The influence of an advecting vortex on the heat transfer to a liquid droplet

Abstract

The unsteady three-dimensional interaction of an initially cylindrical vortex tube with a droplet in a uniform stream is investigated through a numerical solution of the Navier-Stokes equations. Particular attention is given to the effect of the vortex on the droplet convective heat transfer. The transient response of the droplet Nusselt number is sensitive to the geometrical factors that specify the vortex initial position and structure. The time-averaged Nusselt number is approximately the value for the axisymmetric case when the vortex center approaches the droplet along the base flow symmetry axis; otherwise, it varies monotonically with the vortex initial distance from the base flow symmetry axis, vortex circulation, and base flow Reynolds number. Beyond a certain range, the time-averaged Nusselt number reaches an asymptotic value. A correlation quantifying average effects of the vortex advection on the droplet heating, signifying a self-similar pattern in this unsteady problem, has been produced, and is shown to be also applicable to a rigid sphere in a comparable condition. This correlation compliments the existing ones for droplet healing in an axisymmetric flow. Based on these findings, it may be speculated that, in a spray combustion system, the vortex-droplet interactions within the Kolmogorov scale can have significant effects on the droplet convective heat transfer.