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INSTABILITY OF ROTATING MAGNETIC FIELD DRIVEN FLOW IN A COUNTER-ROTATING CYLINDER Alexander Pedchenko and Ilmars Grants Institute of Physics, University of Latvia, Salaspils, Latvia

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Applications of Rotating Magnetic Field (RMF) Continuous Casting of Steel, Aluminum etc Semiconductor Crystal Growth create variety of flows with different properties, combining mechanical and RMF induced rotation stabilize unstable convective flow PROBLEM FORMULATION melt mixing and homogenization

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B RMF RMF & counter-rotation driven flow RMF side-wall boundary layer R z r PROBLEM FORMULATION instability may occur at high RMF w R r w - RMF more stable flow

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Data Translation DT9821 4-channel 24-bit A/D USB module EXPERIMETAL SETUP RMF Inductor Container with liquid metal (Hg) Permanent magnets Rotating table with adjustable rot. speed Registering equipment 340 mm 40 mm Nb-Fe-B magnets B

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EXPERIMETAL SETUP Hg electrodes magnets RMF coils SYSTEM PARAMETERS Container: H/R = 40/20 (mm) = 2 melt: Hg RMF: B = 0…3.8 mT (0 Ta m10 7 ) f = 45; 136 Hz Static magnetic field: [at z = H/2, r = 0] B SMF = 40 mT (Ha=20) Mechanical rotation: = 15 rpm (Re =5500); = 45 rpm; (Re =16500); RMF coils Registering equipment Rotating table Permanent magnets Container with Hg

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EXPERIMETAL RESULTS: Determination of the fluid rotation rate driven by RMF only: * c=1.98( /R o 2 )Ta 5/9 P.A.Davidson, JFM 245, 1992 P.A.Davidson formula * for turbulent flow numerical simulation w/ DC field numerical simulation w/o DC field experiment RMF freq 45Hz experiment RMF freq 136Hz calibration of electrodes by applying abrupt pulse of mechanical rotation = f ( c ) - ? spin-up of fluid spin-down of fluid stable rotation of fluid Container at rest

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EXPERIMETAL RESULTS: Container at rest Fluctuating component of the registered electric potential for different strengths of RMF

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10 5 6 7 0.01 0.1 1 Ta m c = 0.23 ×10 6 (0.75 mT) (2.4 mT) Ta m c = 2.3 ×10 6 Ta m c = 0.45 ×10 6 (1.1 mT) V Ta m = 0 = - 15 rpm = - 45 rpm Ta = o B o 2R o 4 /2 2 - electrical conductivity o - RMF frequency B o - RMF induction R o - container radius - density of the fluid - kinematical viscosity EXPERIMETAL RESULTS: Intensity of fluctuations ( ) vs. magnetic forcing (Ta m )

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NUMERICAL STUDY: (r,f,z,t) - flow velocity; = 0 Boundary conditions: where: Steady axisymmetric solution o (r, z) is linearly unstable to infinitesimal perturbations (r,, z) when an eigenvalue problem with = 0 and has at least one eigenvalue r > 0 f (r,z) - e.m. force o - RMF frequency B o - RMF induction - rotation rate of cavity R o - radius of cavity - viscosity - density

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NUMERICAL RESULTS: Calculation with SMFExperimentFlow reversal Ta values Ta c (Re ) calc.Re 3/2

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NUMERICAL RESULTS: r Ta/10 5 Re ~ exp( r +i I )t t

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NUMERICAL RESULTS: radial coordinate axial coordinate -1 0 1 Azimuthal flow Meridional flow c < 0 (wall direction) c = 0 c > 0 (RMF direction) Ta = 1.5×10 4

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RMF side-wall boundary layer instability may occur at high RMF w R r w - RMF more stable flow Conclusions Still stable flowunstable flow

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Conclusions Concurrent action of RMF and mechanical counter-rotation on the instability onset in cylindrical container with aspect ratio H/R=2 observed experimentally and numerically Strong counter-rotation of the container stabilizes the flow driven by RMF and changes the direction of the meridional circulation Weak counter-rotation of the container (when the RMF driven rotation is comparable to the rotation of the container) destabilize the flow. Concentration of the differential swirl occurs near the axis and Rayleigh stability criterion violated in this area. Regime with rapid instability can be used in applications when additional stirring of the melt is required e.g casting of metals etc.

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