A note on the consistency of hybrid Eulerian/Lagrangian approach to multiphase flows

The aim of the present paper is to introduce and to discuss inconsistency errors that may arise when Eulerian and Lagrangian models are coupled for the simulations of turbulent poly-dispersed two-phase flows. In these hybrid models, two turbulence models are implicitly used at the same time and it is important to check that they are consistent, in spite of their apparent different formulations. This issue is best revealed in the case of very small particles, or tracer-limit particles, where it is assessed that coupling inconsistent turbulence models (Eulerian and Lagrangian) can result in non-physical results, notably for second-order fluid velocity moments. Computations for fluid particles in a turbulent channel flow using several coupling strategies are presented to illustrate this question.