CFD Improved GasLiquid Methodology to High Speed Venting and Bulk-Flyout Problems AIAA-2007-0922.pdf

8/10/2019 CFD Improved GasLiquid Methodology to High Speed Venting and Bulk-Flyout Problems AIAA-2007-0922.pdf

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Application of Improved Gas/Liquid Methodology to HighSpeed Venting and Bulk-Flyout Problems

G. Feldman * , K.W. Brinckman , S.M. Dash , and A. Hosangadi Combustion Research & Flow Technology, Inc. (CRAFT Tech)

Email: [email protected]

Recently developed gas liquid methodology for cavitating flows is applied to higher-speedflows dealing with bulk liquid venting and flyout. The new methodology improves uponearlier VOF methodology, using a unified multi-phase thermodynamic framework andpreconditioning, and, it operates in a multi-element UNS grid. An earlier bulk flyout studyanalyzed using VOF methodology is reviewed and a repeat of this calculation using the newmethodology is described, including application of grid adaptation to improve resolution atthe captured gas/liquid interface. Additional jet in cross-flow and venting problems aredescribed which demonstrate current capabilities.

I. IntroductionHIS paper discusses the application of recently developed gas/liquid methodology for cavitating flows, 1-5 tohigher speed problems dealing with bulk liquid venting and flyout. The analysis of bulk liquid interactions with

a gaseous stream is complex and requires the ability to: (1) fit or capture the deforming gas/liquid interface; and, (2)to predict primary breakup processes along this interface producing droplets or ligaments. In conventionalapproaches, the gas and bulk liquid are treated as distinct, immiscible phases. For problems with complex interfacegeometries and/or where breakup may occur, capturing approaches are more practicable, with volume-of-fluid(VOF) methodology typically being used for applications such as fuel injection in combustion chambers, withempirical breakup relations applied along the captured interface.

T

Earlier applications of density-based VOF methodology (using the CRAFT CFD structured grid code 6,7) tocomplex, high-speed, bulk-flyout problems 8 (described in the next section of this paper) showed both thecapabilities and limitations of this approach. In this work, the ability to capture the dynamics and deformation of aliquid blob, initially moving at supersonic velocity into still air was demonstrated. Working in blob-fixed

coordinates, with modest grid resolution, the deforming and decelerating gas/liquid interface was adequatelycaptured. Later, primary breakup correlations along the interface were applied, which produced droplet sizedistributions that appeared to be quite reasonable.

There were, however, inherent limitations to the VOF approach utilized. A primary limitation was the range ofconditions that could be analyzed. Earlier applications of the VOF methodology for high-pressure problems, such asthe combustion chamber of liquid propellant guns 9, were quite successful because the liquid behaved in acompressible manner. However, for venting or bulk-dispense problems at lower pressures, the liquid behavior wasessentially incompressible making the solution extremely stiff. In addition, high resolution is required at thegas/liquid interface which is not easy to achieve for a rapidly deforming, dynamic blob using structured-gridmethodology.

In the new methodology developed for cavitating flow applications (such as liquid rocket pumps/inducers 10, andvalve and feed systems 11), such limitations for venting/bulk-dispense problems are eased. Instead of using a VOFframework (with different thermodynamic treatments of gas and liquid), a unified, multi-phase thermodynamic

framework is used which is applicable to both gas and liquid phases. Hence, only a single system of fluid equationneeds to be solved without the need to include co-volume terms as in VOF formulations. In addition, the density- based fluid dynamic equations are transformed to a quasi-pressure-based form, and preconditioning is used whichfacilitates integrating the equations for problems with widely disparate speeds of sound. Lastly, this approach is

* Research Scientist, Charlotte, NC, Member AIAA Research Scientist, Pipersville, PA, Member AIAA President & Chief Scientist, Pipersville, PA Associate Fellow AIAA. Principal Scientist, Pipersville, PA, Member AIAA

American Institute of Aeronautics and Astronautics1
mailto:[email protected]:[email protected]


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implemented in our multi-element unstructured grid code, CRUNCH CFD , permitting grid adaptation to be appliedto obtain high-resolution at the gas-liquid interface.

This paper describes IR & D activities performed to assess how this cavitation-derived gas/liquid formulationanalyzes a very different class of flow problems. The cavitation problems analyzed are primarily those of nominallyincompressible liquids with pockets of gas-vapor produced by cavitation. The venting and bulk-liquid dispense

problems of interest involve the interaction of bulk liquid with an airstream, where at high speeds, the gas flow can be highly compressible with shocks, while the liquid can be quite incompressible, particularly at lower pressures.

In Section II, we summarize our earlier analysis of a high-speed, bulk-liquid flyout problem, analyzed using theVOF methodology in the CRAFT CFD structured grid code. Section III describes the new, cavitation-derivedgas/liquid formulation, while Section IV describes its application to the same bulk-liquid flyout problem discussedin Section II. Section V describes liquid-jet in a cross-flow and liquid missile venting problems using the newgas/liquid formulation. Concluding remarks are given in Section VI.

II. Overview of Earlier Gas/Liquid Simulation Using VOF ApproachThe problem of interest is schematized in Figure 1 with early stages involving the ability of a gas/liquid CFD

code to analyze the interaction of bulk liquid with a high speed air stream (the deformation of the bulk liquidinterface and its deceleration) and the formation of droplets at the gas/liquid interface. An interface capturing

procedure was implemented and a VOF (volume of fluid) framework was used whereby both gas and bulk-liquid co-occupy the same computational cells, with void fractions identifying the relative volume occupied by the gas and

liquid. The original analysis was performed in the CRAFT CFD

structured grid code using a density basedframework, with details described in Refs. 7 and 8. Some important physics to note in Figure 1 are the bow shockthat forms ahead of the blob, followed by the downstream formation of ligaments as the liquid begins to interactwith the surrounding flow field. As the ligaments are further elongated, the stripping off of droplets begins to occurat the gas/liquid interface. These droplets are then carried further downstream where secondary breakup and/orvaporization will begin to take place.

Figure 1. Schematic Of Bulk Liquid Fly-Out Problem Showing The Physics Of The Blob In Supersonic Flow.

While this was cutting edge work at the time, there were still key drawbacks to this approach. First, the use of astructured code would not allow the grid to be easily adapted along an arbitrary gas/liquid interface. The surfacetension, shear forces, and liquid volume fraction along the interface will be key parameters in predicting how andwhen the liquid will begin to breakup into droplets. Therefore, capturing and refining the interface is crucial to

predicting primary breakup. Clustering grid points about the dynamic gas/liquid interface is better achieved usingunstructured numerics and an adaptive grid pack age that can readily handle unsteady flows with discontinuities,such as the CRISP solver of Cavallo, et. al 12. The second limiting factor to the original CRAFT CFD methodology was the void fraction approach. Work prior to performing bulk-liquid fly-out problems entailed theanalysis of liquid propellant guns (LPG) where the pressures were very high and the liquid behaved in acompressible manner. However, in analyzing liquid venting or bulk fly-out from missiles, the pressure was much



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lower and the liquid behaved in an incompressiblemanner, which limited the applicability of the gas/liquidframework in the CRAFT CFD code.

Figure 2. Results From Bulk Liquid Fly-OutSimulation Showing That Important Physical

Mechanisms Were Captured.

The original problem modeled was a liquid blobflying through air at Mach 2. The liquid was acylindrical blob 50 cm long and 50 cm in diameter andused properties extracted from our LPG work 9. To

perform this analysis with the CRAFT CFD code, pressures had to be "artificially elevated" to make theliquid behave in a compressible manner. The simulationwas run in a blob fixed framework where the grid movedand decelerated with the blob. The liquid wasimpulsively started at a velocity of 700 m/s. A snapshotof the results is shown . This snapshot showsthe important physical characteristics captured in thesimulation. First, pressure lines show the bow shockthat formed ahead of the blob. Also evident is thegas/liquid interface highlighted by the dark black lines.Liquid ligaments are shown to have formed at both theleading and trailing edges of the blob. This is the regionwhere primary breakup would first occur.

Figure 2

The simulation was first run without a primary breakup model, which made it possible to demonstrate thecapabilities of the gas/liquid formulation alone. A primary breakup model was then added to include more physicsinto the simulation. Refs. 7 and 8 describe details of how the breakup and formation of droplets along the gas/liquidinterface was modeled. Figure 3 shows snapshots of the liquid blob case run without the primary breakup model. Itis clear that without breakup included, the liquid rolls up in an unrealistic manner. The views at 2.0 ms and 2.4 msshow that without a breakup model, the ligaments formed at the gas/liquid interface continue to grow and elongatewithout breaking off from the original blob. The case was then run again, this time making use of the primary

breakup model with results shown in Figure 4 . The snapshots of this simulation taken at 0.45 ms and 1.14 ms looksimilar to the case without primary breakup with some ligaments seen at the leading edge of the blob. However, theremaining snapshots show very different results from the case without primary breakup. There are liquid dropletsseen breaking away from the ligaments, and by 3.81 ms there is very little of the original liquid blob still remaining.

Figure 3. Gas/Liquid Contours From The Simulation Run Without A Primary Breakup Model.



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Figure 4. Gas/Liquid Contours From The Simulation Run With A Primary Breakup Model.

III. Improved Gas/Liquid FormulationBased on the comments above regarding the need for an improved gas/liquid framework for bulk flyout and

venting problems, new methodology developed for cavitating flows was examined. The new methodology entailsextensions to the multi-element UNS code, CRUNCH CFD , and was developed to support the analysis ofcavitation related studies in rocket turbo-machinery, and in ducts and valves used in liquid rocket testing - , ,1 5 10 11 . Inthis new formulation, the independent variables are transformed from a density and internal energy system to a

pressure and enthalpy system. Mixtures of "generalized fluids" follow Amagat's law and not Dalton's law. Thematrix defines the transformation of the variables from to The original system of equations is given by: Q vQ

v=S+DQ E F G

t x y z

+ + + (1)

where

[ ], , , , , , , T iQ u v w Y e k = (2)

The transformed system takes the form:



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vv

Q E F GS D

t x y z

+ + + = + (3)

where

[ ], , , , , , ,

T

v iQ p u v w Y T k =

(4)

Thermodynamic derivatives in this formulation are defined in a completely generalized fashion that works withuser defined equations of state with the transformation matrix given by:

( )

i

i

i

i

i

i

i

y

y

y

y

y

y

y

0 0 0 0 0

0 0 0 0

0 0 0

0 0 0 0 (1 ) (1 ) 0 0

0 0 0 0 0

0 0 0 0

0 0 0 0

i

i

p T

p T

p T

p T

p p T T y

i P i T i Y ij

p T

p T

u u u

v v v

w w w

H h u v w H h H h

Y Y Y

k k k

0

= + +

(5)

For efficient operations over a wide range of Mach numbers, this matrix may be further preconditioned to getwell-conditioned eigenvalues that improve convergence and reduce round-off errors. The following results indicatethat the upgraded formulation provides a robust methodology for predicting high-speed liquid venting and bulk fly-out problems without the previous limitations on system pressure and required liquid compressibility.

IV. Bulk Liquid Fly-Out Studies With Improved Formulation

A. Liquid blob with comparison to earlier workThe earlier liquid blob case was repeated (same conditions) using the new formulation in the CRUNCH CFD

code. The only difference was that in this case we worked in ground fixed coordinates. Thus, a Mach 2 flow was blown over an initially stationary liquid blob, which then moves downstream and eventually equilibrates with thefree stream flow. The solution with CRUNCH is remarkably similar to that earlier obtained with CRAFT.

Mass fraction contours are shown in Figure 5 . The same roll-up of the liquid is seen at the edges, followed bythe elongation of liquid ligaments like the CRAFT CFD solution. Ligament formation is consistent with the resultsexpected in a bulk liquid fly-out problem referenced earlier in Figure 1 . The dark black line in the figures highlightsthe gas/liquid interface, which is defined as the line where liquid and gas concentration are both 50%. It isimportant to resolve this gas/liquid interface, as primary breakup will be modeled to occur along that line. The black

box in the figure serves as a reference to the original shape and location of the liquid blob. The central area of the blob is forced downstream a total of approximately 50 cm (or 1 blob diameter) in 4 ms. The bow shock seen aheadof the liquid blob is formed as expected and can be seen in Figure 6 . Here pressure and liquid mass fractioncontours are shown, and expansion waves can be seen at the trailing edge of the ligaments, which was alsoconsistent with the CRAFT solution. Figure 7 shows velocity vectors superimposed on mass fraction contours,which further highlights the ability of the gas/liquid formulation to capture the liquid roll up. Finally, Figure 8 shows the deceleration of the liquid blob relative to the surrounding flow field. By 7 ms the liquid will have almostequilibrated with the surrounding flow field.



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1 ms 2 ms

3 ms 4 ms

Gas Liquid InterfaceHighlighted In Black

*Black Box shows original liquid blob shape.

Figure 5. Mass Fraction Contours And Bulk Movement Of The Liquid Blob.

1 ms

2 ms

3 ms 4 ms

Figure 6. Pressure And Liquid Mass Fraction Contours.



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1 ms 2 ms

3 ms 4 ms

Figure 7. Liquid Mass Fraction Contours With Velocity Vectors.

Velocity History of Bulk Liquid

0

100

200

300

400

500

600

700

800

0 1 2 3 4 5 6 7 8

Time (ms)

V e

l o c i

t y ( m / s )

Figure 8. Relative Velocity Showing Liquid Blob Deceleration.

B. Liquid blob with grid adaptation As stated earlier, one advantage of the new gas/liquid formulation in the unstructured CRUNCH CFD code was

the ability to perform grid adaptation. The liquid blob case was run again, this time starting with a coarse gr id andthen making use of grid adaptation. The current capabilities of the CRISP CFD grid adaptation package 13 allowthe grid to be refined dynamically as the solution progresses without the need for any user involvement. Uponstarting the problem within CRUNCH CFD , an error estimate is projected ahead of the solution at each time stepto determine the fitness of the current grid. Once the fitness falls below pre-defined levels, the grid is automaticallyadapted based on user defined refinement factors ahead of the current solution. The grid is then adapted based only



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on the original grid, not prior adaptations.This prevents the grid from growingcontinually larger after each adaptation,which could lead to an overly large gridwith too many grid points to runefficiently. The automation feature withinCRUNCH allows the grid to be adequatelyresolved throughout the entire run of the

problem with little user intervention.Figure 9 shows the liquid blob moving

through time, followed by the gridadaptation that corresponded to each timestep in Figure 10 . The initial grid for thiscase was coarser than the grid used for theoriginal high pressure simulation. As the

blob moves through the domain, grid points are clustered along the gas/liquidinterface. This is especially evident in thesnapshots at 3 and 4 ms. As the bluntleading face of the blob expands radiallyoutward, the grid point clustering can beseen from the top to the bottom of thedomain.

Grid adaptation will play an extremelyimportant role in future problems as thegas/liquid capabilities of the code areexpanded to include primary break-up.These droplets will form along the gas/liquid interface, which will require a great deal of grid resolution to beaccurately captured. This interface will be changing both spatially and temporally. The CRISP CFD gridadaptation feature will allow us to resolve the interface without the size of the grid becoming too computationallyexpensive, and without the need for excess user intervention.

1 msec

4 msec3 msec

2 msec

Figure 9. Liquid Blob Moving Through Time With GridAdaptation.

1 msec

4 msec3 msec

2 msecGrid adapts to flow-field features asthe solution marches through time.

Figure 10. Changing Grid As It Adapts To The Blob Moving Through The Domain.



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C. Low pressure liquid blob In this simulation, the liquid blob was analyzed at a pressure of 1 atm. As stated earlier, a deficiency in the

original VOF formulation was the need to artificially boost the pressure to make the liquid behave in a compressiblemanner. Running the blob at a pressure of 1 atm is a precursor to cases that will be simulated at higher altitude, andin general, pushes the limits of the gas/liquid formulation. Due to the stiffness of the equation of state currently usedfor the liquid phase, it was necessary to add a small amount of artificial dissipation to the solution for numericalstability. A more broadly applicable equation of state may be necessary for simulations run at higher altitudes orlower pressures. Mass fraction contours are shown in Figure 11 . Similar to the high pressure cases, the liquid rollsup and forms ligaments at the trailing edge. The pressure contours are shown in Figure 12 . As seen in the higher

pressure blob case, a bow shock forms upstream of the blob. The lower pressure case does look different towardsthe trailing edge; however, as pressure waves show there is not as much expansion as in the high pressure case.

1 ms 2 ms


1 ms 2 ms


3 ms 4 ms3 ms 4 ms

Figure 11. Mass Fraction Contours For Liquid Blob At 1atm.

1 ms

2 ms

3 ms 4 ms

1 ms

2 ms

3 ms 4 ms

Figure 12. Pressure And Liquid Mass Fraction Contours Of Liquid Blob At 1atm.



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V. Jet-In-Cross-Flow StudiesA. 2D and 3D Simulations at Atmospheric Conditions

Another class of gas/liquid interaction problems studied was liquid jet-in-cross-flow problems. These problemsshow the versatility of the gas/liquid formulation in their ability to handle another complicated flow regime, of theliquid jet flowing transverse to the gas. The first cases were simulated at atmospheric pressure (P = 1 atm) andtemperature (T = 300 K) analogous to the liquid fly-out problem. In this case, the cross flow gas was moving with a

velocity of 100 m/s and the liquid jet was moving at a velocity of 5 m/s. The liquid stream was 100% liquid byvolume.

This study was first conducted using a 2D slot jet, with liquid volume fraction contours shown in Figure 13 .Despite the low speed of the liquid, the momentum of the jet allows the liquid to penetrate to a height of about 2.5nozzle diameters. Figure 14 shows velocity vectors for the 2D jet. This gives good perspective on the dynamics ofthe flow field, and shows some important physics that were captured such as the recirculation region downstream ofthe slot. An upstream air boundary layer was not included in this solution, which would have produced a separatedzone upstream of the liquid jet.

For completeness, the 2D case was extended into 3D with a round liquid jet and the same flow conditions asdescribed earlier. Figure 15 show contours of liquid volume fraction at the nozzle centerline. It can again be seenthat the momentum of the jet causes the liquid to penetrate to a height of about 2.1 nozzle diameters. For gas/liquidflows the acoustic speed will vary greatly as the two phases mix, and this is shown in Figure 16 . The acoustic speedis highest in the regions where there is a pure gas or liquid, and drops dramatically as the two phases mix. Finally,

the shape of the jet can be seen in Figure 17 which shows iso-surface contours of constant liquid volume fraction.The jet can be seen rolling-up as the gas and liquid mix downstream.

Liquid Penetration Height~ 2.5 Nozzle DiametersLiquid Penetration Height~ 2.5 Nozzle Diameters

Figure 13. 2D Slot Jet Liquid Penetration Height.

Recirculation regiondownstream of the jetRecirculation regiondownstream of the jet

Figure 14. 2D Slot Jet Velocity Vectors.



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Liquid Penetration Height~ 2.1 Nozzle DiametersLiquid Penetration Height~ 2.1 Nozzle Diameters

Figure 15. 3D Round Jet Liquid Volume Fraction And Jet Penetration Height At Nozzle Centerline.

Acoustic speed is highest in puregas and pure liquid regions.

Acoustic speed drops dramaticallyin regions of gas/liquid mixing.

Acoustic speed is highest in puregas and pure liquid regions.

Acoustic speed drops dramaticallyin regions of gas/liquid mixing.

Figure 16. 3D Round Jet Showing Acoustic Speed Variations As A Result Of Gas/Liquid Mixing.

Liquid Penetration Height~ 2.1 Nozzle Diameters

Jet rollup can be seen as liquid jetand gas cross-flow mix.

Liquid Penetration Height~ 2.1 Nozzle Diameters

Jet rollup can be seen as liquid jetand gas cross-flow mix.

Figure 17. 3D Round Jet Iso-Surface Contours Of Constant Liquid Volume Fraction Shows Jet PenetrationHeight And Jet Roll-Up As The Gas And Liquid Mix.



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B. Case 2 Missile Venting Simulations The second liquid jet-in-a-crossflow problem was simulated with a generic missile body flying at an altitude of

10 km. A six-inch diameter hole at the missile mid-point was vented a liquid/gas mixture. Flow conditions and problem setup are shown in Figure 18 . For this case, the jet was 50% gas/50 % liquid by volume. The jet/free-stream interaction, jet acoustic speed, and computational stability are all highly dependant on the liquid volumefraction of the jet.

As shown in Figure 19 , there is a significant difference in mass fraction and volume fraction at low free-stream jet pressures. While the jet is a 50/50 mix of gas and liquid by volume, it is nearly all liquid by mass. Figure 20 exhibits pressure contours, and a shock is seen to form in front of the liquid jet due to interactions with the freestream. As shown previously for the slot jet in Figure 16 , the acoustic speed is highest for a pure liquid, drops offsharply as the liquid concentration decreases, and then rises sharply again when the mixture becomes a pure gas.This is seen clearly again for the missile at altitude in Figure 21 as the acoustic speed varies by more than an orderof magnitude from the free-stream to the jet, and then rises again as the liquid in the jet diffuses out downstream. InFigure 22 , Iso-Surface contours of liquid volume fraction show how the jet rolls-up as it mixes with the free-stream.

Free-stream:

Altitude = 10 km

Mach Number = 1.6

Velocity = 500 m/s

Pressure = 28008 Pa

Temperature = 233.1 K

Jet:

Liquid Volume Fraction = 51.7%

Liquid Mass Fraction = 99.8%Mach Number = 0.32

Velocity = 33 m/s

Pressure = 12P inf (336100Pa)

Temperature = 300 K

MissileGas/Liquid Jet

Figure 18. Missile Liquid Jet Venting Problem Setup And Definition.

VolumeFraction

MassFraction

Figure 19. Liquid Volume And Mass Fraction Contours For A Missile At 10 km.



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Shock seenahead of the jet.

Figure 20. Pressure Contours Around The Missile And Liquid Jet.

Shock seen ahead of the jet

Large variation in theacoustic speed seen acrossthe jet. Then shown toincrease as the liquiddiffuses out down stream.

Figure 21. Missile Liquid Jet Mach Number And Acoustic Speed Contours.

Looking Downstream Looking Upstream

Jet shown rolling up asit mixes downstream.

Figure 22. Iso-Surface Contours Of Constant Liquid Volume Fraction Of Liquid Venting From Missile.



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VI. ConclusionThe cases described above were all exploratory problems to assess gas/liquid capabilities of the CRUNCH

Code used for cavitation, to bulk flyout and venting problems. It was shown that using the new formulationavailable in CRUNCH , gas/liquid studies could be performed at atmospheric pressure and low altitudes. This wasnot possible using the earlier VOF formulation that required the pressure to be boosted artificially. The addedflexibility of the unstructured numerics in the CRUNCH permits grid adaptation to be incorporated into gas/liquid

studies. This will be vital for primary breakup problems so that the gas/liquid interface can be captured with highfidelity.

Further developments for this work are currently under-way. While it has been shown that the gas/liquidnumerics are capable of handling a wide array of problems, there is still a need to extend the current work to higheraltitude and higher velocity problems. One area of research that may make this possible is the implementation of amore robust equation of state for the liquid. The key area of focus now, however, is on extending the gas/liquidcapabilities to include a primary breakup engineering model. This will further enhance the current simulations byincluding more realistic physics and open up a wide array of problems that can by solved using the CRUNCH CFD code.

AcknowledgmentsThis work was primarily supported by CRAFT Tech IR & D funding.

References1 Hosangadi, A., and Ahuja, V., "Simulations of Cavitating Flows Using Hybrid Unstructured Meshes," Paper No.FEDSM2000-11082, 4 th ASME/JSME Joint Fluids Engineering Conference, Boston, MA, June 11-15, 2000.2 Hosangadi, A. and Ahuja, V., A Generalized Multi-Phase Framework For Modeling Unsteady Cavitation Dynamics AndThermal Effects, Paper No. AIAA-2003-4000, 33 rd AIAA Fluid Dynamics Conference, Orlando, FL, Jun 23-26, 2003.3 Hosangadi, A., Ahuja, V., and Ungewitter, R.J. Simulations Of Cavitating Flows In Turbopumps, Journal of Propulsionand Power, Vol. 20, No. 4, pp. 604-611, July-August, 2004.4 Hosangadi, A. and Ahuja, V., Numerical Study Of Cavitation In Cryogenic Fluids, Journal of Fluids Engineering , Vol. 127,

pp. 267-281, March 2005.5 Hosangadi, A., and Ahuja, V., A New Unsteady Model for Dense Cloud Cavitation, FEDSM2005-77485, 2005 ASMEFluids Engineering Summer Conference, Fifth International Symposium on Pumping Machinery, Houston, TX, June 19-23,2005.6 Hosangadi, A., Sinha, N., and Dash, S.M., "A Unified Hyperbolic Interface Capturing Scheme for Gas/Liquid Flows," AIAA-97-2081, 13 th AIAA CFD Conferences, Snowmass, CO, June 29-July 2, 1997.7

Tonello, N.A., Dash, S.M., and Perrell, E.R., Advanced Computational Framework For Dynamic Bulk-Liquid GasInteractions, AIAA Paper-99-2205, 35th AIAA/ASME/ SAE/ASEE Joint Propulsion Conference and Exhibit, Los Angeles, CA,June 20-24, 1999.8 Perrell, E., Tonello, N.A, Hosangadi, A., Sinha, N., and Dash, S.M., CFD of Complex Three-Dimensional Multi-PhaseFlowfields, Edgewood Chem-Bio Center, ECBC-CR-045, January 2002.9 Hosangadi, A., Sinha, N., Dash, S.M., Wren, G., DeSpirito, J., Coffee, T., and Thompson, "3D Puddle Ignition Study forLiquid Propellant Guns," 32nd JANNAF Combustion Mtg., Oct. 23-27, 1995.10 Hosangadi, A., Ahuja, V., and Ungewitter, R.J., Simulations of Inducers at Low-Flow Off-Design Conditions, FEDSM2005-77395, 2005 ASME Fluids Engineering Summer Conference, Fifth International Symposium on Pumping Machinery, Houston,TX, June 19-23, 2005.11 Ahuja, V., Hosangadi, A., Shipman, J., and Cavallo, P.A., Simulations of Instabilities in Complex Valve and Feed Systems,AIAA-2006-4758, 42 nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Sacramento, CA, 9 - 12 Jul 2006.12 Cavallo, P.A., and Grismer, M.J., A Parallel Adaptation Package For Three-Dimensional Mixed-Element UnstructuredMeshes, Journal of Aerospace Computing, Information, and Communication , Vol. 2, No. 11, pp. 433-451.13 Cavallo, P.A., Arunajatesan, S., Sinha, N., and Baker, T.J., Transient Mesh Adaptation Using an Error Wake and Projection

Method, AIAA Paper 2006-1149, 44th

Aerospace Sciences Meeting, Reno, NV, January 9-12, 2006.


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CFD Improved GasLiquid Methodology to High Speed Venting and Bulk-Flyout Problems AIAA-2007-0922.pdf