Impact of unresolved smaller scales on the scalar dissipation rate in direct numerical simulations of wall bounded flows

Abstract

Passive scalar dynamics in a turbulent channel flow is studied with Direct Numerical Simulation at friction Reynolds number Reτ=160 and Prandtl number Pr=1. The goal of the study is to assess the grid spacing requirement for an accurate estimation of various integral turbulent statistics, with a special focus on the scalar dissipation rate. The implemented spatial resolutions span from the resolution comparable to the similar Direct Numerical Simulations (DNS) studies in the past, to the very fine resolution implemented by Galantucci and Quadrio (2010). All scalar fields are computed in parallel using a single velocity field resolved with the finest resolution, thus reducing the statistical variability. In addition, to confidently assess the grid spacing requirement, we also evaluate the statistical uncertainty. The “standard” resolution of the DNS studies (resolution used by Kim et al. (1987)) is usually sufficient for predictions of first and second-order integral turbulence scalar field statistics. Non-negligible corrections of the fourth-order integral statistics, especially the scalar dissipation variance profile, are observed with enhancement of the scalar resolution from the one used in the “standard” DNS studies to the resolution recommended by Vreman and Kuerten (2014), which is roughly two times finer in each spatial direction. Further resolution enhancements produce only marginal differences.