2019. Vol. 14. Issue 4, Pp. 233–242

URL: http://mfs.uimech.org/mfs2019.4.030,en

DOI: 10.21662/mfs2019.4.030

URL: http://mfs.uimech.org/mfs2019.4.030,en

DOI: 10.21662/mfs2019.4.030

Interaction of an acoustic wave with a multilayer medium containing a bubble liquid layer

Agisheva U.O., Galimzyanov M.N.

Mavlyutov Institute of Mechanics, UFRC RAS, Ufa

Discrete-layered media are interesting to research since properties of each layer can significantly differ from near by ones and this can be used in technological processes. The presence of a small number of bubbles significantly increases the compressibility of the medium while the density of the bubble medium remains close to the density of the carrier liquid. From the applied point of view it is interesting that the energy of the incident wave can be completely absorbed by combining of layer properties (length, volume content of the dispersed phase, etc.). In this work, based on the equations of mechanics of dispersed media, we consider the reflection and propagation of acoustic waves passing at right angles through a three-layer medium in a pipeline containing a layer of bubble fluid. From the condition for the existence of a solution in the form of a decaying traveling wave, dispersion relations are written for each of the possible layers. Based on them, the dependences of the amplitude of the incident and transmitted waves on the propagation velocity of the pulse are analytically derived. The coefficients of reflection and transmission through the interface are obtained both in the general case and in particular cases for each layer. These ratios make it possible to calculate the possible consequences of a wave action on the considered media in the event of emergencies at work and to prevent them.

acoustic wave,

multilayer medium,

bubbles,

dispersion equation,

reflection coefficient,

transmission coefficient

**Problem:** Study of the influence of disturbance frequency and medium temperature on the acoustic wave attenuation coefficient. Analysis of the influence of diffusion on the evolution of harmonic waves.

**Methods:** From the condition for the existence of a solution in the form of a decaying traveling wave, taking into account the effects of acoustic unloading of bubbles, the dispersion equation is written out, numerical calculations for water with vapor-gas bubbles are performed.

In a study was **determined:**

The study of harmonic acoustic waves in a liquid with vapor-air bubbles taking into account diffusion showed that for the problems under consideration this accounting can be significant only for superheated liquids in the low-frequency region. This is due to the increasing role of phase transitions due to an increase in the mass concentration of vapor in the bubbles under the action of capillary forces on the interface.

- Shagapov V.Sh. Propagation of small disturbances in a liquid with bubbles // Journal of Applied Mechanics and Technical Physics. 1977. V. 18. No. 1. Pp. 77–87.

https://sibran.ru/upload/iblock/bb5/bb5cd5e607fc878488eb4f4a6725a1f0.pdf - Azamatov A.Sh., Shagapov V.Sh. Propagation of small disturbances in a vapor-liquid medium // Soviet Physics. Acoustics. 1981. V. 27. No. 2. Pp. 89–96.

http://www.akzh.ru/pdf/1981_2_161-169.pdf - Vakhitova N.K., Shagapov V.Sh. On the propagation of small perturbations in vapor-liquid bubble media // Journal of Applied Mechanics and Technical Physics. 1984. V. 25. No. 5. Pp. 682–689.

https://sibran.ru/upload/iblock/71a/71a1de7a615a2b166abb82f311fe4a3c.pdf - Galimzyanov M.N., Gimaltdinov I.K. and Shagapov V.Sh. Twodimensional pressure waves in a fluid with bubbles // Fluid Dynamics. 2002. V. 37, No. 2. Pp. 294–301.

DOI: 10.1023/A:1015818602291 - Bayazitova A.R., Gimaltdinov I.K., Shagapov V.Sh. Pressure waves in a tube filled with a bubbly mixture with a nonuniform cross-sectional bubble distribution //
Fluid Dynamics. 2006. No. 3. С. 381–390.

DOI: 10.1007/s10697-006-0054-7 - Varaksin A.Y. Fluid dynamics and thermal physics of two-phase flows: problems and achievements // High Temperature. 2013. V. 51, No. 3. Pp. 377–407.

DOI: 10.1134/S0018151X13030073 - Shagapov V.Sh. and Sarapulova V.V. Reflection and refraction of acoustic waves at the interface between a gas and a disperse systems //
Journal of Applied Mechanicsand Technical Physics. 2015. V. 56, No. 5. Pp. 838–847.

DOI: 10.1134/S0021894415050107 - Shagapov V.Sh. and Sarapulova V.V. Characteristic features of rarefaction and refl ection of sound at the boundary of a bubble liquid //
Acoustical Physics. 2015. V. 61, No. 1. Pp. 37–44.

DOI: 10.1134/S1063771014060153 - Agisheva U.O. and Galimzyanov M.N. Evolution of pressure waves acting on a bubble liquid through adjacent boundaries // Journal of Physics: Conf. Series. 2019. V. 1158. 022008.

DOI: 10.1088/1742-6596/1158/2/022008 - Agisheva U.O. and Galimzyanov M.N. Low-intensity pressure waves in a stratified bubbly liquid // Journal of Physics: Conf. Series. 2019. V. 1400. 077045.

DOI: 10.1088/1742-6596/1400/7/077045 - Shagapov V.Sh., Galimzyanov M.N., Vdovenko I.I. et al. Characteristic features of sound propagation in a warm bubble-laden water //
Journal of Engineering Physics and Thermophysics. 2018. V. 91, No. 4. Pp. 854–863.

DOI: 10.1007/s10891-018-1809-9242 - Shagapov V.Sh., Galimzyanov M.N. and Vdovenko I.I. Characteristics of the reection and refraction of acoustic waves at normal incidence on the interface between
«pure» and bubbly liquids // High Temperature. 2019. V. 57, No. 2. Pp. 256–262.

DOI: 10.1134/S0018151X1901022X - Shagapov V.Sh., Galimzyanov M.N. and Vdovenko I.I. Characteristics of the reection and refraction of acoustic waves at oblique incidence on the interface between «pure»
and bubbly liquids // High Temperature. 2019. V. 57, No. 3. Pp. 425–429.

DOI: 10.1134/S0018151X19020184 - Agisheva U.O., Vdovenko I.I. and Galimzyanov M.N. Acoustic waves in a superheated liquid with a gas nuclei //Journal of Physics: Conf. Series. 2019. V. 1158. 022007.

DOI: 10.1088/1742-6596/1158/2/022007 - Agisheva U.O., Galimzyanov M.N. and Vdovenko I.I. Acoustic properties of overheated liquid with gas nuclei during temperature increasing //
Journal of Physics: Conf. Series. 1268(2019). 012014.

DOI: 10.1088/1742-6596/1268/1/012014 - Agisheva U.O., Vdovenko I.I., Galimzyanov M.N. The effect of diffusion on the acoustic properties of a bubble fluid // Multiphase Systems. 2019. V. 14. No. 3. Pp. 165–175 (in Russian).

DOI: 10.21662/mfs2019.3.023 - Isakovich M.A. General Acoustics. Moscow: Nauka. 1973. 496 p (in Russian).
- Nigmatulin R.I. Dynamics of Multiphase Media. New York: Hemisphere, 1991, vols. 1 and 2. P. 360 and P. 464.
- Landau L.D., Lifshits E.M. Hydrodynamics. Moscow: Fizmatlit. Vol. 6. 2001. 736 p (in Russian).
- Nigmatulin R.I., Shagapov V.Sh. and Vakhitova N.K. Effect of the compressibility of the carrier phase in wave propagation in a bubble medium // Doklady. Akad. Nauk SSSR. 1989. V. 304, No. 5. Pp. 1077–1081.