Compressible Turbulence Predicted by Reynolds Stress Models

Turbulence in strongly compressible flows as found in internal combustion engines is investigated with several models of turbulence. The standard k - ϵ model, 2 classical and 4 of the most recent Reynolds Stress models are used in this investigation. The compressible flow with a non-zero velocity divergence necessitates some changes to the incompressible model formulations normally presented. Flows selected for the present study are the spherical, radial and the uniaxial compressions/expansions belonging to the class of flows with irrotational normal strains.

For the selected flows the response of the scalar quantities k and ϵ together with the anisotropy in the normal Reynolds stresses are examined. The initial behavior of isotropic turbulence in the rapid distortion theory (RDT) limit is a variation of k and ϵ as density to the power 2/3 and 4/3, respectively. Anisotropy develops in a direction driven by the strain field and will feed back to the generation of k and ϵ causing each flow case to be different. Most actual flows with compressibility do not have strain rates large enough to satisfy the rapid distortion theory, so the dissipative effects are included in this study.