Computing Compressible TwoFluid Flow

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Computing Compressible Two-Fluid Flow

• DCSE Customer Day
• September 19, 2008

Jasper Kreeft, Jeroen Wackers, Barry Koren
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Contents
Introduction Flow Model Flow Solver Flow
Problems Conclusions

• Introduction
• Flow model
• Flow solver
• Flow problems
• Conclusions

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Introduction
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Two-fluid flow (exhaust gases air)?
Introduction Flow Model Flow Solver Flow
Problems Conclusions
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Two-fluid flow (water air)?
Introduction Flow Model Flow Solver Flow
Problems Conclusions
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Two-fluid interface
Introduction Flow Model Flow Solver Flow
Problems Conclusions
Separates two fluids
Divide domain in small volumes
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Interface Capturing
Introduction Flow Model Flow Solver Flow
Problems Conclusions

• Distinct single-fluid flow models only, not
  applicable
• No boundary conditions at interface

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Euler model
Introduction Flow Model Flow Solver Flow
Problems Conclusions

• No friction
• No heat conduction

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Flow Model
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Euler equations
Introduction Flow Model Flow Solver Flow
Problems Conclusions
Mass transport across boundary
Rate of change of mass
Mass
Momentum Energy
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Interface-capturing model
Introduction Flow Model Flow Solver Flow
Problems Conclusions

• Assumptions
• No mixing
• Equal velocities
• Equal pressures

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Interface-capturing model (cont.)?
Introduction Flow Model Flow Solver Flow
Problems Conclusions

• Assumptions
• No mixing
• Equal velocities
• Equal pressures

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Interface-capturing model (cont.)?
Introduction Flow Model Flow Solver Flow
Problems Conclusions
Volume fraction
Bulk mass
Bulk momentum
Bulk energy
Mass fluid 1
Energy fluid 1
2 equations of state
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Source terms
Introduction Flow Model Flow Solver Flow
Problems Conclusions
Assumption equal velocities
Mass fraction
Assumption equal pressures
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Source terms (cont.)?
Introduction Flow Model Flow Solver Flow
Problems Conclusions
Quasi-1D channel flow 1D two-fluid flow
Pressure force for increment in volume fraction
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Source terms (cont.)?
Introduction Flow Model Flow Solver Flow
Problems Conclusions
Pressure force to keep velocities equal
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Source terms (cont.)?
Introduction Flow Model Flow Solver Flow
Problems Conclusions
Compression or expansion
Isentropic compressibility
Energy exchange to keep pressures equal
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Flow Solver
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Finite-volume discretization
Introduction Flow Model Flow Solver Flow
Problems Conclusions

• Integral form

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• Time stepping
• three-stage explicit Runge-Kutta

• Monotone second-order accurate spatial
  discretization limiter BK
• Flux vector evaluation
  Oshers approximate Riemann solver

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Source-term evaluation
Introduction Flow Model Flow Solver Flow
Problems Conclusions

• Only spatial derivatives
• Consider 1D case

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Source-term evaluation (cont.)?
Introduction Flow Model Flow Solver Flow
Problems Conclusions

• Source-term evaluation in solution space,
• using Osher-type scheme

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Flow Problems
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Shock-tube problems
Introduction Flow Model Flow Solver Flow
Problems Conclusions

• 1D
• Exact solutions known
• Perfect gases

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Translating-interface problem
Introduction Flow Model Flow Solver Flow
Problems Conclusions
Pressure
Volume fraction
Density
Pressure-oscillation-free without special
precaution
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No-reflection problem
Introduction Flow Model Flow Solver Flow
Problems Conclusions

• Shock hitting interface
• Density distributions
• Influence of source term

Without source term
With source term
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Shock-bubble interaction problem
Introduction Flow Model Flow Solver Flow
Problems Conclusions
R22 Higher density and lower ratio of
specific heats than air lower
speed of sound Helium Lower density and higher
ratio of specific heats than air
higher speed of sound
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A motivation for this problem scramjet
Introduction Flow Model Flow Solver Flow
Problems Conclusions

• Supersonic
• combustion ramjet
• Experiments performed by
• Haas Sturtevant (1987)?

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R22 bubble density
Introduction Flow Model Flow Solver Flow
Problems Conclusions
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R22 density (replay)?
Introduction Flow Model Flow Solver Flow
Problems Conclusions
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R22 bubble volume fraction
Introduction Flow Model Flow Solver Flow
Problems Conclusions
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Comparison with experiment
Introduction Flow Model Flow Solver Flow
Problems Conclusions
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Helium bubble density
Introduction Flow Model Flow Solver Flow
Problems Conclusions
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Helium bubble density (replay)?
Introduction Flow Model Flow Solver Flow
Problems Conclusions
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Helium bubble volume fraction
Introduction Flow Model Flow Solver Flow
Problems Conclusions
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Comparison with experiment
Introduction Flow Model Flow Solver Flow
Problems Conclusions
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Conclusions
Introduction Flow Model Flow Solver Flow
Problems Conclusions

• Physical model for compressible two-fluid flow
• Good physical solutions without special
  precaution

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Thank you for your interest
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