Reconstruction of the droplet size distribution in polydisperse sprays using the generalised fully Lagrangian approach

The fully Lagrangian Approach (FLA) has been known for its potential to capture complex structures in gas-droplet flows, for example in case of droplet trajectory crossing, while providing number density values in Lagrangian droplet positions [1, 2]. It has been demonstrated that the FLA is an efficient method for calculating droplet distributions in comparison to other Lagrangian approaches [1]. In [3], a generalised FLA was applied to polydisperse evaporating sprays. In the present paper, it is proposed to use kernel regression to map the Lagrangian droplet data to Eulerian distribution fields. In this approach, the domain of influence of a kernel is linked to the local droplet deformation field, which is provided by the FLA (or gFLA). The advantages of this approach include its ability to retain the structures (caustics and voids) in the droplet cloud, computational efficiency when compared to conventional methods based on counting droplets, for example Cloud-In-Cell, and flexibility to be applied to polydisperse droplets. The proposed methodology has been implemented as additional libraries for the open-source computational fluid dynamics software OpenFOAM, and applied to benchmark steady state and transient flow around a cylinder. The results are in agreement with previously reported observations. It is demonstrated that the new method achieves significant reduction in computational costs if compared with the Cloud-In-Cell approach, this is due to about 10^3 times fewer droplets
being required to reconstruct the droplet fields.