Development of a new dynamic procedure for the Clark model of the subgrid-scale scalar flux using the concept of optimal estimator

Abstract

Accurate prediction of a scalar advected by a turbulent flow is needed for various applications. In the framework of large-eddy simulation (LES), an accurate subgrid-scale (SGS) model for the subgrid-scale scalar flux has to be used. In this work, the performance of various dynamic SGS models is first evaluated by a priori tests through the concept of optimal estimator. Direct numerical simulation (DNS) in homogeneous isotropic turbulence is performed on 5123 grid points. Filtered quantities are extracted from the DNS data using a box or a spectral cut-off filter. The models’ accuracy is then evaluated in term of structural and functional performances, i.e., the model capacity to locally approximate the SGS unknown term and to reproduce its energetic action, respectively. It is shown that the Clark model has the best set of parameters to describe the SGS scalar flux. However, the classic dynamic procedure usually applied to compute the model coefficient leads to a large error. A new dynamic procedure is thus proposed to reduce this error. The results show that the new dynamic model leads to a good accuracy, which is not expectable from a model based only on the parameters of the classic dynamic Smagorinsky model. To better evaluate the improvement of the new dynamic procedure, a posteriori (large-eddy simulation) tests are performed for three different Schmidt numbers. It is shown that the new model allows to improve substantially the prediction of various scalar statistics.