Shape Optimization of Annular Combustors with an Open Source Parallelized Thermoacoustic Helmholtz Solver

Abstract

Thermoacoustic instability occurs in gas turbine combustors due to the dynamic coupling between heat release rate and acoustic oscillations. If the unsteady heat release rate is sufficiently in phase with the acoustic pressure, then the amplitude of the acoustic pressure intensifies. This increases the fatigue of the components and can lead to engine failure. Frameworks that offer quick and accurate results to study thermoacoustic instability are desirable, since the system's stability is extremely sensitive to small changes. In this thesis, we offer a framework that simulates the thermoacoustic behaviour of increasingly complex geometries and suggests design changes through adjoint methods combined with geometry parametrization techniques. We implement an inhomogeneous Helmholtz equation solver, helmholtz-x, written in an open-source framework. The mesh is generated with Gmsh and the solver uses DOLFINx and UFL from FEniCSx. The performance, validity, stability and extensibility of the solver are demonstrated through several examples of thermoacoustic instability, from the one-dimensional Rijke tube to the three-dimensional MICCA combustor. The implementation of Bloch-type boundary conditions is explained and tested. We use helmholtz-x to perform shape optimization of thermoacoustic systems. We first propose a surface parametrization technique, NURBS, to study shape sensitivities of a 30kW laboratory-scale annular combustor (MICCA from EM2C). We parametrize the surfaces of the three-dimensional geometry with NURBS control points. We apply two different strategies, perpendicular boundary movements and control point perturbations, to implement shape changes proportional to these shape derivatives. With NURBS, we apply symmetry-preserving and symmetry-breaking geometry modifications for demonstration. For the plenum and the combustion chamber, we calculate the eigenvalue derivatives with respect to the positions of the NURBS control points. Following these derivatives, we impose displacements on the NURBS control points. We show that this geometry change reduces the growth rate of the unstable modes by increasing the phase shift between the pressure and the heat release rate oscillations. In order to leverage the parametrization capability further, we then introduce the Free Form Deformation (FFD) technique to handle more complex thermoacoustic systems for industrial applications. We study three geometries: Rijke tube and LPP combustor geometries, which are relatively simple demonstration cases, and an industrial aeroengine combustor geometry, which is more complicated. We use the same analysis as in the cases with NURBS parametrization, but for FFD control points. We modify the FFD control point positions in order to reduce the thermoacoustic growth rates of the unstable eigenmodes. These findings show how, when combined with other constraints, the numerical framework we developed, helmholtz-x, could be used to study thermoacoustic oscillations and reduce their growth rates in geometrically parametrized industrial annular combustors through automated geometry changes.