Analysis of the viscous/molecular subgrid-scale dissipation terms in LES based on transport equations: A priori tests

Abstract

One trend in large-eddy simulations (LES) involves the use of a transport equation for the subgrid-scale (SGS) kinetic energy. For problems involving active or passive scalar fields a SGS scalar variance transport equation is also used. The terms from these equations involve sub-filter scale quantities that are not accessible during LES and thus require modelling. By far the greatest challenge for modelling in these equations comes from the viscous and the molecular SGS dissipation terms that represent the final (dissipation) stages of the ‘energy cascade mechanism’ whereby the SGS kinetic energy and SGS scalar variance are dissipated through the action of the molecular viscosity and diffusivity, respectively. In this work direct numerical simulations (DNS) of statistically stationary (forced) homogeneous, isotropic turbulence are used to (i) analyse the topology and spatial localisation of the viscous and the molecular SGS dissipation terms, (ii) assess three models currently used for these terms and (iii) present some guidelines to improve or develop future models for these terms. The models analysed here are (a) the classical model used by e.g. Schumann [1] and Yoshizawa [2], (b) the model used in hybrid RANS/LES by Paterson and Peltier [3], and by Hanjalic [4], and (c) the model for the molecular SGS dissipation of SGS scalar variance from Jiménez et al. [5]. The classical models for the molecular SGS dissipation give very good results in terms of topology, spatial localisation (in the physical space), statistical behaviour and spectral characteristics. Moreover, the model constants approach asymptotically the theoretical values as the Reynolds number and filter sizes increase which supports the use of a constant value in engineering and geophysical applications, instead of using a dynamic procedure for their computation as in Ghosal et al. [6]. For the molecular SGS dissipation of SGS scalar variance the model from Jiménez et al. [5] performs even better than the classical model and should be the preferred model for this term when the Schmidt number is close to 1.0. Finally, all the tests showed that the models used in hybrid RANS/LES tested here give very poor results either in terms of their topological, statistical or spectral characteristics. The reason behind this is connected with the deficient spectral representation of the exact molecular SGS dissipation terms.

Keywords:

• subgrid-scale modelling
• viscous/molecular SGS dissipation
• isotropic turbulence
• direct numerical simulations

Acknowledgement

Carlos B. da Silva is supported by the Portuguese Minister of Science and Technology (MCTES) under ‘Ciência 2007’.