For all its merits, the two-phase SLM presented in Chap. 6 suffers from limitations. Indeed, its construction is tailor-made on one fluid turbulence model (the SLM) so that it is unclear how to proceed from another Langevin model. It seems also to be applicable only for the reduced particle momentum equation and requires closed expressions for the timescale of the velocity of the fluid seen as inputs, even if these drawbacks are related to a class of Langevin formulations. Clearly, new ideas are called for to remove these bottlenecks. In that sense, the objective of this chapter is threefold. It is, first, to report on recent advances allowing to build two-phase GLMs in a consistent manner. By using an alternative formulation, a second objective is to bring out that present two-phase Langevin models contain enough information to be used with the extended particle momentum equation. Finally, the third objective is to develop new approaches to predict the timescales of the velocity of the fluid seen or to derive them from stochastic models based on a two-step formulation, as well as to suggest structure-based models.

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Modeling the Velocity of the Fluid Seen: New Propositions

  • Jean-Pierre Minier,
  • Martin Ferrand,
  • Christophe Henry

摘要

For all its merits, the two-phase SLM presented in Chap. 6 suffers from limitations. Indeed, its construction is tailor-made on one fluid turbulence model (the SLM) so that it is unclear how to proceed from another Langevin model. It seems also to be applicable only for the reduced particle momentum equation and requires closed expressions for the timescale of the velocity of the fluid seen as inputs, even if these drawbacks are related to a class of Langevin formulations. Clearly, new ideas are called for to remove these bottlenecks. In that sense, the objective of this chapter is threefold. It is, first, to report on recent advances allowing to build two-phase GLMs in a consistent manner. By using an alternative formulation, a second objective is to bring out that present two-phase Langevin models contain enough information to be used with the extended particle momentum equation. Finally, the third objective is to develop new approaches to predict the timescales of the velocity of the fluid seen or to derive them from stochastic models based on a two-step formulation, as well as to suggest structure-based models.