Solution and hydrate formation behind a shock wave in liquid with nitrogen — carbon dioxide bubbles in a presence of surfactant

The processes of solution and hydrate formation behind a shock wave of moderate amplitude were studied experimentally in water with bubbles of nitrogen — carbon dioxide mixture at different initial static pressures in the medium and surfactant concentrations. It is shown that these bubbles do not affect significantly the processes of solution and hydrate formation behind a shock wave during the considered periods. The hypothesis about partial hydration of nitrogen from the gas mixture at intense formation of carbon dioxide hydrate was suggested for the conditions, when the pressure behind the wave is less than the equilibrium pressure of nitrogen hydrate formation at a given temperature. The work was financially supported by the President of RF (NSh-3417.2008.8) and Russian Foundation for Basic Research (Grant No. 06-08-00657).     

Shock waves and formation of carbon dioxide hydrate at an increased pressure in the gas-liquid medium

The processes of breaking, solution, and formation of hydrates behind a shock wave of moderate amplitude were studied experimentally in water with carbon dioxide bubbles under different initial static pressures. It is shown that an increase in the static pressure in a gas-liquid medium leads to reduction of critical relative amplitude of the shock wave, corresponding to starting development of Kelvin — Helmholtz instability and bubble splitting into small gas inclusions behind the shock wave front. It is shown that the rates of carbon dioxide solution and hydrate formation behind the shock wave front are close by the value; their dependences on medium and wave parameters are determined. Calculations by the model of gas hydration behind the shock wave are presented. The work was financially supported by the Russian Foundation for Basic Research (grants Nos. 06-01-00142 and 06-08-00657).     

A theoretical model of dissolution and hydrate formation processes in shock waves

A theoretical model for the processes of dissolution and hydrate formation behind a shock wave in a gas-liquid medium with allowance for convective and molecular gas diffusion in the liquid and convective and conductive heat transfer caused by heat release at the interphase boundary due to dissolution and hydrate formation is proposed. A comparison of the model calculations with experimental data is made.     

Propagation of compression waves in bubbly liquid with hydrate formation

The dynamics of planar one-dimensional shock waves applied to the available experimental data for the water-Freon system is studied on the basis of the theoretical model of the bubbly liquid refined with regard for a possible hydrate formation. A scheme is proposed for considering the fragmentation of bubbles in the shock wave, which is one of the main factors of the intensification of the hydrate formation process with the growth of the shock wave amplitude.     

Study on shock wave-induced cavitation bubbles dissolution process

This study investigated dissolution processes of cavitation bubbles generated during in vivo shock wave(SW)-induced treatments. Both active cavitation detection(ACD) and the B-mode imaging technique were applied to measure the dissolution procedure of bi Spheres contrast agent bubbles by in vitro experiments. Besides, the simulation of SW-induced cavitation bubbles dissolution behaviors detected by the B-mode imaging system during in vivo SW treatments, including extracorporeal shock wave lithotripsy(ESWL) and extracorporeal shock wave therapy(ESWT), were carried out based on calculating the integrated scattering cross-section of dissolving gas bubbles with employing gas bubble dissolution equations and Gaussian bubble size distribution. The results showed that(i) B-mode imaging technology is an effective tool to monitor the temporal evolution of cavitation bubbles dissolution procedures after the SW pulses ceased, which is important for evaluation and controlling the cavitation activity generated during subsequent SW treatments within a treatment period;(ii) the characteristics of the bubbles, such as the bubble size distribution and gas diffusion, can be estimated by simulating the experimental data properly.     

Calculation of shock wave propagation in water containing reactive gas bubbles

The entry of a shock wave from air into water containing reactive gas (stoichiometric acetylene–oxygen mixture) bubbles uniformly distributed over the volume of the liquid has been numerically investigated using equations describing two-phase compressible viscous reactive flow. It has been demonstrated that a steady-state supersonic self-sustaining reaction front with rapid and complete fuel burnout in the leading shock wave can propagate in this bubbly medium. This reaction front can be treated as a detonation-like front or “bubble detonation.” The calculated and measured velocities of the bubble detonation wave have been compared at initial gas volume fraction of 2 to 6%. The observed and calculated data are in satisfactory qualitative and quantitative agreement. The structure of the bubble detonation wave has been numerically studied. In this wave, the gas volume fraction behind the leading front is approximately 3–4 times higher than in the pressure wave that propagates in water with air bubbles when the other initial conditions are the same. The bubble detonation wave can form after the penetration of the shock wave to a small depth (~300 mm) into the column of the bubbly medium. The model suggested here can be used to find optimum conditions for maximizing the efficiency of momentum transfer from the pressure wave to the bubbly medium in promising hydrojet pulse detonation engines.     

Interrelation of anode and cathode processes in electrochemical carbon oxidation in a fuel cell with molten carbonate electrolyte

The object to be investigated is a fuel cell with a free molten carbonate electrolyte, which ensures direct electrochemical oxidation of solid hydrocarbons. The polarization characteristics of anode and cathode fuel cell assemblies, and also composition and gas release rate of gaseous products of anode reactions are studied. It is shown that the maximum voltages in the open cell circuit are obtained when the oxygen-carbon dioxide ratio in the cathode gas mixture corresponds to stoichiometric reaction coefficients that ensure replenishment of ions in electrolyte. However, the maximum current density values were obtained with a low carbon dioxide content. It is found that at high current values, anode potential fluctuations are observed. It is shown that carbon monoxide is the product of anode processes, along with carbon dioxide. The carbon monoxide content grows with temperature. The carbon dioxide content grows with increasing current in the fuel cell and with growing carbon dioxide content in cathode gases. The release rate of carbon oxidation products nonlinearly depends on the current value in the fuel cell. It is concluded that there is interrelation between the mass-exchange processes in the fuel cell, which is determined by the balance between cathode gas incoming into the reaction zone, the number of molecules generated during fuel oxidation, molecule dissolution and diffusion into the cathode region, and also the amount of gas released in the form of bubbles.     

A mathematical model of carbon dioxide flooding with hydrate formation

The injection of carbon dioxide into a reservoir that contains methane and water in a free state is investigated. A mathematical model of this process is proposed that suggests the formation of the CO₂ hydrate on the surface of the phase transition separating regions of methane and carbon dioxide. The conditions on the interface are derived, and an asymptotic solution of the problem is found. Critical diagrams are obtained that define parameter ranges in which there is full or partial transition of gaseous carbon dioxide to a hydrate state.     

Propagation of pressure waves in a three-phase medium of cluster structure

The propagation of a step-shaped shock wave in a liquid is investigated experimentally. The liquid contains spherical three-phase clusters (liquid, solid balls, gas bubbles). A comparison of the experimental data on the velocity and wave structure with calculations with the use of the Boussinesq equation for a three-phase cluster medium is made. It is shown that the sound speed in a three-phase medium of cluster structure is higher than in a homogeneous three-phase medium.     

Formation of the distribution function of energetic ions by their drift at the front of a near-Earth bow shock wave

The formation of the distribution function of energetic ions by their drift at the front of a near-Earth shock wave is studied. A substantial effect of the shape of the shock front on the ion spectrum has been revealed. A dependence of the amplitude of the spectrum of reflected ions on the level of the magnetic field turbulence behind the shock front has been established.     

Shock-wave studies of anomalous compressibility of glassy carbon

The physico-mechanical properties of amorphous glassy carbon are investigated under shock compression up to 10 GPa. Experiments are carried out on the continuous recording of the mass velocity of compression pulses propagating in glassy carbon samples with initial densities of 1.502(5) g/cm³ and 1.55(2) g/cm³. It is shown that, in both cases, a compression wave in glassy carbon contains a leading precursor with amplitude of 0.135(5) GPa. It is established that, in the range of pressures up to 2 GPa, a shock discontinuity in glassy carbon is transformed into a broadened compression wave, and shock waves are formed in the release wave, which generally means the anomalous compressibility of the material in both the compression and release waves. It is shown that, at pressure higher than 3 GPa, anomalous behavior turns into normal behavior, accompanied by the formation of a shock compression wave. In the investigated area of pressure, possible structural changes in glassy carbon under shock compression have a reversible character. A physico-mechanical model of glassy carbon is proposed that involves the equation of state and a constitutive relation for Poisson’s ratio and allows the numerical simulation of physico-mechanical and thermophysical properties of glassy carbon of different densities in the region of its anomalous compressibility.     

Modelling of decomposition of a single gas hydrate particle in water behind the shock wave front

The mathematical model of decomposition of a spherical gas hydrate particle in water behind a 1D wave of the stepped profile (rarefaction wave) is suggested. Contribution of the outer and inner heat flux in a particle to the process of hydrate decomposition is studied. The effect of the gas hydrate particle size, pressure and temperature jumps in liquid on gas hydrate decomposition is investigated.     

Self-focusing of wave packets and envelope shock formation in nonlinear dispersive media

The self-action of three-dimensional wave packets is analyzed analytically and numerically under the conditions of competing diffraction, cubic nonlinearity, and nonlinear dispersion (dependence of group velocity on wave amplitude). A qualitative analysis of pulse evolution is performed by the moment method to find a sufficient condition for self-focusing. Self-action effects in an electromagnetically induced transparency medium (without cubic nonlinearity) are analyzed numerically. It is shown that the self-focusing of a wave packet is accompanied by self-steepening of the longitudinal profile and envelope shock formation. The possibility of envelope shock formation is also demonstrated for self-focusing wave packets propagating in a normally dispersive medium.     

A suppressor to prevent direct wave-induced cavitation in shock wave therapy devices

Cavitation plays a varied but important role in lithotripsy. Cavitation facilitates stone comminution, but can also form an acoustic barrier that may shield stones from subsequent shock waves. In addition, cavitation damages tissue. Spark-gap lithotripters generate cavitation with both a direct and a focused wave. The direct wave propagates as a spherically diverging wave, arriving at the focus ahead of the focused shock wave. It can be modeled with the same waveform (but lower amplitude) as the focused wave. We show with both simulations and experiments that bubbles are forced to grow in response to the direct wave, and that these bubbles can still be large when the focused shock wave arrives. A baffle or "suppressor" that blocks the propagation of the direct wave is shown to significantly reduce the direct wave pressure amplitude, as well as direct wave-induced bubble growth. These results are applicable to spark-gap lithotripters and extracorporeal shock wave therapy devices, where cavitation from the direct wave may interfere with treatment. A simple direct-wave suppressor might therefore be used to improve the therapeutic efficacy of these devices.     

Statistical characteristics of an intense wave behind a two-dimensional phase screen

An analysis of the parameters of nonlinear waves transmitted through a layer of a randomly inhomogeneous medium is carried out. The layer is modeled by a two-dimensional phase screen. Passing through the screen plane, the wave acquires a random phase shift. The wave front becomes distorted, and randomly located regions of ray convergence and divergence are formed, in which the nonlinear evolution of the wave alters profoundly. The problem is solved in the approximation of geometrical acoustics. The ray pattern of a plane wave transmitted through the regular screen is constructed. The solution that describes the spatial structure of the field and the evolution of an arbitrary temporal wave profile behind the screen is obtained. Statistical characteristics of the discontinuity amplitude are calculated for different distances from the screen. A random modulation is shown to result in a faster (in comparison with the case of a homogeneous medium) nonlinear attenuation of the wave and in the smoothing of the shock profile. The distribution function of the wave field parameters becomes broader because of random focusing effects.     

Cavitation bubble dynamics

The dynamics of cavitation bubbles on water is investigated for bubbles produced optically and acoustically. Single bubble dynamics is studied with laser produced bubbles and high speed photography with framing rates up to 20.8 million frames per second. Examples for jet formation and shock wave emission are given. Acoustic cavitation is produced in water in the interior of piezoelectric cylinders of different sizes (up to 12 cm inner diameter). The filementary structure composed of bubbles is investigated and their light emission (sonoluminescence) studied for various driving strengths.     

Nonlinear acoustic wave generation in a three-phase seabed

Generation of an acoustic wave by two pump sound waves is studied in a three-phase marine sediment, which consists of a solid frame and the pore water with air bubbles in it. To avoid shock-wave formation, the interaction is considered in the frequency range where there is a significant sound velocity dispersion. Nonlinear equations are obtained to describe the interaction of acoustic waves in the presence of air bubbles. An expression for the amplitude of the generated wave is obtained and numerical analysis of its dependence on distance and resonance frequency of bubbles is performed.     

Spherical focusing of acoustic pulses in a liquid

Nonlinear processes accompanying the focusing of a microsecond acoustic pulse produced by an electromagnetic source shaped as a spherical segment are investigated. The processes are considered to be far from the boundaries of a liquid, in the absence of cavitation. Detailed measurements of the pressure field by a fiber-optic sensor and high-speed photography of the shock front are performed. The pressure field is found to be determined by the nonlinear effects that occur in the course of the propagation of the initial converging compression wave and an edge rarefaction wave. The peak pressure amplitudes at the focus are 75 and ?42 MPa for the compression and rarefaction waves, respectively, at the maximum voltage of the pulse generator in use. The measured length of the compression wave front is equal to the response time of the sensor (8 ns). The pressure amplitude is shown to be limited by the irregularity of the propagation of a shock wave in the form of Mach’s disk. At the focus, the pressure gradient across the radiator axis reaches 0.5 atm/μm, while the diameter of the focal spot is 2.5±0.2 mm. The focus of the edge rarefaction wave formed due to diffraction is located closer to the radiator than the focus of the compression wave, which may facilitate the study of the biological effect of cavitation independently of the shear motion of the medium.     

含少量气泡流体饱和孔隙介质中的弹性波

考虑孔隙流体中含有少量气泡,且气泡在声波作用下线性振动,研究声波在这种孔隙介质中的传播特性.本文先由流体质量守恒方程和孔隙度微分与流体压力微分的关系推导出了含有气泡形式的渗流连续性方程;在处理渗流连续性方程中的气体体积分数时间导数时,应用Commander气泡线性振动理论导出气体体积分数时间导数与流体压强时间导数的关系,进而得到了修正的Biot形式的渗流连续性方程;最后结合Biot动力学方程求得了含气泡形式的位移场方程,便可得到两类纵波及一类横波的声学特性.通过对快、慢纵波的频散、衰减及两类波引起的流体位移与固体位移关系的考察,发现少量气泡的存在对快纵波和慢纵波的传播特性影响较大.     

Normal interaction between a supersonic axisymmetric jet and a surface containing a hole coaxial with the jet

The influence of the position of a supersonic jet source relative to a flat plate and of the size of a hole on it on the amplitude and frequency of shock wave oscillations is numerically investigated by integrating 2D Navier-Stokes equations using the predictor-corrector scheme of the second-order accuracy in time and space. Depending on the source-plate distance, an increase in the hole size raises or lowers the oscillation frequency. The oscillation amplitude decreases with increasing hole size.