Evaluation Of Boundary Conditions For Computational Aeroacoustics

Author : Florian Monteghetti
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (119 download)

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Download or read book Analysis and Discretization of Time-Domain Impedance Boundary Conditions in Aeroacoustics written by Florian Monteghetti and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In computational aeroacoustics, time-domain impedance boundary conditions (TDIBCs) canbe employed to model a locally reacting sound absorbing material. They enable to computethe effect of a material on the sound field after a homogenization distance and have proveneffective in noise level predictions. The broad objective of this work is to study the physical,mathematical, and computational aspects of TDIBCs, starting from the physical literature.The first part of this dissertation defines admissibility conditions for nonlinear TDIBCs underthe impedance, admittance, and scattering formulations. It then shows that linear physicalmodels, whose Laplace transforms are irrational, admit in the time domain a time-delayedoscillatory-diffusive representation and gives its physical interpretation. This analysis enablesto derive the discrete TDIBC best suited to a particular physical model, by contrast with a onesize-fits-all approach, and suggests elementary ways of computing the poles and weights. Theproposed time-local formulation consists in composing a set of ordinary differential equationswith a transport equation.The main contribution of the second part is the proof of the asymptotic stability of the multidimensionalwave equation coupled with various classes of admissible TDIBCs, whose Laplacetransforms are positive-real functions. The method of proof consists in formulating an abstractCauchy problem on an extended state space using a realization of the impedance, be it finiteor infinite-dimensional. The asymptotic stability of the corresponding strongly continuoussemigroup of contractions is then obtained by verifying the sufficient spectral conditions of theArendt-Batty-Lyubich-V ̃u theorem.The third and last part of the dissertation tackles the discretization of the linearized Eulerequations with TDIBCs. It demonstrates the computational advantage of using the scatteringoperator over the impedance and admittance operators, even for nonlinear TDIBCs. This isachieved by a systematic semi-discrete energy analysis of the weak enforcement of a genericnonlinear TDIBC in a discontinuous Galerkin finite element method. In particular, the analysishighlights that the sole definition of a discrete model is not enough to fully define a TDIBC.To support the analysis, an elementary physical nonlinear scattering operator is derived andits computational properties are investigated in an impedance tube. Then, the derivation oftime-delayed broadband TDIBCs from physical reflection coefficient models is carried out forsingle degree of freedom acoustical liners. A high-order discretization of the derived time-localformulation, which consists in composing a set of ordinary differential equations with a transportequation, is applied to two flow ducts.