Prandtl number effect on near wall temperature profile in high-Reynolds number channel flows

Abstract

Prandtl number (Pr) effects on characteristics of the thermal boundary layer were investigated by means of Direct Numerical Simulations (DNS) in high-Reynolds number turbulent channel flows. The molecular Pr conditions were changed from 0.71 to 25.0, and the Reynolds number based on the friction velocity and channel half-width was kept to 1000 in all cases. The mean temperature profiles were good agreements with Kader's empirical equations except for the case of Pr = 25.0. The thicknesses of thermal conduction sub-layer became thinner in proportion to a one third power of Pr. On the other hands, the peak wall-normal heights in temperature intensity became thinner in proportion to a one half power of Pr. In both thermal layers of the conduction and logarithmic, results of quadrant and Kullback-Leibler Divergence (KLD) analyses were shown analogous characteristics in all Pr cases. On the other hand, in the buffer layer, the contributions of sweep and ejection events on wall-normal turbulent heat flux and distribution of KLD were shown the different distributions between in cases of Pr = 0.71 and Pr = 5.0, 25.0.

Keywords

• turbulent heat transfer
• dns
• channel flow
• high-prandtl number