Stochastic modelling of polydisperse turbulent two-phase flows

In this chapter we focus on the Lagrangian stochastic approach to turbulent polydispersed two-phase flows. This chapter has several objectives. The first important objective is to use this interesting and relevant physical subject to apply the mathematical techniques presented in the first chapter. It is important to understand how the stochastic approach actually works and what are the main issues related to it. The second objective is to offer the reader the possibility to become more familiar with particle-laden flows, a sub-field of fluid mechanics which is quite fascinating and important in many industrial and environmental applications. Third, this chapter offers a comprehensive but concise description of the whole formalism needed to develop the stochastic approach to turbulent polydispersed flows. While Lagrangian stochastic models have been put forward since the sixties for single-phase flows (Lundgren, 1967) and applied with success to reactive flows since the seventies (Pope, 1985, 1994), their development and diffusion for polydispersed flows is much more recent (Minier and Pozorski, 1999; Minier and Peirano, 2001). In this sense, the formalism generalises the reactive flow one. Finally, the study of a typical industrial application is shown. This test-case helps to clarify that stochastic models can be used to investigate realistic phenomena (they are computationally performing), and, at the same time, give satisfactory answers in complex problems, for which less refined approaches like two-fluid models are not able to give acceptable results.