Session M26: General Fluid Dynamics: Rotating Flows and Multiphysics Phenomena

Flow induced by a rotating cone: velocity field and stability properties

The flow induced by a cone which rotates around its symmetry axis is a canonical case of interest both from a fundamental and an applied viewpoints. Despite its simplicity, it has received little attention if compared to the case of a rotating disk. The boundary-layer equations in the case of a rotating cone allow for a self-similar solution (see Wu, Appl. sci. Res. 8, 1959) analogous to the von Kármán one for a rotating disk. This solution implies that the wall-normal velocity does not vanish far from the wall, at difference with what expected for a cone of finite size. Moreover, the cone apex induces a large-scale motion in comparison to the boundary layer thickness, which is absent for the rotating disk. In this work we extend the analysis by Wu (1959) to account for viscous corrections and large-scale motion due to the apex, arriving to an original correction which is also self-similar. We furthermore explore the influence of the proposed correction on the estimated stability properties of the flow using a weakly-divergent approach based on the assumption of a slow evolution in the streamwise direction. In addition to a standard approach, which is first-order and in which elliptic terms are excluded, we also propose and apply here a second-order extension.
  

Machine learning predictions for magnetic field time evolution in a Three-Meter liquid sodium spherical Couette experiment

The source of the Earth's magnetic field is the turbulent flow of liquid metal in the outer core. Our experiment's goal is to create an Earth-like dynamo to explore the mechanisms of generating the magnetic field and to understand the dynamics of the magnetic and velocity fields. We observe sub-dynamo states that show gain in the applied magnetic field. Prediction of the magnetic field in MHD turbulence field is a challenging problem. We present results of mimicking the experiment by a reservoir computer deep learning algorithm and compare the results with predictions that are done by other techniques. The experiment is a three-meter diameter outer sphere and a one-meter diameter inner core model with the gap filled with liquid sodium. The spheres can rotate independently up to 4 and 14 Hz respectively, giving a Reynolds number up to 1.5*10⁸. Two external electromagnets apply magnetic fields, while 33 Hall sensors measure the resulting fields. We use this data to train a reservoir computer to predict the time evolution and mimic waves in the experiment. Surprisingly accurate predictions can be made for several magnetic dipole time scales. This shows that such a complicated MHD system’s behavior can be predicted.