Explicit Algebraic Subgrid-Scale Stress Model for Homogeneous Turbulence

Abstract

The whole construct of explicit algebraic Reynolds stress models, as they are known in RANS, is based on the weak equilibrium assumption. By employing this assumption, and in addition, incorporating models for terms in the Reynolds stress transport equations, the system of six partial differential equations can be simplified to an algebraic form. However, the resulting equations are non-linear in terms of the Reynolds stress anisotropy and therefore become implicit. The cause of the non-linearity is the presence of the ratio of kinetic energy production to dissipation (P/E) in the equations. In order to derive an explicit model for the Reynolds stress anisotropy, methods to determine P/E are required. For RANS, there are many variations of the final formulation based on the procedure by which this ratio is determined. Marstorp et al. (2009) provide an extension of this modelling framework used in RANS to LES in order to model subgrid-scale (SGS) stresses. In their formulation, the value of P/E, which in LES is the ratio of SGS kinetic energy production to dissipation, is specified as 1, thereby obviating any need for treating non-linearities in the equations.

In this thesis, the performance of the explicit algebraic subgrid-scale stress model (EASSM) developed by Marstorp et al. (2009) is tested in comparison with the dynamic Smagorinsky model (DSM) at an a priori level using DNS data for forced homogeneous turbulence with and without system rotation. Based on the results of the a priori analysis, a new model, termed as the non-equilibrium EASSM is introduced, which does not require the assumption that P/E = 1. The framework of EASSM demands the determination of the SGS kinetic energy and the time-scale in order to close the system of equation. While Marstorp et al. (2009) use algebraic expressions for determining these additional variables, for the non-equilibrium EASSM, avoiding the assumption that P/E = 1 enables the use of an evolution equation for the SGS kinetic energy. For the time-scale, an algebraic expression is derived as a function of SGS kinetic energy and dissipation. The performance of the non-equilibrium EASSM in comparison with the DSM and the EASSM of Marstorp et al. (2009) is evaluated by conducting LES of forced and decaying homogeneous turbulence, with and without rotation, using the finite volume code-INCA. For forced cases, the non-equilibrium model outperforms other models in terms of mean resolved and SGS kinetic energy predictions, and also gives a good match for the time averaged resolved spectrum with DNS. In the presence of strong rotation, however, all the models fail to capture the right decay rate as observed in DNS. On examining the DNS data for the two decaying cases, it appears that the isotropic scaling used for the modelling SGS kinetic energy dissipation in the non-equilibrium model deteriorates the model performance making it unable to provide the right level of inhibition in the decay of the resolved kinetic energy and dissipation.