Direct numerical simulation of a zero-pressure-gradient thermal turbulent boundary layer up to $\textrm{Pr = 6}$

TL;DR

This study performs direct numerical simulations of zero-pressure-gradient turbulent boundary layers with passive scalars at Prandtl numbers up to 6, providing new high-Prandtl-number thermal boundary layer data and analyzing scalar and velocity statistics.

Contribution

It offers the highest Prandtl number thermal boundary layer simulation in DNS literature, advancing understanding of scalar dynamics at high Prandtl numbers.

Findings

Good agreement with existing turbulence statistics

Spectral analysis reveals energy distribution differences at various Prandtl numbers

Heat flux structures vary with Prandtl number, affecting wall footprint

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 $Re_{\theta}$ up to $1080$. Four passive scalars, characterized by the Prandtl numbers $Pr = 1,2,4,6$ are simulated with constant Dirichlet boundary conditions, using the pseudo-spectral code SIMSON (Chevalier et al. 2007). To the best of our knowledge, the present direct numerical simulation provides the thermal boundary layer with the highest Prandtl number available in the literature. It corresponds to that of water at $\sim$24$^{o}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 temperature profiles, root-mean squared (RMS) velocity and temperature 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 lengthscales for various wall-normal locations. The energy distribution of the heat flux fields at the wall is concentrated on longer temporal structures and exhibits different footprint at the wall, with increasing Prandtl number.