Effect of far-field flow on a columnar crystal in the convective undercooled melt

The growth behavior of a columnar crystal in the convective undercooled melt affected by the far-field uniform flow is studied and the asymptotic solution for the interface evolution of the columnar crystal is derived by means of the asymptotic expansion method.The results obtained reveal that the far-field flow induces a significant change of the temperature around the columnar crystal and the convective flow caused by the far-field flow accelerates the growth velocity of the interface of the growing columnar crystal in the upstream direction and inhibits its growth velocity in the downstream direction.Our results are similar to the experimental data and numerical simulations.     

Linear stability analysis on a spherical particle growing from a binary melt under the far-field flow

The solutions of temperature and solute fields around a spherical crystal growing from a binary melt under the far-field flow are obtained.Based on the results,a linear stability analysis on the spherical interface growing from the binary melt under the far-field flow is performed.It is found that the constitutional supercooling effect ahead of the spherical crystal interface under the far-field flow is enhanced compared with that without the flow.The growth rate of the perturbation amplitude at the up-wind side of the spherical crystal interface is larger than that at the down-wind side.The critical stability radius of the crystal interface decreases with the increasing far-field flow velocity.Under the far-field flow,the whole spherical interface becomes more unstable compared with that without the flow.     

远场来流条件下过冷熔体球晶生长的稳定性

建立了远场来流条件下过冷熔体球晶生长的温度场和浓度场稳态模型,分析了对流对球晶周围温度场和浓度场的影响,并以Trivedi的纯扩散球晶稳定性判据为基础,推导出远场来流条件下过冷熔体球晶生长的临界稳定性判据. 研究表明:远场来流条件下,迎流面的扰动振幅增加速率明显大于背流面的扰动振幅增加速率. 振幅增加速率最大值对应的扰动阶次从迎流面到背流面逐渐减小,随着球晶半径增加而增大. 对流使迎流面的稳定性降低,背流面的稳定性增大. 随着流速的增加,球晶的临界稳定半径减小. 关键词： 球晶 远场来流 界面形态稳定性 Trivedi判据     

溶液中球形晶体溶解的分析

从物质溶液浓度变化角度考虑了球形晶体在溶液中溶解随表面张力的变化,利用渐近方法求出了在溶液中球形晶体溶解的浓度和界面的近似解析解,能够计算出溶解过程中球形晶体溶解的浓度、界面演化形态.研究了表面张力对于溶液中溶质浓度分布、球晶界面形态和溶解速度的影响.结果表明,表面张力促进了球形晶体在溶液中的溶解.随着表面张力参数增大,溶液中在界面前沿的溶质浓度升高,球形晶体的溶解速度增大;随着时间的增加,溶解速度逐渐变大,球形晶体半径逐渐变小,直至溶解结束.     

Effects of non-uniform interfacial tension in small Reynolds number flow past a spherical liquid drop

A singular perturbation solution is given for small Reynolds number flow past a spherical liquid drop. The interfacial tension required to maintain the drop in a spherical shape is calculated. When the interfacial tension gradient exceeds a critical value, a region of reversed flow occurs on the interface at the rear and the interior flow splits into two parts with reversed circulation at the rear. The magnitude of the interior fluid velocity is small, of order the Reynolds number. A thin transition layer attached to the drop at the rear occurs in the exterior flow. The effects could model the stagnant cap which forms as surfactant is added but the results apply however the variability in the interfacial tension might have been induced.     

Interfacial evolution of a spherical particle in a uniaximal straining flow

The growth behavior of a spherical particle in undercooled melt,affected by uniaxial straining flows,is studied.The analytical solution obtained by the matched asymptotic expansion method shows that the uniaxial straining flow effect results in higher local growth rate near the surface where the flow comes in and lower local growth rate near the surface where the flow goes out,and that the uniaxial straining flow causes an initially spherical particle to evolve into an oblate spheroid.     

界面动力学对过冷熔体中球晶生长界面形态的影响

考虑了在非平衡凝固条件下球晶生长过程中界面动力学系数随界面温度的变化,利用渐近分析方法求出了在过冷熔体中球晶生长温度场和界面的近似解析解,研究了非线性界面动力学过冷对于过冷熔体中球晶界面形态和生长速度的影响.研究表明,界面动力学系数越大,球晶的生长速度越快; 反之,表明界面动力学系数越小,球晶的生长速度越慢.与忽略界面动力学的情形比较,在球晶生长过程中依赖于界面温度变化的界面动力学显著地减缓了晶体生长的速度. 关键词： 球晶 界面形态 渐近分析     

On the structure of the velocity field under the free spheroidal surface of a viscous liquid drop oscillating in an electrostatic field

An asymptotic analytical solution to an initial boundary-value problem considering (i) the time evolution of the capillary oscillation amplitude as applied to a viscous spheroidal liquid drop placed in a uniform electrostatic field and (ii) the liquid flow velocity field inside the drop is found. The problem is solved in an approximation that is linear in two small parameters: the dimensionless oscillation amplitude and the dimensionless field-induced constant deformation of the equilibrium (spherical) shape of the drop. Terms proportional to the product of the small parameters are retained. In this approximation, interaction between oscillation modes is revealed. It is shown that the intensity of the eddy component of the oscillation-related velocity field depends on the liquid viscosity and the external uniform electrostatic field strength. The intensity of the eddy component decays rapidly with distance from the free surface. The depth to which the eddy flow (which is caused by periodical flows on the free surface) penetrates into the drop is a nonmonotonic function of the polar angle and increases with dimensionless viscosity and field strength.     

旗面周期摆动的实验研究

用实验方法研究了旗面周期摆动的运动过程,采用改进的算法优化了粒子图像测速仪测量结果,定量得了水洞中摆动旗面的近壁流场信息.通过选定旗面包络上的一个拐点,将其振幅作为特征长度重新计算旗面运动的Strouhal数.多组实验结果中,新的Strouhal数均为0.21左右,这与相同Reynolds数下圆柱绕的Strouhal数结果相近.     

Effect of buoyancy-driven convection on steady state dendritic growth in a binary alloy

The effect of buoyancy-driven convection on the steady state dendritic growth in an undercooled binary alloy is studied. For the case of the moderate modified Grashof number, the uniformly valid asymptotic solution in the entire region of space is obtained by means of the matched asymptotic expansion method. The analytical results show that the buoyancy- driven convection has a significant effect on the needle-like interface of dendritic growth. Due to the buoyancy-driven convection, the needle-like interface shape of the crystal is changed. When the Peclet number that is not affected by the buoyant flow is less than a certain critical value, the interface shape of the dendrite becomes thinner as the Grashof number increases; when it is larger than the critical value, the interface shape becomes fatter as the Grashof number increases. In the undercooled binary alloy the morphology number plays an active role in the interface shape and leads to the buoyancy effect that is different from the situation for the pure melt. The smaller the morphology number is, the more significant change the interface shape has. As the Peclet number further increases, the effect of buoyancy on the interface diminishes eventually.     

Distortion of a spherical gaseous interface accelerated by a plane shock wave

The evolution of a spherical gaseous interface accelerated by a plane weak shock wave has been investigated in a square cross section shock tube via a multiple exposure shadowgraph diagnostic. Different gaseous bubbles, i.e., helium, nitrogen, and krypton, were introduced in air at atmospheric pressure in order to study the Richtmyer-Meshkov instability in the spherical geometry for negative, close to zero, and positive initial density jumps across the interface. We show that the bubble distortion is strongly different for the three cases and we present the experimental velocity and volume of the developed vortical structures. We prove that at late times the bubble velocities reach constant values which are in good agreement with previous calculations. Finally, we point out that, in our flow conditions, the gaseous bubble motion and shape are mainly influenced by vorticity and aerodynamic forces.     

The effects of powder properties on in-flight particle velocity and deposition process during low pressure cold spray process

In cold spray process, impacting velocity and critical velocity of particles dominate the deposition process and coating properties for given materials. The impacting velocity and critical velocity of particles depend on the powder properties and cold spray conditions. In the present study, the in-flight particle velocity of copper powder in low pressure cold spraying was measured using an imaging technique. The effects of particle size and particle morphology on in-flight particle velocity and deposition efficiency were investigated. The critical velocity of copper powder was estimated by combining the in-flight particle velocity and deposition efficiency. The effect of annealing of feedstock powder on deposition and critical velocity was also investigated. The results showed that the irregular shape particle presents higher in-flight velocity than the spherical shape particle under the same condition. For irregular shape particles, the in-flight velocity decreased from 390 to 282 m/s as the particle size increases from 20 to 60 μm. Critical velocities of about 425 m/s and more than 550 m/s were estimated for the feedstock copper powder with spherical and irregular shape morphology, respectively. For the irregular shape particles, the critical velocity decreased from more than 550 to 460 m/s after preheating at 390 °C for 1 h. It was also found that the larger size powder presents a lower critical velocity in this study.     

An examination of the flow induced by the motion of many buoyant bubbles

The results of direct numerical simulations of the motion of many three-dimensional buoyant bubbles in periodic domains are examined. The bubble motion is computed by solving the full Navier-Stokes equations by a parallelized finite difference/front tracking method that allows a fully deformable interface between the bubbles and the ambient fluid and the inclusion of surface tension. The governing parameters are selected such that the average rise Reynolds number is about 25. Two cases are examined. In one, the bubbles are nearly spherical; in the other, the bubbles rise with an ellipsoidal shape. The ellipsoidal bubbles show a much larger fluctuation velocity and by visualizing the flow field it is possible to show that the difference is due to larger vorticity generation and stronger interactions of the deformable bubbles. The focus here is on the early stage of the flow, when both the spherical and the deformable bubbles are nearly uniformly distributed.     

Influences of interfacial damage on the effective wave velocity in composites with reinforced particles

The scattering of elastic waves by a spherical particle with imperfect interface and the multiple scattering by many spherical particles with imperfect interface are studied in this paper. First, the scattering of elastic waves by a spherical particle with imperfect interface, i.e. spring interface model, is studied. Then, the multiple scattering by random distributed particles with interfacial damage in a composite material is investigated. The equations to evaluate velocity and attenuation of effective waves defined by statistic averaging are given. Furthermore, based on the established relation between the effective velocity and interfacial constants, a method to evaluate the interfacial damage nondestructively from the ultrasonic measure data is proposed. The numerical simulation is performed for the Sic-Al composites. The effective velocity is computed to show the influences of interface damage. By using the genetic algorithm, the interfacial damage is evaluated from the synthetic experimental data with various levels of error. The numerical results show the feasibility of the method proposed to approximately evaluate the interfacial damage in a composite material with reinforced particles based on ultrasonic data. Supported by the National Natural Science Foundation of China (Grant Nos. 10672019 and 10272003)     

Effects of particle/matrix interface and strengthening mechanisms on the mechanical properties of metal matrix composites

A randomly distributed multi-particle model considering the effects of particle/matrix interface and strengthening mechanisms introduced by the particles has been constructed. Particle shape, distribution, volume fraction and the particles/matrix interface due to the factors including element diffusion were considered in the model. The effects of strengthening mechanisms, caused by the introduction of particles on the mechanical properties of the composites, including grain refinement strengthening, dislocation strengthening and Orowan strengthening, are incorporated. In the model, the particles are assumed to have spheroidal shape, with uniform distribution of the centre, long axis length and inclination angle. The axis ratio follows a right half-normal distribution. Using Monte Carlo method, the location and shape parameters of the spheroids are randomly selected. The particle volume fraction is calculated using the area ratio of the spheroids. Then, the effects of particle/matrix interface and strengthening mechanism on the distribution of Mises stress and equivalent strain and the flow behaviour for the composites are discussed.     

Wake potential and stopping power for a charged particle moving outside a nanosphere

The interaction of a charged particle with a nanosphere is studied based on the dielectric response theory. We obtain the analytical expressions of the induced potential and stopping power, as the charged particle moving outside the nanosphere with a constant velocity. From our results, since the spherical shape limitation, the well-known V-shaped wake effect tracing the particle cannot be observed clearly no matter at the nanosphere surface or in the bulk. Besides, we also find that the particle can even gain energy from the electron polarization as the particle moves to the nanosphere at relatively low velocity.     

The theory of nonstationary thermophoresis of a solid spherical particle

The theory of nonstationary thermophoresis of a solid spherical particle in a viscous gaseous medium is presented. The theory is constructed on the solutions of fluid-dynamics and thermal problems, each of which is split into stationary and strictly nonstationary parts. The solution of the stationary parts of the problems gives the final formula for determining the stationary component of the thermophoretic velocity of this particle. To determine the nonstationary component of the thermophoretic velocity of the particle, the corresponding formula in the space of Laplace transforms is derived. The limiting value theorems from operational calculus are used for obtaining the dependence of the nonstationary component of the thermophoretic velocity of the spherical particle on the strictly nonstationary temperature gradient for large and small values of time. The factors determining the thermophoretic velocity of the particle under investigation are determined.     

The interface shape of the double-liquid lens

In this article, a differential equation, which describes the shape of the liquid interface in a cylindrical chamber when the density difference of two liquids is zero, is provided. And an analytical solution is found for the differential equation which indicates the interface shape is spherical. And such a result is not independent on the vessel size. In experiment, by means of measuring the focal lengths of liquid lenses with different vessel size, the results show that the focal lengths ratio is quite approximate to the inner radius ratio of the cylindrical chamber, which can inversely verifies that the interface shape of liquid lens with two same density liquids is spherical.     

The influence of a nonuniform acoustic field on small-scale processes at a heterogeneous boundary

An experiment is conducted on estimating the velocity of a Schlichting boundary flow arising when a focused field falls on a rigid boundary in a liquid. The velocity of a small-scale Schlichting flow is determined by an indirect method from the characteristics of the cocurrent Rayleigh flow using the particle image velocimetry method. The velocity of the Schlichting flow attained in experiments gives us the possibility of significantly accelerating mass-transfer processes at a heterogeneous boundary, which is confirmed by experimental results on acoustic intensification of rapid growth of salt monocrystals conducted under strictly controlled laboratory conditions.     

On the gravitational motion of a nonuniformly heated solid particle in a gaseous medium

The steady motion of a nonuniformly heated spherical aerosol particle through a viscous gaseous medium is theoretically studied in the Stokes approximation. It is assumed that the mean temperature of the particle surface may differ appreciably from the ambient temperature. The solution of gasdynamic equations yields an analytical expression for the drag of the medium and the gravitational fall velocity of the nonuniformly heated spherical solid particle with allowance for the temperature dependence of the density of the medium and molecular transfer coefficients (viscosity and thermal conductivity). Numerical estimates show that heating of the particle surface considerably influences the drag force and gravitational fall velocity.