Laminar-turbulent transition in an electromagnetically levitated droplet
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I. INTRODUCTION
ELECTROMAGNETIC levitation (EML) is a technique used for containerless processing of materials. It can be used to produce ultrapure materials, study nucleation and growth kinetics, and produce materials with metastable microstructures and novel properties. Due to its noncontact nature, it can also access the undercooled state. Density and thermal expansion of metastable materials can be derived from volume measurements, surface tension can be obtained from the droplet oscillation frequency, and viscosity as a function of temperature can be determined from the damping of the oscillations. Measurements of these properties are essential to fundamental endeavors such as improving the theory of the liquid state, and also to industrial applications, such as providing material property input for process modeling in casting and alloying operations.[1] This work reports experimental observations regarding flow transition in a spheroidal palladium-silicon droplet levitated electromagnetically under microgravity conditions. The observations were made using video images from the experiments performed in TEMPUS (Tiegelfreies ElektroMagnetisches Prozessieren unter Schwerelosigkeit; containerless electromagnetic processing under weightlessness), a German microgravity EML facility,[2] during the MSL-1 (first microgravity science laboratory) mission of the Space Shuttle (STS-83 and STS-94). Many methods have been proposed to model this flow. Mestel[3] and Sneyd and Moffatt[4] used analytic solutions for both magnetic force and the fluid flow, and a constant R.W. HYERS, formerly Physicist, NASA Marshall Space Flight Center, Huntsville, AL 35812, is Assistant Professor, Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, MA 01002. Contact e-mail: [email protected] G. TRAPAGA, Professor, is with the Laboratorio de Investigacion en Materiales, Cinvestav—Unidad Queretaro, Qro., 76230 Mexico. B. ABEDIAN, Associate Professor, is with the Mechanical Engineering Department, Tufts University, Medford, MA 02155. Manuscript submitted February 15, 2002. METALLURGICAL AND MATERIALS TRANSACTIONS B
effective viscosity to account for fully developed turbulence. El-Kaddah and Szekely[5,6] used numerical solutions for both magnetic force and fluid flow, and the k- model for turbulence. Other researchers[7–17] used combinations of numerical and analytical models and various turbulence models to examine the flow phenomena in EML droplets. However, the droplet represents a new geometry for the study of the transition to turbulence for the magnetohydrodynamic (MHD) flow. Without a guideline for the onset of turbulence, these previous analyses cannot predict physical conditions under which their assumptions are applicable. The new observations presented here will assist in determining the appropriate assumptions for modeling MHD flow in electromagnetically levitated droplets. Earthbound EML systems require large electromagnetic forces to counteract gravity, and these large forces drive strong flu
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