Analysis of Dense Gas Effects in Compressible Turbulent Channel Flows

Abstract

In this work we investigate the influence of dense gas effects on compressible wall-bounded turbulence. Turbulent flows of dense gases represent a research field of great importance for a wide range of applications in engineering. Dense gases are single-phase fluids with a molecular complexity such that the fundamental derivative of gas dynamics [1], which measures the rate of change of the sound speed in isentropic transformations, is less than one in a range of thermodynamic conditions close to the saturation curve. In such conditions, the speed of sound increases in isentropic expansions and decreases in isentropic compressions, unlike the case of perfect gases. For dense gases, the perfect gas model is no longer valid, and more complex equations of state must be used to account for their peculiar thermodynamic behavior. Moreover, in the dense gas regime, the dynamic viscosity μ and the thermal conductivity λ depend on temperature and pressure through complex relationships. Similarly, the approximation of nearly constant Prandtl number Pr= μ c p / λ is no longer valid. Numerical simulations of turbulent dense gas flows of engineering interest are based on the (Reynolds-Averaged Navier–Stokes) RANS equations, which need to be supplemented by a model for the Reynolds stress tensor and turbulent heat flux. The accuracy of RANS models for dense-gas flows has not been properly assessed up to date, due to the lack of both experimental and numerical reference data. DNS databases [2, 3] are then needed to quantify the deficiencies of existing turbulence models and to develop and calibrate improved ones. In this work we first summarize some recent direct numerical simulation (DNS) results [4] for supersonic turbulent channel flows (TCF) of PP11, a heavy fluorocarbon representative of dense gases, at various bulk Mach and Reynolds numbers. The most relevant effects are represented by non-conventional variations of the fluctuating thermodynamic quantities, compared to perfect gases and a strong decoupling between thermal and dynamic effects almost everywhere in the flow, except in the immediate vicinity of the solid wall. Preliminary considerations about the validity of some currently-used models for the turbulent stresses and heat flux are carried out based on a priori comparisons between the exact terms computed from the DNS and their modeled counterparts.