In this paper we demonstrate that the transport equation of the generalised subgrid scale (SGS) turbulent stress tensor is form-invariant but not frame-indifferent under Euclidean transformations of the frame. A new closure equation between the generalized SGS turbulent stress tensor and the resolved kinematic quantities is proposed. The closure equation at the basis of the proposed model (Two-Equation Model, TEM): a) respects the principle of the turbulence frame indifference [ 1]; b) takes into account both the anisotropy of the turbulence velocity scales and turbulence length scales; c) removes any balance assumption between the production and dissipation of SGS turbulent kinetic energy; d) assumes scale similarity in the definition of the second-order tensor representing the turbulent velocity scales. In the proposed model: a) the closure coefficient C which appears in the constitutive equation is uniquely determined without using Germano's dynamic procedure [ 2]; b) the generalized SGS turbulent stress tensor is related exclusively to the generalized SGS turbulent kinetic energy ( which is calculated by means of its balance equation) and the modified Leonard tensor; c) the viscous dissipation e of the generalized SGS turbulent kinetic energy is calculated by solving the e balance equation. The proposed model is tested for a turbulent channel flow at Reynolds numbers ( based on friction velocity and channel half-width) ranging from 180 to 2340.

A dynamic two-equation sub grid scale model / Gallerano, Francesco; E., Pasero; Cannata, Giovanni. - In: CONTINUUM MECHANICS AND THERMODYNAMICS. - ISSN 0935-1175. - STAMPA. - 17:2(2005), pp. 101-123. [10.1007/s00161-004-0190-4]

A dynamic two-equation sub grid scale model

GALLERANO, Francesco;CANNATA, Giovanni
2005

Abstract

In this paper we demonstrate that the transport equation of the generalised subgrid scale (SGS) turbulent stress tensor is form-invariant but not frame-indifferent under Euclidean transformations of the frame. A new closure equation between the generalized SGS turbulent stress tensor and the resolved kinematic quantities is proposed. The closure equation at the basis of the proposed model (Two-Equation Model, TEM): a) respects the principle of the turbulence frame indifference [ 1]; b) takes into account both the anisotropy of the turbulence velocity scales and turbulence length scales; c) removes any balance assumption between the production and dissipation of SGS turbulent kinetic energy; d) assumes scale similarity in the definition of the second-order tensor representing the turbulent velocity scales. In the proposed model: a) the closure coefficient C which appears in the constitutive equation is uniquely determined without using Germano's dynamic procedure [ 2]; b) the generalized SGS turbulent stress tensor is related exclusively to the generalized SGS turbulent kinetic energy ( which is calculated by means of its balance equation) and the modified Leonard tensor; c) the viscous dissipation e of the generalized SGS turbulent kinetic energy is calculated by solving the e balance equation. The proposed model is tested for a turbulent channel flow at Reynolds numbers ( based on friction velocity and channel half-width) ranging from 180 to 2340.
anisotropy; les; scale similarity; sgs turbulent kinetic energy; turbulent frame-indifference; two-equation
01 Pubblicazione su rivista::01a Articolo in rivista
A dynamic two-equation sub grid scale model / Gallerano, Francesco; E., Pasero; Cannata, Giovanni. - In: CONTINUUM MECHANICS AND THERMODYNAMICS. - ISSN 0935-1175. - STAMPA. - 17:2(2005), pp. 101-123. [10.1007/s00161-004-0190-4]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/232255
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