PhD defense - A. Giauque

Flame transfer function and disturbance energies in reacting flows

Delivered by INP Toulouse
Speciality: Fluid dynamics

March 14, 2007 - CERFACS

The general objective of this thesis is to extend the understanding of combustion instabilities by testing models, physical concepts and numerical procedures, and by providing new numerical post-processing tools to do so. Two main aspects of combustion instabilities are studied and lead to many outputs.

• Flame Transfer Function (FTF)
Four different methods for the determination of Flame Transfer Functions (FTFs) in LES have been tested. HF-FFT method, based on harmonic flame forcing and FFT post-processing gives results of global combustion delays that compare well with the experiments. This method also provides the local FTF which gives valuable information about the amplitudes, delays and maximum locations of the local flame response. This method should reveal useful for configurations where the response of the flame is not compact compared to the characteristic wavelength of the excitation, as for distributed reacting cases.
A new WN-WH method based on filtered-white noise forcing and post-processing using the Wiener-Hopf relation is successfully compared to HF-FFT. Though this method should be handled with care, its main advantage is that it gives access to the frequency spectrum of the local FTF with no additional computational cost.
An important aspect of this study is its link with stability analysis of combustors. Obviously, FTFs do have an influence on the frequency and amplification rates of modes in the numerical methods used for combustor stability. This study shows how to construct FTFs which are an important ”brick” of acoustic analysis.


• Disturbance energies and stability criteria in reacting flows
Following the works of Chu and Myers for non-reacting flows, a new nonlinear conservation equation for a disturbance energy in gaseous reacting flows is derived.
A new modular post-processing tool is used here to check the balance closure of disturbance energies on laminar 1D and 2D flames. This tool gives access to all the physical and numerical terms responsible for the evolution of disturbance energies in the flow.
For each equation, major terms are identified and this work proposes two stability criteria for reacting flows. These criteria are validated on the case of an instability developing in a 2D reacting con?guration.
The first criterion extends the linear Rayleigh criterion by taking into account the influence of the fluctuation of the heat flux. This work therefore gives a relevant linear tool for the study of combustion chambers stability.
Besides, it also shows that the entropy disturbance energy cannot be linearized in reacting flows because of the local amplitude of temperature fluctuations. The second criterion is therefore nonlinear to include the influence of the entropy disturbance energy on the global stability. This criterion gives relevant information on the stability when no linearization of the flow is possible.

G. Searby	Senior researcher - IRPHE, Marseille	Referee
C. Bailly	Professor - Ecole Centrale, Lyon	Referee
F. Vuillot	Researcher - ONERA/DSNA	Member
S. Ducruix	Researcher - Ecole Centrale, Paris	Member
F. Nicoud	Professor - University of Montpellier II	Member
T. Poinsot	Senior researcher - IMFT, Toulouse	Advisor