Numerical Simulation of Dispersed Phase Droplets Impingement by a Hybrid Eulerian-Lagrangian Method

This chapter covers the basic theory underlying droplet tracking simulations, using the Eulerian and Lagrangian approaches. The equations of motion in both approaches are detailed, with particular care taken in the mathematical description of the Eulerian conservation equations. A relaxation procedure is added to recover strict hyperbolicity and allow the implementation of an exact Riemann solver on unstructured meshes. A model capable of correcting the collection efficiency to account for splashing and bouncing is presented. Furthermore, a cost-efficient strategy to track the freestream droplets using the Eulerian approach and re-inject the splashed and bounced droplets using the Lagrangian approach is presented. Polydispersity is accounted for using a multi-bin approach, and its effects on the re-injection are highlighted. A restart technique to mitigate computational costs for multi-bin simulations is detailed. Specific examples of collection efficiency predictions are presented for each of these steps, always comparing them to experimental data to show how each of these affects the impingement prediction.