Multipoint optimization of an axial turbine cascade using a hybrid algorithm

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.

Multipoint Optimization of an Axial Turbine Cascade Using a Hybrid Algorithm

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.

Gradient Span Analysis Method: Application to the Multipoint Aerodynamic Shape Optimization of a Turbine Cascade

This paper presents the application of the gradient span analysis (GSA) method to the multipoint optimization of the two-dimensional LS89 turbine distributor. The cost function (total pressure loss) and the constraint (mass flow rate) are computed from the resolution of the Reynolds-averaged Navier–Stokes equations. The penalty method is used to replace the constrained optimization problem with an unconstrained problem. The optimization process is steered by a gradient-based quasi-Newton algorithm. The gradient of the cost function with respect to design variables is obtained with the discrete adjoint method, which ensures an efficient computation time independent of the number of design variables. The GSA method gives a minimal set of operating conditions to insert into the weighted sum model to solve the multipoint optimization problem. The weights associated to these conditions are computed with the utopia point method. The single-point optimization at the nominal condition and the multipoint optimization over a wide range of conditions of the LS89 blade are compared. The comparison shows the strong advantages of the multipoint optimization with the GSA method and utopia-point weighting over the traditional single-point optimization.

Multidisciplinary Multipoint Optimization of a Transonic Turbocharger Compressor

A transonic centrifugal compressor for turbocharger applications has been redesigned by means of a multidisciplinary multipoint optimization system composed of: a 3D Navier-Stokes solver, a Finite Element stress Analyzer, a Genetic Algorithm and an Artificial Neural Network. The latter makes use of a database, containing the geometry and corresponding performance of previously analyzed impellers and allows a considerable reduction in computational effort. The performance of every new geometry is verified by a 3D Navier-Stokes solver. A Finite Element Analysis verifies the mechanical integrity of the impeller. The geometrical description of the impeller has been extended to better adapt the inducer part of the impeller to transonic flows. The splitters are no longer copies of the full blades but specially designed for minimum losses and equal mass flow on both sides. The blade thickness and number of blades are unchanged because defined by robustness and inertia considerations. The operating range is guaranteed by a two-step optimization procedure. The first one provides information allowing a modification of the inlet section to guarantee the required choking mass flow and a more accurate prediction of the boundary conditions for the Navier-Stokes analysis of the modified impeller. The second one predicts the performance curve of the new geometry for which the choking mass flow is known. It is shown how these extensions of the optimization method have led to a considerable improvement of the efficiency and corresponding pressure ratio, while respecting the surge and choking limits without increase of the stress level.