Joint-velocity scalar energy probability density function method for large eddy simulations of compressible flow

The combination of large eddy simulation (LES) and probability density function (PDF) methods is a general framework to model turbulent reactive flows. The coupled approach provides direct closures for the nonlinear subgrid source terms typical of chemically reacting flows. LES-PDF methods have a wide range of applicability and they are started to be used in high-speed flows with strong compressibility effects. However, PDF formulations are more complex in compressible flows, where mechanical and thermodynamic contributions are more coupled. The paper presents a novel PDF framework that uses a full thermodynamic closure (scalar-energy-density-velocity) with the Eulerian Monte Carlo stochastic field approach. The work uses simple closures for the subgrid terms using the advantages of the Eulerian formulation and recasts the stochastic equations in a pseudoconservative form. The resultant formulation is applied to three canonical compressible flows: turbulent shock-tubes, compressible homogeneous turbulence, and a reactive free-moving premixed flame. All cases show large density and pressure fluctuations. The effects of underlying numerical schemes and PDF closures to represent compressible effects are investigated along with the statistical convergence of the method.