2021. Vol. 16. Issue 3–4, Pp. 112–120

URL: http://mfs.uimech.org/mfs2021.3.015,en

DOI: 10.21662/mfs2021.3.015

URL: http://mfs.uimech.org/mfs2021.3.015,en

DOI: 10.21662/mfs2021.3.015

Pressure waves in a tube filled with a liquid with a bubble region in it in the form of a torus

Galimzyanov M.N.

Mavlyutov Institute of Mechanics UFRC RAS, Ufa, Russia

Problems considering the focusing of wave energy in a liquid are related to the problem of making hydroacoustic analogs of laser systems that could absorb an external action and re-emit it with a significant increase in amplitude and energy concentration in an adjusted direction. In this paper, we study two-dimensional axisymmetric wave perturbations in a channel with water containing a toroidal coaxial cluster filled with a water-air bubble mixture. Based on the results of numerical calculations, the dependence of the maximum pressure amplitude formed in the channel on the geometric parameters of the cluster and channel, as well as on the amplitude of the initial impact, is analyzed. It has been established that in the case of a cylindrical cluster the amplitude of the wave signal behind the bubble zone is several times higher than the amplitude for the case of a cylindrical toroidal cluster.

cylindrical channel,

bubble cluster,

bubble liquid,

pressure wave,

toroidal bubble cluster

**Purpose:** Investigation of a pressure wave passing through a bubble toroidal cluster.

**Solution methods:** In this work, as a numerical method for solving a system of partial differential equations, a finite-difference scheme based on the use of the Runge-Kutta method was chosen. This scheme is adapted for solving problems of gas dynamics.

**The result** of the study:

The dynamics of waves of the “step” type into a channel with water containing a coaxial bubble cluster in the form of a toroid has been studied. Based on numerical calculations, the following regularities have been established:

- at certain parameters of the cluster, the pressure wave is focused on the axis of the cylindrical channel.
- an increase in the amplitude of the initial wave to a certain value leads to an increase in the amplitude of the resulting wave focused on the channel axis by more than ten times, a further increase in the amplitude of the initial wave leads to saturation of the amplitude of the resulting wave.
- with an increase in the inner radius of the cluster, the amplitude of the resulting wave on the axis decreases. There is a critical value of the inner radius of the cluster, which depends on the parameters of the system (geometric dimensions of the cluster and channel, dispersity and volumetric content of bubbles in the cluster) at which the amplitude of the resulting wave on the channel axis is less than the amplitude of the tower-like burst inside the bubble cluster.

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