Quasi-analytical solutions of a turbulence-modeling equation on the robustness of decaying homogeneous turbulence

Abstract

The present study introduces third-order quasi-analytical solutions of a turbulence-modeling equation, where the standard k − ϵ model equation is used because this model is commonly and widely used in engineering applications. These quasi-analytical solutions describe the robustness of decaying homogeneous turbulence. In the present study, decaying homogeneous turbulence influenced by a weak fluid acceleration of mean flow, which is equivalent to the small strain of the mean flow, is considered. Here, the small strain of the mean flow only slightly affects the anisotropy of the decaying homogeneous turbulence, as shown in previous experiments. Simplified governing equations are derived from the governing equations of the turbulence modeling by introducing the conditions of the small strain. Here, two nondimensional functions are introduced in order to describe the influence on the turbulent kinetic energy and its dissipation using decay laws of the turbulent kinetic energy and its dissipation. Three constants included in the quasi-analytical solutions could be obtained using observable parameters.