Semi-local scaling and turbulence modulation in variable property turbulent channel flows

Abstract

We theoretically and numerically investigate the effect of temperature dependent density and viscosity on turbulence in channel flows. First, a mathematical framework is developed to support the validity of the semi-local scaling as proposed based on heuristic arguments by Huang, Coleman, and Bradshaw [“Compressible turbulent channel flows: DNS results and modelling,” J. Fluid Mech. 305, 185–218 (1995)]. Second, direct numerical simulations (DNS) of turbulent channel flows with different constitutive relations for density and viscosity are performed to assess and validate the semi-local scaling for turbulent statistics. The DNS database is obtained by solving the low-Mach number approximation of the Navier-Stokes equation. Finally, we quantify the modulation of turbulence due to changes in fluid properties. In the simulations, the fluid is internally heated and the temperature at both channel walls is fixed, such that the friction Reynolds number based on wall quantities is Re ? = 395 for all cases investigated. We show that for a case with variable density ? and viscosity ?, but constant semi-local Reynolds number Re???(?¯¯¯/?w)???????/(?¯¯¯/?w)Re? (where bar and subscript w, denote Reynolds averaging and averaged wall quantity, respectively), across the whole channel height, the turbulent statistics exhibit quasi-similarity with constant property turbulent flows. For cases where Re???Re? across the channel, we found that quasi-similarity is maintained for cases with similar Re?? distributions, even if their individual mean density and viscosity profiles substantially differ. With a decrease of Re?? towards the channel center ( Re??