A systematic study of a droplet breakup process in decaying homogeneous isotropic turbulence using a mesoscopic simulation approach

ABSTRACT

The breakup of a spherical droplet in a decaying homogeneous isotropic turbulence is studied by solving the Cahn–Hilliard–Navier–Stokes equations. This flow provides a great opportunity to study the interactions of turbulent kinetic energy and interfacial free energy and their effects on the breakup dynamics. Three distinct stages of droplet evolution, namely, the deformation stage, the breakup stage, and the restoration stage, are identified and then analysed systematically from several perspectives: a geometric perspective, a dynamic perspective, a global energetic perspective, and a multiscale energy transfer perspective. It is found that the ending time of the breakup stage can be estimated by the Hinze criterion. The kinetic energy of the two-phase flow during the breakup stage is found to have a power-law decay with an exponent $-1.76$, compared to $-1.65$ for the single-phase flow, mainly due to the enhanced viscous dissipation generated by the daughter droplets. Energy spectra of the two-phase flow show power-law decay, with a slope between $-4$ and $-3$, at high wave numbers, both in the Fourier spectral space and in the spherical harmonics space.

KEYWORDS:

• Droplet breakup
• decaying homogeneous isotropic turbulence
• DUGKS
• phase-field
• turbulence-interface interaction

Acknowledgments

This work has been supported by the National Natural Science Foundation of China (NSFC) Basic Science Center Program [award number 11988102] and NSFC [award numbers 91852205,91741101, 11961131006], the Taizhou-Shenzhen Innovation Center, the National Numerical Wind Tunnel program, Guangdong Provincial Key Laboratory of Turbulence Research and Applications [grant number 2019B21203001], Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications [grant number 2020B1212030001] and Shenzhen Science and Technology Program [grant number KQTD20180411143441009]. Computing resources are provided by the Center for Computational Science and Engineering of Southern University of Science and Technology. The authors also wish to thank Dr Victor Chéron, Mr Zelong Yuan, Mr Xiusong Chen, and Mr Mingyu Su for helpful discussions.

Disclosure statement

No potential conflict of interest was reported by the authors. 

Additional information

Funding

This work has been supported by the National Natural Science Foundation of China (NSFC) Basic Science Center Program [award number 11988102] and NSFC [award numbers 91852205, 91741101, 11961131006], the Taizhou-Shenzhen Innovation Center, the National Numerical Wind Tunnel program, Guangdong Provincial Key Laboratory of Turbulence Research and Applications [grant number 2019B21203001], Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications [grant number 2020B1212030001] and Shenzhen Science and Technology Program [grant number KQTD20180411143441009].