Nore C, Léorat J, Guermond J-L, Giesecke A
Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur, CNRS UPR 3251, Rue John von Neumann, 91403 Orsay cedex, France and Université Paris-Sud, Paris, France.
Luth-Observatoire de Paris-Meudon, Place Janssen, 92195 Meudon, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Jan;91(1):013008. doi: 10.1103/PhysRevE.91.013008. Epub 2015 Jan 14.
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.
据观察，只有当旋转圆盘和叶片由软铁制成时，冯·卡门 - 钠（VKS）实验中才会发生发电机作用。本文的目的是对软铁在VKS发电机情形中的作用进行数值研究。这是通过使用一个基于轴对称平均流、局部磁导率分布以及模拟叶片间小速度尺度作用的局部α效应的平均场模型来完成的。旋转叶片的作用由轴对称有效磁导率场建模。确定了赋予数值磁场与实验观测到的几何结构相似的流动的关键特性。根据圆盘的磁导率和叶片的有效磁导率，得到的发电机要么是振荡型的，要么是稳态型的。我们的数值结果证实了铁磁叶轮所起的主导作用。提出了一个VKS发电机的情形。
