A priori evaluation of dynamic subgrid models of turbulence in square duct flow

Abstract

A priori tests of two dynamic subgrid-scale (SGS) turbulence models have been performed using a highly resolved direct numerical simulation database for the case of turbulent incompressible flow in a straight duct of square cross-section. The model testing is applied only to the homogeneous flow direction where grid filtering can be applied without the introduction of commutation errors. The first SGS model is the dynamic (Smagorinsky/eddy viscosity) SGS model (DSM) developed by Germano et al. [1] while the second is the dynamic two parameter (mixed) model (DTM) developed by Salvetti and Banerjee [2]. For the Smagorinsky model we have used both the Fourier cut-off filter and a modified Gaussian filter which has the property that it removes aliasing errors in consistent a priori model-testing for spectral-based datasets. Results largely consistent with those found for plane channel flow are observed but with some slight differences in the corner regions. As found in prior studies of this sort, there is a very poor correlation of the modelled and exact subgrid-scale dissipation in the case of the DSM. The DSM over-predicts subgrid-scale dissipation on average. Instantaneously, the model provides an inaccurate representation of subgrid-scale dissipation, in general underestimating the magnitude by approximately one order of magnitude. On the other hand, the DTM shows excellent agreement with the exact SGS dissipation over most of the duct cross-section with a correlation coefficient of approximately 0⋅9.