Turbulence modeling of compressible flows with large density variation

In this study we highlight the influence of mean dilatation and mean density gradient on the Reynolds stress modeling of compressible, heat-releasing and supercritical turbulent flows. Firstly, the modeling of the rapid pressure-strain correlation has been extended to self-consistently account for the influence of mean dilatation. Secondly, an algebraic model for the turbulent density flux has been developed and coupled to the tensor equation for Reynolds stress anisotropy via a ’local mean acceleration’, a generalization of the buoyancy force. We applied the resulting differential Reynolds stress model (DRSM) and the corresponding explicit algebraic Reynolds stress model (EARSM) to homogeneously sheared and compressed or expanded two-dimensional mean flows. Both formulations have shown that our model preserves the realizability of the turbulence, meaning that the Reynolds stresses do not attain unphysical values, unlike earlier approaches. Comparison with rapid distortion theory (RDT) demonstrated that the DRSM captures the essentials of the transient behaviour of the diagonal anisotropies and gives good predictions of the turbulence kinetic energy. A general three-dimensional solution to the coupled EARSM has been formulated. In the case of turbulent flow in de Laval nozzle we investigated the influence of compressibility effects and demonstrated that the different calibrations lead to different turbulence regimes but with retained realizability. We calibrated our EARSM against a DNS of combustion in a wall-jet flow. Correct predictions of turbulent density fluxes have been achieved and essential features of the anisotropy behaviour have been captured. The proposed calibration keeps the model free of singularities for the cases studied. In addition, we have applied the EARSM to the investigation of supercritical carbon dioxide flow in an annulus. The model correctly captured mean enthalpy, temperature and density as well as the turbulence shear stress. Hence, we consider the model as a useful tool for the analysis of a wide range of compressible flows with large density variation. Descriptors: Turbulence, DRSM, EARSM, active scalar, compressible flow, reacting flow, supercritical flow