Numerical simulations and laboratory measurements are performed to study the flow field and heat transfer in a linear cascade of turbine vanes. The vanes are scaled-up versions of a turbine engine inlet vane but simplified in that they are untwisted and follow the mid-span airfoil shape of the engine vane. The hub endwall is axially profiled while the tip endwall is flat. The hub endwall comprises the focus of the heat transfer investigation. Configurations are considered with and without air injection through three discrete angled (25 degrees to the main flow direction) slots upstream of each vane. The freestream turbulence intensity at the vane cascade inlet plane is 11 (± 2) percent, as measured by a single hot-wire placed perpendicular to the mean flow. The transient thermochromic liquid crystal technique is used to measure the convective heat transfer coefficient at the hub endwall for the baseline case (without air injection through the slots), and the heat transfer coefficient and cooling effectiveness at the same endwall for the cases with air injection at two blowing ratios. Miniature Kiel probes are used to measure the distribution of total pressure upstream of, within, and downstream of one vane passage. Numerical simulations are performed of the incompressible flow using unstructured grids. Hybrid meshes comprised of prisms near solid surfaces and tetrahedra away from the wall are used to resolve the solutions, with mesh refinement up to approximately 2 million cells. For all calculations, the first grid point is within one viscous unit of solid surfaces. A Boussinesq approximation is invoked to model the turbulent Reynolds stresses, with the turbulent eddy viscosity obtained from the Spalart-Allmaras one-equation model. The turbulent heat flux is modeled via Reynolds analogy and a constant turbulent Prandtl number of 0.9. The simulations show that endwall axial profiling results in flow reversal upstream of the vane, an effect that lowers the Stanton number for the baseline flow near the vane leading edge compared to our previous work in a flat-endwall geometry. Predictions of the total pressure loss coefficient show that the peak levels are higher than those measured.
Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations
