Analysis of sound generation by flow past a circular cylinder performing rotary oscillations using direct simulation approach

Abstract

Generation of sound due to laminar flow past a circular cylinder performing rotary oscillations has been studied using a direct numerical simulation approach. Two-dimensional, unsteady, compressible Navier-Stokes equations are directly solved using high resolution, physical dispersion relation preserving schemes. In this work, modifications in the flow induced acoustic noise due to imposed rotary oscillations have been discussed in detail. Simulations have been performed for a Reynolds number Re = 150 and a Mach number M = 0.2 over a wide range of forcing frequencies and amplitudes of rotary oscillation, specifically in the synchronization region. Rotary oscillating motion of a cylinder modifies the vortex shedding patterns in the wake region as compared to the case of flow past a stationary cylinder. The frequency and strength of shed vortices determine the nature of aerodynamic forces acting on the cylinder as well as sound generation. Reduction in sound generation has been observed for some of the forced oscillation cases as compared to the flow past a stationary cylinder case. The Doak’s decomposition methodology has been used to segregate the acoustic and hydrodynamic modes from the momentum density field to understand changes in the radiated sound field for different forcing conditions. Furthermore, disturbance pressure fields have been decomposed into a number of modes based on their significance, using a proper orthogonal decomposition (POD) technique in order to identify and quantify the contribution of the lift and drag dipoles to the sound field. In addition, POD modes of disturbance vorticity fields as well as noise source structures based on approximate Lighthill’s stress tensor are also obtained and related to the generated sound fields. This analysis concludes that the frequency of rotary oscillation dictates the frequency content of the flow induced sound field. Low frequency rotary oscillations trigger sound waves with low frequencies and large wavelengths. As the forcing frequency increases, the corresponding sound field displays shorter wavelengths. Directivity of the sound field is affected by the amplitude of rotary oscillation. A case with higher forcing amplitude distributes sound energy more evenly in all directions as compared to a lower forcing amplitude case. Prescription of rotary oscillations to the circular cylinder significantly alters the frequency, amplitude, and directivity of the generated sound field.