Assessment of Turbulence Models over a Curved Hill Flow with Passive Scalar Transport

Abstract

An incoming canonical spatially developing turbulent boundary layer (SDTBL) over a 2-D curved hill is numerically investigated via the Reynolds-averaged Navier–Stokes (RANS) equations plus two eddy-viscosity models: the (Formula presented.) SST (henceforth SST) and the Spalart–Allmaras (henceforth SA) turbulence models. A spatially evolving thermal boundary layer has also been included, assuming temperature as a passive scalar ((Formula presented.) = 0.71) and a turbulent Prandtl number, (Formula presented.), of 0.90 for wall-normal turbulent heat flux modeling. The complex flow with a combined strong adverse/favorable streamline curvature-driven pressure gradient caused by concave/convex surface curvatures has been replicated from wind-tunnel experiments from the literature, and the measured velocity and pressure fields have been used for validation purposes (the thermal field was not experimentally measured). Furthermore, direct numerical simulation (DNS) databases from the literature were also employed for the incoming turbulent flow assessment. Concerning first-order statistics, the SA model demonstrated a better agreement with experiments where the turbulent boundary layer remained attached, for instance, in (Formula presented.), (Formula presented.), and (Formula presented.) predictions. Conversely, the SST model has shown a slightly better match with experiments over the flow separation zone (in terms of (Formula presented.) and (Formula presented.)) and in (Formula presented.) profiles just upstream of the bubble. The Reynolds analogy, based on the (Formula presented.) ratio, holds in zero-pressure gradient (ZPG) zones; however, it is significantly deteriorated by the presence of streamline curvature-driven pressure gradient, particularly due to concave wall curvature or adverse-pressure gradient (APG). In terms of second-order statistics, the SST model has better captured the positively correlated characteristics of (Formula presented.) and (Formula presented.) or positive Reynolds shear stresses ((Formula presented.) > 0) inside the recirculating zone. Very strong APG induced outer secondary peaks in (Formula presented.) and turbulence production as well as an evident negative slope on the constant shear layer.