Direct Numerical Simulations of Impeller Driven Turbulence and Dynamo Action

The process, in which a magnetic field is amplified by the flow of an electrically conducting fluid, known as dynamo action, is believed to be the origin of many magnetic fields in the universe including the magnetic field of the earth. A successful laboratory experiment investigating the underlying mechanisms is the Von Karman Sodium device, consisting of a cylindrical vessel filled with liquid sodium, stirred by two counter-rotating soft-iron impellers. Despite its success, it leaves important questions unsolved and even raises new ones. The aim of this project are detailed high-resolution direct numerical simulations of the VKS experiment. This type of simulations of a three-dimensional turbulent fluid flow in complex geometries supporting a magnetic field are challenging. We designed a massively parallel pseudo-spectral MHD (magnetohydrodynamics)solver that models the geometry of rotating impellers via a penalisation technique. Benchmarks show a good quantitative agreement with experimental data. The investigation of hydrodynamic properties of the system reveals the generation of conical vortices close to the blades, which may provide a major contribution to dynamo action. We achieve dynamo action in simulations of the full magnetohydrodynamic system. A variation of the impeller material constants (steel!soft iron) towards the experimental value leads to a significant decrease of the dynamo threshold as well as a change of the magnetic field mode as observed in the experiment

Numerical study of impeller-driven von Kármán flows and dynamo action via an immersed boundary technique

Im Dynamoprozess werden Magnetfelder zahlreicher astrophysikalischer Objekte durch die Strömung elektrisch leitfähiger Fluide verstärkt. Das Von Kármán Sodium Experiment, in dem zwei Impeller aus Weicheisen flüssiges Natrium antreiben, dient zur Untersuchung dieses Prozesses. Fragen zur Wechselwirkung der flüssigen und festen Komponenten bleiben jedoch offen. Im Rahmen dieser Arbeit wurde ein Pseudospektral-Verfahren zur Lösung der MHD-Gleichungen mit einer Penalty-Methode zur Modellierung der Impeller kombiniert, um direkte numerische Simulationen dieses Systems durchzuführen. Dies erlaubt Analysen der Geschwindigkeits- und Magnetfeldstrukturen jenseits experimenteller Möglichkeiten. Eine Annäherung an die experimentellen Materialkonstanten führt zu einer Verstärkung des Dynamos und zur Ausprägung der im Experiment beobachteten axialsymmetrischen Magnetfeldgeometrie. Die Simulationen geben zudem Aufschluss über den zugrundeliegenden Mechanismus.In the dynamo process, magnetic fields of numerous astrophysical objects are amplified by the flow of electrically conducting fluids. The Von Kármán Sodium Experiment, in which two soft-iron impellers drive liquid sodium, serves the investigation of this process. Questions concerning the interaction of liquid and solid components, though, remain open. In the frame of this work a pseudo-spectral technique for the solution of the MHD equations is combined with a penalty method for the modelling of the impellers, in order to perform direct numerical simulations of this system. This allows for the analysis of velocity and magnetic field structures beyond experimental capabilities. An approximation towards the experimental material constants leads to an enhancement of the dynamo and to the manifestation of the experimentally observed axisymmetric magnetic field geometry. The simulations also shed light on the underlying mechanism

Dynamo Enhancement and Mode Selection Triggered by High Magnetic Permeability

International audienceWe present results from consistent dynamo simulations, where the electrically conducting and incompressible flow inside a cylinder vessel is forced by moving impellers numerically implemented by a penalization method. The numerical scheme models jumps of magnetic permeability for the solid impellers, resembling various configurations tested experimentally in the von Kármán sodium experiment. The most striking experimental observations are reproduced in our set of simulations. In particular, we report on the existence of a time-averaged axisymmetric dynamo mode, self-consistently generated when the magnetic permeability of the impellers exceeds a threshold. We describe a possible scenario involving both the turbulent flow in the vicinity of the impellers and the high magnetic permeability of the impellers