A mass-conserving volume-of-fluid method: Volume tracking and droplet surface-tension in incompressible isotropic turbulence

• We present a volume-of-fluid method that is locally and globally mass conserving.
• The method is wisp-free, consistent, and second-order accurate.
• Surface tension is accounted for using the continuum-surface-force method.
• We simulate droplet-laden incompressible flows.
• DNS of droplet-laden isotropic turbulence with 7000 droplets and 10243 mesh.

We have developed a volume of fluid (VoF)/projection method for simulating droplet-laden incompressible turbulent flows with uniform density and viscosity. The method is mass-conserving, wisp-free, and consistent (i.e., the VoF function, C, satisfies the condition 0 ⩽ C ⩽ 1).First, we present the results of the VoF method for tracking volumes of initially spherical shape and with zero surface tension in analytical velocity fields (linear translation, solid-body rotation, single-vortex flow, and Taylor–Green vortex) and in incompressible isotropic turbulence at Reλ0 = 75 and 190. These numerical tests show that (i) our VoF method is mass-conserving, consistent, and wisp-free; (ii) for a CFL number of 0.1, the VoF geometrical error has almost a second-order convergence rate for a mesh resolution with more than 10 grid points per diameter; (iii) in the isotropic turbulence case, a resolution of about 32 grid points per diameter of the sphere is required in order to limit the VoF geometrical error below 1%. Then, in order to simulate droplet-laden flows, we have adopted the continuum surface force (CSF) model to compute the surface tension force. We have modified the sequence of the VoF advection sweeps, and show that, in the case of droplet in a translating reference frame, the r.m.s. of the spurious currents is about 1% of the translating velocity. Finally, we present DNS results of fully-resolved droplet-laden incompressible isotropic turbulence at Reλ0=75Reλ0=75 using a computational mesh of 1024310243 grid points and 7000 droplets of Weber number Werms=0.5Werms=0.5, and initial droplet diameter equal to the Taylor length-scale of turbulence.