A priori tests of large eddy simulation of the compressible plane mixing layer

Abstract

Three important aspects for the assessment of the possibilities of Large Eddy Simulation (LES) of compressible flow are investigated. In particular the magnitude of all subgrid-terms, the role of the discretization errors and the correlation of the turbulent stress tensor with several subgrid-models are studied. The basis of the investigation is a Direct Numerical Simulation (DNS) of the two- and three-dimensional compressible mixing layer, using a finite volume method on a sufficiently fine grid. With respect to the first aspect, the exact filtered Navier-Stokes equations are derived and all terms are classified according to their order of magnitude. It is found that the pressure dilatation subgrid-term in the filtered energy equation, which is usually neglected in the modelling-practice, is as large as e.g. the pressure velocity subgrid-term, which in general is modelled. The second aspect yields the result that second- and fourth-order accurate spatial discretization methods give rise to discretization errors which are larger than the corresponding subgrid-terms, if the ratio between the filter width and the grid-spacing is close to one. Even if an exact representation for the subgrid-scale contributions is assumed, LES performed on a (considerably) coarser grid than required for a DNS, is accurate only if this ratio is sufficiently larger than one. Finally the well-known turbulent stress tensor is investigated in more detail. A priori tests of subgrid-models for this tensor yield poor correlations for Smagorinsky's model, which is purely dissipative, while the non-eddy viscosity models considered here correlate considerably better.