Scalar statistics in variable property turbulent channel flows

Direct numerical simulation of fully developed, internally heated channel flows with isothermal walls is performed using the low-Mach-number approximation of Navier-Stokes equation to investigate the influence of temperature-dependent properties on turbulent scalar statistics. Different constitutive relations for density ρ , viscosity μ , and thermal conductivity λ as a function of temperature are prescribed in order to characterize the turbulent scalar statistics. It is shown that the dominant effect caused by property variations on scalar statistics can be parameterized by two nondimensional parameters, namely the semilocal Reynolds number Reτ_★≡Re_τ√{(ρ ¯/ρ_w) }/(μ ¯/μ_w) (the bar and subscript w denote Reynolds averaging and wall value respectively, while Re_τ is the friction Reynolds number based on wall values), and the local Prandtl number Pr★=Pr_w(" close=")λ ¯/λ_w)">μ ¯/μ_w (Pr_w is the molecular Prandtl number based on wall values). Near-wall gradients in Reτ_★ modulate the turbulent heat flux generation mechanism because of structural changes in turbulence. However, the influence of these modulations on the inner scaling of turbulent heat conductivity normalized by local mean viscosity is shown to be weak. Using this observation, a temperature transformation is derived that is invariant of Reτ_★ variations and only exhibits a Pr★-dependent shift.