Application of the Fully Lagrangian Approach to unsteady polydisperse gas-droplet flow simulations with inter-phase coupling

The need to understand droplet behaviour within industrial spray systems has prompted the development of a range of numerical approaches for the computational simulation of such processes. However, in order to obtain a sufficient level of accuracy these simulations typically require a large number of droplets, leading to long computational runtimes and the need to store large amounts of data. The Fully Lagrangian Approach (FLA) offers an attractive way to address this problem by modelling the droplet phase as a continuum whilst retaining the intrinsic detail of individual droplet behaviour, meaning that only a subset of representative trajectories are required to reconstruct the droplet phase mean-field variables to the necessary level of accuracy, and the computational demand is therefore substantially reduced. Recent work has combined the FLA methodology with the statistical learning technique of kernel regression to obtain a physically consistent representation of the droplet phase, and the present work extends the applicability of this procedure to the treatment of a wider class of flows. In particular, inclusion of a droplet size parameter within the FLA formulation enables the modelling of polydisperse droplets that undergo evaporation, thereby supplying a wealth of information about the droplet distribution in space, velocity, and size. Furthermore, it is demonstrated that the kernel regression procedure is able to numerically generate the initial conditions required by the FLA within arbitrarily complex flows. The efficacy of this approach is illustrated for the case of transient flow around a cylinder using OpenFOAM, and results for the statistics of the droplet size distribution that is naturally produced by the generalised FLA are presented. The ability of the FLA to provide accurate source terms for inter-phase coupling is also analysed, and serves to highlight the suitability of the approach for the simulation of industrially relevant spray systems