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 Re τ = 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 + T w and − T w . The influence of Pr on Reynolds transport, on the turbulent diffusivity, α τ , 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 α τ 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.