Preconditioned Navier-Stokes method for two-phase flows with application to cavitation prediction

Robert Francis Kunz, David A. Boger, David R. Stinebring, Thomas S. Chyczewski, Jules Washington V. Lindau, Howard J. Gibeling, Sankaran Venkateswaran, T. R. Govindan

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

An implicit algorithm for the computation of viscous two-phase flows is presented in this paper. The baseline differential equation system is the multi-phase Navier-Stokes equations, comprised of the mixture volume, mixture momentum and constituent volume fraction equations. Though further generalization is straightforward, a three-species formulation is pursued here, which separately accounts for the liquid and vapor (which exchange mass) as well as a non-condensable gas field. The implicit method developed here employs a dual-time, preconditioned, three-dimensional algorithm, with multi-block and parallel execution capabilities. Time-derivative preconditioning is employed to ensure well-conditioned eigenvalues, which is important for the computational efficiency of the method. Special care is taken to ensure that the resulting eigensystem is independent of the density ratio and the local volume fraction, which renders the scheme well-suited to high density ratio, phase-separated two-fluid flows characteristic of many cavitating and boiling systems. To demonstrate the capabilities of the scheme, several two- and three-dimensional examples are presented.

Original languageEnglish (US)
Pages (from-to)849-875
Number of pages27
JournalAnnales de Chimie: Science des Materiaux
Volume25
Issue number3
StatePublished - Jan 1 2000

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Cavitation
Two phase flow
Volume fraction
Computational efficiency
Boiling liquids
Navier Stokes equations
Flow of fluids
Momentum
Differential equations
Gases
Vapors
Derivatives
Liquids

All Science Journal Classification (ASJC) codes

  • Materials Chemistry

Cite this

Kunz, R. F., Boger, D. A., Stinebring, D. R., Chyczewski, T. S., Lindau, J. W. V., Gibeling, H. J., ... Govindan, T. R. (2000). Preconditioned Navier-Stokes method for two-phase flows with application to cavitation prediction. Annales de Chimie: Science des Materiaux, 25(3), 849-875.
Kunz, Robert Francis ; Boger, David A. ; Stinebring, David R. ; Chyczewski, Thomas S. ; Lindau, Jules Washington V. ; Gibeling, Howard J. ; Venkateswaran, Sankaran ; Govindan, T. R. / Preconditioned Navier-Stokes method for two-phase flows with application to cavitation prediction. In: Annales de Chimie: Science des Materiaux. 2000 ; Vol. 25, No. 3. pp. 849-875.
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Kunz, RF, Boger, DA, Stinebring, DR, Chyczewski, TS, Lindau, JWV, Gibeling, HJ, Venkateswaran, S & Govindan, TR 2000, 'Preconditioned Navier-Stokes method for two-phase flows with application to cavitation prediction', Annales de Chimie: Science des Materiaux, vol. 25, no. 3, pp. 849-875.

Preconditioned Navier-Stokes method for two-phase flows with application to cavitation prediction. / Kunz, Robert Francis; Boger, David A.; Stinebring, David R.; Chyczewski, Thomas S.; Lindau, Jules Washington V.; Gibeling, Howard J.; Venkateswaran, Sankaran; Govindan, T. R.

In: Annales de Chimie: Science des Materiaux, Vol. 25, No. 3, 01.01.2000, p. 849-875.

Research output: Contribution to journalArticle

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T1 - Preconditioned Navier-Stokes method for two-phase flows with application to cavitation prediction

AU - Kunz, Robert Francis

AU - Boger, David A.

AU - Stinebring, David R.

AU - Chyczewski, Thomas S.

AU - Lindau, Jules Washington V.

AU - Gibeling, Howard J.

AU - Venkateswaran, Sankaran

AU - Govindan, T. R.

PY - 2000/1/1

Y1 - 2000/1/1

N2 - An implicit algorithm for the computation of viscous two-phase flows is presented in this paper. The baseline differential equation system is the multi-phase Navier-Stokes equations, comprised of the mixture volume, mixture momentum and constituent volume fraction equations. Though further generalization is straightforward, a three-species formulation is pursued here, which separately accounts for the liquid and vapor (which exchange mass) as well as a non-condensable gas field. The implicit method developed here employs a dual-time, preconditioned, three-dimensional algorithm, with multi-block and parallel execution capabilities. Time-derivative preconditioning is employed to ensure well-conditioned eigenvalues, which is important for the computational efficiency of the method. Special care is taken to ensure that the resulting eigensystem is independent of the density ratio and the local volume fraction, which renders the scheme well-suited to high density ratio, phase-separated two-fluid flows characteristic of many cavitating and boiling systems. To demonstrate the capabilities of the scheme, several two- and three-dimensional examples are presented.

AB - An implicit algorithm for the computation of viscous two-phase flows is presented in this paper. The baseline differential equation system is the multi-phase Navier-Stokes equations, comprised of the mixture volume, mixture momentum and constituent volume fraction equations. Though further generalization is straightforward, a three-species formulation is pursued here, which separately accounts for the liquid and vapor (which exchange mass) as well as a non-condensable gas field. The implicit method developed here employs a dual-time, preconditioned, three-dimensional algorithm, with multi-block and parallel execution capabilities. Time-derivative preconditioning is employed to ensure well-conditioned eigenvalues, which is important for the computational efficiency of the method. Special care is taken to ensure that the resulting eigensystem is independent of the density ratio and the local volume fraction, which renders the scheme well-suited to high density ratio, phase-separated two-fluid flows characteristic of many cavitating and boiling systems. To demonstrate the capabilities of the scheme, several two- and three-dimensional examples are presented.

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