Modelling of azimuthal thermoacoustic and aeroacoustic instabilities in axisymmetric geometries

Abstract

To face the current situation of climate change caused by human activities, many states set the goal to reach zero emissions of greenhouse gases by 2050 in order to contain the increase of the mean earth temperature in an acceptable range. To reach such an ambitious goal, a revolution is necessary in the domains of energy production and transportation. Renewable energies are destined to play a major role in this transition, but they cannot be used alone, because of their intermittency and their unpredictable character, preventing a production adapted to the demand of electricity consumption in real time. One of the most promising path to overcome these limitations is the conversion of renewable electric energy into chemical energy by extracting hydrogen from water by electrolysis. This hydrogen can be stored and then burned in turbines to produce electricity according to the demand. Due to their power and their flexibility, gas turbines are unavoidable elements of the energy transition. In the sector of air transportation, the gas turbine is the only mean of propulsion offering enough power for a sufficiently moderate weight, and hydrogen propulsion starts being seriously considered also in this domain. A consequent research effort has been deployed in the last decades to improve the performances of the combustion chambers in land-based and aeronautic gas turbines. New architectures of combustion chambers need to be conceived to provide optimal performances while being adapted to new fuels such as hydrogen and meeting increasingly drastic regulations in terms of reduction of nitrogen oxides emissions. The development of these architectures confronts to the problem of thermoacoustic instabilities, arising from a coupling between the unsteady heat release rate of the flames and the acoustic modes of the combustion chamber. These are frequently annular shaped, especially in aeronautic applications, because this configuration is the most compact, the lightest, and ensures the most homogeneous temperature profile and features the smallest wall surface to cool. In these annular chambers, thermoacoustic instabilities generally involve the first azimuthal acoustic modes. Azimuthal thermoacoustic instabilities are a global phenomenon involving all the volume and all the flames of the chamber. Therefore, their study often necessitates experiments and simulations on a complete geometry, because studies on a sub-part of the geometry fail to account for the global phenomenon. An other difficulty is caused by the degenerate character of the azimuthal acoustic modes, allowing a fascinating variety of dynamic behaviours of thermoacoustic instabilities. The present thesis proposes a low-order modelling approach of the azimuthal thermoacoustic modes, along with experiments. The model, based on the first principles, accounts for the effects of different kinds of asymmetries, delayed flame response, turbulent combustion noise, azimuthal mean flow. It provides a qualitative and quantitative physical interpretation for a large variety of thermoacoustic dynamics observed in combustion chambers, which had never been explained. The low order modelling allows to obtain analytical results and to evaluate globally the interactions between the different parameters of the system, which is generally not possible in higher fidelity approaches like LES or Helmholtz solvers. A similar model is also derived to describe an aeroacoustic instability in a cylindrical chamber, presenting very similar characteristics compared to thermoacoustic azimuthal instabilities, demonstrating that some of the phenomena described in this thesis are not restricted to the field of thermoacoustics, but are also of interest for other fields of physics.