Spray is a core phenomenon in a range of technologies, including medical inhalers, surface coating, electronics cooling, fuel injectors in automotive engineering, and the production of dry powder in pharmaceutical applications. Accurate predictions of droplet dynamics, distribution of droplets and their vapour concentration in space and time are essential for making technologies based on sprays more efficient. The focus of the project is on the development of a novel tool to simulate sprays for engineering applications. The novelty lies in the synthesis and development of mathematical and numerical modelling techniques with the view to be applied to engineering applications. Conventional modelling of droplets is based on tracking individual droplets or small groups of droplets (parcels). This project will take the science to a new level by developing a new mathematical formalism that will be based on droplet size distribution. This will lead to a new strategy for simulation of sprays and will be built around modelling of the evolution of droplet distribution in space and time. This, in turn, will ensure that the new model is computationally more efficient for calculating droplet concentrations than the conventional tracking method. The model will take into account droplet evaporation and condensation, polydispersity of droplets, effect of droplets on the gas flow, and turbulence. Novel approaches in numerical modelling will be developed to ensure efficient, fast, robust and accurate calculations. Another direction of the research will be focused on development of a methodology that will link modelling dense spray near the injector nozzle and dilute mixture of gas and droplet further away from the nozzle and the liquid core. There is a group of methods that focus on modelling of the near-nozzle region and are based on capturing/tracking the liquid-gas interface. When linking these methods with droplet dynamics to obtain the full modelling of spray, one obtains a deterministic description of droplet formation, location and dynamics. In contrast to this, we propose to develop a new model that will be based on droplet size distribution formulation. It will be a hybrid Eulerian-Lagrangian model for dense spray near nozzle and fully Lagrangian model downstream. This will be a significant step forward to modelling of the full process: from spray formation to droplet evaporation or deposition. This approach will be particularly useful for applications where distribution of droplets and their deposits, as well as of droplet vapour, are important for end-product quality, for example surface processing/coating. The new model will be validated against experimental data obtained for a flat fan water injection. The new experiments will focus on droplet spatial distribution as well as droplet size distribution. After validation, we will adapt and test the model for two applications: pressurised-metered dose inhaler and fuel injection. The first study will be done in consultation with Dr Pannala (Biomaterials and Medical Devices and Drug Delivery Research and Enterprise Group). The second one will be conducted in consultation with the industrial partner Ricardo UK Ltd. The main goal of the project is to develop a product, which will be ready to use, compatible with conventional computational fluid dynamics software, and that will enable advanced simulation of spray phenomena for engineering applications. The numerical code to be developed will be implemented as a library to open-source and freely available software OpenFOAM. The final version of the library will be distributed under the MIT license via the online Brighton Research Data Repository. Thus the outcomes of the project will be accessible to a wide community of researchers and engineers interested in spray phenomena.

Despite many previous (mostly experimental) efforts to characterise super-critical injection conditions, they still remain a challenging fluid dynamics problem due to the multi-scale, multi-phase character of the complex physical phenomena that governs it. This proposal aims to offer a systematic approach towards a better understanding and prediction of the transition of sub- critical to super- critical injection phenomena, combining novel state of the art simulations with experiments already performed by the University of Brighton and Sandia National Laboratories for diesel engine conditions. The model will include real gas effects and target both primary and secondary atomization regions at the limit of transition between sub- critical to super- critical conditions. Such an approach is currently lacking from commercial and open source simulation tools. The new framework will be developed within Large Eddy Simulations (LES) and will be based on the extension of ideas also used in probabilistic modelling of flame interfaces (surface density approaches). The major strength of the approach is that it does not include any a priori region-dependent assumptions for the liquid-gas volume fraction in the computational cells, and bypasses the spherical vision of the liquid structures that compose the spray. Thus, it can be applicable both to the near-nozzle and the dilute spray areas, and represent both sharp (as in the case of sub- critical injection) and diffused (more representative of super-critical conditions) interfaces. Our suggested numerical models have the potential to capture the underlying physics of the phenomena even at extreme thermodynamic conditions and therefore can play the role of "virtual experiments", providing valuable access to flow areas and conditions where real experiments face limitations. The numerical framework that will be presented in the proposed research aspires to lead to the creation of the new generation of equipment design tools that will be available to both academic and non-academic sectors and will facilitate the cost effective design of novel high pressure injection systems. Moreover, the outcomes of the research will be disseminated to the academic community through publications in high impact journals and national and international conferences as well as an outreach workshop. These could change the way we currently view the modelling of multiphase problems not only for automotive application but for other disciplines involving super-critical fluids.

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.

This proposal is concerned with the non-trivial generalisation of previously-developed models for the analysis of multi-phase vortex ring-like structures to take into account thermal, swirl and confinement effects. Thermal effects include the presence of thermal gradients in the carrier phase, and heating and evaporation of droplets. Confinement effects will take into account the contribution of walls in the enclosure, which are particularly important in the case of modelling processes in internal combustion engines. Three modelling approaches will be used: Direct Numerical Simulation (DNS), the full Lagrangian approach (the Osiptsov-Lagrangian method) and asymptotic/analytical models. Development of all these approaches for modelling vortex ring-like structures has so far been mainly focused on cases when the contribution of the above-mentioned thermal and confinement effects can be ignored. In the present project, all three above-mentioned approaches will be generalised to take thermal and confinement effects into account. This generalisation is not trivial, especially in the case of the full Lagrangian and asymptotic/analytical approach, and nobody, to the best of our knowledge, has attempted to do this. Modelling will be specifically focused on combustible gas and gasoline internal combustion engines, but it is expected that the methods to be developed could be generalised to a much wider range of applications. Modelling work on the project will be complemented by experimental studies of vortex ring-like structures in the above-mentioned engines. The direct injection of gas and liquid fuel sprays (LPG/CNG and gasoline engines) and the motions of the continuous phase will be studied in a closed, quiescent observation chamber using laser-based measurement techniques. New data to describe the injection velocity profile and droplet concentration will be acquired to support the modelling approaches. The experimental study will take into account heating and confinement. The initial stage of the work will be focused on combustible gas internal combustion engines, which will allow us to restrict our analysis to a one-phase flow, using the DNS and asymptotic/analytical approach. The main new effect taken into account at this stage will be the presence of temperature gradients in the enclosure, swirl and the presence of interior walls. At the next stage the above model will be generalised to take into account the effects of liquid sprays in the enclosure. This new approach to the modelling of multiphase flows will incorporate the jet and droplet break-up models developed as a result of work on the previous EPSRC project EP/F069855/1. Where appropriate, predictions resulting from the full Lagrangian and analytical/asymptotic models will be compared with predictions based on DNS simulations of transient vortex ring-like structures. We will also investigate the feasibility of incorporating of the full Lagrangian and analytic/asymptotic models into the research CFD code KIVA 3 and commercial CFD codes VECTIS and FLUENT. Predictions from numerical and analytical models will be validated against in-house experimental results obtained in combustible gas and gasoline engine-like conditions. The applicability of the results to the optimisation of processes in these engines will be investigated. This will be a collaborative project involving external visiting researchers whose expertise is mainly focused on the development of the numerical and analytical/asymptotic vortex ring models and the full Lagrangian method. This project will ensure a qualitatively new level of physical and mathematical models, as developed in the previously-funded EPSRC project EP/E047912/1, and the currently active project EP/K005758/1. The anticipated overlap in time between the work on this project and currently active EPSRC project EP/K005758/1 will ensure the continuity of research in this direction.

The proposed project is based on the synthesis of mathematical and engineering approaches to simulate gas-droplet flows. It comprises the development of a new mathematical formalism, which will then be applied to enhance an existing approach to simulate two-phase flows. It will make it possible to perform simulations with higher resolution: more accurate calculations, and more physical phenomena will be captured. The project will focus on non-trivial generalisation of the mathematical approach to spray modelling developed by Professor Osiptsov, known as the Fully Lagrangian Approach (FLA). In the mathematical modelling community, this method is known as a promising approach to calculate particle/droplet concentrations. However, its current applications are restricted to simplistic flows with dilute mono-sized admixture. In the framework of the project, droplet evaporation, polydispersity of admixture, and the effect of droplets on the carrier phase (two-way coupling) will be taken into account and incorporated in the model. The corresponding mathematical model will be implemented in the Computational Fluid Dynamics (CFD) software OpenFOAM. The developed model will be applied to simulate the evolution of droplet distribution in sprays formed in direct-injection internal combustion (Diesel and gasoline) engines. The results of numerical simulations will be validated against experimental data provided by colleagues in the Advanced Engineering Centre, University of Brighton. OpenFOAM is an open-source and widely used CFD software, which will make the project outcomes accessible to specialists interested in sprays.