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.

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 τ = 395 for all cases investigated. We show that for a case with variable density ρ and viscosity µ, but constant semi-local Reynolds number Re * τ ≡  (ρ/ρ w )/(µ/µ w )Re τ (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 * τRe τ across the channel, we found that quasi-similarity is maintained for cases with similar Re * τ distributions, even if their individual mean density and viscosity profiles substantially differ. With a decrease of Re * τ towards the channel center (Re * τ < Re τ ), 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 Re * τ 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. C 2015 AIP Publishing LLC. [http://dx

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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 Re τ ≡ 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 (μ/μ w )/(λ/λ w ) (Pr w is the molecular Prandtl number based on wall values). Near-wall gradients in Re τ 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 Re τ variations and only exhibits a Pr -dependent shift.

We use direct numerical simulations to study the effect of thermal boundary conditions on developing turbulent pipe flows with fluids at supercritical pressure. The Reynolds number based on pipe diameter and friction velocity at the inlet is $Re_{{\it\tau}0}=360$ and Prandtl number at the inlet is $Pr_{0}=3.19$. The thermodynamic conditions are chosen such that the temperature range within the flow domain incorporates the pseudo-critical point where large variations in thermophysical properties occur. Two different thermal wall boundary conditions are studied: one that permits temperature fluctuations and one that does not allow temperature fluctuations at the wall (equivalent to cases where the thermal effusivity ratio approaches infinity and zero, respectively). Unlike for turbulent flows with constant thermophysical properties and Prandtl numbers above unity – where the effusivity ratio has a negligible influence on heat transfer – supercritical fluids shows a strong dependency on the effusivity ratio. We observe a reduction of 7 % in Nusselt number when the temperature fluctuations at the wall are suppressed. On the other hand, if temperature fluctuations are permitted, large property variations are induced that consequently cause an increase of wall-normal velocity fluctuations very close to the wall and thus an increased overall heat flux and skin friction.