Adjoint Optimization of Gas Turbine Film Cooling Geometry With Elevated Mainstream Mach Number

Adjoint based shape optimization has the potential to produce real gains in the performance of gas turbine film cooling geometry. This has been demonstrated in previous studies with incompressible mainstream Mach number, using both computational and experimental evidence. Starting from a 7-7-7 shaped film cooling hole as a baseline, the present study investigated such optimization routines using an elevated mainstream Mach number of Ma∞ = 0.75, and is the first of its kind. At this elevated Mach number, supersonic flow and shockwaves were predicted within the 7-7-7 baseline hole. How such behaviors affected the optimization was of particular interest. In addition to the optimization at elevated mainstream Mach number, a control optimization was performed at an incompressible mainstream Mach number of Ma∞ = 0.15. Both the “high-speed” and “low-speed” optimizations were performed using a hole Reynolds number ReD = 10,000, a blowing ratio M = 2.00, and a stagnation temperature ratio TR° = 0.50. Although the resulting optimizations were similar, significant differences were observed and are discussed. After generating each optimization, the resulting geometries were simulated across a wide range of conditions. Computationally, the predicted performance of both geometries was significantly higher than that of the baseline 7-7-7. Each geometry was also additively manufactured and tested experimentally at mainstream Mach numbers of Ma∞ = 0.15 and Ma∞ = 0.50, for a limited range of conditions. Peak experimental performance of both optimizations was greater than the baseline 7-7-7 at Ma∞ = 0.15, but for the range of blowing ratio tested at Ma∞ = 0.50, neither optimization had experimental peak performance greater than the baseline 7-7-7.