Hydromagnetic Taylor–Couette flow at very small aspect ratio

Youd, Anthony J.; Barenghi, Carlo F.

doi:10.1017/s0022112005007743

Cited by 9 publications

(25 citation statements)

References 20 publications

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“…Thus it is reasonable to solve the MHD equations (dimensionless) in the small Prandtl number limit (Youd & Barenghi 2006;Roberts 1967;Zikanov & Thess 1998),…”

Section: Numerical Modelmentioning

confidence: 99%

Reduction of boundary effects in the spiralMRI experiment PROMISE

Szklarski¹

2007

Astron Nachr

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Magnetorotational instability (MRI) is one of the most important and most common instabilities in astrophysics. It is widely accepted that it serves as a source of turbulent viscosity in accretion disks -the most energy efficient objects in the Universe. However it is very difficult to bring this process down on earth and model it in a laboratory experiment. Several different approaches have been proposed, one of the most recent is PROMISE (Potsdam-ROssendorf Magnetorotational InStability Experiment). It consists of a flow of a liquid metal between two rotating cylinders under applied current-free spiral magnetic field. The cylinders must be covered with plates which introduce additional end-effects which alter the flow and make it more difficult to clearly distinguish between MRI stable and unstable state. In this paper we propose simple and inexpensive improvement to the PROMISE experiment which would reduce those undesirable effects.

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“…Thus it is reasonable to solve the MHD equations (dimensionless) in the small Prandtl number limit (Youd & Barenghi 2006;Roberts 1967;Zikanov & Thess 1998),…”

Section: Numerical Modelmentioning

confidence: 99%

Reduction of boundary effects in the spiralMRI experiment PROMISE

Szklarski¹

2007

Astron Nachr

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“…For laboratory liquids like gallium, the magnetic Prandtl number is very small (see Table 1) so the magnetic diffusion time is much shorter than other time scales and fluctuations b of the field B 0 + b are also much smaller than the applied field B 0 . As a result the b adjusts instantaneously to the velocity u and the quasi-static approximation can be used (Roberts 1967;Zikanov & Thess 1998;Youd & Barenghi 2006).…”

Section: Equations and Numerical Modelmentioning

confidence: 99%

“…Except along the axis the magnetic field is current-free. We simulate the axisymmetric 2D flow in cylindrical coordinates (R, φ, z) with the numerical code of A. Youd (see Youd & Barenghi 2006 for details). The code has been modified in order to handle periodic boundary conditions in a way suitable for our needs, the toroidal field was added and different boundary conditions on the endplates were applied.…”

Section: Equations and Numerical Modelmentioning

confidence: 99%

Nonlinear simulations of magnetic Taylor-Couette flow with currentfree helical magnetic fields

Szklarski

Rüdiger

2006

Astron. Nachr.

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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 timedependent 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 ∼ 50 Gauss and axial current ∼ 4 kA for the toroidal field. It is sufficient that the vertical velocity uz 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.

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“…The bottom and top plate are at z = 0 and z = Γ. For details on the numerical method and the boundary conditions see ; Youd & Barenghi (2006). The cylinders are assumed to be perfectly conducting, and the endplates have conductivity ranging from a perfect conductor to a perfect insulator.…”

Section: The Reynolds Number Re Is Defined Asmentioning

confidence: 99%

Boundary layer in the MRI experiment PROMISE

Szklarski¹,

Gerbeth

2008

Astron Nachr

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One of the most convenient approaches to observe experimentally the magnetorotational instability (MRI) is to use a magnetized Taylor-Couette setup. The flow of liquid metal between two rotating, concentric cylinders can become unstable in the presence of an external magnetic field. One of the issues which should be addressed when designing such an experiment is the influence of plates enclosing the cylinders from the top and the bottom. In this paper we discuss properties of the boundary layer which arises near these plates. Our primary concern is the importance of this layer in the MRI experiment PROMISE.

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Hydromagnetic Taylor–Couette flow at very small aspect ratio

Cited by 9 publications

References 20 publications

Reduction of boundary effects in the spiralMRI experiment PROMISE

Reduction of boundary effects in the spiralMRI experiment PROMISE

Nonlinear simulations of magnetic Taylor-Couette flow with currentfree helical magnetic fields

Boundary layer in the MRI experiment PROMISE

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