*Physics and Numerics of Spray Atomization Simulations*. University of Wisconsin-Madison, 2020.

Liquid sprays appear in a wide range of engineering systems, for example, internal combustion engines, irrigation sprays, printing, food processing, and others. The spray formation process, i.e., the process that converts the injected liquid into a cloud of fine droplets, is also known as atomization. This process is a multi-dimensional, multi-scale, turbulent process, with complex topology of the interface.

Fully resolved atomization computations are challenging and computationally expensive. Therefore, most engineering studies, where this process is completely unresolved, depend on lower-order models to describe relevant physics. In the present study, however, we leverage accurate numerical methods along with high spatio-temporal resolution simulations to revisit atomization theory. High fidelity simulations of atomization have only recently become feasible. We have access to spatially resolved data about the liquid and gas distribution along with the velocity field. We are using this data towards developing a better understanding of the atomization mechanisms. A better understanding of the underlying physics ultimately leads to better engineering models.

We also investigate the numerical methods themselves, specifically the surface tension computation. Accurate representation of surface tension depends on the accurate computation of local curvature. This continues to a weakness in the popular simulation methods. This work tries to identify promising curvature schemes in the context of complex flow problems.

The current work is presented as three chapters of this document:

1. A closer look at linear stability theory in primary atomization modeling

Here we look at dominant breakup models. These models are based on the idea that interfacial instability leads to the primary atomization. Here, the underlying assumptions in this theory are outlined and the extent of their validity is established. It is then examined whether these most violent perturbations are actually responsible for the fragmentation of the jet or if there is some other mechanism leading to the breakup.

A main finding from the work shows that while the most unstable modes are captured in the simulations and agree with theoretical predictions that inform the present models, these modes are not directly responsible for fragmenting the liquid core or causing primary atomization. Their action is limited to breaking up the surface of the jet, while the liquid core of the jet remains intact for another 20 jet diameters downstream.

2. Effect of internal nozzle flow on primary atomization

In this part, we study the physics of internal nozzle flow. The focus is on the effect of nozzle asymmetries and imperfections on primary atomization. This is done by adopting three representative geometries, namely two scans of a real injector nozzle, and a canonical configuration with purely external flow.

We find that primary atomization is sensitive to internal nozzle flow; small changes to the nozzle geometry (O(1μm)) affect bulk atomization characteristics (O(1000μm)). Here we explore the underlying mechanism for the same. We find that in spite of more pronounced atomization for the rougher geometry, the magnitude of the turbulent liquid kinetic energy is roughly the same as the smoother geometry. This highlights the important role of mean-field quantities, in particular, non-axial velocity components, in precipitating primary atomization.

3. Evaluating Surface Tension Schemes with Respect to High-Fidelity Atomization Simulations

In complex multi-phase flows like atomization, surface tension is expected to play a vital role in some of the dynamics. Accurate representation of the surface tension force is challenging as it directly tied to the accuracy of the interface curvature calculation. Here, we consider two aspects, first, we analyze three different curvature computation schemes for two-phase flow simulations, and then we evaluate the level of influence these differences in the numerical schemes have on problems of practical interest.

The differences in the accuracy of the three methods is first analyzed through simpler static and dynamic test cases that are common in numerical methods literature. We find that the signed distance-based computation of curvature performs significantly better in these test problems. However, this difference plays a small role in more complex simulations like the retraction of a liquid column. A key finding here is that increasing complexity of the curvature scheme may only lead to marginally better performance in realistic flow problems.