Unsteady three-dimensional model of electric arc. Part 2. Verification

Numerical computations of the electric arc in the external magnetic field have been done for testing the unsteady three-dimensional mathematical model. The arc of a conical and helical shape has been implemented numerically. A satisfactory agreement of the computational results with experimental data points overall to the correctness of the mathematical model and of the computational algorithm.     

Numerical modelling of unsteady heating and melting of the anode by electric arc. Part 1. Mathematical model and computed characteristics of the arc column

The two-dimensional mathematical model in the approximation of a partial local thermodynamic equilibrium of plasma and the technique for numerical computation of the unsteady electric arc characteristics, including the conjugate heat exchange of the electric-arc plasma flow with the treated product (anode) are considered. The results of overall testing of the numerical algorithm point to the correctness of the model and computational technique. The results of the computation of the arc characteristics from the conventional ignition moment until the passage to stationary regime are presented. It is found that a single thermal torus, which scatters fairly quickly in the ambient medium, forms around the arc column.     

Transient vibration phenomena in deep mine hoisting cables. Part 1: Mathematical model

The classical moving co-ordinate frame approach and Hamilton's principle are employed to derive a distributed-parameter mathematical model to investigate the dynamic behaviour of deep mine hoisting cables. This model describes the coupled lateral-longitudinal dynamic response of the cables in terms of non-linear partial differential equations that accommodate the non-stationary nature of the system. Subsequently, the Rayleigh-Ritz procedure is applied to formulate a discrete mathematical model. Consequently, a system of non-linear non-stationary coupled second order ordinary differential equations arises to govern the temporal behaviour of the cable system. This discrete model with quadratic and cubic non-linear terms describes the modal interactions between lateral oscillations of the catenary cable and longitudinal oscillations of the vertical rope. It is shown that the response of the catenary-vertical rope system may feature a number of resonance phenomena, including external, parametric and autoparametric resonances. The parameters of a typical deep mine winder are used to identify the depth locations of the resonance regions during the ascending cycles with various winding velocities.     

Air flow control around a cylindrical model induced by a rotating electric arc discharge in an external magnetic field. Part I

The structure and dynamics of a near-wall gas flow produced by a rotating electric arc discharge in an external magnetic field around a cylindrical model without an incoming flow has been investigated. The electric arc on the model has been produced by a combined electric discharge (low-current rf discharge + high-current pulse-periodic discharge). Permanent magnets with induction B ≈ 0.1 T have been placed inside the cylindrical models. Ring electrodes are arranged on the surface of the model. The structure and dynamics of the near-wall gas flow around the cylindrical model have been investigated using high-speed photography, as well as the shadowgraph and particle image velocimetry (PIV) methods.     

Air flow control around a cylindrical model induced by a rotating electric arc discharge in an external magnetic field. Part II

The effect of twisting a near-wall gas flow around a cylindrical model induced by a magnetoplasma actuator on the external subsonic flow around this model has been studied.     

引入6波段P-1辐射模型的三维空气电弧等离子体数值分析

引入了6波段P-1辐射模型,对三维空气电弧等离子体进行了仿真分析.其特点是不仅考虑了热辐射的发射问题,同时考虑了等离子体内热辐射的自吸收问题.通过计算获得了空气电弧等离子体温度和辐射能量的分布并进行了相应的分析.与净辐射系数方法相比较,P-1模型获得的温度分布较宽,其弧柱电压值更接近于实验测量值.研究表明,6波段P-1辐射模型能够更精确地求解空气电弧等离子体的辐射问题. 关键词： 热辐射 P-1模型 空气电弧等离子体 磁流体动力学     

Mathematical model of calibration curve and results of spectral analysis

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 51, No. 5, pp. 805–810, November, 1989.     

Mathematical structure of the three-dimensional（3D） Ising model

An overview of the mathematical structure of the three-dimensional(3D) Ising model is given from the points of view of topology,algebra,and geometry.By analyzing the relationships among transfer matrices of the 3D Ising model,Reidemeister moves in the knot theory,Yang-Baxter and tetrahedron equations,the following facts are illustrated for the 3D Ising model.1) The complex quaternion basis constructed for the 3D Ising model naturally represents the rotation in a(3+1)-dimensional space-time as a relativistic quantum statistical mechanics model,which is consistent with the 4-fold integrand of the partition function obtained by taking the time average.2) A unitary transformation with a matrix that is a spin representation in 2 n·l·o-space corresponds to a rotation in 2n·l·o-space,which serves to smooth all the crossings in the transfer matrices and contributes the non-trivial topological part of the partition function of the 3D Ising model.3) A tetrahedron relationship would ensure the commutativity of the transfer matrices and the integrability of the 3D Ising model,and its existence is guaranteed by the Jordan algebra and the Jordan-von Neumann-Wigner procedures.4) The unitary transformation for smoothing the crossings in the transfer matrices changes the wave functions by complex phases φx,φy,and φz.The relationship with quantum field and gauge theories and the physical significance of the weight factors are discussed in detail.The conjectured exact solution is compared with numerical results,and the singularities at/near infinite temperature are inspected.The analyticity in β=1/(kBT) of both the hard-core and the Ising models has been proved only for β0,not for β=0.Thus the high-temperature series cannot serve as a standard for judging a putative exact solution of the 3D Ising model.     

Numerical modelling of unsteady heating and melting of the anode by electric arc. Part 2. Numerical characteristics of the anode weldpool

Numerical computations of the electric-arc heating and anode melting were carried out within the framework of the two-dimensional unsteady mathematical model. The influence of the viscous interaction ??plasma-melt??, surface tension forces, electromagnetic forces, and gravitational convection on the formation of the hydrodynamics of the anode melt was considered.     

Estimation of energetic efficiency of heat supply in front of the aircraft at supersonic accelerated flight. Part II. Mathematical model of the trajectory boost part and computational results

The fuel economy was estimated at boost trajectory of aerospace plane during energy supply to the free stream. Initial and final velocities of the flight were given. A model of planning flight above cold air in infinite isobaric thermal wake was used. The comparison of fuel consumption was done at optimal trajectories. The calculations were done using a combined power plant consisting of ramjet and liquid-propellant engine. An exergy model was constructed in the first part of the paper for estimating the ramjet thrust and specific impulse. To estimate the aerodynamic drag of aircraft a quadratic dependence on aerodynamic lift is used. The energy for flow heating is obtained at the sacrifice of an equivalent decrease of exergy of combustion products. The dependencies are obtained for increasing the range coefficient of cruise flight at different Mach numbers. In the second part of the paper, a mathematical model is presented for the boost part of the flight trajectory of the flying vehicle and computational results for reducing the fuel expenses at the boost trajectory at a given value of the energy supplied in front of the aircraft. Sections, formulas, and figures have a numbering continued from the first part of the paper printed in the journal “Thermophysics and Aeromechanics”, 2008, Vol. 15, No. 4, P. 537–548.     

Radiation of electric arc burning in argon

Using real experimentally obtained integral values, the paper deals with modelling of electric arc stabilised by flowing gas. Attention is focused namely on approximate estimation of radiation coefficient of argon. A designed model of electric arc burning in argon of atmospheric pressure inside arc heater’s anode channel is described. The model makes it possible to compute axial and/or radial dependencies of some quantities of interest (temperature, velocity, electric field intensity, arc radius, etc.), and subsequently to judge energy exchange between the arc and its surroundings. Sets of model’s input data, including arc voltage, arc current, argon flow-rate, and flow-rates and temperatures of water cooling individual parts of the arc heater, have been measured during numerous experiments. In a studied case with relatively high argon flow-rate, radiation has been found to be prevailing mechanism of energy transfer from arc to anode channel walls. Based on this finding, techniques have been designed for simple approximate estimation of radiation coefficient of argon in a limited extent of temperatures. As an example, they have been tested on a particular set of measured and computed data. Argon radiation coefficient estimated in this way has been compared with the results of theoretical computations carried out by other authors. Considering simplifications used and differences between a real situation and an ideal theoretical model, agreement of the results is within satisfactory limits.     

Dynamic behaviour of electric arc gas discharge

The time-dependent energy and circuit equations are solved numerically to obtain temperature profiles, current-voltage characteristics and electric field strength vs axial temperature diagrams in the asymptotic region of a wall-stabilized electric arc operated in nitrogen. Dynamic current-voltage characteristics and transient phenomena of the formation of the stationary state during the spark ignition phase are studied. The arc timeconstant for free decay is computed and compared with approximate analytical results. It is found that for fixed initial conditions the arc response to the variable applied voltage is several times longer than the arc time-constant for free decay.The author is grateful to Dr. Z. Sedláek, Dr. M. Hrabovský and Dr. R. Klíma for their stimulating advices and helpful comments.     

Part II. Algebraic tails in three-dimensional quantum plasmas

We review various exact results concerning the presence of algebraic tails in three-dimensional quantum plasmas. First, we present a solvable model of two quantum charges immersed in a classical plasma. The effective potential between the quantum charges is shown to decay as 1/r ⁶ at large distances r. Then, we mention semiclassical expansions of the particle correlations for charged systems with Maxwell-Boltzmann statistics and short-ranged regularization of the Coulomb potential. The quantum corrections to the classical quantities, from orderh ⁴ on, also decay as 1/r ⁶. We also give the result of an analysis of the charge correlation for the one-component plasma in the framework of the usual many-body perturbation theory; some Feynman graphs beyond the random phase approximation display algebraic tails. Finally, we sketch a diagrammatic study of the correlations for the full many-body problem with quantum statistics and pure 1/r interactions. The particle correlations are found to decay as 1/r ⁶, while the charge correlation decays faster, as 1/r ¹⁰. The coefficients of these tails can be exactly computed in the low-density limit. The absence of exponential screening arises from the quantum fluctuations of partially screened dipolar interactions.     

Time-spatial structure of an electric arc anode region

This paper studies the anode region of an eroding anode with a nonstationary arc-root attachment. High-current free-burning short as well as long arcs at atmospheric pressure are investigated. A technique to study the anode region of the arc is suggested. An anode moving perpendicular to the arc axis was used for estimating parameters of the anode jets at a given moment of their development. The mechanism of current transfer in the anode region is considered on the basis of electrophysical and optical-spectroscopic investigations of the arc attachment traces and plasma parameters both of the anode jet and arc column. The anode jet was found to be of importance in the stationary arc operation. The near-anode plasma parameters depend on the effect of the cathode jet. In short arcs (L_a~2 mm), the plasma temperature at the anode exceeds 20000 K, while in long arcs (L_a >50 mm), it falls below 7000 K. At plasma temperature T_a >11000 K, the total arc current in the anode region is transferred through the arc plasma, while at lower temperatures, both the arc column and the anode jet take part in the current transfer     

Cold-hollow-cathode arc discharge in crossed electric and magnetic fields

A crossed-field cold-hollow-cathode arc is stable at low working gas pressures of 10⁻²–10⁻¹ Pa, magnetic-field-and gas-dependent arcing voltages of 20–50 V, and discharge currents of 20–200 A. This is because electrons come from a cathode spot produced on the inner cathode surface by a discharge over the dielectric surface. The magnetic field influences the arcing voltage and discharge current most significantly. When the plasma conductivity in the cathode region decreases in the electric field direction, the magnetic field increases, causing the discharge current to decline and the discharge voltage to rise. The discharge is quenched when a critical magnetic field depending on the type of gas is reached. Because of the absence of heated elements, the hollow cathode remains efficient for long when an arc is initiated in both inert and chemically active gases.     

Processes and properties of electric arc stabilized by water vortex

Experimental investigation of an electric arc stabilized by a water vortex was carried out in a DC arc plasma torch for the power range 90-200 kW. Volt-ampere characteristics of the arc as well as the power balance were determined separately for the part of the arc column stabilized by water and for the remaining part between the nozzle exit and the external anode. The temperature of arc plasma close to the nozzle exit was determined by emission spectroscopy. Negatively biased electric probes in the ion collecting regime were used for determination of the plasma flow velocity. The measured temperatures up to 27000 K, and velocities up to 7 km/s are higher than the values commonly reported for plasma torches with DC arcs stabilized by a gas flow. Mass and energy balances within the arc chamber were determined from the experimental results. The radial transport of the energy by radiation was identified as a decisive process controlling the arc and plasma properties. The balance of radial energy transport was studied. The ratio of energy spent for evaporation of the water to the energy absorbed in the evaporated mass is very low in the water stabilized arc. This is the principal cause of high plasma temperatures and velocities found by the measurements     

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