### ASA 126th Meeting Denver 1993 October 4-8

## 2aPAa8. Analysis of a thermoacoustics prime mover above onset of
self-oscillation.

**Andres Larraza
Anthony A. Atchley
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*Phys. Dept., Code PH/La, Naval Postgraduate School, Monterey, CA 93943
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Nonlinear effects that lead to amplitude saturation in a thermoacoustic
prime mover, are described. The evolution of the acoustic amplitude is
described by a homogeneous Ginzburg equation of the form
dA/dt=(alpha)A-(beta)A[sup 2]. The linear term represents the contribution from
the power output due to the temperature gradient and viscous and thermal
losses. The coefficient (alpha) is positive above onset. The cubic term is a
consequence of the nonlinear induced vorticity at the boundary layer that
originates from irreversible terms. In the approximation considered, the
coefficient (beta) is positive and a steady state results from the balance
between the linear growth and the nonlinear saturation. The steady-state
amplitudes are in qualitative agreement with observations made by Wheatley
[Frontiers in Physical Acoustics, Varena (1986)] and Hofler et al. [see
abstract in this session]. Observations made by Swift [J. Acoust. Soc. Am. 92,
1551 (1992)] on the dependence of acoustic pressure versus heater power are
also in qualitative agreement with the theory. [Work supported by ONR and NPS
Direct-Funding Program.]