Stochastic Modeling of Passive Scalar Transport in Turbulent Channel Flows at High Schmidt Numbers

Abstract

High-Schmidt number flow simulations are challenging since the flow has to be resolved down to the Batchelor scale, which yields high resolution requirements. In order to close the gap between the flow regime of applications and that reachable by numerical simulations, we utilize a stochastic modeling approach, the so-called OneDimensional Turbulence (ODT) model. In the present study, ODT is used as stand-alone tool to investigate the turbulent transport of a passive scalar for Schmidt numbers 1 ≤ Sc ≤ 5000 in incompressible, fully-developed turbulent channel flows for Reynolds numbers Reτ ≤ 2000. The applicability of ODT is assessed by comparing the scalar mean and the root mean square fluctuations to those of reference Direct Numerical Simulations (DNS) and Large-Eddy Simulations (LES) up to Sc = 400. Good qualitative but also quantitative agreement is observed between DNS, LES, and ODT, but ODT underestimates the mean scalar concentration in the bulk by a factor of ≈ 3/4. Otherwise, ODT exhibits the correct boundary layer structure and yields the von Kármán constant for the scalar as κθ = 0.23, which corresponds well to the available reference DNS/LES. ODT is then used to simulate the scalar mass transfer coefficient K+ up to very high Schmidt numbers. The power law K ODT ∝ Sc −0.651 is obtained for Sc > 100 where it is also independent of the Reynolds number. This corresponds to the reference laboratory measurements and DNS/LES, which obey K lab ∝ Sc −0.704. The present study shows that ODT can be a versatile tool for robust and accurate modeling of the turbulent scalar transport up to very high Schmidt and Reynolds numbers.