Post on 15-Jul-2015
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
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 fordifferent scale models.(Cone angle 28o, with cylindricalsection)
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 therising 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)
17oWith cylindrical section (water) 960 0.74
Without cylindrical section (water) 530 0.63
21oWith cylindrical section (water) 940 0.55
Without cylindrical section (water) 780 0.58
28oWith 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 1:0.1 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
References1. 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.