Victor Shatrov

TWO- AND THREE-DIMENSIONAL INSTABILITIES OF THE CYLINDER WAKE IN AN ALIGNED MAGNETIC FIELD

Two- and three-dimensional (2-D and 3-D) instabilities in the wake of a circular cylinder placed in an electrically conducting fluid and subjected to a constant magnetic field aligned with the freestream are investigated numerically. Increasing magnetic fields suppress 2-D instability (vortex shedding), whereas 3-D instabilities are influenced in a more complex way. In the presence of a magnetic field, 3-D instability has been detected below the 2-D stability threshold. This can lead to a reversal of the order of instabilities, i.e., 3-D instability appears at lower Re than 2-D instability.

Three-dimensional linear stability analysis of the flow in a liquid spherical droplet driven by an alternating magnetic field

The paper presents a numerical stability analysis of the flow driven by an alternating (ac) magnetic field in an electromagnetically levitated liquid metal droplet. The basic axisymmetric flow is found to become unstable at Reynolds numbers in the order of 100. The critical Reynolds number Rec and the corresponding most unstable azimuthal wave number m are found for several configurations of the magnetic field depending on the skin-depth δ. For a uniform external ac magnetic field the azimuthal wave number of the most unstable mode is m=3. An additional steady (dc) magnetic field imposed along the axis of symmetry increases the stability of the flow.

Marginal turbulent magnetohydrodynamic flow in a square duct

Direct numerical simulations using a high-order finite-difference method were performed of the turbulent flow in a straight square duct in a transverse magnetic field. Without magnetic field the turbulence can be maintained for values of the bulk Reynolds number above approximately Re=1077 [M. Uhlmann et al., “Marginally turbulent flow in a square duct,” J. Fluid Mech. 588, 153 (2007)]. In the magnetohydrodynamic case this minimal value of the bulk Reynolds number increases with the Hartmann number. The flow is laminar at Re=3000 when the Hartmann number is larger than Ha=12.5 and the flow is turbulent for Ha≦12.0. The secondary mean flow structure at Re=3000 consists of eight vortices located mainly at the Hartmann walls.

Three-dimensional linear stability analysis of lid-driven magnetohydrodynamic cavity flow

We present numerical results of a linear three-dimensional (3D) stability analysis of a square lid-driven cavity flow under the influence of an external magnetic field which is directed parallel to the lid. The Lorentz force has a strong influence on the two-dimensional (2D) flow structure, thereby changing number, shape and strength of the eddies. The resulting 3D stability behavior is rather complex since it depends on the 2D flow structure. Although increasing magnetic fields are able to damp 3D instability, in a parameter region around Re=3100, several branches of the neutral stability curve do exist. For a fixed Reynolds number in this range, an increase of the magnetic field strength may lead to a transition from a stable flow to an oscillatory unstable one.

Basic flow and its three-dimensional linear stability in a small spherical droplet spinning in an alternating magnetic field

We present a numerical analysis of the liquid metal flow and its three-dimensional linear stability in a spherical droplet spinning in an alternating magnetic field. The applied magnetic field is uniform and the droplet spins around an axis parallel to the field. The droplet is assumed to be small so that its deformation by both electromagnetic and centrifugal forces is negligible. We find that a sufficiently fast spinning suppresses and stabilizes the internal flow in the droplet. However, there is a narrow range of rotation rates corresponding to an Ekman number of E≈10−2, where the spinning can destabilize the internal flow. Our results can be useful for the assessment of melt flow conditions in certain material processing technologies using electromagnetic levitation melting techniques.

An Alternating Magnetic Field Driven Flow in a Spinning Cylindrical Container

This paper presents a numerical analysis of the free surface liquid metal flow driven by an alternating current magnetic field in a spinning cylindrical container. The axisymmetric flow structure is analyzed for various values of the magnetohydrodynamic interaction parameter and Ekman numbers. The governing hydrodynamic equations are solved by a spectral collocation method, and the alternating magnetic field distribution is found by a boundary-integral method. The electromagnetic and hydrodynamic fields are fully coupled via the shape of the liquid free surface. It is found that the container rotation may reduce the meridional flow significantly.

Flow Control and Propulsion in Poor Conductors

The possibility to act contactlessly on a fluid flow offered by magnetohydrodynamics (MHD) stimulated the imagination of aerodynamists and naval engineers relatively early. Ritchie [1] appears to be the first using electromagnetic forces to pump electrolytes in 1832. Fig. 1 shows two of his apparatuses. Basically, the horizontal magnetic field component near the pole of a permanent magnet (N) interacts with the mainly vertical electric field between two ring electrodes (w, w’) to set the dilute acid in the angular gap (AB) into rotational motion. In the 1950s, a multitude of aerospace applications of MHD flow control techniques has been envisioned using the fact that at high enough speeds, air