It is well known that surface tension of a liquid has a decisive role in flow dynamics and the eventual equilibrium state, especially in confined flows under low gravity conditions and also in free surface flows. One such instance of a combination of these two cases where surface tension plays an important role is in the microgravity environment of a spacecraft propellant tank. In this specific case both propellant acquisition and residual propellant estimation are critical to the mission objectives particularly in the end-of-life phase. While there have been a few studies pertaining to the equilibrium state in given geometric configurations, the transient flow leading to final state from an initial arbitrary distribution of propellant is rarely described. The present study is aimed at analysing the dynamic behaviour of the liquids under reduced gravity through numerical simulation and also addresses the specific case of propellant flow transient in a cone-in-a-sphere type of tank configuration proposed by Lal and Raghunandan which is likely to result in both improved acquisition and life time estimation of spacecraft. While addressing this specific problem, the present work aims to study the transient nature of such surface tension driven flows in a general form as applicable to other similar problems also. Volume of Fluid (VOF) method for multiphase model in ANSYS FLUENT was adapted with suitable changes for generating numerical solutions to this problem.

1. By
K. Aatresh.
MSc.
Research Supervisor:
Prof B. N. Raghunandan.
Aerospace Department, IISc.

2. Contents
Current Techniques
Literature review
Objective
Formulation
Geometry & Simulation Results
Conclusions

3. Current Techniques
Gauging
Book- Keeping Method
Gas Injection Method
Thermal Propellant Gauging Method
Acquisition
Use of Vanes and Sponges to maintain fuel
near the outlet

4. Literature Review
Early work began after induction of the Apollo program in the 1960’s
Work by Petrash et al1
(1962) on estimation of propellant wetting
times
Computational studies by Hung2
(1990) to find reaction accelerations
to maintain liquid equilibrium
Jaekle’s3
(1991) work on PMD design and
configuration
Studies on time response of cryogenic fuel by Fisher et.al4
(1991)
Sasges et al’s5
(1996) work on equilibrium states

5. Behavioral study on liquids in neutral buoyancy Venkatesh et
al6
(2001)
Research done by Boris et al7
(2007) on rebalancing of propellant
in multiple tank satellites.
Study done on Marangoni bubble motion in zero gravity by
Alhendal et.al8
. The VOF module in ANSYS Fluent was used for
simulation

6. Current project based on the work by Lal & Raghunandan9
Based on the effect of surface tension on the fluid in
microgravity condition
For volume fractions below 10% the propellant tends to
accumulate in the cone
Increased accuracy towards end of life of the satellite
Time scale in which the propellant reached the final
equilibrium configuration remained unknown

7. Image and text courtesy: New Scientist
Lal published his work in the Journal of Spacecraft &
Rockets, Vol.44, p.143 . New Scientist published an article
based on the work.

8. Motivation
Feasibility and experimentation of the technique proposed by
Lal unknown
Private letter addressed to Prof. Raghunandan from NASA
Ames Research Centre quoted as follows
“Is 4 minutes (or possibly up to 8, if absolutely required) long
enough to test your fuel gauge approach? About how many
flights would be required to truly advance development on this
approach to fuel measurement?”
Whether technique can be experimentally tested another
question raised by Surrey Satellite Technologies, UK.

9. Objective
Determine practicality of technique proposed by Lal
What would be the time scales involved
Could an experiment be devised to verify the claim
How long should be the duration for the state of microgravity
Emphasis on time scales due to short zero g times available for
testing
Method to analyse motion of fluid in an enclosed container
dominated by surface tension flows

10. Formulation
ANSYS FLUENT v.13 chosen as the tool of choice to perform
computations
Volume of Fluid (VOF) Method chosen for the current problem
Alhendal et.al showed VOF method a robust numerical
technique for the simulation of gas-liquid two phase flows and
for simulation of surface tension flows
Air chosen as gaseous phase
Water and Hydrazine chosen as liquid phases.

13. First Order Upwind Scheme for spatial discretisation
Implicit Time Integration Scheme for temporal discretisation
SIMPLE algorithm used to calculate pressure field
Iterative time advancement scheme used to obtain solution till
convergence
Residual tolerance for both the momentum and continuity
equations was set to 10-4
Absolute values of residuals achieved found to be O(10−4
) for
velocities and O(10−4
) for continuity

14. Validation
Closed form solution comparison with
capillary rise of water in a 1 mm capillary
tube and a contact angle of 0o
Equilibrium height is 2.93 cm
Numerical simulation of
liquid rise in non-uniform
capillaries by Young
Transient capillary flows
by Robert

15. Young’s setup
Robert’s setup

16. Geometry & Simulation Results
A 2D axisymmetric solver was used
The cone geometry used by Lal modified by adding cylindrical
section
Quadrilateral paved mesh was chosen as the computational grid
Cone angle (α) varied to study change
of rise time

17. Grid independence examined through three levels of grid
refinement with the 17o
cone angle case with 26000, 33000
& 41000 cells

18. Difference in the most coarse and medium meshes was
significant
Difference reduces to less than 5% for rise height for fine and
medium meshes
Liquid level kept horizontal in full scale(dia. = 2m) cases
Most of the liquid present in the annular space

19. Meniscus Height
Simulations run for cone angles (α) of 17o
, 21o
and 28o
Equilibrium states taken from consecutive points with height
difference of less than 1%
Results for the 17o
degree cone angle case without and
with cylindrical section

20. Similar results obtained for rise rate for cone case of 21o
Liquid surface fluctuation without the cylindrical section
Found to be very slight (< 0.5% of the rise height)
Rise height similar in both cases with and & without cylindrical
section
Results for the 21o
degree cone angle case without and with
cylindrical section

21. For 28o
cone angle surface fluctuations very pronounced for case
without cylindrical section
Could be attributed to the steep cone divergence as amplitude
and duration found to increase as the cone angle increased
Rise rate of liquid surface in the cone with cylindrical section
similar in characteristic to the previous cases
Results for the 28o
degree cone angle case without and with
cylindrical section

22. Addition of cylindrical section to the cone was found to
increase the maximum rise height
Steeper and more steady rise rate as compared to cases without
the cylindrical section
Has an effect similar to that of a sponge used in current PMDs
Cylindrical capillary seemed to aid the flow and the collection
of fluid at the base

23. Scaling effects
Two scaled models of the 28o
case simulated
1/2 and 1/10th
scale models of the original tank (radius: 1m)
Simulation yields results similar to full scale model on different
time scale as expected.

24. Third simulation of the 1/10th
scale model run with liquid spread
in the tank
Configuration chosen to imitate general conditions found in
propellant tank in microgravity
Regimes of steep and shallow rise caused by spread out liquid
surface joining and separating at base of cone

25. Final equilibrium position of liquid observed to be in line with
the predictions made by Lal
Simulations run with water &
hydrazine for 1/10th
scale without
cylindrical section
Properties varied with temperature
Case Contact
Angle(degrees)
Tank
Temperature(o
C)
Surface tension
of Water (N/m)
Viscosity
(Ns/m2
) x 10-
3
Surface tension of
Hydrazine (N/m)
Viscosity
(Ns/m2
) x
10-3
A 0 27 0.0725 0.798 0.066 0.876
B 5 27 0.0725 0.798 0.066 0.876
C 0 10 0.0741 1.307 0.068 -
D 0 50 0.068 0.547 - -

26. Case A shows the rise of the liquid column, with water (shown
in blue), 1% higher than that with hydrazine (shown in red)
Initial rate of rise found to be similar for both the liquids
Equilibrium time for water 17% longer
Comparison of meniscus
height with time for Case A
(cylinder absent, liquid spread
around tank)

27. Case B’s rate of rise significantly different from Case A with
change in contact angle.
For water, liquid column stabilized and reached constant
height.
Hydrazine sets itself into an oscillatory motion with a near
constant amplitude
Higher column compared to water
by about 3% at it’s highest
point.
Comparison of meniscus
height with time for Case B
(cylinder absent, liquid spread
around tank)

28. Comparison of rise heights was made for water at different
surface tension values (A=0.0725,C=0.0741,D=0.068 (N/m)
Height vs. time for water at 10o
C(C) shown in black and 50o
C (D)
shown in red very similar
Water at 27o
C shown in blue in Case A however different with
equilibrium times longer as compared to Case C & D
Comparison of meniscus
height with time for Cases
A, C& D for water
(cylinder absent, liquid spread
around tank)

29. Similar comparison for hydrazine at different surface tension values
(A=0.066 N/m, C= 0.068 N/m) made
Case C at 10o
C shown in blue showed
fair amount of fluctuations in
meniscus with large amplitude
Similar behaviour observed
for in Case A at 27o
C shown in
red. But amplitude of these
fluctuation found to be much
lower
Equilibrium time for Case C found to be 20% higher compared to
that for Case A & equilibrium height for Case C was found to be
25% higher

30. (a)
(b)
(c)
(d)

31. Equilibrium State Time Scales
Initial surface configuration taken flat, liquid volume fraction
10% and no liquid present in cone for full scale models
Cone angle (or)
Case
Type of Cone (or) Scale Equilibrium
Time (s)
Final
equilibrium
height (m)
17o
With cylindrical section (water) 960 0.74
Without cylindrical section (water) 530 0.63
21o
With cylindrical section (water) 940 0.55
Without cylindrical section (water) 780 0.58
28o
With cylindrical section (water) 900 0.72
Without cylindrical section (water) 940 0.36

32. Different scales of the 28o
cone angle case
As scale is reduced clear order of magnitude reduction in
equilibrium settling time is seen
Significant difference in settling times for 1/10th
scale model
with flat surface and 1/2 scale model
Type of Cone (or) Scale Initial Surface
Configuration
Equilibriu
m Time (s)
Final
equilibrium
height (m)
With cylindrical section, full
scale model Flat surface 900 0.72
With cylindrical section, half
scaled model Flat surface 68 0.22
With cylindrical section, 1/10th
scale model Flat surface 6.5 0.033

33. Equilibrium times for different physical parameters
(for cone angle of 28o
and 1/10th
scale model liquid spread around tank).
Final equilibrium heights very close to each other
Cone angle (or) Case Liquid Equilibriu
m Time (s)
Final equilibrium
height (m)
Case A
(θ = o0
, T = 27o
C)
Water 68 0.02
Hydrazine 58.2 0.019
Case B
(θ = 50
, T = 27o
C)
Water 50 0.017
Hydrazine
64 0.02 (maximum)
Case C
(θ = o0
, T = 100
C)
Water 60 0.018
Hydrazine 70 0.02
Case D
(θ = o0
, T = 50o
C) Water
46 0.018

34. Conclusions
The addition of the cylindrical section to the cone leads to a
gradual rise in the meniscus
Equilibrium times for all three cases were in order of 300 to 600
seconds for full scale models
Scaled down models of 1/10th
scale have much lower values of
settling time(of the order of tens of seconds)
Intermittent scale models between 1/10th
and ½ can be used to
conduct experiments
Formulation and the solution methodology are very general and
hence applicable to any geometry of interest.
Scaled models can be used for experimental verification via
parabolic flight path testing using fixed wing aircraft

35. References
1. Donald A. Petrash, Robert F. Zappa, Edward W. Otto, “Technical Note –
Experimental Study of the Effects of Weightlessness on the Configuration
of Mercury and Alcohol in Spherical Tanks”, Lewis Research Centre, 1962.
2. R. J. Hung. “Microgravity Liquid Propellant Management”, The University
of Alabama in Huntsville Final Report, 1990.
3. D. E. Jaekle, Jr., “Propellant Management Device Conceptual Design and
Analysis: Vanes”, AIAA-91-2172, 27th
Joint Propulsion Conference, 1991.
4. M. F. Fisher, G. R. Schmidt, “Analysis of cryogenic propellant behaviour
in microgravity and low thrust environments”, Cryogenics, Vol. 32, No. 2,
pp. 230- 235, 1992.
5. M. R. Sasges, C. A. Ward, H. Azuma, S. Yoshihara, “Equilibrium fluid
configurations in low gravity”, Journal of Applied Physics, 79(11), 1996.

36. 6. H. S. Venkatesh, S. Krishnan, C. S. Prasad, K. L. Valiappan, G.
Madhavan Nair, B. N. Raghunandan, “Behaviour of Liquids under
Microgravity and Simulation using Neutral Buoyancy Model”,
ESASP.454..221V, 2001.
7. Boris Yendler, Steven H. Collicott, Timothy A. Martin, “Thermal
Gauging and Rebalancing of Propellant in Multiple Tank Satellites”,
Journal of Spacecraft and Rockets, Vol.44, No. 4, 2007.
8. Yousuf Alhendal, Ali Turan, “Volume-of-Fluid (VOF) Simulations of
Marangoni Bubble Motion in Zero Gravity”, Finite volume Method –
Powerful Means of Engineering Design, pp. 215-234, 2012.
9. Amith Lal, B. N. Raghunandan, “Uncertainty Analysis of Propellant
Gauging System for Spacecraft”, Journal of Spacecraft and Rockets,
Vol.42, No.5, 2005.

37. Thank You