DNS study of turbulent transport at low Prandtl numbers in a channel flow

Abstract

Direct numerical simulations of the velocity and temperature fields for turbulent flow in a channel are used to examine the influence of Prandtl number Pr on turbulent transport. The Reynolds number, based on the half-height of the channel and the friction velocity, is Reτ = 150. Prandtl numbers of 1.0, 0.3, 0.1, 0.05, 0.025 were studied. The bottom and the top walls were kept at constant temperatures of +Tw and −Tw. The influence of Pr on Reynolds transport, on the turbulent diffusivity, ατ, and on the spectral density function of the temperature fluctuations was studied. The observation that spatial variations of the ratio of the turbulent diffusivity to the value observed at Pr = 1.0 are not large is used to propose a method for calculating average temperature fields. The decrease in ατ with decreasing Pr is related to observations of the increased damping of high-wavenumber temperature fluctuations. Molecular conductivity, at smaller Pr, is pictured to act as a filter that renders high-frequency velocity fluctuations ineffective in transporting heat.