# Dr. Muyuan Liu

Work

## Modeling and simulation of droplet collisions under high pressure and far from equilibrium and simulation of splashing

### Research Motivation

Droplet collision plays an important role in spray processes. It influences the droplet size distribution of a spray system by means of different collision outcomes.

The collision dynamics under isothermal condition for Newtonian fluids with the collision outcomes of separated and combined droplets are well understood, in which the influence of the viscosity is a current research topic [1, 2]. In extreme environmental conditions such as in fuel sprays with evaporations, the droplets have different temperature due to different trajectories and evaporation histories, which leads to various surface tensions of the droplets. As a result, the collision dynamic is strongly influenced. The high pressure leads to a large increase in outcome of bouncing, which is still not predictable via numerical simulations. Furthermore, the evaporation pressure also influences the collision dynamic. In the condition of high kinetic energy, the droplet collision will result in an unstable outcome namely splashing. It occurs in sprays generated by multi-nozzles.

Direct numerical simulation is useful in understanding these phenomena.

### Scientific Project

The simulations of droplet collisions are performed with the Finite Volume code Free Surface 3D (FS3D) [3], which solves the Navier-Stokes equation for an incompressible transient two-phase flow. In order to capture the thin lamella in the middle of the collision complex simulating splashing, FS3D is extended with a lamella stabilisation method. A subgrid model based on the lubrication theory is developed with the aim of predictive simulations of bouncing. The superior goal of the project is to develop a thermodynamic consistent sharp interface method for multi-component and multiphase fluid systems.

Splashing phenomena resulted from water droplet collisions are simulated by means of the lamella stabilization method. The simulations predict the detachment of secondary droplets very well as shown in figure 1. The pressure varies between positive and negative as the collision proceeds as shown in figure 2.

### Acknowledgements

The author thanks the German Foundation (DFG) for financial support within the scope of SFB-TRR 75 “Tropfendynamische Prozesse unter extremen Umgebungsbedingungen”.

### Project References

[1] D. Schmidt and M. Dai. Numerical simulation of head-on droplet collision: Effect of viscosity on maximum deformation. Phys. Fluids, 17, (2005): 041701.

[2] C. Focke and D. Bothe. Direct numerical simulation of binary off-centre collision of shear thinning droplets at high Weber numbers. Physics of Fluids, 24(7), (2012): 073105.

[3] M. Rieber. PhD-Thesis. ITRL-Stuttgart, 2004.