Mixed convection in a downward flow in a vertical duct with strong transverse magnetic field

The downward flow in a vertical duct with one heated and three thermally insulated walls is analyzed numerically using the two-dimensional approximation valid in the asymptotic limit of an imposed strong transverse magnetic field. The work is motivated by the design of liquid metal blankets with poloidal ducts for future nuclear fusion reactors, in which the main component of the magnetic field is perpendicular to the flow direction and very strong heating is applied at the wall facing the reaction chamber. The flow is found to be steady-state or oscillating depending on the strengths of the heating and magnetic field. A parametric study of the instability leading to the oscillations is performed. It is found among other results that the flow is unstable and develops high-amplitude temperature oscillations at the conditions typical for a fusion reactor blanket

Nonlinear simulations of magnetic Taylor-Couette flow with current-free helical magnetic fields

The magnetorotational instability (MRI) in cylindrical Taylor-Couette flow with external helical magnetic field is simulated for infinite and finite aspect ratios. We solve the MHD equations in their small Prandtl number limit and confirm with time-dependent nonlinear simulations that the additional toroidal component of the magnetic field reduces the critical Reynolds number from $O(10^6)$ (axial field only) to $O(10^3)$ for liquid metals with their small magnetic Prandtl number. Computing the saturated state we obtain velocity amplitudes which help designing proper experimental setups. Experiments with liquid gallium require axial field $\sim 50$ Gauss and axial current $\sim 4$ kA for the toroidal field. It is sufficient that the vertical velocity $u_z$ of the flow can be measured with a precision of 0.1mm/s. We also show that the endplates enclosing the cylinders do not destroy the traveling wave instability which can be observed as presented in earlier studies. For TC containers without and with endplates the angular momentum transport of the MRI instability is shown as to be outwards.Comment: 6 pages, 11 figure

Patterned turbulence and relaminarization in MHD pipe and duct flows

We present results of a numerical analysis of relaminarization processes in MHD duct and pipe flows. It is motivated by Julius Hartmann's classical experiments on flows of mercury in pipes and ducts under the influence of magnetic fields. The simulations, conducted both in periodic and non‐periodic settings, provide a first detailed view of flow structures that have not been experimentally accessible. The main novelty of the analysis is very long (tens to hundreds of hydraulic diameters) computational domains that allows to discover new flow regimes with localized turbulent spots near the side walls parallel to the magnetic field. The computed critical parameters for transition as well as the friction coefficients are in good agreement with Hartmann's data. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/109939/1/603_ftp.pd

Effect of wall conductivity on turbulent channel flow under spanwise magnetic field

The effect of wall conductivity on turbulence in electrically conducting fluid in the presence of a constant magnetic field is considered. A channel flow with a spanwise magnetic field is analyzed using high-resolution direct numerical simulations performed for the case of low magnetic Reynolds number. It is found that the effect of suppression of wall-normal momentum transfer and reduction of wall friction identified earlier for the flow with perfectly insulating walls is enhanced if the walls are electrically conducting. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/78302/1/515_ftp.pd

Subcritical instability of liquid metal channel flow in the presence of a spanwise magnetic field

The linear and nonlinear evolution of perturbations is investigated in a magnetohydrodynamic channel flow with electrically insulating walls. The applied magnetic field is parallel to the walls and orthogonal to the stream. Linear optimal perturbations and their maximum amplifications over finite time intervals are computed using a scheme based on the direct and adjoint governing equations. It is shown that dominant optimal perturbations are no more the classical streamwise modes and how the flow is two-dimenzionalized for high enough Hartmann numbers. For fixed Reynolds and Hartmann numbers, direct numerical simulations are applied to investigate how the transition to turbulence is affected by the magnetic field. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/60899/1/4140005_ftp.pd