Finite-amplitude acoustics under the classical theory of particle-laden flows. (English) Zbl 1425.74249
Summary: We consider acoustic propagation in a particle-laden fluid, specifically, a perfect gas, under a model system based on the theories of F. E. Marble [“Dynamics of dusty gases”, Ann. Rev. Fluid Mech. 2, 397–446 (1970; doi:10.1146/annurev.fl.02.010170.002145)] and P. A. Thompson [Compressible-fluid dynamics. New York etc.: McGraw-Hill Book Company (1972; Zbl 0251.76001)]. Our primary aim is to understand, via analytical methods, the impact of the particle phase on the acoustic velocity field. Working under the finite-amplitude approximation, we investigate singular surface and traveling wave phenomena, as admitted by both phases of the flow. We show, among other things, that the particle velocity field admits a singular surface one order higher than that of the gas phase, that the particle-to-gas density ratio plays a number of critical roles, and that traveling wave solutions are only possible for sufficiently small values of the Mach number.
MSC:
| 74J30 | Nonlinear waves in solid mechanics |
| 76N15 | Gas dynamics (general theory) |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
| 35M30 | Mixed-type systems of PDEs |
Keywords:
particle-laden flows; finite-amplitude acoustics; traveling waves; singular surfaces; Laplace transformCitations:
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