Analysis and modeling of droplet-droplet interaction and particle-droplet interaction in dispersions

Droplet (fluid) -droplet (fluid) interaction: A numerical investigation of binary droplet collisions in a gaseous phase has been conducted as part of the coalescence modeling project. A volume of fluid (VOF) based interface capturing method, which is characterized by introducing an extra artificial compression term into the volume-fraction transport equation, is employed to capture the liquid-gas interface. The full Navier-Stokes equations coupled with the volumefraction transport equation are discretized on a fixed, uniform grid using the finite volume method. The solution of the volume-fraction transport equation is bounded by an explicit universal multi-dimensional limiter. The simulations cover the coalescence regime of binary droplet collisions. A ghost cell method is introduced in order to simulate retarded coalescence in head-on collisions. In this method, the volume-fraction boundary condition on the symmetry plane is switched to numerically control coalescence at a critical time which is determined by tracking the interface front. The simulated results are compared with attainable experimental data and provide detailed pictures exhibiting the collision processes. The interdroplet pressure, defined by the static pressure on the symmetry plane in head-on collisions, is evaluated. The phenomenological criteria for droplet coalescence model are discussed. Moreover, the multiple entity VOF model and adaptive local grid refinement approach are implemented in OpenFOAM and tested here. For the former, by using two or more VOF indicator functions, the identity of each droplet is preserved and can be detected after contact until coalescence. The multiple entity VOF model is helpful to develop the droplet coalescence model here. For the latter, it can be combined with VOF model to increase the accuracy of the solution particularly in the region of the liquid-gas interface and thus has a potential to capture more details of tiny satellite droplets’ formation. Particle (solid) -droplet (fluid) interaction: Particle-droplet interaction is modeled by VOF method coupled with mesh motion in six degrees of freedom (6-DoF). Here the small solid particle (in the order of 1~10 μm) is represented by a solid object with 6-DoF motion while the liquid droplet (in the order of 10 μm) represented by liquid volume fraction. The preliminary results are presented in this report. Part I: Modeling of droplet-droplet interaction Compressive VOF: In this report, the focus is on the collision process of two equal-sized droplets in a gaseous atmosphere at moderate Weber numbers. Qian and Law [1] presented well time-resolved photographic collision images in all collision regimes for a hydrocarbon/nitrogen system, which have been used as validation reference here. The numerical simulation is performed using the open source CFD code OpenFOAM [2]. A VOF based interface capturing method is applied to deal with the gas-liquid interface. In OpenFOAM, the necessary compression of the interface is achieved by introducing an extra, artificial compression term into the volume-fraction transport equation instead of just using a compressive differencing scheme. Multi-dimensional universal limiter with explicit solution (MULES) (i.e., the current approach to define the compressive velocity field in OpenFOAM) is used to limit the flux of the variables to guarantee a bounded-solution. The continuum surface force (CSF) method is employed to calculate the surface tension force. However, as in the standard VOF