Abstract

This paper presents a gradient-based design optimization of a turbocharger radial turbine for automotive applications. The aim is to improve both the total-to-static efficiency and the moment of inertia of the turbine wheel. The search for the optimal designs is accomplished by a high-fidelity adjoint-based optimization framework using a fast sequential quadratic programming algorithm. The proposed method is able to produce improved Pareto-optimal designs, which are trade-offs between the two competing objectives, in only a few iterations. This is realized by redesigning the blade shape and the meridional flow channel for the respective target while satisfying imposed aerodynamic constraints. Furthermore, a comparative study with an evolutionary algorithm suggests that the gradient-based method has found the global Pareto front at a computational cost which is about one order of magnitude lower.

Highlights

  • The use of the adjoint method [1,2] is nowadays well established for design optimization problems in Computational Fluid Dynamics (CFD)

  • As can be seen, depending on the chosen weight, the final design is a trade-off solution between the low moment of inertia and high total-to-static efficiency, establishing a Pareto front towards the lower left hand corner

  • The highest aerodynamic performance is obtained when the moment of inertia is excluded during the optimization (ω J = 1.0)

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Summary

Introduction

The use of the adjoint method [1,2] is nowadays well established for design optimization problems in Computational Fluid Dynamics (CFD). The advantage of the adjoint approach is the efficient computation of sensitivity derivatives of a given objective function at a cost which is essentially independent of the number of design variables This feature makes the adjoint method attractive to tackle large-scale complex design problems by gradient-based optimization methods. Power 2019, 4, 10 design problem where one objective cannot be improved without penalizing the other, which is shown in this paper using a gradient-based optimization method. Buckley et al [19] show evidence of two local optima for practical multi-point airfoil design problems To investigate this point for a realistic turbomachinery design problem, we compare the results of the gradient-based optimization with the outcome of a stochastic evolutionary optimization strategy which has a higher probability to locate the global optimum, but at much larger computational cost.

Optimization Framework
Optimization Algorithm
Geometry Parameterization
Mesh Generation
CFD and Adjoint Solver
Moment of Inertia Computation
Gradient Evaluation
Problem Statement
Optimization History
Performance Map
Meridional Shape
Blade Shape
Comparison with the Gradient-Free Optimization Algorithm
Results after 80 Generations
Results after 200 Generations
Influence of Initial Design
Conclusions
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