Acoustic Scattering for Rotational and Translational Symmetric Structures in Nonuniform Potential Flow

Abstract

An efficient approach is proposed to predict acoustic scattering with nonuniform potential flow effects for structures with rotational and translational symmetries. The convected wave equation is transformed to Helmholtz and Laplace equations using a time transformation. The boundary-element method is used to formulate scattering by rotationally symmetric structures as two separate block circulant matrix equations and, similarly, as two separate block Toeplitz matrix equations for structures with translational symmetry. Discrete Fourier transform is employed to solve the block circulant systems. The block Toeplitz systems are solved using the generalized minimal residual method along with the discrete Fourier transform. Solving the convected wave equation using structured matrices significantly reduces computational time and storage requirements. To demonstrate the application of the formulation, two exterior acoustic case studies are considered. The first case study examines acoustic scattering from a sphere submerged in potential flow under monopole source excitation. Directivity plots obtained using the proposed technique are compared with analytical results. The second case study examines flow-induced noise generated by a rigid cylinder immersed in low-Mach-number flow, with the effect of mean flow on the scattered acoustic field taken into account using nonuniform potential flow. The fluctuating flowfield is obtained using an incompressible computational fluid dynamics solver. Acoustic sources based on Lighthill’s analogy are extracted from the flowfield data using a high-order reconstruction scheme. Results from the hybrid computational fluid dynamics– boundary-element method technique are presented for turbulent flow past the cylinder, with Reynolds number based on cylinder diameter of and Mach number . The aeroacoustic results are compared with data from literature.