Aerothermal Optimization of Internal Cooling Passages Using a Discrete Adjoint Method

Abstract

Aerothermal optimization is a powerful technique for the design of internal cooling passages because it maximizes heat transfer and simultaneously minimizes pressure loss. Moreover, the optimization is fully automatic, which reduces the duration of design process compared with a human-supervised design approach. Existing optimization studies commonly rely on gradient-free methods, which can only handle a small number of design variables. However, cooling passage designs use complex geometry configurations (e.g., serpentine channels with rib-roughened surfaces) to enhance heat transfer; what is needed is to parameterize the passage using a large number of design variables. To address this need, we perform aerothermal optimization using a gradient-based optimization algorithm along with the discrete adjoint method to compute derivatives. The benefit of using the adjoint method is that its computational cost is independent of the number of design variables. In this paper, we focus on optimizing a U-bend duct, which is representative of a simplified, rib-free turbine internal cooling passage. The duct geometry is parameterized using 135 design variables, which gives us sufficient design freedom for geometric modification. We construct a Pareto front for heat transfer enhancement and total pressure loss reduction by running multi-objective optimizations. We also compare our optimization results with those from the gradient-free methods and demonstrate that we achieve better pressure loss reduction and heat transfer enhancement. The above results show that our gradient-based optimization framework functions as desired and has the potential to be a useful tool for turbine aerothermal designs with full internal cooling configurations.

An Object-oriented Framework for Rapid Discrete Adjoint Development using OpenFOAM

“…The adjoint method was first introduced in fluid mechanics by Pironneau [1] and then extended for aerodynamic shape optimization by Jameson [2]. Since then, the adjoint method has been widely used in gradient-based optimization for various applications, including aerodynamics [3][4][5][6][7][8][9][10], hydrodynamics [11,12], heat transfer [13,14], structures [15], as well as the coupling of the above disciplines [16][17][18][19]. There are two different approaches for implementing the adjoint method: the continuous approach and the discrete approach.…”