CFD methodologies for compressible atomising and cavitating multi-phase flows

Understanding the complex physics involved in compressible multi-phase flows has been a challenging topic in modern Computational Fluid Dynamics. This is particularly true when investigating the unsteady dynamics of flow in high pressure fuel injectors. The high pressure and impulsive nature of these flows lead to transient complex phenomena including flow separation, cavitation, interfacial instabilities and turbulence. These phenomena contribute to evolution of the spray atomisation in a nonlinear sense. Although useful information on injector flows has been obtained experimentally, the extremely small geometry of injector holes (10\\(^{-4}\\) -10\\(^{-3}\\)) and the highly transient nature of nozzle flows still impose spatial and temporal limitations on experimental investigations. High fidelity numerical simulations serve as a promising tool to provide more insights into spray atomisation processes. The injection of fuel sprays can be divided into three stages. In the first stage, turbulence is generated due to flow separation and cavitation in the injector. Subsequently, innozzle turbulence together with high flow inertia and wall shear lead to the development of surface instabilities incurring primary disintegration of the liquid jet into large structures such as ligaments and irregular droplets. In the final stage, large liquid structures further breakup into fine spherical droplets due to turbulent interaction with the gas in the combustion chamber. In this thesis, three new numerical approaches to analysing different stages of the diesel spray evolution are developed. First, an efficiently parallelised Eulerian (Volume of Fluid) - Lagrangian (Lagrangian Parcel Tracking) coupling procedure is implemented. This procedure couples a high-resolution Eulerian description of primary spray breakup to an efficient Lagrangian tracking of droplet parcels for simulating secondary spray atomisation. Secondly, detailed investigation of the onset of cavitation and hydraulic flip in the injector is performed with a new compressible multi-phase Volume of Fluid cavitation code. Modelling of cavitation and air ingestion induced complete flow detachment in the injector is enabled by the use of multi-phase volume fraction transport equations. A modified multi-phase mixture energy equation integrating nonlinear equations of state and cavitation source terms is then developed and employed to enable simulation of the high pressure injection process with improved fidelity, including thermal effects. Finally, the efficiency and resolution of the cavitation code is improved through the implementation of a compressible fractional step pressure-velocity coupling method for all Mach number flows. Particularly, low dissipation and high resolution are achieved using the Kurganov-Noelle-Petrova central-upwind flux scheme. The performance of the developed numerical methods is demonstrated using a range of geometries from a cavitating square channel to injectors with sharp and rounded nozzle entrances at various injection conditions. In addition, the superiority of the all Mach number multi-phase cavitation code in numerical resolution and computing speed is demonstrated by comparing it with the traditional Pressure-Implicit-with-Splitting-of-Operators (PISO) algorithm.