THESE de DOCTORAT - cerfacs

18 Chapter 1: General Introduction
sound propagates through a quiescent homogeneous field, as in the far field for an open flame,
no acoustic-flow interactions exist. In confined domains, on the contrary, this interaction might
be crucial everywhere and therefore acoustic phenomena as scattering or refraction might be
of considerable importance. Other issue to take into account in noise produced by confined
flames is the influence of acoustic boundary conditions, since acoustic waves reflected by the
system boundaries contribute to the overall noise inside the domain. During this thesis, an
acoustic solver has been developed that resolves a simplified version of the Phillips equation.
The purpose of this acoustic tool is to understand the problematic described above and to state
the possible advantages and constraints that a hybrid approach might present when estimating
noise from confined flames. Also, procedures and numerical tools for post-processing LES data
are developed.
An important issue of low Mach number acoustic codes, as the Helmholtz solvers or the acoustic
solver developed during this thesis, is the implementation of reliable acoustic boundary
conditions at inlets/outlets. These boundary conditions are expressed usually in terms of the
acoustic impedance that in turn depends on the mean flow through the boundaries. The acoustic
impedance is difficult to be obtained either experimentally or numerically. In order to obtain
values of the acoustic impedance at the inlet/outlet of the combustion chamber from numerical
CFD simulations it would be necessary to model the entire engine. An alternative then relies
on what is known as quasi-1D Linearized Euler solvers. These numerical tools resolve the linearized
Euler Equations LEE for systems in which changes in the mean flow, due to changes in
the section area, are accounted for (see Fig. 1.2). Despite of this, the majority of the existing linearized
Euler solvers consider isentropic and isenthalpic flows. In other words, neither changes
in entropy nor in the total pressure are allowed. During this thesis, the development of a quasi-
1D Euler solver was performed, in which changes in entropy and total enthalpy through the
domain are considered. As a consequence, a first approximation of the acoustic impedances
at the inlet/outlet of an aeronautical combustion chamber can be obtained including the effect
that compression/expansion stages might have on the acoustics of the system.
1.3 Organization of the manuscript
This manuscript is organized as follows: first, the two considered approaches for the evaluation
of combustion noise (the direct and hybrid approaches) are described in the second chapter.
The governing equations of turbulent reactive flows are exposed as well as the governing
equations for Large Eddy Simulation. Subsequently, both Lighthill’s and Phillips’ analogies
are derived from the governing equations and some overview about the analytical solution of
Lightill’s analogy is provided. The third chapter is focused on the numerical solution of a simplified
Phillips equation. The acoustic code developed during this thesis (AVSP-f) is explained
in order to focus on the discretization of the wave equation and the mathematical procedures
involved in the solution of the underlying linear system. The forth chapter presents the test
cases set up for the validation of the acoustic code including the noise produced by monopole