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The breakup of a spherical droplet in a decaying homogeneous isotropicturbulence is studied by solving the Cahn-Hilliard-Navier-Stokes equations,using the discrete unified gas kinetic scheme combined with thefree-energy-based phase-field model. We focus on the combined effects ofturbulence and surface tension on the breakup process by assuming that the twofluid phases have the same density and same viscosity. The key physicalparameters of the system include the volume fraction (6.54%), the initial Webernumber (21.7), and the initial Taylor microscale Reynolds number (58). Threedistinct stages of droplet evolution are identified, namely, the deformationstage when the initially spherical droplet evolves into an irregular geometricshape with complex structures, the breakup stage when many daughter dropletsare formed, and the restoration stage when the droplets relax towards sphericalshape. These three stages are analyzed systematically from severalperspectives: (1) a geometric perspective concerning the maximum equivalentdiameter, the total number of droplets, total interface area, and probabilitydistribution of droplet diameters, (2) a dynamic perspective concerning theevolution of local velocity and vorticity at the fluid-fluid interface, (3) aglobal perspective concerning the evolution of average kinetic energy /dissipation rate and their Fourier spectra, (4) spherical harmonics basedenergetics concerning simultaneous transfer of kinetic energy across differentlength scales and different radii relative to initial droplet center, and (5)the time evolution of global kinetic energy and free energy of the system.

Study of a droplet breakup process in decaying homogeneous isotropic turbulence based on the phase-field DUGKS approach