A modified two-layer scalar diffusivity description for high Schmidt and Prandtl turbulent boundary layers

In engineering systems operating under high Schmidt (Sc) or Prandtl (Pr) number flow conditions, the demand for near-wall mesh refinement increases significantly, underscoring the need for cost-effective modeling approaches that avoid additional computational overhead. Existing models, which are predominantly designed for low-Sc flows, overlook temporal filtering effects, resulting in inaccuracies in theoretical description and mass transfer predictions. This paper addresses the impact of high Sc or Pr by refining the single-layer scalar diffusivity model. It introduces a switch between scalar filtering and eddy viscosity-dominated regions, leveraging two parameters: κSc, accounting for temporal filtering effects, and κRe, addressing variations in Reynolds number. In addition, we adopted a complementary outer layer term to model the upwarding trend in low frictional Reynolds number condition. Using the two-layer model with unity Sc and/or Pr, a close agreement with the von-Kármán constant in the velocity boundary layer was observed. The modified model demonstrated strong agreement with scalar profiles across a broad range of Sc and friction Reynolds numbers (Reτ) in direct numerical simulation and large eddy simulation data, demonstrating its accuracy at low Reτ and predictive performance at high Reτ. The two-layer model improves the prediction of turbulent mass transfer, providing better alignment with high Sc engineering correlations than existing wall model approach. This study provides valuable insight for modeling the mass and heat transfer processes under high Sc or Pr conditions.