Les instabilités thermo-acoustiques se rencontrent fréquemment au sein des chambres de combustion de toute taille, de la petite chaudière au moteur de fusée. Ces instabilités sont causées par le couplage entre ondes acoustiques et dégagement de chaleur instationnaire. En effet, le passage d'une onde acoustique au travers d'une flamme va moduler son dégagement de chaleur qui, en retour, va générer de nouvelles ondes acoustiques. Lorsqu'une chambre de combustion entre en instabilité, d'importantes variations de pression sont observées ; ces fluctuations peuvent user prématurément le système ou altérer ses performances. L'étude des instabilités thermo-acoustiques a pour but d'améliorer notre compréhension de ces phénomènes complexes afin de les prévenir. L'objectif de ce travail est d'obtenir et d'intégrer au sein de modèles réduits des descriptions précises de la dissipation acoustique – effet stabilisant - et d'interaction flamme/acoustique – effet déstabilisant. Cette étude se décompose en trois axes : La première partie développe le concept de « modèle acoustique réduit » qui permet de prédire les modes acoustiques d'une chambre de combustion. Pour cela, sont prises en compte les dissipations inhérentes à certaines pièces(diaphragmes, injecteurs, ...) ainsi que le couplage flamme/acoustique. Une fois le modèle établi, il convient d'en chercher les solutions à l'aide d'un solveur numérique spécialement conçu pour cette tâche. Dans une deuxième partie, un banc expérimental est utilisé pour caractériser le lien entre perte de charge et dissipation acoustique. Il est montré de manière théorique et expérimentale que la connaissance des pertes de charge au travers d'un élément permet de prédire son comportement acoustique à basse fréquence. La dernière partie concerne le couplage flamme/acoustique et plus spécifiquement l'influence de la température de l'accroche-flamme :une flamme pauvre pré-mélangée air/méthane est stabilisée sur un cylindre dont la température peut être contrôlée. Ainsi, il est montré que l'influence de la température du cylindre sur la flamme – position d'équilibre, dynamique et stabilité - est remarquable. / From small scale energy systems such as domestic boilers up to rocket motors, combustion chambers are often prone to combustion instabilities. These instabilities stem from the coupling of unsteady heat release rate and acoustic waves. This coupling is two sided: flame front perturbations generate acoustic waves while acoustic waves impinging on flame holders can disturb flames attached on them. Important pressure and velocity oscillations can be reached during unstable regimes, that can alter its efficiency or even damage the entire combustion chamber. One major challenge is to understand, predict, and prevent from these combustion instabilities. The objectives of this thesis are twofold: (1) take into account acoustic dissipation and (2)analyze flame/acoustic coupling to obtain Reduced Order Model (ROM) for combustion instabilities. This work is divided into three parts. First, the concept of ROM that gives the acoustic modes of a combustion chamber is introduced. This modeling strategy is based on the acoustic network theory and may take into account flame/acoustic coupling as well as acoustic dissipation. An efficient numerical algorithm dedicated to solve ROMs was designed on purpose and validated on several academical configurations. Second, an experimental rig was commissioned to study mean and acoustic pressure losses across a diaphragm and two swirl injectors. Results show that these two phenomena are linked and can be simply incorporated into ROMs. Finally, flame/acoustic coupling is investigated by using both direct numerical simulations and experiments: a lean premixed V-shaped laminar flame is anchored on a cylindrical bluff-body and we show that its temperature greatly influences the flame mean shape as well as its dynamics.

Indiana University-Purdue University Indianapolis (IUPUI) / In order to conform to pollutant-control regulations and minimize NOx emissions, modern household boilers and central heating systems are moving toward premixed combustors. These combustors have been successful with regards to emissions along with efficiency. However, their implementation has been associated with acoustical instability problems that could be solved through precise optimization in design rather than trial and error experimentation. This thesis introduces an experimental apparatus, which is designed to investigate the acoustic instability problem at the flame level. The goal is an experimental determination of the flame transfer function and comparison of the experimental data with a theoretical model of the flame. An experimental procedure is designed to diagnose the origins of the combustion instabilities by measurement of the flame transfer function. This research is carried out in three steps. The first step is to understand the acoustic instability problem through study of the theoretical models of the flame transfer function and selection of a model, which is most functional in industrial applications. A xiii measurement technique for the flame transfer function is developed according to the required accuracy in measurements, repeatability, and configurability for a wide range of operating conditions. Subsequently, an experimental apparatus is designed to accommodate the flame transfer function measurement technique. The components of the acoustic system are carefully sized to achieve precise measurement of the system parameters such as flows, pressures, and acoustic responses, and the apparatus is built. The apparatus is operated to measure the flame transfer function at several operating conditions. The experimentally measured flame transfer function is compared with a theoretical model for further verification. The experimental apparatus provides an improved assessment of the acoustic instability problem for industrial applications.

<p>Combustion instability, a complex phenomenon observed in combustion chambers is due to the coupling between heat release and other unsteady flow processes. Combustion instability has long been a topic of interest to rocket scientists and has been extensively investigated experimentally and computationally. However, to date, there is no computational tool that can accurately predict the combustion instabilities in full-size combustors because of the amount of computational power required to perform a high-fidelity simulation of a multi-element chamber. Hence, the focus is shifted to reduced fidelity computational tools which may accurately predict the instability by using the information available from the high-fidelity simulations or experiments of single or few-element combustors. One way of developing reduced fidelity computational tools involves using a reduced fidelity solver together with the flame transfer functions that carry important information about the flame behavior from a high-fidelity simulation or experiment to a reduced fidelity simulation.</p> <p> </p> <p>To date, research has been focused mainly on premixed flames and using acoustic solvers together with the global flame transfer functions that were obtained by integrating over a region. However, in the case of rockets, the flame is non-premixed and distributed in space and time. Further, the mixing of propellants is impacted by the level of flow fluctuations and can lead to non-uniform mean properties and hence, there is a need for reduced fidelity solver that can capture the gas dynamics, nonlinearities and steep-fronted waves accurately. Nonlinear Euler equations have all the required capabilities and are at the bottom of the list in terms of the computational cost among the solvers that can solve for mean flow and allow multi-dimensional modeling of combustion instabilities. Hence, in the current work, nonlinear Euler solver together with the spatially distributed local flame transfer functions that capture the coupling between flame, acoustics, and hydrodynamics is explored.</p> <p> </p> <p>In this thesis, the approach to extract flame transfer functions from high-fidelity simulations and their integration with nonlinear Euler solver is presented. The dynamic mode decomposition (DMD) was used to extract spatially distributed flame transfer function (FTF) from high fidelity simulation of a single element non-premixed flame. Once extracted, the FTF was integrated with nonlinear Euler equations as a fluctuating source term of the energy equation. The time-averaged species destruction rates from the high-fidelity simulation were used as the mean source terms of the species equations. Following a variable gain approach, the local species destruction rates were modified to account for local cell constituents and maintain correct mean conditions at every time step of the nonlinear Euler simulation. The proposed reduced fidelity model was verified using a Rijke tube test case and to further assess the capabilities of the proposed model it was applied to a single element model rocket combustor, the Continuously Variable Resonance Combustor (CVRC), that exhibited self-excited combustion instabilities that are on the order of 10% of the mean pressure. The results showed that the proposed model could reproduce the unsteady behavior of the CVRC predicted by the high-fidelity simulation reasonably well. The effects of control parameters such as the number of modes included in the FTF, the number of sampling points used in the Fourier transform of the unsteady heat release, and mesh size are also studied. The reduced fidelity model could reproduce the limit cycle amplitude within a few percent of the mean pressure. The successful constraints on the model include good spatial resolution and FTF with all modes up to at least one dominant frequency higher than the frequencies of interest. Furthermore, the reduced fidelity model reproduced consistent mode shapes and linear growth rates that reasonably matched the experimental observations, although the apparent ability to match growth rates needs to be better understood. However, the presence of significant heat release near a pressure node of a higher harmonic mode was found to be an issue. This issue was rectified by expanding the pressure node of the higher frequency mode. Analysis of two-dimensional effects and coupling between the local pressure and heat release fluctuations showed that it may be necessary to use two dimensional spatially distributed local FTFs for accurate prediction of combustion instabilities in high energy devices such as rocket combustors. Hybrid RANS/LES-FTF simulation of the CVRC revealed that it might be necessary to use Flame Describing Function (FDF) to capture the growth of pressure fluctuations to limit cycle when Navier-Stokes solver is used.</p> <p> </p> <p>The main objectives of this thesis are:</p> <p>1. Extraction of spatially distributed local flame transfer function from the high fidelity simulation using dynamic mode decomposition and its integration with nonlinear Euler solver</p> <p>2. Verification of the proposed approach and its application to the Continuously Variable Resonance Combustor (CVRC).</p> <p>3. Sensitivity analysis of the reduced fidelity model to control parameters such as the number of modes included in the FTF, the number of sampling points used in the Fourier transform of the unsteady heat release, and mesh size.</p> <p> </p> <p>The goal of this thesis is to contribute towards a reduced fidelity computational tool which can accurately predict the combustion instabilities in practical systems using flame transfer functions, by providing a path way for reduced fidelity multi-element simulation, and by defining the limitations associated with using flame transfer functions and nonlinear Euler equations for non-premixed flames.</p> <p> </p><br>