The influence of near-wall density and viscosity gradients on turbulence in channel flows

Abstract

The influence of near-wall density and viscosity gradients on near-wall turbulence in a channel are studied by means of Direct Numerical Simulation (DNS) of the low-Mach number approximation of the Navier-Stokes equations. Different constitutive relations for density ρ and viscosity µ as a function of temperature are used in order to mimic a wide range of fluid behaviours and to develop a generalised framework for studying turbulence modulations in variable property flows. Instead of scaling the velocity solely based on local density, as done for the van Driest transformation, we derive an extension of the scaling that is based on gradients of the semi-local Reynolds number, defined as Re * τ ≡ (ρ/ρ w )/(µ/µ w ) Re τ (bar and subscript w denote Reynolds averaging and wall value, respectively, while Re τ is the friction Reynolds number based on wall values). This extension of the van Driest transformation is able to collapse velocity profiles for flows with near-wall property gradients as a function of the semi-local wall coordinate. However, flow quantities like mixing length, turbulence anisotropy and turbulent vorticity fluctuations do not show a universal scaling very close to the wall. This is attributed to turbulence modulations, which play a crucial role on the evolution of turbulent structures and turbulence energy transfer. We therefore investigate the characteristics of streamwise velocity streaks and quasi-streamwise vortices and found that, similar to turbulent statistics, the turbulent structures are also strongly governed by Re * τ profiles and that their dependence on individual density and viscosity profiles is minor. Flows with near-wall gradients in Re * τ (dRe * τ /dy = 0) showed significant changes in the inclination and tilting angles of quasi-streamwise vortices. These structural changes are responsible for the observed modulation of the Reynolds stress generation mechanism and the intercomponent energy transfer in flows with strong near-wall Re * τ gradients.

Scalar statistics in variable property turbulent channel flows

“…As shown in previous works [11,12,15,16,23,24,30], the semilocal wall coordinate y is effective in accommodating changes in viscous scales due to variable properties, thus providing a meaningful representation for the turbulent velocity statistics. Therefore, all wall-normal profiles are plotted as a function of y in the present work.…”

“…Patel et al [16] showed that the viscous stress h/Re τ (du vD /dy) collapses reasonably well when plotted as a function of y . For the near-wall constant stress layer, this collapse can be written in terms of the turbulent eddy viscosity μ t as…”

“…Following a similar procedure we used to derive u in Ref. [16] The last equality in this equation is valid only in the overlap region. In the region close to the wall (assuming a constant heat flux region), dθ /dy is given as…”

“…In all such cases, the effects of thermophysical property variations can be strong enough to modulate turbulence and the traditional approach of treating temperature as a passive scalar no longer holds. Although turbulence modulation in a turbulent channel flow due to variable thermophysical properties has been investigated in great detail in high-Mach-number flows [9][10][11][12] and in low-Mach-number flows [13][14][15][16], the effect of property variations on scalar transport is not well understood. Lee et al [17] studied the influence of wall heating on turbulent thermal boundary layers with variable viscosity and observed variations in mean scalar, scalar fluctuation, and scalar flux, relative to a reference isothermal flow.…”

“…In order to test the framework and to further investigate the turbulence statistics, a DNS database was generated by solving the low-Mach-number approximation of Navier-Stokes equation in a fully developed internally heated channel flow. Further analysis of the scaling characteristics of turbulent velocity statistics and of turbulence structures were performed by Patel et al [16]. It was shown that the semilocal Reynolds number accommodates the change in viscous scales due to property variations and also provides a measure of near-wall turbulence modulation with respect to a constant property case.…”