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By K. Aatresh.MSc.Research Supervisor:Prof B. N. Raghunandan.Aerospace Department, IISc.
ContentsCurrent Techniques
Literature review
Objective
Formulation
Geometry & Simulation Results
Conclusions
Current Techniques Gauging
Book- Keeping Method
Gas Injection Method
Thermal Propellant Gauging Method
AcquisitionUse of Vanes and Sponges to maintain fuel
near the outlet
Literature ReviewEarly 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
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
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
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.
MotivationFeasibility 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.
ObjectiveDetermine 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
FormulationANSYS 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 ResultsA 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 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
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
Results for the 21o degree cone angle case without and with cylindrical section
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
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 effectsTwo scaled models of the 28o case simulated1/2 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.
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
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(degree
s)
Tank Temperature(
oC)
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 - -
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)
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)
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 10oC(C) shown in black and 50oC (D) shown in red very similar
Water at 27oC 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)
Similar comparison for hydrazine at different surface tension values (A=0.066 N/m, C= 0.068 N/m) made
Case C at 10oC shown in blue showed fair amount of fluctuations in meniscus with large amplitude
Similar behaviour observed for in Case A at 27oC 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
(a)
(b)
(c)
(d)
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
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
ConfigurationEquilibrium 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
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 Equilibri
um Time (s)
Final equilibrium height (m)
Case A ( = o0, T = 27oC)
Water 68 0.02
Hydrazine 58.2 0.019
Case B( = 50, T = 27oC)
Water50 0.017
Hydrazine64
0.02 (maximum)
Case C( = o0, T = 100C)
Water60 0.018
Hydrazine70 0.02
Case D( = o0, T = 50oC) Water
46 0.018
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
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.
Thank You