Large-Eddy Simulation (LES) of settling particle cloud dynamics Ruo-Qian Wang a , Adrian Wing-Keung Law b , E. Eric Adams a,⇑ a Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, MA 02139, USA b School of Civil and Environmental Engineering, Nanyang Technological University, Singapore 639798, Singapore article info Article history: Received 17 October 2013 Received in revised form 1 August 2014 Accepted 8 August 2014 Available online 19 August 2014 Keywords: Euler–Lagrangian Four-way coupling CFD–DEM Sediment disposal Entrainment coefficient abstract A series of Euler–Lagrangian four-way coupling Large-Eddy Simulations (LES) are performed to study the dynamics of settling particle clouds. The numerical method is first validated by comparing with existing experimental results. Then, a parametric study is performed with various initial release shapes, particle sizes, and cloud buoyancies. Three issues are examined in detail, including the initial release aspect ratio, two-phase interactions and polydispersion. Incorporating these factors, empirical relationships are developed to predict the phase separation time and height, the position of the cloud front and the edge radius based on numerical results. The entrainment rate and deposition patterns are also analyzed. These relationships should be useful for engineering applications. Ó 2014 Elsevier Ltd. All rights reserved. Introduction A particle cloud settling through a water column is inherently a two-phase interactive process that is closely coupled. Once released, the particle cloud first accelerates due to the density difference (so called ‘‘acceleration stage’’), and then forms a circu- lating system with the solid particles and a rotating fluid vortex ring (so called ‘‘thermal stage’’). Finally, individual particles sepa- rate from the vortex ring and descend with their terminal settling velocity, while the fluid vortex ring is left behind due to the removal of driving force by the heavier particles (so called ‘‘disper- sive stage’’) (Rahimipour and Wilkinson, 1992; Lai et al., 2013). In this study, we focus on the thermal and dispersive stages of the particle cloud with the initial release of particles in the middle of the water column. The ‘‘acceleration stage’’ is very short with this release configuration, and can therefore be ignored. The key in understanding the coupled system is the two-phase interactions that govern the settling dynamics. The route of momentum transfer differs between the thermal and dispersive stages. In the thermal stage, momentum is transferred from the particles to the fluid generating the vortex flow, which then redis- tributes the solid phase and feeds the momentum back to the particles. Contrary to this interactive loop, the dispersive stage has an open route – the momentum is primarily transferred from the solid to the fluid phase through the settling process, which is then dissipated by viscous diffusion. In other words, momentum is lost after the transfer. Beyond the importance of basic understanding, including the fluid phase in the engineering analysis has practical implications. Sediment particles released in the water body may possess dissolv- able or volatile chemical substance, e.g. organic pollutants in dis- posed dredged sediment. The fluid-phase pollution can pose a secondary impact on the surrounding environment alongside the solid phase. Detailed knowledge of the solid–fluid phase interac- tions can help control and minimize the consequences. Until recently, the tracking of both phases has received little attention. Lai et al. (2013) presented the first study that addresses the dynamics of both phases using the simplified approach of the Hill’s vortex for the fluid phase. We aim to address this issue in fuller detail using the Large-Eddy Simulation (LES) numerical approach as the first objective of the present study. From a physical perspective, the process of particle settlement is an initial value problem where the boundaries are relatively far away compared to the cloud sizes. Thus, the computational domain is relatively simple in geometry, and the initial release con- ditions set the tone for the settlement process. In previous investi- gations, the initial conditions often covered a selected range of several basic parameters, including particle sizes, materials, densi- ties, and total mass (Rahimipour and Wilkinson, 1992; Bühler and Papantoniou, 1991; and Nakatrsuji et al., 1990). The typical particle cloud characteristics that were measured included the penetration depth of the particle cloud front (or centroid) and the cloud radius. Ruggaber (2000) was among the first to systematically vary all the basic parameters mentioned and generalize his results into an http://dx.doi.org/10.1016/j.ijmultiphaseflow.2014.08.004 0301-9322/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel.: +1 617 253 6595. E-mail addresses: rqwang@mit.edu (R.-Q. Wang), cwklaw@ntu.edu.sg (A.W.-K. Law), eeadams@mit.edu (E.E. Adams). International Journal of Multiphase Flow 67 (2014) 65–75 Contents lists available at ScienceDirect International Journal of Multiphase Flow journal homepage: www.elsevier.com/locate/ijmulflow