S. Denisov, V. Dolgikh, R. Khalilov, S. Khripchenko , I. Kolesnichenko, A. Korobkov

1. Laboratory of Hydrodynamics Institute of Continuous Media Mechanics Ural Branch of Russian Academy of Science Perm, Russia FLOWCOMAG Dresden, April 2004 EXCITATION OF VORTEX FLOWS IN PLANE LAYERS OF CONDUCTING FLUID BY ELECTRIC CURRENT OR ALTERNATING MAGNETIC FIELD S. Denisov, V. Dolgikh, R. Khalilov, S. Khripchenko, I. Kolesnichenko, A. Korobkov The research described here was made possible in part by Award #2021 from International Scientific & Technology Center (ISTC)

2. April 2004 Excitation of vortex flows ICMM Introduction – 1 Electric current flowing through the layer of conductive fluid excites magnetic field. It interacts with the magnetic field and generates volumetric forces in the fluid. Under certain conditions these forces may have the vortex component and excite the fluid motion. For example, when the ferromagnetic bodies are placed near the layer they increase the magnetic field of the current in this region. The edges of ferromagnetic bodies produce the magnetic field gradient along the electric current lines, which is the cause of generation of the vortex component of electromagnetic forces. To illustrate this case, we place the rectangular ferromagnetic body near the surface of liquid metal. Then, in the region of the core we can observe the planar vortex flow in the layer (Fig.1). The flow topology strongly depends on the body geometry and on the location of ferromagnetic bodies (Fig. 2a). Fig.1 Fig.2a 1

3. April 2004 Excitation of vortex flows ICMM Introduction – 2 Fig. 2b Thus, if we pass the electric current through the layer of conducting fluid and locate the ferromagnetic bodies of different configuration near this layer, then we produce various vortex flows Fig. 2b. 2

4. April 2004 Excitation of vortex flows ICMM In foundry Using of this EVF - method for mixing of solidifying metal in continuous steel casting machine Using this method, it is possible to stir liquid metals during technological processes. For example, when we pass the electric current through the continuous steel ingot in the continuous casting machine, the machine rolls become ferromagnetic cores and induce the stirring motion in the liquid core of the ingot (Fig.3). Fig.3 3

5. April 2004 Excitation of vortex flows ICMM Electro-vortex flows – 1 The experimental setup used in our research was a rectangular bath filled with liquid gallium of thickness 10mm. The bath sizes in plane were 150x150mm. Two opposite sides of the bath were copper electrodes, which were used to pass the electric current through the layer of liquid metal in the bath. Ferromagnetic cores of different shape were located above and under the bath. The cores were rectangular bodies or C-shape cores (Fig.4). For visualization of the flow in the layer, we disposed the thin layer of HCl solution on the liquid metal surface. The acid interacted with liquid metal and produced gas bulbs. These bulbs showed the motion of liquid metal. Fig.4 5

6. April 2004 Excitation of vortex flows ICMM Hydrodynamics equations The metal flow in our experiment and in the case of stirring the liquid metal core of the continuous ingot can be described by the system of approximate two-dimensional equations for the flat layer of liquid. In these equations, we use the shallow water approximation. Turbulent friction is defined by friction in the viscous sublayer near the upper and lower walls of the liquid layer. 4

7. April 2004 Excitation of vortex flows ICMM Electro-vortex flows – 2 Fig.5 In Fig.5 we can see that the numerical results coincide with the results of physical experiments. So, our mathematical model can be used for describing the hydrodynamical processes in the liquid core of the continuous steel ingot produced by elelectrovortex stirring. 6

8. April 2004 Excitation of vortex flows ICMM Magneto-vortex flows – 1 The effect similar to electrovortex stirring just described takes place when the ferromagnetic cores generate the alternating magnetic field in some region of the liquid metal layer. alternating magnetic field generates the electric current in the layer. The electric current interacts with the field and excites the electromagnetic force which can generate the vortex motion (Fig.6). By analogy with the electrovortex flow excited by the electric current, the vortex flow in liquid metal generated by the alternating magnetic field can be called the magnetovortex flow. Fig.6 7

9. April 2004 Excitation of vortex flows ICMM Magneto-vortex flows – 2 Fig.7 The experimental setup was a shallow rectangular bath of sizes in plane 200x100mm. Gallium alloy of 10mm in depth was poured into the bath. Part of the layer was placed in the gap between the poles of the C-shaped electromagnet under the alternating magnetic field. We observed in our experiment the generation of the planar vortex flow of metal by the alternating magnetic field in the bath. The flow intensity was defined by the value of the magnetic field, and the flow topology defined by the disposition of the electromagnetic core poles on the metal surface. 8

10. April 2004 Excitation of vortex flows ICMM Magneto-vortex flows – 3 The hydrodynamic field of the flow can be calculated by equation (1) used above. For the case of the electrovortex flow, the electromagnetic volumetric forces were obtained from the solution of the approximate two-dimensional equations for magnetic field. These equations were found by reducing the Maxwell equations Numerical results obtained using the approximate equations agree with the results of physical experiments (Fig.8). Fig.8 9

11. April 2004 Excitation of vortex flows ICMM Mixing of Melted Magnesium by MVF Fig.9 Fig.10 We have designed and manufactured the MHD-stirrer for preparation of special magnesium alloys in the rectangular box. This stirrer was used at the Stock company “AVISMA” (Fig.9). The intensity and topology of this motion depended on the magnetic field volume and the magnetic core location (Fig.10). 10