Numerical analysis of flow pattern of impinging liquid sprays in a cold model for cooling a hot flat plate

This paper treats the numerical analysis of two-phase mist jet flow, which is commonly adopted to cool the solidified shell in the secondary cooling zone of the continuous casting process. Flow structures of the two-phase subsonic jet impinging on a flat plate normal to flow, corresponding to the present cooling situation, are solved on the assumption that particles are perfectly elastically reflected from a surface. Again, the numerical experiments concerning mist flows composed of air and water-droplets are made in a cold model. The flow fields for both gas and particle phases strongly depend upon the particle size. When waterdroplets mixing in the mist are very small, the impinging particles travel very closely to the surface. With increasing particle size, particles are reflected from the surface in a far distance. Therefore, also, the case is analysed where a low velocity annular gas-only flow surrounding a round nozzle co-axially is present so that such idle particles may be pushed back to the surface again. This is considered to result in an improvement of the mist cooling efficiency.     

The effect of an unsteady drag force on the structure of a non-equilibrium region behind a shock wave in a gas-particle mixture

For numerical analysis of shock wave propagation in gas-particle mixtures, drag coefficients of a sphere in steady flows are generally used. However, it is shown both experimentally and numerically that a shock loaded solid sphere experiences unsteady drag forces. The paper describes a model of unsteady drag force and its effect on the structure of the non-equilibrium region behind a shock front traveling in a dusty gas. The results are compared with those obtained by using a steady drag coefficient and are discussed. It is demonstrated that the large drag force at the early stage of the interaction between shock-wave induced flow and a solid particle affects the flow structure that is obtained with a steady drag force.      

Rarefied hypersonic flow in a plane channel with a surface glow discharge

The gasdynamic structure of a hypersonic molecular nitrogen flow in a plane channel whose opposite surfaces are segmented electrodes for generating a continuous surface glow discharge is investigated using a two-dimensional computational model. The electrodynamic structure of the surface glow discharge in the hypersonic rarefied gas flow (distributions of the charged particle concentrations, current density, and electric potential) is studied. A two-dimensional conjugate electrical-gasdynamic model consisting of the continuity, Navier-Stokes, and energy conservation equations and the chargedparticle continuity equations in the ambipolar approximation is proposed. The real thermophysical and transport properties of molecular nitrogen are taken into account. It is shown that using a surface glow discharge in a hypersonic rarefied gas flow makes it possible effectively to modify the shock-wave flow structure and hence to consider this type of discharge as additional tool for controlling rarefied gas flows.     

Rotational relaxation of nitrogen in a viscous shock layer at low reynolds numbers

The viscous shock-layer model is used to examine relaxation of rotational degrees of freedom of molecular nitrogen in flow of a rarefied gas near the stagnation flow line around a sphere. It is shown that in the strongly smeared shock-wave region the rotational degrees of freedom can exhibit substantial nonequilibrium, leading to the increase of temperature and an increase of shock-layer thickness as compared with the equilibrium values. The influence of rotational relaxation on the shock-wave structure is discussed, and boundaries are found for the flow regions when rotational relaxation plays on important role,A comparison is made between the results of numerical calculations and experimentally obtained density profiles available in the literature near the stagnation line in flow of a rarefied gas over a sphere [1, 2]. Quite good agreement is obtained between the results of the calculation and experimental data over a wide range of Reynolds numbers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 172–175, July–August, 1977.     

Smooth particle hydrodynamics method for modeling cavitation-induced fracture of a fluid under shock-wave loading

It is demonstrated that the method of smoothed particle hydrodynamics can be used to study the flow structure in a cavitating medium with a high concentration of the gas phase and to describe the process of inversion of the two-phase state of this medium: transition from a cavitating fluid to a system consisting of a gas and particles. A numerical analysis of the dynamics of the state of a hemispherical droplet under shock-wave loading shows that focusing of the shock wave reflected from the free surface of the droplet leads to the formation of a dense, but rapidly expanding cavitation cluster at the droplet center. By the time t = 500 µs, the bubbles at the cluster center not only coalesce and form a foam-type structure, but also transform to a gas-particle system, thus, forming an almost free rapidly expanding zone. The mechanism of this process defined previously as an internal “cavitation explosion” of the droplet is validated by means of mathematical modeling of the problem by the smoothed particle hydrodynamics method. The deformation of the cavitating droplet is finalized by its decomposition into individual fragments and particles.     

Shock-wave-initiated lifting of particles from a cavity

The dynamics of particles of the disperse phase in a turbulent gas flow in planar shock waves sliding along a solid surface with a trapezoid cavity is examined numerically. Lifting of particles from the cavity walls is calculated in the approximation of a rarefied gas suspension. It is shown that the intensity of the transient shock wave and the initial positions of particles have a significant effect on the particle-lifting properties. The height of particle lifting is found to nonmonotonically depend on the initial streamwise coordinate and shock-wave Mach number. It is shown that zones of aggregation and subtraction of particles may be formed at the cavity bottom. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 24–34, January–February, 2007.     

Hypersonic three-dimensional viscous shock layer in a nonuniform gas flow in the neighborhood of the stagnation point

Three-dimensional hypersonic viscous gas flow past smooth blunt bodies in the presence of injection or suction is considered. The effect of the nonuniformity of the approach stream on the shock-wave standoff, the flow structure and the friction and heat transfer coefficients is investigated with reference to the examples of flow from a supersonic spherical source and flow of the far wake type. It is shown that this effect depends importantly on the Reynolds number, the nature of the nonuniformity and the shape of the body.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 136–145, November–December, 1987.     

Numerical simulation of a supersonic gas–solid flow over a blunt body: The role of inter-particle collisions and two-way coupling effects

A supersonic dusty gas flow over a blunt body is considered. The mathematical model of the two-phase gas–particle flow takes into account the inter-particle collisions and the two-way coupling effects. The carrier gas is treated as a continuum, the averaged flow field of which is described by the complete Navier–Stokes equations with additional source terms modeling the reverse action of the dispersed phase. The dispersed phase is treated as a discrete set of solid particles, and its behavior is described by a kinetic Boltzmann-type equation. Particles impinging on the body surface are assumed to bounce from it. Numerical analysis is carried out for the cross-wise flow over a cylinder. The method of computational simulation represents a combination of a CFD-method for the carrier gas and a Monte Carlo method for the “gas” of particles. The dependence of the fine flow structure of the continuous and dispersed phases upon the free stream particle volume fraction α_p∞ and the particle radius r_p is investigated, particularly in the shock layer and in the boundary layer at the body surface. The particle volume fraction α_p∞ is varied from a negligibly low value to the value α_p∞ = 3 × 10⁵ at which inter-particle collisions and two-way coupling effects are simultaneously essential. Particular attention has been given to the particles of radii close to the critical value r_p1, because in this range of particle size the behavior of the particles and their effect on the carrier gas flow are not yet completely understood. An estimate of the turbulent kinetic energy produced by the particles in the shock layer is obtained.     

Transonic transition behind a shock wave traveling through a dust-gas mixture

The results of investigating shock-wave interaction with a particle cloud on the range of transonic relative velocities are presented. Transition of the two-phase flow from the supersonic to the subsonic regime during phase velocity relaxation under conditions of well-expressed gas-phase nonstationarity was observed. The effect of gas acceleration in the subsonic phase interaction region, previously predicted by the authors on the basis of the accelerating screen model, is confirmed experimentally. The presence of a substantial chaotic component of the particle longitudinal velocity, which indicates close internal phase interactions of the collision type, is demonstrated. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 165–173, July–August, 2000. The work received financial support from the Russian Foundation for Basic Research (project N98-01-00722) and INTAS (project N97-2027).     

CFD-DEM investigation into flow characteristics in mixed pulsed fluidized bed under electrostatic effects

Static electricity has an important effect on gas–solid fluidized bed reactor fluidization performance. In the process of fluidization, electrostatic interaction between particles will obviously accelerate particle agglomerate formation, which consequently reduces the fluidization performance. Pulsed gas flow injection is an efficient method to enhance particle mixing, thereby weakening the occurrence of particle agglomerate. In this study, the two-dimensional hybrid pulsed fluidized bed is established. The flow characteristics are studied by using the coupled CFD-DEM numerical simulation model considering electrostatic effects. Influences of different pulsed frequencies and gas flow ratios on fluidized bed fluidization performance are investigated to obtain the optimal pulsed gas flow condition. Results show that in the presence of static electricity, the bubble generation position is lower, which is conducive to the particle flow. Pulsed gas flow can increase the particle velocity and improve the diffusion ability. The bubble generation time is different at different frequencies, and the frequency of 2.5 Hz has the most obvious effect on the flow characteristics. Different gas flow ratios have significant impacts on the particle movement amplitude. When the pulse gas flow accounts for a large ratio, the particle agglomerate tends to be larger. Therefore, in order to improve the fluidization effect, the ratio of pulsed gas flow to stable gas flow should be appropriately reduced to 0.5 or less.     

Numerical simulation of flow fields induced by a supersonic projectile moving in tubes

Numerical study of the shocked flows generated by a supersonic projectile released from a launch tube into a big chamber has been performed in this paper. Based on fixed Cartesian grids, the two-dimensional axisymmetric Euler equations are solved by the fifth-order WENO scheme implemented with moving boundary conditions. Both the level set technique and ghost fluid method are used for capturing the moving interface of the projectile implicitly. The numerical results show that complex shock phenomena exist in the transient shock flow, resulting from shock-wave reflection, shock-wave focusing, shock-wave/projectile interaction and shock-wave/contact surface interactions. The relationships between the acceleration of the projectile and the transient shock flow are also discussed in detail.     

Submerged shocks in conical gas flows in the presence of a mach shock-wave configuration

The results of a numerical study of a new type of singularities in the Mach shock-wave structure realized in supersonic nonsymmetric conical flows over V-wings with a bow shock attached to the leading edges are presented. Within the framework of the ideal gas model we study the changes in the shock system on transition, with increase in the sweep angle, from the region of nonsymmetric Mach interaction of the shocks attached to the leading edges of the wing to the region of special flow patterns, where on the windward cantilever surface a rarefaction flow is realized rather than a flow with an internal shock. It is shown, in particular, that in the region with special wing flow patterns a Mach system of shocks with a submerged shock proceeding from the branch point above the windward cantilever may exist.     

Calculation of particle concentration in the problem of aerosol aspiration into a thin-walled tube

A mathematical model of the problem of aerosol aspiration into a thin-walled tube from a moving gas is developed and particle concentration fields are calculated. In the absence of a particle effect on the gas flow, the carrier medium is calculated in the potential-flow and viscous-flow approximations for an incompressible gas, using boundary-element and finite-volume methods. For the viscous-flow model, a numerical solution is found using the FLUENT program. The particle motion equations are complemented with equations for calculating the concentration along the particle trajectories. The spatial distributions of the particle concentration near and inside the sampler are studied for different ratios of the wind and aspiration velocities and for different Stokes numbers. The effect of nonuniformity of the particle concentration distributions on the aspiration coefficient is discussed.     

Experimental study on near wall transport characteristics of slug flow in a vertical pipe

In this work, the wall shear stress and the mass transfer coefficient of the gas–liquid two-phase upward slug flow in a vertical pipe are investigated experimentally, using limiting diffusion current probes and digital high-speed video system. In experiments, the instantaneous and averaged characteristics of wall shear stress and mass transfer coefficient are concerned. The experimental results are compared with the numerical results in previous paper of the authors. Both experiment and numerical simulation show that the superficial gas and liquid velocities have an obvious influence on the instantaneous characteristics of the two profiles. The mass transfer coefficient has characteristics similar to the wall shear stress. The instantaneous wall shear stress and mass transfer coefficient profiles have the periodicity of slug flow. The averaged wall shear stress and mass transfer coefficient increase with increased superficial gas velocity. However, there is inconsistency in the variation trends of the averaged wall shear stress and mass transfer coefficient with superficial liquid velocity between experimental result and numerical simulation result, which can be attributed to the difference in flow condition. Moreover, the Taylor bubble length is also another impacting factor. The experimental and numerical results all shows that the product scale can not be damaged directly by the flow movement of slug flow. In fact, the alternative forces and fluctuations with high frequency acting on the pipe wall due to slug flow is the main cause for the slug flow enhanced CO₂ corrosion process.     

Unstructured adaptive remeshing finite element method for dusty shock flow

The passage of planar shocks in a dusty gas was investigated to note effects due to particle loading and initial shock Mach number. Two-phase flow equations have been added to a conservative, monotonic flow solver to allow study of compressible particle and droplet flows, which are of importance for shock propagation in two-phase flows and spray propulsion systems. The formulation developed herein employed a conservative Eulerian treatment for the gas and particle phases. The computations were performed using the finite element method-flux corrected transport (FEM-FCT) scheme, which has shown excellent predictive capability of various compressible flows which include both strong and weak shocks. The flux limiting technique was modified to provide monotonic particle velocity fields to increase the scheme's computational stability. Adaptive unstructured methodology based on adapting to high gradients of both the fluid and particle densities was used in conjunction with the conservative shock-capturing scheme to adequately resolve strong flowfield gradients. The shock attenuation of this scheme was then compared with previous experimental and numerical results and was found to yield robust predictions. Various interphase coupling terms were also considered to note their effect on the shock attenuation.This article was processed using Springer-Verlag t_ex Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

The flow structure of dilute gas-particle suspensions behind a shock wave moving along a flat surface

The asymptotic and numerical investigations of shock-induced boundary layers in gas-particle mixtures are presented.The Saffman lift force acting on a particle in a shear flow istaken into account.It is shown that particle migration across the boundary layer leads tointersections of particle trajectories.The corresponding modification of dusty gas model isproposed in this paper.The equations of two-phase sidewall boundary layer behind a shock wave moving at aconstant speed are obtained by using the method of matched asymptotic expansions.Themethod of the calculation of particle phase parameters in Lagrangian coordinates isdescribed in detail.Some numerical results for the case of small particle concentration aregiven.     

Calculation of a Heat Flow from a Spherical Particle in a Diatomic Gas

The problem of heat flow from a uniformly heated spherical particle in a diatomic gas is considered. The paper reports results of numerical calculations for an analog of the Bhatnagar–Gross–Krook model of the collision integral under for purely diffuse reflection of the gas molecules from the surface.     

Transient shock wave flows in tubes with a sudden change in cross section

This paper describes propagation of shock waves within circular cross-section shock tubes with a sudden area change in cross section. A dispersion-controlled scheme was used to solve the Euler equations assuming axisymmetric flows. For experimental visualizations an aspheric cylindrical test section was designed to keep collimated incident light rays parallel once they were reflected or refracted on the inner and outer surfaces of the test section. For effective comparisons with experimental results, equivalent numerical interferograms were constructed to demonstrate effectiveness of the numerical method and verify the observed shock-wave phenomena. The numerical method was used to calculate three further cases with variations of the initial shock-wave Mach number and the flow geometry to clarify the role of these parameters. Complex transient shock-wave phenomena, such as shock-wave reflection, shock/vortex interaction and shock-wave focusing were observed in these cases, and interpreted with shock wave theory. In addition, the research clearly shows that combination of CFD with experiments is effective to highlight physical phenomena in axisymmetric flows. Received 15 June 1996 / Accepted 20 December 1996     

The structure of particle-laden,underexpanded free jets

Underexpanded, supersonic gas-particle jets were experimentally studied using the shadowgraph technique in order to examine the influence of the dispersed particles on the shape of the free jet and the structure of the imbedded shock waves. The particle mass loading at the nozzle exit was varied between zero and one, and two sizes of particles (i.e. spherical glass beads) with mean number diameters of 26 and 45 m were used. It was found that the Mach-disc moves upstream towards the orifice with increasing particle loading. The laser light sheet technique was also used to visualize the particle concentration distribution within the particle jet and the spreading rate of the particle jet. Furthermore, the particle velocity along the jet centerline was measured with a modified laser-Doppler anemometer. These measurements revealed that the particles move considerably slower than the gas flow at the nozzle exit. This is mainly the result of the particle inertia, whereby the particles are not accelerated to sonic speed in the converging part of the nozzle.In order to further explore the particle behavior in the free jet, numerical studies were performed by a combined Eulerian/Lagrangian approach for the gas and particle phases, including full coupling between the two phases. The numerical results showed that the application of different particle velocities at the nozzle exit as the inlet conditions, which were below the sonic speed of the gas phase has a significant influence on the free jet shape and the configuration of the shock waves. These results demonstrate that the assumption of equilibrium flow (i.e. zero slip between the phases) at the nozzle exit which has been applied in most of the previous numerical studies is not justified in most cases. Furthermore, the numerical calculations of the free jet shape and the particle velocity along the jet axis were compared with the measurements. Although correlations for rarefaction and compressibility effects in the drag coefficient were taken into account, the particle velocity along the center line was considerably overpredicted.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Supersonic nonuniform viscous gas flow past a blunt body with supply of gas from the surface

The problem of axisymmetric nonuniform gas flow past smooth blunt bodies at high Mach numbers is investigated. The approach stream is a parallel axisymmetric flow in which the velocity and temperature depend on the radial distance from the axis of symmetry and the pressure is constant. On the axis of symmetry the velocity has a minimum and the temperature a maximum. A characteristic feature of this flow is the existence of two qualitatively different flow regimes: separated [1-4], when in the shock layer on the front of the body there is a closed region of reverse-circulating flow, and unseparated [5, 6], when there is no such zone. In this study the case of unseparated flow is investigated. The equations of a thin viscous shock layer with generalized Rankine-Hugoniot conditions at the shock and boundary conditions on the body that take into account the supply of gas from the surface are solved numerically. The effect of the gas supply on the conditions of unseparated flow is analyzed in relation to the Reynolds number, and the critical values of the nonuniformity parameter a = a_k [5] are obtained. It is shown that at high Reynolds numbers the supply of gas from the surface has practically no effect on a_k, while at low and intermediate Reynolds numbers it reduces the region of unseparated flow. For high Reynolds numbers and an intense supply of gas from the surface an asymptotic solution of the problem is obtained for the neighborhood of the stagnation point. This is compared with the numerical solution.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 122–129, July–August, 1988.The authors wish to thank G. A. Tirskii for useful discussions of the results.