Numerical Investigation of High-Speed Droplet Impact Upon a Solid Surface

Abstract

The impact of high-speed liquid droplets onto a solid surface plays an important role in a wide range of applications including cleaning of semiconductor devices, steam turbines, and supersonic/hypersonic flight. The mechanical loads experienced by high-speed projectiles from atmospheric droplet interactions are critical in assessing their performance and structural integrity. Droplet impact has been widely studied in the incompressible to weakly compressible regime. However, limited work has been conducted on the (highly) compressible regime. High-speed droplet impacts pose a complex multiphysics challenge due to intricate shock interactions, which make predicting surface stresses difficult. The mechanism responsible for generating maximum pressure at large impact speeds remains poorly understood. Most research on high-speed impacts has focused on single droplet impact, leaving the effects of multiple high-speed droplets largely unexplored.

This thesis aims to enhance the current understanding high-speed (highly compressible) droplet impacts through numerical simulations. It seeks to determine the necessary resolution requirements for accurately modeling surface pressure, investigate the role of compressibility in predicting potential surface damage during single droplet impacts, and explore the interactions of multiple impacting droplets. To achieve this objective, high-fidelity numerical simulations of water droplets impacting a rigid wall at Mach numbers greater than 2 are conducted using a second-order accurate method with adaptive mesh refinement and a consistent, conservative Phase-Field approach.

This thesis investigates the model parameters and resolution requirements necessary for performing simulations that accurately capture the physics of high-speed droplet impacts. Accurately predicting the pressure on a surface during impact requires precise modeling of the droplet's air/water interface. Innovative modeling techniques (Phase-Field model) provide control over the numerical interface thickness, necessitating the identification of the correct parameters governing this thickness. The interface thickness and resolution parameters significantly affect both the maximum surface pressure and its wall location. Thin interfaces clearly demonstrate that pressure is generated in a highly compressed air pocket. A balanced combination of resolution parameters and numerical interface thickness can accurately capture the physics while minimizing computational costs.

Building on an understanding of the resolution parameters that enable accurate physics, this thesis then computationally explores the role of compressibility in identifying the mechanism that generates maximum wall pressure. It also examines how increasing droplet speeds intensify compressibility effects, thereby raising the likelihood of potential damage. Notably, the maximum wall pressures occur within an air pocket compressed by the incoming droplet. These pressures exceed those predicted by classical water-hammer theory. However, the center-point pressure aligns with a modified equation accounting for compressibility. From the surface pressure and material properties, the potential deformation can be deduced.

Leveraging the understanding of single high-speed droplet impact, the thesis study explores how changes in droplet spacing and size ratio influence the wall pressures resulting from the impact of two Mach 4 cylindrical droplets on a rigid surface through numerical simulations. The collision of lateral jets from the droplets produces a pressure that is notably higher than single droplet impact, when the droplets are sufficiently close to each other.

By employing numerical simulations with appropriate resolution/model parameters, the pressure exerted on a surface by high-speed droplet impacts can be accurately predicted. This accurate characterization of the surface pressures is critical to predicting mechanical loads/possible damage, with the potential to lead design improvements (enhanced performance/structural integrity) for a number of applications, ranging from supersonic/hypersonic flight to steam turbines.