Experimental and numerical study of rotating magnetic field driven flow in cylindrical enclosures with different aspect ratios

Abstract

Azimuthal velocities of the rotating magnetic field driven flow in a cylindrical container are measured in two different experiments for different aspect ratios (height/radius) of the container and different strengths of the magnetic field. The measured velocities are compared with the calculated ones. A good agreement between the experimental and numerical results is obtained. This validates the experimental techniques, the computational approach, and also the time-averaged model widely used in calculations of RMFdriven flows. It is shown that the average angular velocity normalized by the square root of the magnetic Taylor number grows linearly for the aspect ratios exceeding 1, and non-linearly for smaller aspect ratios. It is shown also that when the magnetic field is sufficiently large, the average angular velocity grows proportionally to the Hartmann number or proportionally to the square root of the magnetic Taylor number. It is shown that the dependence of the average angular velocity on the aspect ratio can be roughly approximated by a power of the ratio radius/height. 1. Introduction. Rotating magnetic fields (RMFs) are widely used in metallurgical and crystal growth technologies for controlling the melt flows and heat and mass transfer characteristics [1–3]. The rotating magnetic field induces a time-averaged azimuthal force, which drives the flow in circumferential direction. In its turn, non-uniform rotation of the liquid induces the azimuthal flow. All three components of the flow affect the heat and mass transfer processes thus yielding a powerful tool for flow and heat and mass transfer control. The RMF-driven flows have been intensively studied during two recent decades both experimentally and numerically (see [2–18] and references therein). In spite of the large number of numerical studies of the RMF-induced flows, there are only few experimental investigations [2–9]. Most of experimental studies examine the influence of RMF on the temperature field or on the properties of grown crystals [2, 8–11], so avoiding the study of the flow field itself. There are very few attempts to measure the fluid velocities directly [3, 7, 14]. In the present study we report direct measurements of the azimuthal velocities of the RMF-driven flow in cylindrical containers of different aspect ratios (height/radius). The measured velocities are compared with the results of calculations, which, in their turn, are performed by two independent approaches. In this way we perform cross-validation of the experimental methodology with the calculations. The main set of results of the present study consists of the experimentally measured and numerically calculated dependencies of the azimuthal velocity in different radial and axial cross-sections of the container on the parameters of the RMF inductor and the geometry of the cylindrical container. A good agreement between the experimental and numerical results provides a rigorous experimental