Propagation of perturbations in a liquid containing gas bubbles

Kedrinskii, V. K.

doi:10.1007/bf00912733

Cited by 24 publications

(22 citation statements)

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“…6b, the fast mode behaves like a precursor of the main wave. This suggests that the origin of precursors of a shock wave reported in Kedrinskii (1968) and Shimada et al (1999) is the fast mode studied here. Experimental observation of similar precursor has recently been reported in a physically di erent context (Falcon et al, 2003).…”

Section: Numerical Results Of Wave Propagationmentioning

confidence: 83%

Linear wave propagation of fast and slow modes in mixtures of liquid and gas bubbles

2004

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A new set of space-averaged equations that governs the dynamics of mixtures of liquid and gas bubbles is derived, where a surface-averaged liquid pressure at the gas-liquid interface is used as a variable as well as volume-averaged pressures, and the liquid compressibility is taken into account. To verify the validity of the model equations, the propagation of linear plane wave in a quiescent mixture is studied theoretically and numerically. It is shown that the compressibility of liquid induces two propagation modes, a fast mode and a slow mode, for all real wave numbers, and if one assumes that the liquid is incompressible there only exists the slow mode. Since the incompressibility approximation has been used for liquid phase in previous studies, the fast mode has not been investigated in detail. In the present study, several important characters of the slow and fast modes are clariÿed. In particular, it is demonstrated that the amplitude of the fast mode is not always small and it can become large when a typical wave number exceeds a critical value.

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Section: Numerical Results Of Wave Propagationmentioning

confidence: 83%

Linear wave propagation of fast and slow modes in mixtures of liquid and gas bubbles

2004

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“…Measured results are compared with available theoretical models. It is shown that resonant interaction of gas-liquid clusters in the wave can increase the amplitude of oscillations in the shock wave.Propagation of pressure waves in a liquid with gas bubbles was considered in much detail both theoretically and experimentally [1][2][3][4][5][6][7][8][9]. It was shown that a nonlinear finite-length disturbance in a liquid with gas bubbles decomposes into solitary waves (solitons).…”

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confidence: 99%

Propagation of pressure waves in a gas-liquid medium with a cluster structure

Dontsov

2005

J Appl Mech Tech Phys

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Propagation of a stepwise shock wave in a liquid containing spherical gas-liquid clusters is experimentally studied. Measured results are compared with available theoretical models. It is shown that resonant interaction of gas-liquid clusters in the wave can increase the amplitude of oscillations in the shock wave.Propagation of pressure waves in a liquid with gas bubbles was considered in much detail both theoretically and experimentally [1][2][3][4][5][6][7][8][9]. It was shown that a nonlinear finite-length disturbance in a liquid with gas bubbles decomposes into solitary waves (solitons). Shock waves in bubbly media can have an oscillating structure. Wave evolution, structure, and decay were studied. A new type of wave structures (multisolitons) was found and examined in the experiments of [10][11][12] in a liquid with gas bubbles of two different sizes with different ratios of bubble radii. The influence of inhomogeneity of the gas-liquid mixture and compressibility of the liquid on the pressure-wave structure was examined in [13,14]. The structure and decay of moderate-amplitude pressure waves in a liquid with bubbles of two different gases and in bubbly media with a stratified structure were experimentally studied in [15,16]. Generation of high-power pressure pulses by spherical bubbly clusters was numerically considered by Kedrinskii et al. [17] who were the first to suggest the problem formulation and to explain the mechanism of shockwave amplification by a spherical bubbly cluster. Interaction of a two-dimensional shock wave with a spherical bubbly cluster in a liquid was experimentally studied in [18].In the present work, we experimentally examined the evolution and structure of a moderate-amplitude shock wave in a liquid containing bubbly clusters.The experiments were performed on a "shock-tube" setup ( Fig. 1). The test section was a vertical thickwalled steel tube with an inner diameter of 53 mm and a length of 1 m. A stainless-steel wire 1 mm in diameter was located at the axis along the test section; the ends of the wire were attached to the test-section walls. The test section was partly filled by a liquid under vacuum, which allowed us to avoid formation of gas bubbles in the liquid. Distilled water was used as the test liquid. In the test section, water was saturated by air to the equilibrium state at room temperature and atmospheric pressure; the experiments were performed under these conditions. Five bubbly clusters (foam-rubber spheres 30 mm in diameter filled by the liquid with gas bubbles) were spit onto the wire by their centers. The upper edge of the upper cluster was located at a distance of 10 mm from the liquid surface. The centers of the remaining clusters were located exactly opposite the pressure gauges G2-G5.The bubbly clusters were prepared on an additional setup as follows. The foam-rubber bubbles were placed into the test volume of the setup and were saturated by distilled water under vacuum. After that air bubbles with an elevated static pressure (as compared to the atmospher...

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“…The main feature of the IKW model is that the bubbly medium is treated as a homogeneous medium in which averaged density, pressure, and velocity are determined. The state of the medium at each time is described by a system of relations, including the equations of state for the mixture and the liquid and gaseous components, which are closed by a kinetic equation -the Rayleigh equation for a single bubble, in which the pressure at infinity on the right side is replaced by the average pressure in the medium [4]. This means that, in essence, the IKW model and its numerical analogs do not consider bubbles and take into account the special property of the medium considered -the pulsation nature of the change in state and the peculiar transfer of the energy of the wave field to the kinetic energy and internal energy of the medium and back.…”

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Dynamics and radiation of a single bubble under conditions of abnormal compressibility of a bubbly liquid

Kedrinskii

2007

J Appl Mech Tech Phys

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An equation is proposed for the pulsation of a single cavity in an abnormally compressible bubbly liquid which is in pressure equilibrium and whose state is described by the Lyakhov equation. In the equilibrium case, this equation is significantly simplified. Numerical analysis is performed of the bubble dynamics and acoustic losses (the profile and amplitude of the radiation wave generated on the bubble wall from the side of the liquid). It is shown that as the volumetric gas concentration k 0 in the equilibrium bubbly medium increases, the degree of compression of the cavity by stationary shock wave decreases and its pulsations decrease considerably and disappear already at k 0 = 3%. In the compression process, the cavity asymptotically reaches an equilibrium state that does not depend on the value of k 0 and is determined only by the shock-wave amplitude. The radiation wave takes the shape of a soliton whose amplitude is much smaller and whose width is considerably greater than the corresponding parameters in a single-phase liquid.Introduction. Although theoretical studies of bubbly media have been performed for a long time, a "collective" velocity potential that would allow one to derive an equation for the pulsation of an individual bubble in a system of interacting bubbles has not been constructed. For example, in models such as the Iordanskii-Kogarkovan Wijngaarden (IKW) model, this interaction is taken into account indirectly, through the pressure field [1-3]. The main feature of the IKW model is that the bubbly medium is treated as a homogeneous medium in which averaged density, pressure, and velocity are determined. The state of the medium at each time is described by a system of relations, including the equations of state for the mixture and the liquid and gaseous components, which are closed by a kinetic equation -the Rayleigh equation for a single bubble, in which the pressure at infinity on the right side is replaced by the average pressure in the medium [4]. This means that, in essence, the IKW model and its numerical analogs do not consider bubbles and take into account the special property of the medium considered -the pulsation nature of the change in state and the peculiar transfer of the energy of the wave field to the kinetic energy and internal energy of the medium and back. If necessary, the model predicts what occurs with any bubble in the system at any point of the space studied. This concept of the interaction of the field and medium turned out to be adequate to real physical processes that occur not only in artificially produced bubbly systems during their interaction with shock waves [4-6] but also in liquid media with natural microinhomogeneities, in which dynamic loading by rarefaction waves (phases) leads to the occurrence of cavitation processes [7]. Garipov [8] was apparently one of the first to undertake an attempt to construct the "collective" potential. A simple model for the interaction of two bubbles and the pressure waves radiated by them was studied by Fujikawa and Takahir...

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Propagation of perturbations in a liquid containing gas bubbles

Cited by 24 publications

References 1 publication

Linear wave propagation of fast and slow modes in mixtures of liquid and gas bubbles

Linear wave propagation of fast and slow modes in mixtures of liquid and gas bubbles

Propagation of pressure waves in a gas-liquid medium with a cluster structure

Dynamics and radiation of a single bubble under conditions of abnormal compressibility of a bubbly liquid

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