Progress in Favré–Reynolds stress closures for compressible flows

Abstract

A closure for the compressible portion of the pressure-strain covariance is developed. It is shown that, within the context of a pressure-strain closure assumption linear in the Reynolds stresses, an expression for the pressure-dilatation can be used to construct a representation for the pressure-strain. Additional closures for the unclosed terms in the Favre-Reynolds stress equations involving the mean acceleration are also constructed. The closures accommodate compressibility corrections depending on the magnitude of the turbulent Mach number, the mean density gradient, the mean pressure gradient, the mean dilatation, and, of course, the mean velocity gradients. The effects of the compressibility corrections are consistent with current DNS results. Using the compressible pressure-strain and mean acceleration closures in the Favre-Reynolds stress equations an algebraic closure for the Favre-Reynolds stresses is constructed. Noteworthy is the fact that, in the absence of mean velocity gradients, the mean density gradient produces Favre-Reynolds stresses in accelerating mean flows. Computations of the mixing layer using the compressible closures developed are described. Full Reynolds stress closure and two-equation algebraic models are compared to laboratory data. The mixing layer configuration computations are compared to laboratory data; since the laboratory data for the turbulence stresses is inconsistent, this comparison is inconclusive. Comparisons for the spread rate reduction indicate a sizable decrease in the mixing layer growth rate.

Numerical Simulation of Interaction of the Heavy Gas Cloud with the Atmospheric Surface Layer

“…However, dependence (33) for L V does not agree with experiments and simulations in Figure 2, where an increase of the cloud height due to mixing is observed, in contrast to the collapse of the cloud predicted by (33). At the same time, simulated dependences of L H (curves 2 and 3 in Figure 3a) approach the analytical dependence (33) (curve 1).…”

“…Unlike the models of stratified flows with small density deviations, for which the Boussinesq approximation is applicable, the development of models of turbulence for the flows with large deviations of density is far from satisfactory [31][32][33]. Therefore, we used simple gradient relations for the turbulent stresses and fluxes which kept tensor invariance in density variable flows [31]:…”

Modelling of pressure–strain correlation in compressible turbulent flow

“…Adumitroaie et al [21], Fujiwara et al [22] and Park et al [3] proposed models for the pressure-strain correlation of compressible turbulent flows. They alter the behaviors of the Reynolds stress anisotropy by changing the pressure-strain term in order to reduce the level of turbulence production.…”

Toward second-moment closure modelling of compressible shear flows

“…Although much progress has been made for incompressible flows (Launder, Reece & Rodi 1975;Speziale, Sarkar & Gatski 1991;Johansson & Hallbäck 1994;Ristorcelli, Lumley & Abid 1995;Girimaji 2000;Sjögren & Johansson 2000), finding an adequate compressible pressure-strain correlation has proven to be an elusive task. Some of the earliest work towards the development of a compressible pressure-strain correlation closure is that done by Cambon et al (1993) and Adumitroaie, Ristorcelli & Taulbee (1999). Cambon et al (1993) propose an exponential decay of the rapid pressure-strain correlation as a function of gradient Mach number.…”