The closure problem of turbulence is still a challenging issue in turbulencemodeling. In this work, a stability condition is used to close turbulence.Specifically, we regard single-phase flow as a mixture of turbulent andnon-turbulent fluids, separating the structure of turbulence. Subsequently,according to the picture of the turbulent eddy cascade, the energy contained inturbulent flow is decomposed into different parts and then quantified. Aturbulence stability condition, similar to the principle of theenergy-minimization multi-scale (EMMS) model for gas-solid systems, isformulated to close the dynamic constraint equations of turbulence, allowingthe heterogeneous structural parameters of turbulence to be optimized. We callthis model the `EMMS-based turbulence model', and use it to construct thecorresponding turbulent viscosity coefficient. To validate the EMMS-basedturbulence model, it is used to simulate two classical benchmark problems,lid-driven cavity flow and turbulent flow with forced convection in an emptyroom. The numerical results show that the EMMS-based turbulence model improvesthe accuracy of turbulence modeling due to it considers the principle ofcompromise in competition between viscosity and inertia.
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