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 and viscosity 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 $R{e}_{\tau }^{\ast }$. 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 $R{e}_{\tau }^{\ast }$ profiles and that their dependence on individual density and viscosity profiles is minor. Flows with near-wall gradients in $R{e}_{\tau }^{\ast }$ ($dR{e}_{\tau }^{\ast }/dy\ne 0$) 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 inter-component energy transfer in flows with strong near-wall $R{e}_{\tau }^{\ast }$ gradients.

arXiv commentSubmitted manuscript under review in JFM

References in corpus (1)

• Turbulent Flow in Pipes and Channels as Cross-Stream "Inverse Cascades" of Vorticity

Cited by in corpus (10)

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• Linear instability of Poiseuille flows with highly non-ideal fluids
• Intrinsic compressibility effects in near-wall turbulence
• Friction and heat transfer in forced air convection with variable physical properties
• Edge state modulation by mean viscosity gradients
• Variable-property and intrinsic compressibility corrections for turbulence models using near-wall scaling theories
• Temperature transformation recovering the compressible law of the wall for turbulent channel flow
• Velocity transformation for compressible wall-bounded turbulent flows with and without heat transfer
• Flux-controlled wall model for large eddy simulation integrating the compressible law of the wall