Single-Point Optimization of the LS89 Turbine Cascade Using a Hybrid Algorithm

Abstract

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.

Numerical optimisation of a micro-wave rotor turbine using a quasi-two-dimensional CFD model and a hybrid algorithm

“…Examining the data for Branin, Goldstein-Price, Hartman 3, and the Fig. 26 Comparison of the convergence rate of the hybrid GA and MATSuMoTo with other hybrid optimisation routines for a the five-dimensional Rastrigin function and b the two-dimensional Rosenbrock function [65,66] two-dimensional Rastrigin demonstrates a wide spread of between the 25th and 75th percentile for both GA and PSO with a number of outliers in particular seen for the GA applied to the Branin problem. Overall, the data show that PSO may converge faster than the standard elitist GA.…”

“…Finally, to see how the hybrid GA and MATSuMoTo fare against other recently introduced hybrid methods, two single trials are run on the Rastrigin function with five parameters and the two-dimensional Rosenbrock function. The comparison is made with another evolutionary algorithm, namely a classical differential evolution (DE) algorithm, hybridised with a steepest descent method developed at the von Karman Institute [65,66]. The convergence rate for both test problems is presented in Fig.…”

Efficient CAD based adjoint optimization of turbomachinery using adaptive shape parameterization

“…The multilevel optimizations performed in [2] used the simplest steepest descent algorithm [135] combined with: (1) a line search to determine the appropriate step size [136]; (2) the projected gradient method [137] to handle the aerodynamic constraints . The latter allows to walk in the direction perpendicular to the constraints whilst reducing the objective.…”