Assessment of Reynolds-Averaged Turbulence Models for Prediction of the Flow and Heat Transfer in an Inlet Vane-Endwall Passage

Predictions of the flow and thermal fields in an inlet vane passage are obtained via solution of the incompressible Reynolds-averaged Navier-Stokes (RANS) equations. RANS predictions of the steady-state solutions are obtained using two scalar eddy viscosity models and full Reynolds stress transport to close the turbulent stress in the momentum equations. The turbulent heat flux is modeled using a constant turbulent Prandtl number. In the geometric configuration of the inlet vane passage, the hub endwall is flat. Calculations are performed for a baseline configuration and an additional configuration in which secondary air is injected through three small, angled slots positioned upstream of the vane leading edge. Solutions are obtained on unstructured grids with the densest mesh comprised of $1.9×106$ elements. The simulations are assessed via an inter-comparison of predictions obtained using the different models, as well as through evaluation against experimental measurements of the Stanton number and cooling effectiveness on the hub endwall. The flow develops from a turbulent boundary layer at momentum thickness Reynolds number 955 prescribed at the inlet to the computational domain, 1.3 axial chord lengths upstream of the vane leading edge. The mean velocity at the inlet is prescribed to match an experimentally-measured profile with low freestream turbulence. For the case with secondary air injection, the blowing ratio was 1.3. Solid surfaces are isothermal at temperatures below that of the mainstream gas. Simulation results show that the vortical structures resolved by the models in the vicinity of the vane leading edge for the baseline case are relatively insensitive to the particular turbulence closure. The elevation in heat flux levels due to entrainment of higher temperature mainstream gas towards the endwall by the horseshoe vortex is captured, Stanton number distributions exhibit adequate agreement with measured values. While there are similarities in the coherent structures resolved by the models, details of their evolution through the passage lead to differences in heat transfer distribution along the endwall. Secondary air injection strongly distorts the flow structure in the vicinity of the leading edge, the vortical structures that develop in the calculations with air injection evolve primarily from the interaction of the fluid issuing from the slots and the mainstream flow. Elevated levels of cooling effectiveness predicted by the models correspond to larger areas of the endwall than measured, peak Stanton numbers are higher than the experimental values.