David J. Chato

Glenn Research Center, Cleveland, Ohio

Jeffery Marchetta and John I. Hochstein

University of Memphis, Memphis, Tennessee

Mohammad Kassemi

National Center for Space Exploration Research, Cleveland, Ohio

Approaches to Validation of Models for Low

Gravity Fluid Behavior

NASA/TM—2005-213832

September 2005

AIAA–2004–1150
The NASA STI Program Office . . . in Profile

Since its founding, NASA has been dedicated to

the advancement of aeronautics and space

science. The NASA Scientific and Technical

Information (STI) Program Office plays a key part

in helping NASA maintain this important role.

The NASA STI Program Office is operated by

Langley Research Center, the Lead Center for

NASA’s scientific and technical information. The

NASA STI Program Office provides access to the

NASA STI Database, the largest collection of

aeronautical and space science STI in the world.

The Program Office is also NASA’s institutional

mechanism for disseminating the results of its

research and development activities. These results

are published by NASA in the NASA STI Report

Series, which includes the following report types:

• TECHNICAL PUBLICATION. Reports of

completed research or a major significant

phase of research that present the results of

NASA programs and include extensive data

or theoretical analysis. Includes compilations

of significant scientific and technical data and

information deemed to be of continuing

reference value. NASA’s counterpart of peerreviewed formal professional papers but

has less stringent limitations on manuscript

length and extent of graphic presentations.

• TECHNICAL MEMORANDUM. Scientific

and technical findings that are preliminary or

of specialized interest, e.g., quick release

reports, working papers, and bibliographies

that contain minimal annotation. Does not

contain extensive analysis.

• CONTRACTOR REPORT. Scientific and

technical findings by NASA-sponsored

contractors and grantees.

• CONFERENCE PUBLICATION. Collected

papers from scientific and technical

conferences, symposia, seminars, or other

meetings sponsored or cosponsored by

NASA.

• SPECIAL PUBLICATION. Scientific,

technical, or historical information from

NASA programs, projects, and missions,

often concerned with subjects having

substantial public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientific

and technical material pertinent to NASA’s

mission.

Specialized services that complement the STI

Program Office’s diverse offerings include

creating custom thesauri, building customized

databases, organizing and publishing research

results . . . even providing videos.

For more information about the NASA STI

Program Office, see the following:

• Access the NASA STI Program Home Page

at http://www.sti.nasa.gov

• E-mail your question via the Internet to

help@sti.nasa.gov

• Fax your question to the NASA Access

Help Desk at 301–621–0134

• Telephone the NASA Access Help Desk at

301–621–0390

• Write to:

 NASA Access Help Desk

 NASA Center for AeroSpace Information

 7121 Standard Drive

 Hanover, MD 21076
David J. Chato

Glenn Research Center, Cleveland, Ohio

Jeffery Marchetta and John I. Hochstein

University of Memphis, Memphis, Tennessee

Mohammad Kassemi

National Center for Space Exploration Research, Cleveland, Ohio

Approaches to Validation of Models for Low

Gravity Fluid Behavior

NASA/TM—2005-213832

September 2005

National Aeronautics and

Space Administration

Glenn Research Center

Prepared for the

42nd Aerospace Sciences Meeting and Exhibit

sponsored by the American Institute of Aeronautics and Astronautics

Reno, Nevada, January 5–8, 2004

AIAA–2004–1150
Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

Available electronically at http://gltrs.grc.nasa.gov
NASA/TM—2005-213832 1

Approaches to Validation of Models for Low 

Gravity Fluid Behavior 

David J. Chato 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Jeffery Marchetta and John I. Hochstein 

The University of Memphis 

Mechanical Engineering Department 

Memphis, Tennessee 38152 

Mohammad Kassemi 

National Center for Space Exploration Research 

Cleveland, Ohio 44135 

Abstract 

This paper details the author experiences with the 

validation of computer models to predict low gravity fluid 

behavior. It reviews the literature of low gravity fluid 

behavior as a starting point for developing a baseline set of 

test cases. It examines authors’ attempts to validate their 

models against these cases and the issues they encountered. 

The main issues seem to be that: Most of the data is 

described by empirical correlation rather than fundamental 

relation; Detailed measurements of the flow field have not 

been made; Free surface shapes are observed but through 

thick plastic cylinders, and therefore subject to a great deal 

of optical distortion; and Heat transfer process time 

constants are on the order of minutes to days but the zerogravity time available has been only seconds. 

Introduction 

Each of the authors of this paper has extensive experience 

modeling low-gravity flow with Computational Fluid 

Dynamics. Dr. Chato, (refs. 1 and 2) working mostly with a 

NASA developed phase field model of the free surface, 

(ref. 3) Drs. Hochstein and Marchetta with the Volume of 

Fluid (refs. 4 and 5)-Continuum Surface Force (ref. 6) code 

ECLIPSE, and Dr. Kassemi with the finite element code 

FIDAP (ref. 7). All codes have their strengths and 

weaknesses and each author has had some success with his 

approach. One of the major hurdles each has encountered is 

a lack of validation data with which to compare his results 

with. Although much drop tower work was conducted in the 

sixties and seventies, it is typically published in a form 

which does not contain enough information to analyze the 

flow field. Most data is published in a few static 

photographs and the bulk of the data is compressed into an 

empirical correlation. Most of the raw drop tower film has 

been lost to the ravages of time. Even when film is 

available, flow visualization is not, so the velocity field is 

inferred rather than measured. At best, one can look at the 

injection of dye and infer the fluid motion roughly from that. 

The purpose of this paper is to examine what research is 

available and open a dialog within the research community 

as to where to go from here. 

The Role of Verification and 

Validation in CFD 

The computational community has spent a great deal of 

time trying to establish methods for insuring the correctness 

of their models. Verification and Validation (V&V) of 

simulations are becoming the primary means for increasing 

and quantifying confidence in computational results in many 

disciplines (ref. 8). Simply, verification is the assessment of 

the accuracy of the solution of a computer model by 

comparison with known solutions. Validation is the 

assessment of the accuracy of a computer model with 

experimental or ‘real’ world data. In verification, the ability 

of the simulation to accurately represent the ‘real’ world is 

not assessed. While the terminology has been used 

informally for years, quantitative V&V is beginning to be 

gain recognition as verification and validation science. In 

the United States, the Defense Modeling and Simulation 

Office (DMSO) of the Department of Defense has been a 

leader in the development of fundamental concepts and 

terminology for V&V (refs. 9 and 10). In addition, the 

Accelerated Strategic Computing Initiative (ASCI) program 

of the Department of Energy (DOE) has also taken a strong 

interest in V&V by recognizing the need for methods, 

procedures, and processes for properly performing and 

quantifying V&V. The field of computational fluid 
NASA/TM—2005-213832 2

dynamics (CFD) has been a pivotal leader in identifying the 

need for verification and quantifying confidence in 

simulation. 

Recognizing the value in both simulation and experiment, 

agencies have gradually shifted research funding more 

equitably in recent years. Despite this awareness, significant 

challenges exist in creating a cooperative working 

environment between computationalists and 

experimentalists. The major obstacle is that experiments 

designed for validation are different from traditional 

experiments. For example, a comparison of simulation 

results and experiment results requires a detailed 

characterization of experiment conditions and uncertainty 

estimation of the measurements. Traditionally, computer 

models were verified, numerical error estimates were 

established, and a minimal validation effort was performed. 

Modern validation activities adopt a tiered approach where 

uncertainty present in experimental parameters, initial 

conditions, and boundary conditions is incorporated into 

deterministic simulations. In essence, this merger emulates a 

nondeterministic simulation by performing multiple 

deterministic simulations that include the experimental 

uncertainty. 

A fundamental strategy has been adopted for verification 

and validation efforts. For verification, the assessment 

begins by the identification and quantification of errors in 

the discretized model. This error is a product of using 

numerical approximations to discretize the exact 

formulation. The accuracy of the computational solution is 

measured with respect to analytic solutions, or highly 

accurate numerical solutions. The second verification task is 

to identify errors in the computer implementation of the 

model or the program. Rigorous debugging activity and 

software quality engineering are essential trademarks of this 

portion of the verification effort. These two principle tasks 

can be distinguished as the difference between code 

verification and solution verification. Software developers 

are aware of the need for, and have been conducting 

extensive verification testing, as a standard practice for 

some time. Roache (ref. 11) provides a detailed 

methodology and procedures for performing verification 

assessment. It is only necessary to refer to this and a few 

related sources to highlight the need to appropriately 

identify tests that are relevant to microgravity simulation 

verification. Because verification assessment is so well 

defined, a summary is sufficient in emphasizing its 

partnership with validation. Although verification can be 

quite challenging, the issues faced by the low gravity fluid 

modeler are not significantly different from any other CFD. 

Verification will not be addressed further in this paper. 

Validation assesses how accurately the computational 

model results compare with experimental data, with 

quantified error, and with uncertainty. It is impossible to 

prove mathematically that a model is validated. Codes 

cannot be validated, only the individual outcomes of each 

simulation are validated. The level of confidence in 

computational predictions of complex physical processes 

can only be inferred from the level of the validation. A 

validation effort should be focused on evaluating the fidelity 

of the mathematical model and not on the solution accuracy 

of the discretized model. From this description, it is apparent 

that comprehensive verification should be performed prior 

to validation. 

In 1992, the AIAA Computational Fluid Dynamics 

Committee on Standards began standardizing the 

terminology, methodology, and philosophy of V&V 

activities in CFD. The AIAA guide (ref. 12) recommends a 

hierarchy for validation activities aimed at identifying 

appropriate experiments, coupled physical processes, and 

levels of complexity. A multi-tier approach begins with an 

experiment aimed at validating a single physical model and 

ends with experiments and simulations of complex 

engineering systems. The number of tiers depends on the 

ability to separate coupled physical processes and the ability 

to select or conduct experiments that are practical and that 

produce quality data for validation. In addition, physical 

complexity such as geometry, temporal character, and 

dimensionality may require additional layers of validation. 

Experiments should be reasonable and yield measurements 

of various system-response events for the purpose of testing 

the simulation. The ability to conduct validation 

experiments can be challenging on many levels. At the 

lowest level, it may be difficult to isolate individual physical 

processes in an experiment and then devise instrumentation 

to measure the events of interest. At the top-tier, the 

acquisition of validation measurements from complex 

systems is complicated by the operational infrastructure or 

hardware. The benchmark database should include 

measurements from a set of experiments designed to span 

several layers of complexity. The experiment must be well 

defined and performed to so that experimental uncertainty 

can be statistically estimated with precision. 

Oberkampf and Trucano (ref. 8) suggest several 

guidelines for designing and conducting validation 

experiments. Among these guidelines, they stress that 

validation experiments should be cooperatively designed by 

experimentalists, model developers, code developers, and 

code users. While joint activities are essential, consideration 

must be given to an experiment environment where results 

are obtained independently to avoid bias. The experiment 

should reflect the physics of interest, and the boundary and 

initial conditions to be used by the code, yet constructed to 

analyze and precisely determine the experimental errors. 

Most importantly, the experiment should embody the 

symbiosis between computational and experimental 

methods. A synergetic relationship between all components 

of the research community should propagate continual 

improvement, knowledge, and accuracy in both 

experimental and computational approaches. 

Although several benchmark databases for validation are 

under development, low gravity fluid behavior is not a 

phenomena included in any database of which the authors 
NASA/TM—2005-213832 3

are aware. It falls to the low gravity fluid behavior 

community to establish their own benchmark cases. The 

next section will present several classic problems of low 

gravity fluid behavior as possible benchmark cases. Note: 

the achievement of true benchmarks in other fields of CFD 

has required dedicated experiments, specifically designed 

with concept of code validation in mind, and there is every 

reason to expect this will also be the case for low gravity 

fluid behavior. 

Low Gravity Problems 

Static Meniscus Shape 

Analysis.—The meniscus problem has been investigated 

by many well known names in numerical modeling 

including Laplace, Rayleigh, Runge, Bashford, and Adams 

(ref. 13). At the beginning of the space age it was the subject 

of several investigations. Reynolds, Saad, and Satterlee 

(ref. 14) reduced the fundamental forces in an 

axisysmmetric free surface to a pair of differential equations 

and then solved them numerically over a parametric range of 

Bond number and wall contact angle. Concus (ref. 13) 

reduced the solution for a right cylinder to a single 

differential equation. He then solved the asymptotic cases of 

very large and very small Bond number analytically and the 

in between cases numerically. Hastings (ref. 15) is notable 

for a computer algorithm to solve for static free surfaces in 

ellipsoidal tanks. 

Drop tower tests.—Drop tower results confirm the 

predictions of analysis for many different shapes including a 

single right cylinder, (ref. 15) concentric cylinders, (refs. 16 

and 17) spheres and ellipsoids, (ref. 18) and even cones 

(ref. 19). The cylinder in a cylinder led to some early fluid 

positioning concepts tested both with water on a Mercury 

flight (ref. 20) and with liquid hydrogen on a sounding 

rocket (ref. 21). Salzman’s (ref. 18) work on spheres and 

ellipsoids is noteworthy for its discussion on the difficulties 

of trying to determine the free surface location from film of 

curved plastic tanks. The main issues are refraction of the 

interface image by the plastic and liquid; and the fact that 

the image of the interface usually appears as a dark band 

rather than a sharp line. 

Model validation.—To test the performance of the phase 

field free surface model (ref. 2) the free surface was allowed 

to move from a flat initial starting condition to the 

equilibrium free surface shape in zero gravity. The 

equilibrium shape in zero gravity, taken from the small bond 

number asymptote of Concus, (ref. 13) is a segment of a 

sphere whose radius is calculated from the following 

relationship for different contact angles 

( ) contact

tank

equiv cos θ = r

r (1) 

Figure 1 shows the evolution of equilibrium free surfaces 

from a flat interface. Agreement for the 60° contact angle is 

very good. Agreement for the 0° contact angle is also good 

except in the region near the wall. Grid resolution has 

truncated the tail of the free surface right at the wall. 

Agreement for the 30° contact angle is fair. Examination of 

the time sequence revealed a strong transient which had not 

quite damped out by the end of the run: as a consequence 

the profile is a little flatter than it should be. 

Meniscus shape in complex geometries.—An interesting 

extension of free surface shape analysis is the Surface 

Evolver code of Brakke (ref. 25) which uses energy 

minimization calculations to predict free surface shape in 

quite complex geometries. Tegart (ref. 26) showed the 

application of the model to actual tank shapes. Dominick 

and Tegart (ref. 27) used the code to compare predicted 

shapes in a complex vane liquid acquisition device with 

visual observation from the FARE II flight experiment. 

Collicott and Weislogel (ref. 28) working with Evolver by 

probing the eigenvalue of the free surface solution were able 

to understand the resistance to wetting of vaned devices. 

They used the theoretical predictions of Concus and Finn 

(ref. 29) to validate their modeling effort. In further work 

Collicott and Weislogel (refs. 30 and 31) extended their 

work to model the behavior of the Vented Tank Resupply 

Experiment (VTRE) (ref. 32) vane device flown as a 

Hitchhiker payload in the shuttle cargo bay, even to the 

extent of modeling the rewetting of the VTRE after an 

intentional spillage of the vane device by high maneuvers. A 

summary of their validation work with Surface Evolver was 

presented in 2003 (ref. 33). 

Issues.—Static Meniscus shape lends itself to analysis 

very well. Experimental data is extensive but limited by 

issues of optical quality. Validation against the analysis has 

proven successful even in cases involving complex 

geometries. 

Time to Reach Equilibrium Static Shape 

Analysis and drop tower test.—The time history of the 

evolution of the free surface for a 0° contact angle can be 

compared to the drop tower tests of Siegert (ref. 22). Siegert 

conducted a series of tests to determine the minimum time 

for fluid packages released in the drop tower to reach an 

equilibrium shape. Most of his results are recorded as the 

time the tip of the liquid interface first crosses the 

equilibrium position. The overall oscillation about the 

equilibrium was observed by Siegert (ref. 22) as well as 

other investigators such as Fung (ref. 23) and Hollister 

(ref. 24). However no quantitative data to determine the time 

accuracy of oscillations was presented. 

Model validation.—Siegert’s 4 cm tank was modeled 

with the phase field code (ref. 2). A time history of the free 

surface position at the centerline is plotted in figure 2. The 

time of first crossing is in excellent agreement with Siegert 
NASA/TM—2005-213832 4

Time oscillations of the free surface are also observed 

although their accuracy is unknown. 

Issues.—Time to reach equilibrium static shape has been 

estimated empirically, but a careful experiment to 

investigate the transients of the process would be useful. 

Reorientation 

Analysis and drop tower testing.—Because of its 

involvement in the Centaur program and its interest in 

low-gravity fluid behavior, the NASA has conducted 

extensive research on the settling thrust maneuver. Lacovic 

et al. (ref. 34) explain the Centaur system as well as the 

difficulties encountered during its development. The 

Centaur uses 27 N of thrust to settle (at settling Bond 

number of 360). In parallel with the Centaur development 

the settling maneuver was investigated in the drop towers. 

Masica and Petrash (ref. 35) explored the motion of vapor in 

inverted partially liquid filled long cylinders and were able 

to develop a correlation using the Bond number. This 

correlation agreed with both 1 g and drop tower tests and 

reduced to the theoretical prediction for the rise rate of large 

bubbles in normal gravity once the bond number exceeded 

12. Salzman and Masica (ref. 36) investigated the motion of 

liquid in propellant tank models. Results for bubble rise 

velocity agree with Masica and Petrash, (ref. 35) but the 

leading edge motion had to be corrected for the effect of the 

spherical tank bottom. They also observed that the liquid 

rebounded in a geyser along the tank center when Weber 

number based on this velocity and tank radius exceeded 4. 

Salzman, Masica, and Lacovic (ref. 37) conducted research 

in a scale model Centaur tank and suggested that far less 

thrust than is currently used would be capable of equivalent 

settling times. This is due to the following phenomena. 

Much of the energy used to start the fluid motion is stored as 

momentum in the bulk liquid. When the liquid reaches the 

bottom of the tank, this momentum causes the moving liquid 

to rebound as a geyser along the tank centerline. High thrust 

levels can even cause the falling liquid to entrain large 

quantities of gas. Sumner (ref. 38) revisited the tests of the 

Centaur development era to minimize the total impulse used 

for settling maneuvers. His work suggested that the 

optimum settling thrusts generate Bond numbers on the 

order of 4 to 6 (rather than 360), but lower thrust levels have 

not been used since the small thrusters required are not 

readily available. There was also the problem that at these 

Bond numbers the low gravity time available from drop 

tower testing was insufficient to observe the liquid settle to 

its final quiescent state, so estimates of settling time were 

extrapolated. 

Modeling.—The advance of digital computer technology 

has allowed low gravity fluids problem to be addressed via a 

different approach, modeling on the computer. Several 

techniques have been developed to model low-gravity fluid 

motion. The large deformation of the free surface during 

reorientation makes it difficult to model with a continuous 

free surface treatment, but several discrete methods have 

been evolved that are fairly successful: First, with the 

marker and cell algorithm which follows tracer particles; 

and then with the volume of fluid codes which move to a 

continuum within the bulk liquid while retaining the discrete 

nature at the free surface. Reorientation and settling have 

been used as a test case for these codes because the axial 

symmetry of the problem allow it to be addressed with a two 

dimensional code. Lacovic (ref. 39) was able to compare the 

simplified cell and marker code ERIE (Bradshaw and 

Kramer, (ref. 40) Bradshaw, Kramer, and Zich) (ref. 41) 

results to the Titan/Centaur flight data and show a favorable 

comparison. Hochstein, Korakianitis, Patag, and Chato 

(ref. 42) were able to match the work of Sumner with a 

modified version of NASA-VOF2D (ref. 4). They then used 

that model to study reorientation in two model tanks. 

Continuing that work, Hochstein et al (ref. 43) investigated 

the efficacy of pulsed thrust in emulating the lower thrust 

levels shown by Sumner to be desirable for efficient 

reorientation. Computational simulations of reorientation in 

a generic Space-Based Orbit Transfer Vehicle (SBOTV) 

propellant tank, and for a 1/5 scale model of that tank, led to 

definition of a settling function, Fs, that relates the vehicle 

delta-v incurred by the reorientation maneuver to the tank 

radius and the effective acceleration, (ae = (total 

impulse)/time). It was shown that for a Bond number of 10 

or greater, the concept of effective acceleration and the 

settling function were effective in correlating the 

computationally predicted reorientation performance for 

both tanks. Figure 3 shows the results and correlation. 

Issues.—Propellant Reorientation has a good 

experimental database to compare to and several useful 

correlations for key velocities. However drop tower time 

constraints prevent the observation of the process in its 

entirety. Model validation has been successful when the 

regime bond number is above 10, regimes below this 

acceleration will require further study. 

Tank Outflow 

Drop tower.—Tank outflow exhibits several interesting 

phenomena in low gravity. One is the draw down of the free 

surface. This results in ingestion of gas into the outlet even 

when a substantial amount of liquid remains in the tank. The 

other is the generation of a geyser from liquid momentum 

when outflow is stopped suddenly. Both of these cause 

trouble for the low gravity tank designer. As a consequence 

the phenomena has been investigated in a series of drop 

tower experiments including Derdul, Grubb and Petrash, 

(ref. 44) Grubb and Petrash, (ref. 45) Berenyi and Abdalla, 

(ref. 46) and Symons (ref. 47). 

Modeling.—Modeling of this phenomenon has been 

somewhat limited. The one model reported (ref. 48) is of 

some significance though because it represents one of the 
NASA/TM—2005-213832 5

first applications of the Volume of Fluid method to low 

gravity flows. 

Issues.—Tank outflow contains a good body of 

experimental data which has been underutilized for model 

validation. Data may be subject to the same optical 

problems as the static cases. 

Tank Inflow 

Drop tower.—Symons (refs. 49 to 52) and Spuckler 

(ref. 53) studied the liquid inflow via axial jet into a broad 

range of tank shapes both empty and partially full. Staskus 

(ref. 54) extends the work of Symons by placing baffles in 

front of the jet. However, no attempt is made to analyze 

these complex flows. Instead results are reported as a ratio 

of improvement to the unbaffled jet Weber number. Labus 

(ref. 55) also studied the effect of baffles including ones that 

break the central jet into several small jets. Aydelott 

(refs. 56 to 58) looks at the problem of a recirculating jet 

where the liquid level is held constant. Results are classified 

into four flow patterns, dissipation, geyser formation, aft 

collection, and circulation. Aydelott's assessment that a drop 

in mixing accompanies the geyser formation/aft collection 

transition indicates the transition's importance. 

Space shuttle.—The Tank Pressure Control Experiment 

(TPCE) has flown three times. The first flight focused on the 

mixing studies of Aydelott. Improvements included actual 

heat transfer data by using a condensing fluid 

(refrigerant 113) and longer duration. Bentz (refs. 59 to 61) 

was able to confirm the geysering and circulating regimes of 

Aydelott, but encountered an asymmetric regime between 

the two that was even more catastrophic to heat transfer than 

aft collection. The second flight of TPCE focused mostly on 

rapid boiling phenomena, but contained some further tests 

on mixing. Hasan (ref. 62) confirmed the findings of Bentz. 

The third flight (Bentz) (ref. 63) was done at a lower fill 

level but confirmed the results of the other flights. 

Computational simulations.—Unless countermeasures 

are provided, solar insolation of an on-orbit cryogenic 

propellant tank will cause evaporation of liquid propellant 

and consequent over-pressurization of the tank. Aydelott’s 

experiments (refs. 56 to 58) were part of a research program 

focused on one proposed countermeasure; a 

Thermodynamic Vent System (TVS). Sacrificial liquid is 

extracted from the tank, cooled by expansion through a 

Joule-Thomson valve, and vented overboard. Another 

stream of liquid is extracted from the tank, flows through a 

heat exchanger to be cooled by the sacrificial fluid and is 

then returned to the tank to suppress temperature rise, and 

thereby suppress evaporation. Hochstein, Gerhart, and 

Aydelott (ref. 64) added several physics modules and 

features to a derivative of the NASA SOLA-VOF Code 

(ref. 48) in an attempt to simulate the mixing induced by an 

axial-jet that reintroduces the cooled liquid to the propellant 

pool. Simulations of several of Aydelott’s experiments 

correctly predicted the flow regime but were less successful 

in accurately predicting geyser height for cases in which a 

stable geyser was observed. Computational predictions for 

temperature fields associated with jet-induced mixing in a 

typical Orbit Transfer Vehicle (OTV) tank were later 

published by Hochstein, Ji, and Aydelott (ref. 65). A further 

modified version of the same code was used to predict onorbit pressurization rates in the absence of an evaporation 

suppression system (Hochstein, Ji, and Aydelott) (ref. 66). 

Another attempt at directly modeling tank pressure history 

during autogenous pressurization, using the FLOW3D 

(ref. 67) was reported by Sasmal et al. (ref. 68) These 

simulations exposed a significant difference between the 

pressurization process in the presence of slush hydrogen as 

compared to the process in the presence of liquid hydrogen. 

Thornton and Hochstein (ref. 69) revisited the mixing 

tests of Aydelott with a computational model built upon the 

foundation of a newer code, (Kothe, Mjolsness, and Torrey) 

(ref. 5). These simulations were again in agreement with the 

observed flow pattern morphology and they were also in 

significantly better agreement with observed geyser heights 

for flows with a stable geyser. The computational simulation 

was used to expand the parameter space of the investigation 

in search of an improved correlation for the prediction of 

geyser height. The resulting correlation employs a jet Bond 

number in addition to the Bond number based on tank 

diameter used in Aydelott’s correlation. The new correlation 

outperforms the old one on both the original drop-tower data 

and the entire collection of geyser heights associated with 

the expanded parameter space. 

Chato (ref. 2) compared phase field model runs to the 

drop tower data of Aydelott. Figure 4 shows the comparison 

between predicted geyser height and fill level for a laminar 

model and the experiment. The model handed the free 

surface deformation, even to the point of modeling geyser 

growth in the regime where the free surface is no longer 

restrained. However, the restraining forces on Jets in the 

Reynolds number 630 to 900 range are seriously under 

predicted. This is believed to be due the lack of turbulence 

modeling which acts to spread the jet over a larger surface 

area thereby reducing the geyser height. Aydelott observed 

in his tests a spread angle of 2° for laminar jets but 12° for 

turbulence. This increased spread will lower the centerline 

velocity more quickly and increase the area of the jet at the 

free surface, decreasing the amount of surface deformation 

required to contain the jet. The under prediction at the 

Reynolds number 450 is harder to explain but is worse at 

low fill levels. It may be due to a slosh baffle at the 

33 percent fill level, which prevents development of a 

hemispherical interface in zero gravity. The baffle acts to 

raise the liquid height at the centerline and flatten the free 

surface, which lessens the surface tension force on the jet. 

This effect was most pronounced for runs with 29 percent 

liquid volume where the measured height of the free surface 

above the jet is actually higher than the runs with 39 percent 

liquid volume. It was considered that free surface height 
NASA/TM—2005-213832 6

above the jet was the more important parameter. Therefore 

model runs matched the free surface height not the liquid fill 

volume. 

In an effort to improve the prediction at higher Reynolds 

number flows a simple turbulence model was introduced. 

Simple mixing length models of turbulence suggest that, for 

the free jet, flow can be approximated by using a constant 

turbulent viscosity. Pope (ref. 70) using the experimental 

data of Hussien et al. (ref. 71) shows that turbulent viscosity 

is constant ±15 percent through the bulk of the jet although 

it does die down to 0 at the edge. Unfortunately Pope 

(ref. 70) gives this constant in a nondimensional form not 

readily available to use in this analysis. Schlicting (ref. 72) 

gives another formula for the average value of turbulent 

viscosity as a function of mean flow rate. Using this formula 

Ht = 0.158 g cm/s when the velocity is 34 cm/s and Ht = 

0.232 g cm/s when the velocity is 50 cm/s. It is a fairly 

simple matter to introduce this as a new viscosity for the 

bulk liquid. Figure 5 shows a comparison between steady 

state geyser heights from these models and the experimental 

geyser heights of Aydelott. The fully turbulent model 

overcorrects resulting in lower predicted geyser heights than 

experimentally measured. 

In an effort to improve the modeling of geyser height a 

parametric variation of the value of turbulent viscosity was 

conducted. Overall a 0.18 g cm/s viscosity was found to 

match the experimental data reasonably well. The model 

still under-predicted slightly most of the data but matched 

the 60 percent fill data very closely. Figure 6 shows a 

comparison between the predicted and measured geyser 

heights. 

Issues.—Tank inflow has been extensively studied 

experimentally. Model validation against this data has been 

only adequate. The core issue appears to be a lack of a 

detailed measurement of the flow field since the free surface 

shape seems quite sensitive to the level of turbulence in the 

inflow jet. Optical distortion is also an issue, particularly 

when the surface deformation is small. 

Pressure Rise and Stratification in Low Gravity 

Panzarella, and Kassemi (refs. 73 to 75) consider the 

difficult problem of low gravity stratification On the ground, 

the liquid normally settles to the bottom of the tank, but in 

microgravity, it may be anywhere. Since the contact angle of 

liquid Hydrogen is nearly zero, it is likely that it will 

completely wet the tank wall. Thus, the initial configuration 

considered by Panzarella, and Kassemi corresponded to the 

situation where the vapor has accumulated into a single 

spherical vapor region completely surrounded by liquid. The 

vapor region is free to evolve over time, and it was shown 

that under normal microgravity conditions it will reach the 

tank wall before there is any appreciable pressure rise. 

The liquid equations were solved by using an in-house 

modified version of the Galerkin finite element code FIDAP 

(ref. 7) that is extended by providing coupling with the 

lumped-vapor model. The temperature and velocity fields 

were discretized using 9-node quadratic elements, and the 

pressure was discretized using a linear discontinuous 

approximation (the three pressure unknowns per element are 

the coefficients of the linear polynomial approximating the 

pressure). The position of each node on the free surface was 

adjusted by using a front-tracking approach. The interior 

nodes were moved using the method of straight spines. They 

were shifted proportionally along straight, nearly radial lines 

passing through the free surface. Validation of code 

predictions is extremely difficult due to the long timescales 

involved in the process and the hazardous nature of the fluid 

of interest. Several approaches could be taken as follows: 

Calibrate the code on ground test and hope the physics 

remains constant over the several order of magnitude shift in 

driving force; Calculate the thermodynamic equilibrium 

process and use as a bound for the solution; Examine the 

results and asses them for reasonableness to what is 

expected. Three cases were considered to study the problem 

over all the relevant timescales. 

In the first case, the spherical vapor bubble is assumed to 

be initially at the center of the tank, and the history of the 

tank pressure as well as the evolution of the liquid flow and 

thermal fields are examined by following the deforming 

bubble as it approaches the tank wall. Its motion is driven 

solely by the buoyancy force resulting from the density 

jump across the liquid-vapor interface. Fluid motion is 

shown in figure 7. Although the motion is reasonably rapid, 

its duration of 600 seconds far exceeds any drop tower test. 

Since the timescale for the vapor bubble to reach the tank 

wall is much shorter than the conduction or convection 

timescales, the second case study focuses on the 

temperature, pressure and flow fields that develop over a 

longer time span while the vapor bubble remains in a fixed 

position near the tank wall. Fluid was still allowed to slip 

over the interface by assuming the vapor shear stress is 

negligible. This permitted the study of the average long-term 

pressurization of the tank. Figure 8 shows the pressure rise 

compared to equilibrium pressure rise and heat transfer for 

this condition. 

Finally, the third case examined the possibility of 

controlling the tank pressure in microgravity with the 

mixing provided by a subcooled liquid jet. Again, the bubble 

is positioned near the wall, and the tank is pressurized for an 

additional 75 days. Three different jet speeds were 

considered, spanning three orders of magnitude. For each 

one, the time required to bring the pressure back down to its 

initial value was determined. Figure 9 shows the pressure 

rise compared to equilibrium pressure rise and heat transfer 

for this condition. 

Issues.—Pressure rise and stratification in low gravity is 

an important issue for model simulation. Thermodynamic 

analysis provides a useful check as to the reasonableness of 

the simulation, but cannot provide enough information to 

validate process transients. The time constants of process 
NASA/TM—2005-213832 7

(on the order of minutes to days) are beyond drop tower test 

capabilities. 

Other Topics 

The preceding history of experimental, analytical, and 

computational research on thermal-fluid processes occurring 

in a reduced gravity environment is useful, but not 

exhaustive. It is concentrated in the field of low gravity 

propellant management. The examples presented help to 

show the issues and concerns with the establishment of 

benchmark cases from the existing literature. 

Other areas of research in low gravity thermal-fluid 

processes may hold analytical and experimental findings of 

value for code validation. For example, an entire body of 

literature is devoted to “materials processing” in a lowgravity environment, (i.e., Sen and Davis, (ref. 75) Sasmal 

and Hochstein (ref. 76)). Another research topic not 

explored in this survey is the use of body forces (such as 

those induced by a magnetic field); to suppress motion; to 

improve the performance of crystal growth processes; to 

produce a desirable motion such as reorientation; or to 

positively position liquids within containers in a low-gravity 

environment (Martin and Holt, (ref. 77) Marchetta and 

Hochstein, (ref. 78) Marchetta et al. (ref. 79)). The 

establishment of a set of V&V benchmark cases against 

which the fidelity of models claiming to simulate thermalfluid processes occurring in a reduced gravity environment 

can be judged will require contributions from the entire 

research community. 

Summary 

A variety of zero-g fluid motion problems have been 

described for which experimental or analytical data are 

available for use in validation of numerical codes. Overall, 

although there has been much sub-scale testing of zero-g 

fluid motion, there are several things lacking in the 

published literature. Most of the data is described by 

empirical correlation rather than fundamental relation. 

Detailed measurements of the flow field have not been 

made. Free surface shapes are observed but through thick 

plastic cylinders, and therefore subject to a great deal of 

optical distortion. Heat transfer research also been highly 

constrained since the time for the processes of interest to 

evolve is greater than that available in drop tower 

experiments. 

Other areas of research in low gravity thermal-fluid 

behavior may hold analytical and experimental findings of 

value for code validation. The examples presented help to 

show the issues and concerns with the establishment of 

benchmark cases from the existing literature. 

The achievement of true benchmarks in other fields of 

CFD has required dedicated experiments, specifically 

designed with the concept of code validation in mind, and 

there is every reason to expect this will also be the case for 

low gravity fluid behavior. Modern flow visualization 

techniques are available to make vast improvements in 

measurement of low gravity fluid behavior. Miniaturization 

of lasers and electronics has reduced the size of the 

instruments required for flow visualization so that testing 

within the constraints of drop towers and other low gravity 

facilities is practical. Modern CFD modeling has great 

potential for use in scaling small scale tests to objects of 

practical size, but without accurate knowledge of the fluid 

flows, heat transfer and surface deformation validation of 

the codes is impossible. The authors’ welcome further 

discussion on the establishment of a set of V&V benchmark 

cases against which the fidelity of models claiming to 

simulate thermal-fluid processes occurring in a reduced 

gravity environment can be judged. 

References 

1. Chato, David J. “Influence of Turbulence on the Restraint of 

Liquid Jets by Surface Tension in Microgravity,” AIAA–

2002–0758, January 2002. 

2. Chato, David J. “Penetration of the Free Surface by Liquid 

Jets in Microgravity,” PhD. Dissertation, Case Western 

Reserve University, January 2004. 

3. Jacqmin, D. “Calculation of Two-Phase Navier-Stokes Flows 

Using Phase-Field Modeling,” Journal of Computational 

Physics 155, 96–127, 1999. 

4. Torrey, Martin D. et al. “NASA-VOF2D: A Computer 

Program for Incompressible Flows with Free Surfaces,” 

LA-10612-MS, Los Alamos National Laboratory, 

December 1985. 

5. Kothe, D.B., Mjolsness, R.C., Torrey, M.D., “RIPPLE: A 

Computer Program for Incompressible Flow with Free 

Surfaces,” Los Alamos National Laboratory, LA-12007-MS, 

1991. 

6. Brackbill, J.U., Kothe, D.B., Zemach, C., “A Continuum 

Method for Modeling Surface Tension,” Journal of 

Computational Physics vol. 100, no. 2, June 1992. 

7. Engelman, S., and R.L. Sani, Finite element simulation of 

incompressible flows with free/moving surface, in: Numerical 

Methods in Laminar and Turbulent Flows, Pineridge Press, 

Swansea, U.K., 1984. 

8. Oberkampf, W.L.; Trucano, T.G., “Verification and 

Validation in Computational Fluid Dynamics,” Sandia 

National Laboratories, SAND2002–0529, 2002. 

9. DoD, “DoD Directive no. 5000.59: Modeling and Simulation 

(M&S) Management,” Defense Modeling and Simulation 

Office, Office of the Director of Defense Research and 

Engineering, www.dmso.mil/docslib. 

10. DoD, “Verification, Validation, and Accreditation (VV&A) 

Recommended Practices Guide,” Defense Modeling and 

Simulation Office, Office of the Director of Defense Research 

and Engineering, www.dmso.mil/docslib. 

11. Roache, P.J., “Verification and Validation in Computational 

Science and Engineering,” Hermosa Publishers, Albuquerque, 

NM, 1998. 
NASA/TM—2005-213832 8

12. AIAA, “Guide For the Verification and Validation of 

Computational Fluid Dynamics Simulations,” American 

Institute of Aeronautics and Astronautics, AIAA-G-077-1998, 

Reston, VA, 1998. 

13. Concus, Paul “Static menisci in a Vertical Right Circular 

Cylinder,” J. Fluid Mech. vol. 34, Part 3, pp. 481–495, 1968. 

14. Reynolds, W.C., Saad, M.A. and Satterlee, H.M. “Capillary 

Hydrostatics and Hydrodynamics at Low G,” Stanford 

University Technical Report LG-3, 1964. 

15. Hastings, L.J. and Rutherford, R. “Low Gravity Liquid-Vapor 

Interface Shapes in Axisymmetric Containers and a Computer 

Solution,” NASA TM X-53790, 1968. 

16. Petrash, D.A. et al. “Effect of Surface Energy on the LiquidVapor Interface Configuration During Weightlessness,” 

NASA TN D-1582. 

17. Labus, T.L. “Liquid-vapor Interface Configuration in Annular 

Cylinders,” NASA TM X-1973, 1970. 

18. Salzmann, J.A. “Low-Gravity Liquid-Vapor Interface 

Configurations in Spherical Containers,” NASA TN-D-5648, 

1970. 

19. Spuckler, C.M. and Abdalla, K.L. “Zero-Gravity LiquidVapor Interface Configuration in Conical Tanks,” NASA TM 

X–2400, 1971. 

20. Petrash, D.A., Nussle, R.C., and Otto, E.W. “Effect of 

Acceleration Disturbances Encountered in the MA-7 

Spacecraft on the Liquid-Vapor Interface in a Baffled Tank 

During Weightlessness,” NASA TN-D-1577, 1963. 

21. Abdalla, K.L., Flage, R.A. and Jackson, R.G. “Zero-Gravity 

Performance of Ullage Control Surface with Liquid hydrogen 

while subjected to unsymmetrical radiant Heating,” NASA 

TM X–1001, 1964. 

22. Siegert, C.E., Petrash, D.A., and Otto, E.W. “Time Response 

of Liquid-Vapor Interface After Entering Weightlessness,” 

NASA TN-D-2458, 1964. 

23. Fung, F.C.W.; “Dynamic Response of Liquid in Partially 

Filled Containers Suddenly Experiencing Weightlessness,” 

Fluid Mechanics and Heat Transfer Under Low Gravity, 

Lockheed Missiles and Space Co. 1965. 

24. Hollister, M.P.; and Satterlee, H.M.; “Low Gravity Liquid 

Reorientation,” Fluid Mechanics and Heat Transfer Under 

Low Gravity, Lockheed Missiles and Space Co. 1965. 

25. Brakke, K.A. “The Surface Evolver,” Experimental 

Mathematics, vol. 1, pp. 141–165, 1992. 

26. Tegart, James, “Three-Dimensional Fluid Interfaces in 

Cylindrical Containers,” AIAA–91–2174, June 1991. 

27. Dominick, S. and Tegart, J., “Orbital Test Results of a Vaned 

Liquid Acquisition Device,” AIAA–94–3027, June 1994. 

28. Collicott, S.H. and Weislogel, M.M. “Corner Radius Effects 

on Capillary Instability in Tank Geometries,” AIAA–2001–

3824, 2001. 

29. Concus, P. and Finn, R. “Dichotomous behavior of Capillary 

Surfaces in Zero Gravity,” Microgravity Sci. Tech III (2) pp. 

87–92, 1990. 

30. Weislogel, M.M. and Collicott, S.H. “Analysis of Tank PMD 

Rewetting Following Thrust Resettling,” AIAA–2002–0757, 

Jan. 2002. 

31. Collicott, S.H. and Weislogel, M.M. “Modeling of the 

Operation of the VTRE Propellant Management Device,” 

AIAA–2002–4140, July, 2002. 

32. Chato, D.J. and Martin, T.A. “Vented Tank Resupply 

Experiment-Flight Test Results,” AIAA–97–2815, July 1997. 

33. Collicott, S.H. and Weislogel, M.M. “Review of Surface 

Evolver Validation Tests for Zero-Gravity Fluids 

Applications,” AIAA–2003–0999. 

34. Lacovic, Raymond F. Frederick C. Yeh, Steven V. Szabo Jr., 

R.J. Brun, Andrew J. Stofan, and James A. Berns. 

“Management of Cryogenic Propellants in a Full Scale 

Orbiting Space Vehicle,” NASA TN-D-4571, May 1968. 

35. Masica, William J. and Donald A. Petrash. “Motion of 

Liquid-Vapor Interface in Response to Imposed 

Acceleration,” NASA TN-D-3005, September 1965. 

36. Salzman, Jack A. and William J. Masica. “Experimental 

Investigation of Liquid-Propellant Reorientation,” NASA TND-3789, January 1967. 

37. Salzman, Jack A. William J. Masica, and Raymond F. 

Lacovic. “Low-Gravity Reorientation in a Scale-Model 

Centaur Liquid Hydrogen Tank,” NASA TN-D-7168, 

February 1973. 

38. Sumner, Irving E. “Liquid Propellant Reorientation in a 

Low-Gravity Environment,” NASA TM-78969, July 1978. 

39. Lacovic. Raymond F. “Centaur Zero Gravity Coast and 

Engine Restart Demonstration on the Titan/Centaur (TC-2) 

Extended Mission,” NASA TM X-71821, October 1975. 

40. Bradshaw R.D. and J.L. Kramer. “An Analytical Study of 

Reduced Gravity Propellant Settling,” NASA CR-134593, 

Feb. 1974. 

41. Bradshaw R.D., J.L. Kramer, and J.L. Zich. “An Analytical 

Study of Reduced-Gravity Flow Dynamics,” NASA 

CR-135023, April 1976. 

42. Hochstein, J.I., Korakianitis, T.P., Patag, A.E., Chato, D.J., 

“Modeling of Impulsive Propellant Reorientation,” AIAA J. 

Propulsion and Power, vol. 7, no. 6, November-December 

1991. 

43. Hochstein, John I., Alfredo E. Patag, T.P. Korakianitis, and 

David J. Chato. “Pulsed Thrust Propellant Reorientation: 

Concept and Modeling,” AIAA Journal of Propulsion and 

Power vol. 8, no. 4, July 1992. 

44. Derul, J.D. Grubb, L.S. and Petrash, D.A. “Experimental 

Investigation of Liquid Outflow from Cylindrical Tanks 

During Weightlessness,” NASA TN D-3746, December 1966. 

45. Grubb, L.S. and Petrash, D.A. “Experimental Investigation of 

Interfacial Behavior Following Termination of Outflow in 

Weightlessness,” NASA TN-D-3897, April 1967. 

46. Berenyi, S.G. and Abdalla, K.L. “Vapor Ingestion 

Phenomenon in Hemispherically Bottomed Tanks in Normal 

Gravity and in Weightlessness,” NASA TN-D-5704, 

April 1970. 

47. Symons, E.P. “Effect of Throttling on Interface Behavior and 

Liquid Residuals in Weightlessness,” NASA TM X-3034, 

May 1974. 

48. Hotchkiss, R.S., “Simulation of Tank Draining Phenomena 

with the NASA SOLA-VOF Code,” LASL Report LA-8163-

MS, 1979. 

49. Symons, E.P.; Nussle, R.C. and Abdalla, K.L. “Liquid Inflow 

to Initially Empty, Hemispherical Ended Cylinders During 

Weightlessness”: NASA TN D 4628: June 1968. 

50. Symons, Eugene P., Nussle, Ralph C., “Observations of 

Interface Behavior During Inflow to an Elliptical Ended 

Cylinder in Weightlessness,” NASA TM X-1719, 

January 1969. 

51. Symons, Eugene P. “Interface Stability During Liquid Inflow 

to Initially Empty Hemispherical Ended Cylinders in 

Weightlessness,” NASA TM X-2003, April 1970. 
NASA/TM—2005-213832 9

52. Symons, Eugene P., Staskus, John V., “Interface Stability 

During Liquid Inflow to Partially Full, Hemispherical Ended 

Cylinders in Weightlessness,” NASA TM X-2348, 

August 1971. 

53. Spuckler, Charles M. “Liquid Inflow to Initially Empty 

Cylindrical Tanks in Low Gravity,” NASA TMX-2613, 

August 1972. 

54. Staskus, John V, “Liquid Inflow into a Baffled Cylindrical 

Tank During Weightlessness,” NASA TM X-2598, 

August 1972. 

55. Labus, T.L., Aydelott, J.C., Andracchio, C.R., “Effect of 

Baffles on Inflow Patterns in Spherical Containers During 

Weightlessness,” NASA TMX-2670, November 1972. 

56. Aydelott, J.C. “Axial Jet Mixing of Ethanol in Spherical 

Containers During Weightlessness,” NASA TM X-3380: 

April 1976. 

57. Aydelott, J.C. “Axial Jet Mixing of Ethanol in Cylindrical 

Containers During Weightlessness,” NASA TP-1487: 

July 1979. 

58. Aydelott, J.C.: “Modeling of Space Vehicle Propellant 

Mixing,” NASA TP-2107: January 1983. 

59. Bentz, M.D., et al. “Tank Pressure Control Experiment-A 

Low-g Mixing Investigation,” AIAA–90–2376. 

60. Bentz, Michael D., “Tank pressure control in low gravity by 

jet mixing,” NASA-CR-191012, March 1993. 

61. Bentz, M.D., Knoll, R.H., Hasan, M.M., Lin, C.S., “Low-g 

fluid mixing-Further results from the Tank Pressure Control 

Experiment,” AIAA PAPER 93–2423, Jun. 1993. 

62. Hasan, Mohammad M., Lin, Chin S., Knoll, Richard H., and 

Bentz, Michael D., “Tank Pressure Control Experiment: 

Thermal Phenomena,” NASA TP 3564, March 1996. 

63. Bentz, Michael D, et al. “Tank Pressure Control ExperimentResults of three space flights,” AIAA Paper 97–2816, 

July 1997. 

64. Hochstein, J.I., Gerhart, P.M., Aydelott, J.C., Computational 

Modeling of Jet Induced Mixing of Cryogenic Propellants in 

Low-G, AIAA–84–1344. 

65. Hochstein, J.I., Ji, H.-C., Aydelott, J.C., “Temperature Fields 

Due to Jet Induced Mixing in a Typical OTV Tank,” AIAA–

87–2017, AIAA 23rd Joint Prop. Conf., June 1987. 

66. Hochstein, J.I., Ji, H.-C., Aydelott, J.C., “Prediction of SelfPressurization Rate of Cryogenic Propellant Tankage,” AIAA 

J. Propulsion and Power, vol. 6, no. 1, pp. 11–17, Jan.–Feb., 

1990. 

67. “FLOW3D; Computational Modeling Power for Scientists 

and Engineers,” Flow Science, Inc., Los Alamos, New 

Mexico, 1988. 

68. Sasmal, G.P., Hochstein, J.I., M.C., Hardy, T.L., “Influence of 

Heat Transfer Rates on Pressurization of Liquid/Slush 

Hydrogen Propellant Tanks,” AIAA–93–0278, AIAA 31st 

Aerospace Sciences Mtg. Jan 1993. 

69. Thornton, R.J., Hochstein, J.I., “Microgravity Geyser and 

Low Field Prediction,” AIAA–00–0858, AIAA 38th 

Aerospace Sciences Mtg., Jan. 2000. 

70. Pope, S.B. Turbulent Flows. Cambridge University Press, 

2000. 

71. Hussien, H.J. Capp, S.P. George, W.K. “Velocity 

Measurements in a High-Reynolds-Number, MomentumConserving, Axisymmetric, Turbulent Jet,” Journal of Fluid 

Mechanics vol. 258 pp. 31–75, 1994. 

72. Schlichting, H.; and Gersten, K. Boundary-Layer Theory. 8th 

Edition Springer-Verlag 2000. Panzarella, C.H. M. Kassemi, 

“On the validity of purely thermodynamic descriptions of 

two-phase cryogenic fluid storage,” Journal of Fluid 

Mechanics 484 (2003) 136–148. 

73. Panzarella, C.H. M. Kassemi, “Pressurization of spherical 

cryogenic tanks in space,” Journal of Spacecraft and Rockets, 

submitted (2003). 

74. Panzarella, C.H., D. Plachta, and M. Kassemi, “Pressure 

control of large cryogenic tanks in microgravity,” 20th Space 

Cryogenics Workshop, Girdwood, Alaska. Also Cryogenics, 

submitted for publication (2003). 

75. Sen, A.K., Davis, S.H., “Steady Thermocapillary Flows in 

Two-Dimensional Slots,” J. Fluid Mechanics, vol. 121, 

pp. 163–186, 1982. 

76. Sasmal, G.P., Hochstein, J.I., “Marangoni Convection with a 

Curved and Deforming Free Surface in a Cavity,” ASME J. of 

Fluids Engineering vol. 116, pp. 577–582, Sep. 1994. 

77. Martin, J.J., Holt, J.B., “Magnetically Actuated Propellant 

Orientation Experiment, Controlling Fluid Motion with 

Magnetic Fields in a Low-Gravity Environment,” NASA TM 

210129, 2000. 

78. Marchetta, J.G., Hochstein, J.I., “A Computational Model of 

Magnetic Positive Positioning in Reduced Gravity,” ST-99-

W.210, IAF 50th Int’l. Astronautical Congress, 

Oct. 1999. 

79. Marchetta, J.G., Hochstein, J.I., Sauter, D.R., Simmons, B.D., 

“Modeling and Prediction of Magnetic Storage and 

Reorientation of LOX in Reduced Gravity,” AIAA–2002–

1005, AIAA 40th Aerospace Sciences Mtg., Jan 2002. 
NASA/TM—2005-213832 10

Figure 1.—Near Equilibrium Free Surface Shapes. 

0

2

4

6

8

10

12

024

Time (sec)

Height at Center Line (cm)

Height

Equilibrium Height

Measurement of Seigert

Figure 2.—Motion of Liquid in Response to the removal of Gravity 8 cm Diameter Tank 

filled to a Starting Flat Height of 10 cm. 

X (cm)

0 1 2 3 4 5 0

2

4

6

8

10

12

14

16

18

20

c) Contact Angle 60 degrees

Ideal

X (cm)

0 1 2 3 4 5 0

2

4

6

8

10

12

14

16

18

20

b) Contact Angle 30 degrees

X (cm)

Y (cm)

0 1 2 3 4 5 0

2

4

6

8

10

12

14

16

18

20

a) Contact Angle 0 degrees

Ideal
NASA/TM—2005-213832 11

Figure 3.—Fs versus Bo for 50 percent filled Space Based OTV. 

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 2 4 6 8 10 12 14 16

Fill height (cm)

Geyser Height/Raduis

17 cm/s measured

17 cm/s calculated

24 cm/s measured

24 cm/s calculated

Figure 4.—Non-Dimensional Geyser Height Comparison Calculated versus 

Measured for Laminar Flow. 
NASA/TM—2005-213832 12

0

1

2

3

0 4 8 12 16

Fill height (cm)

Geyser Height/Raduis

34 cm/s measured

50 cm/s measured

34 cm/s Calculated

50cm/s Calculated

Figure 5.—Non-Dimensional Geyser Height Comparison Calculated versus 

Measured for Full Turbulence. 

0

1

2

3

0 4 8 12 16

Fill height (cm)

Geyser Height/Raduis

50 cm/s measured

50cm/s 0.232 viscocity

50 cm/s 0.18 viscocity

50 cm/s 0.14 viscocity

(one point)

Figure 6.—Non-Dimensional Geyser Height Comparison Calculated versus 

Measured for Parametric Turbulence. 
NASA/TM—2005-213832 13

Figure 7.—Isotherms and streamlines for 

(a) t = 259 s, (b) t = 463 s, and (c) t = 567 s, 

as the initially-centered spherical vapor 

bubble rises only due to buoyancy force.

Figure 8.—The initial (a) pressure rise and (b) net heat flow into 

the vapor with the vapor region at the wall. 

t (days) 

Predicted
NASA/TM—2005-213832 14

Figure 9.—The long-term (a) pressure, (b) saturation 

temperature and (c) total heat before and after 

the subcooled jet is turned on at t = 75 days. 
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

REPORT DOCUMENTATION PAGE

2. REPORT DATE

19. SECURITY CLASSIFICATION

 OF ABSTRACT

18. SECURITY CLASSIFICATION

 OF THIS PAGE

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources,

gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this

collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson

Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18

298-102

Form Approved

OMB No. 0704-0188

12b. DISTRIBUTION CODE

8. PERFORMING ORGANIZATION

 REPORT NUMBER

5. FUNDING NUMBERS

3. REPORT TYPE AND DATES COVERED

4. TITLE AND SUBTITLE

6. AUTHOR(S)

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION/AVAILABILITY STATEMENT

13. ABSTRACT (Maximum 200 words)

14. SUBJECT TERMS

17. SECURITY CLASSIFICATION

 OF REPORT

16. PRICE CODE

15. NUMBER OF PAGES

20. LIMITATION OF ABSTRACT

Unclassified Unclassified

Technical Memorandum

Unclassified

National Aeronautics and Space Administration

John H. Glenn Research Center at Lewis Field

Cleveland, Ohio 44135–3191

1. AGENCY USE ONLY (Leave blank)

10. SPONSORING/MONITORING

 AGENCY REPORT NUMBER

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546–0001

Available electronically at http://gltrs.grc.nasa.gov

September 2005

NASA TM—2005–213832

AIAA–2004–1150

E–15202

WBS–22–614–50–04–11

20

Approaches to Validation of Models for Low Gravity Fluid Behavior

David J. Chato, Jeffery Marchetta, John I. Hochstein, and Mohammad Kassemi

Low gravity; Fluid behavior; CFD

Unclassified -Unlimited

Subject Category: 34

Prepared for the 42nd Aerospace Sciences Meeting and Exhibit sponsored by the American Institute of Aeronautics and

Astronautics, Reno, Nevada, January 5–8, 2004. David J. Chato, NASA Glenn Research Center; Jeffery Marchetta and

John I. Hochstein, University of Memphis, Mechanical Engineering Department, 3706 Alumni Street, Memphis, Tennessee

38152–0001; and Mohammad Kassemi, National Center for Space Exploration Research, 21000 Brookpark Road,

Cleveland, Ohio 44135. Responsible person, David J. Chato, organization code RTP, 216–977–7488.

This paper details the author experiences with the validation of computer models to predict low gravity fluid behavior. It

reviews the literature of low gravity fluid behavior as a starting point for developing a baseline set of test cases. It examines

authors’ attempts to validate their models against these cases and the issues they encountered. The main issues seem to be

that: Most of the data is described by empirical correlation rather than fundamental relation; Detailed measurements of the

flow field have not been made; Free surface shapes are observed but through thick plastic cylinders, and therefore subject

to a great deal of optical distortion; and Heat transfer process time constants are on the order of minutes to days but the

zero-gravity time available has been only seconds.