Modeling Plume and Shock in Convective Turbulence: Non-equilibrium and Supersonic Effects

Abstract:

Turbulence in compressible convective flows with coherent structures like buoyant plumes and strong density gradients like shock front is investigated. In order to develop a turbulence model for such flows, both the non-equilibrium and supersonic effects are incorporated with the aid of the multiple-scale renormalized perturbation expansion methods. Expressions for the turbulent viscosity and diffusivity are obtained, where the deviations from the simplest eddy viscosity and diffusivity are incorporated through the non-equilibrium effects represented by the material derivatives, and the strong compressibility effects embodied by the turbulent Mach number and the density variance. A simple turbulence model constituted by a self-consistent system of equations of the mean and fluctuation fields is presented on the basis of analytical theory of compressible turbulence. Turbulent transport changes associated with a buoyant plume and a high density variance near shock are discussed.