Analysis of sub grid scale modeling of the ideal gas equation of state in hydrogen oxygen premixed flames
Abstract In large eddy simulations (LES) of multicomponent and fully compressible flows, the spatially filtered pressure needs to be evaluated, i.e. the pressure averaged over a volume. The flow is non homogeneous within this volume and the state relationship linking pressure, density, temperature and species mass fractions should not be applied directly to their values resolved on the LES mesh. In practice, the unresolved correlations between density, species and temperature are usually neglected to compute the filtered pressure from the resolved fields. Analyzing one dimensional laminar and three dimensional turbulent H2/O2 space filtered flames under lean and stoichiometric conditions, it is observed that a large part of the error introduced by the linearization of the equation of state can be counterbalanced by expressing the mean molar weight of the mixture with the Reynolds filtered species mass fractions, instead of the density weighted (Favre) mass fractions. A sub grid scale closure for the remaining part of the unknown correlation is also proposed, which relies on a scale similarity assumption. Finally, an approximate deconvolution/filtering procedure is discussed to estimate the Reynolds filtered mass fractions from the density weighted mass fractions, which are the transported quantities in LES flow solvers.