Dynamics of a “collective” bubble in a magma melt flow behind the decompression wave front

Specific features of the dynamics of the wave field structure and growth of a “collective” bubble behind the decompression wave front in the “Lagrangian” section of the formed cavitation zone are numerically analyzed. Two cases are considered: with no diffusion of the dissolved gas from the melt to cavitation nuclei and with the diffusion flux providing an increase in the gas mass in the bubbles. In the first case, it is shown that an almost smooth decompression wave front approximately 100 m wide is formed, with minor perturbations that appear when the front of saturation of the cavitation zone with nuclei is passed. In the case of the diffusion process, the melt state behind the saturation front is principally different: jumps in mass velocity and viscosity are observed in the vicinity of the free surface, and the pressure in the “collective” cavitation bubble remains unchanged for a sufficiently long time interval, despite the bubble growth and intense diffusion of the gas from the melt. It is assumed that the diffusion process (and, therefore, viscosity) actually become factors determining the dynamics of growth of cavitation bubbles beginning from this time interval. A pressure jump is demonstrated to form near the free surface.     

On the application of LDA to bubbly flow in the wobbling regime

 Considerations for applying LDA to bubbly flows with bubbles about 3 to 4 mm in diameter were investigated by means of detailed experiments in the model geometry of a train of bubbles. Both forward scatter and backscatter LDA were studied. The validity of phase discrimination via burst amplitude was tested and special attention was paid to the impact of bubble interface response to the laser beams. Forward and backscatter measurements can be compared well. In both configurations, predominantly the liquid phase is “seen” by LDA. A bubble itself only leads to a velocity realization in special conditions. In those cases the Doppler shift is determined by the motion of the bubble interface which consists of the motion of the center of gravity of the bubble as well as shape oscillations. In backscatter bubbles only give velocity realizations when their “cheeks” pass through the measuring volume virtually perpendicularly. It is shown that the bubble-caused velocity realization frequency is very low for bubbles of the size used. Phase discrimination on burst amplitude does not hold. In ambient cases such as bubble columns one can assume that only the liquid phase is being studied. Received: 4 May 1998/Accepted: 30 September 1998     

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.     

Criterion of formation of a shock wave reflected from a cloud of particles

The problem of the formation of a “collective” shock wave reflected from a cloud of particles, which was previously observed in experiment, is considered. A criterion of formation of a reflected shock wave is obtained based on the numerical and analytical solutions of the problem. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 44–51, May–June, 1998.     

Specific rheology – morphology relationships for some blends containing LCPs

For the blend melts of isotropic polysulfone (PSF) and LC polyester (PES), differing in viscosity more than 10 times, the flow curves with maxima were observed in cone and plate geometry. The low shear rate branch is located near the PSF flow curve, and the high shear rate branch is close to the PES flow curve. At high strains, the formation of the ring-like morphology of the blend sample, accompanied by appearance of maximum on flow curve, was registered. The scaling analysis of the reasons for the ring morphology formation was based on stretching of the large, low-viscous LC droplet, embedded to the high-viscous polymer matrix, in a homogeneous shear field. It was shown that, if the critical Taylor radius is not exceeded, the droplet may form the closed torus. Under strong flows, the PSF melt manifests the “spurt effect”, consisting of a drastic increase of the shear rate when the critical value of the shear stress is reached. The pattern of the blend flow curves with maxima may be explained by a vanishing PSF input to the total shear stress, inherent for blends, while the PES melt continues to be in a liquid state and, consequently, is responsible for the blend viscosity at the high shear rates. The presence of regular heterogeneities in the blend in the form of LC rings may initiate the rupture of the entanglements network of the matrix PSF (close to LC rings) under strong shear flows. The appearance of the low-viscous “cracks” at the critical shear stress will diminish the contribution of the PSF to the blends rheological response. Received: 20 April 1999 Accepted: 28 January 2000     

Mass transfer behavior at bubble surface during nucleate boiling

 Interfacial mass transfer mechanisms played an essential role to the high heat transfer efficiency noted for nucleate boiling. There existed a zone around the bubble surface that exhibited zero net mass flux, termed herein as the “zero-flux zone”. This work investigated analytically the interfacial vaporization and condensation processes around a boiling bubble, based on which the positional dependence of zero-flux zone was derived. For a stationary bubble the zero-flux zone shifted to the upper hemisphere with decreasing wall superheat and/or with increasing contact angle. Moreover, the bubble growth (shrinkage) largely enhanced (retarded) such a trend. At the extreme condition where the bubble grew at a very fast speed the entire bubble surface would be subject to liquid evaporation only. Experiments observed a “thermal jet” emerging from the bubble cap, which was attributed to the interfacial vapor condensation flux at the bubble cap. Received on 11 December 2000 / Published online: 29 November 2001     

Level set method for numerical simulation of a cavitation bubble,its growth,collapse and rebound near a rigid wall

A level set method of non-uniform grids is used to simulate the whole evolution of a cavitation bubble, including its growth, collapse and rebound near a rigid wall. Single-phase Navier–Stokes equation in the liquid region is solved by MAC projection algorithm combined with second-order ENO scheme for the advection terms. The moving interface is captured by the level set function, and the interface velocity is resolved by “one-side” velocity extension from the liquid region to the bubble region, complementing the second-order weighted least squares method across the interface and projection inside bubble. The use of non-uniform grid overcomes the difficulty caused by the large computational domain and very small bubble size. The computation is very stable without suffering from large flow-field gradients, and the results are in good agreements with other studies. The bubble interface kinematics, dynamics and its effect on the wall are highlighted, which shows that the code can effectively capture the “shock wave”-like pressure and velocity at jet impact, toroidal bubble, and complicated pressure structure with peak, plateau and valley in the later stage of bubble oscillating. The project supported by the National Natural Science Foundation of China (10272032 and 10672043). The English text was polished by Keren Wang.     

Influence of wall proximity on the equilibrium temperature of curved interfaces

Equilibrium conditions of a single-component two-phase-system having a plane or a concave interface interacting with a solid wall are the major focus of the paper. The concave interface is termed “closed”, if it forms a vapour bubble, and “opened”, in the case of a common liquid meniscus. The equations derived describe the equilibrium temperature in dependence of the wall distance and the interfacial curvature. They show that an attraction between the vapour-liquid interface and the wall rises the equilibrium temperature. At comparable conditions, the equilibrium temperature is higher for the closed than for the opened interface. Received on 18 December 1997     

Numerical simulation of gas dynamics in a bubble during its collapse with the formation of shock waves

The specific features of calculation of a gas in a spherical bubble located in the center of a spherical volume of weakly compressible fluid are considered. The problems of motion of a cold gas to a point and a spherical piston converging to a point are used to evaluate the algorithm. It is shown that significant errors can arise in calculation of spherical waves in the vicinity of the pole. These errors can be substantially reduced by means of artificial viscosity in the Riemann problem. Institute of Mechanics and Machine Building, Kazan’ Scientific Center, Russian Academy of Sciences, Kazan’ 420111. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 101–110, March–April, 1999.     

On Rectified Diffusion and Sonoluminescence

If acoustically driven, a gas-filled bubble may exist indefinitely even in an unsaturated liquid through a process known as “rectified diffusion.” When the oscillation period is small compared with the gaseous diffusion time, the radius of the steadily oscillating bubble can be determined by asymptotic methods, in the way pioneered by Eller and Flynn (1965). The next term in their expansion is evaluated here and is shown to be significant if the radius of the bubble is small or if the amplitude of its oscillations is large. For the identical level of saturation and the same conditions of excitation, multiple solutions are possible. As a result of resonance between overtones of the frequency of free bubble oscillation with the frequency of the acoustic drive, there generally exist, in addition to a stable large-radius, stable small-radius states. The relevance of the present results to sonoluminescence is briefly discussed. Received 3 January 1997 and accepted 14 April 1997     

Investigation of high-speed combustible gas ignited by a hot gas jetproduced in the shock tube

The high-speed combustible gas ignited by a hot gas jet, which is induced by shock focusing, was experimentally investigated. By use of the separation mode of shock tube, the test section of a single shock tube is split into two parts, which provide the high-speed flow of combustible gas and pilot flame of hot gas jet, respectively. In the interface of two parts of test sections the flame of jet was formed and spread to the high-speed combustible gas. Two kinds of the ignitions, 3-D “line-flame ignition” and 2-D “plane-flame ignition”, were investigated. In the condition of 3-D “line-flame ignition” of combustion, thicker hot gas jet than pure air jet, was observed in schlieren photos. In the condition of 2-D “plane-flame ignition” of combustion, the delay time of ignition and the angle of flame front in schlieren photos were measured, from which the velocity of flame propagation in the high-speed combustible gas is estimated in the range of 30–90m/s and the delay time of ignition is estimated in the range of 0.12–0.29ms. PACS 47.40.Nm; 82.40.FpPart of this paper was presented at the 5th International Workshop on Shock/Vortex Interaction, Kaohsiung, October 27–31, 2003.     

Optimal Control of Nonmodal Disturbances in Boundary Layers

The optimal control of infinitesimal flow disturbances experiencing the largest transient gain over a fixed time span, commonly termed “optimal perturbations,” is undertaken using a variational technique in two- and three-dimensional boundary layer flows. The cost function employed includes various energy metrics which can be weighted according to their perceived importance, simplifying the task of determining which terms are essential for a “good” control scheme. In the accelerated boundary layers investigated, disturbance kinetic energy can be typically reduced by about one order of magnitude. However, it seems impossible to suppress completely over the entire control interval; “good” control strategies still permit approximately an order magnitude growth over the initial energy at some point in the interval. It is shown that the control effort efficiently targets the physical mechanisms behind transient growth. Received 5 February 2001 and accepted 15 June 2001     

Formation Mechanism of Cracks in Saturated Sand

The formation mechanism of “water film” (or crack) in saturated sand is analyzed theoretically and numerically. The theoretical analysis shows that there will be no stable “water film” in the saturated sand if the strength of the skeleton is zero and no positions are choked. It is shown by numerical simulation that stable water films initiate and grow if the choking state keeps unchanged once the fluid velocities decrease to zero in the liquefied sand column. The developments of “water film” based on the model presented in this paper are compared with experimental results.The project supported by the National Natural Science Foundation of China (40025103 and 10202024) and Key Laboratory of Mountain Hazards and Surface Process, Chinese Academy of Sciences. The English text was polished by Keren Wang.     

Three-dimensional CFD simulation of bubble–melt two-phase flow with air injecting and melt stirring

This paper reports on progress in developing CFD simulations of gas bubble–metallic melt turbulent flows induced by a pitched-blade impeller with an inclined shaft. Foaming process of aluminum foams, in which air is injected into molten aluminum composites and the melt is mechanical stirred by the impeller, has been investigated. A two-fluid model, incorporated with the Multiple Reference Frames (MRF) method is used to predict the three-dimensional gas–liquid flow in the foaming tank, in which a stirring shaft is positioned inclined into the melt. Locally average bubble size is also predicted by additively solving a transport equation for the bubble number density function, which accounts for effects of bubble breakup and coalescence phenomena. The computed bubble sizes are compared with experimental data from our water model measurement and reasonable agreements are obtained. Further, simulated results show that the volume averaged total and local gas fractions are generally increased with rising impeller speed and gas flow rate. The local averaged bubble size increases with increasing gas flow rate and orifice diameter and decreasing liquid viscosity, and decreases also with rising rotation speed of the impeller.     

Analysis of the thrust characteristics of jet nozzles designed by various methods

A comparative numerical analysis of the thrust characteristics of axisymmetric jet nozzles designed by various methods is carried out. “Extremal“ nozzles designed by variational methods in the absence/presence of internal shocks (I), so-called “truncated“ nozzles with a uniform characteristic (II), and nozzles designed by the method of conjugate circular arcs (III) are considered. A comparison is carried out for both perfect and real gases (in the latter case the boundary layer gas viscosity is taken into account). It is shown that extremal nozzles are the most efficient, while truncated nozzles are somewhat less so. The thrust characteristics of nozzles designed by the method of conjugate circular arcs for both inviscid and viscous flow are inferior to those of extremal nozzles by 0.7–1%. Moscow, Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 152–162, January–February, 2000. The research was carried out with financial support from the Russian Foundation for Basic Research (project No. 99-01-00891).     

Void growth and cavitation in nonlinear viscoelastic solids

This paper discusses the growth of a pre-existing void in a nonlinear viscoelastic material subjected to remote hydrostatic tensions with different loading rates. The constitutive relation of this viscoelastic material is the one recently proposed by the present authors, which may be considered as a generalization of the non-Gaussian statistical theory in rubber elasticity. As the first order approx-imation, the above constitutive relation can be reduced to the “neo-Hookean” type viscoelastic one.Investigations of the influences of the material viscosity and the loading rate on the void growth, or on the cavitation are carried out. It is found that: (1) for generalized “inverse Langevin approximation” nonlinear viscoelastic materials, the cavitation limit does not exist, but there is a certain (remote) stress level at which the void will grow rapidly; (2) for generalized “Gaussian statistics” (neo-Hookean type) viscoelastic materials, the cavitation limit exists, and is an increasing function of the loading rate.The present discussions may be of importance in understanding the material failure process under high triaxial stress.     

Amorphous and crystalline states of ultrasoft colloids: a molecular dynamics study

In this work, we study the temperature-induced development of “dynamically arrested” states in dense suspensions of “soft colloids” (multi-arm star polymers and/or block-copolymers micelles) by means of molecular dynamics (MD) simulations. Temperature increase in marginal solvents results in “soft sphere” swelling, dynamical arrest, and eventually crystallization. However, two distinct “dynamically arrested” states were found, one almost amorphous (“glassy”) and one with a considerable degree of crystallinity, yet lower than that of the fully equilibrated crystal. It is remarkable that even that latter state permitted self-diffusion in the timescale of the simulations, an effect that underlies the importance of the “ultra-soft” nature of inter-particle potential. The “number of connections” criterion for crystallinity proved to be very successful in identifying the ultimate thermodynamic trend from the very early stages of the α-relaxation. This paper was presented at the Third Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece.     

Single bubble deformation and breakup in simple shear flow

Experiments in a parallel band apparatus and a transparent concentric cylinder device allow the observation of bubble deformation (shape and orientation) and breakup as a function of the viscosity ratio λ and the Capillary number Ca. For viscosity ratios between 3.1 × 10⁻⁷ and 6.7 × 10⁻⁸, critical Capillary numbers Ca _c for bubble breakup between 29 and 45 are found. It is furthermore shown that in the given parameter space no clear distinction between tip breakup and fracture can be made for bubbles. An erratum to this article can be found at     

“Non-free” interaction of plane shock waves and the boundary layer in the neighborhood of the leading edge of a plate with slip

The interaction between a normally impinging shock wave and the boundary layer on a plate with slip is studied in the neighborhood of the leading edge using various experimental methods, including special laser technology, to visualize the supersonic conical gas flows. It is found that in the “non-free” interaction, when the leading edge impedes the propagation of the boundary layer separation line upstream, the structure of the disturbed flow is largely identical to that in the developed “free” interaction, but with higher parameter values and gradients in the leading part of the separation zone. The fundamental property of developed separation flows, namely, coincidence of the values of the pressure “plateau” in the separation zone and the pressure behind the oblique shock above the separation zone of the turbulent boundary layer, is conserved. Moscow. e-mail: ostap@inmech.msu.su. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 57–69, May–June, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 97-01-00099).     

Laminar–turbulent transition in oscillating boundary layer: experimental and numerical analysis using continuous wavelet transform

The laminar–turbulent transition of a forced oscillating boundary layer with a varying pressure gradient is experimentally and numerically investigated for two Strouhal numbers. Time-dependent characterization of the natural instability modes is carried out using continuous wavelet analysis of velocity signals. The periodic evolution of the total growth rates of the most unstable disturbances are measured and compared to the results of the linear stability theory. The “Tollmien–Schlichting” (TS) and “convective” transition modes are identified. It is shown that they correspond to the extrema of opposite signs of the skewness factor of unstable wavelet transform of the most unstable frequencies.