Stabilization of plasma flow in a transverse magnetic field

Results are given of a theoretical and experimental investigation of the intensive interaction between a plasma flow and a transverse magnetic field. The calculation is made for problems formulated so as to approximate the conditions realized experimentally. The experiment is carried out in a magneto-hydrodynamic (MHD) channel with segmented electrodes (altogether, a total of 10 pairs of electrodes). The electrode length in the direction of the flow is 1 cm, and the interelectrode gap is 0.5 cm. The leading edge of the first electrode pair is at x = 0. The region of interaction (the region of flow) for 10 pairs of electrodes is of length 14.5 cm. An intense shock wave S propagates through argon with an initial temperature T_o = 293 °K and pressure p_o = 10 mm Hg. The front S moves with constant velocity in the region x < 0 and at time t = 0 is at x = 0. The flow parameters behind the incident shock wave are determined from conservation laws at its front in terms of the gas parameters preceding the wave and the wave velocity W_S. The parameters of the flow entering the interaction region are as follows: temperature T ₀ ¹ = 10,000 °K, pressure P ₀ ¹ = 1.5 atm, conduction ₀ ¹ = 3000 ^–1·m^–1, velocity of flow u ₀ ¹ = 3000 m·sec^–1, velocity of sounda ₀ ¹ = 1600 m·sec^–1, degree of ionization = 2%, 0.4. The induction of the transverse magnetic field B = [0, B_y(x), 0] is determined only by the external source. Induced magnetic fields are neglected, since the magnetic Reynolds number Re_m 0.1. It is assumed that the current j = (0, 0, jz) induced in the plasma is removed using the segmented-electrode system of resistance R_e. The internal plasma resistance is R_i = h(A)^–1 (h = 7.2 cm is the channel height; A = 7 cm² is the electrode surface area). From the investigation of the intensive interaction between the plasma flow and the transverse magnetic field in [1–6] it is possible to establish the place x* and time t* of formation of the shock discontinuity formed by the action of ponderomotive forces (the retardation wave R_T), its velocity W_T, and also the changes in its shape in the course of its formation. Two methods are used for the calculation. The characteristic method is used when there are no discontinuities in the flow. When a shock wave R_T is formed, a system of nonsteady one-dimensional equations of magnetohydrodynamics describing the interaction between the ionized gas and the magnetic field is solved numerically using an implicit homogeneous conservative difference scheme for the continuous calculation of shock waves with artificial viscosity [2].Translated from Izvestiya Akademiya Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 112–118, September–October, 1977.     

Boundary conditions on a shock wave in a supersonic flow

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 49–56, January–February, 1989.     

液滴对爆炸冲击波的衰减作用

为分析液滴对舰船舱内爆炸冲击波的耗散与衰减作用,通过有限元分析方法,建立冲击波作用于不同尺寸单个液滴和多排液滴的模型,分析冲击波与单个及多个液滴的作用过程及液滴形态变化,对冲击波衰减规律进行分析总结。得到结论如下:单个液滴模型中,小液滴破碎更迅速,破碎的规律性强;大液滴抛撒现象发生较早,抛撒出的小液滴数目多,但整体变化规律性偏差;不同尺寸单个液滴对冲击波有一定的衰减作用,衰减率随液滴尺寸增大而增大,线性规律较明显;成排液滴对冲击波有明显的衰减作用,相同液滴密度下衰减率随着液滴数量的增多而增大,呈现明显的线性特性。     

Attenuation of a shock wave passing through a cloud of water droplets

The mitigation of a planar shock wave caused by a cloud of calibrated water droplets was studied both experimentally and numerically. Experiments were carried out, with different shock wave Mach numbers ranging from 1.1 to 1.8, in a vertical shock tube coupled with a droplet generator which produced a well-characterized cloud of droplets of 120, 250 and 500 μm in diameter. By exploiting such an experimental set-up, we successfully measured the attenuation of a normal shock wave when passing through the water droplet cloud. This series of experiments allowed to identify the main parameters of this investigation and a clear dependence between the attenuation of the shock wave and terms governing the regimes of droplet breakup has been found. On the other hand, to support this experimental approach, 1D unsteady calculations were performed in similar configurations. Although the mathematical model based on an Eulerian/Eulerian approach was actually incomplete, the first comparisons between the experiments and the simulations were rather interesting and pointed out the need to improve the physical model, by taking into account the fragmentation and the vaporization of the droplets submitted to the shock wave as well as the size distribution of the water spray.     

Flowfield characteristics of a transverse jet into supersonic flow with pseudo-shock wave

We performed an experimental investigation of the flowfield of a transverse jet into supersonic flow with a pseudo-shock wave (PSW). In this study, we injected compressed air as the injectant, simulating hydrocarbon fuel. A back pressure control valve generated PSW into Mach 2.5 supersonic flow and controlled its position. The positions of PSW were set at nondimensional distance from the injector by the duct height (x/H) of ?1.0, ?2.5, and ?4.0. Particle image velocimetry (PIV) gave us the velocity of the flowfield. Mie scattering of oil mist only with the jet was used to measure the spread of the injectant. Furthermore, gas sampling measurements at the exit of the test section were carried out to determine the injectant mole fraction distributions. Gas sampling data qualitatively matched the intensity of Mie scattering. PIV measurements indicated that far-upstream PSW decelerated the flow speed of the main stream and developed the boundary layer on the wall of the test section. The flow speed deceleration at the corner of the test section was remarkable. The PSW produced nonuniformity in the main stream and reduced the momentum flux of the main stream in front of the injector. The blowing ratio, defined as the square root of the momentum flux ratio, of the jet and the main stream considering the effect of the boundary layer thickness was shown to be a useful parameter to explain the jet behavior.     

Stability of a plane,ionizing shock wave in a magnetic field

It is shown that with a constant transverse magnetic field present, a plane, ionizing, gas-dynamical shock wave becomes more stable with respect to small displacements of its front from the equilibrium position.Moscow. Translated from Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 122–128, January–February, 1972.     

Nonstationary conducting free flow in a transverse magnetic field

In magnetohydrodynamic flow the viscous friction at the walls can be substantial. The role of viscous friction can be considerably reduced by using a free or a semirestricted flow of the conducting fluid. Nonstationary phenomena in one-dimensional motion of a free plane incompressible fluid flow in a transverse magnetic field are examined. The narrow sides of the flow come into contact with the sectional electrodes connected through external circuits with an active-inductive load. The magnetic Reynolds number and the magnetody-dynamic interaction parameter are assumed to be large. When the electric field due to electromagnetic induction in the channel is much smaller than the field due to the external circuits, the problem can be reduced to the characteristic Cauchy problem for a quasilinear hyperbolic system of first-order equations which can be solved by the method of characteristics using a computer.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 34–39, July–August, 1970.     

Local properties of vertical mercury-argon two-phase flow in a circular tube under transverse magnetic field

Experimental data are presented in this paper on the profiles of local void fraction, bubble impaction rate, bubble velocity and its spectrum, and also bubble length and its spectrum, of mercury-argon two-phase slug flow flowing upwards in a vertical circular tube in the presence of a transverse magnetic field. Decrease in void fraction and increase in bubble velocity are significant when the magnetic flux density is larger than $\text{0.3～0.4}$$\text{T}\text{(Ha ? 100)}$. This effect is discussed by analyzing the bubble size distribution. Recovery of local void fraction profile in the downstream of an obstacle and diffusion of void injected from only one nozzle in the presence of magnetic field are also discussed.     

Unsteady incompressible Couette flow in a uniform transverse magnetic field

Summary The unsteady plane Couette flow of an incompressible, viscous and infinitely conducting fluid in a uniformly imposed transverse magnetic field is studied. The problem is solved in general in a series form by means of a finite Fourier transform, and explicit solutions for two special cases are worked out.     

On the flow of a Bingham fluid passing through an electric field

We study the action of an electric field on a Bingham fluid from the point of view of existence and uniqueness of solutions. We also give an upper bound for the stopping time.     

Quantification of the effect of surface heating on shock wave modification by a plasma actuator in a low-density supersonic flow over a flat plate

This paper describes experimental and numerical investigations focused on the shock wave modification induced by a dc glow discharge. The model is a flat plate in a Mach 2 air flow, equipped with a plasma actuator composed of two electrodes. A weakly ionized plasma was created above the plate by generating a glow discharge with a negative dc potential applied to the upstream electrode. The natural flow exhibited a shock wave with a hyperbolic shape. Pitot measurements and ICCD images of the modified flow revealed that when the discharge was ignited, the shock wave angle increased with the discharge current. The spatial distribution of the surface temperature was measured with an IR camera. The surface temperature increased with the current and decreased along the model. The temperature distribution was reproduced experimentally by placing a heating element instead of the active electrode, and numerically by modifying the boundary condition at the model surface. For the same surface temperature, experimental investigations showed that the shock wave angle was lower with the heating element than for the case with the discharge switched on. The results show that surface heating is responsible for roughly 50 % of the shock wave angle increase, meaning that purely plasma effects must also be considered to fully explain the flow modifications observed.     

Interaction of a supersonic flow with a transverse jet injected through a circular aperture in a plate

A flow pattern created by the interaction of a supersonic flow with a transverse sonic or supersonic jet injected normally to the direction of the main flow through a circular aperture in a plate is considered. The pressure rises in front of the jet owing to the retarding action of the incident flow. The boundary layer building up on the wall in front of the injection nozzle is accordingly detached. The flow pattern in the region of interaction between the jet and the external flow is illustrated in Fig. 1. The three-dimensional zone of detachment thus formed deflects the incident flow from the wall, and in front of the jet a complicated system of sharp jumps in contraction develops. A three-dimensional system of jumps also develops in the jet itself.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No, 5, pp. 193–197, September–October, 1970.     

Rayleigh problem in slip flow with transverse magnetic field

An analytical continuum solution of the Rayleigh problem in slip flow with applied magnetic field is obtained using a modified initial condition and slip boundary conditions. The results are uniformly valid for all times and show that the velocity slip and the local skin friction coefficient remain almost unaffected by the imposition of the magnetic field for small times. They increase however with the magnetic field for large times. The present results reduce to the corresponding results of the hydrodynamic case when there is no magnetic field.Nomenclature A constant - b characteristic length - B magnetic field vector - B ₀ magntidue of the applied magnetic field normale to the plate - B _x magnitude of the induced magnetic field parallel to the plate - C slip coefficient, (2–f)/f - C _f skin friction coefficient, - C _D average drag coefficient - erfc(_x) complementary error function, - E electric field vector - f Maxwell's reflection coefficient - H _a Hartmann number, (B ₀ ² b ²/)^1/2 - nondimensional magnetic parameter - J current vector - Kn=L/b Knudsen number - L mean free path - M Mach number - p constant parameter - P _m magnetic Prandtl number, Re _m/Re= ₀ - q velocity vector - Re Reynolds number, Ub/ - Re _m magnetic Reynolds number, ₀ Ub - t time - nondimensional time, tU/b - u velocity of the fluid parallel to the plate - nondimensional velocity, u/U - U velocity of the plate - Laplace transform of - x, y coordinates along and normal to the plate respectively - y nondimensional distance, y/b - Z nondimensional parameter, 1/Re ^1/2 Kn - ratio of specific heats - boundary layer thickness - velocity slip - viscosity - ₀ magnetic permeability - kinematic viscosity - nondimensional time parameter, ( /Re)^1/2/Kn - density - electrical conductivity