Efficient Lagrangian simulation of electrospray droplets dynamics

Tracking the trajectories of individual droplets in Lagrangian numerical simulations of electrosprays involves a large number of computations, due to the calculation of the electrostatic repulsion force between droplets (space charge force). Two strategies are proposed in this study to reduce such number while preserving accuracy. In one strategy, the force contribution from distant droplets is simplified by replacing the droplet charges belonging to small volumes or cells within the spray with a single charge per cell located at the cell's center-of-charge. In the other strategy, the integration of the droplets' motion in different axial regions of the spray is carried out using two very different time steps, using higher time resolution where the electrical force variation sensed by the droplets is larger. With these methods the CPU time was shortened by a factor of 39 (from 1658 to 42 h), in a simulation of an electrospray characterized by a count mean diameter (CMD) of 8.84 μm and around 26,000 droplets in the steady state. In another spray, comprising about 3400 droplets (CMD=32 μm), the CPU time was reduced by a factor of 4.4. In this case, the CPU reduction is smaller because the proposed methodologies become less efficient with a smaller number of droplets. This study is also concerned with the selection of a proper integration time step. We show that an acceptable upper bound to the time step is based on the proper description of numerical collisions between electrospray droplets. Interestingly, in both systems simulated, a similar maximum acceptable time step is found (2 μs).

► Lagrangian simulations of electrosprays are modeled.
► For large numbers of droplets in the spray, simulations take a long time.
► Lumping space charge into cells reduces the CPU time.
► Tailoring the time step in different spray zones also reduces CPU time.
► Real collisions between droplets are detected in the complete simulations.