Epilogue

Stochastic Large eddy simulation emerges as a promising technique for dispersed turbulent two-phase flows. A stochastic Lagrangian model based on a Langevin-type stochastic diffusion process was described in this e-Book. The primary objective of such modeling is to account for the dispersion and deposition of inertial particles by subfilter or subgrid motion that is discarded by the filtering operation in LES. Particular attention was given to the testing of the model under standard and complete formulations in shear turbulent flows taking into account inertia effects that are caused by density difference between carrier and dispersed phases and the cross-trajectory effects due to gravity.

The stochastic modeling in particle-laden LES is motivated by the inability of RANS and LES using only the filtered velocity field to properly predict transport of inertial particles with Stokes numbers smaller than the smallest resolved turbulence scales. This modeling may be crucial also for LES characterized by an excessive filtering-out of kinetic energy due to the lack of spatial resolution in regions with high shear as such near the wall and zones of recirculation and boundary layer detachment.

This e-Book highlights the progress that has been made to date to improve the predicting capabilities of the large eddy simulation technique for two-phase turbulent flows. It represents only the start of the development and validation process that should be pursued in order to confidently apply this model to an increasing number of applications of industrial and biomedical nature. I hope this e-Book conveys the potential of stochastic large eddy simulation for predicting dispersed turbulent flows and will stimulate the use of the stochastic LES to many other challenging applications.

I have made an attempt to provide sufficient information to understand and to define the approach's potential and practicality. An attempt is also made to evolve general CFD guidelines which may be useful for solving practical engineering problems using stochastic LES. Adequate attention to the key issues mentioned in this e-Book and creative use of the stochastic LES model will make significant contribution to enhancing our understanding of the subject. New advances may be assimilated using the framework discussed in this e-Book.