Multi-objective optimization of an S-type compressor cascade at low transonic inlet conditions

As aircraft engines are expected to achieve increasingly stricter goals in terms of efficiency and reliability, an accurate design of turbomachinery blades for aeronautic propulsion is fundamental. To fulfil this task, in the present work a multi-point and multi-objective optimization of a transonic compressor cascade is performed, in order to maximize pressure ratio and efficiency at three inlet Mach numbers. A commercial CFD code is employed to simulate the flow around the blades at steady conditions on a 2-d structured mesh and to compute the objective functions. A grid validation is performed by testing three different refinement levels against experimental data. A first iterative algorithm is used to identify and impose unique incidence conditions at the inflow, and a second algorithm to search for the maximum achievable pressure ratio while respecting the inlet conditions. An S-type transonic cascade, the NASA ARL-SL19, is used as baseline geometry: only the fore section of the camberline is parametrized using a Bezier curve, using four y-coordinates and one x-coordinate of the Bezier polygon as decision variables. The thickness distribution of the baseline profile is imposed to the generated camberlines to create new geometries. The continuity of the first derivative of the camberline between the parametrized fore section and the fixed rear section is enforced to preserve aerodynamic efficiency. Three optimizations are conducted, namely at inlet Mach numbers 1.2, 1.1 and 0.99, using a heuristic optimization algorithm, the NSGA-II. 20 profiles are evolved from a random pool for 10 generations at each condition, searching for the Pareto fronts of both objective functions. Eventually, an increase in pressure ratio is achieved, as well as a substantial improvement in efficiency at each operative point. The optimized profiles are compared to the baseline geometry, highlighting the dominant effect of the forepart of the chord in the generation of losses, as well as a strong negative correlation between the camber angle near the leading edge and the inflow angle in profiles achieving the highest efficiency. The leading edge of profiles on the Pareto front is progressively shifted downwards as the Mach number decreases, leading to more cambered shapes, while profiles with lowest losses retain the S-shape at Mach 1.2. The results show the ability of the employed optimization algorithm to consistently improve the performance parameters of a transonic cascade with a reduced number of simulations. The small and continuous camber bend with the inlet Mach number of optimized profiles suggest the opportunity of an active geometry control of profile shapes, as to achieve the best performance in a range of operative conditions.