Magnetohydrodynamics equilibrium of a self-confined elliptic plasma ball

A variational principle is applied to the problem of magnetohydrodynamics (MHD) equilibrium of a self-contained elliptical plasma ball, such as elliptical ball lightning. The principle is appropriate for an approximate solution of partial differential equations with arbitrary boundary shape. The method reduces the partial differential equation to a series of ordinary differential equations and is especially valuable for treating boundaries with nonlinear deformations. The calculations conclude that the pressure distribution and the poloidal current are more uniform in an oblate self-confined plasma ball than that of an elongated plasma ball. The ellipticity of the plasma ball is obviously restricted by its internal pressure, magnetic field, and ambient pressure. Qualitative evidence is presented for the absence of sighting of elongated ball lightning.

Parallel Fully-Implicit Computation of Magnetohydrodynamics Acceleration Experiments

A three-dimensional MHD solver is described in the paper. The solver simulates reacting flows with nonequilibrium between translational-rotational, vibrational and electron translational modes. The conservation equations are discretized with implicit time marching and the second-order modified Steger-Warming scheme, and the resulted linear system is solved iteratively with Newton-Krylov-Schwarz method that is implemented by PETS,: package. The results of convergence tests arc plotted, which show good scalability and convergence around twice faster when compared with the DPLR method. Then five test runs are conducted simulating the experiments done at the NASA Ames MHD channel, and the calculated pressures, temperatures, electrical conductivity, back EMF, load factors and flow accelerations are shown to agree with the experimental data. Our computation shows that the electrical conductivity distribution is not uniform in the powered section of the MHD channel, and that it is important to include Joule heating in order to calculate the correct conductivity and the MHD acceleration.

Viscosity-induced mode splitting and potential energy criterion for mode stability

This paper points out that viscosity can induce mode splitting in a uniform infinite cylinder of an incompressible fluid with self-gravitation, and that the potential energy criterion cannot be appropriate to all normal modes obtained, i.e., there will be stable modes with negative potential energy (<0). Therefore the condition >0 is not necessary, although sufficient, for the stability of a mode in an incompressible static fluid or magnetohydrodynamics (MHD) system, which is a correction of both Hare's [Philos. Mag. 8, 1305 (1959)] and Chandrasekhar's [Hydrodynamic and Hydromagnetic Stability (Oxford U.P., Oxford, 1961), p. 604] stability criterion for a mode. These results can also be extended to compressible systems with a polytropic exponent.

Effects of Thermocapillary Convection on the Growth Process in Industrial 8-inch Silicon Czochralski Growth

Czochralski (CZ) crystal growth process is a widely used technique in manufacturing of silicon crystals and other semiconductor materials. The ultimate goal of the IC industry is to have the highest quality substrates, which are free of point defect, impurities and micro defect clusters. The scale up of silicon wafer size from 200 mm to 300 mm requires large crucible size and more heat power. Transport phenomena in crystal growth processes are quite complex due to melt and gas flows that may be oscillatory and/or turbulent, coupled convection and radiation, impurities and dopant distributions, unsteady kinetics of the growth process, melt crystal interface dynamics, free surface and meniscus, stoichiometry in the case of compound materials. A global model has been developed to simulate the temperature distribution and melt flow in an 8-inch system. The present program features the fluid convection, magnetohydrodynamics, and radiation models. A multi-zone method is used to divide the Cz system into different zones, e.g., the melt, the crystal and the hot zone. For calculation of temperature distribution, the whole system inside the stainless chamber is considered. For the convective flow, only the melt is considered. The widely used zonal method divides the surface of the radiation enclosure into a number of zones, which has a uniform distribution of temperature, radiative properties and composition. The integro-differential equations for the radiative heat transfer are solved using the matrix inversion technique. The zonal method for radiative heat transfer is used in the growth chamber, which is confined by crystal surface, melt surface, heat shield, and pull chamber. Free surface and crystal/melt interface are tracked using adaptive grid generation. The competition between the thermocapillary convection induced by non-uniform temperature distributions on the free surface and the forced convection by the rotation of the crystal determines the interface shape, dopant distribution, and striation pattern. The temperature gradients on the free surface are influenced by the effects of the thermocapillary force on the free surface and the rotation of the crystal and the crucible.

Effects of Magnetohydrodynamic Interaction-Zone Position on Shock-Wave/Boundary-Layer Interaction

A third-order weighted essentially nonoscillatory and non-free-parameter difference scheme magnetohydrodynamic solver has been established to investigate the mechanisms of magnetohydrodynamics controlling separation induced by an oblique shock wave impinging on a flat plate. The effects of magnetohydrodynamic interaction-zone location on the separation point, reattachment point, separation-bubble size, and boundary-layer velocity profiles are analyzed. The results show that there exists a best location for the magnetohydrodynamic zone to be applied, where the separation point is delayed the farthest, and the separation bubble is decreased up to about 50% in size compared to the case without magnetohydrodynamic control, which demonstrated the promising of magnetohydrodynamics suppressing the separation induced by shock-wave/boundary-layer interactions.

MHD控制激波诱导湍流边界层分离的机理分析

为了研究磁流体动力学(Magnetohydrodynamics:MHD)加速边界层对激波-湍流边界层相互作用的影响,用高阶有限差分法求解了小磁雷诺数近似的MHD湍流方程.其中,无粘通量采用WENN格式离散、粘性通量采用Roe平均中心差分离散,时间采用半隐式推进,并采取追赶法求解.计算给出了湍流、电场、磁场和电导率等参数对边界层分离的影响,数值结果显示:在同样的逆压梯度下,湍流边界层分离能更快地趋于稳态流场,且分离区比层流小;通过施加洛仑兹力加速,边界层速度型面变得更加饱满、位移厚度减小、分离点和再附点向激波与固壁的交点靠近,分离区尺寸减小甚至最终被消除.