The flow mechanism in a bent,rotating arc

A 5 A arc in a 40% H₂, 60% N₂ mixture under atmospheric conditions is bent by a magnetic field into approximately a semi-circle and rotates with the frequency of the driving magnetic field, the direction of the deflection being shifted back 50° relative to the Lorentz force. The distribution of the gas temperature is determined from the intensity distribution ofH _β, which is measured by a sampling technique and deconvoluted to the local emission coefficient ε _Hβ without resorting to symmetry properties but with due consideration of LTE deviations. The flow velocity component normal to the isothermal surfaces is evaluated from the convective term of the energy balance equation, whereas the tangential component is calculated from the continuity equation. The flow field is composed of 6 vortices and 6 stagnation points and can be regarded as an interaction of 3 basic processes: 1) a mass flow through the arc in the direction of deflection correlated to the curvature of the arc due to inhomogeneous heating, 2) a closed double vortex in the cross-sectional plane of the arc that is caused by the rotational motion, 3) the decay of unstable shear layers in the flow field, by which two additional pairs of vortices are created.     

Rotation of a droplet in a viscous fluid

Unique capabilities for modeling the bulk motion of one liquid in another arise from the use of droplets made of a magnetic liquid. In this paper the low-frequency rotational motion of a magnetic droplet suspended in a viscous liquid is investigated. In this frequency range, the shape of the droplet does not depend on the field frequency and is determined only by its amplitude. An analytic solution has been found in the Stokes approximation to the problem, which generalizes the classic problem of Jeffrey to the case of a liquid ellipsoidal particle. This solution makes it possible to determine the velocity field inside and outside the liquid particle, the moments of the viscous forces acting on the droplet, its coefficient of rotational mobility. Zh. éksp. Teor. Fiz. 112, 1340–1350 (October 1997)     

Theory of the free full-circle arc

A theoretical investigation of the full-circle arc located between two planes is presented. The circular arc shape is due to an applied magnetic field. The basic equations for conservations of mass, momentum, energy, and charge, as well as Maxwell's equations and the equation of state lead to a coupled set of partial differential equations. By means of Green's formula, this set is transformed into a set of integral equations. Using the analytically known Green's function, the system may be solved by an iteration procedure. For a simplified arc model, the quantities of interest are computed: The temperature distribution, the mass flow field, and the external magnetic field necessary to maintain this arc configuration.     

Investigations on the radially free full circle arc

An argon arc, burning between two horizontal, plane-parallel, insulating plates, is bent circularily by an external and its own magnetic field. Except for the small electrode zone, one gets a stationary radially free full circle arc for experimental investigations of magnetohydrodynamic and thermodynamic effects under well defined conditions. The local temperature distributions in the arc cross-section are detected spectroscopically as functions of the arc current and the arc radius or curvature, respectively. By means of the basic equations of conservation of energy, mass, and charge and the known transport properties of argon at atmospheric pressure, the mass flow field in the arc is evaluated. In the arc core it follows the direction of the Lorentz force radially outward counter-balancing the tendency of the curved arc to move inwards thermodynamically. Due to the symmetry to the centre-plane of the arc chamber and the vanishing net flow for the whole system, the gas flow has to stream back in the cold outer arc zones, thereby forming a double whirl. By reasons of the experimental arrangement even a quadruple whirl occurs. Additionally the evaluation yields the specific radiationu(T) of argon being compared with results in the recent literature.     

Experimental and theoretical investigation of high-pressure arcs.II. The magnetically deflected arc (three-dimensional modeling)

While Part I deals with cylindrical arcs, Part II studies the influence of transverse magnetic fields on the arc column for ambient pressures of 0.1-5.0 MPa. If exposed to a magnetic induction of several millitesla, the column of an arc is deflected by the Lorentz forces. In this paper, heat transfer and fluid flow with coupled electromagnetic forces are modeled for the magnetically deflected arc. To verify the predictions, the three-dimensional temperature distributions of the arc column are determined by line and continuum radiation measurements using tomographic methods. These temperature maps are compared with the results of the numerical simulations. To gain insight into the physical professes of the discharge and to make the arc properties available which are not readily measured, a self-consistent numerical model of the arc column is applied to the time-dependent and three-dimensional case. The temperature, velocity, pressure, and current densities are predicted by solving the conservation equations for mass, momentum, and energy, and Ohm's and Biot-Savart's law using material functions of the plasma. A control volume approach facilitates a numerically conservative scheme for solving the coupled partial differential equations. The predictions are in fair agreement with experimental results. A time-dependent fully implicit simulation of the arc was used to investigate the arc instabilities for large magnetic inductions     

气温和颗粒密度对声场中颗粒动力学影响的数值模拟

综合考虑黏性夹带力、Basset力、虚拟质量力和压力梯度力,建立颗粒在声场中的动力学模型,利用变步长四阶RungeKutta算法和二阶隐式Adams插值算法对颗粒的受力和运动进行数值模拟。将模拟和实验得到的颗粒运动特性进行对比,验证数值模拟的正确性。在此基础上,研究气温和颗粒密度对颗粒动力学的影响规律。结果表明,黏性夹带力对颗粒运动起主导作用;气温升高,压力梯度力与黏性夹带力之间的相位差减小,Basset力、虚拟质量力与黏性夹带力之间的相位差增大。研究还发现,气温较低时,颗粒密度对颗粒运动有重要影响,夹带系数随着密度的增加而迅速下降;气温较高时,颗粒密度对颗粒运动的影响较小,颗粒位移振幅和夹带系数相对低温时明显增加。      

考虑金属蒸汽的钨极惰性气体保护焊电弧与熔池交互作用三维数值分析

基于局域热平衡状态假设并考虑金属蒸汽的作用, 建立了钨极惰性气体保护焊电弧与熔池交互作用的三维数学模型. 电弧等离子体的热力学参数和输运系数由温度和金属蒸汽浓度共同决定, 并使用第二黏度近似简化处理金属蒸汽在氩等离子中的输运过程. 在考虑熔池流动时, 主要考虑了浮力、电磁力、表面张力和等离子流拉力的作用. 通过对麦克斯韦方程组、连续性方程、动量守恒方程、能量守恒方程和组分输运方程的耦合求解, 得到了金属蒸汽在电弧中的空间分布、电弧和熔池的温度场、速度场和电流密度分布等重要结果. 通过与未考虑金属蒸汽的结果对比, 研究了熔池上表面产生的金属蒸汽对电弧等离子体行为的影响, 以及电弧等离子对熔池行为的影响. 结果表明, 金属蒸汽主要富集在熔池上表面附近; 金属蒸汽对电弧等离子体有明显的收缩作用, 而对等离子速度和电势影响较小; 金属蒸汽的出现对熔池上表面速度分布和剪切力分布以及熔池形貌并无明显影响. 求解结果与已有的实验结果和计算结果符合良好.     

用格子Boltzmann模型模拟非等温流场

根据微观和宏观之间的质量、动量、能量守恒准则和在原格子Boltzmann模型基础上,建立了几个新的格子Boltzmann模型,使得在外力场中的格子Boltzmann模型得到进一步完善.通过还原宏观流体力学方程,捕捉到了浮力强迫系数与Grashof数之间的关系.所得动量方程和Navier Stokes方程相比,在黏性输运项上有明显的改进,说明黏性应力不但与流体的速度梯度和流体的压缩性有关,而且还与非定常的内能梯度和动量通量有关.该模型对非等温流场的数值结果证明了其具有很好的数值稳定性和适用性. 关键词： Boltzmann模型 平衡分布函数 流体力学方程     

Resolution of the Abraham-Minkowski controversy

The momentum of light inside ponderable media has an electromagnetic part and a mechanical part. The local and instantaneous density of the electromagnetic part of the momentum is given by the Poynting vector divided by the square of the speed of light in vacuum, irrespective of the nature of the electromagnetic fields or the local or global properties of the material media. The mechanical part of the momentum is associated with the action of the electromagnetic field on the atomic constituents of the media, as specified by the Lorentz law of force. Proper interpretation and application of the Maxwell-Lorentz equations within the material bodies as well as at their surfaces and interfaces is all that is needed to obtain a complete picture of the momentum of light, including detailed numerical values at each and every point in space and time. That the Abraham-Minkowski controversy surrounding the momentum of light inside material media has persisted for nearly a century is due perhaps to an insufficient appreciation for the completeness and consistency of the macroscopic Maxwell-Lorentz theory, inadequate treatment of the electromagnetic force and torque at the material boundaries, and an undue emphasis on the necessity of coupling the equations of electrodynamics to those of the theory of elasticity for proper treatment of mechanical momentum. The present paper reports the resolution of the Abraham-Minkowski controversy within the framework of the classical theory of electrodynamics, without resort to such complicating and ultimately unnecessary factors as pseudo-momentum, special surface forces, alternative energy-momentum tensors, and hidden momenta, that have caused so much confusion for such a long period of time.     

Relativistic ponderomotive forces

The interaction of a relativistic classical electron with an inhomogeneous electromagnetic field is investigated. In second-order perturbation theory the motion is separated into fast and slow motions, and the relativistic Newtonian equation is averaged over the fast oscillations. The rate of change obtained for the slow component of the electron momentum is interpreted as a relativistic ponderomotive force. The result is generalized to the relativistic case of the wellknown expression for the Gaponov-Miller force acting on an electron at rest. The expressions obtained for the relativistic ponderomotive forces are very complicated in the general case. They simplify in the limit of a stationary field (pulses of long duration) and a small gradient. The most typical and simplest special case of an inhomogeneous field—a stationary plane-focused beam—is investigated. The main difference between relativistic ponderomotive forces and their nonrelativistic limit is they have multiple components. In addition to the usual force directed along the gradient of the field, the relativistic case is also characterized by force components that do not have the form of the gradient of a potential and are parallel to the wave vector and the direction of the field polarization. It is shown that when a relativistic electron travels in a direction close to the direction of the wave vector of a focused laser beam, these components can greatly exceed the gradient force. A force directed along the field polarization vector arises even when the gradient of the field in this direction is zero. Zh. éksp. Teor. Fiz. 116, 1198–1209 (October 1999)     

Optical velocity measurements of electrolytic boundary layer flows influenced by magnetic fields

Magnetic fields are applied to electrically conducting fluids in order to influence electrochemical processes through the magnetohydrodynamic effect. Various phenomena, e.g. on electrodeposited metal layers, which can be attributed to forced convections were observed. To provide information about acting forces, the laser Doppler velocity profile sensor was applied to measure the transition layer of a Lorentz force influenced flow over a backward-facing step and the velocity boundary layer during copper deposition. With this sensor, the electrolyte convection within < 500 μm of the front of an electrode is measured with a spatial resolution down to 15 μm. The interaction of buoyancy, Lorentz and magnetic field gradient forces is studied by measuring the velocities down to 10 μm in front of the cathode. Inside the concentration boundary layer, complex electrolyte convection is induced, which varies not only in time but also in its structure, depending on the forces present and their influence over time. In inhomogeneous magnetic field configurations, the magnetic field gradient force dominates the velocity boundary layer at steady state and transports electrolyte toward regions of high magnetic gradients, where maximum deposit thicknesses are found. In this way, the measurements confirm the predicted influence of the magnetic field gradient force on the structuring of copper deposits.     

Calculation of the electric potential and the Lorentz force in a transverse flow past a circular cylinder in a nonuniform magnetic field for various configurations of a locally ionized region at the cylinder surface

We obtain a solution to the equation for the electric potential in a locally ionized transverse magnetohydrodynamic flow past a circular cylinder in a nonuniform magnetic field produced by a linear conductor for various configurations of the ionization region. Analytical formulas are derived for the volume density of the Lorentz force acting on the flow in a locally ionized region. The effect of the Hall parameter and of the configuration of the region of the magnetohydrodynamic interaction on the Lorentz force is analyzed. It is shown that an increase in the Hall parameter leads to a decrease in the Lorentz force acting on the flow, and a change in the configuration of the locally ionized region makes it possible to suppress the effect of the Hall parameter on the Lorentz force.     

THE NATURE OF NATURAL CONVECTION IN BINARY GASES DUE TO HORIZONTAL TEMPERATURE AND VERTICAL CONCENTRATION GRADIENTS

Abstract

Results are presented that illustrate the effect of augmenting or opposing thermal and solutal body forces on the flow, temperature and concentration distributions. For augmenting buoyancy forces, the flow field is very similar to that for a single-component fluid. Multicellular flow patterns are observed for opposing buoyancy forces that depend on the buoyancy parameter. The solutal buoyancy force does not dominate the flow field for all values of opposing body forces, because the solutal gradient is vertical. The concentration gradient affects the natural convection through both the additional buoyancy force and the thermophysical properties of the gas mixture.     

Computation of steady flow in the molten pool at electric-arc heating

Peculiarities of the formation of melt hydrodynamics in the molten pool of electric arc as a result of a viscous interaction with the arc plasma flow and the effect of electromagnetic forces are considered. It is shown that in a relatively shallow pool, the role of viscous interaction with plasma flow predominates electromagnetic forces. In a deeper pool, the flow in peripheral upper region is formed as before by a viscous interaction between plasma and melt, and the electromagnetic forces dominate in deep regions.     

Physical hydrodynamic propulsion model study on creeping viscous flow through a ciliated porous tube

The present investigation focusses on a mathematical study of creeping viscous flow induced by metachronal wave propagation in a horizontal ciliated tube containing porous media. Creeping flow limitations are imposed, i.e. inertial forces are small compared to viscous forces and therefore a very low Reynolds number (Re ? 1) is taken into account. The wavelength of metachronal wave is also considered to be very large for cilia movement. The physical problem is linearized and exact solutions are developed for the differential equation problem. Mathematica software is used to compute and illustrate numerical results. The influence of slip parameter and Darcy number on velocity profile, pressure gradient and trapping of bolus are discussed with the aid of graphs. It is found that with increasing magnitude of the slip parameter, the trapped bolus inside the streamlines increases in size. The study is relevant to biological propulsion of medical micromachines in drug delivery.     

Numerical investigation of the flow in the cathode melt droplet of electric arc

The role of electromagnetic forces and the forces of viscous friction with the arc plasma flow in the flow formation within the cathode melt is considered within the framework of numerical modelling; a comparative estimation of the separate influence of each of the above forces is carried out. The melt flow pattern is found to form mainly by electromagnetic forces. The character of the effect of electromagnetic forces is determined to a considerable extent by the ratio of the radius of cathode attachment of the arc on the melt droplet and the rod cathode radius.     

Evaluation of the translational and rotational diffusion coefficients of a cubic particle (for the application to Brownian dynamics simulations)

By estimating the force and torque acting on the cube for the two cases of a uniform flow field and a rotational flow field, we have discussed whether or not there is a coupling between the translational and the rotational motion. From the characteristics of the friction coefficients, we may understand that there is no coupling between the translation motion and the rotational motion in the situation of the Reynolds number being sufficiently smaller than unity. In contrast, in the case of a non-slow flow field with the Reynolds number larger than unity, the coupling characteristics of the motion of a cube is certainly recognised and therefore the interaction with the ambient fluid is characterised by a variety of friction coefficients including friction coefficients that relate the forces acting on the cube to the angular velocities of the rotational motion. Hence, the employment of these translational and rotational diffusion coefficients for a cube enables the implementation of Brownian dynamics simulations for a suspension composed of cubic particles in order to analyse the dynamic characteristics of a cubic particle suspension.

Highlights

1. We have considered a flow problem around a cube in order to numerically clarify the characteristics of the translational and rotational friction or diffusion coefficients.

2. In a slow flow field the motion of the cube need only to be characterised by two friction coefficients, i.e. the translational and rotational friction coefficients.

3. In the case of a non-slow flow field, the coupling characteristics between the translational motion and the rotational motion are recognised.

4. Employment of these diffusion coefficients enables the implementation of Brownian dynamics simulations for a suspension composed of cubic particles.

     

Stable Configuration of Electric Arcs in Transverse Magnetic Fields

Deviations from rotational symmetry of arc columns exposed to transverse magnetic fields cause convection and a momentum transport between the column and its surrounding gas. As a consequence, the arc moves and changes its geometry until it reaches a stable configuration. Based on the momentum transport equation, the arc behavior is discussed under various operating conditions, and stable arc configurations are determined. In particular, the stability-criteria of a balanced arc column in a transverse gas flow and magnetic field is derived. It turns out that the arc becomes unstable with respect to kinks parallel to the applied magnetic field when ? = p?/(B2/8?)?1. (p? = ambient pressure, Bo = applied magnetic field).     

A theoretical study on the unsteady aerothermodynamics for attached flow models

The principle of the unsteady aerothermodynamics was theoretically investigated for the attached flow. Firstly, two simplified models with analytic solutions to the N-S equations were selected for the research, namely the compressible unsteady flows on the infinite flat plate with both time-varying wall velocity and time-varying wall temperature boundary conditions. The unsteady temperature field and the unsteady wall heat flux (heat flow) were analytically solved for the second model. Then, the interaction characteristic of the unsteady temperature field and the unsteady velocity field in the simplified models and the effects of the interaction on the transient wall heat transfer were studied by these two analytic solutions. The unsteady heat flux, which is governed by the energy equation, is directly related to the unsteady compression work and viscous dissipation which originates from the velocity field governed by the momentum equation. The main parameters and their roles in how the unsteady velocity field affects the unsteady heat flux were discussed for the simplified models. Lastly, the similarity criteria of the unsteady aerothermodynamics were derived based on the compressible boundary layer equations. Along with the Strouhal number Stu, the unsteadiness criterion of the velocity field, StT number, the unsteadiness criterion of the temperature field was proposed for the first time. Different from the traditional method used in unsteady aerodynamics which measures the flow unsteadiness only by the Stu number, present results show that the flow unsteadiness in unsteady aerothermodynamics should be comprehensively estimated by comparing the relative magnitudes of the temperature field unsteadiness criterion StT number with the coefficients of other terms in the dimensionless energy equation.     

Production of Fine Particles from Melts of Metals or Highly Viscous Fluids by ultrasonic standing wave atomization

Ultrasonic standing wave atomization (USWA) is a new process capable of atomizing both high surface energy liquids and highly viscous liquids. Atomization is achieved through acoustic forces acting upon a liquid jet which is guided into the central pressure node of a standing wave field. Spherical metal powders with minimum mass median diameters of less than 15 μm have been produced from metal melts with surface tensions of about 0.5 N/m. Organic liquids with viscosities between 1 and 10 Pas have been atomized, yielding mass median diameters from 20 to 330 μm. The influence of different operating parameters on the mass median diameter of metal melts and highly viscous liquids was evaluated. Parameters which were varied were ambient gas pressure, vibration amplitude of the transducers, mass flow rate, density of liquid, viscosity of the liquid, surface tension and the outlet diameter. The powders and sprays were analyzed with laser diffraction particle sizers. The physical background of the atomization process is discussed and an equation for the prediction of the mass median diameter is derived.