Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session H8: Magnetohydrodynamics I 
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Chair: Eric Edlund, Princeton Plasma Physics Laboratory Room: 330 
Monday, November 25, 2013 10:30AM  10:43AM 
H8.00001: A new divergencefreepreserving highorder scheme for magnetohydrodynamics Soshi Kawai We present a new strategy that is very simple, divergencefree, highorder accurate, yet has an effective discontinuouscapturing capability for simulating magnetohydrodynamics (MHD) with shock waves. The new strategy is to construct artificial diffusion terms in a physicallyconsistent manner, and to be built into the induction equations in a conservation law form at a partialdifferentialequation level. The physicallyconsistent manner means that the artificial terms act as a diffusion term only in the curl of magnetic field to capture numerical discontinuities in the magnetic field while not affecting the divergence field (thus maintaining divergencefree constraint). The proposed method is inherently divergencefree both ideal and resistive MHD, with and without shock waves, and also both inviscid and viscous flows. The method is based on finite difference method with colocated variable arrangement, and any linear finite difference scheme in an arbitrary order (i.e., any desirable highorder) of accuracy can be used to discretize the modified governing equations to ensures the divergencefree constraint numerically at the discretization level. Twodimensional smooth and nonsmooth ideal MHD problems are considered to show a superior performance of the proposed method. [Preview Abstract] 

H8.00002: ABSTRACT WITHDRAWN 
Monday, November 25, 2013 10:56AM  11:09AM 
H8.00003: Mixed convection in duct flows with very strong transverse magnetic fields Xuan Zhang, Xinyan Lv, Li Liu, Andrew Schigelone, Oleg Zikanov Mixed convection in flows of liquid metals within ducts with one heated wall and imposed transverse magnetic field is studied using highresolution DNS and linear stability analysis. The main attention is given to the cases of strong heating (the Grashof number up to 10$^{\mathrm{12}})$ and strong magnetic field (the Hartmann number up to 800). Various orientations of the duct, temperature gradient, and magnetic field are studied in our project. This presentation is focused on the configuration of a horizontal duct with bottom heating and horizontal transverse magnetic field. It is found that, while conventional turbulence is suppressed, a new type of convection instability appears at high Hartman numbers. The most unstable modes are the rolls aligned with the magnetic field. Their streamwise wavelength is of the order of the width of the duct and decreases with the Hartmann number as the rolls become localized in the lower part of the duct. In fully developed secondary regimes, transport of the rolls by mean flow leads to strong lowfrequency oscillations of local temperature. [Preview Abstract] 

H8.00004: ABSTRACT WITHDRAWN 
Monday, November 25, 2013 11:22AM  11:35AM 
H8.00005: Simulation of liquid metal duct flow at finite magnetic Reynolds number Vinodh Kumar Bandaru, Thomas Boeck, Joerg Schumacher Turbulent conducting flows at finite magnetic Reynolds numbers occur in magnetohydrodynamic turbulence in plasmas, and in the generation of magnetic fields by the dynamo effect. In simulations the former case is typically studied as box turbulence without walls, and the latter in a closed spherical fluid domain. We are interested in turbulent liquidmetal duct flows in the presence of an exterior localized magnetic field, which is of interest for metallurgical applications. It can be expected to show complex interactions between the field and the flow, which modify both the field and velocity distribution. The evolution of the perturbation in the imposed magnetic field together with the turbulent velocity field in the duct are solved numerically using finite differences through the coupled system of NavierStokes and magnetic field transport equations. Characterizing the continuity of the magnetic field perturbations between the exterior and interior of the domain gives rise to nonlocal boundary conditions which are dealt with the boundary element method. Details of the methodology for numerical computation will be discussed. [Preview Abstract] 
Monday, November 25, 2013 11:35AM  11:48AM 
H8.00006: Transitional liquid metal duct flow near a magnetic dipole Saskia Tympel, Thomas Boeck, Joerg Schumacher The flow transformation and the generation of vortex structures by a strong magnetic dipole field in a liquid metal duct flow is studied by means of threedimensional direct numerical simulations. The dipole is considered as the paradigm for a magnetic obstacle which will deviate the streamlines due to Lorentz forces which act on the fluid elements. The duct is of square crosssection. The dipole is located above the top wall and is centered in spanwise direction. Our model uses the quasistatic approximation which is applicable in the limit of small magnetic Reynolds numbers. The analysis covers the stationary flow regime at small hydrodynamic Reynolds numbers Re as well as the transitional timedependent regime at higher values which may generate a turbulent flow in the wake of the magnetic obstacle. We present a systematic study of these two basic flow regimes on Re and on the Hartmann number Ha, a measure of the strength of the magnetic dipole field. Furthermore, several orientations and positions of the dipole are compared. The most efficient generation of turbulence at a fixed distance above the duct follows for the spanwise orientation which is caused by a certain configuration of Hartmann layers and reversed flow at the top plate. [Preview Abstract] 
Monday, November 25, 2013 11:48AM  12:01PM 
H8.00007: Flow velocimetry for weakly conducting electrolytes based on high resolution Lorentz force measurement. Christian Resagk, Reschad Ebert, Suren Vasilyan, Andreas Wiederhold We demonstrate that a flow velocity measurement can be transformed into a noninvasive force measurement by metering the drag force acting on a system of magnets around a flow channel. This method is called Lorentz force velocimetry and has been developed in the last years in our institute. It is a feasible principle for materials with large conductivity like liquid metals. To evolve this method for weakly conducting fluids like salt water or molten glass the drag force measurement is the challenging bottleneck. Here forces of 10$^{\mathrm{8}}$ and less of the weight force of the magnet system have to be resolved. In this paper different force measurement techniques get tested and compared. For the current setup the magnet system is attached to a state of the art electromagnetic force compensation balance. Different ways of getting the correct force signal out of the two measurement setups will be presented and discussed. For generalization of the measurement principle the Lorentz force is determined for different fluid profiles. In addition to that we have developed new systematic noise reduction methods to increase the resolution of the force measurement techniques by a factor of ten or larger which we will present here. [Preview Abstract] 
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