Voltage-Driven Instability of Electrically Conducting Fluids
Part of the
Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM)
book series (NNFM, volume 82)
This paper consists of two parts dealing with magnetohydrodynamic pinch instabilities in cylindrical and in planar geometry.
The first part of the paper gives a plot for a spectral code in cylindrical geometry that is able to simulate the magnetohydrodynamic (MHD) approximation for very small magnetic Reynolds and Prandtl numbers. The approximated set of evolution equations is appropriate for the fluid behaviour of liquid metals on a laboratory scale under the influence of external and internal magnetic fields. The geometry and the MHD model require the development of a spectral Poisson solver for an expansion partly in Fourier series (axial and azimuthal directions) and partly in Chebyshev polynomials (radial direction). The cylindrical code will be used for the computation of the bifurcation sequence inside a cylindrical cavity filled with liquid metal.
In the second part results for the plane sheet pinch are presented which were obtained using a pseudo-spectral code with Fourier expansions in the three Cartesian coordinates. The planar case involves a space-dependent resistivity: for a given profile of the resistivity a numerical stability and bifurcation analysis is carried out on the basis of the full MHD equations. The most unstable perturbation to the quiescent basic state is the two-dimensional tearing mode. Restricting the whole problem to two spatial dimensions, this mode was followed up to a time-asymptotic steady state, which however proved to be unstable to three-dimensional perturbations even close to the point where the primary instability sets in. For a special choice of the system parameters, the unstably perturbed state was followed up in its nonlinear evolution and was found to approach a three-dimensional steady state.
KeywordsLiquid Metal Hartmann Number Magnetic Reynolds Number Quasistatic Approximation Kink Instability
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