Showing papers on "Hartmann number published in 1990"

Numerical simulation of liquid-metal MHD flows in rectangular ducts

Abstract: To design self-cooled liquid metal blankets for fusion reactors, one must know about the behaviour of MHD flows at high Hartmann numbers. In this work, finite difference codes are used to investigate the influence of Hartmann number M, interaction parameter N, wall conductance ratio c, and changing magnetic field, respectively, on the flow.As liquid-metal MHD flows are characterized by thin boundary layers, resolution of these layers is the limiting issue. Hartmann numbers up to 103 are reached in the two-dimensional case of fully developed flow, while in three-dimensional flows the limit is 102. However, the calculations reveal the main features of MHD flows at large M. They are governed by electric currents induced in the fluid. Knowing the paths of these currents makes it possible to predict the flow structure.Results are shown for two-dimensional flows in a square duct at different Hartmann numbers and wall conductivities. While the Hartmann number governs the thickness of the boundary layers, the wall conductivities are responsible for the pressure losses and the structure of the flows. The most distinct feature is the side layers where the velocities can exceed those at the centre by orders of magnitude.The three-dimensional results are also for a square duct. The main interest here is to investigate the redistribution of the fluid in a region where the magnetic field changes. Large axial currents are induced leading to the ‘M-shaped’ velocity profiles characteristic of MHD flow. So-called Flow Channel Inserts (FCI), of great interest in blanket design, are investigated. They serve to decouple the load carrying wall from the currents in the fluid. The calculations show that the FCI is indeed a suitable measure to reduce the pressure losses in the blanket.

Free convection effects on HMD horizontal channel flow with Hall currents

Abstract: An exact solution of MHD channel flow between two horizontal parallel plates taking into account free convection currents and the Hall currents is presented. Solutions for the primary and secondary velocity, the induced magnetic field, the skin friction, and the temperature are derived. The velocity field and magnetic field are shown on graphs, and the values of the skin friction and the rate of heat transfer are indicated on tables. The results are discussed in terms of the hall parameter, the Hartmann number, and the Grashof number. >

F.E.M. in steady MHD duct flow problems

Abstract: The governing equations and the boundary conditions of steady incompressible magnetohydrodynamic (MHD) problems are adapted to the case of steady MHD flow in simply connected cross sections with arbitrary wall conductance. The problem is then solved numerically by means of the finite element method based on the weighted residual approach, and solutions for industrially relevant Hartmann numbers and non-symmetric kinetic fields are presented.

Creeping flow of a conducting fluid past axisymmetric bodies in the presence of an aligned magnetic field

Abstract: The use of strong magnetic fields for the control of particle settling in metallic systems is investigated in the limit of small inertial and magnetic Reynolds numbers. Finite element calculations of flow around axisymmetric bodies show that the drag increases proportional to the intensity of the magnetic field B or the Hartmann number Ha. The flow field forms boundary layers, which thin with increasing Ha, along surfaces parallel to the flow. For axisymmetric bodies, the boundary layer separates as the poles of the surface are approached and encloses regions of almost stagnant fluid. These regions spread upstream and downstream along the body with increasing Ha, thereby trapping the particle in a column of stagnant fluid. The pressure difference between the leading and trailing fluid columns is responsible for the increased particle drag. Asymptotic analysis with Ha≫1 confirms the scalings from the computations and clarifies the flow structure near the body.

Duct flows in a transverse magnetic field

Abstract: The properties of duct flows in the presence of an applied magnetic field are among the basic problems in MHD. In laminar fully established regimes the component of the magnetic field which is perpendicular to the velocity is the only one to be relevant. And, since inertia is zero, the Reynolds number becomes irrelevant. Two particular examples, the Hartmann flow and the Couette MHD flow illustrate the general properties of parallel steady flows (section II). The important dimensionless number in this type of flow is the Hartmann number Ha = (o/pv) 1/2 B 0 a, the square of which represents the ratio between Laplace forces and viscous forces. This number is usually quite large in laboratory experiments and because of this, viscosity is not negligible only in thin boundary layers. In particular, along any wall perpendicular to the applied magnetic field, a Hartmann layer develops (section III), which is of primary importance since it controls the core flow. The electrical conductivity of the walls is also vital. It always arises from the condition of closure of electric current streamlines, and it governs the global electromagnetic resistance to this type of flow.

The effect of magnetic field on two-phase liquid metal flow

Abstract: In this paper, the basic equations of two-phase liquid metal flow in a magnetic field are derived, and specifically, two-phase liquid metal MHD flow in a rectangular channel is studied, and the expressions of velocity distribution of liquid and gas phases and the ratioK0 of the pressure drop in two-phase MHD flow to that in single-phase are derived. Results of calculation show that the ratioK0 is smaller than unity and decreases with increasing void fraction and Hartmann number because the effective electrical conductivity in the two-phase case decreases.