  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 the 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 $\text{Re} \sim 10^4$ for EML,
$\text{Re} \sim 10^3$ for ADL, and $\text{Re} \sim 10^1$ 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 the 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.
