  The aim of the present paper is to introduce and to discuss inconsistencies
errors that may arise when Eulerian and Lagrangian models are coupled for the
simulations of turbulent poly-dispersed two-phase flows. In these hydrid
models, two turbulence models are in fact implicitely used at the same time and
it is essential to check that they are consistent, in spite of their apparent
different formulations. This issue appears in particular in the case of
very-small particles, or tracer-limit particles, and it is shown that coupling
inconsistent turbulence models (Eulerian and Lagrangian) can result in
non-physical results, notably for second-order fluid velocity moments. This
problem is illustrated by some computations for fluid particles in a turbulent
channel flow using several coupling strategies.
