This paper presents a constrained multipoint optimization of the LS89 turbine cascade. The objective of the optimization consists in minimizing the entropy losses generated inside the cascade over a predefined operating range. The operating range is bounded by two operating points respectively characterized by a downstream isentropic Mach number of 0.9 and 1.01. During the optimization, two aerodynamic constraints are imposed in order to conserve the same performance as the original cascade. The first constraint is established on the outlet flow angle in order to achieve at least the same flow turning as the LS89 turbine. The second constraint limits the mass-flow passing through the optimized cascade. The optimization is performed using a hybrid algorithm which combines efficiently a classical evolutionary algorithm with a gradient-based method. The hybridization process between both methods is based on the Lamarckian approach which consists in incorporating directly the gradient method inside the loop of the evolutionary algorithm. In this methodology, the evolutionary method allows to globally explore the overall design space while the gradient-based method locally improves certain designs located in the most promising regions of the search space. First, the better performance of the proposed hybrid method compared to the performance of a classical evolutionary algorithm is demonstrated on two benchmark problems. Then, the methodology is applied on a turbomachinery application in order to minimize the losses in the linear LS89 cascade.
The optimization process allows to find a new blade profile which reduces the entropy losses over the entire operating range by at least 9.5 %. Finally, the comparison of the flows computed in the baseline and in the optimized cascades demonstrates that the reduction of the losses is due to a decrease of the entropy generated downstream the trailing edges and within the passages between the optimized blades.