PhD defense - K. Wieczorek

Numerical study of mach number effects on combustion instability

Delivered by University of Montpellier II
Speciality: Mathematics

November 8, 2010 - CERFACS

The development of gas turbines towards lean combustion increases the susceptibility of the flame to flow perturbations, and leads more particularly to a higher risk of combustion instability. As these self-sustained oscillations may affect the performance of the combustion device or even cause structural damage, it is very important to be able to predict this behaviour at the design level. The methods used at present for the description of combustion instabilities are numerous and range from powerful yet very CPU time demanding LES and DNS calculations to low-order network models.
An intermediate method consists in solving a set of equations describing the acoustic field using a finite volume technique. This allows to take into account geometrical details that cannot be represented by network models, but needs less time and resources than a LES calculation. It is therefore this latter approach that has been used for conducting the present study.
This thesis discusses the impact of a non zero Mach number mean flow field on thermo-acoustic instability. The study is based on the linearized Euler equations, which are stated in the frequency domain in the form of an eigenvalue problem and solved using a finite volume technique. Using the linearized Euler equations rather than the Helmholtz equation avoids making the commonly used assumption of the mean flow being at rest, and thus allows to take into account convection effects and their impact on the stability of the system. Among the mechanisms that can be studied using the present approach is namely the impact of convected entropy waves. This is especially interesting in combustion applications, where hot spots are created in the flame zone and then transported downstream by the mean ?ow, where they may interact with the acoustic field in zones of non-uniform mean flow.
In order to investigate the problem of thermo-acoustic instability for quasi-1D and 2D configurations, two numerical solvers have been developed and are presented in this thesis. The results obtained with these codes are compared to results of a Helmholtz solver, analytical models and experimental data. In order to asses the effect of the mean flow terms on the modes’ stability, an analysis of the disturbance energy budget is performed. Finally, the aspect of the eigenmodes being non-orthogonal and thus allowing for transient growth in linearly stable systems is adressed.

T. Schueller	Researcher - EM2C, Ecole Centrale Paris	Referee
A. Morgans	Professor - Imperial College, London	Referee
B. Mohammadi	Professor - CERFACS, Toulouse	Member
S. Moreau	Researcher - University of Sherbrooke, Canada	Member
W. Polifke	Professor - Technische Universität München, Germany	Member
U. Schröder	Professor - RWTH Aachen, Germany	Member
F. Nicoud	Professor - University of Montpellier II	Advisor