PDF model based on Langevin equation for polydispersed two-phase flows applied to a bluff-body gas-solid flow

The aim of the paper is to discuss the main characteristics of a complete theoretical and numerical model for turbulent polydispersed two-phase flows, pointing out some specific issues. The theoretical details of the model have already been presented [Minier and Peirano, Phys. Rep. 352, 1 (2001)]. Consequently, the present work is mainly focused on complementary aspects that are often overlooked and that require particular attention. In particular, the following points are analyzed: the necessity to add an extra term in the equation for the velocity of the fluid seen in the case of two-way coupling, the theoretical and numerical evaluations of particle averages and the fulfillment of the particle mass-continuity constraint. The theoretical model is developed within the probability density function (PDF) formalism. The important physical choice of the state vector variables is first discussed and the model is then expressed as a stochastic differential equation written in continuous time (Langevin equation...

[1]  J. Minier,et al.  On the Lagrangian turbulent dispersion models based on the Langevin equation , 1998 .

[2]  R W Hockney,et al.  Computer Simulation Using Particles , 1966 .

[3]  M. Reeks.  On the continuum equations for dispersed particles in nonuniform flows , 1992 .

[4]  C. W. Gardiner,et al.  Handbook of stochastic methods - for physics, chemistry and the natural sciences, Second Edition , 1986, Springer series in synergetics.

[5]  E. Peirano,et al.  The pdf approach to turbulent polydispersed two-phase flows , 2001 .

[6]  P. Kloeden,et al.  Numerical Solution of Stochastic Differential Equations , 1992 .

[7]  J. Schnakenberg,et al.  Gardiner: Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences/Bass und Stitch: Laser Handbook, Vol. 5 , 1986 .

[8]  B. Launder,et al.  Progress in the development of a Reynolds-stress turbulence closure , 1975, Journal of Fluid Mechanics.

[9]  Yoshihiro Saito,et al.  Simulation of stochastic differential equations , 1993 .

[10]  L. Arnold.  Stochastic Differential Equations: Theory and Applications , 1992 .

[11]  K. Squires,et al.  Direct numerical simulation of turbulence modulation by particles in isotropic turbulence , 1998, Journal of Fluid Mechanics.

[12]  J. Riley,et al.  Equation of motion for a small rigid sphere in a nonuniform flow , 1983 .

[13]  Hermann Haken,et al.  Synergetics: an overview , 1989 .

[14]  Farzad Mashayek,et al.  Non-isothermal dispersed phase of particles in turbulent flow , 2003, Journal of Fluid Mechanics.

[15]  Olivier Simonin,et al.  Eulerian Prediction of the Fluid/Particle Correlated Motion in Turbulent Two-Phase Flows , 1993 .

[16]  Farzad Mashayek,et al.  Analytical description of particle/droplet-laden turbulent flows , 2003 .

[17]  Jean-Pierre Minier,et al.  Derivation of a PDF model for turbulent flows based on principles from statistical physics , 1997 .

[18]  Probabilistic formalism and hierarchy of models for polydispersed turbulent two-phase flows. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  R. Clift,et al.  Bubbles, Drops, and Particles , 1978 .

[20]  S. Pope,et al.  A Hybrid Algorithm for the Joint PDF Equation of Turbulent Reactive Flows , 2001 .

[21]  D. Williams.  STOCHASTIC DIFFERENTIAL EQUATIONS: THEORY AND APPLICATIONS , 1976 .

[22]  Jinchao Xu,et al.  Assessment of Numerical Accuracy of PDF/Monte Carlo Methods for Turbulent Reacting Flows , 1999 .

[23]  Brian Launder,et al.  Second-moment closure: present… and future? , 1989 .

[24]  David E. Stock,et al.  Particle Dispersion in Flowing Gases—1994 Freeman Scholar Lecture , 1996 .

[25]  Patrick Jenny,et al.  PDF simulations of a bluff-body stabilized flow , 2001 .

[26]  Stephen B. Pope,et al.  Particle method for turbulent flows: integration of stochastic model equations , 1995 .

[27]  Olivier Simonin,et al.  Continuum modelling of dispersed two-phase flows , 1996 .

[28]  Radu Balescu,et al.  Statistical dynamics: matter out of equilibrium , 1997 .

[29]  S. Pope.  Lagrangian PDF Methods for Turbulent Flows , 1994 .

[30]  Jean-Pierre Minier,et al.  Weak first- and second-order numerical schemes for stochastic differential equations appearing in Lagrangian two-phase flow modeling , 2003, Monte Carlo Methods Appl..

[31]  Stephen B. Pope,et al.  Comment on the article "An effective particle tracing scheme on structured/unstructured grids in hybrid finite volume/PDF Monte Carlo methods" by Li and Modest , 2003 .