As vortex ring-like structures in two-phase mixtures occur in a wide range of systems such as gasoline engines, appropriate mathematical models of such processes would allow engineers to rapidly test novel ways of optimising and improving a range of engineering systems before resorting to costly experimental evaluation of new technologies. This proposal is therefore concerned with the generalisation of a mathematical approach known as the full Lagrangian approach (also known as the Osiptsov-Lagrangian method) to enable it to model vortex ring-like structures in two-phase mixtures. The main focus of the project will be on the development of this approach to enable its use in the modelling of three-dimensional processes within a Computational Fluid Dynamics (CFD) framework. The project will also investigate the possibility of constructing new mathematical models of vortex ring-like structures, to take into account additional complications relevant to certain engineering applications such as the effect of an elliptical core. This new approach to the modelling of multiphase flows will incorporate the jet and droplet break-up models developed through a currently active EPSRC project EP/F069855/1. Where appropriate, predictions resulting from the new models will be compared with predictions based on three dimensional numerical simulations of transient vortex ring-like structures, based on the conventional research CFD code KIVA 3 and commercial CFD code FLUENT. A feasibility study will also be performed into the modelling of these vortex ring-like structures based on the combination of the full Lagrangian approach for the dispersed phase and the vortex method for the carrier phase to examine the advantages and limitations of the different mathematical approaches. Finally, predictions from numerical and analytical models will be validated against in-house experimental results obtained in gasoline engine-like conditions allowing an assessment to be made into the applicability of using the models for the characterisation of processes in gasoline engines. This will be a collaborative project involving external consultants Professor A. Osiptsov (Lomonosov Moscow State University, Russia) and Dr. F. Kaplanski (Tallinn Technical University, Estonia), whose expertise is mainly focused on the development of the full Lagrangian method for multiphase flows and semi-analytical vortex ring models. It will be led by Professor S. Sazhin, whose expertise includes the development of new physical models of fuel droplet and spray processes as applied to modelling internal-combustion engines. The co-investigators Dr. S. Begg and Professor M. Heikal will advise on the relevance of the models to automotive applications and provide the experimental data required for the validation of the models. A Research Fellow will be included in the project. This project will ensure a qualitatively new level of physical and mathematical models, developed in the previously funded EPSRC project EP/E047912/1, supporting the collaboration between the PI, co-investigators and Dr F. Kaplanski, and the currently active project EP/F069855/1.