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Experimental and theoretical study of the dynamics of self-sustained oscillations in a standing wave thermoacoustic engine

Abstract : A model for the description of the transient regime leading to steady-state sound in a quarter-wavelength thermoacoustic prime mover is proposed, which is based on the description of the unsteady heat transfer in the system, coupled with an ordinary differential equation describing wave amplitude growth/attenuation. The equations are derived by considering a cross-sectional averaged temperature distribution along the resonator, and by assuming that both the characteristic time associated with heat diffusion through the stack and that associated with the thermoacoustic amplification are much larger than the acoustic period. Attention is here focused on the only mechanism of saturation due to heat transport by sound within the stack. The numerical solving of the governing equations leads to the prediction of the transient regime, which is compared with experimental results for several values of the heat power supplied to the system and for several positions of the stack in the resonator. The model reproduces the experiments quite well, notably showing that a small diminution of the temperature in the vicinity of the hot end of the stack is associated to an overshoot of wave amplitude growth, while heat diffusion through the whole stack impacts the subsequent evolution of wave amplitude leading to steady state. Additional experimental results exhibiting complicated regimes of wave amplitude evolution are provided, which are not reproduced by the present model.
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M. Guedra, G. Penelet, Pierrick Lotton. Experimental and theoretical study of the dynamics of self-sustained oscillations in a standing wave thermoacoustic engine. Journal of Applied Physics, American Institute of Physics, 2014, 115 (2), ⟨10.1063/1.4861879⟩. ⟨hal-01877692⟩

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