Evaluation of Eulerian multi-fluid versus Lagrangian methods for ejection of polydisperse evaporating sprays by vortices.
Résumé
The simulation of polydisperse evaporating sprays is both a crucial issue for industrial applications and a challenge for modeling and scientific computing. The usual Lagrangian approaches can lead to a very high computational cost or to a low level of resolution if not enough numerical parcels are used. Besides, they induce coupling difficulties between the two phases involved. Among the recently developed Eulerian models, the multi-fluid model allows the detailed description of polydispersity and size/velocity correlations of droplets. Such an approach has been shown to be derived from the Williams spray equation by Laurent and Massot under the assumption of mono-kinetic spray number density functions conditioned by size. This assumption defines the validity limit of the multi-fluid model. However, two key issues are still to be tackled : the validation in multi-dimensional configurations and the evaluation of the level of accuracy of such models versus the reference Lagrangian one. In this work we study the impact of the mono-kinetic assumption in a multi-dimensional configuration at three levels : mathematical structure of the system, numerical method needed to cope with the singularities and physical interpretation and validity limit of the simulations. We then evaluate the accuracy and computational cost of Eulerian models versus Lagrangian solvers in unsteady configurations.
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