Multi-fluid modelling of laminar polydisperse spray flames: origin, assumptions and comparison of sectional and sampling methods

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Abstract
A first attempt at deriving a fully Eulerian model for polydisperse evaporating sprays was developed by Tambour et al with the so-called sectional approach. However, the complete derivation of the sectional ‘multi-fluid’ conservation equations from the Boltzmann-type spray equation was never provided, neither was the set of underlying assumptions nor the comparison with the classical Lagrangian model: the sampling method. In this paper, we clarify the set of assumptions necessary in order to derive the multi-fluid sectional model from the spray equation at the ‘kinetic level’ and provide the derivation of the whole set of conservation equations describing the dispersed liquid phase. Whereas the previous derivation is conducted in any space dimension, we restrict ourselves to one-dimensional stationary flows where the droplets do not turn back and derive a Eulerian sampling model which is equivalent in this context to the usual Lagrangian particle approach. We then identify some situations, even within thi...

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