# Aero-acoustics and noise

## Introduction

Sound can be understood as the pressure fluctuation in the medium. Acoustics is the study of sound propagation in the medium. AeroAcoustics deals with the study of sound propagation in air. With the stringent conditions imposed on the Aircraft industries for noise pollution, the focus now is shifting towards predicting the noise generated for a given aerodynamic flow. AeroAcoustics is an advanced field of fluid dynamics where in the flow scale is reloved to the acoustic levels. The first head-start in the field of AeroAcoustics is given by Sir James Lighthill when he presented an "Acoustic Analogy". With proper manipulation of the Euler equations, he derived a wave equation based on pressure as the fluctuating variable, and the flow variables contributing to the source of fluctuation. The resulting wave equation can then be integrated with the help of Green's Function, or can be integrated numerically. Thus, this equation can represent the sound propagation from a source in an ambient condition. With the success of acoustic analogy, many improvements were made on the derivation of the wave equation. Two common form of equation used in acoustic analogy are the Ffowcs Williams - Hawkins equation and the Kirchoff's Equation. Though Acoustic Analogy is able to solve the problem of noise prediction to a greater extent, the focus is now shifting towards direct computation, wherein the noise is computed directly by the flow solver. Ofcourse acoustic analogy is still applied in the far field propagation. But the near field sound generation is resolved to a grater extent. Large Eddy Simulation is widely used for these studies. DNS is still unreachable for problems of practical dimensions. The industries rather require a code that can provide them results in a day than a month. Hence, RANS based models (like JET3D by NASA) are also widely used in the industries. One of the main difficulties in Computational AeroAcoustics is the scale of the problem. Acoustics waves have a reasonably high velocity compared to the flow structures and at the same time, nearly 10 orders smaller in magnitude. Also, due to the propagation to long distances, the numerical scheme should be less dissipative and less dispersive. The CFD solvers have inherent dissipation to ensure stability. This makes most of the robust CFD solvers incapable of simulating acoustic flows. Advanced schemes such as Dispersion Relation Preserving (DRP) schemes, compact schemes etc. aim at less dispersive solution. Still, with the current computational capability, acoustic computation for a problem of practical interest is still out of reach.