A-PRIORI TESTS OF LARGE-EDDY SIMULATION OF THE COMPRESSIBLE PLANE MIXING LAYER

Three important aspects for the assessment of the possibilities of Lar ge Eddy Simulation (LES) of compressible flow are investigated. In par ticular the magnitude of all subgrid-terms, the role of the discretiza tion errors and the correlation of the turbulent stress tenser with se veral subgrid-models are studied. The basis of the investigation is a Direct Numerical Simulation (DNS) of the two- and three-dimensional co mpressible mixing layer, using a finite volume method on a sufficientl y fine grid. With respect to the first aspect, the exact filtered Navi er-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 neglec ted in the modelling-practice, is as large as e.g, the pressure veloci ty subgrid-term, which in general is modelled. The second aspect yield s the result that second- and fourth-order accurate spatial discretiza tion 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 (c onsiderably) coarser grid than required for a DNS, is accurate only if this ratio is sufficiently larger than one. Finally the well-known tu rbulent stress tenser is investigated in more detail. A priori tests o f subgrid-models for this tenser yield poor correlations for Smagorins ky's model, which is purely dissipative, while the non-eddy viscosity models considered here correlate considerably better.