The Oblique Fall of an Acoustic Wave on the Boundary of a Multifractional Gas Suspension with Polydisperse Inclusions
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The Oblique Fall of an Acoustic Wave on the Boundary of a Multifractional Gas Suspension with Polydisperse Inclusions D. A. Gubaidullin1* and R. R. Zaripov1** (Submitted by A. M. Elizarov) 1
Institute of Mechanics and Engineering, Federal Research Center Kazan Scientific Center, Russian Academy of Sciences, Kazan, Tatarstan, 420111 Russia Received March 2, 2020; revised March 13, 2020; accepted March 20, 2020
Abstract—This article is devoted to the study of the oblique fall of an acoustic wave from a pure gas to the boundary of a multifraction gas suspension with polydisperse inclusions of different sizes and materials. A mathematical model that allows to determine the reflection coefficient when an acoustic wave falls obliquely on the interface between two media is presented. Dependencies of the reflection coefficient on the disturbance frequency were calculated. Influence of the oblique angle of acoustic wave on the dependence of the reflection coefficient was established. DOI: 10.1134/S1995080220070161 Keywords and phrases: acoustic wave, reflection coefficient, polydisperse inclusions.
1. INTRODUCTION Interaction of acoustic waves with multiphase media is an interesting problem. Previously, a number of aspects on this topic were studied in the works [1–14]. This paper is devoted to the study of the reflection of acoustic waves from the interface between a pure gas and a multifractional mixture with polydisperse inclusions. It will be taken into account that each fraction of the mixture will be described by an arbitrary function of the size distribution of inclusions. The analysis is based on the method, reported in work [15], and we use an equation for speed of sound in such multiphase media (dispersion relation), which was obtained in [10]. 2. MATHEMATICAL MODEL To determine the reflection coefficient of plane acoustic waves from the interface of two media, we will use the method, described in paper [15]. Let us consider the incidence of an acoustic wave at some angle at the interface of two media. In further discussion, we will assume that index 1 refers to the media where the acoustic wave falls, and index 2 refers to the media where the acoustic wave passes. The wave incidence angle will be calculated from the normal of the interface between two media. Then according to [15], the reflection coefficient can be determined from the following formula ρi Ci Z2 − Z1 , Zi = , i = 1, 2. (1) R= Z2 + Z1 cos θi Here ρ is the density, C is the speed of sound, θ1 is the oblique angle and θ2 is the trajectory angle. The angle of trajectory θ2 can be determined from equation C2 sin θ1 . sin θ2 = C1 * **
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THE OBLIQUE FALL OF AN ACOUSTIC WAVE
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Suppose that an acoustic wave falls on the interface between air and a multifractional polydisperse gas suspension. In this case the speed of sound in such gas-particle mixture is determined from the formula [2] ω Cgp = . (2) Re(Kgp ) Here ω is the frequency perturbation, Re is the real part of complex wave number Kgp , index g
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