AIAA-2000-0858 Paper

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AIAA-00-0858Microgravity Geyser and Flow FieldPredictionR.J Thornton and J.I. HochsteinThe University of Memphis

Memphis, TN

7/27/2019 AIAA-2000-0858 Paper


AIAA-00-0858

American Institute of Aeronautics and Astronautics1

MICROGRAVITY GEYSER AND FLOW FIELD PREDICTIONR.J. Thornton*, and J.I. Hochstein†,

The University of Memphis

Memphis, Tennessee

ABSTRACT

Modeling and prediction of flow fields and geyser formation in microgravity cryogenic propellant tanks

was investigated. A computational simulation was used

to reproduce the test matrix of experimental results

performed by other investigators, as well as to model

the flows in a larger tank. An underprediction of geyser height by the CFD code led to a sensitivity study to

determine if variations in surface tension coefficient,

contact angle, or jet pipe turbulence significantly effect

the simulations, it was determined that computationalgeyser height is not sensitive to slight variations in any

of these items. An existing empirical correlation based

on dimensionless parameters was re-examined in aneffort to improve the accuracy of geyser prediction.

This resulted in the proposal for a re-formulation of two

dimensionless parameters used in the correlation; the

non-dimensional geyser height and the Bond number. It

was concluded that the new non-dimensional geyser height shows little promise. Although further data will

be required to make a definite judgement, the

reformulation of the Bond number provided correlations that are more accurate and appear to be

more general than the previously established correlation.

NOMENCLATURE

a = Acceleration

Bo = Bond Number

D = Diameter F = Flow Characterization Parameter G = Non-Dimensional Geyser Height R = Radius

We = Weber Number

ρ = Density

σ = Surface Tension Coefficient

Subscripts

AYD = Aydelott

j = Jet at the Liquid-Vapor Interface

* Research Assistant, Mechanical Engineering, Member AIAA† Professor/Chair, Mechanical Engineering, Member AIAA

Copyright © 2000 The American Institute of Aeronautics and Astronautics Inc.

All rights reserved.

o = Jet Pipe Outlet RF = Re-Fitt = Tank

TH = Thornton-Hochstein

tj = Tank/Jet

INTRODUCTION

Often spacecraft missions require the vehicle to store

rocket propellants for future use. In the case of

cryogenic liquid propellants, tank self-pressurizationcan be a significant problem. Despite insulation,

incident solar radiation heats the cryogenic fluid

causing liquid to vaporize and raise the pressure inside

the tank. If this self-pressurization were allowed to

continue unchecked, the tank would rupture. A stronger tank could help, but this would require an undesirable

increase in vehicle mass. Another solution to the tank

pressurization problem is to vent the tank. Tank ventingis undesirable because it wastes valuable propellant. In

addition, due to the lack of gravity to positively orient

the propellant in a predictable manner, it would beimpossible to locate a vent where it could be certain

that only vapor would be vented. In fact, even in partially filled tanks, it is possible that the entire tank

surface could be wetted due to the influence of surface

tension in a microgravity environment.

An alternative solution to the tank self-pressurization

problem is a Thermodynamic Vent System, or TVS1, 2.The TVS would extract a small portion of the bulk

liquid from the tank and pass it through a Joule-

Thomson valve resulting in a reduction in temperature

as well as pressure. Once cooled, the fluid would berouted through a heat exchanger, which is used to cool

a separate flow of propellant extracted from the bulk

liquid. If the fluid leaving the Joule-Thomson valve is a

two-phase mixture, it will continue changing phase inthe heat exchanger until it is completely vaporized and will eventually be sacrificially vented overboard. The

other stream of cooled liquid could then be pumped

from the heat exchanger back into the tank and injected through an axial jet pipe located at the fore end of the

tank. The jet flow provides several benefits including

mixing of the bulk liquid, which helps to reduce

temperature gradients and in turn helps prevent

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evaporation of the propellant. Introduction of the cooled

liquid also reduces the temperature of the bulk fluid. Inaddition, if the jet has a moderate amount of momentum

it can cause the formation of a geyser at the

liquid/vapor interface. The increased surface area of the

free surface due to the formation of a geyser would help

promote condensation, thus reducing the pressure evenfurther. At higher levels of jet momentum, the geyser

will strike the opposite end of the tank and either form a

separate pool or “roll” down the tank walls re-mixingwith the bulk fluid. As the fluid comes around the tank

walls, there will also be a cooling effect on the wall.

However, the addition of excessive kinetic energy tothe bulk fluid would eventually result in undesirable

heat generation through viscous dissipation.

A morphology has been defined based on four distinct

flow patterns that occur when an axial jet is injected into the bulk liquid region of a propellant tank in a

microgravity environment

1

. These flow patterns aredefined as follows (Figs. 1 and 2):

I. Dissipation of the jet in the bulk liquid region.

II. Geyser Formation.

III. Collection of jet liquid in the aft end (opposite of the jet inlet) of the tank.

IV. Liquid circulation over the aft end of the tank and

down the tank walls re-mixing with the bulk liquid.

Fig.1. Flow Patterns I and II.

The ability to predict the flow pattern for any given

combination of tank geometry, tank fill level,

gravitational acceleration, and jet momentum is crucial

for optimization and implementation of a TVS. A studyof geysers and their formation is therefore a necessary

task in the development process of the TVS concept.

Fig. 2. Flow Patterns III and IV.

COMPUTATIONAL MODEL, ECLIPSE

The complexity and expense of microgravityexperimentation severely limits the amount of data that

can be, and has been, collected on microgravity geyser formation. Therefore, an attractive alternative is the use

of CFD, computational fluid dynamics, to model the

geyser flows. The use of a CFD code can significantlyreduce the cost of investigating the microgravity geyser

phenomena, as well as allow for easy manipulation of

parameters such as tank size, fluid properties, jetmomentum levels, and gravitational acceleration levels.

The ECLIPSE code was used for the computational

studies in this work. ECLIPSE was chosen for its

previously demonstrated ability to model themicrogravity geyser flows of interest here3, 4. ECLIPSE

has evolved from the RIPPLE5 code developed at Los

Alamos National Laboratory. RIPPLE is a descendent

of the NASA VOF2D code, and was developed tomodel “transient, two-dimensional, laminar,

incompressible fluid flows with free surfaces of general

topology.”5

The flow field is discretized into finitevolumes to form a regular non-uniform mesh. RIPPLE

models free surfaces with volume of fluid (VOF) data

on the mesh, and a continuum surface force (CSF)

model is used to model surface tension. Staggered grid

differential equation approximations result in a systemof algebraic equations that are solved by a two step

projection method employing an incomplete Choleskyconjugate gradient (ICCG) solution technique for the

pressure Poisson equation (PPE)5. One of the features

added to RIPPLE to produce ECLIPSE is the

implementation of the two-equation Jones-Launder-

Pope k −ε turbulence model.

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Computational Model Fidelity and Sensitivity

It has been demonstrated that ECLIPSE and its predecessors do a credible job of predicting geyser flow

pattern as defined by the four-pattern morphology

previously presented 1. Given the dearth of low-gravity

geyser data, test cases in these previous studies

included configurations with gravity levels as high as 1-g. The focus of the present research was on low-gravity

environments with completely turbulent jets, which

reduced the pool of available experimental data to only14 test cases in which a geyser was formed, (Flow

Pattern II). Fig. 3 shows the measured geyser height,

displayed in dimensionless form, as a function of theWeber number and Bond number as defined by

Aydelott2.

Boa R

j

= =

ρ

σ

2

acceleration force

surface tension force(1)

WeV R

D

o o

j

= =

ρ

σ

2 2inertia force

surface tension force(2)

Gh

R

g

t

= =

geyser height

tank radius(3)

Also displayed in Fig. 3 are the geyser heights predicted

by ECLIPSE for these cases. Although the correct flow pattern is indeed predicted, the computational

predictions consistently underpredict geyser height.

This underprediction averages 44% with a standard

deviation of only 9.4% about this mean. Although this

level of agreement should be useful for predictingtrends, and has been useful for predicting flow patterns,

it prompted an investigation into the sensitivity of the

computational simulation to user specified parameters;surface tension coefficient, contact angle, and inlet

turbulence quantities.

Aydelott’s experiments were conducted in plexiglas

tanks that were cleaned with the utmost care prior to

filling with ethanol; even a small amount of

contaminant can significantly alter the surface tension

coefficient, σ . The literature does not indicate that any

of the physical properties of the fluid were measured

and it appears that all calculations related to theexperiments have been performed using standard

published values for these properties. To study the

sensitivity of the simulation to the value of σ ,simulations of a case with a measured geyser height of

6.5 cm and a computationally predicted height of 3.66

cm were rerun with σ specified to be 90% and 80% of

Fig. 3. Aydelott’s experimental non-dimensional geyser heights1 and computational simulations of these

experiments as a function of Weber and Bond number.

Experimental Non-Dimensional Geyser Height

Computational Non-Dimensional Geyser Height

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the published value for ethanol. Reducing sigma by

20% resulted in an 8% (0.31 cm) increase incomputationally predicted geyser height. Although this

is a small improvement, it does not fully account for the

difference between predicted and measured heights.

Further, although the lower value improves the

predictions, and the lowered value might be appropriateif there was a slight contamination of the ethanol, there

is no evidence in the literature that there was

contamination and there is no rationale for selecting aspecific value for sigma other than the standard

published value. In fact, because the value of σ is sosensitive to even slight contamination of the fluid, it is

somewhat comforting to know that the predicted geyser

height is not particularly sensitive to the value of this parameter.

The second parameter to be examined in the sensitivity

study is the contact angle between the liquid and the

tank wall, α . Actual propellant/aluminum/vapor combinations and the experiment ethanol/plexiglas/air

combinations exhibit very small contact angles. Toavoid divide-by-zero difficulties in the simulations, the

contact angle in the standard simulations has been

specified to be 2 degrees. A sequence of simulations

was run with increasing values of α for the same test

case that was used for the σ -sensitivity study.

Increasing α all the way to 30 degrees resulted in anincrease in predicted geyser height of only 0.3%. It is

therefore concluded that geyser height is relatively

insensitive to contact angle.

The final group of parameters examined as part of thesensitivity study are the turbulence kinetic energy, κ ,

and the turbulence energy dissipation rate, ε , at the exitof the jet-pipe. Standard simulations are run using

values computed using published correlations for fully

developed flow in a pipe. To examine the sensitivity of

geyser height to this fairly crude assumption, three

additional simulations were performed. The first used values for these parameters were simply half of the

values computed from the correlations. The second and

third used values of κ were selected to produce aturbulent viscosity at the pipe outlet equal to 10% and

1% (respectively) of the fully developed value. The

increase in geyser height was less than 8% for any of these cases. Although this is an improvement in the

predictive accuracy of the computational simulation,

there is no clear rationale for using these reduced

values. Again, as concluded for the σ -sensitivity study,

it is comforting to show that geyser height is not

particularly sensitive to the specified value of κ or ε and

all standard simulations for this study were performed

using values computed using the standard correlationsfor full developed pipe flow.

What conclusions can be reached about the fidelity of

the computational model? In the past, thecomputational model has been asked to simply predict

which of the four flow patterns will be produced by a

given jet/tank/filling combination and it still does so

with good reliability. For the present research, the

more challenging task of accurately predicting geyser height for flow pattern II configurations was selected as

the fidelity criterion. The computational simulation

consistently underpredicts geyser height with a standard deviation about the mean error of less than 10%.

Although the source of this error has not been

identified, it seems to be consistent. A sensitivity study

to examine the influence of σ , α , κ inlet , and ε inlet on

simulated geyser height was conducted because it wasfelt that these parameters were the most likely to have

different values between the simulation and the

experiment. Although the simulations predictive

accuracy could be improved by changing σ , κ inlet , and

ε inlet in a reasonable manner, a sound justification for making these changes could not be established. It is

reassuring to note that although the predictions

improved, the predicted geyser height is not particularlysensitive to these parameters that may not be known á

priori with great precision in a spacecraft design

environment. Based on all of this information, it was

concluded that ECLIPSE is still a very useful tool for predicting jet-induced flow patterns in a propellant

tank, that it consistently underpredicts geyser height,

and that it should be useful for exploring the

relationships between the various parameters that

influence geyser production in a low-gravity

environment.

DIMENSIONLESS MODELING

Small scale testing was conducted during the late

1970’s and 1980’s to investigate the geyser phenomena.

Through drop tower testing performed in the NASA

LeRC Zero Gravity Facility, Aydelott2 determined that

the inertia, acceleration, and surface tension forces arethe primary factors affecting geyser formation in a

microgravity environment. From these forces, he

deduced that the main parameters in the dimensional

analysis should be the jet velocity, liquid density and surface tension, acceleration environment, geyser

height, and selected characteristic lengths. Using theBuckingham Theorem, Aydelott established three

dimensionless groups pertinent to predicting geysers

and geyser height. These dimensionless groups are the

jet-Bond number Bo, the Weber number We, and a non-

dimensional geyser height G. Aydelott formed hisdimensionless groups as presented in Equations (1), (2),

and (3) above.

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Aydelott concluded from his data that a linear relation

existed between the non-dimensional geyser height and the Weber number. He also assumed that the non-

dimensional geyser height should be inversely

proportional to the Bond number. Through a least-

squares deviation curve fit of turbulent experimental

data the following geyser height prediction correlationwas developed by Aydelott:

F We

Bo=

− +

+

0 5 16

1 0 6

. .

.(4)

where F is the flow characterization parameter and is

expected to equal the dimensionless geyser height, G.

To formulate a reliable correlation applicable to

propellant tank microgravity geyser prediction ingeneral, it is necessary to not only recognize the proper

dimensionless groups, but also identify the proper length scales in these parameters. As seen in Equations

(1), (2), and (3) Aydelott uses three different length

scales, the tank radius Rt , jet pipe radius Ro, and the jetradius at its point of impact with the liquid-vapor

interface R j. The shape and curvature of the liquid-

vapor interface once a geyser begins to form becomes

quite complex (Fig. 4). Therefore, the determination of an appropriate length scale must take into account

whether the formation of a geyser is dependent on

“local” effects (i.e. in the vicinity of the actual geyser),“global” effects (i.e. tank scale effects), or a

combination of the two.

Fig. 4. Typical free surface shape of a microgravity

geyser.

Non-Dimensional Geyser Height, G

Aydelott’s experimental correlation was formulated with Weber and Bond numbers dependent only on the

jet properties making them “local” parameters. If the

“local” effect only model is accepted, and Aydelott’s

original formulations of Bo and We are assumed to be

appropriate, it seems reasonable that the non-dimensional geyser height should also be scaled with

the jet radius instead of the tank radius. It should be

noted that all of Aydelott’s experiments were conducted in configurations with the same tank radius to jet radius

ratio. Therefore, it is possible that Aydelott’s

correlation may not perform well when applied to tankswith a tank to jet radius ratio that is different from the

experiment configuration; while a reformulation of the

non-dimensional geyser height to include the jet radius

may provide improved accuracy.

The proposed new non-dimensional geyser height uses

the jet diameter at the liquid-vapor interface determined by approximate expressions2.

Gh

DTH

g

j

= (5)

Several analyses have been made to determine the

validity of this new non-dimensional geyser height,

GTH , utilizing Aydelott’s experimental data as well as

computational data.

Bond Number, Bo

The Bond number is the ratio of acceleration force tosurface tension force, and can have both “local” and

“global” effects on geyser formation. In a no geyser

situation, the tank Bond number will dictate the shapeof the free surface, and at least partly so in a geyser

situation. Three different formations of the Bond

number were considered for the geyser problem. The

jet-Bond number Bo or Bo j (Equation (1) used byAydelott), the tank Bond number Bot (using the tank

diameter as the characteristic length scale, Equation

(7)), and a combination tank/jet-Bond number Botj (using the tank and jet diameters, Equation (8)).

Bo a Dt

t =

ρ

σ

2

(7)

Boa

tj

D Dt j

=

ρ

σ

c h(8)

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Although in certain circumstances, the “local” or

“global” surface tension effects may dominate the physics of geyser formation, most cases are likely to

involve both. Incorporating the tank or tank/jet-Bond

number may be a feasible way to account for both

“local” and “global” surface tension effects. An

investigation was conducted to determine if either Bot or Botj could be used to produce a correlation with

better predictive ability than the existing correlation

based on Bo j.

Weber Number, We

The Weber number is the ratio of the inertia force to

surface tension force. In the geyser problem, the Weber

number primarily describes the interaction between the

momentum of the jet impacting on the free surface and the restoring force due to surface tension. Therefore, the

jet-Weber number (Equation (2)) used by Aydelott still

appears to be the appropriate formulation, and has

therefore been employed throughout this study.

NON-DIMENSIONAL GEYSER HEIGHT STUDY

A combination of experimental and computational data

was used to evaluate the predictive utility of the proposed dimensionless geyser height. The

experimentally measured and computationally predicted

geyser data presented in Fig. 3 was supplemented with

the results of several additional simulations. Twelve

simulations were run using the same tank as the

experiment but with parameter values specified to provide a better spread of data over the We- Bo space of

Fig. 3 than was available from the experiment. Another set of cases were defined to almost duplicate the

experiment conditions except for a tank with a diameter

equal to 150% of the diameter of the experiment tank.

It should be remembered that the computationalsimulations consistently underpredict geyser height.

Therefore, in the following evaluations, computational

and experimental data are segregated as appropriate.

All of the correlations developed in this study were produced using a least-squares regression method. The

root mean square (RMS) error between a correlation’s

predicted geyser height and that measured in theexperiment, or predicted directly by the simulations,

was selected as the measure of quality for this study.

Experiment Data - Experiment Correlations

The first correlation presented in Table 1 is the original

correlation, (Equation (4)), developed by Aydelott for

all of his experiments including cases not part of the present study. The second correlation is a refit of the

original formulation using only the data presented inFig. 3. The third correlation uses the same formulation

but replaces the tank radius with the jet impact diameter

to form the new dimensionless geyser height, GTH .As can be seen from Table 1, the refit of the original

correlation provided a slight improvement in the

correlation’s accuracy for the Fig. 3 data, while the use

of the newly proposed non-dimensional geyser height

resulted in a decrease in accuracy. Fig. 5 presents themeasured non-dimensional geyser heights (G) as a

function of these three flow characterization parameters

(F ). It also shows three straight lines representing alinear fit to each of the data sets using these three

formulations.

Table 1. Experimental data correlation results.

Fig. 5. Experimental non-dimensional geyser height asa function of the three formulations of Table 1

(lines are linear fit to each correlation’s data set).

Computational Data - Experiment Correlations

The experimental tests were all simulated with

ECLIPSE, as were similar cases with the 50% enlarged tank. The geyser heights of these simulations where

predicted using the same three correlations of Table 1

developed strictly from experiment data. Although thequality of the predictions was significantly lower than

Table 1 because the simulations consistently

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7

Flow Characterization Parameter F

N o n - D i m e n s i o n a l G e y s e r H e i g h t G

New G Correlation

Original G Refit Correlation

Original Correlation

Original G Refit Correlation

New G Correlation


Corelation Expression RMS Error

Aydelott 0.203

Aydelott Refit 0.190

New

Formulation

G TH

0.388

F We

Bo AYD =

− +

+

0 5 16

1 0 6

. .

.

F

We

Bo AYD RF /

. .

.=

− +

+

0 34 145

1 0 63

F We

BoTH =

− +

+

3 43 5 69

1 198

. .

.

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underpredict geyser height, the relative performance of

the correlations was not different from that of Table 1.

Computational Data - Computational Correlations

Computational Data for the Experiment Tank

Geyser heights predicted by the computationalsimulations for the original experiment conditions were

used to refit the original correlation formulation, and

the new non-dimensional geyser height formulation, to produce the results presented in Table 2. The

experiment tank has a 0.4 cm diameter jet pipe,

hemispherical heads, a 10 cm diameter, and a total

length of 20 cm. The new formulation does not

outperform the original formulation.

Table 2. Correlations from original tank computational

data only.

Computational Data for the Enlarged Tank

The conditions of the experiment cases were

reproduced in a tank with a diameter equal to 150% of

the diameter of the experiment tank. This “enlarged”tank has a 15 cm diameter and a total length of 25 cm.

The resulting data was again used to fit the two

correlations and once again the new formulation did not

outperform the original one.

Table 3. Correlations from enlarged tank computational

data only.

Correlations Based on Data from Both Tanks Applied to Both Tanks

The computational data from both tanks was used to fit

correlations for both non-dimensional geyser heights.Table 4 outlines these results. Fig. 6 is a plot of the non-

dimensional geyser height and flow characterization

parameter for both tanks.

Fig. 6. Computational non-dimensional geyser height

for both tanks as a function of the two formulations of Table 4 (lines are linear fit to each correlation’s data

set).

Table 4. Correlations from computational data of both

tanks.

Original Tank Correlations Applied to Enlarged Tank

In an actual design situation, the correlation from a test

tank will be applied to a different sized tank. To seehow the two versions of the correlations perform when

applied to tanks of differing size, the original tank

computational correlations (Table 2) were used to

predict the geyser height in the enlarged tank. Table 5outlines these results.

Table 5. Results of the original tank correlationsapplied to the enlarged tank data.

0

1

2

3

4

5

0 1 2 3 4 5



New G Correlation



New G Correlation

Correlation Expression RMS Error

Aydelott 0.155

New

Formulation

G TH

0.172

F We

Bo AYD =

− +

+

0 014 0 73

1 0 71

. .

.

F We

BoTH =

− +

+

0 48 176

1 116

. .

.


Aydelott 0.121

New

Formulation

G TH

0.158

F We

Bo AYD =

− +

+

0 028 0 66

1 114

. .

.

F We

BoTH =

− +

+

0 29 182

1 119

. .

.


Aydelott 0.160

New

Formulation

G TH

0.179F We

BoTH =

− +

+

0 43 185

1 122

. .

.

F We

BoTH =

+

0 66

1 083

.

.


Aydelott 0.200

New

Formulation

G TH

0.219

F

We

Bo AYD =

− +

+

0 014 0 73

1 0 71

. .

.

F We

BoTH =

− +

+

0 48 176

1 116

. .

.

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Enlarged Tank Correlation Applied to Original Tank

The enlarged tank computational correlations (Table 3)were used to predict geyser height in the original tank.

This is the only case where the newly proposed non-

dimensional geyser height matched the accuracy of the

original non-dimensional geyser height correlation.

Table 6. Results of the enlarged tank correlations

applied to the original tank data.

G Study Summary

As can be seen from Tables 1-6, the desired

improvement using the jet diameter normalized non-

dimensional geyser height was not realized. In all but

one case (the enlarged tank correlations applied to the

original tank), the original correlation was moreaccurate in predicting geyser height. It is possible that

as more data for a wider variety of configurations

becomes available it may appropriate to reinvestigate

the GTH formulation for the non-dimensional geyser height parameter. However, given the currently

available data, the present study leads to the conclusion

that the original formulation is superior and should beused.

BOND NUMBER RE-FORMULATION

To determine if the tank-Bond number, Bot , or the

tank/jet-Bond number, Botj , can provide improved

geyser prediction, correlations were refitted in a manor similar to the non-dimensional geyser height study.

These refitted correlations were based-on the original

experimental data as well as the computational predictions for both the original and the enlarged tank.

Experimental Data - Experiment Correlations

Again, the experiment data was used as a starting point

for the correlation study. Table 7 presents a summary of the performance of the Bot correlation, the Botj

correlation, and the original Aydelott correlation ( Bo j),in predicting experimentally measured geyser height.

The Bot correlation shows a slight improvement over

the original correlation whereas the Botj correlationshows a whopping 35% improvement in predictive

accuracy. Ideally, a correlation would result in a direct

prediction of G, (i.e. F = G). This is precisely the result

indicated in Fig. 7 where it can be seen that the linear

fit to both the Bot and the Botj correlation data sets haveslopes near unity and would pass nearly through the

origin.

Table 7. Experimental data correlations for various

Bond number formulations.

Fig. 7. Experimental non-dimensional geyser height as

a function of the three Bond number correlationversions of Table 7 (lines are linear fit to each

correlation’s data set).

Computational Data - Computational Correlations

Again, to study the effects of different tank configurations the computational data from the original

and enlarged tanks were used in various combinations

to study the performance of the proposed correlations.

Original Tank DataTable 8 presents the predictive performance of the three

formulations using coefficients determined fromsimulated geyser heights for the original tank when the

correlations are applied to precisely that data set. Again

the Bot correlation slightly outperformed the originalcorrelation and the Botj correlation was the best

performer resulting in a 19% improvement over the Bo j

correlation.

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3 3.5



Jet-Bo Correlation (Aydelott)

Tank-Bo Correlation

Tank/Jet-Bo Correlatioin

Jet-Bo Correlation

Tank/Jet-Bo Correlation

Tank-Bo Correlation


Aydelott 0.223

New

Formulation

G TH

0.221

F We

Bo AYD =

− +

+

0 028 0 66

1 114

. .

.

F We

BoTH =

− +

+

0 29 182

1 119

. .

.


Tank-Bond

Number 0.234

Tank/Jet-

Bond

Number

0.161

Jet Bond

Number 0.250

F We

Bo Bo

t t

=− +

+

0 57 160

1 0 016

. .

.

F We

Bo Bo

tjtj

=− +

+

0 60 186

1 0 079

. .

.

F We

Bo Bo

j j

=− +

+

05 16

1 0 6

. .

.

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Table 8. Original tank computational data correlations

for various Bond number formulations.

Enlarged Tank Data

Table 9 presents the predictive performance of the three

formulations using coefficients determined from

simulated geyser heights for the enlarged tank when thecorrelations are applied to precisely that data set. In this

instance, both the Bot and the Botj correlationssignificantly outperformed the Bo j correlation by 49%

and 29% respectively.

Table 9. Enlarged tank computational data correlations

for various Bond number formulations.

Correlations Based on Data from Both Tanks Applied to Both Tanks

The computational data from both tanks was used to fit

all three correlations. Table 10 and Fig. 8 present the performance of these correlations. All three correlations

seem to provide the desired “direct” prediction of

geyser height, (G = F ). However, an error reduction of

approximately 30% can be noted for either the Bot or

the Botj correlations compared to the Bo j correlation.

Table 10. Both tank computational data correlations for

various Bond number formulations.

Fig. 8. Computational non-dimensional geyser height

for both tanks as a function of the three Bond number

correlation versions of Table 10 (lines are linear fit to

each correlation’s data set).

Original Tank Correlations Applied to Enlarged Tank

Again, the correlations developed from the original tank

computational data were applied to the enlarged tank.

This was done to give some indication of theapplicability of the correlations developed from a test

tank to a different size tank. Table 11 shows the results,

this time with the Bot correlation yielding an RMS error

reduction of 38% over the Bo j correlation.

0

0.5

1

1.5

2

0 0.5 1 1.5 2


N o n - D i m e n s i o n a l G e y s e r

H e i g h t G

Jet-Bo Correlation

Tank-Bo Correlation


Jet-Bo Correlation

Tank-Bo Correlation



Tank-Bond

Number 0.131

Tank/Jet-

Bond

Number

0.125

Jet Bond

Number 0.155

F We

Bo Bo

t t

=− +

+

0 25 0 95

1 0 023

. .

.

F We

Bo Bo

tjtj

=− +

+

0 20 0 96

1 0 081

. .

.

F We

Bo Bo

j j

=− +

+

0 014 0 73

1 0 71

. .

.


Tank-Bond

Number 0.062

Tank/Jet-

Bond

Number

0.086

Jet Bond

Number 0.121

F We

Bo Bo

t t

=− +

+

014 0 76

1 0 013

. .

.

F We

Bo Bo

tjtj

=− +

+

0 082 0 72

1 0 062

. .

.

F We Bo

Bo

j j

=− +

+

0 028 0 661 114. .

.


Tank-Bond

Number 0.108

Tank/Jet-

Bond

Number

0.116

Jet Bond

Number 0.160

F We

Bo Bo

t t

=− +

+

014 0 78

1 0 015

. .

.

F We

Bo Bo

tjtj

=− +

+

0 084 0 77

1 0 062

. .

.

F We

Bo Bo

j j

=

+

0 66

1 083

.

.

7/27/2019 AIAA-2000-0858 Paper



Table 11. Original tank computational data correlations

applied to the enlarged tank.

Enlarged Tank Correlations Applied to Original Tank

Likewise, the enlarged tank correlations were applied to

the original tank with similar results, (Table 12).

Table 12. Enlarged tank computational data correlations

applied to the original tank.

Bond Number Study Summary

As can be seen from Tables 7-12, the Bot and Botj correlations consistently outperform the Bo j correlations

in prediction of geyser height. This holds true for both

the experimental and the computational data sets.

Figure 7 shows the improved predictive capability withthe best performance produced by the Botj correlation.

F We

Botj

=

− +

+

0 6 186

1 0 079

. .

.(9)

Based on the data and analyses presented, it isrecommended that this new correlation be used for the

design of future spacecraft propellant management

systems.

SUMMARY AND CONCLUSIONS

Design of future spacecraft propellant management

systems employing a Thermodynamic Vent System

(TVS) to suppress tank self-pressurization will require

prediction of geyser formation in the propellant pool.

Although an experiment-based correlation exists for predicting TVS jet-induced flow patterns in a propellanttank, the data on which this correlation has been

developed is very limited due to the high cost of

experimentation in a reduced-gravity environment.

Although very challenging, computational simulation provides a very attractive alternative to experimentation

for gaining insight into the geyser formation process

and for developing improved correlations for design.

The existing correlation assumes that the geyser heightcan be predicted if the jet-Bond number and the jet-

Weber number are known. To begin the present study,

the limited data set of drop-tower experiments wassimulated using the ECLIPSE code. Comparison

between experiment and simulation show a consistent

underprediction of geyser height within a relatively

narrow error band. A sensitivity study was undertakento determine if the underprediction was due to an

unexpectedly strong dependence of simulated geyser

height on user-specified parameters that may not be

precisely known for the experiments and also may not

be well know for real applications. This study showed that geyser height is nearly independent of contact

angle. Although it depends on the value of surfacetension coefficient and the jet inlet turbulence, geyser

height is not unexpectedly sensitive to these parameters.

To more fully populate the Bo-We space on whichdimensionless geyser height depends, twelve additional

computation-only data points were acquired, (using

ECLIPSE), to evaluate the predictive capability of

proposed correlations. All of the available experiment

data is for configurations with the same ratio of tank diameter to jet diameter. Therefore, another set of

computation-only data points was acquired, (using

ECLIPSE), for a larger tank/jet ratio to better evaluatethe range of applicability of the proposed correlations.

A re-evaluation of dimensionless parameters and

correlations previously used to predict geysers led to aninvestigation into reformulation of the non-dimensional

geyser height and the Bond number. Experimental and

computational data were employed to reformulate

geyser height prediction correlations. The quality of acorrelation’s prediction was judged by the RMS error

between predicted geyser height and either the

measured or computationally simulated geyser height.


Tank-Bond

Number 0.123

Tank/Jet-

Bond

Number

0.148

Jet Bond

Number 0.200

F We

Bo Bo

t t

=− +

+

0 25 0 95

1 0 023

. .

.

F We

Bo Bo

tjtj

=− +

+

0 20 0 96

1 0 081

. .

.

F We

Bo Bo

j j

=− +

+

0 014 0 73

1 0 71

. .

.


Tank-Bond

Number 0.145

Tank/Jet-

Bond

Number

0.152

Jet Bond

Number 0.223

F We

Bo Bo

t t

=− +

+

014 0 76

1 0 013

. .

.

F We

Bo Bo

tjtj

=− +

+

0 082 0 72

1 0 062

. .

.

F We

Bo Bo

j j

=− +

+

0 028 0 66

1 114

. .

.

7/27/2019 AIAA-2000-0858 Paper



Although a new formulation of the non-dimensional

geyser height was proposed after a re-examination of the physics of geyser formation, correlations base on

this new parameter showed consistently worse

performance in predicting geyser height than the

existing correlation. In only one instance did the results

of the new formulation match the original correlation’s predictive capability. It is therefore concluded that the

existing non-dimensional geyser height results in

superior predictive capability and should be used for future work.

In contrast with the failure of the dimensionless geyser height reformulation, correlations based on a new

formulation of the Bond number show great promise.

Correlations were developed based on three different

formulations of the Bond number. The existingcorrelation used the jet-Bond number, Bo j , in which thecharacteristic length is the diameter of the jet at impact

with the free surface. The first alternate formulationuses the tank diameter as the characteristic length to

produce the tank-Bond number, Bot . The characteristiclength of the second alternate formulation uses a

combination of the two, ( D Dt j

), to produce a

tank/jet-Bond number, Botj . Correlations based on these

alternate formulations consistently outperform the

correlations based on the “original” parameter, Bo j .Perhaps most striking is the 35% reduction in predictive

error when the Botj correlation is compared to the

original correlation for the experiment data on whichthe original correlation was based. It is hoped that the

correlations based on small-scale experiments will be

useful for predicting the performance of a TVS in anactual spacecraft tank. To test the sensitivity of thecorrelation’s predictive accuracy to changes in tank

size, correlations with coefficients computed for the

experiment tank were used to predict geyser formation

in a larger diameter tank, and vice-versa. In both cases,

the new Bond number formulations significantlyoutperform the existing formulation.

Future work should focus on increasing the quantity of reliable data on geyser formation in a reduced gravity

environment. Experimental data will be expensive and

time consuming to obtain. If the quality of the

computational simulation can be further improved, itmay provide a less expensive path to acquiring the

necessary information. The new correlations developed

during the present study show clearly improved

performance for the available data. These correlations,and the ECLIPSE code, are currently the best available

tools for predicting geyser formation in a reduced

gravity environment. As such, they should be used for

the design of future experiments and, where required,

for future spacecraft.

REFERENCES

1. Aydelott, J.C. “Axial Jet Mixing of Ethanol InCylindrical Containers During Weightlessness.”

NASA TP-1487, 1979.

2. Aydelott, J.C. “Modeling of Space Vehicle

Propellant Mixing.” NASA TP-2107, 1983.

3. Wendl, J.C., Hochstein, J.I., and Sasmal, G.P.

“Modeling of Jet-Induced Geyser Formation in a

Reduced Gravity Environment.” AIAA-91-0801,1991.

4. Wendl, M.C. "Jet Induced Mixing of Propellant in

Partially Filled Tanks in a Reduced Gravity

Environment." Magisterial Thesis. WashingtonUniversity, St. Louis, Missouri, 1990.

5. Kothe, D.B., Mjolsness, R.C., and Torrey, M.D.

“RIPPLE: A Computer Program for Incompressible Flows with Free Surfaces.” LA-

12007-MS, 1991

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