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An experimental linear stability study of a thermoacoustic prime-mover is performed for different values of the mean pressure between 0.5 and 10 bars. The damping rate is carefully obtained as a function of the temperature gradient |∇T| enforced along the stack, up to the instability onset at |∇T|c. These results are then confronted with the predictions of a numerical model based on Rotts’ theory used with complex frequencies, in which the prime-mover is seen as a feedback loop in the electrical analogy. The experimental results are found to reasonably comply with Rott’s theory as soon as the mean pressure exceeds 2 bars. Below this value substantial discrepancies are found, as confirmed by the work of Yazaki. Above the instability onset, the saturated wave amplitude is measured as a function of |∇T|−|∇T|c for fixed pressure. The bifurcation to the nonlinear saturated wave has been tentatively determined as subcritical, although thermal inertia effects make it look supercritical.

First, the stability properties of a linear thermoacoustic prime-mover are determined experimentally. For different values of the mean pressure between 0.5 and 10 bars, the damping rate is carefully obtained as a function of the temperature gradient |∇T| enforced along the stack, up to the instability onset at |∇T|c. These results are then confronted with the predictions of a numerical model based on Rott’s theory used with complex frequencies, in which the prime-mover is seen as a feedback loop in the electrical analogy. The experimental results are found to comply with Rott’s theory as soon as the mean pressure exceeds 2 bars. Below this value, which pertains to the merging of facing stack boundary layers, substantial discrepancies are found, as confirmed by the work of Yazaki. Second, the saturated wave amplitude has been measured as a function of |∇T|−|∇T|c for fixed pressure above the instability onset. The bifurcation to the nonlinear saturated wave may be subcritical, although thermal inertia effects make it look supercritical.