection as long 29

as the Grashof number is very much greater than the Reynolds number based on discharge velocity. The effect of increased discharge velocity will probably tend to increase the value of hg. The comparison of theory with experiment is separately discussed for the two basic cases, namely, the moving ambient case and the moving heat flux case. 1. Moving Ambient Case In this case there is heat exchange between the ambient and the tank wall through a heat-transfer coefficient ho. The corresponding gas-temperature response is given by Eq. (63). Assuming that hg is essentially the same as in the adiabatic container, an approximate value of ho can be determined by comparing experimental data with analytical results calculated for h = 2 and for several values of ho. Figure 22 indicates that hr-ft2-~F ho = 1 Btu/hr-ft2-OF is a reasonable value for the average outside coefficient of heat transfer. Figure 23 is a plot of gas-temperature distribution 90 seconds after beginning of discharge. As may be seen in this plot, theory and experiment agree very closely for hg = 2. Note that in the region of the interface, the floating thermocouples indicate a sharp temperature gradient, whereas at this point the theory predicts a sudden change from gas temperature to the initial liquid saturation temperature. The fixed thermocouple 3 inches above the liquid-gas interface measures slightly below the theoretical temperature at that point. This probably results from the thermal lag of the thermocouple owing to its heat capacity and its relatively recent emergence from the liquid bulk. 3o

Figure 24 shows the wall-temperature distribution as computed with the theory, Eq. (64), for three inlet gas temperatures. Experimental results for an inlet gas temperature of 482R are shown. It will be observed that the experimental data fall above but are closely parallel to the theoretical curve. It is believed that this results primarily from the use of T. = 140lR in Eq. (64), the same value of T2 as for the gas-temperature response, Eq. (63). Whereas T~ = 140~R is reasonable for the gas temperature, it has been observed in experiment that owing to heat transfer with the ambient and to condensation of pressurizing gas on the cold wall in the region of the interface, the wall actually enters the gas space at a somewhat higher temperature. Should this be allowed for in the theory, it would cause the curves in Fig. 24 to fall higher and move in line with the experimental results. As an indication of this, the saturation temperature at 50 psia, the pressure of gas, is shown on Fig. 24, which could be used as a base for the theoretical curves. 2. Moving Heat Flux Case In this case the heat transfer is imposed in the form of a constant heat flux on the outer surface of the container. The theoretical model for this case has the heat flux imposed only on that portion of the wall above the liquid-gas interface and, thus, must move down the wall with the speed of the interface. Hence the name "moving heat flux," as described above. The response of both gas and wall temperatures is given by Eqs. (65) and (66), respectively. As a special case of the moving heat flux an adiabatic, or zero heat flux condition (q" = 0), will first be studied. This is convenient as it is 31

possible to control an adiabatic condition experimentally quite practically, thus providing a check of the theory for this limiting condition. It will be observed that Eqs. (65) and (66) for this condition (q" = 0) become identical with the corresponding results for the moving ambient case, Eqs. (63) and (64) when q = 1 (i.e., ho = 0), as would be necessary. Experimental results for comparison with the theory, Eqs. (65) and (66), for q" = 0 are given in Figs. 25-27. These data were taken with the apparatus shown in Figs. 2-7. The annular container acted as the thermal guard providing an accurately controllable adiabatic environment for the container. As may be observed, a fairly favorable comparison is obtained between the theory for both the gas and wall temperatures for this case. Comparison of the theoretical results with experimental data for the case of finite heat flux is given in Figs. 28-33. The range of heat flux (q") in these data is from 0 to 2166 Btu/hr-ft2. The experimental apparatus employed is that shown in Figs. 2-7. The heating effect is obtained from the disipation of electric current in electrical resistance ribbon tightly wound around the test container in four separately controlled sections, as described previously. Electrical power is measured by a Weston 310 wattmeter, and the heat flux is found from the ratio of measured electrical power to the outside container area covered by the resistance wire. At the lower heat flux (up to 1083 Btu/hr-ft2), the agreement between theory and data is reasonably favorable. These results are given in Figs. 28-30. However, a tendency for the experimental data to fall below the theoretical curve is observed. This is especially true of the wall temperature 32

at the upper sections of the container. The gas temperatures as measured by both the floating and fixed thermocouples are in notable agreement, as seen in Fig. 29. In general, however, up to approximately 1083 Btu/hr-ft2 heat flux, the theory and experimental data are in reasonable accord, At higher heat flux a distinct departure is observed between the theory and experimental data. This comparison is found in Figs. 31 and 32, which show the gas- and wall-temperature distributions corresponding to a heat flux of 2166 Btu/hr-ft2. The departure is most strikingly evident in Fig- 32 where the wall temperature is measured at the container top to be as much as 200'F below the theoretical prediction. An examination of the wall temperatures in the annular guard disclosed the probably reason for this discrepancy. The annular guard wall temperatures were much higher than those in the container wall at corresponding elevations in the upper regions of the assembly. This suggested the possible expansion of the heater ribbon away from the container at the higher heat flux, thus reducing significantly the transfer or heat to the container itself with, consequently, a much lower measured wall temperature in those regions, (This was later confirmed to be the case and will reported later.) An opposite effect would, of course, be found on the annular tank since expansion of the heater ribbon would tend to cause the wire to be pressed. more closely to the wall From these results it appears necessary to abandon the use of externally wound electrical resistance wire for heat flux measurements, at least in the higher ranges of heat flux. At the moment consideration is being given 33

to the design of a radiant device for the transfer of a specified heat flux. It is felt that the departure of theory and data at these higher heat fluxes is not a result of an inadequate theory, but that the present experimental system did not impose the same conditions on the physical system as used in the theory. A summary of the data for the moving heat flux case is given in Fig. 35 which shows the final mean gas density as a function of inlet gas temperature for a range of heat flux. The solid lines represent the theory. As may be seen, the gas densities fall away from the theory at the higher heat flux. The theory probably predicts a truer result and the difference may be attributed to those effects discussed above. 34

IIo BOILING OF A CRYOGENIC FLUID UNDER REDUCED GRAVITY The test platform as described in Quarterly Progress Report No, 2, 1960, has been constructed, and is shown in Fig. 34. A 74-lb dummy load is mounted on the platform to simulate the test package during preliminary drop tests to check the performance of the buffer assembly in decelerating the test platform. The buffer assembly was received from the manufacturer during this period. After several tests, it was apparent that the test platform was receiving too large an initial shock upon impact with the buffer piston, due to the necessity of accelerating the piston before the declerating action of the hydraulic oil can become effective. To reduce this shock, the mass of the piston was reduced to approximately half its original value by reducing the wall thickness. In addition, a heavy-duty spring was mounted on the piston. As the spring is compressed, it serves to accelerate the piston before contact with the test platform is made, reducing the impact. Figure 35 is a view of the hydraulic buffer assembly and shows the test platform as it would appear at the moment of impact. To obtain a quantitative measure of the impact shock and of the performance of the buffer assembly, a 1000-g piezoelectric accelerometer is mounted on the test platform and a strain-gage-type pressure transducer is mounted on the buffer piston face. The accelerometer measures the deceleration of the test platform and the pressure transducer records the pressure behavior in the hydraulic cylinder. The data will be displayed simultaneously on a 35

dual-beam oscilloscope and recorded with a polaroid camera. This information will permit the evaluation of the techniques to be attempted in reducing the initial impact shock. A test-platform release mechanism has been constructed and tested, with satisfactory performance. The platform is suspended by a single 17-gage chrome "A" wire. To release the platform, the wire is melted by passing through it approximately 50 amp from a 220.v source by means of clips spaced 1/2 in. apart. Figure 36 is a view of the burning wire mechanism, showing the wire, clips, and the electrical contact which swings free as the platform drops. The release mechanism has two major advantages over a mechanical type. No side forces are imposed on the test platform during release and the physical parting of the wire link permits the determination of the instant of release by electrical measurements. Safety interlocks are provided so that the test platform cannot be released unless certain necessary conditions are fulfilled. These conditions are indicated by lights on the control panel and are as follows: 1. The buffer piston must be in its uppermost position. 2, The door of the safety enclosure surrounding the buffer must be closed. 3- The "basement ready" switch must be closed by the observer at the basement level. 4. The "p:latform ready" switch must be closed at the upper platform level.

When these conditions are fulfilled, the platform may be released from the control panel by closing a "drop" switch. The safety interlock system is diagrammed in Fig. 37. A three-station intercom system has been installed to permit voice communication between the control panel, basement level, and upper platform level. The 0- to l-g accelerometer to be used in measuring the platform accelerating during its drop has been received from the manufacturer. It is rated to withstand a maximum acceleration of 50 g's. Should the impact upon deceleration be greater than this, the accelerometer will be shock-mounted to protect it. Attempts are presently being made to reduce the initial impact and will be continued during the next period. An insulated container for the liquid nitrogen test package is being constructed. A 1/2-in. aluminum sphere has been obtained for use as a calorimeter in the transient boiling process and is being instrumented. Preliminary tests will be made at normal gravity before installation of the reduced gravity test platform. 37

III. HEAT TRANSFER TO A CRYOGENIC FLUID IN AN ACCELERATING SYSTET The construction of the hardware for the test vessel to be used with a cryogenic fluid has been completed. The test vessel was shown in Fig. 18 of Quarterly Progress Report No. 2, 1960. Assembly is approximately 75% complete, requiring only calibration of the thermocouples to continue. The thermocouples, used for measuring heater surface and liquid temperatures, are being calibrated at three fixed points; the mercury freezing point, equilibrium between solid and vapor C02, and equilibrium between liquid and vapor nitrogen. Three thermocouples, 1/32-in. OD, are inserted radially in the heater cylinder at the same level, 1/16 in. below the heater surface to obtain an average temperature. The surface temperature will be calculated by extrapolating the measured temperature to the surface, using a temperature gradient calculated from the measured heat flux. With the present apparatus it is not possible to condense the vapor nitrogen due to boiling, nor continuously to replenish the supply of liquid nitrogen with the system under rotation. To keep the time required for the heater surface temperature to attain the possible new steady-state value due to acceleration as short as possible, the thermal inertia of the heater block must be as low as possible. Hence, the heater block is made as thin as possible consistent with a thickness sufficient to smooth irregularities in heat flux which may be present at the face in contact with the electrical heater resistance elements.

Figure 38 shows a cross section of the heater assembly. The heating suface is one end of a copper disc 3 in. in diameter by 3/4 in. thick. A thin copper skirt, 0.002 in. thick, is soldered around the edge to provide a continuous surface and at the same time keep the heat losses by conduction from the periphery to a minimum. Woods metal (meltin point = 87~C) was used as the solder metal to avoid deformation of the thin copper skirt which would otherwise occur with the normal type of soft solders. The thickness of the copper disc does not permit inserting thermocouples at different levels to measure the temperature gradient. With this configuration the heat flux is expected to be below 25,000 Btu/hr-ft2, and the error due to extrapolating the measured temperature using a calculated temperature gradient is expected to be small. The construction of the mercury slip ring, described in Quarterly Progress Report No. 2, 1960, for transmitting a stable, large d-c current to the rotating number has been completed and tested. Upon applying 6 v d-c to a resistive load such that a current of 8 amp was drawn through the slip ring, the variation in current upon rotation was 1.5 ma peak-to-peak at twice the rotational frequency. By doubling the voltage for the same current, the variation was reduced to less than 1 ma peak-to-peak, as might be expected. The variation occurs because it was necessary to split the pairs of slip ring rods in semi-circular segments for assembly purposes. Every half revolution the orientation of the rings is such that the electrical resistance path through the mercury is increased by a slight amount. iThis could be eliminated. by a major design change, but is not deemed desirable at this stage. 39

Upon assembly of the test vessel described above and completion of experimental runs for boiling data from the flat plate, the mercury slip ring will be used to obtain data on the influence of acceleration (increased force fields) upon the peak heat flux with a cryogenic fluid. In the interim, some preliminary data will be obtained with water as the boiling fluid to determine if the trends are consistent with fluids of widely varying properties. Figure 39 shows a preliminary design of a cylindrical heater configuration wherein the acceleration vector will be parallel to the heating surface. Such a configuration will permit the investigation of the influence of heating surface orientation on the boiling characteristics of a cryogenic fluid in the presence of force fields greater than normal gravity. Tubular heater elements are to be tightly coiled and inserted within a copper ring. The spaces between will be filled with a metal such as soft solder to conduct the heat from the heater elements to the copper ring. The outer surface of the copper ring acts as the heat-tranlsfer surface. By the judicious use of insulating materials and air spaces, the heat losses through the ends of the cylinder will be kept at a minimum, providing the desired radial flow of heat through the copper ring. Thermocouples in the copper ring will be used for measuring the surface temperature. It is anticipated that with this orientation, the contribution of nonboiling convective heat transfer with increasing acceleration will-be quite significant. To isolate the contribution due to boiling, the sequence of the experimental program will be first to employ the flat plate heater, where the 40

acceleration vector is normal to the heated surface, and then to conduct the experiments with the cylindrical heating surface, where the acceleration vector is parallel to the heating surface. 41

REFERENCES 1. Campbell, G. A., and Foster, R. M., Fourier Integrals, Van Nostrand Co., 1948, p. 79, Par. 655.1. 2. Rizika, J. W., Trans'. ASME, No. 78, 1407 (1956). 3. Arpaci, V. S., and Clark, J. A., Trans. ASME, 80, p. 625-634 (1958). 4. Clark, J. A., Arpaci, V. S., et al., No. 2, UMRI 03583, University of Michigan, Ann Arbor, Michigan, July, 1960. 5. McAdams, W. H., Heat Transmission, third edition, McGraw-Hill, 1954. 42

vent vent S/O M/O REG: pressure regulator svalvety q M/O: manual opercated i I S/O solenoid operated fast cting vent ( pressure gage M/O D4 valve xshut-off M/0 eft co, ~~~~shlt-ofT fil S/0 S/b MAIN REG CONTlINER SURGE TANK te fast-acting heat exchanger shut-off " M/0 l shut-off REG M/O REG vent vent S/O M/O LIQUID N2 DEWAR 2500 psi N2 BOTTLE Fig. 1. System for pressurized discharge test.

Fig. 2. Photograph of experimental apparatus Fig. 3. Photograph of experimental apparatus.

Fig. 4. Photograph showing li quid nitrogen f illing apparatus.,1, Fig. 5. Photograph of main container. ~iiii:cij'itt~i Fig. ~ ig 5. Phtgrp hotongrp ofi maitrn container. praus

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PRESSUR.I ZNG INLET VE NTS PISTON LEVEL INDICATOR CONTACT WIRES FLO ATI NG THERMOCOUPLE COLUMN HEATERS 4 GASSPACE 1/?. STAINLESS STEEL FiOATING TH IN- WALl, /. A I. 0 THER MOCOUPLES TUBES 12 I.D. ALUMINUM PIPE 606 1- T6 WALLTHICKNESS tEXED POSITION THERMOCOUPLES ANNUILAR CONTAINER \ISCHARGE LINE FOR BOTH MAIN AND ANNULAR CONTfINERS Fig. 7. Sectional view of main and annular containers.

230 VOLTS'"~t IQ ~ I^ I I @AMMEER O VOLTMETER HTR HEATER VARIAC VARIAC VARIAC VARIAC XFMR TRANSFORMER ___ X ___''' XFFMR I 1 T A 1 HTR - HTR -- - HTR - LHTR Fig. 8. Resistance heater wiring diagram.

SEC T/O/V -A VL ENARGED V/E-W OF FLOAT/NG T E THERMOCOU/PLE S Z6 16 8iY' 6 q A r-ig. 9. Themc I! To II' i system. ] 9' /s. t I!1113.9 ALL D/IMNES/O/S -ARE IN INCHES A A Q TI-IERMOCOL/PLE /vNO Fig. 9. Thermocouple locations in system.

....: 4 F~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ig.10

WEIGHT OF LIQUID NITROGEN IN TANK (LOAD CELL)..................... a'";AS',' t \:e X A:T \+O':~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ io CLR }IC/A<SBF IN~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i PISTON LEVEL INDICATOR JOE-,~~~~~~~~~~A C~~~~~~~~~~~~~~~~~~~~ TANK PRESS RE.E Fes.LET GAS TEMPERATURE 1.i 7,~~~i Fig. 11. A typical Sanborn oscillographic record of a run.

_-II ~ 2,v T ACNK ZSMAFS. 26S'VC. EL EC7rOL YE/c Z CO~N~~DE~~NSEiioN OFF Fig. 12 Wiring.iagram of liquid level indicator

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CASE 1 CASE I Moving Heat Flux Moving Ambient Temperature t(X,9) T(.X,e) movingh GAS h 0 interf ace UQUlID container wall Fig. 14. Analytical model.

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0.9 ___ ___ ~~~~~~~~~~~~~~~~~~~~~~~~~Tg 0.9 T - - 0.8 - _ - - - hg ~~~~~~~~~~~=0 - - - - 0..7 LL 0.6 ___ U.0. DISCHARGE qE0.5 a__u z 0.4 w ao 0.3 4 CASE I H F (q) INAIO EI Z CONTAINER AND AMBIENT.__ __ ____ __ _ __ _ _ _ _ _ _ _ _ _ o.2 0. 6 *120 SECS P * 50 PSIA 0. I * EXPERIMENTAL RUNS WITH NO HEAT FLUX - ---- THEORY 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 INLET GAS TEMPERATURE, Tg:R Fig. 21. Mean density vs. inlet temperature - zero heat flux.

600 CASE I: CONVECTIVE HEAT TRANSFER BETWEEN CONTAINER AND AMBI ENT 500 TINLET GAS AMBIEN 2 hg:3 BTU/HR-FT 2-F 20 O 0 yI BTU/HR -FT F =90 SECS. OM 400 P I50 PSIA. EXPERIMENTAL DATATO FIXED THERMOCOUPLES RUN 51 o FLOATING THERMOCOUPLES w _ __ THEORY 300 Cr h9 3 GAS - LIID w Li O I D~ w 200 TSATURATION @ PGAS 100 V _ LIQUID-GAS INTERFACE 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 TOP OF BOTTOM OF CONTAINER X FT. CONTAINER Fig. 25. Gas temperature distribution in container at 90 seconds from discharge.

400 CASE I: CONVECTIVE HEAT TRANSFER BETWEEN CONTAINER AND AMBIENT hg=3 BTU/HR-FT -~F 350 \ _ h, = I BTU/HR-FT" F Tg =600 ~O = 120 SECS. p = 50 PSIA. ~ EXPERIMENTAL RUN 51E, | \Tg =5000R] Tg=482 R THEORY 300 o.. -Tg =4000OR w Id c 1 250 w I-. -J 200 Tsot. @O 50 psia I 50 Ti Tsat. @14.7 psio 100 0 0.5 1.0 1.5 2.0 2.5 3.0 TOP OF BOTTOMS OF CONTAINER DISTANCE X, FT CONTAINER Fig. 24. Wall temperature distribution at end of discharge.

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7~~~~>W5.WSt: 0.....,,,v.... s5 8....vi P x a' r _1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Kra nii m 020j1 l i! i-I _^; _-:.........0 0,; Fig. 34. Reduc ed gravity test assembly. Fig. 35. Hydro-+.l inbufe fo aretig tstasemly. ex~~~~~~~~~i Fig. 39. Hydraulic buffer for arresting test assembly.

Fig. 56. Eiectrical release mechanism for test assembly.

PtfS71// PhA7TFRM BAIMENr IROP.. )DOWFt RaEAPY RE3aY REAPY stADY Fig. 57. Diagram Of saf ety interlock system.

Chromn,gn p/q7~g 7 54(r face c~002 copper // foil___ Pfj th17 nlcAIl~ef —-- - --— 002 — _crre T Fg58 Pltheigeeetfrroeiflis Fig. 38. Plate heating element for cryogenic fluids.

Ther- rcooup/e, A cce/era f;o Te-r/en h eno h dat n - e/ A C. m eXle~A Aleatli \ I I ~~i I dFc. 74r/r ~Sturface\, A., idT 1, /hea4er ele.,enfs -~..>~~~~~~ e~m~hemd /, c SoIder Cop'er Ri'n? Fig. 39.vertically oriented surface for crygenic fluids. Fig. 59. Sketch of proposed vertically oriented surface for cryogenic fluids.

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