Direct numerical simulations of supersonic turbulent channel flows of dense gases

Abstract

The influence of dense-gas effects on compressible wall-bounded turbulence is investigated by means of direct numerical simulations of supersonic turbulent channel flows. Results are obtained for PP11, a heavy fluorocarbon representative of dense gases, the thermophysics properties of which are described by using a fifth-order virial equation of state and advanced models for the transport properties. In the dense-gas regime, the speed of sound varies non-monotonically in small perturbations and the dependency of the transport properties on the fluid density (in addition to the temperature) is no longer negligible. A parametric study is carried out by varying the bulk Mach and Reynolds numbers, and results are compared to those obtained for a perfect gas, namely air. Dense-gas flow exhibits almost negligible friction heating effects, since the high specific heat of the fluids leads to a loose coupling between thermal and kinetic fields, even at high Mach numbers. Despite negligible temperature variations across the channel, the mean viscosity tends to decrease from the channel walls to the centreline (liquid-like behaviour), due to its complex dependency on fluid density. On the other hand, strong density fluctuations are present, but due to the non-standard sound speed variation (opposite to the mean density evolution across the channel), the amplitude is maximal close to the channel wall, i.e. in the viscous sublayer instead of the buffer layer like in perfect gases. As a consequence, these fluctuations do not alter the turbulence structure significantly, and Morkovin’s hypothesis is well respected at any Mach number considered in the study. The preceding features make high Mach wall-bounded flows of dense gases similar to incompressible flows with variable properties, despite the significant fluctuations of density and speed of sound. Indeed, the semi-local scaling of Patel et al. (Phys. Fluids, vol. 27 (9), 2015, 095101) or Trettel & Larsson (Phys. Fluids, vol. 28 (2), 2016, 026102) is shown to be well adapted to compare results from existing surveys and with the well-documented incompressible limit. Additionally, for a dense gas the isothermal channel flow is also almost adiabatic, and the Van Driest transformation also performs reasonably well. The present observations open the way to the development of suitable models for dense-gas turbulent flows.

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

“…In [9] the TCF configuration was simulated for a dense and a perfect gas at various Mach and Reynolds numbers. The computational domain (sketched in Fig.…”

“…[24,25]) and is considered to be a reasonably accurate semi-theoretical model for calculating the viscosity based on the knowledge of a few thermophysical input parameters (see [26] for more details). A full description of the model equations is given in [9], Appendix A. The dense fluid considered in the following simulations is the perfluoro-perhydro phenanthrene, (chemical formula C 14 F 24 ), called hereafter with its commercial name PP11.…”

“…DNS databases are then needed to quantify the deficiencies of existing turbulence models and to develop and calibrate improved ones. First contributions to the DNS of decaying homogeneous isotropic turbulence were reported in [7,8], while the influence of dense gas effects in wall-bounded turbulent flows was investigated in [9].…”

“…In this work, we use recent DNS results [9] for supersonic turbulent channel flows of PP11 (a heavy fluorocarbon representative of dense gases) to carry out a priori tests of the validity of some currently-used models for the turbulent stresses and heat flux. Specifically, we examine the behavior of the modeled eddy viscosity for some low-Reynolds variants of the k − ε model for dense gas flows at various bulk Mach and Reynolds numbers and compare the results with those found in perfect gas TCF at similar conditions.…”

Strong scaling of numerical solver for supersonic jet flow configurations

“…Large eddy simulations require a significant amount of computational resources to provide high fidelity results. The scientific community has been using up to hundreds of million degrees of freedom on simulations of turbulent flow configurations [6,12,18,32]. Researchers and engineers need to be certain that calculations are run with maximum parallel efficiency when allocating computational resources because the access to supercomputers is often restricted and limited.…”