microgravity flow transients in the context of on-board propellant gauging

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


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


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



(water)

780 0.58



(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