NASAlTP-20 12-216483 

Risk Assessment and scaling for the SLS 

LH2 ET 

Viatcheslav (Slava) Osipov 

Ames Research Center, Moffett Field, California 

Halyna Hafiychuk 

Ekaterina Ponizovskaya-Devine 

Dmitry Luchinsky 

Michael Khasin, 

Vadim Smelyanskiy 

December 2012 
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NASA/TP-20 12-216483 

Risk Assessment and scaling for the SLS 

LH2 ET 

Viatcheslav (Slava) Osipov 

Ames Research Center, Moffett Field, California 

Halyna Hafiychuk 

Ekaterina Ponizovskaya-Devine 

Dmitry Luchinsky 

Michael Khasin, 

Vadim Smelyanskiy 

National Aeronautics and 

Space Administration 

Ames Research Center 

Moffett Field, CA 94035-1000 

December 2012 
Acknowledgments 

Available from : 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757 -5802 
ABSTRACT 

In this report the main physics processes in LH2 tank during prepress and rocket flight are 

studied. The goal of this investigation is to analyze possible hazards and to make risk 

assessment in proposed LH2 tank designs for SLS with 5 engines (the situation with 4 engines 

is less critical). For analysis we use the multinode model (MNM) developed by us and presented 

in a separate report and also 3D ANSYS simulations. We carry out simulation and theoretical 

analysis the physics processes such as (i) accumulation of bubbles in LH2 during replenish 

stage and their collapsing in the liquid during the prepress; (ii) condensation-evaporation at the 

liquid-vapor interface and tank wall, (iv) heating the liquid near the interface and wall due to 

condensation and environment heat, (v) injection of hot He during prepress and of hot GH2 

during flight, (vi) mixing and cooling of the injected gases due to heat transfer between the 

gases, liquid and the tank wall. We analyze the effects of these physical processes on the 

thermo- and fluid gas dynamics in the ullage and on the stratification of temperature in the liquid 

and assess the associated hazards. A special emphasize is put on the scaling predictions for 

the larger SLS LH2 tank. 

CONTENT 

Introduction .. ..... ....... .... .......... ............ ... ... .... .... .......... ..... ....... ... .. ....... ........ ... ......................... ........ .. ... .. ... ..... 2 

1. Boiling near the tank wall and bubbles' collapsing: scaling of the bubbles' volume .... .. .... .. .. .... .. .. .... . 3 

1.1. Nucleate boiling of liquid in the boundary layer near the wa ll. ........ .............. ........ .. .. .................. 4 

1.2. Co ll apsing of the bubb les duri ng the prepress .... .. .... .. .. .. .. .. ... ........ .. .. .. .. .... .. ... ......... .... .. ... .. .. ...... .. 4 

2. Main processes of heat transfe r' i n the LH2 tank ...... ... .............. .......... .. .. .... .. .. .. .. .... .... ..... ........ .. .. .. .... .. . 5 

2.1 . Condensation-evaporation at the liquid-vapor inte rface .. .... .. .... .. .. .. ...... .. ...... .. .. .... .... .......... .. ....... 6 

2 .2. Cooli ng of the ull age gas by condensation at the interface .... .. .. ... ....... .............. .... .. .. .... .... ...... .. ... 9 

2.3 . Evaporation near the wa ll-li quid-gas interface .......... .. .... .... .... .. .. ............ .. . : .. ............ .. .. .. .... .. .... . 10 

2.4. Heating of the tank wall by the hot gas: the main mechanjsm of the gas coo li ng .. .... .... .... .. ...... 10 

3. Ull age pressure and temperature stratifi cati on ................... .............. .. .. ...... .. .......... ......... .. .. ... .... ......... 11 

3.1. Fitting of the MNM and He pulses parameters to the Space Shuttle data ........ .. .. .. .. .. .... .. .. ... ..... 11 

3.2. Scaling considerations for the LH2 tank for SLS with 5 engines .. .. ...... .. .. .. .... .. ...... .. .. .. .. .... .. ..... 16 

4. Temperature stratifi cation in the liqui d ..... .. .. ... .... .. .... ...... .... .. ............... .. ..... ... .. .. .. ........ ..... .... .. .... .... .. . 18 

4.1 .. ...... .. .. .... .. .. .... .... .. .. .. .. ........ .. .. ... ... .. .... ..... ......... ...... .. .. .. ...... .. ........ .. ...... .... ... ..... ..... .... ....... .. ........ .. ..... 18 

4.2 .. .. .... .. .. ..... .. .. .... ... ... ........... .. ...... .. .. .... ..... .... ....... .... .. .. .. ... ... .... ... ....... .. ... .. ....... ........ ..... ... .... ...... .. .. .... ... 19 

4.2.1. Natural convection correlations .. .. .......... .. ........... .. .. .. .... .. .. ...... ... .. ...... .. ............ .. ...... 19 

4.2.1. Natural convection in the LH2 tank .. .. .. .... .. .. .. .. .... .. .. .... ......... ...... ....... ... .................. .. 28 

4.3 Temperature stratifi cation in the LH2 tank .... .. .. .. ... ....... .. ...... .... .. .. ..... .... ... ...... .. .... .. .. .. .... .. .... ... ... .. .. . 30 

1 
5. Effect of sloshing to LH2 tank .. ....... .............. ............. .. ................... .... ....... .... ............................. .. ... .. 34 

5. 1. Longitudinal sloshing waves ................ .. .. .. ...... .. .. ...... .................. .. .......... .. .. .... .. .. .............. .. ... .... 34 

5.2. Axially excited sloshing: generation of droplets ........ ....... ........ .......... ....... ... .............................. 39 

6 Conclusion ...... .. .. .. ........ .. .. .. ..... .. ....... .. .................... .. .. .. .. .. .... .. .. .... ............ .... .. .. ...... .... .. .... .. .. ................... 41 

7 Appendix .... ..... ... .................. .............. ....... .. ......... ...... .. .... ............ .. .................. .... .... ....... .. ................... .. .. 43 

References .... .. .. ......... .. ............. .. ......... ... .......... ......... .. .. .. .... ..... : ..... .. .. ... .... ... ... ....... .......... .. .......... .. ............. 43 

2 

Nomenclature 

p = density 

p = pressure 

Pc = critical pressure for gas 

T = temperature 

T c = critical temperature for gas 

Ts = surface or interface temperature 

u = velocity 

c = sound velocity 

M = Mach number, M = u/c, Mo = u/co 

Cv = specific heat for the constant volume 

Cp = specific heat for the constant 

y pressure 

g = ration of specific heats; y= cpfcv 

R = gravity 

Rt = radius 

St = radius of tank 

Ssu = surface of tank cross-section 

r = total surface of tank 

Lo = thermodiffusion length 

qL = heat of evaporation 

hT = heat transfer coefficient 

j = mass flow density [j = up] 

J = mass flow [ J = upS] 

q = heat flow density 

Q = heat flow 

= convection heat flow 

= radiation heat flow 

= thermal expansion coefficient 

= boundary layer thickness 

= thermal conductivity 

= kinematic viscosity 

Introduction 

L = dynamical viscosity 

Pr = Prandtl number, Pr=~Cpfk 

Ra = Raleigh number 

Rex = Reynolds number 

Gr = Grashof number 

Nu = Nusselt number 

Subscripts: 

g = gas 

L = liquid 

env = environment 

t = tank 

w = tank wall 

ull = ullage 

eva = evaporation 

p =condensation 

con 

d 

Abbreviations: 

LH2 

GH2 

MNM 

SLS 

3D 

= Liquid Hydrogen 

= Gaseous Hydrogen 

= Multinode Model 

= Space Launch System 

= Three dimensional 
We study main physical processes in the LH2 tank during the prepress and rocket flight. The 

goal of this research is to analyze the hazards associated with the functioning of the external 

cryogenic LH2 tank of the Space Shuttle (Fig .1) during the pre-pressurization process and in the 

course of the flight and their scalability to the proposed SLS design with 5 engines (the situation 

with 4 engines is less critical). We use both the protocol, material parameters, and the telemetric 

data for Shuttle flights [1 , 2] to fit an uncertain parameter of the multinode model (MNM), 

developed in our group with use results of the works [3-5]. After an appropriate rescaling MNM 

is further applied to study the temperature stratification, the ullage pressure dynamics and the 

associated risks in the LH2 tank in the framework of the proposed SLS designs. 

E 

" 'Ii-+-'I- +--Ht---I6 

Fig.I. Design of the Shuttle tanks: the shape and pa rameters of th e LH2 tank 

1. Boiling near the tank wall and bubbles' collapsing: scaling of the 

bubbles' volume 

LH2 is characterized by a low temperature of boiling [6-8]. Therefore, a very weak heating of 

the liquid boundary layer near the tank wall by the environment heat flow Q =qenvSsur leads to env 

boiling LH2 (Fig .1-1) by creating bubbles. We show below that the total volume of the bubbles is 

2 

proportional to the tank height squared Ht due to increase both of the power Q and the rising env 

time of the bubbles. 

3 
I 

I 

I 

I 

I 

'

H

PARAMETERS

,=29.4m and 

: ~ \ ~ I S.=774m': 

1 R1=4m; 

I P,=2"R,: 

I PL=70.87kg/m'; 

I QL= 4.5x10sJ/kg; 

I CL =9660J/kg/K; 

KL=O.1W/Klm; 

I ~L=1 o- Pa ; t 

I TL =20.4K; I 

I J>. = O.023K-' ; I 

I R"2=4124Jlkg/K; 

1 p,=p/(RH1T J: 

p=1atm. 

Fig.I-I. Boiling near the LH2 tank wall due to the environmental heat flux. 

1.1. Nucleate boiling of liquid in the boundary layer near the wall 

During the replenish stage bubbles are generated near the tank wall due to the heat flux qenv 

from the hot environment. The bubbles mass generation rate can be assessed as 

_ q . S .. . 2 

m = <f .. • >u, rn ::::: O.35ka / sec at q = 200w / m bubble > b"bhl. .:> env (1) 

qL 

The velocity of bubbles rising under the buoyancy force is given by 

V. dvbub V. ( ) Cd 2 S 

P vapor bub dt=g bub P I. - P vapor - 2 P LVbUb bub' 

Sial 8g rbub v ~ --- bub 3C' 

d 

(2) 

Here we estimated the typical size of the bubble is by the LH2 capillary 

radius r

capill = ~2o-LH2 / gpL = 2mm ( o-un = 1.7 .10-

3 N / m). The bubbles number density along 

the tank wall can be approximated using 

dPbubble = dPbubble V Slal = q ", S sul' :::::> P (x) = q ",S sul' X 

d d bub bubble Sial 

t X q L q I. V bubble 

(3) 

Eq. (3) implies 

V. = H f' P bubble (X) d = v.0 [ H, J2 

bubble ex bubble H a P bubble,O 10 

(4) 

It follows that the bubble volume is a quadratic function of the tank height length Ht. 

1.2. Collapsing of the bubbles during the prepress 

4 
During the initial stage of the prepress bubbles will collapse due to increase of the pressure 

from 1 amt to 3.2atm over -16 sec. The characteristic time-scale of the collapsing can be 

estimate from the energy balance 

4 2 K (T,b - '0J Nu - V. 

TCrbllb L Iii, ·tcollaps - bllbP s,vaporq L' rbllb 

where P s,vapor is density of saturated H2 vapor at p=3atm and 

( 

stal J

I

/

2 

( J

I

/

3 

Nusselt number Nu

l 1bo = 0.332 P L Vbllb;:bllbble,o C~L >:::; 50, 

The bubble surface temperature is determined by the ullage pressure [9] 

We find from Eq . (5) 

( J

I/ 5.3 

T,(p) = ~ L , T, = 25K at p = 3.2atm 

Pc 

2 

t = P vaporq Lrbubble,O 1 1 5 

II , t colla,we < sec at p > . atm co apse 3K (T _ T )Nu ,," 

L sb L IrbO 

(5) 

(6) 

(7) 

Thus, the bubbles will collapse completely during of the initial stage of the He injection, 

leading to increase of the ullage volume. The ullage and bubble volumes in Space Shuttle are 

Vbubble=58.25fe and VUllage=372 fe (see Table1), i.e. Vbubble / Vullage =16%. While, in SLS LH2 tank 

with 5 engines Vbubble=162.25ft3 and VUllage=620 ft3, i.e. Vbubble / Vullage =26%. This effect has to be 

taken into account in the simulation of LH2 tank and in particular of the prepress regime. 

2. Main processes of heat transfer in the LH2 tank 

The general heat balance in the ullage LH2 tank (Fig . 2-1 ) can be written as 

(8) 

Here Q,yecl +Qenv is the total heat added to the ullage tank as a result of hot gas injection 

from the diffuser and the interaction with environment. This heat is spent on heating the gas 

inthe ullage, 

5 
V" ul lage volume 

p ullage pressure 

Diffusor T ullage temperature 

T" wall temperature 

Fig.2-1. LH2 tank design. Main physical processes and variables 

Q uI/age , heating the tank wall, Qwall' and on condensation-evaporation processes including 

heating of the surface layer of the liquid , QL. The heat flows associated with these processes 

are sketched in Fig. 2-1 , which also defines the variables of the physical model. 

We now proceed to analyzing these pathways and estimating their relative importance for 

the problem of temperature stratification and pressure dynamics in the ullage. 

2.1. Condensation-evaporation at the liquid-vapor interface 

A possible risk associated with the condensation-evaporation processes at the liquid-gas 

interface is a deviation of the ullage pressure from its permissible bounds (Fig.1). Here we 

analyze the evaporation of LH2 due to the hot He or GH2 injection from the diffuser. We notice 

that the change of the ullage pressure is slow (-sec) compared to the timescale of 

thermalization of the liquid-vapor interface « 0.1 msec). As a consequence, the quasiequilibrium near the interface is established for all times with the surface temperature Ts 

determined by the vapor pressure P vapour = P GH2 [9] : 

( J

ill. ( Jl. T. ~ p; x CT) ~ (9) 

Here Tc =33.2K and Pc =13.2atm are the critical temperature and pressure of hydrogen, Ps is 

the pressure of saturated vapour near the interface and A=5.3 for H2 (see Fig . 2-2) [6-8]. 

6 
20 25 30 35 

1 P . j2 + . T . T2 . T3 . T4 . T 5 . Ogl~ _ ." , = J1 + .J: J3 . +.J4 ~5 . + JG + J7 

Substance Ji/lOI h/102 h i4/l0-1 I0 '" J6/ 1O-(' h/lO- P 

liydrogen - 0 , 1059 -0.3515 0.3787 - 2.360 .5f)3 - Hi.I8 125.0 

0.1 0!----;----::;:-'---:-:" - -;;;;-"'- ,,,---,;;-- --!,s . . OXYlSon o~~ ~62S - O.362'l 0.2652 - 0.1000 0 .154.'1 

I!""PUA ~f{OIC J 

Fig.2-2 Dependence of saturated vapor pressure on the surface temperature ofLH2 

Note, that ps=1atm at Ts=h =20.4K The partial H2 vapor pressure is PGH2,,=3.2atm=47psi and 

PGH2"=2.25atm=32psi during the pre press and flight, respectively. For such pressures the liquid 

surface temperature Ts> h Since T: > TL and ~ > T: the convection of both liquid and vapor 

is absent. (Moreover, our 3D simulations have also shown that the convection induced by the 

hot gas injection from the diffuser and natural convection near the wall is relatively small near 

the gas-liquid interface.) Thus, the heat balance in condensation-evaporation processes is 

established mainly by means of thermo-diffusion at the given surface temperature sr GH~ . The 

thermodiffusion is driven by the equation 

aT a2T 

C L,gPL.g ---;;t = K L,g 3t2 ' T(O,t)=T:=const, T(r,oo)=TLO (10) 

The solution of is 

aT a2T 

CL PL - = K L - T(O,t) = T. = const, T(r,oo) = o .g .g at .g at 2 ' 

Here Pl ,Cl , K L are the density, heat capacity, and thermo-conductivity of liquid (gas- ",g ",g .g 

vapor); x=o is the liquid-vapor interface, erf is the error function . Using Eq. 

Error! Reference source not found. we find that the heat flux from the heated surface to the 

interface 

. ( ) ___ ~ 8T(X,t) 1 = C LP L

K L (T: - TJ2 = J T: - TL 

q L x,l K L K J. ' 

Ox x=o Jrt Jr L DL 

where Lm. = J JrK,,' is thennodiffusion lenght and 12, = S" j, C LP L 

This makes it possible to estimate the condensation mass flow j cond from the following 

balance equation: 

/) . ()'J ( (' (T T)) - Q' Q' - S (or 'j 'j ~ K Tg-T.) 'L.n .. ,d = .Jm nd l ' L CfL + UN ~ g - S - L - g - L \ LDI,Ct) - g LDg (t) , 

. KI CLPL (Ts - TJ- GH2C H2 H2 (Tg - T.) 

) cooo (t) = ( ) 

q L + CGH 2 Tg - T.,. 

(11 ) 

(12) 

7 
--- ---- 

Here the first term in the left part of Eq . (12) describes the condensation heat flow rate and 

the second describes the evaporation flow rate . The mass of condensed vapor is given by (11) 

I 

M cond(t) = f SL (t)jconAt)dt (13) 

o 

According to Eq. (12) condensation will be dominant whenever 

( Tg - T/PcoJ ) < (T/Pco.J - TJ K K ~C L , ~ (PcoJ = 1'" (pcox J1I5.3 

CDx CDx P CDx Pc 

(14) 

According to the condition (14), the condensation is dominant when the gas temperature 

near the liquid-vapor interface T 9 < 70K during the prepress when p""3.2 atm and T 9 < 65K 

during the flight when p""2.25atm. For the estimation of the thermo-diffusion length in the gas 

we used characteristics of pure H2 prevalent in the vicinity of the interface. This result agrees 

with the experimental data [10] presented in Fig. 2-4. The point in Fig . 2-4, right correspond of 

our estimation for p=32psi. 

MNM simulation showed that the effective temperature of the ullage gas near the interface 

is less than 70K. Therefore, the condensation is dominant in the LH2 tank during the prepress 

(Fig.2-5) when the partial GH2 pressure is higher than 2atm (Fig.2-6). However, it is expected 

(see estimation in Fig. 2-4, left) that the condensation mass flux is relatively small in comparison 

with rates of injection of both hot He UHe=0.6kg/sec) and H2 UH2=OA 7kg/sec) from the tank 

diffuser. We note that the condensation rate found in MNM simulation is an overestimate since 

a higher averaged temperature in a relatively wide layer is used to calculate the rate . 

8 

Fig.2-3: Temper ature profile near the liquid-gas interface 

- 320 60 100 loW 130 220 

Temperature gas near tile interface, K 

10 20 fK) 

F1gure 16, - OirKllon Of mass fl ull as l'unctkm of bulk 1Iuid le ~nlun~$ . nd tan ~ pressure fOf'" h)'drogtn, 

Fig. 2-4 Eva porated mass (left) and critical temper ature (right) as function of va por He pressure: 

th eoretica l estimations (left at PGH2=2.25atm) and experimental da ta (9] 
r-'-l------,--------,,--- - -,------, ~ 0.4 tT-/=~====r----r--1 

(/) 

(/) 0.3 CO ID E ~ 10 . c 0.2 

5 ~ 

m S . ~ 0.1 

c C 

~ 0 ·· .;g O · 

§ § U -5 L-_l-'-00----'-SO-----'0,.=---SJ...... 0 ------'100 0 -0.1 lc'-:OO:----~ ----':-----!:--------'l00 

Time, sec Time, sec 

Fig. 2-5. Time-traces of the condensation flow rate (left) and the condensed mass (right). 

Results of the MNM simulation. 

Fig. 2-6. Partial pressures of H2 vapor and He near the liquid-vapor interface. Results 

of the MNM simulation. 

2.2. Cooling of the ullage gas by condensation at the interface 

The heat flux into the liquid associated with the condensation is given by 

. d(j (T - T) J¥C P Q == _ gL = K g s S (t) = (T - T)S (I) g g g , 

gL dt g LDg (t) L g s L m 

Kt LDg = - g- is thermodiffusion lenght in the gas 

CgPg 

The total heat due to the condensation of GH2 can be estimated as 

QgL (tprepress) ~ 4.6 x 105 J and QgL (tnigh,) ~ 10

6 J 

(15) 

(16) 

The heat of injected He during of the prepress (t;::100sec) and the total heat of injected hot 

GH2 during the flight (tHigh! =500sec) are estimated as follows 

QHe = C T J = 8 7 . 107 J O CH2 = C T, J = 9 1· 108 J inject p,He He He t prepre, . . , inject p,CH 2 CH 2 CH i flight' . (17) 

9 
Thus, the condensation weakly affects the general ullage heat 

balance: QgL (t flight) / Q nject < 1 % . The effect of condensation strengthens considerably due 

to the sloshing (see Section 5). 

2.3. Evaporation near the wall-liquid-gas interface 

The hot injected GHe or GH2 heats the tank wall causing heat flow along the wall . This flow 

will induce evaporation of liquid near the wall-liquid-gas interface (Fig 2-7). The heat flow is 

Given by the following expression: 

O R d ( 

dT ) 2 d K (T) (T" ,,. - T,. ) WL = 2Jr , '" KJV - . ~ JrR, '" JV s !1d 

clx IlOterface HIS 

The evaporation flow J and the evaporated mass M near the wall-liquid-gas evap,w evap,w 

interface can be estimated from the heat balance equation 

1 - 27rRdK(T)(Tws - TJ 1 _ 27l:R,d".Kws (T,,, - I:) M -fl dt evap.w q L - , HI HI S I1d 'ev{/p ,'" - M ' eVlIp ,w - evap,w 

ws qL ws 

MN M simulat ion 

Interface '~OO~E::-O -.al=--_-=-~ --::lO~O --:::10----':<J~;)c---:3:) 

T l!a 

T, +3K 

t;;:~ artL'f"pntp:ess stiHt 

/",.Ts 3D simu lation 

terface 

~2,35 

136 '31 13& 119 140 '''I 142 l .. j , .... 145 ,41t 147 1.'! 

Y, inch 

(18) 

(19) 

Fig. 2-7 Heat and mass eva poration flows near the wa ll-liqu id-gas interface (left); Wall temperature 

stratification (results of 3D, in center, and ofMNM, right, simulation). 

It follows from the MNM and 3 D simulation ( KJV dT J 5 4000 ~ [(T -T )< 30K, dx l intelface m ws S 

Kws"-'17W/m/K and t.d > 0.15m]. Therefore, according to Eq. (19) ws 

J evap ,w < O.8g / sec, M evap,w < 0.04kg during the prepress (20) 

Note that the total mass of gas in the ullage is greater than 16kg. The condensed vapor mass 

accumulated during the prepress is - OAkg (see Sec. 2.1). Thus the effect under consideration 

is negligibly small during the flight due to T ---* T (Fig. 2-7, right). ws s 

2.4. Heating of the tank wall by the hot gas: the main mechanism of the 

gas cooling 

The heat flow from the hot gas in the ullage at Tg to the tank wall at Tw can be written as 

10 
· d( ~H' h (T T) h 0.15 K (T ) (R )1/3 25 W q"w= _ ·_ = gw g- w' gw = -- g g ax :::::: - 2- ' ~ dl x m K 

Ra

x 

= gj3grCgpg(p, Tg)(Tg -1',,,)x3

, If =(1+(0.492J9116J-16/9 

f.lgKg(Tg) Pr 

(21 ) 

Here we use the correlation formulas for the turbulent regime (see Section 4.2.1) as the 

Rayleig h number Ra >3 x 1010 and Re >105 for x>1m. The heat transfer coefficient hgw and the x x 

temperature length I = K / h do not depend on x gw g w 

(lg>v ~ 4.5mm for p = 2.4atm, Tg = 300K, 1',v = 120K). 

The total heat flux is 

(22) 

The temperatures of the ullage and the tank wal l depend on the coordinate x along the wall. 

For the numerical simulations the temperature dependences of the specific heat Cw and thermal 

conductivity for AI-Li 2195 alloys have been used. The changes in the temperature of ullage gas 

and in the temperature of the tank wall during the prepress are shown in Fig.2-8. The solid lines 

are plots of MNM-simulated time-traces of temperatures near the top (upper red curve) and 

bottom of the tank (blue). The wall temperature T (t) increases quickly during the initial stage w 

due to the small value of C) TL)= 18J/kgK at T==23K that increases strongly to 840J/kgK at 

T=255K. 

250'---~----~--~--------~ 

_ 200 

;;s 

i 1 50 

~ E 

>-'" 1 00 8, 

ro 

::5 50 

0 

I 46.2K 

~0~0---_~a~0---~670--~470~~2~0==~ Time 

C. 

~ 

t 

~ 

~ 

100 

90 

80 

70 

60 

50 

d O 

30 

20 

1 0 

- 1 00 -ao -60 -dO - 20 

Time 

Fig. 2-8 Time traces of the ullage and wall temperature during th e prepress. 

H eating of the tank wa ll is the main mechanism of the hot gas cooling in the ullage. 

3. Ullage pressure and temperature stratification 

o 

3.1. Fitting of the MNM and He pulses parameters to the Space Shuttle 

data 

11 
The values of main parameters at the end of replenish (EOR) stage and at the engine start 

command (EST) are shown in Table 1 (from [1]). The variation of ullage pressure during the 

period, t = -103sec to t = 100, is shown in Fig . 3-1 [1]. The pre-pressurization starts at 

~~.~p,.ess = - } 02.8sec with injection of the hot He and finishes at t=-86.5sec. The nominal He flow 

rate is J He=1 .3Ib/sec =0.6kg/sec and He temperature is T= 572.4R=318K. The nominal 

parameters of supply of gaseous He or H2 for STS -115 are presented in Table 1 . 

EOR 

Ambient Pre me: 

llage Pre \Ire: 

Ullage Pre llre: 

Liquid Le\'el: 

lIaee \" olllme: 

ll<lge M<l : 

Total T[lllk Volume: 

Bubble \ 'oJUJlle: 

Liqllid Volume: 

Yented LH_ Den ify: 

LH2 Propellallt Load: 

...... _t~~;?§: ;.; :~. ~~ ~: .. ; .. ~~~~::~s:.~~~~~ .... ~, .. ::~. :::-.... ~ ::::: 

: .. ,·_-,;---,·-1 " .... +--1'-- _. ___ 1'': 5atml·· ....... ,._ .... . 

::" ... :::·:t·=:=~:·:~.~~·::i:=:-'.:t::::::t . ;=i ~;;~J:=·· .~ .. :::: ... :::.::::~=.::::~ ••••• ' ••• ~ __ ••• _M ': .•• ! , ..j .... :. .- :-1 

lO'-:-! .• m::---:: .• o,----_:!:: .o--. ...,':-- .2Jo::----!:O--!: 20--.:'.:-i o ---::&o':---;!;e:,,----:-!l~ 

Time,sec 

Fig. 3-1. Time traces of the ullage pressure 

Table 1: Nominal LH2 tank (STS 115) 

1.024a tm 14.65 P i<l I 

0._0 P ig: 

1-+.85 p-i[l 

1044.6 Xt 

10.5m3 372 n 

27 Ibm 

1498m3 5_.91.- fr 

1.6;111)3 ... 58.25 fr3 

1486m3 52.-1 -+ fT' 

4.4125 lba/ft 

231 ,5 8 lb01 

113 Ibm 

ll[lge Pre nre: .., _ . .>5 P ig 

II[lge Pre me: 3.24atm 47 psi[l 

GHe (Anti-lee) Ma Added: I Ibm 

GHe (Prepre . fa :\dded: "Ibm 

llilge Yoitulle @ ESC 27.1Sm3 959 ff 

llage Ma rt! ESC 68 Ibm 

ET Liquid Volume @ ESC :2.3_0 ft3 

ET Liquid Ma (. E 231.475 Ib", 

Pre lei LH_ Den-iry 442·L 7 Ibo ft3 

Predicted LH2 age to T-O: 1.79_ Ib", 

LH2 Tran fen-ed to ME : 5 Ibm 

Max imum He flow JHe=1.3Ib/sec=O.6kg/sec Londed LH_ at T-O: 2_9.625 10m 

Predicted llage \·oluill - % [ 1.83 

Max imum H2 flow JH2=3xO.35Ib/sec=0.476kg/sec Liquid \ ·01 1II lle 

Required llage \ ·olllme - 00 1..--+ 

of Liquid \"oitune 

The ullage pressure drops at! 2: ~~ ress due to cooling of the hot injected He (see Sec. 2.3) 

and expansion of the ullage volume under the pressure increase. Pulses of He injection are 

applied when the ullage pressure drops below the threshold value of P th =20.54 psig=35.2psia. 

The form of the He mass flow pulses is shown in Fig. 3-2. In more detail, the pulses have 

amplitude i He =0. 3/b/sec=0. 136kg/sec and their form is given by: 

. . {I -exp ( - (t - t;) I r from), t < ti + r p 

J(t) :::: J He ( (23) 

exp - (t - ti-Tp) / rtail ) , t >ti +Tp 

where at t=ti the ullage pressure drops to the threshold value of P th and i-pulse is generated. 

12 
I '" 0.02 -I - -

o o 0.5 2.5 

Fig. 3-2: The form of the He mass flow pulses. 

Ullage temperature stratification and gas velocity distribution during the first stage of the 

prepress found in 3D simulation are shown in Figs. 3-3 and 3-4. Temperature distributions 

during the prepress and first stage of the flight are shown in Fig . 3-5. One can see that 

temperature smoothly decreases from the high temperature near the tank top (T"='300K) to the 

low temperature at the interface (T:,'23K) during the prepress, and the temperature distributions 

becomes more pronounced during the flight (Fig.3-5). 

We chose a single fitting parameter of MNM , numerical coefficients f3u in the velocity 

correlation for the turbulent natural convection (see Eg . (25) ), in such a way as to fit the 

temperature distribution found in the 3D simulation (Figs. 3-3 - 3-5). The sawtooth modulations 

of the ullage pressure induced by the He pulses were fitted to the telemetric data. For the fitting 

we chose parameters of He impulses in Eg. (23) (The pulse duration T and its front and tail 

pulse 

durations T and T ) . front tail 

(R ~IJ) "3 f3 C (T ) 3 

h"" = 0 15[3 K ax fJ 0 R gcosrp, T L.CP L,g LIV - T L X F . " UG r:x; "x, a x 

X flL.c K L,g 

11 , = [3 U (x) U (x.) = O. 78~ ( Rax Pr )1/2 r:x; f3 XII2 Of' U (x.) = [g[3TQenv

x J

I/3 

" .x " N 'N , I + 0 494 P 2/3 " N I C Xi . r L.GP L.g 

(24) 

i N = 27rR,rmkDxti,v ,PUG r:x; [3"x 6/5

, 

Dx = O. 565x[ (1 + 0.494Pr

2l3 ) / RaxPr23fl5J r:x; x7flO 

Amplitude of He mass flow was 1.3Ib/sec =0.6kg/sec. The fitting gave the following values 

for the parameters: 

• l3 u= 0.2 

• T = 0.12sec, T . = OAsec, and T = OAsec 

front ta,l pulse 

13 
... ---.. .. 

., 

" ,. 

,. 

II 

c...===--.J ... t~ ___ I 

Fig. 3-3: Distribution of the ullage temperature (upper) and velocity (below) during the 

first stage of the prepress: 3D simulation at t=10sec (Ieft)-and 16sec (right) after the 

prepress start. 

=-~ ~ 

...... "" )tI .. tS 

, .. " )4)21 "' .. 'IOM I"" 1111':1 "", lJoo.tl 

115.tO 

.... 

" xu "" .. ., .. 

Fig. 3-4: Temperature stratification during the prepress: Results of the 3D simulation for 

different times after the beginning of prepress. 

14 
300 line2 Tank top 

250 

200 

'" oi 

~ 150 

8. 

E 100 

~ 

50 

2 3 

Line length, m 

250 

200 

~ 

~ 150 

a 

l!! 

~ E 100 ., 

.... 

50 

300 

250 

200 ~ 

oj 

:; 150 

iii 

Q; E 100 

II> 

.... 50 

linel 

Tank top 

B 20s } , ft .. - 255 prepr e ssst art 

- 40. 

- 10sdraine 

after start 

Interface 

2 3 

Line length, m 

Tank top 

line3 

0 2 4 5 

line length , m 

Fig. 3-5: Temperature stratification during the prepress and the first stage of the 

Shuttle flight: Results of 3D simulation for different times after prepress start. 

Stratification of the ullage and wall temperature found in a MNM simulation is shown in Fig. 

3-6. Results of fitting time-traces of the ullage pressure and temperature near the tank top, 

where the thermo-sensor is located, are shown in Fig. 3-7. We see that the results of the MNM 

simulations fit well the STS-115 data. We emphasize that the only fitting parameter of the MNM 

was the numerical coefficient u in the correlation relation for the natural convection velocity (Eq. 

(24)). This coefficient depends on the fluid's properties and is essentially independent on the 

tank design. Therefore we used MNM with this fitting parameter for analysis of the rescaled LH2 

SLS tank. 

250.,----r-- -........,..-~ -~ ---:J 100 

g 

'" " e 

'" Co 

E 

.. 

.... 

= 

~ '" 

L- ~_~_~_~~_L-~~~~ 

·100 ·80 ·60 

10 

· 100 ·80 ·60 ·40 ·20 20 40 60 80 

TIme (s) 

Fig. 3-6. Stratification of the ullage (left) and wall temperature (right) during the prepress and the initial stage of the flight. Results of the MNM simulation. 

15 
45 

LJ---L--~ ---L--J--- --~ 

-100 -80 -60 -40 -20 0 29 40 60 

TIrre (5) 

-4 00 

--- sirrulation 

--- STS11 5 

~~J 

I 

I 

-450 '---' __ ---'-__ --"-__ -'-----'-__ -L--__ -'----''----' 

-100 -80 -6 0 -40 -20 0 20 40 60 

Time(s) 

Fig. 3-7: Time-traces of ullage pressure (left) and ullage temperature (right) near the 

tank top during the pre-press and the initial stage of the flight. Results of MNM 

simulation. 

3.2. Scaling considerations for the LH2 tank for SLS with 5 engines 

The MNM with fitting parameter ~u= 0.2 are further used in modeling the prepress and fight 

regimes for the proposed design of the SLS LH2 tanks to assess the associated risks. Results 

of these simulations for 5/3 scaling SLS tank are shown in Figs. 3-8 and 3-9. Fig . 10 illustrates 

the ullage temperature distribution in 5/3 scalable SLS Lh2 tank found from 3D simulation for 

prepress stage. We increased the mass flows of injected He and GH2, and also ullage volume 

and tank volume, due to its extension , in 5/3 times. 

It can see from comparison of Figs. 3-4 and 3-6 with Figs. 3-8 and 3-10 that the temperature 

stratification is more pronounced in the 5/3-rescaled SLS LH2 tank due to a lesser mixing of the 

initial cold and injected hot gases. Results presented in Figs.3-7 and 3-9 indicate that the time 

traces of the ullage pressure in Space Shuttle tank and in 5/3-rescaled LH2 tank are close. 

However the numbers of the sawtooth variations of the ullage pressure initiated by injection of 

He impulses during the prepress are different because of difference in the GHe masses and 

surfaces of the tank wall corresponding to the ullage volumes in Space Shuttle and SLS tanks . 

250 ..------_----~----......., 120 

Tank top 

100 

;;;-

'" '5 

'" :;; 

Co 

E 

Q) 

>-

ro 

3: 

interface 

0 

· HXl ·50 0 50 "rre (5 ) 

Fig. 3-8. Stratification of the ullage (left) and wall temperature (right) during the pre-press 

and the initial stage of the flight for 5/3 scalable SLS Lh2 tank. Results of MNM 

sim ulation. 

]6 
r

4S 

~------~------~------~------~ sO r-r------~------~----~--___::--_, 

.f'-...J~· 

-100 ,ri'f"' 

40 iZ 

·150 '--__ ~:..c..;.:~ f -;; -200 

~ " -250 

~ -300 I-

-350 

-400 J 450 ~------~------~----~-------J 

1O~------~------~------~------~ -100 -50 50 100 ~oo ~ 0 ~ 

Time (, ) 

100 Ti rre (, ) 

Fig. 3-9: Time-traces of ullage pressure (left) and ullage temperature (right) near the 

tank top during the pre-press and the initial stage of the flight for 5/3 scalable SLS LH2 

tank. Results of the MNM simulation. 

We see that the observed time trace of the ullage pressure for SLS 5/3-rescaled LH2 tank falls 

within the permitted bounds (see Fig . 3-11) 

Gas Mixture. 

Tem~rature 

290.9 

272.7 

254.5 

236.4 

21 8 .2 

200.0 

181.8 163.6 

145.5 

127.3 

109.1 

90.9 

72.7 

54.5 36.4 

18.2 

0.0 

(K] 

Temperature 

Contour 3 

(K] 

97.1 

9:2.8 

86.5 

84.2 

79.9 

75.7 

71.4 . 67.1 

62.8 

58.5 

54.2 

SO.O 

45.7 41.4 37.1 

32.8 

28.6 

24.3 

20.0 

Fig.3-10: Temperature stratification in 5/3 scalable SLS Lh2 tank: Results of 3D 

simulation for different times after the beginning of the prepress . 

.. . 

~ ~ A O . 

:;! 

~ 

~ 

l>:! 

"-

::,: :S5 . ::3 

'S 

e 

~ 

~ :so. w 

2 5 . 

__ M INIM U M 

Io.4 INI .... U """ - 3 StO M A 

- - - l CO- 2 - 12 001 FIGURE. 3.3 . 2 - 3 .8 ( IRN IC - 16!1o?) 

oJ ~. ____________ • ______ . ____ ~ ________ .• __ "'(Q1ot. 'tc? ... <::q " '''i:(tI". ''''i''' C) __________ ._. _____ _ 

It.: :::::;:: -.;:-.:-..:-.:-..:-.:.-.:-.: -.::::-:-~ ~~- ~- --. -------------- ----:~~~=:-~-:.: ~. ~ 

-.-

t 0 . 0 

-.-.-. ----.. --. 

100. 2 0 0 . .300 . --'--""""0'0. __ a !) ~. 

TIM C f" ROM S R O leNITIO .... (T- O). ( S EC) 

Fig. 3-11 . Requirements to the ullage pressure [1] 

17 
4. Temperature stratification in the liquid 

The temperature stratification patters in the tank is shaped by two main physical processes: (i) 

condensation-evaporation on the gas-liquid interface and (ii) natural convection along the tank 

wall (Figure 4-1). 

1. Condensation-evaporation: 

J > 

2. Turbulent natural convection : 

~"lOcm 

qw=2DDW/m 

GH2 

PGH2=2.25atm 

=5~300K 

1-------- ---- -, 1 - - _ __ 1 

L _____________ I 

l,,30m 

~ O"8m -.,. 

Temoeraturl 

II<] 

21 .0 

20.9 20.9 20.9 

20.8 20.8 20.8 20.7 

20.7 20.7 20.6 

20.6 20.5 20.5 

20.5 

20.4 

20.4 

Fig.4-1. Physical processes contributing to the temperature stratification in cryogenic 

tank 

4.1 Heating of liquid in the boundary layer near the gas-liquid interface 

The liquid layer near the liquid-gas interface is heated due to condensation. The surface 

liquid temperature is determined by the partial pressure of H2 vapor P GH2 near the interface (Eq. 

(9» . It can be seen from Fig. 2-6 that the partial GHe pressure near the interface 

PGH2<32psi=2.25atm. Therefore, the surface liquid temperature, according to Eq. (9), is T5 ~ 

23.8K (Ts-TL ~ 3.4K). The width of this overheated liquid layer is determined by the 

thermodiffusion length (Fig. 4-1) of the liquid (Eq. (11» which increases with time and 

approaches a value of LDL = 1.5crn toward the end of the flight. This conclusion explains results 

of 3D simulation presented in Fig . 4-2 that shows temperature stratification in the liquid near the 

interface in the end of the flight (tHight=500sec). 

The upper bound for the mass of the overheated liquid in this layer can be estimated as 

M ~ O.SS(tjl' I )PLLD,,(tjl'gI ) = 30kg while the total LH2 mass in the filled tank is 105,OOOkg . warm Ig'll 'J..J I 11 

] 8 

The heat flow into the liquid associated with the condensation is given by 

() _ dQ,. = K (Ts - TL ) S (t) = (T - T )S (t)JKLCLPL ·L dt L LDL (t) L S L L 7rt 

The total heat associated with the condensation of GH2 is 

QL (t) ~ (T. - TL)SL )KLCLPL (4t Ill"), Q L(tflight) ~ 5 x 105 J 

while the total heat of GH2 injected during the flight (tHight =500sec) is 

(25) 

(26) 
= Pllflagl tank = 2.5.108 J 

r-l 

Q injeCI = C FOx r;,ylin/iliglli = 3.4· J08 J, Jinj = l.3kg / sec, r;,lj = 800R = 444K 

Thus, the additional heat of this overheated layer has a relative small value: 

QL (t jlighl) I Q njeci = 0. 1 % . 

4.2 Heating of liquid in the boundary layer near the wall 

4.2.1. Natural convection correlations 

- - - 

(27) 

There is a constant heat flow across the tank wall qw-200W/m2 . The natural convection flow 

generated by this heat is highly turbulent in a large tank such as LH2 tank. With characteristic 

Reynold number Re-1 06 . As a consequence a theory dealing with the natural convection in the 

tank is a theory of turbulent flows. Due to the notorious closure problem (Figure 4-2) little 

progress can be done by a rigorous mathematical analysis of the equations of motion and 

additional physical assumptions have to be made which cannot by derived from the equations of 

motion and the boundary conditions. These assumptions have to be validated by comparison of 

the theoretical predictions with the experiment. We note that the results of this subsection are 

applicable to natural convection in both the liquid and the ullage space, provided the 

Boussinesq approximation (Figure 4-2) hold. 

19 
The problem of turbulent natural convection 

Boussinesq ClppruximCltion: 

P = PoQ. + pT')"" Po T=T - T. 

Averaged momentum 

transfereq-n Det/l. + uyIT! - I//);Ti + !3gT' = O. 

(Navier-Stokes): 

Averaged energy 

Transfer eQ-n: 

Continuity eq-n: 

BoundClry (onditions: v w = 0 v 

n T' r n "'1" 02T' vru + Uyj ,.L = X( IF . 

= 0, 1', ) and q ttl or T 'W 

Closure problem: 'u2 =I- u2 U =I- 'U V, te. 

Fig.4-2. The closure problem for the turbulent flow 

In contrast to the forced convection there seems to be no consensus in the literature about 

what are the correct assumptions for the natural convection theory [11-16]. In what follows we 

outline the physical picture which is correct in our opinion, derive certain correlation relations 

based on this picture and validate the predictions by comparison to experimental evidence and 

high fidelity simulations wh ich we believe to be correct. 

To set up the stage for the discussion, let's consider Figure 4-3, which depicts a turbulent 

flow near the wall due to the natural convection . One should distinguish two characteristic 

length-scales of this flow: the viscous or conduction length-scale I, and the turbulent length 

scale O. The former lengh-scale corresponds to the inner sublayer of the flow, where the heat 

and momentum are transferred by thermodiffusion and viscous fiction, respectively (for LH2 the 

Prandtle number is -1 , therefore both the thermal diffusion and the viscous friction are 

characterized by the same length-scale). 

20 
.

--- --- - --- ----------- --- -

-

Turbulent natural convection. length-scale separation 

Conduction (viscous) length scale: 

l = 1/ /Pp = X' pP p/, l/~ (

:Ie )1/-1 ( :l )1 /-1 

g, qw gfjfJw 

Turbulent lengt h scale: (5 

(to be determined be low) 

I - O.5mm - ;,zOcm 

(Shuttle. LHl tank) 

Fig.4-3. Length-scales separation in the turbulent natural convection 

The latter length-scale, 0, corresponds to the outer region of the turbulent boundary layer, 

where the transport of both heat and momentum is carried out by the turbulent pulsations. For 

well-developed turbulent flow as in the LH2 tank, there is a huge separation between the two 

length-scales with ratio 1/0- 10-

3 . 

The turbulent heat and momentum transport is highly efficient. Therefore, we expect that the 

all the heat absorbed by the viscous sublayer from the wall is transferred into the outer turbulent 

sublayer (Figure 4-4). This is a very powerful assumption and it leads to very different results 

from those obtained by assuming that rather the total momentum flux from the wall is 

transferred into the outer sub layer, as happens in forced convection and as was assumed in an 

influential paper by Eckert and Jackson [12]. 

Assuming the heat flux qw into the outer region, where the microscopic (as distinguished 

from the turbulent) viscosity and thermo conductivity are negligible, we are left with the following 

physical variables which can determine the characteristic velocity and temperature scales in the 

outer region : heat flu x, qw, gravity acceleration g, volumetric expansion coefficient, specific heat 

CL , density p and streamwise coordinate along the wall x. Out of these variables one can build 

just a single velocity scale u and a single temperature scale T ' = T - T oc (T ~ is the temperature 

in the bulk of the liquid far away from the wall) [13]: 

(28) 

where A and B are empirical constants, which have to be determined from an experiment. 

Remarkably, the temperature is seen to decrease streamwise! This counterintuitive prediction 

can be understood if one realizes that the heat absorbed from the wall is diffused by the 

2 J 
turbulent pulsations in ever increasing width of the turbulent outer layer 0 down the stream, 

leading to a smaller temperature increase per same heat absorbed. 

Constant heat flux assumption 

Assumption l « 6 q(O) ~ q(l) 

On the dlmensloMI grounds [*], the turbulent 

characteristic (-average) velocity Is 81ven by 

/'-"'lIIll '~ ) 1/ u ~_ ~ '{'Fi":P Empirical (:OnsUlnt 

--~-----(function$ of PrJ 

And t he temperature (deficit) T =T -T_ : 

T' -( " -fL) 2/3 ( .)-1/:3 - \ ) C 9 ........ - - pP 

- _____ Empirical constant 

(functions of Prj 

The average temperature In the turbulent outer layer decreases streamwlse l 

• W. K. George and S. P. Capp, A theory for narural oonvection rurbulent boundary layers next to heated 

>'f:'!rtical surfaces, Int. 1. Heat Mass Transfer 22, p.813 (1979) 

Fig.4-4. Assumption of constant heat flux into the outer turbulent region. 

To calculate the actual x-dependence of 0 we consider the heat balance for a certain control 

volume in the boundary layer (Figure 4-5): 

(29) 

Eqs.(29-30) imply that the width of the outer region grows linearly with the streamwise 

coordinate x, o~x . This fast growth explains the decrease of the characteristic temperature in 

the turbulent region with the height of the tank x. 

22 
Estimation of the turbulent boundary layer width 

The heat balance equation: 

~ ~ CLPuTfO 

t 

Heat flux inm the 

wotrol volume 

Heat flux out of 

the wntrol volume 

Y

' ' - r, (...!:L) .•.. l

t

, ,.JJ_)-l - u £""" fl.N 

The turbulent c:harac:reristic (""avt!l<Jge) tempel<Jture dec:reases streamwise: the tl,Jrbl,Jlenc:e 

stirs the a bsorbed heat in the ever wide r OOI,J nda ry lave r strea mwise: 8 "'" . ' 

Fig.4-S. Estimation of the turbulent boundary layer width. 

A very important consequence of the predicted streamwise temperature decrease is that the 

main temperature change occurs in the inner conductance region of width Iw. In fact, near the 

wall the temperature changes linearly with the distance from the wall y: 

So the change of the temperature over the width Iw of the conductance region 

I1T ~ qj", 

CdJK 

(30) 

(31 ) 

is independent of x, i.e., for sufficiently large x it becomes much larger than the 

characteristic turbulent outer region temperature scale T' X - 1

/ 3 . It follows that for large x the 

temperature of the wall is 'I.v ~!Y.T + Too , which sets the characteristic scale of the temperature in 

the conductance region . This is a very important conclusion which means essentially the 

temperature increase of the boundary layer due to the heat flux is independent of the height of 

the tank for sufficiently large tanks (Figure 4-6). 

The foregoing argument can be considered as a theoretical justification of the constant heat 

transfer coefficient for the natural convection h, which is a very well established empirical 

correlation relation, known in the literature [17]: 

23 
q", = h (1'.., - Too ) 

h = 0.15K[ ~ Pr(l + t.p(Pr ))J'3 

G - gfJ(T.., -Teo ) ~ - 2 

V 

(32) 

Pr = V / K 

lf1(Pr) = [I + (0.492 / Pr t 6 T6/9 

An important contribution of our theoretical analysis is assertion that not only is the wall 

temperature constant for the constant heat flux turbulent natural convection. but that the heating 

essentially occurs in the conductance sublayer only, i.e., that b.T = T.v - Too ' This latter property 

allows one to calculate not only the characteristic temperature in the inner sublayer but its width. 

too, which is important for the stratification analysis. 

constant eat trans er coe ,elent 

For large x the temperature gradient is substantial only in the viscous sublayer of width L 

This can explain the constant heat transfer coefficient for turbulent boundary layer. 

Empirical constants 

In the inner (vi.s.cous/conduction) sublayer: 

q uTI T,(, - T -- ,. \; ....., ---

CLp Y I 

q = Il (T'l' - T, , ) 

Le., the heat codficient his independentoh., 

which explains a well~stablished empirical heat-transfer 

correlation: 

Fig.4-6. Constant heat transfer coefficient. 

The precise value of the temperature drop near the wall I'J = T. .. - Too , including the 

numerical factor, can be calculated using the empirical expression for the heat transfer 

coefficient (33). 

24 

To summarize the main predictions of the foregoing theoretical arguments: 

The absorbed heat is accumulated in the turbulent outer sub layer 

The width of the turbulent sublayer increases streamwise 

As a consequence the average temperature in the turbulent sublayer 

decreases streamwise 
The temperature gradient is substantial in the conductance (viscous, 

inner) boundary sublayer 

The temperature is streamwise constant in the conductance boundary 

sublayer 

The important implication of these predictions , if proved (experimentally/numerically) correct, 

for the temperature stratification in the tank is the following : The temperature of the warm layer 

accumulated beneath the gas/liquid interface is independent of the tank height. In other words, 

the temperature stratification pattern is essentially invariant with respect to the tank rescaling . 

By "essential" we mean heating which is likely to be of any consequence from the Net Positive 

Suction Pressure Condition (NPSP) perspective. 

Now we precede to validation of the correlation relations by comparing our predictions to 

experiments and high fidelity simulations. In 1988 a series of experiments on the natural 

convection in the air (Figure 4-7) has been published in Refs. [14-15], which is considered one 

of the most reliable data on the natural convection to date. 

Validation of correlations. Comparison to experimental data. 

Natural convection of air along a vertIcal flat plate 

T=6OC T=15C 

• T. Tsuji and Y. Nagano, "Characteristics ofa Turbulent Natural Convection Boundary Layer along a Vertical Flat P1ateU

, 

InU Heat Mass Transfer, 31, pp. 1723-1734 (1988) . 

• T. Tsuji and Y. Nagano, " Turbulence Measurements in a Natural Convection Boundary Layer along a Vertical F1at Plate", 

InU Heat Mass Transfer, 31, pp. 2101-2 III (1988). 

Fig.4-7. Turbulent natural convection in the air. Experimental setup. 

A large vertical copper plate was heated to T=60°C, while the surrounding air was held at 

T=15°C. The air was entrained from beneath by the turbulent convection and raised along the 

wall where the hot wire detectors were placed, measuring the temperature and velocity 

distribution. We have simulated the experiment and plotted the results against the experimental 

data (Figure 4-8). 

25 
1.21 

1 

C 

'go.s, Q 

~06 Ol 

tU 

Q5 0.4 > tU 

(a) 

3D Simulations of the experiment 

() ~-~------, 

0; 

I 

'2

'~f

~ 

----::---~---=2 

log(x) 

3D simulation 

Experiment [1,2] 

U'1na.,' '" .1/3 

Eckert a nd Jackson - ---------

?I ~ rt, 1/ 2 ""TrW,' " . 

• 3D simulation reproduces well the measured correlations 

• Measurements apparently conflict with Eckert's correlation 

[1]1: lSlJjl"nd '( ~no, ' 'O'I:Iraderlstlts eX" 'JJlbulent NattJral CCilW'ction BOOnd:.y ~ "'all!: 3 VeriiGJI flat Flate", Inti Heat M3SS 'h1s fer, 

vd, :11, No Il, pp- 1713-1734 (19IlIl). 

11]1: lSlJjl 3f1d '( ~no, "lIJlboJlence Me3SU'ement:s ., 3 NattJr.-.I COfIvectlon BOOnd3ry Layer 3 100 I!: 3 Vert:iC31 Fbt Pbtl!!", Int.! Hm t Mass 

Transfer, Vd. :U, No ~ pp. l 10l-l 111 (19B8). 

[3] E. R. G. ~rt 3f1d 1: W. Jad<::son, An3~1! of Free-CalW'ction BOOnd:.y ~ on flat Flate, Nation'" Ad~OIV COItlmlttee for Ael'Ol'latJtlts 

tl!!dilllGJI memorandum No. ZW7, wa'-"'Ingtcr'l, Septl!!mb« 1950 

Fig.4-8. Turbulent natural convection in the air( High fidelity Simulation). 

In addition, comparison to the predictions of Ref. [12] has been performed. The comparison 

is particularly important in view of the fact that correlations proposed in Ref.[12] have been 

widely used in NASA related research for computation of stratification in tanks [18-22] . The 

results (Fig. 4-8) demonstrate a good correspondence of experimental data to our numerical 

simulations, supporting the predicted X-1

/

3 scaling of the characteristic velocity, Eq.(29). The 

scaling predictions of Ref. [12] are clearly at odds with these results . 

The next piece of validation comes from simulation of the natural convection of G02 in a 

large cryogenic tank (Figure 4-9). The walls of the tank were kept at T=90K, while the bulk 

temperature of the gas was T=1 OOK. There results of the simulation are plotted on Figure 4-10. 

We see that the predicted X-1

/

3 scaling of the characteristic velocity, Eq.(29) is confirmed by the 

results of the simulation. 

26 
Validation of the correlations. Natural convection of GOx in a tank: 3D 

simulation 

T=SOK 

~M 

IRI 

2,437 

PI1 09 1.()782 

~S5 

20.28 

11/6 00 

19473 

tS),* 

t8~ 

1$.l ~1 

l$t~ 

17, 36 1'7509 

H.82 

'I6a!>5 

1&.27 

I~OO 

~. 

168 

55 

"7 137 

l~ 

11(1 

105 

095 

084 

07. 

~ 

0 .S3 

Q1~ 

0 .32 

O?I 

01 . 000 

Ims'-') 

Fig.4-9. Natural convection of G02 in a cryogenic tank. High fidelity simulation. 

Simulation of natural convection of GOx in a tank. Results - - - -- ~ 

simulation ___ ~ 

II!)ear flt 

1lrna 

10 

3D simu lations support the predided staling of the 

cha raderistic velocity 

Fig.4-10. Natural convection of G02 in a cryogenic tank. High fidelity simulation 

results. 

27 
4.2.1. Natural convection in the LH2 tank 

As the further step toward the problem of the temperature stratification in the LH2 tank we 

performed the simulation of the temperature and velocity profiles of the turbulent boundary layer 

flow for the natural convection in LH2 tank (Figure 4-11). The initial (and the bulk) temperature 

of LH2 was taken T =20 4K. The temperature of the gas-liquid surface (1.4 m from the top of 

the tank) was kept at Ts=23.8K, which corresponds to the partial G02 pressure in the ullage 

PG02=2.25atm. The heat flux through the wall was qw=200W/m2

. The simulation was performed 

for liquid dynamics over 500 sec. At t=50sec after the beginning of the heating , the turbulent 

natural convection flow is expected to have developed. The estimate for the characteristic time T 

of the turbulent flow development is u. lO sec , where 0-10cm is the boundary layer 

width and u.-1 cm/sec is the scale of turbulent velocity pulsations as measured in the 

simulations. 

Natural convection in LHl tank. 

: _ O.:I'm m 

" 

1.t rv ~ .1/3 

b rv /10 

I nte raction with tile interface affE!lCb tile dynamics in the uppe r part 

batndary layer: apparent wid:h of the turbulent Ixmnc:llar'li3yer siYinks 

Fig.4-11. Natural convection in LH2 tank. Velocity and temperature profiles. 

The profile for the temperature in the vicinity of the wall is seen to comply with predictions of 

the theory : 1',y - Tao ~ O.8K , as calculated using the known heat flux and correlations (A33), the 

width lw ~ O.5mm as calculated using relation 8.T ~ 1',y - Tao ' Eqs. (31) and (33). Velocity profiles 

corresponding to lines 4 and 5 on Figure 4-11 are seen to collapse on a single graph after the 

best-fit rescaling of velocities by x 1/3 and length by X8/10 The latter scaling deviates a bit from the 

predicted linear dependence of the turbulent outer region width 0, which we attribute the finite 

Reynolds number effect. However the velocity profiles at lines 1,2 and 3 are seen to deviate 

substantially from the prediction of the theory, namely, the apparent turbulent outer region width 

o is found to saturate at certain value. This deviation could in principle lead to heating the outer 

layer above the temperature predicted by the correlations (29) and therefore should be 

examined carefully . The simulation results presented in Figure 4-12, give the clue to the 

solution. The structure of the turbulent flow in the upper part of the tank is much more complex 

28 
than in the asymptotic theory of natural convection , which neglects effect of the boundary - the 

gas-liquid interface. Due to this effect, at sufficiently large time t, the descending flow starts to 

develop, which interact with the ascending flow due to the natural convection. We expect that 

this interaction leads to development of the turbulent shear layer which projects deeply in the 

bulk of the liquid far beyond the point, where the velocity of the raising flow vanishes. As a 

consequence, we expect that the actual width of the turbulent flow is much wider than an 

apparent width in Figure 4-11 as assessed from the raising flow velocity profile 

Natural convection in LH2 tank. 

t"SOOs·ec 

tV 

u 

Fig.4-12. Natural convection in LH2 tank. Effects of the liquid-gas interface. 

To test our conjecture we numerically computed the distribution of the turbulent kinetic 

energy near the wall for lines 2 and 3 at t=500sec (Figure 4-13). The results of the simulations 

show that in fact the turbulence is spread far beyond the zero-velocity point, leading to an 

efficient heat transport away from the wall. Even if the scaling for this dynamics deviates from 

the prediction of the asymptotic theory of natural convection, the main physical rational which 

lies in the basis of (i) the constant heat transfer coefficient law (33) and (ii) prediction that the 

heating of the liquid is essentially confined to the conductance sublayer of width Iw, is still valid. 

That is, the turbulence efficiently diffuses the absorbed heat in the large volume of liquid, so that 

the main drop of the temperature takes place in the conductance inner region . 

The results of simulation support the foregoing arguments (Figure 4-14): the temperature at 

the wall, taken at t=500sec is found to stay almost constant along the wall and correspond very 

accurately to the predicted value T.v - Too ~ O.8K , the characteristic width of the heated 

sublayer iw="O.5mm corresponds well to the theoretical estimate, too. 

29 
Natural convection in lH2 tank. 

0.25 

0.20 

:i 

~ O.1S 

g~ 

] c: 

.Q 0.10 cu ..... tII)~ l!E 

~ 0.05 ::;) 

<u::: 

.••••••••• -0,011-

-C.05 

0.0 0.2 0.4 ; 0 .6 0 .8 1 .0 

Tl~ sec 

Ap~ tent" turbulent boundary ~f width does: not (Otl'e$pOnd to ~ rqi.on cf 

turbulel1t flow, whlch;$ mU(h Ia*, dlJe to the interaction with the descendiJ:l« 

flow. 

The turbulent hut tral'l$port (ontinJ.le$ into the regiOn of deftendin& flow 

Ie.-fin& to efficient diffusiOn of heat in $til/larger turbulert rcgion. 

Fig.4-13. Turbulent pulsations vs. average velocity; t=500sec. 

IFieI 

1" .. 

1" 05 

atura convection In tan . 

" . ,.----- --- ---, 

u.s UqUidtempereture along the 'MtU 

tl.O t= SOOsec 

~o -2' 5 .JO ~t ~ 

Tank bottom Pofytln, LH'l tlt, .fI\ Interfae< 

21.2 

::Jl 21.0 

~ e 

&.2o.i 

. 

E 

t20.6 'w 

20""' -- ,.; 

o o.dou 0.001 0 {).OO 16 O.0iJ20 0.00 26 0.00) 

UnsltPt UIlot. m 

Thetutbule~ ctrffusionof r.e~ p_sefroc:iel'lt intr.e Shuttle 1.H2 tJnk! tr.e 

tempe rature of tr.e wall ~i$e$Ul'lt afly col1lttal'lt as predicted by tr.e tr.eory. 

For borge r (SLS) tJnk tr.e turbulel'lCe is expeeted to be even laser, IUdil'l« to 

even more effoc:ient ciflusion of ~ and d« ruse of tr.e temper~ure in tr.e 

turbulel'lt boundary l"'iCr. 

Fig.4-14. Inner sublayer temperature distribution; t=500sec. 

4.3 Temperature stratification in the LH2 tank 

The foregoing results have important implications for the temperature stratification in the 

tank. In fact, the ullage pressure is P ull "='33psi=2.25atm during the flight which corresponds to 

the boiling temperature Tboil"='24K. On the other hand, the predicted near-wall temperature 

T=21 .2K corresponds to the pressure of saturated vapor Ps,vap=1 .1 atm. The temperature of the 

30 
- - --

turbulent outer layer is much lower and corresponds essentially to still lower pressure 

Ps,vap=1atm. Therefore, the heating of the liquid due to the natural convection does not create a 

hazard : the Net Positive Suction Pressure condition is satisfied during the flight due to large 

ullage pressure Pull ~33psi=2 25atm . In fact the Net Positive Suction Pressure (NPSP) 

condition for the LH2 tank reads: 

Pull + Phead -/'-.pfrlc - Ps,va/TL(t,X)) > 5psi (33) 

The hydrostatic pressure Phead is negligible for LH2. The frictional pressure drop ~Pfri c is 

determined by drop the thinnest segment of the feedline of the RS-25D engine and is also small 

compared to pull. We note that since it is a function of the engine only, it is expected to be the 

same for SLS. (Estimation of the frictional pressure drop in tubes is carried out in Appendix.) 

Thus , NPSP condition will hold for the whole LH2 volume of the rescaled rocket perhaps 

only with the exception of very thin layer near the interface of thickness <1.5cm and with 

temperature 23K:sT:s 24K, This conclusion hold for higher values of the environment heat 

density flow so long as the near wall temperature is (much) smaller than 23.8K, which 

corresponds to the wall temperature for the critical value of the environmental heat flux 

iJm ",,. = 950W / m

2 

T-stratification in the lH2 tank in the Shutde 

,-

1:2 

--_._-

3 4 

---"'_J~~---~t ( ~ "'~~a \ "'-""-' .. - - - --""-"l 

24.0 

23.6 

!IC: 23.0 

Ii 

:; 2.2.5 ;;; 

&'22.0 

E 

co 

... 2·I.S 

21.0 

. 

LH2 

&I ba .. d;wy ~ 

finllilva" · us •• 

20,5 ··'·}-··~~·T~Ci!!·········' ··· ······ ·· ·' ···· ·· -········ · ......... T 6 

o 0.0:2 0.04 0.011 O.OS 0.10 0 .t2 0 .1 4 0 .16 

l n t Length , m 

Fig.4-15. Temperature stratification in the LH2 tank in the Shuttle; t=500sec. 

The temperature stratification pattern observed in the simulation (Fig. 4-15) corresponds 

well to the theoretical predictions. The warmest layer adjacent to the gas-liquid interface has 

temperature decreasing from T=23.8K to about T=21 .2K, as predicted, over the legthscale of 

-1 cm , which corresponds to the thermodiffusion length scale IDL = 1.5cm calculated for t=500sec. 

The much wider weakly warmed layer at 20.4<T<21 .2 is associated with the contribution of the 

outer turbulent sublayer of the natural convection. Based on the typical velocity in the 

ascending flow and its width (Fig. 4-11) the width of this weakly warmed layer can be estimated 

to be > 8m. To predict the temperature profile in this layer one has to acquire a better 

understanding of the transient characteristics of the turbulent flow pattern of ascending and 

31 
....

--- - - - - 

descending flows near the wall. However, for the scaling predictions for larger tanks it is 

important that the upper limit on the temperature in this layer is expected to stay at or below 

T=21 .2K: this is due to even more developed turbulence in larger tanks, leading to stronger 

mixing and diffusion of the absorbed heat in larger bulk of liquid. This latter prediction was 

verified in a simulation of LH2 dynamics in a taller (by the factor 4/3) tank (Figure 4-16), which 

shows that the wall temperature T:::::21 K is independent of the size of the tank. 

The near-wall temperature distribution in a large LH2 tank 

_, , .. ~mL ~ l~ ., . ~~~~~~~~--~~--~.--~~-4 I ... r------~...., ---~ 

n.. .,.. ...... --------i-, T=21.2K 

" 

no 30m LH2 tank, .,. 40m LH2 tank, 

~ "-' T=5OOsec ~ ..... T=SOO-C i 

I:: h I i:: ~ I ------;;j- -- --~~.-- - :: ;; ---- ---·~-=:.:.:=·;;r r- -----... , ',. ,OJ ,.. .. 

raikbon.om lntrrr... raltbonom Im.mee 

The wall temperature is independent of the size of tank as predicted! 

FigA-16. Temperature distribution along the wall in a large (40m high) LH2 tank vs. 

the Shuttle LH2 tank (30m high) ; t=50sec, 500sec. 

Our predictions have been verified for the real Shuttle data (Fig. 4-17) for the temperature of the 

incoming fluid in the engine. 

32 

Temperature stratification data in the Shuttle LH2 tank 

l.H temperature at 17lnch manifold (data tromthe flight 

STSIlS). Temperature of the I nco mill/ fuel at the erxi d the 

flight rises to T=2L4K. EstImates ghles T=21.2 for the heat ftLtX 

q=1!Xf,N/m" 2 

~~-,_-_r-~--~-~-_4--r_-~ 

... __ .. _ .... L ..... j ........ : ........ ~ ....... ~ ........ L._ .... .: .. _ ..... : T=21.2X 

~ :: ::: ~ --;--- ~...clf.5 .- __ _ eo: -: --------r--- ----;---" ----;------ --t-------;----- -: ~ .-.t2 - - _.----- .-- --- -~- -- ----..;..--- ---:----- --- ~-------' -------! 

E :::: i : j!!!.....cl2.5 -------_:_ -------' _______ _ ~ __ __ ___ .:. ___ ____ : _ _ _ _ _ _ ~ _______ -'. ______ _ : 

~ ~ 0 m ~ m • ~ ~ Tn-e,sec I 

Estimation of the width of the warm I 

upper layer gives the expected time -£ .. (30 - 21RlfuJi¥')600~"400S= at which the warm LH 2 arrives at 1IR' 30 

the detector 

Fig.4-17 Temperature stratification data vs. predictions for the LH2 tank in the Shuttle. 
- 

One can see that both prediction of the near wall temperature T=21 .2K and the width of the 

weakly warmed liquid layer >8m, correspond well to the data. In fact, the temperature of the 

incoming fluid rises to 21.4K in the end of the flight (the uppermost 1.5cm layer of the liquid at 

T=23.8K is shut-off), and taking the width of the warm layer 10m, we predict the beginning of 

the warm layer inflow at t=400sec. 

In addition, we performed simulation and theoretical estimates of the stratification in Saturn 

LH2 tank, which we compared to the experimental data (Fig . 4-18), as published in [23]. 

,. 

, .. 

Temperature stratification in Saturn LH2 tank 

, , 

• -bo-...,.,... _ ........ -0 l _ _ 

C H' _ 0"" - ..... - 0. _ __ , a 

E 

E '\....~ \I. ... )0;1. _ . Q 

. ...... y.; l • • _ 0 

.,,::. . ...... t" .. ) 

3 

4 

U I .. 

~, ,._· .... _., I 

~(471) t:(<47J ~l'I7J 

111;--- -;-' -r' --+' .....;';-, 

JI 

Fig.4-18 Temperature stratification data vs. predictions for the LH2 tank in Saturn. 

To summarize the main results of our work on the temperature stratification: 

1. Analysis of the turbulent natural convection correlation relations and the 

condensation-evaporation processes on the gas/liquid interface leads to a fairly accurate 

estimates of the liquid stratification pattern in LH2 tanks in the Space Shuttle and Saturn 

and predictions for larger tanks. 

2. The main risk from the NPSP condition perspective is due to condensationevaporation heating of a thin layer near the gas-liquid interface. 

3. The temperature stratification is essentially invariant under the rescaling of the 

tank. 

4. The interaction of the ascending natural convection flow with the descending 

forced convection flow leads to deviation from the theoretical predictions in the upper 

part of the tank. 

5. However the interaction leads to development of a larger region of turbulence 

where the heat is efficiently diffused. As a consequence the main heating occurs still in 

the conductance (viscous) sub layer where the temperature is independent of the height 

of the tank 

6. The temperature in the turbulent region is of no consequence from the NPSP 

condition standpoint. It is low in the Shuttle and is expected to be still lower in the larger 

tank (SLS) due to stronger turbulence. Numerical simulations of the LH2 dynamics in a 

larger tank support the validity of the theoretical arguments. 

33 
.

----- - - - - - - - - - -- - - 

5. Effect of sloshing to LH2 tank 

Intensive sloshing of cryogenic liquid (LH2) can occur after the start due to vibration of the 

rocket. Two main types of sloshing are shown in Fig.5-1 : (i) the longitudinal sloshing waves 

excited by lateral forces and (ii) the axial sloshing (capillary waves) excited by parametrically 

forced oscillations. 

F 

( 

Fig.S-1 Two main types of sloshing: (i) Longitudinal sloshing waves excited by lateral 

forces (left); (ii) Axial sloshing (capillary waves) excited parametrically by axial vibrations 

(right) 

5.1. Longitudinal sloshing waves 

To understand main characteristics of the longitudinal sloshing waves (Fig. 5-2) consider a 

rigid tank with ideal inviscid liquid. We suppose that the surface waves are linear and the flow is 

potential 

em shift. + C.m. shift 

n =lmode n =2mode n =3mode 

Fig.S-2 Main modes of longitudinal sloshing 

Let us estimate the frequency of the surface oscillation assuming that the tank has 

cylindrical shape and that the motion is harmonic. In this case the velocity potential cD satisfies 

Eq .(35) 

i1cP ::= O (34) 

a2<I> a<I> --+ g --;:::- == 0 at at the free surfacez == h / 2 

at

2 oz 

a<D I an == 0 at wa ll boundaries z == - h 12and r ::: Rr : 

where h is height of the liquid level and n is a normal to the surface wall, g is a gravity. 

Analytical solution of the eigen-value problem is 

_ cosh [A"'n(z / a + h I 2a) <D /IIn (r,z,e) - J j(Alllnr / a)cos(me) (35) 

cosh[ A,mn h I a] 

34 
.

- -- ~--- 

which represents eigen-functions and eigen-frequencies 

oi = gAmn tanh("t h / a) mn mn (36) 

a 

where rand e are the radial and angular coordinates , a is the tank radius, and Amn 

(m,n=O,1 ,2 .. ) is a root of the eigen value equation dJ1(Amnr/a)/dr = 0 for r = a, w is the angular 

frequency . The values of Amn for m =1 (cosS) are A1n. =~n. Numerical values of n are: 1 = 1.841 , 

=5 331, 3 = 8.536 . .. n+1 ~ n + TT. For m = 1 the potential varies in the angular coordinate as 

cose, the wave is "up" over half the circumference and "down" over the other half. 

Eigen-frequency of flexural sloshing oscillations is a function of the radius, gravity 

acceleration g, height of the tank h and values Amn. For the first nonsymmetrical mode (m=n=1) 

such frequency is presented as a function of tank radius in Figure 5-3 (left) and the oscillations 

as a function (a,h) is presented in Fig.5-3(right). It can be seen that for radius Rt=4.2m the 

period of the longitudinal antisymmetric sloshing wave is about T osc=3 sec. 

It should be noted that formula (36) doesn't contain density of the liquid, therefore the 

eigen-frequencies will be the same for liquid oxygen tank of the same radius. 

08,-----.,-----~--~----, 

0.7 . . , , 

0.6 

~ 

'" 0. ' ::=, 

,:; 

() 0.4 

~ 0 0.3 .... 9 

~ 

0.2 

5 

····· .. · .. ·:···· ····· ·····+-·-· i1 5: io l- t· .. · , , ~ " g 0.4 ............ ; ........... : ................ j ............. . <U . : 

::l : CT : : ?J 0.2 ................ j ................ . 

tZ j ~ : , .- - --' 

: lih=O 5ml: , 0, 2 3 4 ' o 

0.1 

30 :25 20 15 10 

Radius of tile t:l1lk. III , o Radius, m 

Fig.5-3. Frequencies of flexural mode oscillations for different tank radios and height 

The longitudinal sloshing is responsible for three main effects: (i) sliding of cold liquid along 

the hot wall: (ii) growth of the area of the liquid surface; and (iii) mixing of the warm surface 

layer with the underlying cold layer. 

(i) At the start of flight the motion of the rocket can induce an longitudinal sloshing wave 

with an amplitude A and period T .The cold liquid in contact with hot tank wall will heat up wave osc 

and evaporate. An upper bound on the evaporated mass can be estimated form the following 

condition: the heat accumulated in the wall is spent to heat the liquid and the vapor and to the 

evaporation, Q = Q : wall vapor. 

A.,,,,,, 

Q ",all = p",d",TC R, f O=intcrface 

C (T (y))(T (y) T)dy~C P d TCR LI (T -T) HI wall wall S \II W HI ,~.Lwave wall s' (37) 

35 
Liquid Wall, T wall HotwalJ 

Liquid, TL 

2Rt=8.4m 

Fig.5-4. Sloshing brings cold liquid in contact with the hot tank wall 

where we used the fact that the thermodiffusion length in AL 2195 L (T )::::: 7mm is larger than 

o osc 

the wall width d 1:::::5 mm. It follows from Eq. (37) that the maximum mass and volume of wal 

evaporated vapor during t=T are osc 

(38) 

The pressure jump is calculated using the heat balance equation as follows : 

dE = - pdV + dQw => V 4J = - r p!J.V + M evapCpTgas' II V = allp , r- 1 r- 1 

a == 0.3 ;:i -expansion coeffecient of the LH2 thank 

II - M evapR gasT gas 

tJ7- V + ' 

ullage,O ay P ullage 

4J < 0.027 atm for Aevap ~ 15cm, V,,"age = 27 m

3

, ~ :::: l OOK 

4Jmax = 0.25atm for max sloshing amplitude Aevap = l .4m 

(39) 

We see that for the highly improbable hazardous event when the amplitude of longitudinal 

sloshing oscillation at the moment of the engine start (t = - 6sec) equals its maximum value 

Awave=1.4m the maximum volumes of evaporated vapor and the pressure jump can 

reach v'vap = 5.6m3 

and !J.p ~ 0.25 atm for T osc =3sec . 

After the start (t > 0) the stationary longitudinal sloshing waves accelerate condensation by 

(ii) increasing the area of the liquid surface (minor effect); (iii) mixing the heated surface liquid 

layer with adjacent cold LH2 with T=T L (major effect). As a consequence, the thickness of the 

heated surface layer decreases but the interface temperature does not change, determined by 

36 
the partial GOx pressure: T =Ts(PGo) =23.8K. The condensation flow rate at the liquid-gas 

interface is limited by the heat balance between the hot gas T near the surface and the liquid . 9 

surface with T=T : s 

. (t) =[K ~ - TL - K Tg -~ ] 1 (40) 

j cond L LL (t) g Lg (t) q L + C H2 (Tg - ) . 

The maximum value of the condensed mass M d induced by the sloshing can be con 

estimated assuming complete mixing of the surface layers of cold and warm liquid over each 

period of oscillation. Due to such intensive mixing the width of the heated liquid layer over a 

fraction ~ of the surface area will be very small at end of each oscillation, LL ~O (Fig. 5-5). 

, Vapor zone Vapor zon e 

------------- "-i-------- liquid zone I 

Liquid, TL 

Temperature Temperature 

Fig. 5-5. Sketch of the temperature distribution before and during the sloshing 

In this case the first term in the right part of Eq. (40) is much larger than the second. 

Therefore, the mass condensed over one period can be estimated as 

) _T"'fc * ) *( ) ) KLCLPL ( {4ToscJ cond (~sc - SLJconAtj dtj {:::j SL ~ - TL () -- , (41) 

o q L + CH2 Tg -'F.r 1[ 

The total condensed mass induced by the longitudinal waves over the time of t is given by 

M s/osh (/) = M (T) ML + SL (_t J M L + SL = ~Rf2 + A.:ave . cond cond osc S T ' S R (42) L ruc L f 

The total condensation flux is equal to 

M s/osh ( ) 

a J s/osh = Inax cond t = 0 02'"' kg m x cond . .) sec t ~~ 

~(PGH2 ) = 23.8K, 24K < Tg ~ SDK near th e interface 

It should be compared to the much larger the flux of the injected hot 

G H2 : J GH 2 = 0.35 ::c = 0.476 -'f!c x [ Nnozz'e 13], N.lOzz/e - nozzle nozzle in SLS 

Thus , the longitudinal sloshing waves cannot appreciably change the ullage pressure. 

Effect of sloshing is expected to be even smaller for the SLS since the flow rate of injected 

hot GH2 will increase with larger nozzle number. However, SLS vehicle has higher thrust and 

one can expect stronger vibrations due to adding one or two RS-25 engines. 

Conclusion about the acceleration of condensation by the longitudinal sloshing is confirmed 

by experimental data [23] presented in Fig . 5-6. The pressure in the ullage space increases 

from 15psi to Po =35 psi due to hydrogen pressurization with temperature 40K during 15sec. 

37 
After 50 sec lateral vibrations are observed with frequencies f=0.95Hz (non-resonance 

influence) and 0.74Hz (resonant vibrations stimulate intensive sloshing). The ullage pressure 

slowly decreases in the case of the vibrations with f=0.95Hz and sharply drops in the case of 

the resonant vibrations with f=0.74Hz. 

i I Poi I , , J 

35 ... ... ··· :··· ·· ··· .... ·-·:·-··········l·· .. ·i-· ... r-·····-.. 

10 

b) 0 5 0 1 00 150 200 250 300 

TIME (SEC) 

60 

:z 50 rn 

ill J:: 

!.40 " .. 

~ :r 

Q 

w 

r 

~ 2 0 ~ ~ .... ~···-· · .. ····--·L.·· __ L ...... _ .. L.. ___ .. . 9 : -<>- INITIAL 

~ 1 0 ' ¥" : . ;-.... . ... ... + ........ ~ AJ-1'Efl RAMP 

: } - FINAL (Rl"IG >870) Il o h--i-~'-4-t- I ' , :4- d) 30 ~o 50 60 10 eo ao 

FLUID TEMPERATURE (A) 

Fig. 5-6. Sketch of the tank and the internal instrumentation (a), pressure response for 

the sloshing test (b), wall temperature (c) and ullage space temperature (d). 

The condensation flow density rate can be estimated from the equations 

(44) 

It follows from Eq. (44) 

. 4 5 . 3 kg ) d I ::::: - . LV - , - for resonance (f=0.74Hz) con, m-sec . 

for Po=35psi, p,=20psi, Llt=20sec,V ,1 =0.35V, k=O.63m3

, S= 1.6m2

, u age :til (45) 

. ") 3 - -4~ ) d 2 ::::: .J . . LV 2 for non-resonance (f=09SHz) con , m sec 

We use the data of Eq. (45) for estimation of the condensation rate for LH2 tank 

- " ( )"2 kg J d ::::: J , J I . . \ a k T e/', =:: O. 16 for resona nce in fl uence (f, =0. 74Hz) con COil _ - n os - --

(46) . . ' ( f )'/2 kg l cond ::::: l cullcl,I, S tank ~sc 2 ::::: O.0 14secfor non-resonance infl uence (f2 =0.95Hz) 

The foregoing estimation :~~~' == O.025{£ for the condensation rate for intensive sloshing 

given by Eq. (42) agrees with the data of Eq. (46). 

38 
5.2. Axially excited sloshing: generation of droplets 

The thrust oscillations initiate axial excitation and lead to Faraday instability of the liquid 

surface. Intensive oscillations of these modes can result in the liquid level discontinuity and 

generation of the liquid droplets under the liquid-gas interface. This process will change heat 

balance on the interface. Evaporation of the cold liquid droplets into the hot ullage gas can 

increase the ullage pressure during the beginning stage of the flight. At the same time enlarging 

the cold surface can accelerate condensation. Since the rate of evaporation of liquid hydrogen 

depends on partial pressure of gaseous H2, in the case where He is used as the pressurization 

gas we expect enhanced evaporation and consecutive increase in a ullage gas pressure. For 

gaseous Hydrogen pressurization these droplets will enhance the condensation rate. 

Theoretical treatment of the droplet ejection is given in many articles . Linear theory is 

described by dispersion relation obtained from equation (34) with the same boundary 

conditions, where for small wavelength capillary waves we should take into account surface 

tension a : 

(47) 

where k=2rr/A, A as the wavelength , is the wave number and p is the liquid density. At small 

k« 1 this equation is identical to equation (36): 

:, = gA,/Ui tanh(AITII,h / a) (48) 

a 

The nonlinear dynamics of the droplet formation and ejection is extremely complicated and 

strongly depends on the rocket vibrations spectrum. Here we carry out a simplified analysis of 

this dynamics. The typical diameter of ejected droplets is about [24,25] 

d ::::: (0" I P ) 113 OJ -2/3 (() = 27rj (49) drop L L , 

where P L =70kglm3 and 0L =0. 0017Nlm are liquid density and surface tension, co is vibration 

frequency (rv=27tfvibr) . Characteristic values of ddrop are shown in Fig.5-7 (left). 

E 

~ 

<!) 

E 

ro 

o 

Fig.5-7. The typical diameter of ejected droplets as a function of the thrust 

oscillation frequency (left) ; generation of droplets under action of supercritical vibration 

acceleration Ed>O [26]. 

39 
- - 

Each projectile area of diameter dproj ;::5ddrop ejects the droplet with a rate given by [24,25] 

dn / dt == Ii :::: 04& ~8a> [S-I],&,, :::: (a",br - a,,) / a", (50) 

a" ::::0.26(0- / p) 1/3a> 4/3 

Here a, OJ are vibration acceleration and frequency, ad is the critical driving acceleration for 

the onset of droplet ejection. The droplet ejection occurs when the frequency and amplitude of vibration Avibr 

satisfy the condition: 

avibr :::: A"ihra>2 > a" or A"ibr > Ac :::: O.lmm(1 OOHz / f VibJ

2

/

3

, 

Ac :::: 0.25mmfor f:::: 25Hz, Ac :::: 65f..1mfor f =:; 200Hz 

(51 ) 

Sufficiently strong vibrations can occur only after the start. At this point the thermo-diffusion 

length in the liquid has increased to the value of La (100sec);::7mm during the prepress (t ;:: 

100sec). This value is much greater than the typical drop diameters: . 

LD =::: 7mm » dc/rap for f > 50Hz. It follows that the inner temperature of generated droplets 

T is close to the surface temperature of the liquid T (p ). Therefore, the liquid mass drop s GH2 

evaporated due to the vibration is very small. Indeed, the mass evaporated from the surface of 

single droplet s during the droplet life-time tdrlife can be estimated as 

drop 

(t ) :::: f IP"" +l

d

"", . (t)dt < J ",", (t )s ''''' t t = { 2h,", 

mevap "r/i/e s "rop J evap - S "rfi/e ' "r/ife ' pr~n L g 

(52) 

where hdrop is the maximum height an ejected droplet rises above the surface (see Fig. 6-7). 

The total evaporated mass is given by 

dNtota/ S . 

M < () :::: ( ) Ln "mp evap - m evaop {dr/i/e {mcond {drop . I , 

dt ..sproj 

dNtora' S Ii l 

h ~- L drup.· _ (ndrop were - ,llrllOll dt S pro) dt (53) 

Here dN';,~~ / dt is total number of droplets ejected over unit time from the liquid surface SL. 

Taking into account Eq. (52) and condition d . R! Sdd Sd I s . :::: 4 / 25 we conclude from pro) rop , rop pro) 

Eq.(53) that the total evaporation mass is a negligible quantity 

M < J t t . 41idr(l) :: 4Jevap (Tprepre.\S )t. < _1_, 

evap - evap ( press ) dr/ife 25 - 25 ' n,hop - ,.-

f dr/i/e (54) 

J evap :-:; M evap / t:::: 0.16Jeva/T prepress ) :-:; O.8 g / sec 

In the estimation we used the results of calculation presented in Sec.2 (see Fig . 2-4) 

J evap (~rep ess ) ~ 5 g / sec . 

An appreciable effect can occur only as a result of combined action of intensive longitudinal 

and axial sloshing vibrations (Fig . 5-5, left)). The maximum value of the condensed mass 

40 
induced by sloshing waves can be estimated assuming intensive mixing of surface layers of 

cold and warm liquid during each period. Due to such mixing the thickness of some area of the 

heated surface layer ~ will very small at end of each oscillation, Ll-+O (Fig. 5-5). Droplets 

generated by the axial sloshing will have T near T , except for a very thin surface layer Ll-+O 

l . 

near the surface having T=Ts(PGH2). In this case the maximum value of the condensed mass 

m on the surface s of a single droplet during the droplet life tdrlife can be estimated as 

cond drop 

m (t ) ~ s M=.(I"",) ~ s.., (7; (PGH' ) - T,l JK, C,p, 41"", 1 ~ '~ (55) cOlld drlife drop S C (T T ) , dr/if· L q L + fl2 g - s 77: g 

and the total condensation flux from all the ejected droplets is 

dNlolO1 

( ) S· (t )n . jlOlCl1 _ (t ) drop _ 4 L m drlife dmp · /' 1 fi · A >A -m --- - n. '-. - - 0 1 C concl dr/ife dt. 25 ' ,,,"op - vibr ' 

S drop I drlife 

(56) 

Using ~ ~ SL / 3 and t dr/ife 2h op / g ~ 0.02 sec we obtain from Eq.(56) that the total mass 

flow rate of condensed vapor on all ejected droplets is about ~~:; < O.09kg / sec. We notice that 

the mass flow rate of injected hot GH2 is much more: J Cfl2 = O.35 fe7 = 0.476t£ x[Nllozzle / 3] . 

As a result of the condensation the ejected droplets will be heated and falling back into the 

liquid will increase the temperature of the liquid surface layer. The width of the heated surface 

liquid layer can be found from the heat balance equation 

j lolal [ C (T T)] - C (T T)S [ liquid drop qL + GH2 g - s • t - LPL s - L L' heated' 

[ liquid () _ S: ( 8LD (t))(' f )'" n t _ 2h","" heoled f - SL 25Jr f drlife J""'I' , drlife - g ' (57) 

Thus, combined action of longitudinal and axial sloshing vibrations can lead to formation of 

relatively thick hazard surface layer of heated liquid with temperature T::::23.BK, thickness 

Lz 7.5cm, volume , v,"'aJ= Slank :~ d/ 2=2m and mass M'",Q/= V,leCdPL = 140kg . Total mass of 

LH2 in the tank is 105,000kg 

SLS vehicle has higher thrust and expected vibrations due to adding one or two RS-25 

engines. At the same time the mass flow rate of injected hot GH2 increases with the engine 

number. All the effects under consideration are taking place in a narrow layer adjacent to the 

interface. Therefore the influence of these effects on both the mass and the heat balance in the 

tank will not be critical. However, the effect of heating of relatively thin layer to T:::::23.8K can 

arise in LH2 SLS tank because possible intensive longitudinal and axial sloshing vibrations . 

6 Conclusion 

We performed theoretical investigation of main physics processes in LH2 tank during prestarting prepress and rocket flight that can lead to possible hazards in the case of rescaling of 

main parameters of Shuttle with regard to proposed LH2 tank designs for SLS with 5 engines 

(the situation with 4 engines is less critical). Our investigations based both on theoretical 

analysis and on MNM and 3D simulations allow us to make the following conclusions 

4 1 
1. Hazard analysis for LH2 ET shows that the pressure control bandwidth remains almost 

the same for the SLS. 

2. The MNM can reproduce accurately the pressure during pre-press and blow down . 

3. For the GHe and GH2 flow rates and the initial ullage volume rescaled by 5/3 for the 

SLS LH2 ET, no new hazards are found for the tank performance; the temperature stratification 

is more pronounced in the rescaled SLS tank. 

4. The bubble formation at the tank wall does not scale with the tank length but it's effect is 

still relatively small and will not considerably affect the performance. 

5. Effect of condensation and evaporation are also relatively small. 

6. The temperature stratification of the liquid reveals a structure consisting of three layers: 

(i) The upper hearted layer of thickness less than O.6in=1 .5cm at the end of the flight and 

with temperature 21.2K<T < 23.8K; 

(ii) The intermediate warm layer of width <8in=20cm at the end of the flight and with 

temperature 20.6K<T < 21 .2K; 

(iii) The lower warm layer with 20AK <T <21 .6K of width -10m at the end of the flight. 

In (i), both the temperature and the width of this layer are invariant under the 5/3 rescaling of 

the tank length. In (ii-iii), the sub-layer is formed due to the rising warm liquid flow with T=21 .2K 

forming in a thin boundary layer near the wall and accumulating near the interface. These sublayers will increase by a factor of 5/3 under the scaling but its temperature will be T< 21 .2K. 

7. The NPSP condition holds for the rescaled rocket with the exception of the upper 

hearted layer of thickness less than O.6in=1 .5cm. Maximum mass and energy of such 

5 

overheated liquid with T=23.8 is less than 30kg and 2.5x10 J. Total LH2 mass and energy in the 8 

filled tank are 105270kg and 3Ax10 J. Therefore, it does not play the role in the ullage 

temperature stratification and pressure dynamics. 

8. Intensive longitudinal sloshing waves induced by the laterally excited rocket vibration 

change weakly the temperature liquid and ullage stratification and the ullage pressure during the 

flight. Maximum rate of condensation flow arising due to the strong mixing of the warm surface 

liquid layer with the cold deep layers is limited by value of :;~~' == 23 ~. The mass flow rate 

of injected hot gas (GH2 or GOx) is much more Jeox (t) =0.476 :!c x (nllozzle / 3) , n nozzle is nozzle 

number in the SLS. 

9. The vertical vibrations with the amplitude Avibr and the frequency fvibr such as 

ibr > Ac = O. lmm(1 OOHz / fvibl.l3 induce generation of the warm droplets under the liquid-gas 

interface. Effect of axially excited vibration sloshing on LOx tank is extremely small as the 

temperature of generated warm droplets is very close to the interface temperature and 

condensation is depressed. 

10. Combined action of intensive longitudinal and axial sloshing vibrations can induce 

relatively great condensation and formation of relatively thick hazard surface layer of heated 

liquid with temperature T=T s(PGOx), The rate of the condensation can 

reach ~~~~ == O.09kg / sec and thickness, volume, and mass of surface heated layer can reach 

LL=7.5cm , V=4m3

, and 280kg. Total LH2 mass and energy in the filled tank are 105270kg. 

11 . The longitudinal and axial sloshing waves cannot appreciably change the ullage 

pressure. Effect of sloshing is expected to be even smaller for the SLS since the flow rate of 

injected hot GH2 will increase with larger nozzle number. However, SLS vehicle has higher 

thrust and one can expect stronger vibrations due to adding one or two RS-25 engines. 

Combined action of intensive longitudinal and axial sloshing vibrations can lead to formation of 

relatively thick hazard surface layer of heated liquid with temperature T::::23.8K, thickness 

L::::::7 .5cm and volume (mass) V=4m3.(280kg). 

12. SLS vehicle has higher thrust and expected vibrations due to adding one or two RS-25 

engines. While the mass flow rate of injected hot gases increases with the engine number. All 

the effects under consideration are taking place in a narrow layer adjacent to the interface and 

42 
,,--------- -

the influence of these effects on both the mass and the heat balance in the tank will not be 

critical. However, the effect of heating of relatively thin layer to T"'23.8K can arise in LH2 SLS 

tank because of possible intensive longitudinal and axial sloshing vibrations. 

7 Appendix 

The pressure drop in a tube with turbulent flow due to the wall friction can be estimated as 

/1.p = 0 02 p U 2 lUbe Re Re = ~ U = L Re = L (1 J( )-lf4 ur J J 

fric . L "2' , t;lIbe J1 L Jrt;lIbeP L Jrt;ubeJ1L 

( J( J

2 ( Jlf4 [ J( J7f4 ( J19/4 

0.02 I J J I J r 6.p = __ lube _ L_ L =6.p ~ _ I. ~ 

fric P I. t;lIbe Jr'"r ~be Jr'"rllbe JiL fric,O ' 1lIbe,O J LO '"rllbe ' 0 

Re > 4 X 107 for J L > 200kg / sec and t;ube > 0.2m (turbul ent condition) 

Requirement for the feedline follows form Eq.(58) 

P frie < O.latm for J=200kglsec (3engines) at tube rad ius rtllbe >7.5cm(3in) 

or for J=333kglsec (5engines) at tube radius rn1 be >9cm(3 .5in) 

(58) 

(59) 

Thus, in order to keep the same pressure drop in the feedlines in scalable SLS LH2 tank it is 

necessary to increase the tube radius on 20% or 10% for nozzle number N =5(4): 

nozzle 

C~~: 0 } U:::J" J' = [/:::.]" " ( N " )"" , 

( 

"rllbe J = 1.2(1. 1) for n nozzle == 5(4) and flUbe = I'"be,o ' 

t;lIbe ' 0 

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45