Three-dimensional MHD flows in rectangular ducts with internal obstacles

Abstract

This paper presents a numerical simulation of the magnetohydrodynamic (MHD) liquid metal flow around a square cylinder placed in a rectangular duct. In the hydrodynamic case, for a certain parameter range the well-known Kármán vortex street with three-dimensional flow patterns is observed, similar to the flow around a circular cylinder. In this study a uniform magnetic field aligned with the cylinder is applied and its influence on the formation and downstream transport of vortices is investigated. The relevant key parameters for the MHD flow are the Hartmann number M, the interaction parameter N and the hydrodynamic Reynolds number, all based on the side length of the cylinder. The Hartmann number M was varied in the range 0 6 M 6 85 and the interaction parameter N in the range 0 6 N 6 36. Results are presented for two fixed Reynolds numbers Re = 200 and Re = 250. The magnetic Reynolds number is assumed to be very small. The results of the numerical simulation are compared with known experimental and theoretical results. The hydrodynamic simulation shows characteristic intermittent pulsations of the drag and lift force on the cylinder. At Re = 200 a mix of secondary spanwise three-dimensional instabilities (A and B mode, rib vortices) could be observed. The spanwise wavelength of the rib vortices was found to be about 2-3 cylinder side lengths in the near wake. At Re = 250 the flow appears more organized showing a regular B mode pattern and a spanwise wavelength of about 1 cylinder side length. With an applied magnetic field a quasi-two-dimensional flow can be obtained at low N ≈ 1 due to the strong non-isotropic character of the electromagnetic forces. The remaining vortices have their axes aligned with the magnetic field. With increasing magnetic fields these vortices are further damped due to Hartmann braking. The result that the 'quasi-twodimensional' vortices have a curvature in the direction of the magnetic field can be explained by means of an asymptotic analysis of the governing equations. With very high magnetic fields the time-dependent vortex shedding can be almost completely suppressed. By three-dimensional visualization it was possible to show characteristic paths of the electric current for this kind of flow, explaining the action of the Lorentz forces.

Spatial evolution of a quasi-two-dimensional Kármán vortex street subjected to a strong uniform magnetic field

“…8,25,26,38 Surprisingly, this non-monotonic trend is also observed in a wake-type vortex using the SM82 model. 15 This observation is supported by more recent findings, 27 where the transition to two-dimensionality of wake vortices occurs at relatively low interaction parameter (1 < N < 5). It is hence anticipated that the SM82 model will be able to provide some trustworthy insights into the two-dimensional wake behaviour beyond the parameter ranges where it is formally applicable.…”

“…However, the rate of peak vorticity decay is in good agreement further downstream. This observation can be attributed to the transition to a two-dimensional state, as discussed by Mück et al 27 In their 3D simulations at a low interaction parameter (N d = 1), they observed that the spanwise velocity fluctuation tends to zero farther from the cylinder and that the vorticity diffuses along the magnetic field lines, an evidence of two-dimensionality.…”

“…8,26 However, it has been found that the orientation of the magnetic field plays an important role in the decay of wake vorticity. Numerical investigation of three-dimensional (3D) MHD flows 27 reveals that the vortices whose axes are aligned with the magnetic field persist far downstream, whereas vortices perpendicular to the magnetic field are rapidly damped. This observation is in agreement with the previous experimental investigation by Branover, Eidelman, and Nagorny, 9 where the intensity of velocity fluctuation is preserved for an extended period of time when the vortices are aligned with the magnetic field but get suppressed when they are perpendicular to the magnetic field.…”

Modeling of liquid metal duct and free-surface flows using CFX.

“…Calculations, however, will be costly. Indeed, perhaps the most comprehensive study of an MHD duct flow with DNS has been performed in [15]. The code has been specifically developed for the geometry studied, and thus was faster than the commercial codes.…”

Liquid magnetohydrodynamics — recent progress and future directions for fusion

“…The damping of 2D turbulence in channels with different shaped cross sections was addressed in [38]. A theoretical investigation of how 3D Kármán vortices are influenced by a transverse magnetic field was performed in [39]. Kármán vortex shedding from a square cylinder between electrically insulated parallel plates was also simulated in [40] using 3D adequately predict conducting wall flows with side-layer jets.…”