Developing Computational Tools for Modern Aeroacoustic Research

Sammanfattning: The thesis presents the author s research on numerical methods for Com-putational Aeroacoustics and the development of computational tools with direct applicability in industry. The designers in the gas-turbine industry, require accurate methods for predicting the onset and the frequencies of dangerous (pressure) oscillations, like the ones which typically occur in Lean Premixed Pre-vaporized (LPP) combustors. These modern gas turbine combustors could suffer significant damages or even total mechanical destruction, within fractions of seconds, due to these instabilities. Thus, one is interested in determining the resonance frequencies and the acoustic modes of complex industrial geometries, like a gas turbine com-bustor or an ejection nozzle, for instance. These resonance frequencies we refer to as the eigenvalues and the corresponding acoustic modes are called the eigenmodes of the acoustic system. The Implicitly Restarted Arnoldi Method (IRAM) is a robust and e cient method for solving numerically large generalized eigenvalue problems, of the form: [A][X]= lambda [B][X],where [A] and [B] are large sparse matrices, [X] is called the eigenvector and lambda is the corresponding eigenvalue. The Arnoldi method e ciently computes only a small set of eigenvalues and the corresponding eigenmodes for these very large systems, which typically occur in industry (for example a combustion chamber). As a first step, using IRAM and assuming that the acoustic system can be described by a simple model based on the wave equation with appropriate boundary conditions, the author developed a fast algorithm called ARNO-WAVE, and a computer code called ARNO3D based on this algorithm, which can be used to compute these resonance frequencies and the corresponding modes. This code uses a Galerkin finite-volume discretization on unstruc-tured grids made of tetrahedral cells. In a second step, the author has extended the applicability of the pro-posed method by using the Linearized-Euler equations instead of the wave equation, to include also the effects of variable (in space) flow conditions on the sound propagation. The new algorithm, called ARNO-LEE, is based on a Multidimensional Upwind second order discretization using the Low Diffusion A (LDA) distribution scheme. The eigensolver implementing this algorithm, called ARN-EU-3D, has been modified to work with complex numbers. The ARNO-LEE algorithm is capable of computing not only the resonance frequencies quencies and modes but also the stability of these modes. The results obtained with both codes have been compared and validated on a series of test cases, for which analytical solution exists. These algorithms based on the Arnoldi method prove to be well suited for large acoustic com-putations. The ARNO-WAVE and ARNO-LEE algorithms have been used to compute the resonance frequencies and the acoustic modes for several industrial applications.