R. I. Nigmatulin
Russian Academy of Sciences
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Physics of Fluids | 2005
R. I. Nigmatulin; Iskander S. Akhatov; Andrey S. Topolnikov; Raisa Kh. Bolotnova; N. K. Vakhitova; Richard T. Lahey; Rusi P. Taleyarkhan
HYDRO code model of the spherically symmetric motion for a vapor bubble in an acoustically forced liquid is presented. This model describes cavitation bubble cluster growth during the expansion period, followed by a violent implosion during the compression period of the acoustic cycle. There are two stages of the bubble dynamics process. The first, low Mach number stage, comprises almost all the time of the acoustic cycle. During this stage, the radial velocities are much less than the sound speeds in the vapor and liquid, the vapor pressure is very close to uniform, and the liquid is practically incompressible. This process is characterized by the inertia of the liquid, heat conduction, and the evaporation or condensation of the vapor. The second, very short, high Mach number stage is when the radial velocities are the same order, or higher, than the sound speeds in the vapor and liquid. In this stage high temperatures, pressures, and densities of the vapor and liquid take place. The model presented herein has realistic equations of state for the compressible liquid and vapor phases, and accounts for nonequilibrium evaporation/condensation kinetics at the liquid/ vapor interface. There are interacting shock waves in both phases, which converge toward and reflect from the center of the bubble, causing dissociation, ionization, and other related plasma physics phenomena during the final stage of bubble collapse. For a vapor bubble in a deuterated organic liquid e.g., acetone, during the final stage of collapse there is a nanoscale region diameter 100 nm near the center of the bubble in which, for a fraction of a picosecond, the temperatures and densities are extremely high 10 8 K and 10 g/cm 3 , respectively such that thermonuclear fusion may take place. To quantify this, the kinetics of the local deuterium/deuterium D/D nuclear fusion reactions was used in the HYDRO code to determine the intensity of the fusion reactions. Numerical HYDRO code simulations of the bubble implosion process have been carried out for the experimental conditions used by Taleyarkhan et al. Science 295, 1868 2002; Phys. Rev. E 69, 036109 2004 at Oak Ridge National Laboratory. The results show good agreement with the experimental data on bubble fusion that was measured in chilled deuterated acetone.
Journal of Fluid Mechanics | 2000
R. I. Nigmatulin; I. Sh. Akhatov; N. K. Vakhitova; R.T. Lahey
A spherically-symmetric problem is considered in which a small gas bubble at the centre of a spherical flask filled with a compressible liquid is excited by small radial displacements of the flask wall. The bubble may be compressed, expanded and made to undergo periodic radial oscillations. Two asymptotic solutions have been found for the low-Mach-number stage. The first one is an asymptotic solution for the field far from the bubble, and it corresponds to the linear wave equation. The second one is an asymptotic solution for the field near the bubble, which corresponds to the Rayleigh-Plesset equation for an incompressible fluid. For the analytical solution of the low-Mach-number regime, matching of these asymptotic solutions is done, yielding a generalization of the Rayleigh-Plesset equation. This generalization takes into account liquid compressibility and includes ordinary differential equations (one of which is similar to the well-known Herring equation) and a difference equation with both lagging and leading time. These asymptotic solutions are used as boundary conditions for bubble implosion using numerical codes which are based on partial differential conservation equations. Both inverse and direct problems are considered
Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy | 2004
R. I. Nigmatulin; Rusi P. Taleyarkhan; R.T. Lahey
Abstract This paper extends the experimental and numerical results presented previously and addresses the major criticisms raised. In addition, the most recent results are discussed. In acoustic cavitation experiments with chilled (ɛ0 °C) deuterated acetone (C3D6O), the production of tritium and 2.45 MeV neutrons [which are characteristic of deuterium-deuterium (D-D) fusion] was observed during vapour bubble implosions in an acoustic pressure field. Similar experiments with deuterated acetone at room temperature (ɛ20 °C) and control experiments with normal acetone (C3H6O), at both 0 and 20 °C, showed no statistically significant increases in either tritium level or neutron emissions. Numerical simulations of the processes that account for the shock waves generated in the liquid and within the collapsing bubbles supported these experimental observations and showed that high densities and temperatures (° 108 K) may be achieved during bubble cloud implosions, yielding the conditions required for D-D nuclear fusion reactions. The present paper treats the bubble fusion experiments and theoretical results in greater detail than was possible in the previous publications, contains some refinements, addresses some important questions raised by reviewers and critics and discusses possible applications of this interesting phenomenon.
Fluid Dynamics | 1976
R. I. Nigmatulin; V. Sh. Shagapov
The structure of a stationary shock wave in a liquid containing gas bubbles is investigated theoretically. For the description of such a two-phase mixture the two-velocity two-temperature model with two pressures is used [1], taking into consideration the small-scale frictions, the noncoincidence of the velocities, temperatures, and pressures of the phases, and the oscillations of the bubbles. The existence of shock waves having a discontinuity surface in front as well as of shock waves with continuous structure is shown. It is shown that unlike the two-phase mixtures of gas with drops or particles where the structure of the wave depends mainly on the interphase friction, in two-phase mixtures of a liquid with bubbles the behavior of the wave and its structure depends essentially on the interphase heat transfer. Wave characteristics, such as the wavelength of the pulsations, their damping decrement, do not have a monotonic dependence on the parameters governing the intensity of heat transfer and do not lie between the corresponding values for isothermic and adiabatic regimes of behavior of the bubbles. Shock waves in liquids with gas bubbles were investigated theoretically and experimentally in [3–7]. A detailed review of the work up to 1971 is given in [8].
Fluid Dynamics | 1977
R. I. Nigmatulin; N. S. Khabeev
The nonlinear problem of thermal, mass, and dynamic interaction between a vapor-gas bubble and a liquid is considered. The results of numerical solution of the problem of radial motion of the bubble caused by a sudden pressure change in the liquid, illustrating the behavior of vapor-gas bubbles in compression and rarefaction waves, are presented. The corresponding problem for single-component gas and vapor bubbles was considered in [1, 2].
Advances in heat transfer | 2006
R.T. Lahey; Rusi P. Taleyarkhan; R. I. Nigmatulin; Iskander S. Akhatov
Publisher Summary This chapter presents a discussion on sonoluminescence (SL) and the search for sonofusion. The field of multiphase flow and heat transfer has many important practical applications. An interesting and important subset of this field has to do with the bubble dynamics associated with sonofusion and/or SL phenomena. The chapter discusses the phenomena of multibubble sonoluminescence (MBSL) in which multiple bubbles formed by cavitation grow and collapse in the induced pressure field, giving off light pulses during bubble implosions. Some interesting hypotheses and models concerning the origin of these light pulses have included mechanisms associated with (1) triboluminescence, (2) electrical microdischarge, (3) mechanochemical models, (4) chemiluminescence model, and (5) Hot Spot model. While research continues to improve our understanding of the interesting phenomena associated with SL, most researchers believe the validity of the extended Hot Spot model. The chapter illustrates through diagrams a typical setup for a double detector technique, bubble radius and photon detection systems, and a laser beam polarized parallel to the paper illuminating a spherical bubble. The chapter concludes with a discussion on neutron-induced bubble nucleation.
Journal of Applied Mechanics and Technical Physics | 1998
R. I. Nigmatulin; V. Sh. Shagapov; V. R. Syrtlanov
We consider the specifics of decomposition of gas hydrates under thermal and depressive action on a porous medium completely filled with a solid hydrate in the initial condition. The existence of volumetric-expansion zones, in which the hydrate coexists in equilibrium with water and gas, is shown to be possible in high-permeable porous media. The self-similar problems of hydrate decomposition upon depression and heating are studied. Ii is shown that there are solutions according to which hydrate decomposition can occur both on the surface of phase transitions and in the volumetric region. We note that, in the first case, decomposition is possible without heat supply to a medium and even with heat removal.
Journal of Applied Mathematics and Mechanics | 1997
I. Sh. Akhatov; N. K. Vakhitova; G.Ya. Galeyeva; R. I. Nigmatulin; Damir B. Khismatullin
Abstract The following spherically symmetric problem is considered: a single gas bubble at the centre of a spherical flask filled with a compressible liquid is oscillating in response to forced radial excitation of the flask walls. In the long-wave approximation at low Mach numbers, one obtains a system of differential-difference equations generalizing the Rayleigh-Lamb-Plesseth equation. This system takes into account the compressibility of the liquid and is suitable for describing both free and forced oscillations of the bubble. It includes an ordinary differential equation analogous to the Herring-Flinn-Gilmore equation describing the evolution of the bubble radius, and a delay equation relating the pressure at the flask walls to the variation of the bubble radius. The solutions of this system of differential-difference equations are analysed in the linear approximation and numerical analysis is used to study various modes of weak but non-linear oscillations of the bubble, for different laws governing the variation of the pressure or velocity of the liquid at the flask wall. These solutions are compared with numerical solutions of the complete system of partial differential equations for the radial motion of the compressible liquid around the bubble.
Nuclear Engineering and Design | 1994
R. I. Nigmatulin; K.I. Soplenkov
Abstract The outflow of high pressure liquid (in particular, water) to the atmosphere from a closed tube (of length a few metres and diameter more than a few centimetres) because of sudden destruction of one bottom is theoretically investigated. Evaporation takes places on the nucleus bubbles. The number of nuclei depends on the quality of the liquid or its purification. The process involves flashing evaporation of the liquid. There are two rarefaction waves at the initial stage. The velocity of the first wave (elastic forerunner) is sound speed in the one phase liquid and equals about 1000 m s−1. After the elastic forerunner the liquid becomes superheated because the pressure drops and evaporation begins. The velocity of the second rarefaction wave is about 1–10 ms s−1. There is intensive bubbly evaporation on and after the second wave. Intensity of the outflow is determined by the intensity of evaporation on the interface of the bubbles and by intensity of fragmentation of the bubbles because of their relative slip velocity in the liquid (0.1–1 m s−1). The fragmentation of the bubbles significantly intensifies the evaporation because of augmentation of the bubbly interface. The degree of non-equilibrium or superheating behind the forerunner in water grows with the increasing initial temperature T0. For T0 After forerunner reflection from the closed bottom, intense evaporation is initiated near the bottom. Then the equalization of the pressure along the tube occurs (quasi-static homobaric stage). There is good correlation with experimental data.
NONLINEAR ACOUSTICS AT THE TURN OF THE MILLENNIUM: ISNA 15, 15th International Symposium | 2001
R. I. Nigmatulin; I. Sh. Akhatov; N. K. Vakhitova; E. Sh. Nasibullayeva
A mathematical model which describes the behavior of a gas bubble cluster in an external acoustic field is presented. According to this model the bubbles of different ambient radii are assumed to be submerged into a spherical liquid volume. The boundary of this volume is considered as a cluster’s boundary. This model includes a set of coupled Rayleigh-type equations for bubble radii and cluster radius. The dynamics of a single bubble cluster excited by external periodic pressure is considered. The problem has been solved numerically under the assumption of spherically-symmetric oscillations of bubbles and the cluster’s boundary. A synchronization phenomenon has been found; namely, the numerical results have shown that bubbles of different initial radii in a cluster collapse in phase. Moreover, it has been noted that at some parameter values such a synchronization may lead to the intensification of bubble collapse.