Enhancing Turbulence Modeling With Compressibility Corrections: A Revised Approach to Dissipation and Pressure–Strain Correlations

Abstract This research employs the Reynolds stress model (RSM) to replicate compressibility effects on turbulence. Academic studies have consistently highlighted the critical role of the interaction between pressure–strain correlations and dissipation mechanisms in advancing the accuracy of RSM predictions. The primary objective of this study is to enhance predictive precision by incorporating compressibility corrections into both the standard turbulent dissipation model and the pressure–strain correlation model. It is demonstrated that the incompressible model equation for turbulent dissipation fails to perform adequately in compressible turbulence within high-speed shear flows, even when compressible pressure–strain models are included. To address this limitation, a compressibility correction for the Cϵ1 coefficient is proposed, enabling accurate computations of compressible homogeneous shear flows and compressible mixing layers. The proposed model is derived from an exact temporal derivative equation of fluctuating velocity, establishing a relationship between Cϵ1 and key compressibility parameters: the turbulent Mach number, the gradient Mach number, and the convective Mach number. A custom computational code employing a finite difference scheme was developed specifically to simulate compressible turbulent mixing layers. Results are presented for compressible homogeneous shear flows under various initial conditions, compared with direct numerical simulation (DNS) data, as well as for compressible mixing layers using experimental data. The findings indicate that the proposed model demonstrates strong potential for improving predictions in compressible turbulence scenarios.