Investigação matemática e numérica dos mecanismos de geração de ruído em escoamentos cisalhantes livres

Abstract

This thesis aims to broaden the knowledge of the physical mechanisms responsible for transforming the energies of turbulent flows into acoustic energy, as well as to identify and interpret the terms of the equations that model the generation of aerodynamic noise. In this sense, the work contributes by presenting the decomposition of the tensor of Lighthill in six terms and interpreting them in order to understand the physics modeled by each one. The contribution of the work also occurs in the development of numerical methods based on finite differences optimized for the solution of the flows of the type of temporal mixing layer and of the spatial mixing layer. Numerical methods were optimized using Genetic Algorithms to reduce numerical dispersion and diffusion errors, thus obtaining a seven-point stencil for calculating spatial derivatives and a four-stage stencil for calculating time derivatives, both with optimized coefficients. The main challenges encountered in the implementation of the computational code were the non-reflexive boundary conditions based on the Navier-Stokes characteristic equations that, because they have particularities related to each domain boundary, makes it difficult to implement them generically. Finally, the investigation of the acoustic field generated by the temporal and spatial mixing layer flows and their relations with the development of fluid dynamics is presented. From the point of view of the sound production, it is observed that the vorticity equations are one of the main mechanisms of sound generation in low Mach number flows, the term that is the model of the net kinetic energy and the term connected to the modeling of the rotational movement of the fluid, both of which originate in the Lighthill tensor, which contribute most to the total noise measured in the distant field of the two types of flows studied.