A new turbulence model based on scale decomposition

Based on the characteristics of the multi-scale and similarity at different scales in turbulent flow, this study proposes a scale decomposition for solving the turbulence problem of incompressible Newtonian fluid. The solution domain is decomposed into two-level scales, with the large scale component representing mean flow and large scale eddies, while the small scale one captures turbulent fluctuations. The problem is addressed at the large scale through equations of motion, and the influence of turbulent fluctuations on the mean flow is approximated using equivalent eddy methods. The equivalent eddy effects are further divided into convective and diffusion components, expressed as functions of mean quantities in the large scale. The modified Navier-Stokes equations are formulated to ensure closure in the large scale framework. A numerical simulation is employed to verify these equations, specifically investigating flow around a cylinder under varying Reynolds numbers. The study ultimately establishes a general-purpose turbulence model, which holds significant potential for engineering applications.