Acoustic Response of a Vibrating Elongated Cylinder in a Hydrodynamic Turbulent Flow

Abstract

The present paper contains the results of the numerical analysis of the interaction between a Newtonian incompressible turbulent flow and a linear elastic slender body, together with the influence of the fluid–structure interaction (FSI) on the noise generation and propagation. The purpose is to evaluate the differences in term of acoustic pressure between the case where the solid body is rigid (infinite stiffness) and the case where it is elastic (finite stiffness). A partitioned and implicit algorithm with the arbitrary Lagrangian–Eulerian method (ALE) is used for the interaction between the fluid and solid. For the evaluation of the turbulent fluid motion, we use a large eddy simulation (LES) with the Smagorinsky subgrid scale model. The equation for the solid is solved through the Lagrangian description of the momentum equation and the second Piola–Kirchoff stress tensor. In addition, the acoustic analogy of Lighthill is used to characterize the acoustic source (the slender body) by directly using the fluid dynamic fields. In particular, we use the Ffowcs Williams and Hawkings (FW-H) equation for the evaluation of the acoustic pressure in the fluid medium. As a first numerical experiment, we analyze a square cylinder immersed in a turbulent flow characterized by two different values of stiffness: one infinite (rigid case) and one finite (elastic case). In the latter case, the body stiffness and mean flow velocity are such that they induce the lock-in phenomenon. Finally, we evaluate the differences in terms of acoustic pressure between the two different cases.