Transients in Surface Tension Driven Flows in Microgravity

K. Aatresh.
MSc, Aerospace Department, IISc.
Prof B. N. Raghunandan.
Aerospace Department, IISc.

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

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

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
 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

 Behavioral study on liquids in neutral buoyancy Venkatesh et
al6(2001)
 Study done on Marangoni bubble motion in zero gravity by
Alhendal et.al8. The VOF module in ANSYS Fluent was used for
simulation
 Work by Lal & Raghunandan9 on the effect of surface tension on
the fluid in microgravity condition

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.

Motivation & Objectives
 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.
 Scales involved & duration for the state of microgravity to devise
an experiment
 Method to analyse motion of fluid in an enclosed container
dominated by surface tension flows

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.

 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

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

 Young’s setup
 Robert’s setup

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

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

 Difference reduced 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
Initial configuration of liquid.
( scale 1:1, cone angle 17o)
Comparison of rise heights for different
mesh sizes.

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

 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
a) Initial state of liquid with flat surface. (b) Final equilibrium state.
(scale 1:1, cone angle 28o, with cylindrical section)

 Rise rate of liquid surface in the cone with cylindrical section
similar in characteristic to the previous cases
 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

Scaling effects
 Two scaled models of the 28o case simulated
 1:0.5 and 1:0.1 scale
models of the original tank
(radius: 1m).
 Simulation yields results
similar to full scale model
on different time scale as
expected.
Normalized height vs. time for
different scale models.
(Cone angle 28o, with cylindrical
section)

 Third simulation of the 1:0.1 scale model run with liquid spread
in the tank
 Configuration chosen to imitate general conditions found in
propellant tank in microgravity
(a) Modified initial state of the liquid. (b) Final equilibrium state.
(scale 1:0.1, cone angle 28o.)

 Simulations run with water & hydrazine for 1:0.1 scale
without cylindrical section
 Three different values of temperature; of 27oC, 50oC chosen.
 Properties varied with temperature
 Two values for contact angle of 0o and 5o chosen based on
the work of Bernadin et.al8
Varying Surface Tension Values

 Equilibrium times are far apart for water and hydrazine
 Liquid meniscus found to be oscillating for the 5o contact angle
case for hydrazine
 Variation of rise heights not of much significance
 Time scales obtained conducive for experimentation
Parameter(Constant)
Water Hydrazine
Equilibrium
time (s)
Equilibrium
height (m)
Equilibrium
time (s)
Equilibrium
height(m)
 = 0o (T = 27oC)
68
0.02 58.2 0.019
 = 5o (T = 27oC) 50 0.017 64 0.02(max)
Temperature 10oC ( = 0o) 60 0.018 70 0.02
Temperature 50oC ( = 0o) 46 0.018 - -
changing physical conditions.
(1:0.1 scale, initial liquid configuration: spread out state).

Variation with Gravity
 Study made with the change in gravitational level
 Observed that as g kept reducing final equilibrium height
increased.
 Expected since a
reduction in the
gravitational force
magnifies the effects
of surface tension.
Effect of change in gravity on the
rising liquid meniscus.
(1:0.1 scale, initial liquid
configuration: spread out state).

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
28o

 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 1:0.1 scale model with
flat surface and 1:0.5 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

Conclusions
 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)
 Since the physics governing the propellant behaviour is the same
irrespective of the scale, intermittent scale models between
1/10th and ½ with equilibrium times suitable to zero-g test
conditions can be used to study the geometry.
 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

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.

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.

Transients in Surface Tension Driven Flows in Microgravity

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