Turbulence originating from the compromise-in-competition between viscosity and inertia

• Turbulence from compromise-in-competition between viscosity and inertia.
• Stability criterion is successfully applied for closure of turbulence model.
• A meso-scale model, namely EMMS-based turbulence model, is proposed.
• Meso-science provides a new viewpoint for exploring fluid turbulence.

Fluid flows in chemical engineering are mainly characterized by the coexistence of turbulent and non-turbulent fluids. Nonetheless, in traditional turbulence models, the laminar portion of the fluid flow is often neglected and constitutive laws are expressed to describe fully turbulent states within computational grids. We perceived this situation is a source of inaccuracies in modeling practical engineering flows. In this work, a stability criterion for turbulent flows, originating from the principle of compromise-in-competition between viscosity and inertia, is used to obtain closure in the turbulence model, which defines the energy-minimization multi-scale (EMMS)-based turbulence model. Analogous to two-phase flow, the model regards single-phase complex flows as a mixture of turbulent and non-turbulent fluids, and the effect of meso-scale eddy structure on the effective coefficient of viscosity is also considered. The EMMS-based turbulence model is tested against three benchmark problems, namely, the lid-driven cavity problem, flow through a conical diffuser, and flow over an airfoil using experimental and direct numerical simulation (DNS) data. Numerical results show that the EMMS-based turbulence model improves the accuracy of turbulence modeling, demonstrating its feasibility and practicality for accurate simulations of engineering complex flows.