Development of a suitable numerical solution algorithm for the two-phase Euler-Lagrange approach with four way coupling in spray simulation

The most common method of simulating liquid spray in a gaseous environment is the Eulerian Lagrangian approach where the gas phase is solved by the Euler method and the liquid phase by the Lagrange method. In the dense regime, the effect of the liquid phase on the gas phase and also the effect of the droplets on each other are of great importance. Due to the strong coupling between the gas phase and liquid phase, numerical solution of these equations is one of the main challenges of this approach. In this study, two SIMPLE based algorithms for solving these equations are presented. To do this task, a Lagrangian-Eulerian computer code was developed for the two-phase flow equations. To evaluate the proposed approaches, the diesel fuel spray was solved and by comparing results, the appropriate algorithm was selected. The results showed solving the liquid phase equations at the beginning of the SIMPLE iteration loop and then making two corrections in the appropriate position inside the algorithm, provides a suitable method for solving governing equations of the spray with the assumption of four-way coupling in the Eulerian-Lagrangian approach.