Construction of an Approach for Evaluation of Droplet Collision Models under DDM Framework Based on an Improved Beer's Law

In spray simulations, uncertainties in the collision incidence predictions always exist for droplet collision models under the discrete droplet model (DDM) framework. In this study, Beer's law, which is used for electromagnetic radiation and light absorption, was improved to evaluate the accuracy of droplet collision models by eliminating the shadow effect among the light-absorbing (stationary) parcels. In addition, the range of parcel numbers in the computational domain was carefully calibrated to ensure the appropriate implementation of Beer's law. Based on the improved Beer's law, a theoretical evaluation method of the computational efficiency of droplet collision models was proposed to conduct a qualitative analysis. Using the above methods, a complete approach for evaluating the accuracy and efficiency of droplet collision models was established. Three representative collision models, including the O'Rourke model, the Nordin model, and the no-time-counter (NTC) model, as well as a new hybrid stochastic/trajectory (HST) collision model, were evaluated comprehensively. The convergence and dependence of the predicted collision incidence on various factors, including parcel radius, grid size, reference frame velocity, and droplet number represented by one parcel, were investigated. It was found that the HST model shows relatively better performance on the collision incidence compared with the other collision models in most cases, especially when one parcel represents multiple droplets. The NTC model achieves the highest computational efficiency, and the computational cost of the construction of the adaptive collision cells in the NTC model and the HST model constitutes a major proportion of the total time consumption.