Title: On physical constraints for multi-scale turbulence closure models

Authors: K. Stawiarski, K. Hanjalic

Addresses: Thermal and Fluids Sciences Section, Department of Multi-scale Physics, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands. ' Thermal and Fluids Sciences Section, Department of Multi-scale Physics, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands

Abstract: This paper deals with a generalisation of physical constraints for the family of two-scale eddy viscosity turbulence models, aimed at deriving general model coefficients. The focus is on models in which – next to the transport equation for the turbulence kinetic energy – two additional equations are solved to provide separately the scales of the energy-containing eddies and of the dissipative processes. The natural choice for accounting for spectral dynamics is to solve separate equations for the spectral energy flux dominated by the energy-containing eddies, ε_p, and for the energy dissipation ε_T. We give a critical evaluation of the physical constraints derived for three generic turbulent flows, which can be used to determine model coefficients. The analysis is presented for a generic variable φ, which can subsequently be transformed into any other scalar scale variable, allowing one to analyse the properties and performances of different equations.

Keywords: turbulence modelling; multi-scale modelling; second moment closure; non-equilibrium flows; generic flows; physical constraints; turbulence closure models; eddy viscosity turbulence; transport equation; turbulence kinetic energy; turbulent flows; heat transfer.

DOI: 10.1504/PCFD.2005.006747

Progress in Computational Fluid Dynamics, An International Journal, 2005 Vol.5 No.3/4/5, pp.120 - 135

Published online: 05 Apr 2005 *

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