Simulation of an Elliptical Cylinder Sedimentation Process by using the Lattice Boltzmann Method Combined With the Smoothed Profile Method
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In this work, the results obtained from the simulation of sedimentation of an elliptical cylinder in a viscous fluid are presented. The fluid flow velocity and pressure fields are evaluated by the famous lattice Boltzmann method (LBM). A smoothed profile method (SPM) is considered to enforce the no-slip boundary condition at the curved boundaries of the elliptical cylinder. The coupling between LBM LBM: Lattice Boltzmann Method and SPM SPM: Smoothed Profile Method is done by adding a hydrodynamic force term to the discretized version of the lattice Boltzmann equation. At first, the developed numerical code is validated by applying it to the unbounded laminar flow over an elliptical cylinder for different values of Reynolds number, Re. Later, simulations are carried out for sedimentation of an elliptical particle in a closed enclosure by considering different values for Re defined by terminal settling velocity of the cylinder. The robustness and accuracy of present simulation technique is assessed by comparing the particle trajectories and orientations obtained at different Re with the results from the existing literature. It is observed that, over a period of time, the particle attains steady state constant velocity and sediments horizontally when Re is low (Re=1.9) and moderate (Re=12.6). Whereas, an oscillating pattern for the sedimentation velocity is observed when Re is 32.9.
Abstract
In this work, the results obtained from the simulation of sedimentation of an elliptical cylinder in a viscous fluid are presented. The fluid flow velocity and pressure fields are evaluated by the famous lattice Boltzmann method (LBM). A smoothed profile method (SPM) is considered to enforce the no-slip boundary condition at the curved boundaries of the elliptical cylinder. The coupling between LBM LBM: Lattice Boltzmann Method and SPM SPM: Smoothed Profile Method is done by adding a hydrodynamic force term to the discretized version of the lattice Boltzmann equation. At first, the developed numerical code is validated by applying it to the unbounded laminar flow over an elliptical cylinder for different values of Reynolds number, Re. Later, simulations are carried out for sedimentation of an elliptical particle in a closed enclosure by considering different values for Re defined by terminal settling velocity of the cylinder. The robustness and accuracy of present simulation technique is assessed by comparing the particle trajectories and orientations obtained at different Re with the results from the existing literature. It is observed that, over a period of time, the particle attains steady state constant velocity and sediments horizontally when Re is low (Re=1.9) and moderate (Re=12.6). Whereas, an oscillating pattern for the sedimentation velocity is observed when Re is 32.9.
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