Constrained Aeroacoustic Shape Optimization Using the Surrogate Management Framework

Abstract : Reduction of noise generated by turbulent flow past the trailing-edge of a lifting surface is a challenge in many aeronautical and naval applications. Numerical predictions of trailing-edge noise necessitate the use of advanced simulation techniques such as large-eddy simulation (LES) in order to capture a wide range of turbulence scales which are the source of broadband noise. Aeroacoustic calculations of the flow over a model airfoil trailing edge using LES and aeroacoustic theory have been presented in Wang & Moin (2000) and were shown to agree favorably with experiments. The goal of the present work is to apply shape optimization to the trailing edge flow previously studied, in order to control aerodynamic noise. There are several considerations in choosing a tractable optimization method for the trailing-edge problem. The primary concern is the computational expense of the function evaluations, and additional considerations include availability of gradient information and robustness of the optimization method. Although adjoint solvers have been successfully applied for gradient-based optimization in aeronautics problems (for example in Jameson et al. (1998)), they present difficulties with implementation, portability, and data storage for unsteady problems. Approximation modeling was used for trailing-edge optimization in Marsden et al. (2002), and results showed significant reduction in acoustic power with reasonable computational cost. In these methods, optimization is performed not on the expensive actual function, but on a surrogate function, which is cheap to evaluate. Although the approximation method presented in Marsden et al. (2002) was effective, it lacks rigorous convergence properties.