Due to the large compressibility of gas bubbles, layers of a bubbly liquid surrounded by pure liquid exhibit many resonances that can give rise to a strongly nonlinear behavior even for relatively low-level excitation. In an earlier paper [Druzhinin et al., J. Acoust. Soc. Am. 100, 3570 (1996)] it was pointed out that, by exciting the bubbly layer in correspondence of two resonant modes, so chosen that the difference frequency also corresponds to a resonant mode, it might be possible to achieve an efficient parametric generation of a low-frequency signal. The earlier work made use of a simplified model for the bubbly liquid that ignored the dissipation and dispersion introduced by the bubbles. Here a more realistic description of the bubble behavior is used to study the nonlinear oscillations of a bubble layer under both single- and dual-frequency excitation. It is found that a difference-frequency power of the order of 1% can be generated with incident pressure amplitudes of the order of 50 kPa or so. It appears that similar phenomena would occur in other systems, such as porous waterlike or rubberlike media.

This paper presents a nonlinear, time-domain model of thermoacoustic devices based on cross-sectional averaged equations. Heat transfer perpendicular to the device axis--which lies at the core of thermoacoustic effects--is modeled in a novel and more realistic way. Heat conduction in the solid surfaces surrounding the fluid medium is included. Contrary to the previous versions of this model [Watanabe et al., J. Acoust. Soc. Am. 102, 3484-3496 (1997)], the present version does not require artificial damping and is numerically robust. The model performance is illustrated on several examples: a prime mover, an externally driven thermoacoustic refrigerator, and a combined prime mover/refrigerator system.

The simplified quasi-one-dimensional model of thermoacoustic devices formulated in Part I [Watanabe et al., J. Acoust. Soc. Am. 102, 3484–3496 (1997)] is studied in the nonlinear regime. A suitable numerical method is described which is able to deal with the steep waveforms that develop in the system without inducing spurious oscillations, appreciable numerical damping, or numerical diffusion. The results are compared with some experimental ones available in the literature. Several of the observed phenomena are reproduced by the model. Quantitative agreement is also reasonable when allowance is made for likely temperature nonuniformities across the heat exchangers.

A weakly nonlinear theory of the thermoacoustic instability in gas-filled tubes is developed in the time domain by exploiting the difference between the instability time scale and the period of standing waves. By carrying the expansion to fourth order in the perturbation parameter, explicit results for the initial growth, nonlinear evolution, and final saturation are obtained. The dependence of the saturation amplitude upon the temperature difference in the stack, the tube geometry, stack plate spacing, Prandtl number, and other parameters is illustrated.

In earlier work [Watanabe et al., J. Acoust. Soc. Am. 102, 3484–3496 (1997)] a quasi-one-dimensional nonlinear model for thermoacoustic devices was developed. The model reduces exactly to the well-known Rott theory upon linearization, but numerical work has shown that it is also able to predict nonlinear features in agreement with experiment. In this work, a weakly nonlinear analysis of the model is carried out for conditions close to the linear stability threshold. The level at which the amplitude of the linearly unstable perturbation is predicted to saturate compares favorably with numerical calculations and experiment. On the basis of the result, the effect of several design variables such as nonuniformity of the resonator cross section, stack plate spacing, and others is explored. [Work supported by the Office of Naval Research.]