An energy-consistency-preserving large eddy simulation-scalar filtered mass density function (LES-SFMDF) method for high-speed flows

Abstract

An energy-consistency-preserving large eddy simulation-scalar filtered mass density function (LES-SFMDF) method is developed to improve the existing LES-SFMDF method in high-speed flows, especially supersonic flows. The high-speed source term in the SFMDF transport equation is analysed theoretically from a new point of view, and then several primary principles are proposed for the LES-SFMDF to achieve a good consistency even along discontinuities. Based on these principles and further theoretical analysis, the high-speed source term of the enthalpy in the SFMDF is modelled and computed from both MC and LES variables rather than the usually used solely LES variables. This new LES-SFMDF method is used for simulating the flows in a shock tube and in a subsonic temporally developing mixing layer. This method shows a better particle energy consistency than the existing method when applied across discontinuities in supersonic laminar flows. Unlike the existing method, with this energy-consistency-preserving LES-SFMDF method, particle energy consistency is consistent with particle mass consistency so that particle energy consistency can benefit from particle velocity correction. This method also demonstrates robustness for various numbers of particles.