First Hybrid Turbulence Modeling for Turbine Blade Cooling

Introduction G AS turbines require proper cooling mechanisms to protect the airfoils from thermal stresses generated by exposure to hot combustion gases. The problem becomes aggravated by the growing trend to use higher turbine inlet temperatures to generate more power. Thus, film cooling is used as a cooling mechanism, and it works in the form of row of holes located in the spanwise direction, through which cold jets are issued into the hot crossflow. The penetration of cold jets into the main flow creates a complex flowfield. Systematic investigation of such flowfield started in late 1950s. Figure 1 shows the schematic of a single round jet injected in the crossflow at an angle α = 35 deg. The figure also describes the boundary conditions applied at different faces. Even though use of symmetry boundary condition at the hole centerline would reduce the computational time by half, its use is avoided as it prevents the possibility of capturing the unsteady asymmetric vortical flow patterns. This geometry is well accepted by the gas-turbine community and has been extensively studied1 for cooling performance for a wide range of blowing ratios, M = ρ j Vj/ρfsVfs, where ρ and V are density and normal velocity, respectively, for jet j and freestream fs. Goldstein2 correlated film cooling effectiveness η = (Tfs − T )/ (Tfs − Tj ) with the parameter x/Mb, where x is the downstream distance; M is the blowing ratio; b is the slot width; and Tfs, T , and Tj are the temperatures of crossflow, blade, and jet, respectively. Sinha et al.1 carried out experimental work to study the relationship between the fluid-thermal parameters of jet and film cooling effectiveness using a row of inclined holes. The mixing of a jet in a cross stream is a fully three-dimensional phenomenon.3 Amer et al.4 pointed out that the flow predictions are greatly affected by the selection of the turbulence model. Roy5 documented the cooling performance of 12 different arrangements of holes with a combination of blowing ratio M , distance between the holes L , and jet angle α using a upwind-biased finite volume code and standard k–ω turbulence closure model. Garg and Rigby6 resolved the plenum and hole pipes for a three-row showerhead film cooling arrangement with Wilcox’s k–ω turbulence model. Heidmann et al.7 used Reynolds-averaged Navier–Stokes (RANS) to compute the heat transfer for a realistic turbine vane with 12 rows of film cooling holes with shaped holes and plena resolved. Though these studies provide good details of the flow, the anisotropic dynamic nature of the spanwise vortices that affect the film cooling process are more complex than that can be captured by the mixing models used in aforementioned papers. Acharya8 compared the re-