Development of Thermal Wall Functions through Direct Numerical Simulation

This study performs a direct numerical simulation (DNS) of a turbulent boundary layer that develops spatially on a flat plate under a zero pressure gradient. The investigation focuses on the influence of Prandtl numbers on passive scalar transport. The Navier-Stokes equations and scalar transport equations are solved using a spectral element method (SEM). Various molecular Prandtl numbers are analyzed, mainly in the liquid metals range, to observe their impact on scalar behavior, particularly in the outer region of the boundary layer. The results reveal significant insights into the statistical behavior of scalars, highlighting differences in near-wall streak spacing and coherence between velocity and scalar fields based on Prandtl number variations. Probabilistic methods further identify intermittency near the wall and in the outer region, providing a comprehensive view of the scalar-field dynamics influenced by Prandtl numbers.