Direct Comparison of Particle-Tracking and Sectional Approaches for Shock Driven Flows

Abstract

Dispersed-phase flows are important for a wide variety of problems, and several numerical approaches for the solution of dispersed-phase flows have been proposed and implemented in the past. The present research implements two popular approaches to dispersed-phase flows: the Lagrangian particle-tracking approach and the Eulerian sectional approach. A direct comparison between the two methods is made for a range of shock driven seeded flow-fields. First, different drag models are investigated using the particle-tracking method for a range of conditions, and then direct comparisons between the two methods are made for shock speed attenuation and shock-wave profiles. In addition, resolution requirements are investigated to determine the number of sections and the number of particles required to obtain good agreement between the methods, and then two-dimensional simulations are done to investigate the effect of each method on more complicated flow-fields. Results showed both methods can be used to obtain very similar results, although each method has benefits and drawbacks. The glass particles were then replaced with water droplets, and the effect of vaporization and droplet breakup were then investigated. Although vaporization was well represented with the sectional approach, different droplet breakup models had to be implemented for the different approaches, with some significant differences in the resultant droplet distributions. The reason for this is that breakup models require a droplet deformation time before breaking up, and thus a droplet history. This droplet history is difficult to implement in sectional approaches (and Eulerian methods in general), and so the breakup model must be changed. Similar profiles could be reproduced with the sectional method, but significant differences persisted. The results did show, however, that the Eulerian sectional approach is a viable method for computing complex, multi-dimensional flow-fields and can provide significant numerical advantages when compared with Lagrangian particle-tracking methods, especially in flooded environments such as examined here.