E-Jiang Ding

Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation

An efficient and robust computational method, based on the lattice-Boltzmann method, is presented for analysis of impermeable solid particle(s) suspended in fluid with inertia. In contrast to previous lattice-Boltzmann approaches, the present method can be used for any solid-to-fluid density ratio. The details of the numerical technique and implementation of the boundary conditions are presented. The accuracy and robustness of the method is demonstrated by simulating the flow over a circular cylinder in a two-dimensional channel, a circular cylinder in simple shear flow, sedimentation of a circular cylinder in a two-dimensional channel, and sedimentation of a sphere in a three-dimensional channel. With a solid-to-fluid density ratio close to one, new results from two-dimensional and three-dimensional computational analysis of dynamics of an ellipse and an ellipsoid in a simple shear flow, as well as two-dimensional and three-dimensional results for sedimenting ellipses and prolate spheroids, are presented.

The dynamics and scaling law for particles suspended in shear flow with inertia

The effect of inertia on the dynamics of a solid particle (a circular cylinder, an elliptical cylinder, and an ellipsoid) suspended in shear flow is studied by solving the discrete Boltzmann equation. At small Reynolds number, when inertia is negligible, the behaviour of the particle is in good agreement with the creeping flow solution showing periodic orbits. For an elliptical cylinder or an ellipsoid, the results show that by increasing the Reynolds number, the period of rotation increases, and eventually becomes infinitely large at a critical Reynolds number, Re c . At Reynolds numbers above Re c , the particle becomes stationary in a steady-state flow. It is found that the transition from a time-periodic to a steady state is through a saddle-node bifurcation, and, consequently, the period of oscillation near this transition is proportional to [mid ] p − p c [mid ] −1/2 , where p is any parameter in the flow, such as the Reynolds number or the density ratio, which leads to this transition at p = p c . This universal scaling law is presented along with the physics of the transition and the effect of the inertia and the solid-to-fluid density ratio on the dynamics. It is conjectured that this transition and the scaling law are independent of the particle shape (excluding body of revolution ) or the shear profile.

Extension of the Lattice-Boltzmann Method for Direct Simulation of Suspended Particles Near Contact

Computational methods based on the solution of the lattice-Boltzmann equation have been demonstrated to be effective for modeling a variety of fluid flow systems including direct simulation of particles suspended in fluid. Applications to suspended particles, however, have been limited to cases where the gap width between solid particles is much larger than the size of the lattice unit. The present extension of the method removes this limitation and improves the accuracy of the results even when two solid surfaces are near contact. With this extension, the forces on two moving solid particles, suspended in a fluid and almost in contact with each other, are calculated. Results are compared with classical lubrication theory. The accuracy and robustness of this computational method are demonstrated with several test problems.

Dynamics of particle sedimentation in a vertical channel: Period-doubling bifurcation and chaotic state

The dynamics and interaction of two circular cylinders settling in an infinitely long narrow channel (width equal to four times the cylinder diameter) is explained by direct computational analysis. The results show that at relatively low Reynolds numbers (based on the average particle velocity and diameter), the particles undergo complex transitions to reach a low-dimensional chaotic state represented by a strange attractor. As the Reynolds number increases, the initial periodic state goes through a turning point and a subcritical transition to another periodic branch. Further increase in the Reynolds number results in a cascade of period-doubling bifurcations to a chaotic state represented by a low dimensional chaotic attractor. The entire sequence of transitions takes place in a relatively narrow range of Reynolds number between 2 and 6. The physical reason for the period-doubling transitions is explained based on the interaction of the particles with each other and the channel walls. The particles undergo near contact interactions as settling in the channel. To accurately capture the dynamics, the computational method requires accurate resolution of the particle interactions. The computational results are obtained with our lattice-Boltzmann method developed for suspended particles near contact. The results show that even in the most simple and ideal multiparticle sedimentation, the system undergoes transition to complex dynamics at relatively low Reynolds number.