Influences of initial streamwise rotation of a droplet under a uniform flow

TL;DR

This study investigates how initial streamwise rotation affects droplet deformation and vortex dynamics under uniform flow using numerical simulations, revealing distinct shape families and vortex behaviors influenced by rotation rate.

Contribution

It introduces a detailed numerical analysis of rotating droplet deformation, identifying new shape families and vortex release mechanisms at lower Reynolds numbers than previous studies.

Findings

Droplet shapes vary with rotation rate: biconvex, convex-concave, biconcave.

Vortex ring release occurs at lower Reynolds numbers than for solid spheres.

Rotation influences droplet deformation and vortex dynamics significantly.

Abstract

A spherical droplet is given an initial rotation in the streamwise direction and is impulsively accelerated by a uniform free stream. Numerical results for the deformation and dynamics of the droplet are obtained by utilising a finite volume staggered mesh method with a moving mesh interface tracking scheme. The fluid dynamics videos of the droplet are presented in the Gallery of Fluid Motion, 2010. By initially rotating the droplet in the streamwise direction, the droplet deforms differently depending on the non-dimensional rotation rate, $\Omega^*$. The families of droplet shape are, in ascending $\Omega^*$, biconvex, convex-concave and biconcave. While the biconvex and convex-concave families are due to the compression by the combined vortex ring (the lee side of the interface). The biconcave family is formed because of the huge surface tension at the droplet edge that restrains further deformation there. In a special case, the biconcave family releases the combined vortex ring from the droplet. The release of the vortex ring is observed to be at $Re$ one order of magnitude lower than a similar mechanism observed for the flow past a solid sphere. This release of the vortex ring has led to a series of events and a reduction in $C_D$.