Fluid Mechanics of Inertial Particle-Laden Flow

This work addresses the role of particle scale inertia on the motion of hard spherical particles suspended in a Newtonian fluid. We have utilized lattice-Boltzmann method to solve for the motion of particles in the fluid. The particles in the suspension are neutrally buoyant; therefore, a same level of inertia is carried by solid and liquid phase.;In the first phase, the microstructure and rheological properties of suspensions are studied. The suspensions are subjected to simple shear flow and the properties are studied as a function of Reynolds number. The flow-induced microstructure is studied using the pair distribution function. Different stress mechanisms, including those due to surface tractions (stresslet), acceleration, and the Reynolds stress due to velocity fluctuations are computed and their influence on the first and second normal stress differences, the particle pressure and the viscosity of the suspensions are detailed. The probability density functions of linear and angular accelerations are also presented.;Next, we present our results on the topology of particle pair trajectories. The pair relative trajectory is studied both for pairs which are isolated and for pairs in suspension of large solid fractions. For the suspension, the average trajectory and aspects of its dispersion are considered. The pair trajectories in a dilute inertial suspension have the same basic features as the streamlines around an isolated particle at similar Re, with reversing, in-plane and off-plane spiraling, and open but fore-aft asymmetric trajectories. The origin of the off-plane spirals is examined in detail, and the zone of these spirals is found to become smaller with increasing Re. The average pair trajectory space in a suspension of finite volume fraction is found to be qualitatively similar to the dilute suspension pair trajectories, as the spiraling and reversing zones are retained; the influence of volume fraction and Re on the extension of the different zones is described. The role of the average pair trajectory in setting the microstructure of the suspension is analyzed through a convection equation description of the pair probability, showing extreme accumulation at contact consistent with sampling from simulation. The influence of the microstructure on the bulk rheology is also evaluated.;Finally we present and discuss an interesting observation on inertial particle-laden flow over an obstacle. Experimental observations of the flow of a dilute suspension over an obstacle with circular cylindrical shape in a microchannel have demonstrated that the wake zone formed behind the obstacle at moderate Reynolds numbers is depleted or completely devoid of particles. The Reynolds number of the flow generates extended closed-streamline wakes but is below the transition to an unsteady wake. Using lattice-Boltzmann simulations, the trajectory of a single particle (small relative to the bluff body) is analyzed and shown to form a limit cycle inside the wake. The motion of the particle on the limit cycle trajectory is stable and a single particle does not move further than limit cycle. With increase of the number of particles in the wake, trajectories are distorted due to interactions and particles are pushed out of the wake zone. The average number of particles in the wake zone decreases with time and the wake region moves toward a depleted state, as time proceeds.