Browsing by Author "Karpov, Sergey"
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Item A Nonlinear Model of Thermoacoustic Devices(The Journal of the Acoustical Society of America, 2002-10) Karpov, Sergey; Prosperetti, AndreaThis 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.Item A Simplified Model for Linear and Nonlinear Processes in Thermoacoustic Prime Movers. Part II. Nonlinear Oscillations(The Journal of the Acoustical Society of America, 1997-12) Yuan, H.; Karpov, Sergey; Prosperetti, AndreaThe 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.Item Linear thermoacoustic instability in the time domain(The Journal of the Acoustical Society of America, 1998-06) Karpov, Sergey; Prosperetti, AndreaAn approximate time-domain description of the development of the thermoacoustic instability in gas-filled tubes is developed by exploiting the difference between the instability time scale and the period of standing waves. The perturbation results compare very favorably with the exact frequency-domain theory of Rott. The perturbation results are further simplified by introducing a short-stack approximation which is numerically much simpler and only slightly less accurate. An approximate expression for the critical temperature gradient accounting for viscous effects and other design features is also derived. In addition to the fundamental mode of a tube closed at both ends, the theory includes higher modes as well as open-end boundary conditions.Item Nonlinear saturation of the thermoacoustic instability(The Journal of the Acoustical Society of America, 2000-06) Karpov, Sergey; Prosperetti, AndreaA 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.Item Nonlinear wave interactions in bubble layers(The Journal of the Acoustical Society of America, 3/1/2003) Karpov, Sergey; Prosperetti, Andrea; Ostrovsky, Lev A.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.