An adaptive-mesh Cahn-Hilliard Navier-Stokes (CH-NS) model for resolving film- and filament- breakup in primary jet atomization*

The development of scalable and accurate numerical methods to model primary jet atomization over a long time horizon is challenging. A viable method must capture complex interfacial phenomena (breakup/coalesce) at disparate scales across long time horizons while preserving structure (mass, interface, droplet statistics) and exhibiting computational scalability. Here, we address the challenge of preserving the interface's structure by dynamically adapting resolution in a CH-NS model, thereby preventing artifacts from polluting the breakup statistics. The CH-NS model is endowed with mass conservation. However, when droplet sizes become comparable to the interface thickness (Cn number), there is a coalescence of smaller droplets with nearby bigger droplets (Ostwald ripening). Reducing the Cn number everywhere is infeasible as it increases compute requirements. Therefore, it becomes important to selectively identify the regions of the small drops/filaments/films to enforce lower Cn, ensuring a balance between computational cost and accuracy. We showcase improved results of primary jet atomization simulations that incorporate on-the-fly detection of small drops and filaments to reduce the Cn number, coupled with improved numerical schemes that enforce degenerate mobility.