Abstract
We extend our existing hp-finite element framework for non-conducting magnetic fluids (Jin et al., 2014) to the treatment of conducting magnetic fluids including magnetostriction effects in both two- and three-dimensions. In particular, we present, to the best of our knowledge, the first computational treatment of magnetostrictive effects in conducting fluids. We propose a consistent linearisation of the coupled system of non-linear equations and solve the resulting discretised equations by means of the Newton–Raphson algorithm. Our treatment allows the simulation of complex flow problems, with non-homogeneous permeability and conductivity, and, apart from benchmarking against established analytical solutions for problems with homogeneous material parameters, we present a series of simulations of multiphase flows in two- and three-dimensions to show the predicative capability of the approach as well as the importance of including these effects.
Highlights
Magnetohydrodynamics (MHD) studies the behaviour of electrically conducting fluids under the existence of a magnetic field [6,15,30]
When considering problems with different fluid phases [16,41], as well as problems where the induced strain rate alters the distribution of 1⁄21⁄2l, which in turn changes the magnetic field distribution, magnetostrictive effects become important [26,27]
D [ @ XN and, in general we do not require that @ X 1⁄4 @ X or @ X 1⁄4 @ X The difference between the homogeneous isotropic conducting fluid and a magnetostrictive conducting fluid is that, the Neumann boundary for the fluid domain contains the total stress tensor, which is more realistic at describing the actual physics since, in real experiments, terms making up the contributions to the applied traction cannot be identified separately
Summary
Magnetohydrodynamics (MHD) studies the behaviour of electrically conducting fluids under the existence of a magnetic field [6,15,30]. When considering problems with different fluid phases [16,41], as well as problems where the induced strain rate alters the distribution of 1⁄21⁄2l, which in turn changes the magnetic field distribution, magnetostrictive effects become important [26,27] In order to include magnetostrictive effects with ease, it makes sense to revisit the governing equations for MHD and instead express the ponderomotive force f EM in terms of the divergence of a stress tensor 1⁄21⁄2rEM f EM 1⁄4 r 1⁄21⁄2rEM ; ð5Þ which, in turn, permits more general coupling mechanisms to be considered.
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