Formation mechanism of cavitating spalls

The dynamics of formation of cavitation zones in a liquid upon reflection of a shock pulse from the free surface is studied numerically in a one-dimensional formulation using the Iordanskii-Kogarko-van Wijngaarden two-phase model. It is shown that the formation of a system of cavitation zones (clusters) with a dynamically increasing volume concentration of the gas phase near the free surface is due to oscillations of the structure of the rarefaction wave profile. The fast relaxation of tensile stresses in the cavitation zone ends in the formation of a quasistationary mass-velocity field, which provides for almost unbounded growth of cavitation bubbles in subsurface clusters and explains the occurrence of the spall layers observed in experiments. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 65–73, March–April, 2008.     

Evolution of the structure of viscoelastic liquid media upon pulse volume tension

It is shown experimentally that the unbounded bubble cavitation in a highly viscous liquid (glycerin) can develop only in a regime of very slow volume tension of a liquid sample. Upon pulse volume tension, cavitation in the sample damps at the initial stage (the bubbles do not reach pronounced sizes) and fragmentation occurs because of perturbations generated on its free surface. The mechanism of bubble growth from micropores in a thixotropic medium (gel) is explained based on experimental results and theoretical estimates. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 105–111, January–February, 2000.     

Rheological model of volume stretching of newtonian liquids

An equation of state for a volumetrically stretched cavitating liquid medium that holds in the entire span of volume concentrations of bubbles ranging from cavitation nuclei to the stage of formation of a cellular foam structure is obtained based on a proposed macrorheological model. The dependence of the modulus of volume elasticity of a liquid on the volume concentration of bubbles is plotted, and a method for estimating the relaxation time for tensile stresses in cavitating liquid media is proposed. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 35–46, January–February, 1998.     

Multiphase fluid dynamics and transport processes of low capillary number cavitating flows

To better understand the multiphase fluid dynamics and associated transport processes of cavitating flows at the capillary number of 0.74 and 0.54, and to validate the numerical results, a combined computational and experimental investigation of flows around a hydrofoil is studied based on flow visualizations and time-resolved interface movement. The computational model is based on a modified RNG k-ε model as turbulence closure, along with a vapor-liquid mass transfer model for treating the cavitation process. Overall, favorable agreement between the numerical and experimental results is observed. It is shown that the cavi- tation structure depends on the interaction of the water-vapor mixture and the vapor among the whole cavitation stage, the interface between the vapor and the two-phase mixture exhibits substantial unsteadiness. And, the adverse motion of the interface relates to pressure and velocity fluctuations inside the cavity. In particular, the velocity in the vapor region is lower than that in the two-phase region.     

Parametric Analysis for a Single Collapsing Bubble

This work presents a sensitivity analysis for cavitation processes, studying in detail the effect of various model parameters on the bubble collapse. A complete model (Hauke et al. Phys Rev E 75:1–14, 2007) is used to obtain how different parameters influence the collapse in SBSL experiments, providing some clues on how to enhance the bubble implosion in real systems. The initial bubble radius, the frequency and the amplitude of the pressure wave are the most important parameters determining under which conditions cavitation occurs. The range of bubble sizes inducing strong implosions for different frequencies is computed; the initial radius is the most important parameter characterized the intensity of the cavitation processes. However, other parameters like the gas and liquid conductivity or the liquid viscosity can have an important effect under certain conditions. It is shown that mass transfer processes play an important role in order to correctly predict the trends related with the effect of the liquid temperature, which translates into the bubble dynamics. Moreover, under some particular circumstances, evaporation can be encountered during the bubble collapse; this can be profitably exploited in order to feed reactants when the most extreme conditions inside the bubbles are reached. Thus, this paper aims at providing a global assessment of the effect of the different parameters on the entire cycle of a single cavitating spherical bubble immersed in an ultrasonic field. This work has been partially supported by Ministerio de Ciencia y Tecnologia, under grant number CTM2004-06184-C02-02.     

Single cavitation bubble generation and observation of the bubble collapse flow induced by a pressure wave

This study utilizes a U-shape platform device to generate a single cavitation bubble for a detailed analysis of the flow field characteristics and the cause of the counter jet during the process of bubble collapse caused by sending a pressure wave. A high speed camera is used to record the flow field of the bubble collapse at different distances from a solid boundary. It is found that a Kelvin–Helmholtz vortex is formed when a liquid jet penetrates the bubble surface after the bubble is compressed and deformed. If the bubble center to the solid boundary is within one to three times the bubble’s radius, a stagnation ring will form on the boundary when impinged by the liquid jet. The fluid inside the stagnation ring will be squeezed toward the center of the ring to form a counter jet after the bubble collapses. At the critical position, where the bubble center from the solid boundary is about three times the bubble’s radius, the bubble collapse flow will vary. Depending on the strengths of the pressure waves applied, the collapse can produce a Kelvin–Helmholtz vortex, the Richtmyer–Meshkov instability, or the generation of a counter jet flow. If the bubble surface is in contact with the solid boundary, the liquid jet can only move inside-out without producing the stagnation ring and the counter jet; thus, the bubble collapses along the radial direction. The complex phenomenon of cavitation bubble collapse flows is clearly manifested in this study.     

Optimization of shock-wave action on a spherical bubble in an ideal incompressible liquid

The possibility of controlling the oscillations of a spherical gas bubble in an ideal incompressible liquid is subjected to theoretical analysis. Liquid surface tension forces are not taken into account. The optimization process realizing a maximum of the radius amplitude and a maximum of the gas pressure in the bubble for a given impulsive change of pressure at infinity is considered. A shock-resonance bubble oscillation procedure giving stepwise pressure changes at the extrema of the radius is constructed. This problem is of interest in connection with the investigation of cavitation erosion [1] and processes in biological tissues [2–4]. Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–178, September–October, 1988.     

Subsonic compressible cavitation flow past a plate at small cavitation numbers

A solution of the problem of symmetric inviscid compressible cavitation flow past a plate at small cavitation numbers is presented. Kazan’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 94–104, July–August, 1998. This research was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00111).     

Direct numerical simulation of a liquid sheet in a compressible gas stream in axisymmetric and planar configurations

A thin liquid sheet present in the shear layer of a compressible gas jet is investigated using an Eulerian approach with mixed-fluid treatment for the governing equations describing the gas–liquid two-phase flow system, where the gas is treated as fully compressible and the liquid as incompressible. The effects of different topological configurations, surface tension, gas pressure and liquid sheet thickness on the flow development of the gas–liquid two-phase flow system have been examined by direct solution of the compressible Navier–Stokes equations using highly accurate numerical schemes. The interface dynamics are captured using volume of fluid and continuum surface force models. The simulations show that the dispersion of the liquid sheet is dominated by vortical structures formed at the jet shear layer due to the Kelvin–Helmholtz instability. The axisymmetric case is less vortical than its planar counterpart that exhibits formation of larger vortical structures and larger liquid dispersion. It has been identified that the vorticity development and the liquid dispersion in a planar configuration are increased at the absence of surface tension, which when present, tends to oppose the development of the Kelvin–Helmholtz instability. An opposite trend was observed for an axisymmetric configuration where surface tension tends to promote the development of vorticity. An increase in vorticity development and liquid dispersion was observed for increased liquid sheet thickness, while a decreasing trend was observed for higher gas pressure. Therefore surface tension, liquid sheet thickness and gas pressure factors all affect the flow vorticity which consequently affects the dispersion of the liquid.      

High-speed visualisation of primary break-up of an annular liquid sheet

In this experimental study, a thin annular moving water sheet is placed between two annular co-flowing air streams. The shear at the interface gives rise to Kelvin–Helmholtz type instabilities and promotes development of a sinuous surface wave at the gas–liquid interface. The amplitude of the surface wave is amplified as it travels downstream of the nozzle exit until it ruptures forming spanwise and streamwise ligaments. The liquid sheet is illuminated with high-powered halogen lamps. High-speed imaging is used in this study to qualitatively visualise the structure of the spray—of particular interest is the evolution of the spray into a ligament structure during the primary break-up and the role the outer air stream plays in this process. Sequences of images with high temporal resolution (∼2,000 fps) are recorded for image processing and analysis of the surface waves and ligament formation. A preliminary analysis of the waveform of the outer gas–liquid interface of the annular liquid sheet over a range of conditions shows the sheet Strouhal number to increase with increasing gas to liquid momentum ratio. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Cavitation structures formed during the rebound of a sphere from a wetted surface

We use high-speed imaging to observe the dynamics of cavitation, caused by the impact and subsequent rebound of a sphere from a solid surface covered with a thin layer of highly viscous liquid. We note marked qualitative differences between the cavitation structures with increase in viscosity, as well as between Newtonian and non-Newtonian liquids. The patterns observed are quite unexpected and intricate, appearing in concentric ring formations around the site of impact. In all cases, we identify a distinct radius from which the primary bubbles emanate. This radius is modelled with a modified form of Hertz contact theory. Within this radius, we show that some fine cavitation structure may exist or that it may be one large cavitation bubble. For the non-Newtonian fluids, we observe foam-like structures extending radially with diminishing bubble sizes with increase in radial position. Whereas for the Newtonian fluids, the opposite trend is observed with increasing bubble size for increasing radial position. Finally, we compare our experimental observations of cavitation to the maximum tension criterion proposed by Joseph (J Fluid Mech 366:367–378, 1998) showing that this provides the lower limit for the onset of cavitation in our experiments.     

Cavitation,Invertibility, and Convergence of Regularized Minimizers in Nonlinear Elasticity

We prove that energy minimizers for nonlinear elasticity in which cavitation is allowed only at a finite number of prescribed flaw points can be obtained, in the limit as ε→0, by introducing micro-voids of radius ε in the domain at the prescribed locations and minimizing the energy without allowing for cavitation. This extends the result by Sivaloganathan, Spector, and Tilakraj (SIAM J. Appl. Math. 66:736–757, 2006) to the case of multiple cavities, and constitutes a first step towards the numerical simulation of cavitation (in the nonradially-symmetric case).      

An experimental study of liquid jets formed by bubble-shock wave interaction in dilute polymer solutions

 This paper describes experiments in which a shock wave, emanating from the collapse of a cavitation bubble, causes a second bubble to collapse, thereby producing a liquid jet. A comparison of the jets formed by bubble collapse in dilute solutions of polyacrylamide and polyethylene oxide, and in their Newtonian counterparts, shows that in the polymer solutions liquid jet development is markedly suppressed. The implications of these findings are discussed in the context of cavitation damage. Received: 3 September 1998/Accepted: 23 July 1999     

In situ force-balance tensiometry

 Although a fundamental physical parameter, surface tension is difficult to measure. Common tensiometry inaccuracy comes from failure to control air–liquid–solid contact conditions, or account for liquid meniscus geometry and buoyancy corrections. This paper describes an in situ tensiometry technique, based on withdrawal of a thin-walled tube from the liquid interface, that enforces a known air–liquid–solid contact condition. This technique can be pursued at any level of experimental hygiene. Experimental results for filtered tap water, an alcohol–water solution, and a surfactant–water solution show that results repeatable to three significant digits are obtained with modest effort for a variety of geometrical parameters. Received: 7 October 1997/Accepted: 23 April 1998     

Conditions for Development of Cavitation in Scleronomous Media

An energy inequality that determines the conditions for development of cavitation in scleronomous media in the range from liquid (bitumens, paints, and gels) to solid (lead, aluminum, copper, etc.) plastic media is constructed upon pulse tension in terms of the viscoelastic–plastic model. A relation that allows one to determine the time of negative–pressure relaxation during the growth of cavitating pores in a medium is derived. With allowance for the previously obtained conditions for development of bubble cavitation in a relaxing field of negative pressure in shock wave–loaded liquids, this result allows one to separate a class of condensed media capable to cavitate under pulse loading.     

Transport of Viruses Through Saturated and Unsaturated Columns Packed with Sand

Laboratory-scale virus transport experiments were conducted in columns packed with sand under saturated and unsaturated conditions. The viruses employed were the male-specific RNA coliphage, MS2, and the Salmonella typhimurium phage, PRD1. The mathematical model developed by Sim and Chrysikopoulos (Water Resour Res 36:173–179, 2000) that accounts for processes responsible for removal of viruses during vertical transport in one-dimensional, unsaturated porous media was used to fit the data collected from the laboratory experiments. The liquid to liquid–solid and liquid to air–liquid interface mass transfer rate coefficients were shown to increase for both bacteriophage as saturation levels were reduced. The experimental results indicate that even for unfavorable attachment conditions within a sand column (e.g., phosphate-buffered saline solution; pH = 7.5; ionic strength = 2 mM), saturation levels can affect virus transport through porous media.     

Gas-dynamic signs of explosive eruptions of volcanoes. 1. Hydrodynamic analogs of the pre-explosion state of volcanoes, dynamics of the three-phase magma state in decompression waves

Experimental data and results of numerical simulations of the magma state dynamics in explosive eruptions of volcanoes are presented. The pre-explosion state of volcanoes and the cavitation processes developed in the magma under explosive decompression are studied under the assumption that the intensity of explosive volcanoes does not exert any significant effect on the eruption mechanisms. In terms of the structural features of the pre-explosion state, a number of explosive volcanic systems are close to hydrodynamic shock-tube schemes proposed by Glass and Heuckroth. High-velocity processes initiated by shock-wave loading of the liquid may be considered as analogs of natural volcanic processes, which have common gas-dynamic features and common kinetics responsible for their mechanisms, regardless of the eruption intensity. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 3–12, November–December, 2008.     

Mass transport effect on the heat transfer coefficient during boiling of multicomponent mixture

In this work a simplified calculation method taking into account the effect of mass transport on the heat transfer coefficient (HTC) during boiling of multicomponent mixture has been elaborated. The calculation results were compared with own experimental data for ternary system methanol–isopropanol–water and Grigoriev data [1] (acetone–methanol–water). The experiments were performed in different hydrodynamic conditions such as: pool boiling and liquid evaporation at the free surface of the falling film. The experimental data covered wide range of heat fluxes from 6 to 30 kW/m² in the case of liquid evaporation from the falling film and from 30 to 240 kW/m² for pool boiling. The analysis of the results indicates that the mass transfer resistance in the liquid phase caused a significant reduction of experimental value HTC in comparison to so-called ideal HTC.     

Strength of water under pulsed loading

Experiments were performed to study the strength of water under conditions of pulsed extension, which is typical of the interaction between a triangular compression pulse and a free surface. The tests were performed in a wide (40–1000 MPa) range of rariation in the amplitude of the compression pulse at deformation rates of 10⁴−10⁵ sec⁻¹. It is found that as the compression-pulse amplitude increases from 150 to 1050 MPa, the strength of water decreases from 46 to 22 MPa. The deformation rate was found to have little effect on the strength. The possibility of using the model of homogenous nucleation (formation of cavitation nuclei) to interpret the data obtained is discussed. Institute of Chemical Physical, Russian Academy of Sciences, Chernogolovka 142432. Translated from Prikladmaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 198–205, July–August, 2000.     

Gas-dynamic signs of explosive eruptions of volcanoes. 2. Model of homogeneous-heterogeneous nucleation. Specific features of destruction of the cavitating magma

The dynamics of state of the crystallite-containing magma is studied within the framework of the gas-dynamic model of bubble cavitation. The effect of crystallites on flow evolution is considered for two cases: where the crystallites are cavitation nuclei (homogeneous-heterogeneous nucleation model) and where large clusters of crystallites are formed in the magma in the period between eruptions. In the first case, decompression jumps are demonstrated to arise as early as in the wave precursor; the intensity of these jumps turns out to be sufficient to form a series of discrete zones of nucleation ahead of the front of the main decompression wave. Results of experimental modeling of an explosive eruption with ejection of crystallite clusters (magmatic “bombs”) suggest that a cocurrent flow of the cavitating magma with dynamically varying properties (mean density and viscosity) transforms to an independent unsteady flow whose velocity is greater than the magma flow velocity. Experimental results on modeling the flow structure during the eruption show that coalescence of bubbles in the flow leads to the formation of spatial “slugs” consisting of the gas and particles. This process is analyzed within a combined nucleation model including the two-phase Iordansky-Kogarko-van Wijngaarden model and the model of the “frozen” field of mass velocities in the cavitation zone. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 167–177, March–April, 2009.