Stability of explicit navier-stokes procedures using k-ε and k - ε/algebraic reynolds stress turbulence models

Robert Francis Kunz, Budugur Lakshminarayana

Research output: Contribution to journalArticle

36 Citations (Scopus)

Abstract

A three-dimensional explicit Navier-Stokes procedure has been developed for application to compressible turbulent flows, including rotation effects. In the present work, a numerical stability analysis of the discrete, coupled system of seven governing equations is presented. Order of magnitude arguments are presented for flow and geometric properties typical of internal flows, including turbomachinery applications, to ascertain the relative importance of grid stretching, rotation and turbulence source terms, and effective diffusivity on the stability of the scheme. It is demonstrated through both analysis and corroborative numerical experiments that: (1 ) It is quite feasible to incorporate, efficiently, a two-equation k-ε{lunate} turbulence model in an explicit time marching scheme, provided certain numerical stability constraints are enforced. (2) The role of source terms due to system rotation on the stability of the numerical scheme is not significant when appropriate grids are used and realistic rotor angular velocities are specified. (3) The direct role of source terms in the turbulence transport equations on the stability of the numerical scheme is not significant when appropriate grids are used and realistic freestream turbulence quantities are specified, except in the earliest stages of iteration (a result which is contrary to that generally perceived). (4) There is no advantage to numerically coupling the two-equation model system to the mean flow equation system, in regard to convergence or accuracy. (5) For some flow configurations, including turbomachinery blade rows, it is useful to incorporate the influence of artificial dissipation in the prescription of a local timestep. (6) Explicit implementation of an algebraic Reynolds stress model (ARSM) is intrinsically stable provided that the discrete two-equation transport model which provides the necessary values of k and ε{lunate} is itself stable.

Original languageEnglish (US)
Pages (from-to)141-159
Number of pages19
JournalJournal of Computational Physics
Volume103
Issue number1
DOIs
StatePublished - Jan 1 1992

Fingerprint

Reynolds stress
turbulence models
Turbulence models
Turbulence
Turbomachinery
Convergence of numerical methods
turbomachinery
numerical stability
turbulence
grids
Angular velocity
Turbomachine blades
Turbulent flow
Stretching
time marching
Rotors
internal flow
flow equations
angular velocity
blades

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Cite this

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abstract = "A three-dimensional explicit Navier-Stokes procedure has been developed for application to compressible turbulent flows, including rotation effects. In the present work, a numerical stability analysis of the discrete, coupled system of seven governing equations is presented. Order of magnitude arguments are presented for flow and geometric properties typical of internal flows, including turbomachinery applications, to ascertain the relative importance of grid stretching, rotation and turbulence source terms, and effective diffusivity on the stability of the scheme. It is demonstrated through both analysis and corroborative numerical experiments that: (1 ) It is quite feasible to incorporate, efficiently, a two-equation k-ε{lunate} turbulence model in an explicit time marching scheme, provided certain numerical stability constraints are enforced. (2) The role of source terms due to system rotation on the stability of the numerical scheme is not significant when appropriate grids are used and realistic rotor angular velocities are specified. (3) The direct role of source terms in the turbulence transport equations on the stability of the numerical scheme is not significant when appropriate grids are used and realistic freestream turbulence quantities are specified, except in the earliest stages of iteration (a result which is contrary to that generally perceived). (4) There is no advantage to numerically coupling the two-equation model system to the mean flow equation system, in regard to convergence or accuracy. (5) For some flow configurations, including turbomachinery blade rows, it is useful to incorporate the influence of artificial dissipation in the prescription of a local timestep. (6) Explicit implementation of an algebraic Reynolds stress model (ARSM) is intrinsically stable provided that the discrete two-equation transport model which provides the necessary values of k and ε{lunate} is itself stable.",
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Stability of explicit navier-stokes procedures using k-ε and k - ε/algebraic reynolds stress turbulence models. / Kunz, Robert Francis; Lakshminarayana, Budugur.

In: Journal of Computational Physics, Vol. 103, No. 1, 01.01.1992, p. 141-159.

Research output: Contribution to journalArticle

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