Stochastic Modeling of Turbulent Scalar Transport at Very High Schmidt Numbers

A stochastic modeling approach, the so-called One-Dimensional Turbulence (ODT), is used to study passive scalar transport in incompressible, fully-developed, turbulent channel flows up to very high Schmidt numbers Sc = ν/Γ ∼ 10⁴ (kinematic viscosity ν, scalar diffusivity Γ). Good agreement is obtained between ODT and Direct Numerical Simulation (DNS) results with respect to the mean, the fluctuation statistics, and the dimensionless mass transfer coefficient K⁺. ODT yields the mass transfer coefficient to become independent of the Reynolds number at high Schmidt numbers, which is similar to reference laboratory measurements and DNS. The present ODT results exhibit the power law K⁺ ∝ Sc^−0.65 with a scaling exponent that is only slightly larger than in the reference laboratory measurements and DNS. The results obtained suggests that ODT can be a versatile tool for turbulent transport modeling in a wide range of physical parameters. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)