Thermo-electrical regime of a vertical electrolyzer: Estimates of the effects of electric conductivity and gas evolution

Some estimates of the distribution of the electric field and current in a vertical electrolyzer are made. The homogeneity criterion, connecting electrode sizes, working space thickness, electrolyte conductivity, and electrode conductivity is obtained. This criterion is verified in numerical calculations. The effects of the gas phase in a vertical electrolyzer are estimated under homogeneous and nonhomogeneous distributions of the potential with height in the working space. It is shown that, under conditions when two-phase models of a liquid with bubbles can be used, the effect of the gas phase on the potential and current distributions with height is insignificant in a number of cases. The research results can be used to select proper electrode materials and to verify and interpret the results of numerical modeling of two-phase electrolyte hydrodynamics in the working space of a vertical electrolyzer.     

A phase field method for simulating morphological evolution of vesicles in electric fields

A phase field method is developed to investigate the morphological evolution of a vesicle in an electric field, taking into account coupled mechanical and electric effects such as bending, osmotic pressure, surface tension, flexoelectricity, and dielectricity of the membrane. The energy of the system is formulated in terms of a continuous phase field variable and the electric potential. The governing equations of the phase field and the electric field are solved using the Galerkin weighted residual approach. The validation and robustness of the algorithm are verified by direct comparisons of the obtained numerical solutions with relevant experimental results. The morphological evolution of an axisymmetric vesicle under an electric field is studied in detail. The results demonstrate that the present method can simulate complex morphological evolutions of vesicles under coupled mechanical–electrical fields.     

Vertical focusing study in the central region of the CYCIAE-100 cyclotron

The vertical focusing is one of the primary problems in the central region of cyclotrons. This focusing effect brought about by the magnetic field is inclined to be weak near the center of the machine due to the fact that the flutter is small, while the electric focusing forces incurred from the dee gaps become very strong. Since the electric focusing effect is dependent on the RF phase, we have proceeded to carry out analytical calculations and numerical simulation about the vertical focusing in the central region of CYCIAE100, including magnetic focusing, electric focusing and the defocusing effect from the space charge effect. All the results have been used for the design of the central region for CYCIAE-100 and a good vertical focusing has been obtained.     

Quantum collisional evolution of a one-dimensional fermi gas: Numerical solution

We present a numerical solution to the problem of the quantum collisional evolution of a one-dimensional Fermi gas. The equation governing this dynamics is non-markovian non-linear and can be solved exactly in this case. We observe two distinct time scales associated with the relaxation process, one connected with the establishment of correlations in the system and which is very short as compared to the second one, related to the evolution of the one-body density, once correlations are established.     

Photogalvanic current in electron gas over a liquid helium surface

We study the stationary surface photocurrent in 2D electron gas near the helium surface. Electron gas is assumed to be attracted to the helium surface due to the image attracting force and an external stationary electric field. The alternating electric field has both vertical and in-plane components. The photogalvanic effect originates from the periodic transitions of electrons between quantum subbands in the vertical direction caused by a normal component of the alternating electric field accompanied by synchronous in-plane acceleration/deceleration due to the electric field in-plane component. The effect needs vertical asymmetry of the system. The problem is considered taking into account a friction caused by the electron-ripplon interaction. The photocurrent resonantly depends on the field frequency. The resonance occurs at field frequencies close to the distance between well subbands. The resonance is symmetric or antisymmetric depending on the kind (linear or circular) of polarization.     

Comparison between level set and phase field method for simulating bubble movement behavior under electric field

In this study, based on different numberical simulation methods, the gas-liquid two-phase flow is taken as the research object. By coupling the continuity equation of incompressible fluid, Navier-Stokes equation, electric field equation and other control equations, a multi-field coupling model for rising bubbles in viscous fluids is established, and numerical simulations are carried out. The two-phase popularity of coupled electric field is studied, and the effect of electric field on bubble motion is analyzed.The Level-set and phase field method are used to track the changes of deformation and rupture during the rising of the bubble. The accuracy and validity of the two methods are verified by mass conservation. At the same time, the calculation area is determined for the accuracy of calculation, and the optimal mesh size is calculated by using mesh independence test. Compared with the level set method, the phase field method has a certain improvement in the calculation efficiency and accuracy. Among them, the calculation efficiency of the phase field calculation method in the same grid is increased by 5 times, and by 3 times in the vertical electric field environment. Moreover, using the phase field method is easier to capture the bubbles slight changes while they are rising, and the quality of the simulation results is better.The simulation analysis of bubble rising process under coupled electric field by two methods shows that under the interaction of electrostatic force, buoyancy and surface tension, the bubble is stretched into an ellipsoid along the direction of the electric field line, and the ratio of the length to the short axis is proportional to the applied electric field strength. In addition, the bubble rising velocity is affected by the electric field, and the vertical electric field accelerates the rising of the bubble.     

II. Recirculation flow induced by a bubble stream rising in a viscous liquid

The recirculation flow induced by the rising motion of a bubble stream in a viscous fluid within an open-top rectangular enclosure is studied. The three-dimensional volume averaged conservation equations are solved by a control-volume method using a hybrid finite differencing scheme to describe the liquid phase hydrodynamics. The momentum exhange between the bubbles and the liquid phase is modeled with a source term equals to the volumetric buoyancy force acting on the gas in the bubble stream. The volumetric buoyancy force accounts for in line interactions between bubbles through the average gas volume fraction in the gas liquid column which depends on the size and the rising velocity of bubbles. The fluid flow within an open-top rectangular enclosure is further investigated by particle image velocimetry for a bubble stream rising in a water-glycerol solution. The measured fluid velocities in a vertical plane are compared with the predictions of the numerical model over a wide range of fluid viscosity (43 mPa s-800 mPa s) and gas flow rates. Finally, the recirculation flows resulting from the interaction of two neighbouring vertical bubble streams are studied. Received: 23 July 1997 / Revised: 19 December 1997 / Accepted: 11 May 1998     

Vertical focusing study in the central region of the CYCIAE-100 cyclotron

The vertical focusing is one of the primary problems in the central region of cyclotrons. This focusing effect brought about by the magnetic field is inclined to be weak near the center of the machine due to the fact that the flutter is small, while the electric focusing forces incurred from the dee gaps become very strong. Since the electric focusing effect is dependent on the RF phase, we have proceeded to carry out analytical calculations and numerical simulation about the vertical focusing in the central region of CYCIAE-100, including magnetic focusing, electric focusing and the defocusing effect from the space charge effect. All the results have been used for the design of the central region for CYCIAE-100 and a good vertical focusing has been obtained.     

Landau problem with a general time-dependent electric field

The time evolution is studied for the Landau level problem with a general time dependent electric field E(t) in a plane perpendicular to the magnetic field. A general and explicit factorization of the time evolution operator is obtained with each factor having a clear physical interpretation. The factorization consists of a geometric factor (path-ordered magnetic translation), a dynamical factor generated by the usual time-independent Landau Hamiltonian, and a nonadiabatic factor that determines the transition probabilities among the Landau levels. Since the path-ordered magnetic translation and the nonadiabatic factor are, up to completely determined numerical phase factors, just ordinary exponentials whose exponents are explicitly expressible in terms of the canonical variables, all of the factors in the factorization are explicitly constructed. New quantum interference effects are implied by this result. The factorization is unique from the point of view of the quantum adiabatic theorem and provides a seemingly first rigorous demonstration of how the quantum adiabatic theorem (incorporating the Berry phase phenomenon) is realized when infinitely degenerate energy levels are involved. Since the factorization separates the effect caused by the electric field into a geometric factor and a nonadiabatic factor, it makes possible to calculate the nonadiabatic transition probabilities near the adiabatic limit. A formula for matrix elements that determines the mixing of the Landau levels for a general, nonadiabatic evolution is also provided by the factorization.     

光折变聚合物PVK∶5CB∶C_(60)中生色团动态取向的研究

考虑到聚合物基体对生色团的取向的阻尼作用 ,以及外电场对生色团的极化作用 ,在已有的生色团气体取向模型基础上 ,建立了非气体取向模型 .并利用数值计算方法求解了这一非气体取向模型方程 .讨论了外加电场、温度对生色团取向的动态过程和稳态分布的影响 ,比较了两模型的计算结果 .采用椭圆偏振法 ,测量了光折变聚合物PVK∶5CB∶C60 中的生色团 5CB在聚合物基体PVK中动态取向过程 .给出了生色团的稳态和动态取向参量随外加电场和温度的变化关系 .理论与实验的比较 ,进一步证明了非气体取向模型的合理性     

Pressure based finite volume method for calculation of compressible viscous gas flows

A pressure based, iterative finite volume method is developed for calculation of compressible, viscous, heat conductive gas flows at all speeds. The method does not need the use of under-relaxation coefficient in order to ensure a convergence of the iterative process. The method is derived from a general form of system of equations describing the motion of compressible, viscous gas. An emphasis is done on the calculation of gaseous microfluidic problems. A fast transient process of gas wave propagation in a two-dimensional microchannel is used as a benchmark problem. The results obtained by using the new method are compared with the numerical solution obtained by using SIMPLE (iterative) and PISO (non-iterative) methods. It is shown that the new iterative method is faster than SIMPLE. For the considered problem the new method is slightly faster than PISO as well. Calculated are also some typical microfluidic subsonic and supersonic flows, and the Rayleigh–Bénard convection of a rarefied gas in continuum limit. The numerical results are compared with other analytical and numerical solutions.     

Thermally induced evolution of phase transformations in gas hydrate sediment

Thermally induced evolution of phase transformations is a basic physical-chemical process in the dissociation of gas hydrate in sediment (GHS). Heat transfer leads to the weakening of the bed soil and the simultaneous establishment of a time varying stress field accompanied by seepage of fluids and deformation of the soil. As a consequence, ground failure could occur causing engineering damage or/and environmental disaster. This paper presents a simplified analysis of the thermal process by assuming that thermal conduction can be decoupled from the flow and deformation process. It is further assumed that phase transformations take place instantaneously. Analytical and numerical results are given for several examples of simplified geometry. Experiments using Tetra-hydro-furan hydrate sediments were carried out in our laboratory to check the theory. By comparison, the theoretical, numerical and experimental results on the evolution of dissociation fronts and temperature in the sediment are found to be in good agreement.     

弱光强空间屏蔽光伏明孤子的动态演化特性

在忽略晶体损耗和扩散效应的情况下，讨论了加外电场的光伏光折变晶体中弱光强空间屏蔽光伏明孤子及其演化特性，在弱光强条件下得到了空间屏蔽光伏明孤子的解析解表达式，与运用数值计算的方法所得到的结果十分吻合，该方法解决了以往数值求解动态演化方程时必须先数值求解常数分方程或积分方程的问题，讨论了参量失配情况下空间屏蔽光伏明孤子的动态演化特征。     

单泡超声空化仿真模型的建立及其动力学过程模拟*

为了模拟单泡超声空化的动力学特性,建立了单泡超声空化的有限元仿真模型,基于流体动力学控制方程和流体体积分数模型,利用有限元分析软件模拟了超声驱动下水中单泡的空化动力学过程。结果表明:单泡随时间的演化规律是先缓慢膨胀到最大后迅速塌缩;泡内压强与气体密度变化与单泡体积变化成反比;在膨胀阶段,泡外压强与气体密度沿着泡的径向向外递减;在压缩阶段,泡外在声压垂直方向的压强与气体密度要大于声压激励方向的压强和气体密度。该文分析结果将为超声空化动力学过程模拟及研究提供参考。     

Bubble motion in inclined pipes

Highly nonlinear free-surface flows in vertical, inclined, and horizontal pipes are analyzed. The problem of bubble motion in a vertical pipe is closely related to the Rayleigh-Taylor instability problem. Inclined pipe flows are intensively studied as related to gas and oil transportation. A new theory of motion of large bubbles in pipes is developed. As distinct from previous approaches, which relied on semiempirical methods or numerical fitting, analytical methods of potential theory and complex analysis are used. A careful comparison of 2D and 3D solutions is presented. It is shown that a higher dimensionality may not correspond to a higher bubble velocity. For the first time, free-surface flows in inclined pipes are analyzed by means of direct numerical simulation, which makes it possible to develop a new approach to the Rayleigh-Taylor instability problem (bubbles with wedge-and cone-shaped noses).     

差分干涉CT技术诊断激波管界面不稳定性

对差分干涉计算机层析技术诊断激波加载下气柱界面不稳定性的可行性进行初步理论和实验研究。针对有限投影数的联合代数重建算法,提出了一种新的投影矩阵计算方法,采用特定投影方向,各投影方向具有不同采样间隔。投影方向的对称性和投影线的规律性使计算过程大为减化。用该重建算法对气柱密度场进行数值模拟,结果表明4方向投影能够重建激波作用下气柱演化初期的体密度场,8方向投影基本能够重建演化中期的体密度场。用差分干涉系统对激波管气柱进行3方向诊断的实验结果表明,差分干涉计算机层析技术用于激波冲击下的气柱不稳定性密度场诊断是可行的。     

差分干涉CT技术诊断激波管界面不稳定性

对差分干涉计算机层析技术诊断激波加载下气柱界面不稳定性的可行性进行初步理论和实验研究。针对有限投影数的联合代数重建算法,提出了一种新的投影矩阵计算方法,采用特定投影方向,各投影方向具有不同采样间隔。投影方向的对称性和投影线的规律性使计算过程大为减化。用该重建算法对气柱密度场进行数值模拟,结果表明4方向投影能够重建激波作用下气柱演化初期的体密度场,8方向投影基本能够重建演化中期的体密度场。用差分干涉系统对激波管气柱进行3方向诊断的实验结果表明,差分干涉计算机层析技术用于激波冲击下的气柱不稳定性密度场诊断是可行的。     

Radiation from a short vertical dipole in a metal-backed rod array

Based on an effective medium approach, we investigate the problem of radiation of a short vertical electric dipole embedded in a metal-backed dielectric rod array. We obtain the radiated electromagnetic field in the form of a Sommerfeld integral, and calculate the near and far electric fields for both lossless and lossy rod arrays. The characteristic equation for the guided modes is derived and solved. The guided modes are found to be slow waves and their propagation constants and modal distributions are extracted. All theoretical results are compared with full-wave simulations.     

一种求解逆风下火焰沿柱状燃料传播的数值方法

1引言近十几年来，国内外许多人对火焰沿薄燃料层的传播进行了研究，但很少涉及到火焰沿柱状燃料的传播。图1为所研究问题的物理模型。火焰的传播涉及到气固两相的相互作用，两相界面上存在能量和质量的交换，气相中存在着气气间的化学反应，固相中存在着裂解反应。当参考坐标系团结在火焰前锋上时，该火焰传播问题成为一准稳态问题，燃料以一固定速度供给火焰。2数学模型2．1守恒方程气相的所有守恒方程均服从下列通用方程：其中、，L和一分别表示通用变量、广义扩散系数和广义源项。固相包括：质量守恒方程：。。能量守恒方程：2．2边界…     

Analytical models of lateral power devices with arbitrary vertical doping profiles in the drift region

By solving the 2D Poisson's equation, analytical models are proposed to calculate the surface potential and electric field distributions of lateral power devices with arbitrary vertical doping profiles. The vertical and the lateral breakdown voltages are formulized to quantify the breakdown characteristic in completely-depleted and partially-depleted cases. A new reduced surface field (RESURF) criterion which can be used in various drift doping profiles is further derived for obtaining the optimal trade-off between the breakdown voltage and the on-resistance. Based on these models and the numerical simulation, the electric field modulation mechanism and the breakdown characteristics of lateral power devices are investigated in detail for the uniform, linear, Gaussian, and some discrete doping profiles along the vertical direction in the drift region. Then, the mentioned vertical doping profiles of these devices with the same geometric parameters are optimized, and the results show that the optimal breakdown voltages and the effective drift doping concentrations of these devices are identical, which are equal to those of the uniform-doped device, respectively. The analytical results of these proposed models are in good agreement with the numerical results and the previous experimental results, confirming the validity of the models presented here.