Numerical investigations for a chain of particles settling in a channel
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Numerical investigations for a chain of particles settling in a channel Saqia Jabeen1 · Kamran Usman1 · Khuram Walayat2 Received: 11 June 2019 / Revised: 26 August 2019 / Accepted: 30 September 2019 © OWZ 2019
Abstract The present work deals with the numerical investigation for a chain-like formation of suspended particles of circular shape in fluid flow. An explicit volume integral approach for the calculation of hydrodynamic forces acting on the particle’s surface is used. A collision strategy proposed by Glowinski, Singh, Joseph and coauthors for the treatment of colliding or approaching particles is used. The direct simulation technique (fictitious boundary method) achieves the solution of incompressible flow along with moving rigid bodies. The Eulerian based approach which is independent of particle size, particle shape and number of particles is adopted to solve the fluid-particle phenomena in the computational domain. The fluid domain consisting of a multigrid finite element background is considered and the whole numerical process is carried out through open source code FEATFLOW. Numerical experiments for settling particles which are close together forming chain like formations are performed and analyzed. The study is carried out using different configurations of particle positions resulting in different chain patterns. Consequences of such patterns on particles’ motion and on the fluid-particle system is discussed. Keywords Particle sedimentation · Direct numerical simulation (DNS) · Finite element fictitious boundary method (FEMFBM) · Multigrid · DKT motion
1 Introduction The interaction of particles in the fluid can be seen in many natural and industrial processes such as sedimentation, agglomeration, granular flows and multi-phase flows. There is a need for fundamental knowledge of the mechanism of such particle interactions resulting in chain-like formations leading to drafting, kissing and tumbling (DKT) phenomena accompanied by the particle collisions in the modelling of particulate flow [1, 2]. To study the solid-liquid flows [3, 4] several numerical approaches have been developed during the last decades. For modeling the particulate phase two main approaches can be found. These approaches are continuum approach and the discrete approach. In a continuum approach the mass of particle is considered as a synthetic continuum and is based on the solution of the underlying * Kamran Usman [email protected] 1
Department of Mathematics, Air University, PAF Complex, Islamabad 44000, Pakistan
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China
2
conservation equations. Basically, this approach works for specifically flow regimes [5]. The successful application of kinetic theory has been developed by Chapman et al. [5] and Ogawa et al. [6] for rapid granular flow using the concept of a granular temperature. The model related to plasticity theory have been developed for s
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