A low-re RSTM model for computations of heat transfer and fluid flow for impingement and convective cooling

A new Reynolds stress transport model (RSTM) aimed for engineering applications is proposed with consideration of near-wall turbulence. This model employs the SSG pressure strain term, the ω equation, and the SST model for the shear stresses at the near-wall region (say y⁺ less than or equal 30). The models are selected based on the following merits: The SSG RSTM model performs well in the fully turbulent region and does not need the wall normal vectors; the ω equation can be integrated down to the wall without damping functions; The SST model is a proper two-equation model that performs well for flows with adverse pressure gradient, while most two-equation models can have a good prediction of the shear stresses. A function is selected for the blending of the RSTM and SST. Three cases are presented to show the performance of the present model: (1) fully developed channel flow with Reτ = 395, (2) backward-facing step with an expansion ratio of 1.2 and Re = 5,200 base on the step height, (3) circular impingement with the nozzle-to-wall distance H = 4D and Re = 20,000.