title: Low Mach number analysis of idealized thermoacoustic engines with numerical solution.
abstract: A model of an idealized thermoacoustic engine is formulated, coupling nonlinear flow and heat exchange in the heat exchangers and stack with a simple linear acoustic model of the resonator and load. Correct coupling results in an asymptotically consistent global model, in the small Mach number approximation. A well-resolved numerical solution is obtained for two-dimensional heat exchangers and stack. The model assumes that the heat exchangers and stack are shorter than the overall length by a factor of the order of a representative Mach number. The model is well-suited for simulation of the entire startup process, whereby as a result of some excitation, an initially specified temperature profile in the stack evolves toward a near-steady profile, eventually reaching stationary operation. A validation analysis is presented, together with results showing the early amplitude growth and approach of a stationary regime. Two types of initial excitation are used: Random noise and a small periodic wave. The set of assumptions made leads to a heat-exchanger section that acts as a source of volume but is transparent to pressure and to a local heat-exchanger model characterized by a dynamically incompressible flow to which a locally spatially uniform acoustic pressure fluctuation is superimposed.
authors.affiliation: Laboratoire de Mécanique Appliquée, Université des Sciences et de la Technologie d'Oran Mohamed Boudiaf, BP 1523, EL-M'naouer Oran 31000, Algeria.
authors.forename: Omar
authors.initials: O
authors.lastname: Hireche
authors.forename: Catherine
authors.initials: C
authors.lastname: Weisman
authors.forename: Diana
authors.initials: D
authors.lastname: Baltean-Carlès
authors.forename: Patrick
authors.initials: P
authors.lastname: Le Quéré
authors.forename: Luc
authors.initials: L
authors.lastname: Bauwens
mesh_terms: D000162:Acoustics / Q000295:instrumentation*; D003198:Computer Simulation; D004735:Energy Transfer; D004738:Engineering / Q000295:instrumentation*; D004867:Equipment Design; D016014:Linear Models; D008962:Models, Theoretical; D009038:Motion; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted; D011312:Pressure; D015203:Reproducibility of Results; D013016:Sound; D013696:Temperature