Topology Optimization of Noise Reduction Structure for Aeroacoustic Sound Source

Abstract

In this research, we present an aeroacoustic topology optimization method considering aeroacoustic sound source through Lighthill’s equation. In terms of expanding the physics system of topology optimization to the aeroacoustics, this research has originality. In the previous relevant researches for acoustic topology optimization, the Helmholtz equation has been widely used with a simple sound source such as monopole sound source or incident sound source. On the contrary, in our topology optimization research for noise reduction structures, aeroacoustic sound source distributed in an area due to the turbulent flow is considered rather than a simple sound source. Lighthill's equation is known for the acoustic analogy method in which flow-induced sound source and consequential sound propagation is separately computed. In Lighthill's equation, the left hand side describes wave propagation and the right hand side describes aeroacoustic sound source. In other words, Lighthill's equation is an inhomogeneous acoustic wave equation with a sound source due to the turbulent flow. To generate the aeroacoustic sound source of Lighthill’s equation, we used stochastic noise generation and radiation (SNGR) method, which synthesizes fluctuating velocity of turbulent flow from mean flow properties obtained by stationary incompressible Reynolds averaged Navier-Stokes (RANS) simulation with k-epsilon turbulence model. In this research, two-dimensional Lighthill’s equation is solved in frequency domain by finite element method. In our topology optimization examples, design problems to reduce noise level are performed for the top structure of noise barrier and for the internal structure of muffler. To use a gradient-based optimization algorithm, material properties of finite elements are parameterized by continuous design variables between 0 and 1. To overcome the difficulties of making continuous design variables converge to the discrete values (0 or 1), density filter and sigmoid function are utilized. Gradients of objective function for design variables are calculated by adjoint variable method and method of moving asymptotes (MMA) optimization algorithm is used. In the noise barrier problem, design domain is limited to the top area of noise barrier and topology optimization results are investigated according to different random aeroacoustic sound sources, frequency ranges, and various optimization conditions. In particular, we found that the symmetry design domain condition helps to obtain a more realistic optimized structure. In the muffler problem, optimized structures in the porous media as well as in the air media are investigated.