THESE de DOCTORAT - cerfacs
THESE de DOCTORAT - cerfacs
THESE de DOCTORAT - cerfacs
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Contents<br />
1 General Introduction 13<br />
1.1 Noise in a combustion chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15<br />
1.2 Scope of the present work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17<br />
1.3 Organization of the manuscript . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18<br />
2 Computation of noise generated by combustion 20<br />
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20<br />
2.2 Direct Computation of noise through Large Eddy Simulation . . . . . . . . . . . 23<br />
2.2.1 Governing equations of turbulent reacting flows . . . . . . . . . . . . . . 23<br />
2.2.2 Large Eddy Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24<br />
2.3 Hybrid computation of noise: Acoustic Analogies . . . . . . . . . . . . . . . . . . 26<br />
2.3.1 An energy expression useful for acoustics . . . . . . . . . . . . . . . . . . 26<br />
2.3.2 Lighthill’s Analogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29<br />
2.3.3 Phillips’ Analogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33<br />
2.3.4 Solving Lighthill’s analogy analytically . . . . . . . . . . . . . . . . . . . . 37<br />
3 Development of a numerical tool for combustion noise analysis, AVSP-f 41<br />
3.1 Discretizing the Phillips’ equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 42<br />
3.2 Boundary Conditions in AVSP-f . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46<br />
3.3 Solving the system Ax = b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47<br />
3.3.1 On the Arnoldi algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 50<br />
3.3.2 The least square problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 53<br />
3.4 GMRES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54<br />
3