A New Droplet Collision Algorithm

The droplet collision algorithm of O'Rourke is currently the standard approach to calculating collisions in Lagrangian spray simulations. This algorithm has a cost proportional to the square of the number of computational particles, or “parcels”. To more efficiently calculate droplet collisions, a technique applied to gas dynamics simulations is extended for use in sprays. For this technique to work efficiently, it must be able to handle the general case where the number of droplets in each parcel varies. The present work shows how the no-time-counter (NTC) method can be extended for the general case of varying numbers of droplets per parcel. The basis of this improvement is analytically derived. The new algorithm is compared to closed-form solutions and to the algorithm of O'Rourke. The NTC method is several orders of magnitude faster and slightly more accurate than O'Rourke's method for several test cases. The second part of the paper concerns implementation of the collision algorithm into a multidimensional code that also models the gas phase behavior and spray breakup. The collision computations are performed on a special collision mesh that is optimized for both sample size and spatial resolution. The mesh is different every time step to further suppress the artifacts that are common in the method of O'Rourke. The parcels are then sorted into cells, so that a list of all the parcels in a given cell are readily available. Next, each cell is individually checked to see if it is so dense that a direct collision calculation is cheaper than the NTC method. The cheaper method is applied to that cell. The final result is a method of calculating spray droplet collisions that is both faster and more accurate than the current standard method of O'Rourke.