Direct numerical simulation of a zero-pressure-gradient turbulent boundary layer with passive scalars up to Prandtl number Pr = 6

Abstract

The objective of the present study is to provide a numerical database of thermal boundary layers and to contribute to the understanding of the dynamics of passive scalars at different Prandtl numbers. In this regard, a direct numerical simulation (DNS) of an incompressible zero-pressure-gradient turbulent boundary layer is performed with the Reynolds number based on momentum thickness ${\textit {Re}}_{\theta }$ ranging up to $1080$ . Four passive scalars, characterized by the Prandtl numbers ${\textit {Pr}} = 1,2,4,6$ are simulated using the pseudo-spectral code SIMSON (Chevalier et al., SIMSON : a pseudo-spectral solver for incompressible boundary layer flows. Tech. Rep. TRITA-MEK 2007:07. KTH Mechanics, Stockholm, Sweden, 2007). To the best of our knowledge, the present DNS provides the thermal boundary layer with the highest Prandtl number available in the literature. It corresponds to that of water at ${\sim }24\,^{\circ }{\rm C}$ , when the fluid temperature is considered as a passive scalar. Turbulence statistics for the flow and thermal fields are computed and compared with available numerical simulations at similar Reynolds numbers. The mean flow and scalar profiles, root-mean-squared velocity and scalar fluctuations, turbulent heat flux, turbulent Prandtl number and higher-order statistics agree well with the numerical data reported in the literature. Furthermore, the pre-multiplied two-dimensional spectra of the velocity and of the passive scalars are computed, providing a quantitative description of the energy distribution at the different length scales for various wall-normal locations. The energy distribution of the heat-flux fields at the wall is concentrated on longer temporal structures with increasing Prandtl number. This is due to the thinner thermal boundary layer as thermal diffusivity decreases and, thereby, the longer temporal structures exhibit a different footprint at the wall.