Project A3: Magnetically induced instabilities in duct flows

PI: Leo Bühler (KIT)
Partners: KIT, TUI, CU

1. Scientific case for the project

1.1 Background

Liquid metal flows in channels with different wall electric conductivities are of importance for many industrial applications in metallurgy and crystal growth as well as for the design of nuclear fusion reactors with magnetic confinement of the plasma. Under the action of strong magnetic fields, liquid metal flows in electrically conducting ducts exhibit jet-like velocity profiles in thin boundary layers along walls parallel to the magnetic field. The velocity in these layers may exceed several times the mean velocity depending on magnetic field strength and electrical conductance of the walls. These layers become unstable already at relatively small Reynolds numbers [1]. A linear stability analysis predicts a critical Reynolds number for the onset of instabilities, which is almost one order of magnitude smaller than the one obtained experimentally [2]. An exhaustive explanation for this discrepancy has not been found yet. Numerical and experimental investigation of instabilities in parallel layers has received increasing attention in the last years due to their significant influence on heat and mass transfer (corrosion) in duct flows and therefore on the performance of liquid metal devices and blankets for fusion reactors [3,4]. An applied magnetic field tends also to damp 3D flow perturbations and supports the formation of 2D structures aligned with the magnetic field. Electromagnetic damping of instabilities is exploited, e.g., in metallurgical casting processes.

1.1 Most important goals of the planned work

The focus of the proposed experimental and numerical work is the study of the onset of time-dependent instabilities in liquid metal magnetohydrodynamic (MHD) duct flows and the transition of unstable flow patterns to fully developed MHD turbulence. The aim is quantifying transport properties of such flows as a function of magnetic field, flow rate, duct aspect ratio and electrical properties of the walls. Moreover, instrumentation for highly accurate electric potential measurements has to be developed and tested. Results are used to validate time-dependent numerical simulations that are carried out in parallel. The complementary theoretical study should support the physical interpretation of experimental data, enhance the understanding of observed phenomena and analyze ranges of parameters not reachable experimentally. It will also help to improve models for simulation of turbulent MHD flows.

2. Existing competencies and infrastructure

Magnetohydrodynamic experiments are performed since many years in the MEKKA laboratory at KIT using sodium-potassium and gallium-indium-tin (GaInSn) as working fluids. Current experiments focus on the study of MHD flows in a scaled mock-up of the European lead-lithium test blanket module for the fusion reactor ITER [5]. In addition to this applied research, performed within European fusion programs, experiments are carried out to study fundamental problems in MHD flows, like instabilities in boundary layers in electrically conducting ducts. In order to investigate these time dependent phenomena, a new liquid metal loop using GaInSn has been designed and manufactured [6]. The circuit consists of two identical pump channels, which feed the central test section (Fig. 5). The double-loop design is ideal for investigation of magnetically induced flow instabilities, since it leads to an unperturbed symmetric velocity profile at the entrance of the test section. Flanges are used to connect ducts and bends to ensure optimal flexibility for instrumentation and components’ replacement. The entire loop is placed in a strong uniform magnetic field up to 2T, generated in probably the largest dipole magnet operated in a European liquid metal research facility. In a first experimental campaign the loop will be used to test new liquid-metal measuring techniques and improve available instrumentation, like movable electric potential probes (Fig. 6) [7]. In the frame of the Helmholtz-Allianz the circuit will be operated with a number of test sections with different aspect ratios and wall electric conductivities.
For the theoretical description of MHD flows two different numerical codes will be used, one developed at KIT and one by the MHD group at TU Ilmenau, which is known for its work on turbulent flows [8]. The KIT code is based on the finite volume package openFOAM [9]. It is highly flexible, it can be applied to any geometry with arbitrary wall electric conductivity and it has been already used to simulate MHD flows in complex geometries. The TUI code is a parallel finite-difference code on a structured mesh [10], it is limited to straight ducts with insulating or perfectly conducting walls and is the preferred choice for studies of flows at very large Reynolds numbers. It works efficiently even on computational grids with more than 109 grid points and on more than 1000 processors. Both codes have demonstrated their reliability on supercomputers (see projects at the national supercomputing center in Jülich). In addition, Coventry University will analyze the MHD duct flow instability by a more analytically based approach which has recently proven as very efficient [11,12]. The combined expertise in simulations with strong magnetic fields (KIT, CU) and turbulence (TUI) will be essential for the numerical investigations of the project.

Fig. 5: GaInSn loop: the two lateral MHD pump channels feed symmetrically the central test section. Fig. 6: Velocity profile in the measuring channel and driving mechanism for the electric potential probe.

3. Resource planning and Budget Justification

A full scientist position is needed at TUI since the numerical studies use different methods including hydrodynamic stability and analysis of turbulent flows. They include code development and large-scale supercomputer simulations, which require considerable experience. Two PhD students are planned at KIT, one for the experimental work and one for 16 numerical activities. The theoretical studies at CU on MHD duct flow stability will be supported by a work contract.

Links: Close relations exist to projects A2, B1 and the YIG on measurement techniques.


[1] A.L. Ting, J.S. Walker, T.J. Moon, C.B. Reed, B.F. Picologlou, 1991, Linear stability analysis for high-velocity boundary layers in liquid-metal magnetohydrodynamic flows. Intern. Journal of Eng. Science, 29 (8) 939–948.
[2] C.B. Reed, B.F. Picologlou, 1989, Side wall flow instabilities in liquid metal MHD flow under blanket relevant conditions. Fusion Technology, 15, 705–715.
[3] L. Bühler, S. Horanyi, 2009, Measurements of time-dependent liquid metal magnetohydrodynamic flows in a flat rectangular duct. Fus. Eng. & Design, 84, 518-521.
[4] J. Priede, S. Aleksandrova and S. Molokov, 2010, Linear stability of Hunt’s flow. Journal of Fluid Mechanics, 649, 115-134.
[5] L. Bühler, C. Mistrangelo, 2011, Determination of flow distribution in a HCLL blanket mock-up through electric potential measurements. Fus. Eng. and Design, 86, 2301.
[6] L. Bühler, C. Mistrangelo and C. Koehly, 2011, Layout of an Experimental Liquid-Metal Circuit Based on MHD Considerations, IEEE Transactions on Plasma Science, in press.
[7] C. Mistrangelo, L. Bühler, 2010, Perturbing effects of electric potential probes on MHD duct flows. Experiments in Fluids, 48, 157–165.
[8] D. Krasnov, M. Rossi, O. Zikanov and T. Boeck, 2008, Optimal growth and transition to turbulence in channel flow with spanwise magnetic field. J. Fluid Mech., 596, 73-101.
[9] C. Mistrangelo, L. Bühler, 2011, Development of a numerical tool to simulate magnetohydrodynamic interactions of liquid metals with strong applied magnetic fields, Fusion Science and Technology, 60 (2), 798-803.
[10] D. Krasnov, O. Zikanov, T. Boeck, 2011, Comparative study of finite difference approaches in simulation of magnetohydrodynamic turbulence at low magnetic Reynolds number. Computers and Fluids, 50 (1), 46-59.
[11] J. Priede, S. Aleksandrova, S. Molokov, 2010, Linear stability of Hunt’s flow. J. Fluid Mech. 649, 115-134.
[12] J. Priede, S. Aleksandrova, S. Molokov, 2012, Linear stability of magnetohydrodynamic flow in a perfectly conducting rectangular duct. J. Fluid Mech., in press