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Acoustic propagation in inhomogeneous fluids: regularization via the introduction of fine particles
Arch. Mech. 72 (1), 59-73, 2020, DOI: 10.24423/aom.3370
Keywords: inhomogeneous fluids; Laplace transform; particle-laden flow; singular surface theory
Abstract
It is shown, using analytical methodologies, that the velocity field blow-up suffered by vertically ascending acoustic waves in an isothermal atmosphere can be eliminated via the introduction of fine particles. Assuming the inhomogeneous generalization of the particle-laden flow model known as the (linearized) Marble–Thompson model-1, it is established that bounded, exponentially decreasing, shock amplitudes can be obtained provided the mass fraction of particles exceeds a critical value, for which an exact expression is derived. Lastly, supporting numerical results are presented, special cases are discussed, and possible follow-on studies are noted.