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

<jats:p>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 Reτ = 395 for all cases investigated. We show that for a case with variable density ρ and viscosity μ, but constant semi-local Reynolds number Reτ∗≡(ρ¯/ρw)/(μ¯/μw)Reτ (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 Reτ∗≠Reτ across the channel, we found that quasi-similarity is maintained for cases with similar Reτ∗ distributions, even if their individual mean density and viscosity profiles substantially differ. With a decrease of Reτ∗ towards the channel center (Reτ∗&lt;Reτ), we show that the anisotropy increases and the pre-multiplied stream-wise spectra reveal that this increase is associated with strengthening of the large scale streaks in the buffer layer. The opposite effect is observed when Reτ∗ increases towards the channel center. The present results provide an effective framework for categorizing turbulence modulation in wall-bounded flows with variable property effects, and can be applied to any Newtonian fluid that is heated or cooled.</jats:p>