Simulation of impact of a hollow droplet on a flat surface

Despite many theoretical and experimental works dealing with the impact of dense continuous liquid droplets on a flat surface, the dynamics of the impact of hollow liquid droplets is not well addressed. In an effort to understand dynamics of the hollow droplet impingement, a numerical study for the impact of a hollow droplet on a flat surface is presented. The impingement model considers the transient flow dynamics during impact and spreading of the droplet using the volume of fluid surface tracking method (VOF) coupled with the momentum transport model within a one-domain continuum formulation. The model is used to simulate the hydrodynamic behaviour of the impact of glycerin hollow droplet. It is found that the impact and spreading of the hollow droplet on a flat surface is distinctly different from the conventional dense droplet and has some new hydrodynamic features. A phenomenon of formation of a central counter jet of the liquid is predicted. With the help of simulations the cause of this phenomenon is discussed. Comparison of the predicted length of the central counter jet and the velocity of the counter jet front shows good agreements with the experimental data. The influence of the droplet initial impact velocity and the hollow droplet shell thickness on the impact behaviour is highlighted.     

Characteristic regimes of premixed gas combustion in high-porosity micro-fibrous porous media

Dynamical behaviour of the premixed flame propagating in the inert high-porosity micro-fibrous porous media has been studied numerically. Effects of mixture filtration velocity, equivalence ratio and burner transverse size on the flame structure have been investigated and the regions of existence of different combustion regimes have been determined. It was found that the influence of the hydrodynamic instability on the flame dynamics is significant in the case of the moderate and high filtration velocities and this effect is negligible at the low velocities. At the moderate filtration velocities the effect of hydrodynamic instability manifests in the flame front deformation and in particular in the flame inclination. It was found that the flame can be stabilized within the whole interval of the filtration gas velocity, whereas in the ordinary porous media the standing wave is settled only at fixed value of gas filtration velocity. This finding is in line with recent experimental results on combustion in micro-fibrous porous media (Yang et al., Combust. Sci. Tech. 181 (2009), 1–16). Possible physical interpretation of the flame anchoring effect may be given on the base of present numerical analysis. At the high filtration velocities the hydrodynamic instability manifests itself in periodical appearance of the moving wrinkles on the flame front surface which forms non stationary high temperature trailing spots behind the leading part of the flame front. Such dynamics may be associated with splitting wave structures which were revealed in previous experiments (Yang et al., Combust. Sci. Tech. 181 (2009), 1–16).     

Pulsed laser evaporation: equation-of-state effects

Theoretical study of laser ablation is usually based on the assumption that the vapor is an ideal gas. Its flow is described by gas dynamics equations [1, 2]. The boundary conditions at vaporization front are derived from the solution of the Boltzmann equation that describes the vapor flow in the immediate vicinity of the vaporizing surface (so-called Knudsen layer) [1]. This model is applicable within the range of temperatures much lower than the critical temperature of target material. In the present work, a general case is considered when the temperature of the condensed phase is comparable to or higher than the critical temperature. The dynamics of both condensed and gaseous phases can be described in this case by the equations of hydrodynamics. The dynamics of vaporization of a metal heated by an ultrashort laser pulse is studied both analytically and numerically. The analysis reveals that the flow consists of two domains: thin liquid shell moving with constant velocity, and thick low-density layer of material in two-phase state. Received: 2 March 1999 / Accepted: 28 May 1999 / Published online: 21 October 1999     

Optimization of an off-axis nozzle for assist gas injection in laser fusion cutting

The aerodynamic features of the gas flow during laser fusion cutting are an essential factor influencing the cut performance. For this reason it has been a subject of some studies to explain the interactions of the gas jet with the workpiece and to design different gas injection systems with the aim of preventing the drawbacks of the conventional cutting heads.An off-axis cutting head with a de Laval nozzle to inject a supersonic gas jet has been previously demonstrated to be an effective design to achieve a complete removal of the molten material from the cutting front and to avoid the formation of the recast layer. In the present work, the fundamentals and procedures to adjust the main factors determining the efficiency of this gas injection system are described. Specifically, the gas flow inside the cut kerf is analysed by means of flow visualization using the Schlieren technique.     

Hydrodynamic instability of premixed flame propagating in narrow planar channel in the presence of gas flow

The paper analyses the hydrodynamic instability of a flame propagating in the space between two parallel plates in the presence of gas flow. The linear analysis was performed in the framework of a two-dimensional model that describes the averaged gas flow in the space between the plates and the perturbations development of two-dimensional combustion wave. The model includes the parametric dependences of the flame front propagation velocity on its local curvature and on the combustible gas velocity averaged along the height of the channel. It is assumed that the viscous gas flow changes the surface area of the flame front and thereby affects the propagation velocity of the two-dimensional combustion wave. In the absence of the influence of the channel walls on the gas flow, the model transforms into the Darrieus–Landau model of flame hydrodynamic instability. The dependences of the instability growth rate on the wave vector of disturbances, the velocity of the unperturbed gas flow, the viscous friction coefficients and other parameters of the problem are obtained. It is shown that the viscous gas flow in the channel can lead, in some cases, to a significant increase in instability compared with a flame propagating in free space. In particular, the instability increment depends on the direction of the gas flow with respect direction of the flame propagation. In the case when the gas flow moves in the opposite direction to the direction of the flame propagation, the pulsating instability can appear.     

Rayleigh instability in liquid-crystal jets

Capillary instability of isothermal incompressible liquid-crystal (LC) jets is considered within the linear hydrodynamics of uniaxial nematic LCs. Free boundary conditions with strong tangential anchoring of director n at the surface are formulated in terms of the mean surface curvature ? and the Gaussian surface curvature G. The static version of the capillary instability is shown to depend on the elasticity modulus Κ, the surface tension σ₀, and the radius r₀ of the LC jet, expressed in terms of the characteristic parameter κ = Κ/σ₀r₀. The problem of the capillary instability in LC jets is solved exactly, and a dispersion relation that reflects the effect of elasticity is derived. It is shown that increase in the elasticity modulus results in decrease in both the cut-off wavenumber k and the disturbance growth rate s. This implies an enhanced stability of LC jets in comparison to ordinary liquids. In the specific case where the hydrodynamic and orientational LC modes can be decoupled, the dispersion equation is given in a closed form.     

Simulation of front motion in a reacting condensed two phase mixture

The computational technique is developed in order to provide the scale capturing for numerical simulation of the thermal processes. The thermal front motion and gas flow dynamics as well as the rate of particle growth during the Carbon Combustion Synthesis of Oxides (CCSO) were predicted using the numerical simulation. In CCSO the exothermic oxidation of carbon nanoparticles generates a self-sustained thermal reaction front that propagates through the solid reactant mixture converting it to the desired complex oxides. The combusted carbon is emitted from the sample as carbon dioxide and its high rate of release increases the product porosity and friability. It was shown that the complicated finger front instability can be developed during the carbon combustion synthesis. This phenomenon results from a vortex gas flow in the reaction zone fed by the carbon dioxide co-flow and oxygen counter-flow filtration.     

Three-dimensional consideration of jet impingement onto the kerf in relation to laser cutting process: Effect of jet velocity on heat transfer rates

In laser cutting process, an assisting gas is used to improve the mass removal rate from the cutting kerf and protect the kerf surfaces from the high temperature exothermic reactions, such as oxidation reactions, during the cutting process. Therefore, heat transfer rates from the kerf wall and the skin friction along the kerf surface are important for quality cutting. In the present study, jet emerging from a conical convergent nozzle and impinging onto the kerf surface is investigated in relation to the laser cutting process. The flow field in the kerf, the heat transfer rates from the kerf wall, and the skin friction along the kerf surface are computed for four average jet velocities at the nozzle exit and two kerf wall wedge angles. The ratio of the stand-off-distance (distance between the nozzle exit and the kerf top surface) to nozzle diameter is selected as H/D=2.2., where H is the stand-off-distance and D is the nozzle exit diameter. The kerf wall temperature is kept at 1500 K to resemble the laser cutting process. It is found that the Nusselt number increases sharply at the kerf inlet and decreases towards the kerf exit for the kerf wall angle of 0°. However, it increases gradually in this region for the kerf wedge angle of 4°. The skin friction decreases along the kerf surface.     

Solution of the Boltzmann equation for electrons in the discharges in metal vapour-helium mixtures

The Boltzmann equation was applied to the electron gas in the positive column in a helium-metal vapour mixture discharge. The problem was solved both numerically and approximately taking into account elastic and inelastic collisions of electrons with helium and metal atoms as well as mutual impacts of electrons. Separately the influence of Zn, Cd and Hg atoms on the mean kinetic energy, the mobility (drift velocity) and the diffusion of the electrons was investigated. Approximative relations for those quantities were found and a physical interpretation of their behaviour is given.     

The numerical study of shock-induced hydrodynamic instability and mixing

Based on multi-fluid volume fraction and piecewise parabolic method (PPM), a multi-viscosity-fluid hydrodynamic code MVPPM (Multi-Viscosity-Fluid Piecewise Parabolic Method) is developed and applied to the problems of shock-induced hydrodynamic interfacial instability and mixing. Simulations of gas/liquid interface instability show that the influences of initial perturbations on the fluid mixing zone (FMZ) growth are significant, especially at the late stages, while grids have only a slight effect on the FMZ width, when the interface is impulsively accelerated by a shock wave passing through it. A numerical study of the hydrodynamic interfacial instability and mixing of gaseous flows impacted by re-shocks is presented. It reveals that the numerical results are in good agreement with the experimental results and the mixing growth rate strongly depends on initial conditions. Ultimately, the jelly layer experiment relevant to the instability impacted by exploding is simulated. The shape of jelly interface, position of front face of jelly layer, crest and trough of perturbation versus time are given; their simulated results are in good agreement with experimental results.     

On the possible mechanism of the jet noise intensification near a wing

A qualitative model of the mechanism of intensification of jet noise issuing from a nozzle located near a wing is proposed. A two-dimensional model problem on the diffraction of a plane acoustic wave at the edge of a nozzle nozzle located near a half-plane simulating the wing edge is formulated. It is shown that diffraction on the wing edge of Kelvin-Helmholtz instability waves developing from the edge of the nozzle can lead to the significant intensification of the acoustic energy radiated into the far field.     

The influence of the thermal wake due to pulsating optical discharge on the aerodynamic-drag force

The influence of a thermal wake due to gas injection and due to a pulsating optical discharge (POD) on the aero-dynamic-drag force of a body in a supersonic air flow with Mach number M = 1.45 are experimentally examined. With the help of a single-component aerodynamic balance, the influence of the injected subsonic jet and the thermal wake produced by POD on the aerodynamic drag of a hemisphere-on-cylinder model was studied. It is shown that the observed aerodynamic-force reduction phenomenon can be made more pronounced by increasing the laser power and pulse repetition frequency, or by decreasing the distance between the model and the pulsating optical discharge. The maximum aerodynamic-force reduction (up to 15%) due to the thermal-wake action was observed at a maximum laser-radiation power of W = 2.3 kW and at a pulse rate of f = 90 kHz. The joint effect due to the argon jet and due to the POD caused an aerodynamic-drag force reduction reaching 30%.     

Neutrino crown of a protoneutron star and analysis of its convective instability

A numerical solution to the problem of the structure of the neutrino crown of a protoneutron star that is formed upon an iron-star-core collapse, which is peculiar to all massive stars at the end of their thermonuclear evolution, is given. The structure of a neutrino crown, which is semitransparent to neutrino radiation from a spherical layer between the neutrinosphere and the front of the accretion shock wave, is determined by a set of nonlinear ordinary differential equations of spherically symmetric neutrino hydrodynamics with allowance for a complete set of beta processes in a Boltzmann free-nucleon gas and an ultrarelativistic Fermi-Dirac electron-positron gas that form neutrino-crown matter. The problem of consistently taking into account nonequilibrium neutrino-absorption and neutrino-emission processes and the problem of formulating boundary conditions for a neutrino crown were the main problems in constructing the numerical solution in question, which was obtained by means of a dedicated algorithm. The problem at hand features a number of parameters: the protoneutron-star mass, M₀; the rate of accretion of the outer layers of the collapsing star being considered, ⊙M₀; the effective temperature of the neutrinosphere and the effective neutrino chemical potential there, T _veff and ψ _veff, respectively; and, finally, the total neutrino emissivity of the neutrinosphere, $L_{v\tilde v} $ . Two of these parameters, M₀ and $L_{v\tilde v} $ , are varied within broad intervals in accordance with the hydrodynamic theory of a collapse. On one hand, the numerical solutions constructed in the present study give an idea of the physical conditions in the immediate vicinity of a protoneutron star in the course of its continuing gravitational collapse; on the other hand, they make it possible to obtain exhaustive information about its convective instability, which is the most important property of a so-called soundless collapse—that is, a collapse not accompanied by an explosion of a supernova scale. The increment of the development of a convective instability is obtained at a linear stage, this giving sufficient grounds to introduce the hypothesis that the instability in question plays a key role in the origin of observed gamma-ray bursts. More precisely, these bursts may result from the development of the instability at the subsequent nonlinear stage, which has yet to be studied theoretically—in particular, on the basis of non-one-dimensional numerical models of neutrino hydrodynamics.     

Onset of Unsteady Horizontal Convection in Rectangular Tank at Pr=1

The horizontal convection within a rectangular tank is numerically simulated. The flow is found to be unsteady at high Rayleigh numbers. There is a Hopf bifurcation of Ra from steady solutions to periodic solutions, and the critical Rayleigh number Rac is obtained to be Rac = 5.5377×10^8 for the middle plume forcing at Pr = 1, which is much larger than the value previously obtained. In addition, the unstable perturbations are always generated from the central jet, which implies that the onset of instability is due to velocity shear （shear instability） other than thermally dynamics （thermal instability）. Finally, Paparella and Young＇s first hypotheses [J. Fluid Mech. 466 （2002） 205] about the destabilization of the flow is numerically proven, i.e. the middle plume forcing can lead to a destabilization of the flow.     

The shear diffusion coefficient for generalized theories of gravity

Near the horizon of a black brane in Anti-de Sitter (AdS) space and near the AdS boundary, the long-wavelength fluctuations of the metric exhibit hydrodynamic behaviour. The gauge–gravity duality then relates the boundary hydrodynamics for generalized gravity to that of gauge theories with large finite values of 't Hooft coupling. We discuss, for this framework, the hydrodynamics of the shear mode in generalized theories of gravity in d+1$d+1$ dimensions. It is shown that the shear diffusion coefficients of the near-horizon and boundary hydrodynamics are equal and can be expressed in a form that is purely local to the horizon. We find that the Einstein-theory relation between the shear diffusion coefficient and the shear viscosity to entropy ratio is modified for generalized gravity theories: Both can be explicitly written as the ratio of a pair of polarization-specific gravitational couplings but implicate differently polarized gravitons. Our analysis is restricted to the shear-mode fluctuations for simplicity and clarity; however, our methods can be applied to the hydrodynamics of all gravitational and matter fluctuation modes.     

预混气体燃烧火焰闪烁现象分析

在低速射流的预混火焰和扩散火焰中都存在火焰闪烁现象。对扩散火焰,其机理已比较明确,是由于浮力诱导引起的一种水力学不稳定性。而对预混火焰闪烁现象则存在水力学不稳定性和热驱动不稳定性两种观点。本文根据水力学不不稳定性观点,把预混火焰的闪烁现象看成是包围火焰锋面的已燃混气层中内、外区间在垂直方向上的相对脉动,应用Ｋｅｌｖｉｎ－Ｈｅｌｍｈｏｌｔｚ不稳定性机理进行了分析,获得了火焰闪烁频率与重力和压力的关系式,并与已有的结果作了对比。     

Crisis of hydrodynamic drag of drops in the two-phase turbulent flow of a spray produced by a mechanical nozzle at transition reynolds Numbers

When processing experimental data for the hydrodynamics of a two-phase flow in a spray produced by a mechanical nozzle, we revealed an anomaly in the behavior of the hydrodynamic drag of drops: the drag coefficient turns out to be four to seven times lower than the previously known values. Several hypotheses are put forward to explain the anomaly. It is found that, when the gas flows around drops under highly turbulent conditions, an “early” (i.e., observed even at transition Reynolds numbers, Re>50) crisis of drag resistance of drops takes place. This new physical phenomenon allows us to account for a number of features of the two-phase flow that are observed in the experiment. Among these features is, in particular, the fact that the momentum transferred to the gas is roughly half the initial momentum of the liquid jet.     

Gas dynamics of a supersonic radial jet. Part I

The gas dynamics of a supersonic radial jet was studied under conditions close to cold spraying. The jet visualization was performed for exhaustion into submerged space with atmospheric pressure and jet impingement to a target. For the cases of swirled and unswirled supersonic radial jets, the pressure profiles measured by a Pitot tube were taken for different distances from the nozzle outlet and for different widths of supersonic part δ _ex = 0.5?2 mm and for prechamber pressure in the range p ₀ = 1?2.5 MPa.