Turbulent particle dispersion in arbitrary wall-bounded geometries: A coupled CFD-Langevin-equation based approach A. Dehbi * Paul Scherrer Institut, Department of Nuclear Energy and Safety, Laboratory for Thermal-hydraulics, 5232 Villigen PSI, Switzerland article info Article history: Received 21 December 2007 Received in revised form 10 March 2008 Available online 15 March 2008 Keywords: Continuous random walk Langevin equation Inhomogeneous turbulence Wall-bounded flows CFD DNS abstract A Lagrangian continuous random walk (CRW) model is developed to predict turbulent particle dispersion in arbitrary wall-bounded flows with prevailing anisotropic, inhomogeneous turbulence. The particle tracking model uses 3D mean flow data obtained from the Fluent CFD code, as well as Eulerian statistics of instantaneous quantities computed from DNS databases. The turbulent fluid velocities at the current time step are related to those of the previous time step through a Markov chain based on the normalized Langevin equation which takes into account turbulence inhomogeneities. The model includes a drift velocity correction that considerably reduces unphysical features common in random walk models. It is shown that the model satisfies the well-mixed criterion such that tracer particles retain approximately uniform concentrations when introduced uniformly in the domain, while their deposition velocity is van- ishingly small, as it should be. To handle arbitrary geometries, it is assumed that the velocity rms values in the boundary layer can locally be approximated by the DNS data of fully developed channel flows. Benchmarks of the model are performed against particle deposition data in turbulent pipe flows, 90° bends, as well as more complex 3D flows inside a mouth-throat geometry. Good agreement with the data is obtained across the range of particle inertia. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction Turbulent flows which transport particulates are quite often encountered in a vast array of environmental, industrial, and med- ical applications. Examples of particle-laden flows can be found in atmospheric dispersion of pollutants, sediment transport in rivers, drug delivery in human airways, fouling in compressor and turbine blades, chemical pulping, nuclear fission products transport, etc. Hence, an accurate description of particle transport is of great prac- tical importance. While particle transport in isotropic and homoge- neous turbulent fields has been extensively studied (Yeung and Pope, 1989; Squires and Eaton, 1991), wall-bounded flows have not comparatively attracted the same attention. In the latter, boundary layers form close to the walls, and turbulence is strongly anisotropic and inhomogeneous, which renders the problem quite a bit more complicated. Of particular importance in boundary layer flows is the understanding of mechanisms responsible for particle preferential concentration (Marchioli and Soldati, 2002), which in turn explain many macroscopic features such as the particle depo- sition rates on the walls. The heart of the particle dispersion prob- lem resides in modeling the random velocity fluctuations which particles encounter along their trajectories. As summarized by Dehbi (2008), one can distinguish two main families of methods to treat particle dispersion in fluid flows: Eule- rian and Lagrangian. In the Eulerean or ‘‘two-fluid” approach, the particles are regarded as a continuous phase for which the aver- aged conservation equations (continuity, momentum and energy) are solved in similar fashion to the carrier gas flow field (Zhang and Prosperetti, 1994). The Eulerean approach is particularly suit- able for denser suspensions when particle–particle interactions are important and the particle feedback on the flow is too large to ignore. The main challenge facing Eulerian-type, two-fluid ap- proaches resides in accurately defining the inter-phase exchange rates and closure laws which arise from the averaging procedures (Drew, 1983). In addition, the strong coupling between the phases renders the Eulerean approach quite delicate to handle, especially at boundaries where the solid phase may be removed or reflected. The Lagrangian approach (Maxey, 1987) treats particles as a dis- crete phase which is dispersed in the continuous phase. The parti- cle volume loading is usually assumed negligible, so that particles have no feedback effect on the carrier gas and particle–particle interactions are neglected. In the Lagrangian framework, the con- trolling phenomena for particle dispersion in the field are assessed using a rigorous treatment of the forces acting on the particle. In general, the detailed flow field is computed first, then a represen- tatively large number of particles are injected in the domain, and their trajectories determined by following individual particles until 0301-9322/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmultiphaseflow.2008.03.001 * Tel.: +41 56 310 27 11; fax: +41 310 27 99. E-mail address: abdel.dehbi@psi.ch International Journal of Multiphase Flow 34 (2008) 819–828 Contents lists available at ScienceDirect International Journal of Multiphase Flow journal homepage: www.elsevier.com/locate/ijmulflow