The Generalised Fully Lagrangian Approach for Polydisperse Sprays. Implementation of a two-way coupling model in OpenFOAM.

The generalised fully Lagrangian approach (gFLA) is an extension of the original fully Lagrangian approach (FLA, also known as the Osiptsov’s method), which aims to model polydisperse evaporating sprays. The FLA is known for its advantages in application to particle-laden flows. This approach makes it possible to capture detailed structures in the particulate clouds, including where particle trajectories cross and particles collect in narrow regions. Together with this the FLA is also an efficient method for calculating admixture distributions [1, 2]. In [3], the generalised FLA was applied to polydisperse evaporating sprays for the first time. It was shown that while the gFLA maintained advantages of the original FLA, there was a need to develop a robust method for interpolation of Lagrangian data to a Eulerian mesh. This was achieved by implementation of kernel regression [4], which takes advantage of the continuum description provided by the FLA to realize the potential computational economy of the pproach through an efficient statistical procedure. The kernel regression retains the detail of complex structures in droplet clouds, caustics and voids, by sizing the kernel domain of influence using the information about the local droplet deformation field provided by the FLA or gFLA.
This work is focused on two-way coupling, where the effect of droplets on the carrier phase is taken into account. The kernel regression enables efficient calculation of the terms in momentum and mass exchange. The implementation has been validated against the existing two-way coupling procedures within OpenFOAM, see Figure 1 for comparison of momentum coupling term values in a steady state flow around a cylinder. The OpenFOAM case uses injections of 1001 particles every 0.01 seconds to achieve a sufficient number of particles, whilst the FLA case uses injections of 101 particles every 0.1 seconds to represent the same mass loading. The newly developed solver is applied to model respiratory aerosol dispersion in order to demonstrate the combination of accuracy and computational efficiency which the gFLA is capable of providing.