A Modified Gas-Kinetic Scheme for Turbulent Flow

TL;DR

This paper introduces a gas-kinetic scheme for turbulent flow simulation that inherently accounts for the degree of rarefaction and models turbulence without relying on linear stress-strain relations, improving accuracy in complex flows.

Contribution

The paper develops a modified gas-kinetic scheme integrating turbulence modeling directly into the numerical framework, avoiding traditional eddy viscosity assumptions.

Findings

Better capture of shock-turbulent boundary layers

Improved simulation of flows challenging for RANS methods

Automatic consideration of the degree of rarefaction in turbulence modeling

Abstract

By analogy with the kinetic theory of gases, most turbulence modeling strate- gies rely on an eddy viscosity to model the unresolved turbulent fluctuations. How- ever, the ratio of unresolved to resolved scales - very much like a degree of rarefaction - is not taken into account by the popular conventional schemes, based on the Navier- Stokes equations. This paper investigates the simulation of turbulent flow with a gas- kinetic scheme. In so doing, the modeling of turbulence becomes part of the numerical scheme: the degree of rarefaction is automatically taken into account; the turbulent stress tensor is not constrained into a linear relation with the strain rate. Instead it is modeled on the basis of the analogy between particles and eddies, without any as- sumptions on the type of turbulence or flow class. The implementation of a turbulent gas-kinetic scheme into a finite-volume solver is put forward, with turbulent kinetic energy and dissipation supplied by an allied turbulence model. A number of flow cases, challenging for conventional RANS methods, are investigated; results show that the shock-turbulent boundary layer is captured in a much more convincing way by the gas-kinetic scheme.