A Priori Tests of RANS Models for Turbulent Channel Flows of a Dense Gas

Abstract

Dense gas effects, encountered in many engineering applications, lead to unconventional variations of the thermodynamic and transport properties in the supersonic flow regime, which in turn are responsible for considerable modifications of turbulent flow behavior with respect to perfect gases. The most striking differences for wall-bounded turbulence are the decoupling of dynamic and thermal effects for gases with high specific heats, the liquid-like behavior of the viscosity and thermal conductivity, which tend to decrease away from the wall, and the increase of density fluctuations in the near wall region. The present work represents a first attempt of quantifying the influence of such dense gas effects on modeling assumptions employed for the closure of the Reynolds-averaged Navier-Stokes equations, with focus on the eddy viscosity and turbulent Prandtl number models. For that purpose, we use recent direct numerical simulation results for supersonic turbulent channel flows of PP11 (a heavy fluorocarbon representative of dense gases) at various bulk Mach and Reynolds numbers to carry out a priori tests of the validity of some currently-used models for the turbulent stresses and heat flux. More specifically, we examine the behavior of the modeled eddy viscosity for some low-Reynolds variants of the k − ε model and compare the results with those found for a perfect gas at similar conditions. We also investigate the behavior of the turbulent Prandtl number in dense gas flow and compare the results with the predictions of two well-established turbulent Prandtl number models.

High-subsonic boundary-layer flows of an organic vapour

“…Density fluctuations are correlated with pressure ones, unlike the perfect gas, where the near-wall streaks correspond directly to high- and low-density fluid. A priori analyses of several RANS models based on these DNS databases was conducted by Sciacovelli, Cinnella & Gloerfelt (2018). If the modelled eddy viscosity behaves in the same manner as for air flows at similar conditions, the agreement with turbulent Prandtl number models is less conclusive due to the reduced thermal boundary layer.…”

Numerical Investigation of Supersonic Dense-Gas Boundary Layers

“…Nevertheless, reliable experimental measurements are still difficult to obtain. To this purpose, high-fidelity datasets, as those provided by DNS, represent an effective tool for getting insight into the physics of turbulent dense-gas flows and for the assessment of lower-fidelity models [8].…”