Enabling Passive Scalar Wall Modelling in Large Eddy Simulation for Turbulent Flows at High Schmidt or Prandtl Numbers

Abstract This study investigates near-wall diffusive flux modeling for passive scalar transport in turbulent flows with high Schmidt (Sc) or Prandtl (Pr) numbers. Under these conditions, the diffusion boundary layer becomes significantly thinner than the velocity boundary layer. Capturing the concentration boundary layer presents challenges due to additional scaling in the viscous-diffusive regime. For DNS, mesh resolution requirements to capture passive scalar behavior near the wall are more stringent than those for Kolmogorov scales in pure hydrodynamics investigations. Consequently, wall-resolved approaches in both RANS and WMLES demand excessive wall refinement, limiting their practicality for high Reynolds numbers and industrial applications. In this work, we focus on turbulent flow without an adverse pressure gradient. Existing wall models fail to provide accurate estimates of wall diffusive flux for passive scalar transport at high Sc. This failure arises from the breakdown of the assumption of eddy diffusivity asymptotic behavior. Using such models for simulating surface processes (e.g., flow-accelerated corrosion) in RANS and WMLES can lead to non-negligible errors. Our study introduces a two-layer scalar diffusivity model to enhance wall modeling capabilities in passive scalar transport at high Sc or Pr numbers.