MHD Channel Research Articles

Two-Dimensional Flow inside MHD Ducts with Transverse Asymmetries

D of MHD generator channels, in particular of the diagonally connected type, with appreciable Hall currents Jx (of the order of 1 A/cm) and with appreciable diameters (of the order of 1 m) must give special attention to the transverse flow asymmetries that develop inside the channel due to the pressure gradient normal to the electrode walls that is induced by the presence of Hall currents. In the present work, the compressible turbulent flow of seeded plasma in MHD channels is analyzed by a two-dimensional formulation that solves the equations of motion (including the ymo men turn equation) by an implicit finite difference scheme. The numerical method solves for all the unknowns, including the gasdynamic pressure and pressure gradient, across the channel at every numerical step taken in the streamwise direction. The present work will show that the Hall current density component Jx, if sufficiently large, can cause asymmetries in the mean gas velocity profile and other gasdynamic profiles.

One-Dimensional Equations for MHD Channel Flows

A analysis is made to clarify the physical meanings of the mean variables, the axial variations of which are described by one-dimensional channel flow equations. The analysis is based on the general conservation equations for mass, momentum, and total enthalpy and leads to a) a list of assumptions necessary to get the commonly used one-dimensional equations, and b) the relations between the distributions of the flow parameters over the channel cross section and the mean values.

Effects of homogeneous and heterogeneous reactions on the dispersion of a soluble matter in a MHD channel flow

An analysis of the dispersion of a solute in an incompressible, viscous, electrically conducting fluid flowing between two non-conducting plates, under the action of a transverse magnetic field has been carried out on the assumption of an homogeneous irreversible first-order chemical reaction and heterogeneous reaction. Expressions for the effective Taylor diffusion coefficient have been derived in both cases. It is observed that the effective Taylor diffusion coefficient decreases due to an increase in the homogeneous reaction rate constant and also due to an increase in the heterogeneous reaction at the catalytic walls. An increase in M, the Hartmann number, leads to a decrease in the effective Taylor diffusion coefficient whereas an increase in K, the loading parameter, leads to an increase in the effective Taylor diffusion coefficient.

Effect of Radiative Cooling on the Temperature Distribution in MHD Channel Flows

Effect of Radiative Cooling on the Temperature Distribution in MHD Channel Flows

Investigation of some factors, limiting enthalpy extraction of MHD-generators

Several of the most important factors which influence the efficiency of converting the thermal energy of a plasma flow into electrical energy are discussed and categorized on the basis of an approximate one-dimensional analysis. It is shown that to achieve more than 20–30% enthalpy extraction (thermal efficiency) is a serious scientific and technical problem. In general the realization of this goal involves the utilization of plasma sources with high gas temperature and pressure, acceleration of the plasma to high Mach numbers, utilization of supersonic MHD channels with a moderate divergence ratio together with appropriate techniques to minimize electrode voltage losses and to prevent boundary layer separation and elimination or suppression of effects which arise from this separation. In order to make further progress toward large efficiencies it will be necessary to (1) develop methods for slowing down a supersonic flow as energy is extracted without the formation of shock waves as subsonic velocities are approached, and (2) utilize non-equilibrium ionization phenomena, even in molecular gases.

Experimental study of plasma flow in a disk MHD channel under conditions of spontaneous formation of a current layer

The results of an experimental study of the plasma flow in a disk channel under conditions of strong hydromagnetic interaction are presented. It is shown that if the condition RemH 0 2 /8π≥0.2 is satisfied for the magnetic Reynolds number at some point of the stream, then a current layer develops at that point characterized by a high electric-current density and high conductivity and temperature. The formation of the current layer leads to strong local retardation of the stream, the appearance of a shock wave, and a number of other nonlinear hydromagnetic phenomena. The experimental results are in agreement with theoretical studies conducted earlier.

Temperature Distributions of MHD Channel Flows with Finite width

Temperature Distributions of MHD Channel Flows with Finite width

Experimental Study of Mixed Convection Heat Transfer in an MHD Channel

Experimental Study of Mixed Convection Heat Transfer in an MHD Channel

Influence of hall effect and ion slip on velocity and temperature fields in an MHD channel

The combined influence of viscosity, Hall effect and ion slip on hydrodynamic fields and on heat transfer is investigated. The exact solutions for velocity, induced magnetic field and temperature are derived for the laminar MHD flow in a flat channel assuming a small magnetic Reynolds number, finely segmented electrodes, fully developed flow and uniform heat flux at channel walls. The internal generation of heat is not considered. The Kantorowitsch method of variational calculus is employed to approximate the complicated velocity distribution.

Combined forced and free convection MHD channel flow in entrance region

The entrance problem of convective magnetohydrodynamic channel flow between two parallel plates subjected simultaneously to an axial temperature gradient and a pressure gradient is investigated numerically. Both constant heat flux and constant wall temperature cases are considered. The solutions match to the fully developed solutions after a certain entrance length. It is found that an applied transverse magnetic field may reduce the entrance length of the velocity considerably, but has little effect on the temperature development. At high Hartmann number, the velocity entrance length is inversely proportion to M 2 as it was predicted by Shercliff in the absence of free convection. However, a sufficient large free convection may prolong the developing process considerably.

Effect of Plasma Injection on Cold Wall Type MHD Generator

It is known that a cold wall type MHD generating channel has a sufficient durability, but on the other hand it has large electrode losses. In order to improve the generating performance the idea of the electrode boundary layer control is introduced the MHD channel. The plasma injection method is selected as the most available one. The experiments are carried out varying the injected-to-mainstream mass flow ratios. The results indicated that a remarkable improvement can be obtained. The generalized representations of this effect on the MHD generating performance have been established by means of the ideal model.

Boundary Layer Cooling Effect on Semi-Hot Wall Type MHD Channel

In an MHD channel a cold thermal boundary layer is induced above a cold wall, and if the adiabatic wall were placed following the cold wall, it might be kept cool due to the effect of the upstream cold layer. This effect can be called the boundary layer cooling effect, which may be applied to a semi-hot type MHD channel. Numerical calculations of the energy equation and approximate theory by using the heat-flow balance represented the dependency of the adiabatic surface temperature on the various upstream conditions. It is concluded that the appropriate selection of the width and the surface temperature of the upstream cold wall can set the surface temperature of the adiabatic wall in a semi-hot temperature region by this cooling method. Moreover, the experiments using an MHD channel confirmed this effect, and the surface temperature reached a temperature in the semi-hot temperature region.

Influence of Segmentation and Ambipolar diffusion on MHD Nonequilibrium Boundary Layers

The compressible laminar and turbulent boundary-layer equations representing the fiow of cesium seeded argon plasma over successive segments of the cathode wall of an MHD channel were investigated and solved for both finite and intinite rates of reaction. The equations solved include the electron energy and the electron continuity equations as well as the usual global boundary-layer equations. The effects of finite rates of reaction and ambipolar diffusion are considered, and the inner boundary conditions for both the electron energy and the electron continuity equations are obtained by investigating a sheath analysis. The governing equations are solved using a finite-difference scheme without introducing a local similarity assumption. The finite rate results are considerably different from the infinite rate ones. The main reason is the ambipolar diffusion which depletes the electrons near the wall. No special problems have been found in the solution of the turbulent flow equations. This is due to the high mobility of electrons. (auth)

Structure of a collisionless boundary layer and turbulent damping of ions

The flow of a low-pressure plasma in a MHD channel is unstable in a number of cases. The instability can be caused by a current flowing across the magnetic field. In this study we investigate an unstable, turbulent flow of a rarefied plasma near the “magnetized electrodes,” representing plane magnetic dipoles. Owing to the growth of microscopic turbulence near the electrodes, the maximum density of the current that is induced in the plasma is localized and turbulent damping of the incoming flow occurs. The energy of damping goes into the turbulent heating of the plasma. Under these conditions a structure of the boundary layer is found for a stationary flow. The characteristic transverse dimension of the boundary layer is considerably less than the particle mean free path; therefore, such a boundary layer can be called “collisionless.”

Calculation of plane electric fields in channels of magnetohydrodynamic instruments

The local and integral characteristics of flat MHD channels are studied with allowance for longitudinal and transverse edge effects and heterogeneities in the distributions of conductivity and stream velocity. An analysis is made of the effect of the finite dimensions of the insulating inserts in the longitudinal edge effect and of the modular construction of the side wall in the transverse edge effect on the output parameters of MHD channels. The solution of the problem is based on reduction of the initial quasilinear elliptical equation for the electrical potential with allowance for Ohm's law to an integral equation of the Fredholm type relative to the current density.

Dissipative effect on convective MHD channel flow

By means of a numerical analysis viscous and Joulean dissipations are considered in a combined forced and free convective MHD flow between two vertical plates that are subjected simultaneously to a pressure and a temperature gradient. It is shown that the dissipations tend to increase the flow rate and decrease the heat transfer, and they destabilize the system when the high temperature is at the lower side.

The boundary layers of a fully ionized two-temperature plasma with given component temperatures at an electrode

The flow of a plasma with different component temperatures in the boundary layers at the electrodes of an MHD channel is investigated without any assumptions as to self-similarity. For the calculation of the electron temperature, the full energy equation for an electron gas [1] is solved with allowance for the estimates given in [2]. In contrast to [3, 4], the calculation includes the change in temperature of electrons and ions along the channel caused by the collective transport of energy, the work done by the partial pressure forces, and the Joule heating and the energy exchange between the components. The problem of the boundary layers in the flow of a two-temperature, partially ionized plasma past an electrode is solved in simplified form by the local similarity method in [5–7]. In these papers, either the Kerrebrock equation is used [5, 6] or the collective terms are omitted from the electron energy equation [7].

Electric field in a MHD channel of rectangular cross section in the presence of the hall effect: PMM vol. 37, n≗3, 1973, pp. 459–468

The present paper deals with the spatial distribution of the electrostatic potential in a channel with two electrodes in the presence of the Hall effect. The velocity profile is inhomogeneous and corresponds to the velocity diminishing down to zero at the channel walls. The problem of determining the electric field in the channel is reduced to that of solving a boundary value problem with mixed boundary conditions for an elliptic type equation. One of the versions of the Wiener-Hopf method is used in the course of solution. The three-dimensional distribution of the electric field in a MHD channel has been studied, because of considerable difficulties of mathematical nature encountered, only for the simplest cases of isotropically conducting media, i. e. for the cases when the walls have uniform conducting properties, or when an electrode zone is present in the channel [1–7]. For the anisotropic conductivity of the medium only plane problems have been studied [8, 9].

On heat transfer in mhd channel flow

On heat transfer in mhd channel flow

Investigation of the boundary layers of a fully ionized two-temperature plasma on the nonconducting wall of a MHD channel

Investigation of the boundary layers of a fully ionized two-temperature plasma on the nonconducting wall of a MHD channel