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

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 k₀ 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 k₀ = 3%. In the compression process, the cavity asymptotically reaches an equilibrium state that does not depend on the value of k₀ 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. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 51–57, May–June, 2007.     

Self-similar solutions of the problem of displacement of one gas by another in an axisymmetric case with a quadratic drag law

A problem of piston-induced displacement of one gas by another in cracks (porous media) in an axisymmetric case with a quadratic drag law is studied. Self-similar solutions for determining the dynamic characteristics (velocity and pressure) of the displacing and displaced gases are constructed in quadratures. The velocity and pressure are studied as functions of a self-similar variable for several initial conditions and parameters. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 87–92, September–October, 2008.     

Two-cell detonation: losses effects on cellular structure and propagation in rich H2–NO2/N2O4–Ar mixtures

Detonation experiments in H₂–NO₂/N₂O₄–Ar mixtures (Equivalence ratio 1.2 and initial pressure lower than 0.1 MPa) confined in a tube of internal diameter 52 mm reveal two propagation regimes depending on initial pressure: (1) a quasi-CJ regime is observed along with a double cellular structure at high pressures; (2) at lower pressures, a low velocity detonation regime is observed with a single structure. Transition between this two regimes happens when the spinning detonation of the larger cell vanishes. Each detonation regime is characterized by velocity and pressure measurements and cellular structure records. Coherence between all experimental data for each experiment leads in assumption that losses are responsible for the transition between one regime to another. In a second part, we study such behaviour for a two-step mixture through numerical simulations using a global two-step chemical kinetics and a simple losses model. Numerical simulations qualitatively agree with experiments. Both detonation regimes with their own cellular structures are reproduced.     

Re-initiation phenomenon of gaseous detonation induced by shock reflection

The two-dimensional, time-dependent, reactive Navier–Stokes equations including the effects of viscosity, thermal conduction and molecular diffusion were solved to reveal the wave evolution and chemical dynamics involved in the re-initiation process. The computation was performed for hydrogen–oxygen–argon mixtures at the low initial pressure (8.00 kPa), using detailed chemical reaction model. The results show that, the decoupled leading shock reflects on the right wall of the vertical branch. High temperature and pressure behind the reflected shock induce the generation of hot spots and local explosion. Therefore, the re-initiation of gaseous detonation occurs. In the re-initiation area, there exist very high OH concentration and no H ₂ concentration. However, in front of reflected shock, there exist relatively high H ₂ concentration and no OH radicals. Additionally, the shock–flame interaction induces RM instability. This results in the fast mixing between hot reacted gas mixture and the relatively cold unreacted gas mixture and accelerates the chemical reactions. However, the shock–flame interaction contributes much less to the re-initiation, in contrast with shock reflection. The transition of leading shock from regular reflection to Mach reflection happens during the re-initiation. The computed evolution of wave structures involved in the re-initiation is qualitatively agreeable with that from the experimental schlieren images.      

Supersonic flow deceleration in plane and axisymmetric channels

Supersonic perfect gas flow in plane and axisymmetric channels with the same duct contour is studied on the basis of a numerical solution of the two-dimensional Navier-Stokes and Euler equations. The calculations were carried out at an inlet Mach number M_∞=4 for various Reynolds numbers and “bell-mouth“ half-angles. The effect of these parameters, as well as that of the flow three-dimensionality, on the flow pattern is demonstrated. In particular, the existence of viscous flow regimes providing the most effective supersonic flow deceleration and a higher degree of total pressure recovery as compared with the inviscid flow is established. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 143–152, March–April, 1998. The study was carried out with the support of the Russian Foundation for Fundamental Research (project No. 95-01-01129a).     

Effect of distributed gas injection on aerodynamic characteristics of a body of revolution in a supersonic flow

Results of experimental and numerical investigations of the effect of gas injection through a permeable porous surface on the drag coefficient of a cone-cylinder body of revolution in a supersonic flow with the Mach number range M _h = 3–6 are presented. It is demonstrated that gas injection through a porous nose cone with gas flow rates being 6–8% of the free-stream flow rate in the mid-section leads to a decrease in the drag coefficient approximately by 5–7%. The contributions of the decrease in the drag force acting on the model forebody and of the increase in the base pressure to the total drag reduction are approximately identical. Gas injection through a porous base surface with the flow rate approximately equal to 1% leads to a threefold increase in the base pressure and to a decrease in the drag coefficient. Gas injection through a porous base surface with the flow rate approximately equal to 5% gives rise to a supersonic flow zone in the base region.     

Behavior of the unsteady jet of a mixture of a pressurized gas and dispersed particles discharged from a circular duct into the atmosphere

The unsteady axisymmetric jet produced by discharge of a mixture of a pressurized gas and dispersed particles from a circular duct into the atmosphere is studied within the framework of two-velocity, two-temperature gas dynamics. An attempt is undertaken to allow for the effective pressure due to random particle motion. The collision mechanism is found to be essential to radial expansion of the flow. Experimental data that support the results obtained are reported. Mozhaiskii Military Spacecraft Engineering Academy, St. Petersburg 197082. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 151–157, January–February, 1999.     

Numerical study of the interaction of a supersonic gaseous jet with a planar target

Various regimes of interaction of an axisymmetric supersonic underexpanded jet of a gas with both a finite and an infinite planar target are studied numcrically. The model of an idcal perfect gas and one variant of Godunov's highly accurate scheme are used. The calculated and experimental frequency spectra of pressure oscillations in the center of the target are compared: their good agreement is obscrved. Institute of Numerical Simulation. Siberian Division, Russian Academy of Sciences. 660036 Krasuoyarsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 106–111, July–August, 2000.     

Numerical solution of the problem of shock tube flow development with transverse diaphragm withdrawal

The time-dependent two-dimensional perfect gas flow which occurs in a channel with a constant cross-section as a result of the transverse withdrawal of a diaphragm to provide an initial pressure difference is studied numerically using a second-order-accurate method. The evolution and interaction of the main wave disturbances is analyzed in detail on the basis of the solutions obtained. Volgograd. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 147–154, March–April, 1994.     

Forced oscillations of a layer of a viscoelastic material under the action of a convective pressure wave

The longitudinal and transverse components of deformation of the surface of a flat layer of a viscoelastic material glued onto a solid base under the action of a traveling pressure wave are determined. The coating compliance is described by two components corresponding to two components of surface displacement. The dimensionless compliance components depend only on the viscoelastic properties of the material, the ratio of the wave length to the layer thickness λ/H, and the ratio of the wave velocity to the velocity of propagation of shear oscillations V/C _t ⁰ . Data on the dynamic compliance are presented for 0.3 < λ/H < 30 and 0.1 < V/C _t ⁰ < 10. The compliance is demonstrated to be determined by its absolute value and by the phase lag of strain from pressure. The effect of viscous losses in the material and compressibility of the latter on the dynamic compliance is analyzed. An anomalous behavior of the compliance with the wave velocity being greater than a certain critical value is explained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 90–97, March–April, 2007.     

Nonlinear gas oscillations in a closed tube driven by the aperiodic motion of a piston

Nonlinear gas oscillations in a closed tube driven by the aperiodic motions of a piston as a result of the action of the external and internal pressure drop are studied. The external pressure takes two values alternating at the moment of change of direction of motion of the piston. Two models of the motion of the gas are considered. Model 1 is formed by a system of equations representing the mass, momentum, and entropy conservation laws. As distinct from model 1, model 2 includes the total energy conservation law in place of the entropy conservation laws. Kazan’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 134–142, March–April, 1998. The work was carried out with partial support from the Russian Foundation for Fundamental Research (project No. 96-01-00484).     

Processes of hydrate formation and dissolution behind a shock wave in a liquid containing gas bubbles (mixture of nitrogen and carbon dioxide)

The processes of dissolution and hydrate formation behind a moderate-amplitude shock wave in water containing gas bubbles (mixture of nitrogen and carbon dioxide) are studied in experiments with different initial static pressures in the medium and concentrations of carbon dioxide in bubbles. An increase in static pressure in the gas-liquid medium is demonstrated to enhance the influence of the non-reacting gas (nitrogen) on the processes of dissolution and hydrate formation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 178–187, March–April, 2009.     

Mechanism of compressive stress formation during weak shock waves impact with granular materials

 Certain aspects of wave propagation and the dynamic reaction of a granular material when subjected to a long-duration impulse load are studied. In the majority of studies published on this subject the unsteady pressure behavior at the end-wall covered by a layer of granular material was observed and documented. However, up to now little attention was given to explaining the physical mechanism of this process. Experimental results, obtained in the course of this study, regarding the pressure fields inside granular layers of different materials, clearly show that the compaction effect strongly depends on the characteristics of the medium. This phenomenon manifests itself by changing the gas-particle interaction in the course of the gas filtration, and by variation in the contribution of the different forces and effective stress, σ, to the energy exchange between the gas, the particles and the shock-tube wall. The material permeability,  f, the relative density, ν, and the particle response time, τ _p , are the most important parameters affecting the stress formation at the end-wall covered by the granular layer. In addition to the effect of the material parameters, the effective stress, σ, was found to strongly depend on the granular layer height, h. Based on detailed pressure measurements a qualitative analysis regarding the role of the particle rearrangement in the formation of the unsteady peak at the end-wall was performed. The phenomenology of the particle–particle interaction includes rotation and consolidation of the granules and movement or sliding of particle planes within the layer over each other. Most of these processes are frictional in their nature. They are related to the energy losses and affect the profile and magnitude of the compressive stress as measured at the shock-tube end-wall covered by the granular layer. Received: 10 June 1996/Accepted: 15 October 1996     

Pressure growth dynamics during freezing of a closed volume of water with dissolved gases

A model for the freezing of a closed volume of water with dissolved gases is proposed and studied numerically. It is shown that gas release during ice formation leads to a considerable time delay in the time of a sudden pressure increase. In the freezing process, the pressure depends not only on the volume of ice formed but also on the freezing rate, which is determined by the cooling rate and the geometry and dimensions of the freezing volume. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 85–92, November–December, 2006.     

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.     

Effect of external flow on the flow rate of a gas discharged through an orifice

The dependence of the flow coefficient of a gas jet ejected from an orifice/nozzle into a subsonic/transonic cross-flow on the flow and the jet Mach numbers, the off-design ratio, the nozzle inclination angle, β, and other determining parameters is considered. The physical nozzle flow pattern is constructed on the basis of experimental data obtained for 0.3< M_∞<1.75 and β=60°, 90°, and 120°. The results of measuring the pressure upstream and downstream of the orifice and on the windward and leeward orifice generators are presented. It is shown that the flow rate coefficient of a jet ejected into a cross-flow may exceed that of a similar jet outflowing into a flooded space. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 65–70, May–June, 1998.     

Visualizing near-surface concentration fluctuations using laser-induced fluorescence

A method for observing near-surface fluctuations in pH caused by a water–air flux of carbon dioxide under conditions of ambient atmospheric carbon dioxide levels is developed and tested. Peaks in fluorescence intensity measured as a function of pH and turbulence are shown to be consistent with predictions from a chemical kinetics model of CO₂ exchange. The square root of the frequency of the pH fluctuations scale linearly with independently measured bulk air–water gas transfer velocities in agreement with surface divergence models for air–water gas transfer. These data indicate that the method proposed here is tracking changes in near-surface CO₂ concentrations. This laser-induced fluorescence method can be used to study the air–water exchange of CO₂ in wind-wave tunnels without the need for elevated CO₂ concentrations in the gas phase.     

On a gas source in a constant force field

The nonbarochronic regular partially invariant submodel of the equations of gas dynamics is studied. The submodel reduces to an implicit ordinary differential equation of the first order for an auxiliary function X = X(x). The physical quantities (velocity, density, and pressure) are expressed in terms of the function X. The properties of the solutions of the equation are investigated and interpreted physically in terms of gas motion. The existence of a shock-wave solution is proved. The properties of the shock adiabat are studied. It is shown that the results obtained are new and differ significantly from the results for the case of no constant force. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 3–16, November–December, 2006.     

Pressure Relaxation in a Hole Surrounded by Porous and Permeable Rock in Hole Pressure Tests with Gas Injection

The pressure testing of a hole in porous and permeable rock by gas injection is considered. An integral equation for the hole pressure relaxation is obtained whose numerical and analytical solutions describe the dependence of the relaxation time of hole pressure on the reservoir properties of the surrounding porous rock as well as on the initial gas content and the initial pressure gradient in the hole. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 109–118, January–February, 2006.     

Linearized Burnett Equation for the Dynamic Pressure of a Relativistic Gas

The linearized Burnett equation for the dynamic pressure of a relativistic gas of hadrons is calculated from a relativistic kinetic theory. It is shown, as in a previous paper [1], that the coefficient of the term with a non-homogeneous temperature field, – the heating term – is bigger than the one with the divergence of the four-velocity, – the bulk viscosity term.