Optimization of Forcing Parameters of Film Cooling Effectiveness

An optimization strategy is described that combines high-fidelity simulations with response surface construction, and is applied to pulsed film cooling for turbine blades. The response surface is constructed for the film cooling effectiveness as a function of duty cycle, in the range of DC between 0.05 and 1, and pulsation frequency St in the range of 0.2–2, using a pseudo-spectral projection method. The jet is fully modulated and the blowing ratio, when the jet is on, is 1.5 in all cases. Overall 73 direct numerical simulations (DNS) using spectral element method were performed to sample the film cooling effectiveness on a Clenshaw-Curtis grid in the design space. The geometry includes a 35-degree delivery tube and a plenum. It is observed that in the parameter space explored a global optimum exists, and in the present study, the best film cooling effectiveness is found at DC = 0.14 and St = 1.03. In the same range of DC and St, four other local optimums were found. The physical mechanisms leading to the forcing parameters of the global optimum are explored and ingestion of the crossflow into the delivery tube is observed to play an important role in this process. The gradient-based optimization algorithms are argued to be unsuitable for the current problem due to the non-convexity of the objective function.