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NASA Technical Memorandum 106201AIAA-93-1968 NASA-TM-106201

I°IC15001=I06_

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Mixing and Transient Interface Condensationof a Liquid Hydrogen Tank

C.S. Lin

Analex CorporationBrook Park, Ohio

and

M.M. Hasan and T.W. NylandLewis Research CenterCleveland, Ohio

Prepared for the29th Joint Propulsion Conference and Exhibitcosponsored by the AIAA, SAE, ASME, and ASEEMonterey, California, June 28-30, 1993

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https://ntrs.nasa.gov/search.jsp?R=19930019063 2018-09-01T00:10:02+00:00Z

MIXING AND TRANSIENT INTERFACE CONDENSATION OF A LIQUID HYDROGEN TANK

C.S.Lin

AnalexCorporation3001AerospaceParkway

, Brook Park, Ohio 44142

M.M. Hasan and T.W. NylandNational Aeronautics and Space Administration

Lewis Research CenterCleveland, Ohio 44135

Abstract h heightmeasuredfrom thetankbottom

Experimentshavebeenconductedtoinvestigatethe hfg latentheatofcondensation

effect of axial jet-induced mixing on the pressure reduc- Ja liquid Jakob number, Cp(T 8 - Tb)/hfgtion of a thermally stratified liquid hydrogen tank. The L tank heighttank was nearly cylindrical, having a volume of about0.144 m3 with 0.559 m in diameter and 0.711 m long. A mc average mass condensation rate at the

mixer/pump unit, which had a jet nozzle outlet of liquid-vapor interface0.0221 m in diameter was located 0.178 m from the tank P tank pressusrebottom and was installed inside the tank to generate the

axial jet mixing and tank fluid circulation. The liquid Pr Prandtl number of bulk liquid

fill and jet flow rate ranged from 42 to 85 percent (by Qj jet volume flow ratevolume} and 0.409 to 2.43 m3/hr, respectively. Mixingtests began with the tank pressure ranging from 187.5 to Ri Richardson number evaluated at the be-238.5 kPa at which the thermal stratification results in ginning of each test, g/3(T B - Tj} i Hj/uj 2

4.9 to 6.2 K liquid subcooling. The mixing time and Rej jet Reynolds number, uj d/vtransient vapor condensation rate at the llquid-vaporinterface are determined. Two mixing time correlations, Stc average condensation Stanton number de-based on the thermal equilibrium and pressure equilib- fined in Eq. (8)

rium, are developed. Both mixing time correlations are Tb,Tj, bulk liquid temperature, jet temperature,expressed as functions of system and buoyancy param- Ta,Tdome interaee temperature, and domeeters and compared well with other experimental data. temperatureThe steady state condensation rate correlation of Soninet al. based on steam-water data is modified and ex- (T s - Tj) i initial jet subcooling of each test

pressed as a function of jet subcooling. The limited liq- tin,t* mixing time, dimensionless mixing timeuid hydrogen data of the present study shows that themodified steady state condensation rate correlation may (tm)th,(tm) p mixing time based on the thermal andbe used to predict the transient condensation rate in a pressure equilibrium, respectively

taxing process if the instantaneous values of the jet sub- jet velocitycooling and the turbulence intensity at the interface are uj

employed. V! liquid volume

Nomenclature Va average rms turbulent velocity (or turbu-lence intensity} at the liquid-vaporinterface

• Am liquid-vapor interface areaGreek Symbols

Cp specific heat of liquid

D tank diameter /3 thermal expansion of liquid

d jet nozzle diameter /_1,_2 constants defined in Eq. (10)v kinetic viscosity of liquid

g gravitational acceleration

H liquid height from the tank bottom P liquid density

Hj jet submergence depth or the distance be-tween nozzle outlet and liquid surface

Introduction Okitaand Oyama 3

Fluid mixing such as axial jet-induced mixing is a / \/ kft

preferred me o. o,od°e / " r (3)ph_e system in a closed container in which the fluid is tm = 5.5/D2 it H_'S

forRej > 5000

thermally stratified. 1 A typical example is the thermal _u-_.dJ(DJ t

destratiffcation and the pressure reduction of a cryogenic

storage tank by axial jet-induced mixing. As the tank is Wollen 4

subjectedtoexternalheating,thefluidisthermallystra- D 2tiffed and the tank pressure increases with a rate usually t m 3.46 m (4)

higherthanitshomogeneouspressureriserate.By using ujd

a mixer,thetankfluidiscirculatedand thesubcooled * • 3

jetcan be directedtowardstheliquid-vaporinterface.Forcomparmonpurpose,OkltaandOyama recalculatedThe mixingofthetankfluidinducedby thejetcan de- the data of Fox and Gex2 and obtainedthe follow-

ztroy the temperaturestratificationand inducethe ingcorrelationwhich isindependentofjet Reynolds

vapor condensationat the interface,resultingin the number:reductionoftankpressure.Once theliquidtemperaturestratificationiseliminated,thebulkliquidtemperature

isnearlysaturated.Consequently,the continuationof r__,_,n[D___._UH_.Sfor Rej > 7000 (5}mixing will not further reduce the tank pressure. In- tm = .2.6

stead,themixerpower input,which may be significantfora cryogenicstoragesystem,wil[eventuallybecomeheatand increasetheboilofflosses.Therefore,themix- From the above correlations,it is found that for

ingprocess,which involvesthemixingtimeand theva- H/D closeto one the dimensionlessmixing time,tm

por condensationrateattheinterface,needstobewell = tmUjd/D 2,rangedfrom 2.6to9.Sinceallthe aboveunderstoodsuchthatthepressurecontrolsystemcanbe testsusedthedye oracid-basemethod,themixingtime

properlydesignedand operated, resultswere based on the concentrationequilibriumwhich may be comparabletothethermalequilibrium.

Fluidmixingprocesshas beenextensivelyinvesti-

gatedand numerous correlationsto predictthemixing Poth and Van Hooks conducteda mixing testby

timehave beenproposed.However,theconcepttofor- usingliquidhydrogenstoredintheNuclearPropulsionmulatethemixingtimedatadifferfromonetoanother. Module (NPM) Mars BrakingStage.The mixingtime

Most ofthetestswere conductedwithcylindricaltanks forthetank pressureto reachitsequilibriumvalueis

usingwaterasthetestfluidwitha uniformtemperature aboutand injecteddye ofequaldensitytoeliminatethebuoy-

ancy force. Some of the previous studies on mixing time D2are as follows: t m -- 2.1 m (6)

ujd

Fossett and Prosser 1Similar experiments were conducted by Meserole et al.6using Freon 11 at various jet diameters and liquid

°'l:t m 8 9 for Rej > 4500 (1) heights. They concluded that the mixing time deter-(Q,-_I/2j,jj mined from the pressure decay is essentially equal tothat based on the equalization of temperatures through-

out the bulk liquid. Also, the mixing time only variesslightly with fill levels. It seems that their data may be

Fox and Gex 2 correlated as

t

- D2t m = 118 H1/2D 1 1 for Rej :> 2000 (2) tm = 3.9__ for Rej > 20 000 (7)

Re_/6 (ujd)4/s gl/6 ujd

The reduction of tank pressure is mainly due to the and by12

vapor condensation at the interface. The mixing time

definition based on the pressure equilibrium should be ujd' --]affected by the pressure decay rate which is controlled Vs : 10.04_ 2 _ (7.14/_2 _ 3.06_1 }by the vapor condensation rate at the interface and the "-ff

' thermodynamic state of the vapor.

Several experiments have been conducted for the for 0.5 < H < 3 (10)measurement of the steady state vapor condensation rateat the liquid-vapor interface in a jet-induced mixingtank. Thomas 7 measured the condensation rate of steam where _1 -- 0.34 and _2 --" 0.24. Lin and Hasan 13on water surfaces mixed by a submerged turbulent jet numerically solved the conservation equations with k-eand attempted to correlate his data based on the theo- turbulence model and obtained thatretical model proposed by Theofanous et al8. Theofanousmodel suggests that the condensation heat transfer _(

coefficient be proportional to the Reynolds number to a v s = _2.39 for 0.5 < _H< 3 (11)power of 0.75. Dominick 9 investigated the effects of jet D Dinjection angle and jet flow rate on the condensationrate in a Freon 113 tank. The interface heat transfer was Equation (11) yields/91 -- 0.33 and/_2 = 0.23 which axeobserved to increase as jet injection angle became more in good agreement with the results of Ref. 12. It is notednormal to the interface. Dominick 9 correlated his data that Eqs. (9) to (11)were obtained for a cylindrical tankby using the correlation form which was developed for with the jet nozzle outlet located near the tank bottom.a turbulent jet impinging on a fiat surface. In this The liquid height from the tank bottom (H) is nearly

correlation, the average heat transfer coefficient increases the same as jet submergence depth (Hi). For most of thewith increasing jet Reynolds number to a power of 0.73. practical applications, they are not the same and Hj isSonin et al.10 obtained an empirical correlation for the suggested to be used instead of H.rate at which a pure vapor condenses on the free surfaceof a turbulent liquid in a steam-water system, for the This paper presents the experimental results of theconditions where buoyancy effects are insignificant. The pressure decay of a liquid hydrogen tank mixed by anvapor was saturated and the vapor condensation was axial turbulent jet directed normally towards the liquid-controlled by the interface turbulence at the liquid side. vapor interface. The controlling variables axe the jetTheir vapor condensation rate correlation is expressed as volume flow rate and liquid fill level. Since the tank

pressure is decreasing during the fluid mixing, the con-

mchfg densation rate is changing with time because of theStc = change in jet subcooling. The steady state condensation

AsPCpvs(T6 - Tb) (8) rate correlation developed by Sonin et al.10 is modified

to be expressed as a function of jet subcooling its - Tj).The transient condensation rate during the mixing-- 0.0198 Pr-°'33(1 - 0.5 Ja)process is then predicted by this modified steady statecondsensation rate correlation using the instantaneous

where Stc is the average condensation Stanton number jet subcooling. The correlations of the mixing time,and mc is the average vapor mass condensation rate at based on both the thermal equilibrium and the pressurethe interface. The liquid subcooling (Ts - Tb) and equilibrium, axe developed and axe compared with otheraverage turbulence intensity at the interface (Vs) axe experimental data.mainlyresponsibleforthevaporcondensationrate.The

averageturbulentrms velocityat theinterface,vs,is The Experimentdeterminedby11

The mixingtestsaxeperformedin a nearlycylin-

v s = 21.1 exp 1.2 for 3.1 < _H < 4.2 steel tank containing multilayer insulation (MLI) withinD the vacuum annulus. The lid is composed of a fiat flange

' which supports a short cylindrical section with an19) inverted dome bottom. The space between the flange

and the cylindrical section is evacuated and insulated test, the sampling rates of the measurement are variedwith MLI to minimize heat leak through the dome from from once every 2 sec to once every 10 sec. The mixer isthe environment. With the lid in place, the interior walls turned off when the pressure measurement does notof assembled tank form a cylindrical storage volume show any pressure decrease for a specified period of time.with dome ends. The assembled tank then has an inter- The vent valve is then open and the test is terminated.

nal volume of about 0.144 m3 with an internal height of0.711 m and an inside diameter of 0.559 m. Because of Results and Discussion

the lid mounted penetrations and the coupling of the lidwalls to ambient temperatures at the tank flange, the Four series of experiments consisting of 12 tests haveheat leak is very nonuniform. The average wall heat flux been conducted. Table 1 shows the experimental condi-for the tank is experimentally determined and ranges tions for all the tests. The liquid fill ranged from 42 tofrom 5.15 to 51.5 W/m 2 for fill levels ranging from 30 to 85 percent (by volume} and the initial liquid subcooling85 percent. The Shuttle Centaur mixer is installed near due to thermal stratification ranged from 4.9 to 6.2 K.the central part of the tank bottom with the jet nozzle The jet flow rates varied from 0.409 to 2.45 m3/hr.outlet located about 0.178 m from the bottiom. The jet During each test period, the liquid fill level and thenozzle has an inner diameter of 0.0221 m. With the dome temperature hardly changed. Therefore, only their

mixer on, the tank fluid is withdrawn and ejected initial values are shown in the table.through the jet nozzle normally towards the liquid-vaporinterface, resulting in axial jet-induced mixing in the Figures 2(a) to (d) show the tank pressure decay astank. Figure l(a) shows a rough sketch of the tank. It is a function of time for various jet volume flow rates. Itnoted that the dewar used in the present mixing test is is seen that the pressure decay rate is higher for theindeed the receiver dewar of the no-vent fill tests in higher jet flow rate as the result of the enhanced vapor

Ref. 14. The details of the structure, piping systems and condensation at the liquid-vapor interface. Also note inthe data acquisition system can be found in Ref. 14. Figs. 2(a) to (d), the lowest jet flow rates substantially

increase the mixing time. The typical liquid temperature

Liquid height is measured by a capacitance level distributions as functions of time are shown in Figs. 3(a)probe. An instrument tree containing silicon diodes and and (b). The liquid temperature is completely destrati-thermistors at varying heights is in direct contact with fied and the tank pressure reaches its equilibrium value.the tank fluid. The accuracy of the silicon diodes is This equilibrium pressure is nearly the same as the

about 0.6 K at LH2 temperatures. SIX silicon diodes are saturation pressure corresponding to the uniform bulklocated at 0.5-, 20-, 40-, 50-, 60-, and 80-percent fill liquid temperature of the tank. For the tests of the sameheight to measure the fluid temperatures. Four thermis- series, the tank almost reaches the same equilibriumtom are utilized to indicate the presence of liquid or pressure. This is because their initial experimental con-

vapor. The capacitance level probe is calibrated against ditions such as liquid fill, tank pressure, and fluid tern-the thermistors (point sensors} and is found to agree perature distributions are nearly the same and thuswithin 0.0254 m for liquid levels greater than 10 percent, should have the same equilibrium state when the tankThere are two additional silicon diodes used to measure is completely mixed.

the tank dome temperatures. Figure l(b) illustrates thetemperature sensor and thermistor locations for the test The mixing characteristics for all the tests are giventank. Pressure transducers are used to provide continu- in Table 2. The jet Reynolds number ranges from 27 900

ous pressure measurement throughout the system with to 166 300. A Richardson number, Ri, is also includedan estimated accuracy of +1.7 kPa. A silicon diode and in Table 2 to characterize the effect of buoyancy. Thea flow meter are also installed in the transfer line of the definition of the Richardson number is based on the ini-

mixer unit to measure the jet temperature and jet tial jet subcooling (Ts - Tj) i, jet submergence depth

volume flow rate, respectively. (Hi}, and jet velocity (uj). The value of Richardsonnumber ranges from 0.07 to 2.62. Two mixing times are

Before each test, the tank is vented to 40 to 60 kPa shown in the table: (tm)th and (tin}p. The mixing time,at a specified liquid fill level. In order to establish the (tm)th, is defined as the time required from the start ofinitial conditions for each test, the tank vent valve is a mixing operation to the time when the liquid tempera-then closed. Due to the ambient heat flux through the ture is destratified. The mixing time, (tin)p, is defined astank wall, the tank pressure increases and the liquid the time required from the start of a mixing operationbecomes thermally stratified. When the tank pressure to the time when the equilibrium tank pressure isreaches a preset level, the mixer is turned on at a speci- achieved. Table 2 shows that, for small Ri, the dimen-* . . o

fled jet volume flow rate and the test is considered to sionless mixing time (tm)th is independent of the, jetbegin. The data for the liquid fill level, fluid tempera- Reynolds number. The dimensionless mixing time (tm)thtures, tank pressure, and jet flow rate are measured as a function of Richardson number is shown in Fig. 4.starting just prior to activating the mixer. During each As shown in Fig. 4 the effect of buoyancy on the mixing

time isnegligibleforRi < 0.5.The smallvalueofRi may be differentas shown inTable2. Ifthe tank is

can be obtainedby increasingthejetvelocity(uj)or completelymixed and thebulkliquidisstillsubcooled,decreasingthegravitylevel(g).Therefore,thedimen- the condensationprocessand the pressuredecrease

sionlessmixing time forthe highjetflowratesin a continue.Inthiscase,(tm)thislessthan(tin)p.The lownormal-gravityconditionmay be appliedtothelowjet liquidfilldatashowsthisphenomena.Ifthecondensa-

flowratesinazero-gravityenvironment,assumingthe tionprocessstopsbeforethetankiscompletelymixed,

effect of liquid-vapor interface configuration is neglected.' then (tm)th is greater than (t) This may happen formp"Using the form of the correlation developed by Okita very high jet volume flow rates. It is obvious that the

• and Oyama 3, the mixing time data shown in Table 2 value of (tin) p can not be correlated simply by the sys-can be correlated as tern parameters as those expressed in Eq. (12). The

value of (tm) p depends on the pressure decay rate whichis controlled by the condensation rate at the liquid-

(t*)t h = (tm)thUjd vapor interface and the thermodynamic state of theD2 vaporregion(particularlythevapormass).Thiscan be

examined by simplylookingat the equationof the

pressurechangerateforan isothermalvaporregion.15

iHr4.3 Ri < 0.5 (12a) However,forcomparisonpurpose,thevalueof(tin)p as- a functionofRi isplottedinFig.5.Similartothatfor

(tm)th , buoyancy increases the value of (tin) p. With neg-= ligible buoyancy, the value of (tin) p increases with

decreasing fill level. This is because the larger vapor

HI.5 mass for the low fill level delays the pressure decay rate.(3.2 + 2.0 Ri) Ri > 0.5 (12b) This phenomena was also observed by Meserole et al. 7

but was not discussed. Our data may be correlated bythe following equation:

Equation(12a)shows that,forRi < 0.5,the mixing (tm)pujdtime (tm)th decreases linearly with increasing jet velocity (t*)p =for a given tank system and decreases with decreasing D2fill level. This finding is consistent with that of Okita

and Oyama. 3 However, the constant 4.3 in Eq. (12a) for four liquid hydrogen system is smaller than the con- 3.3 Ri < 0.5 (14a)

[stant 5.5 in Eq. (3) obtained by Okita and Oyama 3 for =a water system. For higher Richardson number

(Ri > 0.5), the mixing time is higher (as shown in (2.6 + 2.1 Ri) Ri > 0.5 (14b)Fig. 4) due to the opposing effect of the buoyancy.Equation (12b} gives the quantitative effect of buoyancyon the mixing time. It is noted that in terms of jet For Ri less than 0.5, the constant 3.3 in Eq. (14a) isvolume flow rate and total liquid volume, Eqs. (12a) slightly less than the constant 3.9 obtained from

and (12b) can be rearranged to be of the form: Meserole et al.'s 7 data for a Freon 1I system. It isnoted that for a space system in which the gravity effect

(tm}thQj is neglected, Eqs. (12a) and (14a) may be used topredict the mixing times (tm)th and (tm)p, respectively.

V1

Vapor condensation at the interface is the keymechanism to reduce the tank pressure. For a well

dD 0.s insulated tank, the interface condensation processes are3.8__ Ri < 0.5 (13a} generally determined by the system parameters (such as0.5

" V1 tank geometry _md size, jet nozzle size, and liquid

= height), fluid properties, liquid subcooling, jet flow rate,

0.89(3.2+ 2.0Ri}dD°'5 Ri > 0.5 (13b) and buoyancy.Figures6(a)and (b)show thejetsub-" 0.5 coolingas a functionof timeforhighjetflowrates.

V1 With thecorrespondingchangeoftankpressureshown

inFigs.2(b) and (d),two conclusionscan be drawn.

First,for a givenjetflowrate,pressuredecay rate

Sincethe tankpressureiscontrolledby'whathap- decreaseswithtimedue to thedecreaseinjetsubcool-

pensinthevaporregion,thevaluesof(tm)thand (tin)p ing.Secondly,fora givenjetsubcooling,higherjetflow

yields a greater pressure decay rate. This is because the Using Sonin et M.'s10correlation, Stc = 0.0198 Pr -0"33,vapor condensation rate increases with increasing jet we havesubcooling and with the enhanced turbulence intensity

near the interface (due to the increased jet flow rate). T s - TjTB - Tb =

The vapor condensatin rate correlation developed by /D/2 ['u'_i/ (18)Sonin et al. 10 is expressed as 1 + (0.0198 Pr-0"33) va '

St c = mchfg Equation (18) indicates that the diameter ratio (D/d) isAsP Cpvs(Ts - Tb) (15) the key parameter controlling the difference between the

liquid subcooling(T. - Tb) and jet subcooling (Ts

_ - T i For the system used in the present experiment,= 0.0198 Pr-°'33(1 0.5 Ja) j).the value of (T. - Tb) is nearly half of (Ts - T..), if thevalue of vs is calculated by Eq. (11). Using ___. (18),Sonin et al.'s 1° condensation rate correlation becomesSince this correlation is for steady state, there is a direct

relationship between the interface temperature (Ts),

bulk liquid temperature (Tb), and jet temperature (TI). m c hfgThe subcooled jet is the real driver to induce the vapor Stc=

coondensation. The subcooled jet (TI) approaches and As pCpvs(T s - Tj)sweeps over the interface, and induces the vapor conden-

,on**eTow*or*eeneryI/ rthrough this condensation process and leaves the inter- x 1 + (0.0198 Pr -°'33) vaface at a temperature Tb. Therefore, the bulk liquid

temperature (Tb) is greater than the jet temperature(T.) and is less than the interface temperature (T,). Inj = 0.0198 Pr -°'33 (1 - 0.5 Ja)the mixing test, the condensation process is transient be-cause the interface temperature keeps decreasing. It maybe difficult to measure the temperature Tb because the where the fluid properties are calculated based on thecondensation-induced thermal layer is growing and the temperature Tb which is obtained from Eq. (18). It is

temperature Tb is changing with time. Therefore, it will noted that Eq. (18) holds for a steady state condition.be helpful if the liquid subcooling (TB- Tb) in Eq. (15) Assuming Sonin et al.'s 1° condensation rate correlationcan be expressed as a function of the jet subcooling its is applicable to a transient state, the instantaneous val-

- Tj) which can be easily obtained in the experiment, ues of (Ts - Tb), (Ts - Tj), and v s should be used. Un-fortunately, the information to predict v s as a function

Based on the mass and energy balance, Lin and of time is not available. Theoretically, the steady stateHasan 16 have theoretically obtained the following rela- value of v s can be used only when the tank has been

tionship between (T s - Tj) and (Tb - Tj) for an insu- completely mixed and the required mixing time is thatlated system: predicted by Eq. (12a). This steady state value of vs can

be determined by Eqs. (9) and (11) for high H/D andlow H/D, respectively. The average turbulence intensity

Tb -Tj (vs) is expected to increase with time in a mixing

mchfg T. - Tj 116) process. If one uses the steady state value of vs, the--- condensation rate is expected to be overpredicted at

A'pCpujiT" - TJ) [D/_(1 + iia) least in the initial time period of mixing process. Thiseffect of transient v, may be decreased with increasingjet flow rate because the mixing time is shorter.

For Ja << 1, one can obtainBased on the limited temperature measurements in

the vapor region, curve fitting is used to estimate the

St c = mchfg vapor temperature distribution as a function of time.A,p Cpv,(T, - Tb) The typical fluid temperature distribution as a function

(17) of time is shown in Figs. 7(a) and (b). The vapor is su-

ujfT__b-- Tj/fd _ perheatedwiththe temperaturedifference(Td°me- Ts)- equal to about 65 K. The solid line is the resulting

v, l T, TbJ_D J curve-fitted temperature distributions at the time when

6

the mixing process starts. The vapor mass is obtained be expressed by Eq. (18) as a function of the jet subeool-

based on the curve-fitted one-dimentional temperature ing (Ts - Tj) and the average turbulence intensity (Vs)distribution. Most of the vapor mass is confined in the at the interface.region near the interface where the vapor temperaturesare much lower. Figures 8(a) to (e) show the estimated 4. The steady state condensation rate correlation of

• vapor mass as a function of time for the high jet flow Eq. (19) may be used to predict the transient condensa-rates (Ri < 0.5}. The vapor mass predicted by using tion rate in a mixing process if the instantaneous valuesEq. (19) with the steady state value of vs is also in- of jet subcooling and average turbulence intensity at the

• eluded in the figures for comparison. As expected the interface are employed. However, if the liquid surfacecondensation rate is generally overpredicted. This is breakup occurs due to high jet flow rate, Eq. (19) may

mainly due to the use of the steady state value of v s and underpredict the vapor condensation rate.slightly due to the vapor superheat. The comparison ap-pears to improve as the jet flow rate increases. It isnoted that the condensation rate is underpredicted at References

the jet flow rate of 2.43 m3/hr as shown in Fig. 8(c},which is the highest flow rate used in the experiment. 1. Fossett, H., and Prosser, L.E., "The Application ofThis may be because at this high jet flow rate liquid Free Jets to the Mixing of Fluids in Bulk," Pro-surface breakup occurs and Sonin et al's 1° condensation ceedings of the Institute of Mechanical Engineers,rate correlation does not apply. Therefore, the present vol. 160, no. 2, pp. 224-252, 1949.data suggests that Sonin et al.'s 1° steady state condensa-tion rate correlation may be used to predict the tran- 2. Fox, E.A., and Gex, V.E., "Single-Phase Blendingsient condensation rate in a mixing process if the of Liquids," J. AIChE. vol. 2, no. 4, pp. 539-544,instantaneous values of the jet subcooling and the aver- 1956.age turbulence intensity at the interface are used.

3. Okita, N., and Oyama, Y., "Mixing CharacteristicsConclusion in Jet Mixing," Chem. Eng. Japan, vol. 27, no. 4,

pp. 252-259, 1963.Experiments were conducted to investigate the mix-

ing time and transient vapor condensation rate at the 4. WoUen, M.A., "Evaluation of Jet Induced Mixingliquid-vapor interface in a thermally stratified liquid for Centaur LH2 Tank," NASA TM-096083-333,hydrogen tank mixed by an axial jet. Two mixing time 1983.

definitions, based on the thermal equilibrium (tm)th and

pressure equilibrium (tm)p, have been used. Under the 5. Poth, L.J., and Van Hook, J.R., _Control of Ther-conditions and parameter ranges in the present study, modynamic State of Space-Stored Cryogens by Jetthe following conclusions can be drawn: Mixing," J. Spacecraft, Vol. 9, No. 5, pp. 332-336,

1972.

1. The Richardson number (Ri) defined in the pres-ent study is an appropriate parameter to characterize 6. Meserole, J.S., Jones, O.S., Brennan, S.M., andthe effect of buoyancy in the determination of mixing Fortini, A., "Mixing-Induced Ullage Condensation

times (tm)th and (tin) p. If the Rtchardson number _s less and Fluid Destratification," AIAA Paper 87-2018,than 0.5, the buoyancy effect is neglected. Therefore, the 1987.dimensionless mixing time for the high jet flow rates ina normal-gravity condition may be applied to the low 7. Thomas, R.M., _Condensation of Steam on Waterjet flow rates in a zero-gravity environment if the effect in Turbulent Motion, _ Int. J. Multiphase Flow, vol.of liquid-vapor interface configuration is neglected. 5, no. 1, pp. 1-15, 1979.

2. For Ri < 0.5, the mixing times (t)-- and (t) 8. Theofanous, T.G., Houze, R.N., and Brumfield,. . . m_n mpcan be predicted by Eqs. (12a) and (14a), respectively. L.K., "Turbulent Mass Transfer at Free, Gas-LiquidThese equations may also be applied to a space syatem Interfaces, with Applications to Open-Channel,in which the gravity effect is negligible. Buoyancy delays Bubble, and Jet Flows," Int. J. Heat Mass Transfer,

the mixing process. Equations (12b) and (14b) give the Vol. 19, pp. 613-624, 1976.

' predictions of (tm)th and (tm)p, respectively, for Ri> 0.5 based on the system used the the present study. 9. Dominick, S.M., "Mixing Induced Condensation

Inside Propellant Tanks, _ AIAA Paper 84-0514,3. For a steady state condensation process with 1984.

negligible buoyancy, the liquid subcooling (Ts - Tb) can

10. Sonin, A.A., Shimko, M.A., and Chun, J.H., "Vapor in Heat and Mass Transfer, Sidney, Australia, JulyCondensation onto a Turbulent Liquid--I. The 14-19, 1991, Transport Phenomena in Heat andSteady State Condensation Rate as a Function of Mass Transfer, J.A. Reizes, ed., pp. 1526-1537,Liquid-Side Turbulence," Int. J. Heat Mass Trans., 1992.Vol. 29, No. 9, pp. 1319-1332, 1986.

14. Moran, M.E., Nyland, T.W., and Papel], S.S.,11. Brown, J.S., Khoo, B.C., and Sonin, A.A., "Rate "Liquid Transfer Cryogenic Test Facility--Initial

Correlation for Condensation of Pure Vapor on Hydrogenand Nitrogen No-Vent Fill Data," NASATurbulent, Subcooled Liquid," Int. J. Heat Mass TM-102572, 1990.Trans.__._.._.,Vol. 33, No. 9, 1990.

15. Lin, C.S., and H_an, M.M, "Self-Pressurization of12. Brown, J.S., Helmick, M.R., _d Sonin, A.A., a Spherical Liquid Hydrogen Storage Tamk in a

"Vapor Condensation at aTurbulent Liquid Surface Microgravity Environment," AIAA Paper 92-0363,in Systems with Possible Space-Based Applic_- 1992.tions,_ AIAA Paper 89-2846, July 1989.

16. Lin, C.S., and H_san, M.M, "Vapor Condensation13. Lin, C.S. and Hasan, M.M., "Effect of Liquid on Liquid Surface Due to Laminax Jet-Induced

Surface Turbulent Motion on the Vapor Conden- Mixing," J. Thermophysics and Heat Transfer,sation in a Mixing Tank," Proceedings of the 4th vol. 5, no. 4, pp. 607-612, 1991.International Symposium on Transport Phenomena

TABLE 1.--THE INITIAL AND FINAL CONDITIONS OF THE TEST

Test Liquid fill, Initial conditions Final Dome Jet flowseries percent conditions, temperature, rate,

P, Td .... Qi-by height by volume P, T, - Tj, kPa K ma]hr

kPa K

A1 76 85 235.1 6.1 43.4 63.9 0.568A2 74 83 202.7 6.1 38.6 67.2 .772A3 73 81 238.5 6.2 40.0 75.6 .681B1 72 80 199.2 5.5 42.0 77.8 .409B2 71 78 200.6 5.4 36.5 82.2 1.045B3 70 77 187.5 5.2 36.5 85.0 1.635B4 68 75 188.2 5.2 37.9 88.9 2.430C1 42 44 184.0 4.9 57.9 129.4 .409C2 41 42 188.9 5.0 57.9 137.2 .681D1 66 73 218.5 6.2 46.9 91.1 .454D2 64 71 208.2 5.9 41.4 96.1 1.158D3 63 70 197.8 5.7 42.0 97.2 1.863

TABLE 2.--THE MIXING CHARACTERISTICS OF THE TEST

Test Qj, Rej Ri H/D (tta)th, (tin)p, _ (t_,)pse_ie_ mS/hr rain rain (H/D) °'s

AI 0,568 38,600 1.68 0.968 3.73 3.54 6.62 6.18A2 .772 53,200 .77 .943 2.06 1.60 5.04 3.80A3 .681 47,600 1.09 .928 2.37 2.27 5.15 4.75B1 .409 27,900 2.62 .916 6.60 6.77 8.67 8.52B2 1.045 70,900 .40 .903 1.33 1.03 4.50 3.31B3 1.635 111,500 .15 .877 .80 .60 4.30 3.02B4 2.430 166,300 .07 .852 .55 .40 4.45 2.99C1 .409 28,400 .68 .526 2.80 4.13 4.86 6.20C2 .681 46,900 .31 .513 1.37 1.80 4.01 3.77D1 .454 29,900 2.09 .826 4.60 4.47 7.07 6.24D2 1.158 77,200 .30 .801 1.03 .97 4.10 3.45D3 1.863 124,500 .11 .789 .66 .56 4.26 3.21

F Ud o SiliconDiode

I- IIIIIIIIlilllllllllllilllllillfl/lilllllll._1 o Thermister

o

_fI ,,_u,0Ioo

Mixer_,_ oo

(a) (b)Figure1.---Thesketchforthetest tankandthe locationsof tem-

peraturesensorsandthermisteminthetank.

250-

z_ Oj. 0.'568m3/hr

200. • Qj = 0.681m3/hr

Io Qj = 0.772 m3/hr

15o. _.

• I I0. 100.

50, ,_

230.

I " Qj= 0.409m3/hr

I

m 180. m j o Qj. 1.045 m3/hrn o-_ o _ a Qj = 1.635m3/hr

= _ x Qj = 2.430 m3/hr_130. o_ .o

C o

n

_- 80. _o

"30" , ...............................

0 2 3 4 5 6 7 8Time, Min.

(b) Test sedes B.

Figure 2.raThechange of tank pressureas e functionof time.

10

200- i

• Qj = 0.409m3/hr

150- _ o Qj= 0.681m3/hr

"° \ '\ I I100- _

1-

_ 50..

O° , 0 i i J _ • i i i , 0 , , i , = , i , J = i ,

(c)TestseriesC.

230-,

• Qj= 0.454 m31hro Qj= 1.158 m3/hr

180.-_" •° _,. • QI = 1.863m3/hr

,_ la0.n 1o

C io_ oI- 80. =-

..o _ .,3o; - -

0 1 2 3 4 5 6 7 8

Time, Min.(d) Test sefles D.

Figure 2.--Concluded.

11

24-

o

v22. •

_.= •(o • • 70%,Tso. 20'E e 60%treesd

•___ • = 40%treesd

o° 'o ° 8_o °o o................--°'18- o ,,,,,,*• *,,._ i_ii_ t}_,_** _ _ • 0.5%treesd,,-I oo

_tt_ ,A**** ll-,i 'li*.•o oo•ol • •

16-0 0.2 0.4 0.6 0.8 1 1.2 1.4

• Time, Min.(a) Test sedes B, Qi" 1.635m3/hr.

24-

22. _'_"o _

Oo "-,..,

% %_'._, • 41%,Ts_20. %I_- =a_ i "% o 40%treesd

__;_. %- "' --._" ,, = 20%treesd"O o_Am, ...__ ,.o" x __ , 0.5%treesd:..318. _..._._= ,,,

6 o , , , ,

0 0.5 .5 2 2.5 3Time, Min.

00)Test sefles C, QI" 0.681 m3/hr.

Figure3.raThechangeof liquidtemperatureasafunctionofUme.

12

10-

9• _ - ,,_

E 8. /

.=_<5 _ Eq. 12 b

×'-" ,,I""E;-" 4o E "LEq. 12a"_'-- 3c

E 2a 1

00 0.5 1 1.5 2 2.5 3

RichardsonNumber,RiRgum 4.--The dlmenslordassmixingtime(basedon the

thermalequilibrium)asa functionof Richardsonnumber.

10-O.

E 9",=. O°

8 Eq. 14 b-_:p-

7 wf •o_ 6- ir" P-

"_ " J Test _5 ,,_4. Series4- •II

3u Eq. 14a o B"_ 2 "- C -E 1 -A D -

c5 0 I0 0.5 1 1.5 2 2.5 3

RichardsonNumber,Ri

Figure5.--The dknensionlessmixingtime (basedon• the pressureequilibrium)as a functionof Richardson

number.

13

6. , .... _) I t I I i

5. i% • Qj = 1.04Sm3/hr _°o_ _ o QI - 1.158m3/hr :-

ee o Qj = 1.635 m3/hr • • Qj. 1.863 m3/hr4 .%=

• Oj=2"430m3/hr " _ I IO • • OI 0 • 0

o • I oc0 i 0 •0 •

_ 2, ' -%

_1" =o : •

O,.o=.-- J

-10 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 ._ 0 0.2 0.4 0.6 0.8 1.2 .4 1.6 1.8

Time, Min. Time, Ain.(a)TestredesB. (b)TestseriesD.

Rgure&--Thechangeofthejetsubcoollngasafunctionof time.

14

0.9 J0.8. x-o _-. -

•_ i L Interface0.6--r' . w

0.5-: =.Q)C._o0.4- _ i

" 0.3. • t -0 Min.

E 0.2-! • o t- 0.3 Min.

0.1 :. " x t = 0.6 Min.

0 i " , , , I', , , I . , ,(a)Test series B, Oi= 1,045 m3/hr.

-,

0.9- /

o.8igo.7-_:0.6-: _- L._.Interface

0.5-: = ..r4)Q

0.4-!. --. , , ,

"P::0.3-! - I • t=Oiin.m IE 0.2-! : o t= 0.1Min.

0.1-! ..• _ t=0.3Min.

0"i " , ,', I,,. I , , ,0 10 20 30 40 50 60 70 80 90 100

FluidTemperature,K(b)TestseflesB,Qi'=1.635ma/'nr.

Figure7.raThe fluid temperaturedlstdbutlonasa functionof height.

15

0.035 -

0.03 .i • Experiment

._, Predictionc_ 0.025

0.02 \

0.015 _[:L

> 0.01

0.005

0 0.1 0.2 0.3 0.4 0.5 0,6 0.7 0.8Time,Min.

(a)Test series B, Qj = 1.045 m3/'nr.

O.O3- O.O35-

0.025 tX 0.03

0.02i! _ _ 0.025_'.- K- \ _ oo_

:_ 0.015 "_"I ' :__, _ 0.015 ." 1_"

> 0.01 • _ _--- :_ 0.01 ")

0.005 ' 0.005

0 00 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 0.05 0.1 0.15 0.2

Time, Min. Time, Min.

(b) Test sedes B, Qj= 1.635m3/hr. (c)TestsedesB,Qj = 2.430m3/hr.

0.04 0.045

0.035 _ 0.04

0.03

"" 0.03 _o.o_s \" 0.025:; 0.02 _; _ •\ _ oo2:_-o.o_5 -- _ o.o15.! "<• )>

0.01 _ 0.01 ,! _ _• _

0.005 0.005 .! ,

0 0 !0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Time,Min. Time,Min. '

(d)Test seriesD, Qj: 1.158m3/hr. (e)Test seriesD,Qj = 1.863m3/hr.Rgum 8._The changeof vapormassasa functionof timeand itscomparisonwiththepredictionbased onthe condensation

rate correlationequation.

16

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1. AGENCY USE ONLY (Leave blank) 12. REPORT DATE a. REPORT TYPE AND DATES COVERED

I June 1993 Technical Memorandum4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

)

Mixing andTransient Interface Condensationof a LiquidHydrogenTank

6. AUTHORIS) WU-50(_42-73

C.S.Lin, M.M. Hasan,andT.W.Nyland

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATIONREPORT NUMBER

National Aeronautics and SpaceAdministrationLewis Research Center E-7910Cleveland,Ohio 44135-3191

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORINGIMONITORINGAGENCY REPORT NUMBER

NationalAeronautics andSpaceAdministration NASA TM-106201Washington,D.C. 20546-0001 AIAA-93-1968

11. SUPPLEMENTARY NOTES

Preparedforthe29thJointPropulsionConferenceandExhibitcosponsoredbytheAIAA,SAE,ASME,andASEE,Monterey,California,June28-30,1993. C.S.Lin,AnalexCorporation,3001AerospaceParkway,BrookPark,Ohio44142;andM.M.HasanandT.W.Nyland,NASALewisResearchCenter.Responsibleperson,C.S.Lin,(216)433--0138.

1211.DISTRIBUTIONIAVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

Unclassified- Unlimited' SubjectCategory 34

13. ABSTRACT (Maximum 200 words)

Experiments have been conducted to investigate the effect of axial jet-induced mixing on the pressure reduction of athermally stratified liquid hydrogen tank. The tank was nearly cylindrical, having a volume of about 0.144 m3 with0.559 m in diameter and 0.711 m long. A mixer/pump unit, which had a jet nozzle outlet of 0.0221 m in diameter waslocated 0.178 m from the tank bottom and was installed inside the tank to generate the axial jet mixing and tank fluidcirculation.The liquidfill andjet flow rate rangedfrom 42 to 85 percent(by volume) and 0.409 to2.43 m3/hr,respectively.Mixing tests began with the tank pressure ranging from 187.5 to 238.5 kPa at which the thermal stratification results in4.9 to 6.2 °K liquid subcooling. The mixing time and transient vapor condensation rate at the liquid-vapor interface aredetermined.Two mixingtime correlations,based on the thermalequilibriumand pressureequilibrium,are developed. Bothmixing time correlations are expressed as functions of system and buoyancy parameters and compared well with otherexperimentaldata. The steadystate condensationratecorrelationof Soninet al. basedon steam-waterdata is modifiedandexpressed as a function of jet subcooling. The limited liquid hydrogendata of the present study shows that the modifiedsteady state condensation rate correlation may be used to predict thetransient condensationrate in a mixing process if theinstantaneousvalues of jet subcoolingand turbulence intensity at the interfaceare employed.

14. SUBJECT TERMS 15. NUMBER OFPAGES

Liquidhydrogen, Jet-inducedmixing; Mixingtime; Liquid-vaporinterface; 1916. PRICE CODEVaporcondensation A03

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITYCLASSIFICATION 20. UMITATION OF ABSTRACTOF REPORT OF THIS PAGE OF ABSTRACT

Unclassified Unclassified Unclassified

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----__ IIIUlSpace Administration

Lewis Research Center ADDRESSCORRECTIONREOUESTEDCleveland,Ohio 44135

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