Why Are Relationships Between Lagrangian and Eulerian Scales Necessary for Gas-Particle Flow Modeling?

Simulation of Gas-Particle flows can be fulfilled by Lagrangian modeling of the dispersed phase. Each type of Lagrangian method, Monte-Carlo/Eddy Interaction or Markov Chain models, needs the knowledge of Lagrangian scales associated with the turbulent flow under consideration and the type of particle dispersing in the gas carrier flow. Unfortunately, Lagrangian quantities (as well the interesting moving Eulerian time scale, that given by a sensor which would move with the mean fluid velocity) are still difficult to be obtained directly by most experimental measurement techniques (except by very recent techniques such as PIV.PTV.), contrary to Eulerian scales scales, such as those classically obtained from a fixed hot-wire or LDA control volume. It is therefore of great importance to have available accurate relationships between Eulerian and Lagrangian scales, based on fluid flow properties as well as particle characteristics.