Fluid flow and heat transfer in levitated droplets were numerically
investigated. Three levitation methods: electro-magnetic levitation
(EML), aerodynamic levitation (ADL), and electro-static levitation
(ESL) were considered, and conservative laws of mass, momentum,
and energy were applied as common models. The Marangoni effect
was applied as a velocity boundary condition, whereas heat transfer
and radiation heat loss were considered as thermal boundary conditions.
As specific models to EML, the Lorentz force and Joule heat
were calculated based on the analytical solution of the electromagnetic
field. For ADL model, besides the Marangoni effect, the flow driven
by the surface shear force was considered. For ADL and ESL models,
the effect of laser heating was introduced as a boundary condition. All
the equations were nondimensionalized using common scales for all
three levitations. Numerical simulations were performed for several
materials and droplet sizes, and the results were evaluated in terms of
the Reynolds number based on the maximum velocity of the flow in the
droplet. The order of magnitude of Reynolds numbers was evaluated
as Re ∼ 10
4 for EML, Re ∼ 10
3 for ADL, and Re ∼ 10
1 for ESL. Based on the simulation results, we proposed simple
formulas for predicting the Reynolds number of droplet internal convection using combinations of nondimensional
numbers determined from physical properties of the material and the driving conditions. The proposed formulas can
be used as surrogate models to predict the Reynolds numbers, even for materials other than those used in this study.
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