1. Investigation of Elementary Processes of Non-Newtonian Droplets Inside Spray Processes by Means of Direct Numerical Simulation

Binary droplet collisions play an important role as an essential elementary process in sprays. They significantly influence the droplet size distribution. In order to give an improved prediction of the outcome of droplet collisions, understanding of the influence of the liquid rheology on the collisions as well as on the flow dynamics inside the colliding droplets is necessary. In this work, we have investigated binary droplet collisions by means of Direct Numerical Simulation (DNS) of two-phase incompressible Navier–Stokes equations using the Volume-of-Fluid (VOF) code Free Surface 3D (FS3D). A pivotal aim of the study is to derive mechanistic models for the outcome of collisions which can be used for scale-reduced simulations such as Euler–Euler and Euler–Lagrange simulations. In order to reach this goal, we have investigated various kinds of collisions, such as collisions of shear-thinning, non-isoviscous, and viscoelastic droplets. We have also developed and implemented various numerical algorithms to overcome the numerical difficulties in simulating different kinds of collisions.

In droplet collisions at high Weber numbers, extremely thin liquid lamellae appear. These lamellae must be reproduced in the numerical simulation in a physically meaningful way. A stabilization algorithm is therefore developed to prevent the lamellae from rupture without restrictions on the mobility and deformability of lamellae.

DNS of collisions of shear-thinning droplets show that almost all viscous dissipation occurs during the initial phase of the collision. Because of this, an effective constant viscosity can be found which leads to the same collision dynamics as with shear-thinning viscosity. This effective viscosity can be found both for head-on and off-center collisions and can be determined from simulation of just the initial phase of the collisions.

In order to simulate the collisions of droplets with unequal viscosity, an extension of the VOF method has been made by solving an additional transport equation to obtain the polymer mass fraction distribution inside the collision complex. To capture the delayed coalescence observed in experiment, a coalescence suppression algorithm has been developed. The results obtained in this way agree well with the experiment and give a deep insight into the hydrodynamic penetration and encapsulation processes.

To simulate viscoelastic two-phase flow problems, the VOF method has been extended to capture the rheological properties of the Oldroyd-B fluid. To alleviate the High Weissenberg Number Problem in the simulation of viscoelastic flow, stabilization approaches have been adapted and implemented in FS3D. The simulation results show that the viscoelastic effect is reflected in the oscillation process during the collision, and the elasticity restrains the deformation of the collision complex.

A mechanistic model, based on the model developed by Roisman et al. [26], has been extended by treating the evolution of lamella thickness and the dependence of the lamella thickness on the radius separately. With this extension, the model can predict the head-on collisions with significant influence of viscosity. The model parameters are gained by simulation of the initial phase of the collision without requirement of fine mesh resolution. This hybrid model has the advantage of massively reduced computation time compared to full DNS (below 1 %) and shows good agreement with simulation and experiment.