The analysis of thermoacoustic machines (motor and refrigerator) by a low Mach number approach has been pursued along several axes: (a) numerical study of the threshold of thermoacoustic instability and analysis of the influence of a resistive load on the triggering of a thermoacoustic motor (see figure 1, thesis L. Ma, collab. L. Bauwens, University of Calgary) and (b) adaptation of the code to the study of a thermoacoustic refrigerator and parametric study (collab. O. Hireche, K. Nehar Belaïd, USTO Oran).
We have also modeled and studied the thermoacoustic instability at the origin of the starting of a “musical” thermoacoustic engine, in the framework of the Art&Sciences project “Thermophonia” 2016 (collab. J. Rémus, artist Ipotam Mécamusique, V. Daru, F. Jebali , C. d’Alessandro and B. Katz. A study of the modeling and simulation of the conditions of sound start-up was carried out. Two thermophones as well as adapted measurement benches have been installed and tested.
Finally, we obtained in 2017 a funding for the development and study of a thermoacoustic heat pump for ground transportation (ANR TACOT, carrier H. Bailliet PPRIME, collab. PPRIME, LAUM, LMFA, PSA company).
We are particularly interested in the numerical simulation of the effects related to the compactness of the machine envisaged and the high acoustic level generated: natural convection phenomena in the regenerative stack considered as a porous medium, multi-dimensional effects related to the complexity of the geometry, non-linear acoustics in porous medium.
The first 3D numerical studies in fluid cavity, partially filled with porous medium, to estimate the convective flows in a specific geometry of thermoacoustic machine, have been performed. The results of the simulations, in excellent agreement with the experiment at P’, show that these flows are three-dimensional and of the same order of magnitude as the acoustic streaming, if not larger (collab. O. Hireche, C. Weisman, V. Daru, Y. Fraigneau, H. Bailliet, I. Ramadan).
Acoustic streaming is a phenomenon that reduces the efficiency of thermoacoustic systems. Rayleigh streaming represents the second order mean flow superimposed on the dominant acoustic oscillation. It is generated by the viscous effects associated with the interaction between the acoustic wave and the solid walls. A numerical study of the nonlinear flow (Navier-Stokes compressible code in plane or axisymmetric geometry, V. Daru) has been performed. The deformation of the flow in nonlinear regime is in agreement with the experimental results (collab. H. Bailliet PPRIME, I. Reyt). The physical mechanisms responsible for the observed flow type changes and in particular the appearance of additional cells are analyzed by several approaches: direct simulation and resolution of the equations averaged over an acoustic period. The results of the numerical studies and the analogy with an entrained cavity flow have shown that inertia is not the mechanism responsible for the flow mutation at high acoustic levels. Numerical and experimental studies (see figure 2) have also shown the existence of two regimes of streaming flow: a regime for which the dependence of the axial streaming velocity on the axial acoustic velocity amplitude is quadratic and a second regime for which this dependence becomes linear. The second regime appears when the amplitude of the radial streaming velocity exceeds the amplitude of the acoustic radial velocity, the change of regime being due to the non-linear interaction between the acoustics and the streaming.