123 research outputs found
Boundary-integral method for poloidal axisymmetric AC magnetic fields
This paper presents a boundary-integral equation (BIE) method for the
calculation of poloidal axisymmetric magnetic fields applicable in a wide range
of ac frequencies. The method is based on the vector potential formulation and
it uses the Green's functions of Laplace and Helmholtz equations for the
exterior and interior of conductors, respectively. The work is particularly
focused on a calculation of axisymmetric Green's function for the Helmholtz
equation which is both simpler and more accurate compared to previous
approaches. Three different approaches are used for calculation of the Green's
function depending on the parameter range. For low and high dimensionless ac
frequencies we use a power series expansion in terms of elliptical integrals
and an asymptotic series in terms of modified Bessel functions of second kind,
respectively. For the intermediate frequency range, Gauss-Chebyshev-Lobatto
quadratures are used. The method is verified by comparing with the analytical
solution for a sphere in a uniform external ac field. The application of the
method is demonstrated for a composite model inductor containing an external
secondary circuit.Comment: 8 pages, 4 figure
Absolute versus convective helical magnetorotational instability in a Taylor-Couette flow
We analyze numerically the magnetorotational instability of a Taylor-Couette
flow in a helical magnetic field (HMRI) using the inductionless approximation
defined by a zero magnetic Prandtl number (Pm=0). The Chebyshev collocation
method is used to calculate the eigenvalue spectrum for small amplitude
perturbations. First, we carry out a detailed conventional linear stability
analysis with respect to perturbations in the form of Fourier modes that
corresponds to the convective instability which is not in general
self-sustained. The helical magnetic field is found to extend the instability
to a relatively narrow range beyond its purely hydrodynamic limit defined by
the Rayleigh line. There is not only a lower critical threshold at which HMRI
appears but also an upper one at which it disappears again. The latter
distinguishes the HMRI from a magnetically-modified Taylor vortex flow. Second,
we find an absolute instability threshold as well. In the hydrodynamically
unstable regime before the Rayleigh line, the threshold of absolute instability
is just slightly above the convective one although the critical wave length of
the former is noticeably shorter than that of the latter. Beyond the Rayleigh
line the lower threshold of absolute instability rises significantly above the
corresponding convective one while the upper one descends significantly below
its convective counterpart. As a result, the extension of the absolute HMRI
beyond the Rayleigh line is considerably shorter than that of the convective
instability. The absolute HMRI is supposed to be self-sustained and, thus,
experimentally observable without any external excitation in a system of
sufficiently large axial extension.Comment: 16 pages, 15 figures; minor revision, Phys. Rev. E (in press
Role of soft-iron impellers on the mode selection in the VKS dynamo experiment
A crucial point for the understanding of the von-K\'arm\'an-Sodium (VKS)
dynamo experiment is the influence of soft-iron impellers. We present numerical
simulations of a VKS-like dynamo with a localized permeability distribution
that resembles the shape of the flow driving impellers. It is shown that the
presence of soft-iron material essentially determines the dynamo process in the
VKS experiment. % An axisymmetric magnetic field mode can be explained by the
combined action of the soft-iron disk and a rather small -effect
parametrizing the induction effects of unresolved small scale flow
fluctuations
Paradox of inductionless magnetorotational instability in a Taylor-Couette flow with a helical magnetic field
We consider the magnetorotational instability (MRI) of a hydrodynamically
stable Taylor-Couette flow with a helical external magnetic field in the
inductionless approximation defined by a zero magnetic Prandtl number
(\Pm=0). This leads to a considerable simplification of the problem
eventually containing only hydrodynamic variables. First, we point out that the
energy of any perturbation growing in the presence of magnetic field has to
grow faster without the field. This is a paradox because the base flow is
stable without the magnetic while it is unstable in the presence of a helical
magnetic field without being modified by the latter as it has been found
recently by Hollerbach and Rudiger [Phys. Rev. Lett. 95, 124501 (2005)]. We
revisit this problem by using a Chebyshev collocation method to calculate the
eigenvalue spectrum of the linearized problem. In this way, we confirm that MRI
with helical magnetic field indeed works in the inductionless limit where the
destabilization effect appears as an effective shift of the Rayleigh line.
Second, we integrate the linearized equations in time to study the transient
behavior of small amplitude perturbations, thus showing that the energy
arguments are correct as well. However, there is no real contradiction between
both facts. The linear stability theory predicts the asymptotic development of
an arbitrary small-amplitude perturbation, while the energy stability theory
yields the instant growth rate of any particular perturbation, but it does not
account for the evolution of this perturbation.Comment: 4 pages, 3 figures, submitted to Phys. Rev.
Ambivalent effects of added layers on steady kinematic dynamos in cylindrical geometry: application to the VKS experiment
The intention of the ''von Karman sodium'' (VKS) experiment is to study the
hydromagnetic dynamo effect in a highly turbulent and unconstrained flow. Much
effort has been devoted to the optimization of the mean flow and the lateral
boundary conditions in order to minimize the critical magnetic Reynolds number
and hence the necessary motor power. The main focus of this paper lies on the
role of ''lid layers'', i.e. layers of liquid sodium between the impellers and
the end walls of the cylinder. First, we study an analytical test flow to show
that lid layers can have an ambivalent effect on the efficiency of the dynamo.
The critical magnetic Reynolds number shows a flat minimum for a small lid
layer thickness, but increases for thicker layers. For the actual VKS geometry
it is shown that static lid layers yield a moderate increase of the critical
magnetic Reynolds number by approximately 12 per cent. A more dramatic increase
by 100 until 150 per cent can occur when some rotational flow is taken into
account in those layers. Possible solutions of this problem are discussed for
the real dynamo facility.Comment: 24 pages, 11 figures, minor changes, to appear in European Journal of
Mechanics B/Fluid
Electromagnetic induction in non-uniform domains
Kinematic simulations of the induction equation are carried out for different
setups suitable for the von-K\'arm\'an-Sodium (VKS) dynamo experiment. Material
properties of the flow driving impellers are considered by means of high
conducting and high permeability disks that are present in a cylindrical volume
filled with a conducting fluid. Two entirely different numerical codes are
mutually validated by showing quantitative agreement on Ohmic decay and
kinematic dynamo problems using various configurations and physical parameters.
Field geometry and growth rates are strongly modified by the material
properties of the disks even if the high permeability/high conductivity
material is localized within a quite thin region. In contrast the influence of
external boundary conditions remains small. Utilizing a VKS like mean fluid
flow and high permeability disks yields a reduction of the critical magnetic
Reynolds number for the onset of dynamo action of the simplest non-axisymmetric
field mode. However this decrease is not sufficient to become relevant in the
VKS experiment. Furthermore, the reduction of Rm_c is essentially influenced by
tiny changes in the flow configuration so that the result is not very robust
against small modifications of setup and properties of turbulence
Towards a precession driven dynamo experiment
The most ambitious project within the DREsden Sodium facility for DYNamo and
thermohydraulic studies (DRESDYN) at Helmholtz-Zentrum Dresden-Rossendorf
(HZDR) is the set-up of a precession-driven dynamo experiment. After discussing
the scientific background and some results of water pre-experiments and
numerical predictions, we focus on the numerous structural and design problems
of the machine. We also outline the progress of the building's construction,
and the status of some other experiments that are planned in the framework of
DRESDYN.Comment: 9 pages, 6 figures, submitted to Magnetohydrodynamic
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