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We describe a novel approach to the mathematical modeling and computational simulation of fully three-dimensional, electromagnetically and thermally driven, steady liquid-metal flow. The phenomenon is governed by the Navier-Stokes equations, Maxwell’s equations, Ohm’s law, and the heat equation, all nonlinearly coupled via Lorentz and electromotive forces, buoyancy forces, and convective and dissipative heat transfer. Employing the electric current density rather than the magnetic field as the primary electromagnetic variable, it is possible to avoid artificial or highly idealized boundary conditions for electric and magnetic fields and to account exactly for the electromagnetic interaction of the fluid with the surrounding media. A finite element method based on this approach was used to simulate the flow of a metallic melt in a cylindrical container, rotating steadily in a uniform magnetic field perpendicular to the cylinder axis. Velocity, pressure, current, and potential distributions were computed and compared to theoretical predictions.

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Air flow in air jet weaving machines is complicated: it is unsteady, turbulent, and can be compressible or incompressible depending on the velocity. A separated flow model is developed to simulate air flow through the guide channel, which is half open and corrugated. Subsonic air flow in the guide channel is investigated as a simplified model of air flow in a single nozzle air-jet filling insertion system. The drag coefficient in the guide channel and propelling force acting on the yarn are calculated. Theoretical predictions of drag coefficient and propelling force are in good agreement with ex perimental data obtained for the same conditions.

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