The design of radial compressors is typically a trade-off between peak performance at the design conditions and maintaining a good efficiency over a wide operating range. In the present paper, a gradient-based optimization of the well-known SRV2 radial compressor is presented. The optimization problem is formulated to increase the total-to-total efficiency of the compressor at peak efficiency while maintaining a wide operating range. To achieve an efficient optimization strategy, a gradient-based optimization method is used. Gradients of the RANS solver are obtained through the adjoint approach, leading to a computational cost that is almost independent of the degrees of freedom. A total of 44 design parameters are used to define a rich design space for the radial compressor impeller. A Sequential Quadratic Programming algorithm is used as optimizer and achieves an optimal design in less than 20 major iterations. The optimization process allows to significantly increase the efficiency of the SRV2 compressor at peak efficiency while maintaining the operating range of the baseline. Detailed analysis of the flow field in baseline and optimized compressors reveal the mechanisms which allow to improve the performance of the baseline compressor.

This paper presents a multipoint optimization of the LS89 cascade. The objective of the optimization consists in minimizing the entropy losses generated inside the cascade over a predefined operating range. 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. The second constraint limits the mass-flow passing through the cascade. The optimization is performed using a hybrid algorithm which combines a classical evolutionary algorithm with a gradient-based method. The hybridization between both methods is based on the Lamarckian approach which consists in incorporating the gradient method inside the loop of the evolutionary algorithm. In this methodology, the evolutionary method allows to globally explore the design space while the gradient-based method locally improves certain designs located in promising regions of the search space. First, the better performance of the hybrid method compared to the performance of an evolutionary algorithm is demonstrated on benchmark problems. Then, the methodology is applied on the LS89 application. The optimization allows to find a new 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.

This paper presents a single point optimization of the LS89 turbine vane cascade for a downstream isentropic Mach number of 0.9. The objective of the optimization is to minimize the entropy generation through the cascade while maintaining the flow turning of the baseline geometry. The optimization is performed using a hybrid optimization algorithm which combines two main families of optimization methods, namely an evolutionary algorithm and a gradient-based method. The combination of these two methods aims to correct their respective main disadvantage which are the poor convergence performance of the evolutionary and the trend to get trapped in local minima of the gradient-based method. The hybrid algorithm implemented in this work is based on the Lamarckian evolution and consists in incorporating directly the gradient-based method inside the loop of the evolutionary algorithm. In this approach, the evolutionary algorithm performs a global exploration of the design space while the gradient-based method improves the convergence rate of the evolutionary algorithm. The better performance of the developed hybrid method, compared to a classical evolutionary algorithm, is first demonstrated on two analitycal functions used as benchmark problems. Subsequently, the hybrid algorithm is used to optimize LS89 turbine vane, resulting in a new design with about 20 percent lower entropy production compared to baseline geometry. A thorough flow analysis shows that the improvements are largely due to a significant decrease in trailing edge losses, which is characterized by a higher base pressure. A previous optimization of the LS89 cascade has been already realized using a classical gradient-based method. This optimization converged towards a new design which reduces the entropy rise by a factor of 11 percent. Therefore, the comparison between this optimum and the one found using the proposed method demonstrates that the hybrid algorithm allows to locate a better minimum by performing a global exploration of the design space.

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.

The present paper addresses the multi-objective aerodynamic shape optimization of the two-dimensional LS-89 turbine cascade. The objective is to minimize the entropy generation at subsonic and transonic flow conditions while maintaining the same flow turning. Nineteen design variables are used to parametrize the geometry. The optimization problem is used to compare two major classes of optimization algorithms and at the same time deduce if this problem has multiple local solutions or one global optimum. A first optimization strategy uses a gradient-based Sequential Quadratic Programming algorithm. This SQP algorithm allows to directly handle the non-linear constraints during the optimization process. An adjoint solver is used for computing the sensitivities of the flow quantities with respect to the design variables, such that the additional gradient computational cost is nearly independent of the number of design variables. In addition, the same optimization problem is performed with a gradient-free - metamodel assisted - evolutionary algorithm. A comparison of the two Pareto-fronts obtained with both methods shows that the gradient-based approach allows to find the same optimum at a reduced computational cost. Moreover, the results suggest that the considered optimization problem is uni-modal. In other terms, it is characterized by a single optimal solution.