Direct simulation of particle-laden viscous flows and their applications

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University of Delaware
In this dissertation, we conduct direct simulations of particle-laden viscous flows with dual objectives: the first is the implementation and validation of the mesoscopic lattice Boltzmann (LB) approach for particle-laden viscous flows, and the second concerns two specific applications of this approach, namely, turbulent suspension flow and microscale porous media flow with colloid deposition and migration. The LB approach solves continuum-fluid flows indirectly by discretizing the Boltzmann equation using a minimum set of discrete velocities. It reproduces the incompressible Navier-Stokes equation in the limit of low effective Mach number of the system. Most previous validations of the LB approach concern relatively simple viscous flows. In this study, we apply the LB approach to more complex problems with curved fluid-solid interfaces, and compare directly with a novel hybrid Navier-Stokes based approach (Physalis) developed by Professor Prosperetti's group at Johns Hopkins. We have demonstrated systematically the accuracy and parallel efficiency of the LB approach and showed that the LB approach is particularly effective for simulating fluid-flow systems containing a large number of spherical solid particles. The study of turbulent suspension flow was motivated by the open question concerning the impact of the presence of finite-size inertial particles on the turbulent carrier flow, and the interaction between the particles. For this purpose, a particle-resolved simulation method was developed based on the multiple-relaxation-time lattice Boltzmann equation (MRT-LBE). The no-slip boundary condition on the moving particle boundaries was handled by a second-order interpolated bounce-back scheme. The mesoscopic particle distribution functions at a newly converted fluid lattice node were constructed by the equilibrium distribution with non-equilibrium correction. An elastic repulsive force model was utilized to prevent particle-particle overlap. The code was parallelized with MPI and was found to be computationally efficient with an excellent scalability. The method is first validated using unsteady sedimentation of a single particle and a multi-particle random suspension. It is then applied to a decaying isotropic turbulence laden with particles of Kolmogorov to Taylor microscale size. At a given particle volume fraction, the dynamics of the particle-laden flow is found to depend mainly on the effective particle surface area and particle Stokes number. The presence of finite-size particles enhances viscous dissipation at small scales while reducing kinetic energy at large scales. This is in accordance with related studies. However, the normalized pivot wavenumber is found to depend not only on the particle size, but also on the relative ratio of particle size to flow dissipation range scales as well as the particle-to-fluid density ratio. Moreover, strong modulation is observed within half particle radius near particle surface, and local profiles are are found to be self similar with proper normalization. The second application pertains to colloid and colloid-facilitated contaminant transport and retention in soil porous media. Specifically, we intend to quantify the colloid deposition mechanism under unfavorable conditions where both the colloid surface and grain surface are negatively charged. This application consists of two components, the simulation of microscopic viscous flow in a three-dimensional porous channel, and the transport of sub-micron colloids in this model geometry. We apply simultaneously the MRT-LBE method and the hybrid Physalis method. The latter handles the no-slip boundary condition by coupling an analytical Stokes expansion valid in a narrow but finite region near a particle surface with the numerical solution outside the particle. The mesoscopic LBM is shown to be superior to the hybrid macroscopic approach, especially when there exist multiple grain-grain and grain-wall contact points. Colloid transport and deposition were then simulated by a Lagrangian tracking approach, under the combined influence of hydrodynamic forces, Brownian force, and physicochemical forces. With the given solution ionic strength and physicochemical condition, capture of colloids by the secondary energy minimum (SEM) were demonstrated. The local hydrodynamic retardation is shown to reduce the ability for colloids to move into the SEM, but does not prevent this to occur. Before being captured by the SEM, colloid trajectories are shown to depend on local porosity, flow convergence, and contact points. After capture, the interaction between particle inertia, DLVO forces and local hydrodynamic interaction play a prominent role. These results provide a new level of details on colloid transport and retention that are not easily achievable in physical experiments.