Hyperbolic equivalent k-ϵ and k-ω turbulence models for moment-closures

摘要: The ten-moment equations are considered as a first-order alternative of Navier-Stokes equations when the effect of heat transfer is negligible. This model takes the form of first-order hyperbolic conservation laws, which carry many numerical advantages. However, the applicability of this model is still limited due to the lack of appropriate turbulence models. Applying the Reynolds-averaging concept to the ten-moment model, a set of governing equations for turbulent flow can be obtained, which is referred to as the Reynolds-averaged ten-moment equations. The traditional turbulence models designed for the Reynolds-averaged Navier-Stokes (RANS) equations are not ideal for the Reynolds-averaged ten-moment equations, as the extra partial differential equations (PDEs) introduce second-order derivatives. These terms destroy the pure hyperbolic nature of the original system of equations, which consequently …