The closure problem of turbulence is still a challenging issue in turbulence
modeling. In this work, a stability condition is used to close turbulence.
Specifically, we regard single-phase flow as a mixture of turbulent and
non-turbulent fluids, separating the structure of turbulence. Subsequently,
according to the picture of the turbulent eddy cascade, the energy contained in
turbulent flow is decomposed into different parts and then quantified. A
turbulence stability condition, similar to the principle of the
energy-minimization multi-scale (EMMS) model for gas-solid systems, is
formulated to close the dynamic constraint equations of turbulence, allowing
the heterogeneous structural parameters of turbulence to be optimized. We call
this model the `EMMS-based turbulence model', and use it to construct the
corresponding turbulent viscosity coefficient. To validate the EMMS-based
turbulence model, it is used to simulate two classical benchmark problems,
lid-driven cavity flow and turbulent flow with forced convection in an empty
room. The numerical results show that the EMMS-based turbulence model improves
the accuracy of turbulence modeling due to it considers the principle of
compromise in competition between viscosity and inertia.Comment: 26 pages, 13 figures, 2 table