NASAlTP-20 12-216485 

Risk Assessment and scaling for the SLS 

LOx ET 

Viatcheslav (Slava) Osipov 

Halyna Hafiychuk 

Ekaterina Ponizovskaya-Oevine 

Michael Khasin, 

Vadim Smelyanskiy 

Ames Research Center, Moffett Field, California 

December 2012 
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NASAlTP-20 12-216485 

Risk Assessment and scaling for the SLS 

LOxET 

Viatcheslav (Slava) Osipov 

Halyna Hafiychuk 

Ekaterina Ponizovskaya-Oevine 

Michael Khasin, 

Vadim Smelyanskiy 

Ames Research Center, Moffett Field, California 

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 we analyze the transpiration cooling by He bubble injection of the long LOx 

tank feedline heated by the environment heat. We consider possible hazards that can arise in 

the proposed design of the SLS core stage where the feedline length is much longer than that 

used in the Space Shuttle. 

CONTENT 

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

1. Ma in physical processes and pathways of heat transfer in the LOx tank ............ .. ...... .. .. .. .... .... ....... ..... ... 4 

1.1. Condensation- evaporation processes ... .... ........... .. .. .... .. .. ................ .. ...................................... .. .... 5 

1.2. Collapsing of bubbles du ring the in itial stage of the pre-pressuri zation .. ................... ...... .. ........ .. 9 

1.3. Heating of liquid in the boundary layer near the interface ................... .. ......... ........ .................. .... 9 

1.4. Heating of liqu id in the boundary layer near the wall... ............... .. ... ................. .. ...... .. .... .. ......... 10 

1.5. Heating of the tank wall by hot gas: ma in mechanism of the gas cooling .... .... ....... .... .. .... .. ....... 11 

2. Pre-pressurizati on regime and fitting the Shuttle data ................ .. ....... .. .. .... .. .. .. ........... ...... .. .. .... .. ...... 12 

3 Operation during the fight... ...... .. ........ ... .. .. .. .................... .... .. ........ .. .... .... .. .... .... ......... .. .... ... .. .. .. ...... .. .. .. .. 18 

4 The limiting case offully mixed gases ......... ........ .. ... .. ......... ......... ..................... .. ....... .. .. ................. ....... 22 

5 Scaling of the risks ............ .. .... .. .................. ....... .. ............. .................. .. ..... .. ... .......... .. .... .... .. ... ....... .... 25 

5. 1. Scaling of pressure near the feed I ine top and bottom .. .... .. ........ .. .. .... .. ....... ............................. .. .. .. .. 25 

5.2. Scaling of shape and size of the LOx tank fo r SLS with 5 engines ............. ....................... .. ... .. . 25 

6 Effect of sloshing in the LOX tank ........................ . " ..... ..... ...... .... ...... .................... ... .. .... ...... .... ..... .. .. .. ... 27 

6. 1. Longitudinal sloshing waves ...... .......... .. .............. ............... ... .... ... ... ...... ...... ................ ...... ......... 28 

6.2. Axially exc ited sloshing: generation of droplets .............. .... .. .. ....... ...................... ........... ......... .. 30 

6.3. Combined acti on of longitudinal and axial sloshing vibrations ............... .. ... .. ........................... .. .... 32 

Conclusion .... ............. ............. .... .... .. .... ........ .... ....... .. .. ... ..... ..... .. ............ ..... ............. ...... ....... ... ... .. ...... ..... .. 33 

References ...... ....... ............. ..... .... ..... ........ ... .... ... ............ ..... .... ... ... ..... .. .. .... ... .... ..... ... ..... ............. ...... ... .. ..... 35 
Nomenclature 

p = density 

p = pressure 

Pc = critical pressure for gas 

T = temperature 

T c = critical temperature for gas 

T s = 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= cplcv 

R = gravity 

Rt = radius 

St = radius of tank 

Ssu = surface of tank cross-section 

r = total surface of tank 

LD = thermodiffusion length 

qL = heat of evaporation 

hr = heat transfer coefficient 

j = mass flow density [j = up] 

J = mass flow [ J = upS] 

q = heat flow density 

Q = heat flow 

Qc = convection heat flow 

Q R = radiation heat flow 

I3r = thermal expansion coefficient 

o = boundary layer thickness 

k = thermal conductivity 

v = kinematic viscosity 

Introduction 

f.l = dynamical viscosity 

Pr = Prandtl number, Pr=f.lCplk 

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 :::: Liq uid Hydrogen 

GH2 :::: Gaseous Hydrogen 

MNM :::: Multinode Model 

SLS :::: Space Launch System 

3D :::: Three dimensional 

Here we study main physical processes taking place in LOx tank during the prepressurization stage and the rocket flight. The goal of this research is to analyze the risks 

associated with the functioning of the external LOx tank of the Space Shuttle (Fig.1) during the 

pre-pressurization and in the course of the flight and their scaling to the proposed SLS design 

with 5 engines (the situation with 4 engines is less critical). The risk assessment for the 

replenish stage is presented in a separate report. 

We use both the protocol [1] and the telemetric data [2] for Shuttle fl ights to fit an uncertain 

parameter of the multinodes model (MNM) developed in our group using results of 

2 
Fig.1. Design of the Shuttle tanks: the shape and parameters of the LOx tank 

3 
LOx tank with the 

shape of LH2 tank 

with parameters 

Vu =3.88 m3 

Vl =9 17.5 m3 

Fig.2. The shapes of the LOx tanks analyzed in this work 

works [3-5]. After an appropriate rescaling the model is further applied to study the temperature 

stratification, the ullage pressure dynamics and the associated risks in the LOx tank in the 

framework of the proposed SLS designs. This constitutes the risk scaling problem. Two different 

designs of the LOx tank will be considered . The first is tank of the shape of LOx Shuttle tank 

(Fig.1), but with elongated central part to contain 5/3 of the Shuttle tank LOx volume (Figure 2, 

left). The second is tank of the shape of LH2 tank of the Shuttle, rescaled to contain 5/3 of the 

Shuttle tank LOx volume (Figure 2, right). 

1. Main physical processes and pathways of heat transfer in the LOx 

tank 

The general heat balance in the LOx tank can be written as 

(1) 

Here Q ;nj ecI + Qe,)s the total heat added to the tank as a result of hot gas injection from the 

diffuser and the interaction with environment. This heat is spent on heating the gas in the ullage, 

Qulloge ' heating the tank wall, Q woll ' and on condensation-evaporation processes including 

heating of the surface layer of the liquid , QL' The heat flows associated with these pathways 

are sketched in Fig. 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. 

4 
Vu ullage volume 

p ullage pressure 

T ullage temperature 

Tw wall temperature 

Fig.1-1. Main physical processes, variables and pathways of heat transfer. 

1.1. Condensation-evaporation processes 

The timescale of the ullage pressure changes is large (-1 sec) compared to the timescale of 

thermalization of the liquid-vapor interface, which can be estimated as follows [6]: 

',hermo = (2;r2KL CLPJ1"opoJZ) / (P;L (7;. )q,n < O.lm sec (2) 

Here P L,g' CL,g' KL ,g are density, heat capacity, and thermo-conductivity of liquid (vapor); 

Rvapor- gas constant; qL - heat of vaporization. As a consequence, the quasi-equilibrium near the 

interface can be assumed for all times with the surface temperature Ts determined by the 

vapor pressure P vapour = P GOx [6 ,7] : 

r, ~ r,( p;~. r, p,(I) ~ p,(;')' (3) 

Here Tc and Pc are the critical temperature and pressure of the gas, Ps is the pressure of the 

saturated vapour and the constant A=7.2 for oxygen [7] . Note, that ps=1atm at T=TL=90K, during 

of the prepress and flight PGo/ 1atm and Ts >TL (T/ PGOx=2.25atm=36psi)=100K > TL =90K). 

The mass flow at the interface is limited by the heat balance_between the hot gas and the cold 

liquid surface. In what follows we analyze the condensation-evaporation processes during the 

pre-pressurization . Condensation-evaporation during flight is discussed in Section 3. 

The condensation of GOx prevails over the evaporation during the first stage of prepressurization (Fig.1-2, -152s < t < -138sec). This result can be understood as follows . In the 

beginning of He injection (t= -152sec, see Section 2) the Ox vapor is compressed toward the 

liquid-gas interface due to the relatively high density of GOx. As a consequence the partial 

pressure of GOx increases (Fig. 1-3). 

5 
~ .--r---'---~-----' 

~ • 0.1 Q) 

"§ 

C0 05 .2 

~ a 

•••••• __ ._ •.•••• _._ __ . w •• _ •••••• _ 

, 

~ I ~ 8 ·0.05 ""'15~: ------,J':----:-50I::-----! 

Time. sec 

~' l -, I F . , 

I':§B-,- -----------1----3= ::1 ~ 0

1

" :-_.- ------.--;-. .. - -,---.--- ·T·-·------1 

-g , , i ' 0 .0.5 ' , . --- (.) · 150 -100 ·50 0 

Time, sec 

Fig.1-2. GOx condensation mass flow and total condensed mass. Results of MNM 

simulation. 

Accordingly, the condensed mass accumulates at this stage and reaches the maximal value 

of -1 kg which supports the estimations presented in the text. At the later stage (-138 sec <t<O 

sec) the condensation rate is seen to oscillate due to the pressure modulations and decreases 

on average as predicted. The average condensed mass decreases at this stage. 

The 3D simulations confirm this conclusion (Fig.1-4). The growth of the GOx partial pressure 

stimulates condensation of the compressed GOx, accompanied by the rise of surface 

temperature 

. ff. 15' 10· ff. 1 8 ;:-: <1::;.. 0 ---~--~----, 

m ~ :; ~ 1.6 

~ ~ ~ ~ 

~ M 

~ 5 ro 

~ t u 

.f. oL.l.:-----,.,OO --30o':-----!O 0 1 -:: 15O:-----c:,00~---:-50:O----! 

Time, sec Time, sec 

Fig.1-3: Partial pressure dynamics of GOx and GHe during the pre-pressurization in 

the ullage layer near the liquid-gas interface. Results of MNM simulation. 

6 

Inflation 30 Layers 

First Layer - 0.1 mm !:!, F'''''''''' 090 

0 85 0.' 0'. 0 71 

He Flow gg~ 

T=316K g~ 0'. 0 ... 0." 034 

030 025 

0.21 01. 

o n 0.07 

002 

Fig.1-4. Stratification mass fraction of GOx and He during the pre-pressurization 
in accordance with Eqs. (2). The liquid surface temperature 1', is determined by the partial 

pressure Peox of Ox vapor near the interface: 1', > TL at Peox ~·1.7Satm > ps(T)=1atm, where 

TL is the liquid temperature far from the interface. The temperature profile near the interface 

and the heat flows are schematically shown on Fig . 1-S. 

Fig.1-5: Temperature profile near the liquid-gas interface 

Since 1', > 7;_ and ~ > 1', the convection of both the liquid and the vapor is absent. 

Moreover, our simulations have also shown that the convection induced by the hot gas injection 

from the diffuser and natural convection near the wall is indeed very small near the gas-liquid 

interface. Thus, the heat balance in condensation-evaporation processes is established mainly 

by means of thermo-diffusion for the given surface temperature Ts( Peo) . The solution of the 

one-dimensional heat equation 

aT a

2

T C P - =K - L,g L,g at L,g ax2 ' 

for the boundary condition T(O,t)=1', =const, T(x,ctJ) =TL is given by 

T(x,!) =TL +(1', -TL)erf( CL,gPL,gX

2 J 

4KL ,g' 

(4) 

(5) 

Here PL ,CL , K L are density, heat capacity, and thermo-conductivity of liquid (vapor); x=O 

,g ,g ,g 

corresponds to the liquid-vapor interface, and erf is the error function. Using Eq . (5) we can find 

the heat flux from the warm interface into the liquid: 

'J' ) - _ aT(x,t)I _ _ 1', - TL -_ (X ,f - K L - KL -

ax x=O L f)L 

(6) 

Here L f)L is characteristic thermo-diffusion length in the liquid. This makes it possible to 

estimate the condensation mass flow j cond from the following balance equation : 

. . . ( 1'- 1' T - T] ) = ' / S ( + " T - T = - 0 = I) I " > L - K g s m"" l eOlA) L ( h ULIX ( g s)) Q L "-'g . L \ LDL (t) g LD/t) , 

~ K C P (T - T ) - ~ K C ~ (T - T ) . () _ L L L s L COx COx COx g s 

) COlIC/ t - C( ( )) "TC qL + C COx Tg - 1', 

(7) 

7 
The first term in the left-hand side of Eq. (7) describes the condensation flow rate and the 

second one describes the evaporation flow rate. The total mass of the condensed vapor is 

given by 

I 

M cond(t) = f SL(t))COfld(t)dt, M colld(t)oc..Ji atS (t)~const (8) 

o 

According to Eq . (7) condensation will be dominant whenever 

( Tg - T. (PcoJ ) < (T. (PcoJ - TL ) K K L , T. (PcoJ = T;, (Pcox JII7 

COx coxPcox Pc 

(9) 

where for the estimation of the thermo-diffusion length in the gas we can use parameters of 

the pure Ox, which is prevalent in the vicinity of the interface as argued above. We note that 

Eqs . (7)-(9) are valid during the flight as well (see Section 3). 

At the early stage of the pre-pressurization, condition (9) is satisfied. As argued above, the 

partial pressure of the compressed GOx vapor is controlled by the pressure of the injected He, 

PGox""1 .75atmi during the early stage of pre-pressurization (Fig .1-3). In this case the surface 

temperature T/p=1.75)=97.5 > TL =90K and the condition (9) holds provided ~ <450K, 

which is certainly satisfied (temperature of injected He is 320K). Estimation [Eq. (8)] of the total 

condensed mass during the early stage of pre-pressurization ( -14sec ) gives M cond ~ lkg. 

This estimate is supported by the results of the simulation (Fig. 1-2). Since the initial mass of 

the vapor is Meox = Ps,& V:ll age = l7kg and the mass of injected He is about 6kg, the condensed 

mass constitutes about 4% of the total mass of the gas in the ullage. (We note that the mass 

fraction of the gas involved in the condensation-evaporation is considerably smaller during the 

flight, see Sec.3). 

At the later stage of pre-pressurization (-138sec < t < 0) the vapor becomes mixed with hot 

He and the GOx partial pressure will drop (Fig .1-3). The gas temperature near the interface 

T 9-1 OOK (Fig. 1-6). Therefore, at this stage the condensed mass decrease. The foregoing 

theoretical predictions are verified by the results of MNM simulation plotted in Figs.1-3 and 1-6. 

~- 200 

:::J 

"§ 150 OJ 

0. 

ai 1SO .... 

:::J 14(1 

ro a; 1):) 

0. 120 E 

.8 110 E 100 

~ ro 100 

50 S 90 c;;;;;...;;;;;~;;.-______ - ___ --__ ........ 

·160 ·140 ·120 .100 ·80 ·60 ·40 ·20 0 · 160 ·140 ·120 · 100 ·80 ·60 ·4 0 ·20 

Time, se c Tim e, sec 

Fig.1-S. Ullage and wall temperature during the pre-pressurization: upper red and blue 

curves for the layers near top and bottom of the tank, respectively. Results of the MNM 

simulation. 

We note that at the later stage of pre-pressurization weak modulations of the partial 

pressure of GOx (Figure 1-3) are observed in Fig.(1-3). These modulations are due to 

pulsations in the hot He injection from the diffuser (see Section 2). The pulsations have been 

neglected in our estimations but the average decrease of the partial LOx pressure in the vicinity 

of the interface supports the theoretical argument. The average decrease of the partial pressure 

is accompanied by the decrease of the surface temperature (Fig. 1-6) which displays 

modulations as well. 

The condensation-evaporation during the flight is discussed in Section 3. 

8 
1.2. Collapsing of bubbles during the initial stage of the prepress urization 

Ullage pressure increases from 1 atm to 2.45atm during the pre-pressurization (-152sec <t< -

138sec) due to injection of GHe. Therefore, the LOx becomes strongly overcooled and the 

bubbles which can be present in the liquid start to collapse. The characteristic time of collapsing 

can be estimated from the following heat balance equation 

S K ( 1'" bubble - TJ d S d 

- bubble L t = bubbleP s ,oxq L rbubble ' 

rbubble 

2 (t) - 2 (1 - _ t _ ) t _ b~Jbble, ,O L bubble - bubble,O t ' collaps - 2K (T _ ~ ) 

collaps I, s ,bubble L 

(10) 

Here Ts,bub is bubble surface temperature that is determined by the ullage pressure 

T = T ( P ullage J l17.3 t = o.2sec ( rbUbble,o ) 2 s ,bubble c , col/apse l ' 

P c mm (11 ) 

t collapse = 1.2S(S)sec at rbubble,Q = 2.S( S)mm. 

Here we took into account that P ullage= 2.45 atm during the pre-pressurization (-138sec<t<0). 

Then, T s,bubble =102K and the density of saturated vapour in the bubbles is P s,ox = 3.48kg / m

3

. 

Validity of estimations given by Eq . (10) was confirmed by numerical simulations based on a 

more elaborate model of bubbles' collapsing in overcooled liquids [8]. Duration of the pre-press 

is longer than 1 OOsec. Thus , all bubbles are expected to collapse by the start time t=O. 

1.3. Heating of liquid in the boundary layer near the interface 

The liquid surface layer is heated due to condensation. It can see from Fig . 1-3 the partial 

GOx pressure near the interface PGox<1.7atm. Therefore, the surface temperature of the liquid 

according to Eq. (3) is T5 :5 97K (T5-TL :5 0.7K). The width of this warm liquid layer near the gasliquid interface is determined by the thermodiffusion length of the liquid which increases with 

time and approaches a value of LOL = 6mm toward the end of the flight. 

The upper bound on the mass of heated liquid can be estimated as 

M.nax ~ SCtjlighJ pLLoL (tflight) ~ 400kg. This value is negligible compared to the total LOx mass in 

the filled tank, 627,500kg. 

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

Q _ d(j,. =K (1',-TJ S (t) =(T- T )S (t))KLCLPL L dt L LOL (t) L S L L 7ft (12) 

The total heat associated with the condensation of GOx can be estimated as 

(13) 

9 
Ta/lk waLL \ 

18 :::: (120+-I00)}; 

GH2+G'H e 

Fig. 1-6: Heated layers near the interface and the tank wall 

The total heat of GOx injected during the flight (tflj9h! =500sec) is 

Q illj ect == C pOxY;,u.Ji,'/ flight == 3.4 .108 J , 

Q - C M T - C lIl/age ~ank III/age - pax cox III/age - pax R 

Cox 

J illj == 1.3kg / sec, Y;,u = 800R = 444K 

(14) 

We conclude that the relative heat content of the heated liquid layer is a small: 

QL ( lflight ) / Q rject == 3%. 

1.4. Heating of liquid in the boundary layer near the wall 

Heating of LOx near the tank wall occurs due to the environmental heat 

flux, rJ.""" = eL""'')'l;J,,k which causes free convection of the liquid near the wall . The convection 

flow is turbulent and can be described by the following relations , discussed in a separate report: 

( )

"3 

q. _ d(! h(T - T) =K (Tuv - T,J h = 0.15K Rax 

t:" lI.'j r' d LW L L l 'Lw - L ' 

t ~ x (15) 

where I Lw is effective thickness of the heated layer near the wall. Here we use correlations for 

the turbulent free convection flow as in this case Rayleigh number Rax >3x 1012 for x>1m (x is 

the elevation of liquid layer counted from the tank bottom). We note that the values of I Lw and 

heat transfer coefficient hw do not depend on x. According to Eq . (15) the temperature 

increase of LOx layer near the wall is less than O.7K: (TLW - TJ < 0.7 K for typical 

environmental heat fluxes, ej""vu' = (130-;.- 200)W / m2 . The total mass of the slightly heated liquid 

in the boundary layer can be estimates as follows : 

10 
M W x ,T"J 907K $ 2 15kg(360kg) for 3 (5) engines. 

(16) 

We note that the total LOx mass in the tank is 627,500kg (1 ,046,OOOkg) . Thus, the mass 

fraction of the heated liquid (TLW R;; 90.7 K) near the wall is negligible quantity and does not play 

a role in the ullage temperature stratification and pressure dynamics. Moreover, the thin warm 

liquid layers with T ~ 90.7K near the interface and the tank wall, i.e. a slight stratification of LOx, 

does not lead to breach of condition NPSP = Pull + Phead - P frie - Ps,va/T,) > 30 psi for the net 

positive suction pressure due to high hydrostatic head pressure Phead (see below Sec. 5.1). 

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

cooling 

The heat flux from the ullage at Tg to the tank wall at Tw can be written as 

i 1 gw == dqdt !!,w = h 

gw 

(T 

g - T) w' 

h 

gw = 0.1X 

5 K 

g g 

(T ) (Ra 

x 

)1 /3 ~2 0~ m 2 K ' 

(17) 

K 

II = - g ~ Imm fior p = 2.4atm, T = 425K , T = 250K. .. w h g w 

w 

Here we use the correlation formulas for the turbulent regime corresponding to large 13 

Rayleigh number Ra > 7x 10 for x-1 m. The total heat flow is x 

(18) 

The temperature of the ullage and the tank wall depends on the coordinate x along the wall. 

Temperature dependences of the specific heat Cw for AI alloys used for the tank is shown in 

Fig .1-7. 

'I' 

l~ I " 

-2.23 33 81.1 1«.3 11)0 255 3 10.' 366 -422 477 SJ) Sst -22.5 33 88.7144.3200 255 311 366 42.2 .11 533 589 

Fig. 1-7: Specific heat for AI Alloys 2195 (left) and 2219 (right) 

These dependences were used for our MNM numerical simulations. For the estimation we 

assumed Tg = const, C", (T:J = (C",) = const and hg>v = const . Then Eq. (18) implies 

11 
dT,v :::: (Tg - T,J T = T - (T - T )ex ( _ _ t ) 

dt T (T) ' II' g g wO P T ' 

p w p 

Tg>v (T,,,) = (C ~P ll' ,Tg>v 150 secat (C w ) ~ 600J/kgK. 

g>v 

(19) 

The changes in the temperature of ullage gas and in the temperature of the tank wall are 

shown in Fig.1-S. The solid lines are plots of MNM-simulated time-traces of temperatures near 

the top (red) and bottom of the tank (green). The dashed lines are MNM-simulated time traces 

of the tank wall temperature near the top (red) and the gas-liquid interface of the tank (green). 

The blue solid lines give the estimated tank wall temperature near the tank top and the interface 

according to Eq .(13) for Tgw=150sec. These analytical curves correspond fairly well to the results 

of the MNM simulation (Fig. 1-S). 

is 

500 r-----~----~------r------,----~ 

, .. ·7"f ·_ ...... ·_ .... ·.. .. ............. ,._ ......... .. Ullage gas temperature : W : 

.................... J............ \1. .................... : ..... :: ~~ ature .... . 

80 100 

Fig. 1-8 Time traces of the ullage and wall temperature: solid curves are MNM 

simulation results and dashed curves are analytical results 

It it follows from Eqs . (12),(13) and (14) the heat transferred from the hot gas to the tank wall 

Q wall = Q inject +Q e ll V -Q ullage -Q L 68·· J , 

Qinject = C pOxT;njJinl j/ight = 3.4 . 10

8 J , (20) 

Q = YPllllage (tj/igIIl YVtank :::: 2.45 · 108J 0 = S t . 3.7 J ullage 1 ' ___ en v q env tank fli ght YThus we conclude that heating of the wall is the main mechanism of gas cooling in the 

ullage. 

2. Pre-pressurization regime and fitting the Shuttle data 

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

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

period, t = -300sec to t = 0, is shown in Fig. 2-1 [1]. The nominal parameters of liquid and gases 

supply for STS -115 are presented in Table 2 [1]. The replenish stage ends at t = -300sec, i.e., 

300sec before the start. The pre-pressurization starts at ~~~pr ss = - 152.8sec with injection of 

the hot He. The nominal He flow rate is r He =0.3Ib/sec = 0.136kg/sec and He temperature is T= 

572.4R=318K (see Table 2). 

12 
After the EOR one observes a leak of LOx which increases abruptly and reaches the rate of 

181b/s = 9.1kg/s (Fig . 2-2). Therefore, the ullage volume at ~~p",ss can be estimated as follows: 

\'SO) = \\~OR +8.lkg / s ill / PL ::::: 5m3

, 61::::: (300 - 152.8)s = 157.2s 

where the liquid level x~~) = l.09m is measured from the top of the tank downward. Hot He 

is supplied during the time I1 ~~press = (152.8 - 13 8.8) sec = 14sec until the pressure reaches 

20.54 psig=2.42atm (Fig. 2-1). At ~~epr s = - 138.8sec (liquid level x~~) = 1 A 06>n ) the ullage 

volume 

:1 - _·_ /IL. = _ 138 8sec fT<plOSS • 

20 " 

~ I ~ fS ·~~·~ 

i .. J ~ I V toJ ", 5m3 

n: '] '" ~ V,). "' 8S :/---- ;;- • • 1 ...... t<Ol "" - 1:52.8sec 

E OR ~: Ptepress 

t= -6 sec 

Vu]=9.09m3 

ESC 

~ .~ ~---"~-------- ~------~~--

Time, sec 

Fig. 2-1: Time-trace of the ullage pressure (STS 115). 

increases to V </I) = V ESC _ 9 kg 138.8sec/ p == 8m3 . We also used the fact that the ullage volume /I iii L sec 

V (I ) - V (O) 

increases with the pressure approximately as V,,,(p) = v,SO) + ,,/ "I (p- Po) due to the tank 

P I - P O 

wall elasticity and the lowering of LOx level. 

The temperature , partial pressure and densities of GOx and He stratify at 

~p ess = - 138.8sec as shown in Figs. 1-3 and 1-4 (MNM simulation) and Figs. 2-3 and 2-4 (3~ 

simulation). 

--.. "~ .. - Bleed flow of LOx from ET 

!~ .,.. . 

Time, sec 

Fig. 2-2: Time-trace of leakage from Lax tank during stages EaR through ESC (STS 

115). 

13 
Table 1: EOR through ESC (from t=-300sec to t=O) including pre-press (8TS-115) 

Am.bient Pr ssur ~ 

NoS(' CODe t.P 

Ullage Pressure: (above ref) 

Ullage Pressure: 

Ullage Pr~ure: 

Liquid Le~-e.l : 

UUage Volume: (X=O.929m} 3 .87 9m3 

Ulla~e Mass: 

Total Tank Voltune: 55S.S1m3 

Bubble Volume: 1.133m3 

Liquid Volume: 550.Sm3 

Vented LO_ Densl ry: 

L O_ Propellant Load: 627.5 T 

XT375 - ETtop 

XT396.7- 0.5ru do\vn 

1462 ps.ia 

0.01 psi 

0.64 psid 

0.65 psi 

15._7 psia 

4L5&Xt 

137ft' 

361b.:n 

19.617ftl 

40 ft3 

19.440 ftl 

71 .161bd tY 

1.383,336 lb", 

XT412 - O.95ru down (initial liquid level = ullage) 

£SC Througb T -0 

L0 2 Losses Prior to ESC: 5,904 Ibm 

GHe (Auti-lce) Mass Added: 1 .1b", 

GHe (Prepress) Mass Addt'd: 13 Ibm 

Ullaze Pressure: 22.0 psig 

Ullage Prt'ssure: 36.62 psia 

tJllageVolume llP. ESC (X=l.S14m)3_1 ~9 09m3 

Ul.1age Mass @ ESC 49 Ibm 

ET Liquid olWlle @ ESC 19.354 ~ 

ET LIquid M.1SS @ ESC 1.377.432 Ibm 

Press'd L02 Density 71.17 lbdff 

Predicted L02 Usage to I-O: 9,530 Ibm 

LOl Transferred to SSlvIEs: 1 72 l~ 

Loaded L02 at T-O: 1,367,730 Ibm 

Predicted Ullage Volume - % of 1.66 

Liquid Volume 

Required Ullige \ olume - % 1.59 

of Liquid \ olurue 

The ullage pressure drops at! ~ pr ss > - 138sec due to cooling of the hot injected He (see 

Sec. 1.4) and expansion of the ullage volume. Pulses of He injection are applied when the 

ullage pressure drops below the threshold value of P th =20 .54 psig=2.42atm (nominal value, 

Table 2). The results for the pressure time-trace from 3D simulation are presented in Fig. 2-5. 

Rectangular He pulses of nominal duration 0.5sec and nominal amplitude 

j He =O.3/blsec=O.136kg/sec (Table 2) were used for the simulation. 

One can see from Eq. 2-5 the time-trace pressure deviates from the telemetric data during 

the pre-pressurization stage. This divergence is a consequence of (i) the deviation of the actual 

pulse shape (Fig. 2-6) from the rectangular shape and (ii) the deviation of the experimental 

threshold pressure P th from its nominal value 20.54 psig used in the simulation. We 

incorporated the actual (experimental) rather than nominal value of the threshold and the actual 

pulse shape in the MNM simulation which shows an excellent agreement with the telemetric 

data (Fig. 2-7). In more detail, the pulses have amplitude j He=O.3/blsec=O.136kg/sec and their 

form is given by: 

. . { 1 - exp ( - (t - IJ I r f rOll1 ) , I < Ii + r p 

}(t)=}He 

exp(- (t-li - rp) l rWi/ ), t >ti +rp 

(21 ) 

where at t=t; the ullage pressure drops to the threshold value of Pth and i-pulse is generated. 

14 
r

Gas Mixture. 

Temperature 

· 316.91 

· 302.73 

288.55 

274.36 

260.18 

246.00 

231 .82 

217.64 

203.45 

. 189.2 7 

175.09 

160.91 

· 146.73 

· 132.55 

· 118.36 

· 104.18 

90.00 

(KJ 

Table 2 . Tank Ullage Pressure Dispersions 

PARAMETER NOMINAL VALUE 30 VARIATION 

Trajectory Normal & Early RTLS 

SS ME #1 #2 #3 

• Pressure t 3560 3584 3579 +42.4/ -55.9 psi 

• Temperature t 830 B20 852 +31.9 / -39.9 oR 

• Orifice Area 0.02871 0.02761 0.02944 ±2% 

• Nominal Power Level 104.5% 104.5% 104.5% 

• L0 2 Flowrate 933 .28Ib,,/ sec +6.33/ -6.78Ib,,/sec 

UlI;lge Volume ;II End of 137fe ±22.3 ft3 

Replenish 

Pre·Pressurization 

• Transducer Accuracy . Tavis Right Experience ± 0.4 psi 

• Drain Back I Seal Leak 21.4 Ib."lsec ± 1.5 Ib."lsec 

• Max. Hold Time Osee 5.0 min. 

He Pre-press Supply 

- Flowrate 0.3Ib.,./see ± 0.05 Ib.,./see 

- Supply Temperature 572.4°R + B.7 / ·19.5 oR - Valve Open Time 0.5 sec .± 0.1 sec 

Ullage Pressure 31 To _0.54 psid + 0.176/ . 0.348 psi 

Am bient Temperature 79.7so

F 48.8/81 .6 of 

L02 Splash EHecls 

• Splash Coefficient 4.375' .±0.3S 

Wall 

Temperature 

111 .69 

110.34 

108.98 

107.63 

106.27 

104.91 

103.56 

102.20 

100.85 

99.49 

98.13 

96.78 

95.42 

94.07 

92.71 

91.36 

90.00 

IKJ 

Fig. 2-3: Stratification of the ullage and wall temperature of GOx/He during the prepressurization. Results of 3D simulation. 

15 
350 '-' -- -~,.--------- 1 

, -,-" ... --.-~, _._---- , ,-------'-,---_ . ....,-_ .... _-+._. __ . ----

--- '---y---- -

I 

I ;-

;' - line 1 i Ga,M_..! 

-; 250 '-

D 

Y~-----h _ Temperatun: --.Je ~~~~~ 1 8. ' llll.rCace ~~ ~ 

IIIII"~ 260.18 - ~200 

!! 246.00 I .... 

f 

D 

i 150 ! ~ I 203.45 ' 

189.27 ~I' 17509 

16091 

146.73 I 132.55 

~ i I . 

100 t-___ -- -- I--_1·T~IJ1_; · - - --- .,_._-- . 118.36 ..... -

1 104 18 ! 

I ,I 90.00 I I 11<1 i S0 ~~~ _~~~~~ __ ~~.- .i~ .. ~ 

· 2 ·1.5 ·1 · 0.5 a Y ["' J 

Fig. 2-4: Temperature distribution along line 1 on a tank section at ~~presr = -138sec 

corresponding to the pressure p=2.42atm (see Fig. 2-5). Results of the 3D simulation. 

35 Tr===================~~~~~~~ 

30 I C) --3D-Slmulatlon --LOxShuttle ET tank . ·[25 

OJ-

=:; 20 <II 

fII 

e 15 DOJ 

~10 

::> 

5 

-1 50 -100 - 50 o 50 100 

Time, sec 

150 

Fig.2-5: Ullage pressure during the pre-pressurization and the first part of the flight: 

STS115DB telemetry (red) and 3D simulation (blue). 

(ii""O.12 . 

rn i ! 

.:r 0. 1 ' I - I ! 

~ 0 .08 . --!-- -' --t--; u:: I I *006 -- --~ 

~ 0.04 -- . 

~ 0.02 -' 

, --'--+---':: I :---+---I 

05 , '5 2.5 

Time(s) 

Fig. 2-6: The form of the He mass flow pulses. 

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

correlation for the turbulent natural convection (see Eq. (22», in such a way as to fit the 

temperature distribution found in the 3D simulation (Figs. 2-3 and 2-4). 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. (21) (the pulse duration T and its 

pulse 

front and tail durations T and T ). front tail 

J6 
-fJ - () - ()-0178 v ( Ra,t Pr )1/2 

f{ 1/2 - ( )_[gfrQenvx ]lI3 UN ,x - "UN X , U N Xi -. - 2/3 IX f/"X or UN Xi -

X i 1+ 0.494Pr CL,CP L,g 

(22) 

. 2 R s: f{ 3 1/30 

i N = 7<''1ank U xU '' ,xP UG IX f/"X , 

0, = O.565x[ (1 + 0.494 Pr

2/3

) / Rax Pr

2311 5

]ex: X7110 

The fitting gave the following values for the parameters: 

• = 0.05 

• T = O.09sec, T = 0.5sec, and T /. sec. front tail Plio' 

• The threshold pressure for a He pulse generation P th is chosen to fit experimental data 

shown in Fig. 2-7. 

Result of fitting the ullage pressure is shown in Fig. 2-7. We see that results of the MNM 

simulations fit very well the STS-115 data. We reemphasize that the only fitting parameter for 

the MNM, was the numerical coefficient u in the correlation relation for the natural convection 

velocity. This coefficient depends on properties of the fluids and is essentially independent of 

the tank design. Therefore we used MNM with this fitting parameter for analysis of the LOx SLS 

tank. 

25 

.9' 20 

en 

Q... 

15 

Q) 

I.-

:::J 

(f) 10 (f) 

Q) 

I.-

0.. 5 

0 

-1 50 -100 -50 o 

Time, sec 

Fig.2-7 : Ullage pressure during the pre-pressurization: STS115DB telemetry (red) and 

MNM simulation (blue). Results of the fitting with J3u=O.05, T = O.09sec, T . = O.5sec, and 

front tall 

T = O.7sec. 

pulse 

Result of fitting of the MNM simulations of the ullage pressure teeth induced by the He 

pulses for other Space Shuttle flight is shown in Fig . 2-8. In order to fit the STS135 telemetry 

data He pulse parameters were changed only - 10% in comparison with the STS 115 values 

(Fig .2-7). 

17 
------.-------~--------~------~------~------~ 

Ol '8. 22 

(l) 

~ 21 

(/) 

(/) 

(l) 20 '-

0... 

-260 -240 -220 

Time, sec 

-200 -180 -1 60 

Fig_2-8: Ullage pressure during the pre-press (-280sec<t<-160sec): 5T513S08 

telemetry (green) and MNM simulation (blue). Results of the fitting with l3u=O.OS, T = front 

O.09sec, T = 0.45sec, and T = O.7Ssec. tail pulse 

The fitting parameters of the MNM are further used in modeling the pre-pressurization and 

fight regimes to assess the risks for the proposed design of the SLS tanks (Section 5). 

Numerical MNM and 3D simulations of the time-traces of the temperature of the ullage and 

wall at some regions of the tank are shown in Fig. 2-9 for = 0.05 and rectangular He pulses of 

nominal amplitude JHe=O.3/b/sec=O.136kg/sec and duration 0.5sec. One can see that the 

corresponding curves for MNM and 3D simulations are closed enough (see also below Fig. 3-6). 

These results substantiate choose the value of = 0.05. 

450 MNM simulation 

~ 

400 

'" ~ 350 

iii 300 

8. 

E 250 

0!-

w 200 

go 

5 150 --Xt375 

100 --Xt421 

50 -f-.-.----,.--,-..-,--.---r---r---r-.-J ·200 ·150 · 100 -SO 0 50 100 150 200 260 

Time, sec 

200 

'" 

~ 180 

~ &. 160 

lj 

I- 140 

~ 120 

100 

-150 -100 50 0 SO 100 lS0 200 

Time, sec 

400 

'" e 350 

.2 i 300 

E :!!- 250 

E '" 200 

::; 

1 50 

100 

220 

2 0 0 i i 180 1 

~ 160

i! 140 1 ~ 20 ~ j 

100 

3D simolatio/1 

--Xt375 

~.( I ' \j 

--Xt421 

-150 -100 -SO 0 50 1 00 150 

Wall 

te m pera ture 

in the points 

Time, sec 

-150 -1 00 -50 0 50 100 150 

Time, sec 

Fig.2-9: Time-traces of temperatures of ullage (upper line) and tank wall (lower line) in 

various layers in the tank: green curve corresponds to the layer near tank top. Results of 

the MNM simulation (left) and 3D simulation (right). 

3 Operation during the fight 

The GOx is used to cool the nozzles, where it is heated to the temperature T GOx= 

800R=444K. The hot gas is further injected into the LOx tank to keep the pressure at the 

required value which would otherwise decrease due to the LOx level lowering during the fight. 

18 
The rates of the LOx propellant and hot GOx flows controlling the ullage pressure are shown in 

Fig .3-1. 

u 

Q) 7.6 II) EM 

:B 8.0 

i 5.2 ns 

~ ~ 

.2 3.6 

II. 28 N ' 

02.0 (!) 

iii 1.2 

Engines 1, 2, and 3 \\ 

---M."lmuITI Vlleg. Pr."ur. Case 

... .• Minimum Vllage prtssur. Cas. 

G02flow 2.59 kg/sec 

'00.4 • 'C 

I- '--";;'0"""""502-7.:, OO;;--:;<:5O:-:::;; 200-;;-;;:;-; 5O:--::C:300C:-;;-;: 50;--;;40~0 -'4"'50;--;:50:-::-0 ---: 550' 

Time, sec 

.5 8000 

E 

STS-115 - Telemetry Data 

~ 6000 

(!l 

i4000 

(U 

IX: 

~ 2000 

o 

u:: 

>< 0 --1 

o 

..J 

Engines 1 

Total LOx Flow - 1,296 kg/sec 

·2000'-,--.,----,-::-=----::-=---c==-_-:=:-_-==_-;:-;! ·100 0 100 200 300 400 500 600 

Time, sec 

Fig.3-1: Flow rates of hot GOx into the tank and LOx from the tank during the flight. 

To fit the 8T8-115 data [2] the form of dips seen on the curves in Fig. 3-1 was slightly 

modified for the MNM simulations (- 10%). The rates correspond to the nominal values 

presented in Fig. 3-1. Result of fitting the ullage pressure and temperature are shown in Figs. 3-

2 and 3-3, respectively. The ullage pressure falls within (20 5~14 5) psig range and the 

temperature -- within (-100~100 F=(200~310)K range. We see that the results of MNM pressure 

simulations fit fairly well the 8T8-115 data (Fig .3-2). 

The deviation of the simulated temperature from the data is substantial during the flight but 

small at the pre-pressurization stage (t<O, Fig.3-3). In the latter case, as can be seen in Fig. 3-4, 

the width of the transition region for the temperature is very small « 2cm) and we conjecture 

that the temperature sensor is located outside this region. The observed deviation of the 

experimental and simulated temperature during the flight (Fig. 3-3) can be attributed to location 

of the detector in the relatively cold transition region which is larger during the flight, - 5cm (Fig. 

3-4). Another possibility for the deviation is suggested by the 3D simulations (Fig . 3-5) which 

shows pocket of relatively cold gas in trapped in the upper corners of the ullage, where 

presumably the detector was located. These pockets are absent during the pre-pressurization 

(Fig. 2-3), which is a consequence of the relatively low density of He compared to GOx. 

Time traces of the ullage and wall temperatures at various locations in the tank are shown in 

Fig. 3-6. They correspond well to the pronounced temperature stratification detected in the 3D 

simulation (Figs. 3-5 and 3-6). The 3D simulation also shows that the initial complex 

temperature distribution (Fig. 3-5, t=2sec) is transformed into almost flat layers after 10sec. 

This result justifies the approach adopted in the MNM. 

30 ,, -~--- -.---.----. 

OJ 25 

~ 20 U .. /'M'fMM/'!r-N~~~~~ 

(]) :s 15 1-··' , ·················.;···· .. ············~·· 

12 10 (]) 

ct 5 

LL----~---~---~-- ~ 

-150 -100 -50 0 50 100 

Time, se c 

~ 2.5 

ill 

:s 2 (/) 

(/) 

ill cl: 1.5 

~---~--- ---~---~-~ 

-150 -100 -50 0 50 100 

Time, sec 

Fig_ 3-2: Time-traces of ullage pressure during the pre-press and the initial stage of 

the flight in relative (left) and absolute units (right). 5T511508 telemetry (red) and MNM 

simulation (blue). 

J9 
--'---r---' ~- ~-~ 

LL 100 

-400 L..J..... _ _ -'-_ _ -"--_---' _ _ --'-__ -'-_---' 

-150 -100 ·50 0 50 100 150 

Time, sec 

Fig. 3-3: Time-trace of ullage temperature during the pre-pressurization and the initial 

stage of the flight near the tank top where the thermo-sensor is located: STS115DB 

telemetry (red) and MNM simulation (blue). The green curve shows time-trace of the wall 

temperature. 

20 

440 WaU localim tioll 

400 ~ :::.:: 

! 360 

~ 320 <u '" 

Co 

E 280 

oS 

cI) 240 E 

>< 200 E 

(I) 

'" 160 (!) 

120 

0 0.1 0.17 Distance from wall. m 

Fig. 3-4: Ullage temperature radial distribution at the level of the thermo-sensor 

location. Results of 3D simulation. 

Start of urainina t=O Tempenltun" tli lI ibuti n 

'" / Gas Mixture. TemDerature 

316.91 

302.73 

288.55 274.36 

, 260.18 

t 246.00 r 231.82 

i 217.64 

r 203.45 

t 189.27 

t 175.09 , 160.91 

146.73 

132.55 

118.36 

· 104.18 

90.00 

[KJ 

Velocity distl"ibutioll 

Wa ll 

111.69 110.34 

108.98 107.63 106.27 

104.91 t 103.56 t 102.20 · 100.85 

[KJ 

99.49 

98.13 96.78 

95.42 94.07 92.71 91 .36 90.00 

Fig.3-5: Temperature and velocity distributions at t = 2sec and t = 10sec after the start 
Fig . 3-6 shows that the increase of the wall temperature lags behind the growth of the ullage 

temperature. The lag is T gw ~ 1 OOsec which confirms theoretical predictions based on the 

estimates in Sec. 1.5. Time-traces of the partial pressures of GOx and He are shown in Fig . 3-

7. 

.sa 3'-0 

Red - layer near the tank top / ' 00 Red - layer near ~ 300 

~ 350 the tank top 

<Ii 

:s 250 

ro 

~ 200 

E 

ill 

l- I"/! 

~ 100 

Blue - layer near liquid-gas interface Blue - layer near liquid-gas interface 

50 - 150 50 - 100 -50 0 50 100 150 -150 -100 ·50 0 50 100 150 

Time, sec Time, sec 

- -1 5 15 

- -1 50. 

- -147. 

- -142. 450 - -138_ 

---13 2_ 

"" 4 00 8 -122. 

~ 3 50 --112_ 

;;; - -102. 

~ 3 0 0 - -152. 

E - las .. 250 I- - 20s .. 

co - 40. .!!! 2 0 0 

=> - 50s 

1 50 - 60_ 

- 70s 

1 00 - 80. 

- 90s 0 - 1 -2 -3 ... -5 -6 -7 - 100. line length . m - 110. 

Fig.3-6: Time-trace of temperatures of gas ullage (left) and tank wall (right) in various 

layers in the tank: red and blue curves correspond to the layers near tank top and gasliquid interface, respectively. Results of the MNM simulation. 

ro x 10' 0.. 5~----~----~----~----~----~ 

5 

ro 1 ~XT10~ __ -. ____ -. ____ -. ____ -. ____ ~ 0.. .8, 

~ 1.6 :::l 

~ 1.4 

0. 

ro 1.2 

t:: 

~ 1 

x 

·100 ·50 0 50 100 0 0.8 15.L-----1 .Loo---- 50~----...L.---- ...L.------'100 

Ti me, sec Time, sec 

Fig.3-7. Time-traces of partial pressure of gaseous Ox and He in ullage layer near the 

liquid-gas interface. Results of the MNM simulation. 

Dynamics of the condensation rate and the condensed mass are shown in Fig . 3-8. 

Evaporation is seen to override condensation during the first stage of the flight (O<t< 1 Osec, 

Fig.3-8). This result is explained by the stratification of partial pressure of Ox and He gases and 

the dynamics of the ullage pressure. Indeed, the ullage pressure drops sharply during of the first 

stage of the flight (Fig. 3-2) following a rapid decrease of the liquid's level. The partial GOx 

pressure drops and approaches 1 atm (Fig. 3-7, left). As a consequence, the interface 

temperature Ts decreases to the value Tl (see Eq. (3» and the condition Eq.(9) breaks down , 

implying that evaporation becomes dominant. Later on, the partial GOx pressure increases 

(Fig. 3-7, left) due to the GOx pumping. As a result, evaporation becomes overridden by 

21 
condensation (Fig. 3-8). Total mass of the condensed Mcond :5 1kg (Fig. 3-8, right), i.e., it is 

negligible compared to the total mass injected hot GOx: MGox=1.3kg/sec x 100sec=130kg. This 

means that in contrast to the pre-pressurization stage the contribution of condensationevaporation process to the overall mass and heat balance during the flight (t>O) is very small. () 8l 02 r-r----,--- - ,--- --,-- ---r-- --, 

0, 

~ 

a5 a 1 

~ 

100 

Time, sec 

-100 -50 0 

Time, sec 

50 100 

Fig.3-8. GOx condensation rate (left) and total condensed mass (right). Results of the 

MNM simulation. 

4 The limiting case of fully mixed gases 

The pronounced stratification of both ullage temperature and partial pressure of GOx and He 

was found in the 3D simulation (Fig. 3-5). The stratification is also observed in the MNM 

simulation provided one uses the value f3u= 0.2 in the correlation for the velocity given by Eq. 

(22). This value of f3u is chosen in the MNM simulation to best fit the average velocities given by 

the 3D simulation. It should be noted that the value of f3u for small variations of the gas density 

where the correlations Eq . (22) strictly hold is f3u"'" 1. For large temperature gradients near the 

wall the variations of the gas density may be substantial. Therefore, it is instructive to consider 

the ullage gas dynamics for f3u= 1, where due to higher velocity of natural convection near the 

wall, the temperature stratification almost totally vanishes (Fig . 4-1) and stratification of partial 

GOx and He pressure is very weak (FigA-2). 

3S0 I---.- ---.--~:=::~G~~~ 

~ 300 

~ 2S0 ::l 

1§ 200 Q) E 1S0 

Q) 

100 

~--~ ~--~-~--~-~ 

-1 S0 -100 -so 0 so 100 1S0 

Time, sec 

Fig.4-1: Ullage temperature time-trace at various locations in the tank: red and blue 

curves correspond to the layers near tank top and interface, respectively. Results of the 

MNM simulation for f3u= 1. 

22 
a. '" 

i 1.6 ::J 

<J) 

~ 1.4 

C. 

interface 

15 x 10' 

ci 

:; 10 

'" <J) 

~ 

c. eo 1.2 t ~ 5 

~ 1 ~ x ~ 

o ~ 

(9 L-...----~--- -------'-' I 0 ~::__--_:_:_::__--~,...__----L..J 

-150 -100 -SO 0 -150 -100 -SO 0 

Time, sec Tim e, sec 

Fig. 4-2: Time-traces of partial pressure of GOx and He in the ullage; red and blue 

curves correspond to layers near the top and the bottom of the tank, respectively. 

Results of the MNM simulation for f3u= 1. 

However, even in this limiting case of total mixing of the two gases , the time traces of the 

ullage pressure and temperature do not change considerably (see FigA-3 .;.-Fig . 4-5). 

30 

0') 25 

'en 

Q. 20 

ai 15 I-

::J 

~ 10 (l) 

ln.. 

0 

-150 -1 00 -50 0 50 100 150 

Time, sec 

Fig. 4-3: Time-traces of ullage pressure. STS115DB telemetry (red) and MNM 

simulat ion (blue). Results of the MNM simulation for f3 u= 1. 

30 ~------~-- --~---- ------ -~ 

0) 25 'a 20 

~ 15 

m 10 

d: 5 

; ; 1 Stratification {3 u= 0,2 

~- -L ______ ~ _ _ _ ~ _ _ _ _ -L ___ ~ 

-150 - 100 -50 0 50 1 00 

Time, sec 

Fig. 4-4: Time-traces of ullage pressure; blue for stratification (f3u= 0.2) and green for 

total mixing case (f3u= 1). Results of the MNM simulation. 

23 
2oo -------.------ ------ ------~-----. 

LL 100 

~ o 

:J 

~ -100 

0... 

E -200 

~ -3 00 

Total mixing Ilu = 1 

Stratificati on l3u = 0.2 

-400 '-'----------'---------'--------'--------'---------' -1 50 -100 -50 0 50 100 

Time, sec 

Fig. 4-5: Time-trace of ullage temperature near the tank top: blue for stratification 

(/3u= 0.2) and green for total mixing case (/3u= 1). Results of the MNM simulation. 

In the case of total mixing the average condensation rate and, accordingly, the total 

condensed mass are smaller than those for stratification (Fig . 3-7, f3u= 0.2) during the late prepressurization stage (Fig. 4-6, t<O). On the other hand, they are essentially identical during the 

early pre-pressurization stage and the flight (Fig . 4-6, t>O). The decrease of the condensation in 

the absence of stratification during the pre-pressurization stage is explained by the increase of 

the gas temperature and decrease of the partial pressure of GOx near the interface compared 

to dynamics with stratification. The partial pressure decrease leads to decrease of the surface 

temperature r. in the right-hand-side of inequality(9), while the rise of the gas temperature 

Tg makes the left-hand side of the inequality larger. Both lead to inhibition of condensation and 

acceleration of evaporation, which explains the observed dynamics (Fig. 4-6). 

24 

,,----~----~----.-----,-----. F 2~----~----r----.----.---~ 

gll .......... = ...... , m 

E 

c ~ili .Q 

~ ~ ~ C ~15 W 

W U ~ ~ c c 0 o -0.25 '-':-::------':-:-----~-----'-------:'::----' <-) <-) -150 100 

. . 

Total mixing I!J, = 1 

-1 .; .................. j ................. : ........ . 

~ ~ ~ 

-2 +··········1···· 

-3 _L

1S....,0----_1..L00.,.----_-::'SO'-----'-0 -----::'-:------' 100 

Time, sec 

Fig.4-6. GOx condensation rate (left) and condensed mass (right). Results of the 

MNM simulation for f3u= 1. 
5 Scaling of the risks 

5.1. Scaling of pressure near the feedline top and bottom 

The pressure in LOx tank feedline is high due to hydraulic pressure of a large mass of LOx. 

The total pressure near feedline top Ptop and bottom Pbot are 

PhOl101II = gPL (Hlank - Lullage + Lpipe ) + Pullage = 5.9 atm (t < -150s,Pullage := ParnJ 

PlOP = gPL (H tank - LlIl/age ) + PlIl/age = 2.56 atm (5.45atm at max acceleration), 

(23) 

The pressures during pre-pressurization for 3 and 5 engines are approximately equal to 

{

2.6 (3 .6) atm at 1 < - 152s, Pullagc ~ 1atm 

A ~ , op 4 (5)atm at - 138s < t < 0, Pullagc ~ 2.45atm 

{

5.9 (9.2) atm (I < -152s, Pullage ~ latm) 

P botlom ~ 

7.3(1O.6)atm(-138s <t <0, P ullagc 2.45atm) 

(24) 

The Shuttle achieves maximal acceleration grocket=2.5go at the point t=80sec, when the liquid 

level is 1.69m above the tank bottom (Fig.5-1). The maximal top and bottom pressures 

corresponding to total acceleration g = 3.5go are approximately equal 

PlOP := 5.8(8 .5)atm at t>50sec, Pullagc ~ 1.75atm, 

Pbotlom = 17.5 (28)atm (t>50sec, PuJJagc ~ 1.75atm) 

(25) 

For estimation of the hydrostatic pressure in the feedline for the SLS tank with 5 engines we 

assume that the tank height and pipe length scale as 5/3Htank and 5/3Lp;pe (Htank =15.05m and 

Lp;pe =29.4m are the parameters of Shuttle LOx tank). 

30 

"I. 2& ...... 

E 

~ 20 

0 

~ 15 

~ 

"ii 

~ , 0 

~ 

t 5 ~ 

..<: 

'" 0 

r 

E 

14 ~~~~~----~--~ 

e' 

~ 12 o 

.D 

.. 

~ 10 .- - - - ---- - ------------- E 

~ .. 

~ 8 ." 

·5 

c:r 

~ L----- ---- ---- ----~ 

+-r--.-J...r 10-

0 --2--rOO--3 .. 00~-.0,.-0---,50-0 --i600 -200 -100 o 100 Time(s) 

200 

Time , sec 

Fig.S-1 Time traces of Shuttle acceleration (left) and the liquid level in the tank (right). 

Thus, the maximal pressure at the bottom of the feed line for SLS with 5 engines will reach 

28atm. Such high pressure in the pipe and the engine's inlet has to be taken into account for the 

development of SLS. 

5.2. Scaling of shape and size of the LOx tank for SLS with 5 engines 

Two possible shapes of the SLS tanks are considered in this work: (i) the Shuttle LOx-tank 

shape and (ii) the Shuttle LH2-tank shape with volume upscaled to 5/3 of the Shuttle LOx tank 

(Fig. 5-2). The diffuser size is changed in the case (ii) (Fig.5-2) to prevent contact with the liquid 

surface. The initial ullage volume Vo and the volume in end of pre-pressurization V1 , i.e., at the 

points t=-152sec and t=-138 sec (see Fig. 2-1), respectively, are increased by the factor 5/3: 

Vo=8.43m3 and V1=13.2m3

. The fluxes of hot He and GOx are also increased by the factor of 

25 
5/3 compared to the Shuttle. Fig. 5-2 also shows the gas velocity field near the diffusers for both 

shapesofLOxSLS~ta ~. ______________________________________ ~ 

Diameler 6. 25 " 

Length 30.0-1" 

Difl\l~er 

I J ..-=--.-.........,.-.-.,. 

• 

Di.ffuser Diameter J 1.52" 

LeI/gill J 6. 3" 

Fig.5-2 The shapes of SLS tanks and diffuser considered in this work: (i) the ShuttleLOx-tank shape (left); (ii) the Shuttle-LH2-tank shape (right). 

Predicted time-traces of the ullage pressure and temperature for the two shapes of SLS 

tanks are shown in Fig. 5-3 and compared to the Shuttle nominal time-traces. 

26 

Multi-node Model 

~ 2.2 : . - - -. -- .. _+ ... _.J § 2.4 

""t ' . : ..... -.. :. ......... J 

j ,, ~-:=-~~-::-: l~ t~~ 1:: r:: ~:~~~~=::I .:. ··:·::· r .... _. <t: 1.2 ..•. , .... . _ ...• __ . .;.-_ .• -•..•.• -+_ ... __ ... ..... _ .. _-.. _ .. . 

·151) -100 ·50 0 

Time, sec 

50 100 

-'OO ,-r----.---r----.---r-- --, 

100 

2. 4 

~ ;' .2 

.,-

~ 2 ,0 

CL.. 1.8 ., 

~ 1.6 

.0 

..:( 1..4 

, .2 

230 

260 

240 

'" i220 

~ " 200 

8. 

E 180 

~ 

0160 

~ 3 1<40 

120 

100 

•• 

3D Simulation 

~- scaled 5/3, LH2 tonk shope 

_150 -100 -50 50 100 150 

·150 

Time, .!lee 

AI (luI 'cl uj 

rhl11tmpUUfJlrc 

SClIsor (YI396) 

-100 

Time, sec 

100 

Fig.5-3 Predicted time traces of ullage pressure and temperature for different shapes 

of the SLS LOx tanks. Results of MNM and 3D simulations. 
..

- 

2.8 r-----r----.----;====================rr 

2.6 

E 24 .', 

......., . ',-----.. ro .... 

, 

, 

, 

, 

, 

.... ...... 

--nominal 

- - scaled 5/3 LOx tank shape 

--scaled 5/3 LH2 tank shape 

----. upper limit 

----. o~r imit 

.... _---......... .. .... 

'--- -------- --~ -.. 

1.4 

o 20 

--.... ;:-<' -.... -_--"' 

40 60 

Time, sec 

--', ...... .... _------- 80 100 

Fig.5-4 Predicted time traces of ullage pressure for different shapes of the SLS LOx 

tanks. Results of the MNM simulation. 

2.8 

2.6 

E 2.4 ..... 

ro 2.2 

(l) 

'- 2 ::J 

~ 1.8 

(l) 

'- 1.6 0.... 

1.4 

0 

--nominal 

--scaled 5/3 

" "" -- scaled, ullage 10% less 

'--------_______________ _-__ - __ - _. ~~~::ii~lil:;e 30% less 

, 

, 

, 

, 

, 

, 

, 

, 

-- - __ - -----. o~r imits 

'---------------------

20 40 60 

Time, sec 

80 100 

Fig.5-5 Predicted time traces of ullage pressure for LH2 shape of the SLS LOx tanks 

with different initial ullage volumes. Results of the MNM simulations. 

One can see that the time-traces of ullage pressure for the two LOx tank designs are close 

to one another. It is important to note that the predicted pressure time-traces lie within the band 

of acceptable ullage pressure (Fig. 5-4). However, the pressure time-trace for the LOx tank of 

shape (ii) lies very close to lower bound of the band, creating hazardous situation. To analyze 

the possibilities of controlling the risks we carried out the simulation for several other initial 

ullage volumes and showed that the situation can be substantially improved if the initial ullage 

volume in the LOx tank is decreased by 10% (Fig.5-5). 

6 Effect of sloshing in the LOX tank 

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

rocket. Sloshing of cryogenic liquids can change the ullage pressure due to variations of the 

heat and mass fluxes at the liquid-vapor interface and near the tank wall. Two main types of 

sloshing are shown in Fig . 6-1. Generally, the motion of the LOX tank during the lift-off can be 

decomposed into three major components: twang , breathing , and oscillation. The twang occurs 

27 
before the lift-off, while the breathing and the oscillation occur during the lift-off. The twang 

occurs approximately 5 seconds before the lift-off when the main engines are ignited and the 

Shuttle is released from the launch pad. When the main engines are ignited, a torque is created 

around the attachment point of the rocket boosters which makes the entire vehicle tilt [9]. The tip 

of the ET tilts as far as 30 inches from the rest position and then returns back. When the tank 

returns to the near vertical position the solid rocket boosters are ignited and the launch takes 

placre:..:.. _____________ --, 

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) 

This motion initiates oscillations of the liquid surface with period Tosc-2.5 sec and amplitude 

aosc<O.5m (Fig . 6-2). 

0.5 r--------...,--------, 

E 

Tank top position : h------~------~ 

o 5 10 

Time, sec 

Fig.6-2 Tilting of the Shuttle from the vertical direction after the lift-off (left) and 

typical sloshing oscillations (right). 

6.1. Longitudinal sloshing waves 

The rocket oscillation leads to variation of the liquid level near the tank wall [12,13]. Our 3D 

simulations showed that the wall temperature near the liquid-vapor interface is lower than the 

boiling temperature (T boil>1 OOK at p>2.25atm) for distance from the interface less than O.75m 

during both pre-pressurization and the flight (see Fig. 6-3). It means that the variation of the 

liquid level near the tank wall will not stimulate evaporation of the liquid provided the oscillation 

amplitude aosc is smaller than O.75m. This condition is apparently satisfied even for the Shuttle 

(see Fig. 6-2). 

The SLS design differs from the Space Shuttle construction in that no torque on the rocket is 

created by the engines ignition. As a consequence the hazard associated with the twang of the 

ET is essentially eliminated in the SLS design. 

28 
.

-- -

180 

~ 160 

~ ::1 

1U 

~ 140 

E 

.$ 

ro 

~ 120 

100 

a -6s - -10s 

--205 

o "234567 

Distance from interface along the wall , m 

Fig.6-3 Distribution of the wall temperature near the liquid-vapor interface for different 

times (x=O is the interface position for a given time). Results of 3D simulation. 

After the start (t > 0) the stationary longitudinal sloshing oscillating waves enhance 

condensation due to (ii) increasing the area of the liquid surface and (mainly) due to (ii) mixing 

the heated surface liquid layer with adjacent cold LOx with T=T L' As a result of mixing the 

heated surface layer became narrower but the interface temperature did not change, it is given 

by the partial GOx pressure: T =T/ PGo) :::::100K. The condensation flow rate at the liquid-gas 

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

surface with T=T : s 

(26) 

The maximum value of the condensed mass M d induced by the intensive 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 S; of the surface area will be very small at end of each oscillation , LL-O (Fig. 6-4). 

, Vapor zone Vapor zone 

Uquldlone 

Liquid, TL 

Temperature Temperature 

Fig. 6-4. Sketch of the temperature distribution before and during the sloshing 

In this case the first term in the right part of Eq. (26) is much larger than the second . 

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

29 
(27) 

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

M slosh(t) - M (T) ML + SL (_t_J (28) cOl1d - conti osc S T ' L ose 

The total condensation flux is equal to 

M SloSh( ) 

max j Slosh = max cOlld t = 0.26 kg cond t sec (29) 

forS~;:::: SL 13, T,(PGH2 ) == l OOK, lOOK < Tg $200K near the interface 

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

Jeox = 2.6 !~ x [Nllozzle 13], N no-ale - number of nozzles 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 GOx 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. 

6.2. 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 th·e 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 Oxygen 

depends on partial pressure of gaseous Ox, 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 oxygen pressurization these droplets will enhance the condensation rate. 

Dispersion relation for small wavelength capillary wave can be presented as [12,13]: 

0) 2 = ( gk + : e) tanh(kh) 

where a is surface tension, k=2n/A, A as the wavelength , k is the wave number and p is the 

liquid density. At small k« 1 

0/ = gAmn tanh(A h / a) (30) mn mn a 

The nonlinear dynamics of the droplet formation and ejection is very completed and strongly 

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

dangerous effect. The typical diameter of ejected droplets is about [14,15] 

d ""(CJ / p)1/3 CO -Z/3 0) = 27[j (31) drop L L , 

where P L =1141kgl m3 and OL =0. o 135Nlm are liquid density and surface tension, co is 

vibration frequency (aJ=27tfvibr) . Characteristic values of d drop are shown in Fig.6-5 

(left): d"roJ25Hz):::: O.8mm mdd J200Hz) "" O.2mm. 

30 
:- :. iU 

E 

o " r··· ·;······ ··:······· ·····"·· -· ·· ·-·- 1 

Fig.6-5. Typical diameter of ejected droplets depending on thrust oscillation 

frequency (left) and generation of droplets under action of supercritical vibration 

acceleration Ed>O [13]. 

Each projectile area of diameter dproj r::::5cidrop ejects the droplet with a rate given by [14,15] 

dn / dt =='-7 = O. 04£(~ 8m [5-

1

], Gd = (avibr - ad) / ad' 

ad =O.26((J" / p)1/3m4/3 (32) 

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

the onset of droplet ejection. The droplet ejection occurs if vibration acceleration avibr >ad, i.e. 

when the frequency and amplitude vibration Avibr satisfy the condition: 

2 - lJ. / /" 2/ 3 avibr = A"ibrCO > ad or A"ibr > Ae = 0.lmm(6)l1z J vibJ , 

Ae = O.2mm/or /=25Hz,Ae = 50f-lm/or /=200Hz 

(33) 

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 Lo (100sec)r::::7mm during the prepress (t r:::: 

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

diameters: LD :::: 5mm» ddrep for f > 50Hz). It follows that inner temperature of generated 

droplets T is close to the. surface temperature of the liquid T (PG ). Therefore, the liquid drop s Ox 

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

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

drop 

~H- . J""", (I "",)s,., ph,., m el'ap (tdrlijJ = 5drop J evop (t)dt ::; S t dr/ife ' t drlife = --, pr~SJ L g 

J () = S (Tg -~(P 2) )jK P ~(P H2 )-Tdrop )J L el'ap t L (()) r-: ' 

qL +Cg Tg -TL '-1m 

(34) 

where hdrop is the maximum height an ejected droplet rises above the surface (see Fig. 6-5). 

The total evaporated mass is given by 

dN10IG1 S 11. , M < () ~ - ( ) L ar<,p t evap - m evaop tdrlife dt t - m eond tdrop , 

5 pro} 

d'N101G1 S 11. d 

h drop L d .. up - _ 11. drop 

were --= , n ,lrup dt 

dt Spro} 

(35) 

31 
Here dN~~:; I dt is total number of droplets ejected over unit time from the liquid surface SL. 

Taking into account Eq. (34) and condition d .';::j 5dd ,Sd Is . = 4 / 25 we conclude from pro) TOp rop pro) 

Eq.(35) that the total evaporation mass is a negligible quantity 

4Ji l 4J (T )t M < J (t )t ~ < evap prepress 

evap - evap press dllife 25 - 25 

. 1, , n dro < -- p -

r dr/ife (36) 

Jevap ::::; M evap / t = O.1 6Jevap (Tprepress )::::; O.03g / sec 

In the estimation we used the results of calculation presented in Sec.2 (see Fig. 2-8) 

e>'ap (~repre.sJ S O.2g 1 sec . 

6.3. Combined action of longitudinal and axial sloshing vibrations 

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

and axial sloshing vibrations (Fig , 6-4, left» . The maximum value of the condensed mass 

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 S~ will very small at end of each oscillation , LL-40 (Fig. 6-4). Droplets 

generated by the axial sloshing will have T near T , except for a very thin surface layer LL-40 L, 

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

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

cond drop 

(

t ) 0 M =,,(t,,,!,) = S''''' (T,(PGm ) - TJ ..}K ,C,p, 4tM'I' I ~ p hd.' (37) m cond drlife S drop S C (T _ T ) , drlife 

L q L + H2 g 5 Jr g 

The total mass flow rate of condensed vapor on all ejected droplets is 

dNlOtal (4) S' (t ) 1 1 J lOlal = met . )~ = - L

m 

dr/ife I tlmp Ii , S - '- for A . >Ac 

cond drlife dt 25 ' orup vtbr' 

S drop L drl ife 

_1_ '" hi" = t hd"" t drop' t drlife ' IT drlife g 

(38) 

Using ~ ';::j SL 13 and (dr/ife ';::j drop 1 g ';::j O,02sec we obtain from Eq .(38) that the total mass 

flow rate of condensed vapor on all ejected droplets is ~~~~ < 0.45kg / sec . We notice that the 

rate of injected hot GOx mass flow is much higher: 

- 6( ) kg . Jeox - 2. N,wzzle / 3 sec , N nozzle - number of nozzles In SLS . 

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 

Jlolal [ C (T T)] - C (T T.) S Zliquid drop q L + COx g - 5 ' t - LP I, 5 - L L . healed' 

liquid S; ( 8Lo (t)) ( )'n . ) 2hd"" = - " f · . 7 t .. = -- fhealeAt) S L 25IT t drlife I clrop ' d'N- g ' (39) 

f li'll/id ( ) < 5L ( ) - 5 fi . < _1_ ~ 0 02 healed t jliglll - f) t jlig/ll - em or 11"'UI' - , {drlife ~ . sec 

t drlife 

32 
-- - - ----- 

- - --- - 

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""'23.8K, thickness 

L-::::5cm, voiume, Vlleor =SW1~:~ed / 2 ~d.4 3 and mass M;J(10' == V;",oIPl ~ 1600kg. Total mass of 

LOx in the tank is 627500kg. 

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

engines. At the same time all the effects under consideration are taking place in a small layer 

adjacent to the interface and the mass flow rate of injected hot GOx increases with the engine 

number. 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::::100.8K can 

arise in LOx SLS tank. 

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

engines. At the same time all the effects under consideration are taking place in a small layer 

adjacent to the interface and the mass flow rate of injected hot GOx increases with the engine 

number. 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""100.8K can 

arise in LOx SLS tank. 

Conclusion 

We performed theoretical investigation of main physics processes in LOX 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 LOX 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 ANSYS package simulations allow us to make the following 

conclusions. 

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

the same for the SLS. The time-traces of SLS LOx tank ullage pressure and temperature were 

calculated after an appropriate rescaling of the relevant parameters . The rescaling takes into 

account the increase by factor 5/3 of the linear dimension of the tank compared to the tank of 

the Shuttle. The rescaled parameters include flows of hot He and GOx, and also initial volumes 

of ullage and liquid in the tank. The predicted time-traces of the ullage pressure are found to fall 

within the acceptance limits for both SLS LOx tank shapes. 

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

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

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

is more pronounced in the rescaled SLS tank. Such stratification occurs due to slow mixing of 

GOxlHe gases: the heavy cold GOx localizes near the liquid surface and the injected hot light 

He accumulates near the tank top. The stratification is predicted theoretically and confirmed 

and scaled by the MNM and 3D simulations. 

4. Parameters of the MNM, developed in our group, were fitted to make the MNM 

reproduce the ullage temperature stratification observed in the 3D simulations. Remarkably, it 

is found that an accurate correspondence between the model and the 3D simulations is 

achieved by fitting just a single parameter: the scale of the velocity of natural convection in the 

turbulent boundary layer near the tank wall. 

5. The MNM reproduces with high accuracy the telemetric data of saw-tooth modulations of 

the ullage pressure during pre-pressurization stage, which result from injections of He pulses. 

This accuracy only required fitting the shape of the He pulses. Likewise, the model is found to 

reproduce fairly well the telemetric Shuttle data of the ullage pressure variation during the flight. 

33 
6. The ullage pressure in LOx tank is shown to be essentially insensitive to temperature 

stratification: a model calculation implies that even in the case of complete mixing of the cold 

and hot gases, where the temperature stratification is absent, the ullage pressure time-trace 

does not change significantly. 

7. In contrast to the SLS LOx-shaped tank, the time-trace of the ullage pressure in SLS 

tank with LH2 shape is found to approach the lower acceptance limit. It is shown that this 

hazard can be eliminated by a decrease of the initial ullage volume in the tank . 

S. Theoretical analysis of bubbles dynamics in LOx has been analyzed. It was shown that 

generated bubble volume increases as the tank height squared . Collapse of the bubbles .during 

the early stage of the pre-pressurization has been demonstrated. 

9. Condensation-evaporation flows are found to weakly affect the ullage pressure. First, 

the condensation is controlled by the high pressure of GOx in the ullage. In contrast to one's 

naNe expectations, even in a hypothetical case where the gas temperature in the vicinity of the 

liquid-vapor interface reaches the temperature of the injected He (320K) or GOx (SOOR=444K), 

it is condensation rather than evaporation which is dominant during the early pre-pressurization 

stage and the flight In reality, due to stratification the actual temperature near the liquid-gas 

interface is much lower, which leads to strong suppression of evaporation during all stages of 

the pre-pressurization and the flight. Second, the condensation is controlled by the slow heat 

transfer rate in the LOx. It is predicted that the total condensed mass during the prepressurization and the flight is negligible. Therefore, large change of ullage pressure relating to 

condensation-evaporation process at the liquid-vapor interface is unlikely. 

10. The estimated temperature of the interface is lower than 100K and the estimated 

thickness of the heated liquid layer is smaller than 1 cm. This layer corresponds to the total 

mass of the heated liquid which is less than 450kg during the fight (tfli9hl =500sec). This mass is 

negligible compared to the total LOx mass in the filled tank, which is 627,500kg. Therefore, it 

does not play the role in the ullage temperature stratification and pressure dynamics. It was 

also found that the total heat associated with the condensation of GOx is much less than the 

heat of hot GOx injected during the flight. 

11 . Slight temperature stratification of LOx is formation of thin warm liquid layers with 90< T 

~ 98K near the interface and a layer with temperature T~ 90.8K due to the liquid rising flow 

inside a very thin layer of thickness about O.5mm. This liquid stratification does not play the role 

in the ullage temperature stratification and pressure dynamics and does not lead to breach of 

condition NPSP = Pull + PIJead - P ;ric - Ps,va/TJ > 30 psi for the net positive suction pressure due 

to the high hydrostatic head pressure P head near the feedline bottom. 

12. 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 ~~,~' = O.26{£ . The mass flow rate 

of injected hot GOx is much moreJGo (t) 2.6~ (nnOZ leI 3), n nozzle is nozzle number in the 

SLS. 

13. The vertical vibrations with the amplitude Ayibr and the frequency fyibr such as 

A,'ibr > Ac = O.lmm(lOOHz 1/ "ib,.)2J3 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. 

14. 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=Ts(PGoJ . The rate of the condensation can 

reach :~:; = 0.45kg I sec and thickness, volume, and mass of surface heated hazard layer can 

34 
reach Ll =5cm, V=1.4m3

, and 1570kg, relatively. Total mass of LOX in the tank is 

627,500kg x(nn= /e / 3). 

15. A possible hazard is related to the increased length of the tank and the feed line joining 

LOx tank with the engines in the SLS. The height of the tank for SLS with 5 engines is about 

25m and length of the feed line is about 50m. The hydrostatic head pressure near the bottoms 

of the tank and the feedline are 2.6amt and 9.2atril, respectively. The rocket acceleration during 

the fight reaches 2.5go causing the pressures to increase to 17atm and 29 atm, respectively. 

Such high hydrostatic pressures have to be taken into account in the process of manufacturing 

the feedline and the engine pumps with LOx propellant. 

References 

[1J External Tank, Propulsion Data Book, No. 80900200103, Lookheed Martin, 2005. 

[2] "STS-115 ET-MPS Predicted Performance", Marshall Space Flight NASA Center Report, 

4160JP-06-4011 , Aug ust, 2006. 

[3] L. Norquist, "External tank for the Space Shuttle Main Propulsion System", J. Spacecraft, 

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