ABSTRACT
Combining theoretical arguments and numerical simulations, we demonstrate that the metal pad roll instability can occur in a centimeter-scale setup with reasonable values of the magnetic field and electrical current and with metal pairs that are liquid at room temperature. We investigate two fluid pairs: gallium with mercury (immiscible pair) or gallium with GaInSn eutectic alloy (miscible pair).
ABSTRACT
It is numerically demonstrated by means of a magnetohydrodynamic code that precession can trigger dynamo action in a cylindrical container. Fixing the angle between the spin and the precession axis to be 1/2π, two limit configurations of the spinning axis are explored: either the symmetry axis of the cylinder is parallel to the spin axis (this configuration is henceforth referred to as the axial spin case), or it is perpendicular to the spin axis (this configuration is referred to as the equatorial spin case). In both cases, the centro-symmetry of the flow breaks when the kinetic Reynolds number increases. Equatorial spinning is found to be more efficient in breaking the centro-symmetry of the flow. In both cases, the average flow in the reference frame of the mantle converges to a counter-rotation with respect to the spin axis as the Reynolds number grows. We find a scaling law for the average kinetic energy in term of the Reynolds number in the axial spin case. In the equatorial spin case, the unsteady asymmetric flow is shown to be capable of sustaining dynamo action in the linear and nonlinear regimes. The magnetic field is mainly dipolar in the equatorial spin case, while it is is mainly quadrupolar in the axial spin case.
ABSTRACT
It has been observed that dynamo action occurs in the von-Kármán-Sodium (VKS) experiment only when the rotating disks and the blades are made of soft iron. The purpose of this paper is to numerically investigate the role of soft iron in the VKS dynamo scenario. This is done by using a mean-field model based on an axisymmetric mean flow, a localized permeability distribution, and a localized α effect modeling the action of the small velocity scales between the blades. The action of the rotating blades is modeled by an axisymmetric effective permeability field. Key properties of the flow giving to the numerical magnetic field a geometric structure similar to that observed experimentally are identified. Depending on the permeability of the disks and the effective permeability of the blades, the dynamo that is obtained is either oscillatory or stationary. Our numerical results confirm the leading role played by the ferromagnetic impellers. A scenario for the VKS dynamo is proposed.
ABSTRACT
We present hydrodynamic and magnetohydrodynamic (MHD) simulations of liquid sodium flow with the PLUTO compressible MHD code to investigate influence of magnetic boundary conditions on the collimation of helicoidal motions. We use a simplified cartesian geometry to represent the flow dynamics in the vicinity of one cavity of a multiblades impeller inspired by those used in the Von-Kármán-sodium (VKS) experiment. We show that the impinging of the large-scale flow upon the impeller generates a coherent helicoidal vortex inside the blades, located at a distance from the upstream blade piloted by the incident angle of the flow. This vortex collimates any existing magnetic field lines leading to an enhancement of the radial magnetic field that is stronger for ferromagnetic than for conducting blades. The induced magnetic field modifies locally the velocity fluctuations, resulting in an enhanced helicity. This process possibly explains why dynamo action is more easily triggered in the VKS experiment when using soft iron impellers.
ABSTRACT
We present numerical solutions of the flow in precessing spheres and spherical shells with small (r(i)/r(o)=0.1) inner cores and either stress-free or no-slip inner boundary conditions. For each of these three cases we consider the sequence of bifurcations as the Reynolds number Re=r(o)(2)Ω/ν is increased up to ~1280, focusing particular attention on bifurcations that break the antipodal symmetry U(-r)=-U(r). All three cases have steady and time-periodic symmetric solutions at smaller Re, and quasiperiodic asymmetric solutions at larger Re, but the details of the transitions differ, and include also periodic asymmetric and quasiperiodic symmetric solutions in some of the cases.
Subject(s)
Computer-Aided Design , Models, Theoretical , Rheology/instrumentation , Rheology/methods , Computer SimulationABSTRACT
It is numerically demonstrated by means of a magnetohydrodynamics code that precession can trigger the dynamo effect in a cylindrical container. When the Reynolds number, based on the radius of the cylinder and its angular velocity, increases, the flow, which is initially centrosymmetric, loses its stability and bifurcates to a quasiperiodic motion. This unsteady and asymmetric flow is shown to be capable of sustaining dynamo action in the linear and nonlinear regimes. The magnetic field thus generated is unsteady and quadrupolar. These numerical evidences of dynamo action in a precessing cylindrical container may be useful for an experiment now planned at the Dresden sodium facility for dynamo and thermohydraulic studies in Germany.
ABSTRACT
In the von Kármán Sodium 2 (VKS2) successful dynamo experiment of September 2006, the observed magnetic field showed a strong axisymmetric component, implying that nonaxisymmetric components of the flow field were acting. By modeling the induction effect of the spiraling flow between the blades of the impellers in a kinematic dynamo code, we find that the axisymmetric magnetic mode is excited. The control parameters are the magnetic Reynolds number of the mean flow, the coefficient measuring the induction effect alpha, and the type of boundary conditions. We show that using realistic values of alpha, the observed critical magnetic Reynolds number, Rm;{c} approximately 32, can be reached easily with ferromagnetic boundary conditions. We conjecture that the dynamo action achieved in this experiment may not be related to the turbulence in the bulk of the flow, but rather to the alpha effect induced by the impellers.
ABSTRACT
Three-dimensional (3D) superflows past a circular cylinder are studied by numerically integrating the nonlinear Schrodinger equation. 3D initial data are built from the two-dimensional (2D) stationary vortex nucleation solutions. Quasistationary half-ring vortices, pinned at the sides of the cylinder, are generated after a short time. On a longer time scale, either 3D vortex stretching induces dissipation and drag, or the vortex is absorbed by the cylinder. The corresponding 3D critical velocity is found to be well below the 2D one. The implications for experiments in Bose-Einstein condensed gas and low-temperature helium are discussed.
