Evaluation of a subgrid model for the Arrhenius reaction rate in a jet

Large eddy simulation (LES) of combustion problems involve highly nonlinear terms that, when filtered, result in a contribution from subgrid (subfilter) fluctuations of the scalar, Z, to the filtered value. The subgrid contribution requires modeling. In the approximate reconstruction using moments (ARM) method, a surrogate scalar field is obtained from the available filtered field by approximate reconstruction, a purely mathematical procedure, as well as additional physics-based information required to match specific scalar moments, in the simplest case, the subgrid variance. Here, we present results from a priori and a posteriori studies of the ARM model in the case of a spatially evolving plane jet. The nonlinearities considered are of two types: a polynomial function and an exponential function. A priori analysis, using data from direct numerical simulation (DNS), is carried out using different filter sizes. One of these filter sizes is chosen to perform a LES and obtain a posteriori results with a dynamic eddy diffusivity model. The a priori tests show that the ARM model is able to capture the subgrid part of the variance accurately over a wide range of filter sizes and reasonable well for higher polynomials up to an eighth power as well as the exponential nonlinearity. The a posteriori case shows good behavior of the subgrid model, similar to that in the a priori test.