Mass, momentum, and energy transfer by the propagation of acoustic solitary waves
This paper considers the mass, momentum, and energy transfer accompanied by the propagation of the acoustic solitary wave in a gas-filled tube. As was demonstrated previously [J. Acoust. Soc. Am. 99, 1971-1976 (1996); Phys. Rev. Lett. 83, 4053-4056 (1999)], the propagation of the solitary waves is made possible by connecting a periodic array of Helmholtz resonators axially with the tube. The solitary wave can convey the mass, momentum, and energy steadily with a constant speed that is subsonic but nearly equal to the linear sound speed. It is emphasized that the quantities transferred are of first order in magnitude. Formulating the basic equations in the conservation form, the total amount of the mass, momentum, and energy transferred is obtained by using the solitary-wave solutions. It has the upper bounds determined by the limiting solitary wave, which are proportional to the size of the resonator and the inverse of its natural frequency. In evaluating the energy transfer, a clear distinction should be made between the gas-dynamic energy and the acoustic energy. The former, which contains the first-order quantity whereas the latter begins with the quadratic ones, is to be used to determine the energy transfer in the form of heat (internal energy) associated with the mass transfer.
Sugimoto
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Department of Mechanical Science, Graduate School of Engineering Science, University of Osaka, Toyonaka, Japan.