Scalar statistics in variable property turbulent channel flows

Abstract

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.

A posteriori tests of subgrid-scale models in strongly anisothermal turbulent flows

“…This leads to a strong temperature-velocity coupling, notwithstanding the compressibility effects due to velocity being negligible. Analyses of strongly anisothermal channel flows have been carried out using large-eddy simulations [11,34,35,54,55,56,53,47,48,63,8] and direct numerical simulations (DNS) [44,41,62,3,4,17,19,21]. As the velocity of the fluid is low compared to the speed of sound, the low Mach number equations may be used to relieve the numerical constraints related to acoustic waves.…”

Turbulence in a heated pipe at supercritical pressure

“…Additionally, it was found that the viscous shear stress is a universal function in the inner layer when expressed in the semi-local parameter,, where h is half-channel height. It was later shown in Patel, Boersma & Pecnik (2017) that the statistics of a scaler (such as temperature) can also be scaled using the semi-local Reynolds number and a semi-local defined as . The above idea was further used in Pecnik & Patel (2017) to derive a so-called semi-local scaled transport equation for turbulence kinetic energy, in which the viscous terms are scaled with and the turbulence production is governed by the gradient of the van Driest velocity.…”

“…1995) and to a lesser extent the effect of variable viscosity as well (Trettel & Larsson 2016; Patel et al. 2017) under conditions when buoyancy is not significant or is omitted. A common goal of these studies is to find a suitable normalisation so that the non-dimensionalised turbulence is unchanged from that of the equivalent constant-property flow.…”

Turbulence modelling for flows with strong variations in thermo-physical properties

“…In equations ( 6) and ( 7), the Reynolds shear stress and turbulent heat flux were modelled using the Boussinesq approximation and the gradient diffusion hypothesis, respectively. In [24], it was seen that the turbulent Prandtl number, P r t , varies around unity for the low-Mach number cases, implying that there is a strong analogy between the momentum and scalar transport. Therefore, we have approximated P r t = 1 also for the high-Mach number case.…”