[show abstract][hide abstract] ABSTRACT: We present some results issued from the fully resolved direct numerical simulations of a 3-D liquid-solid fluidized bed, experimentally investigated by Aguilar Corona (2008). In these simulations, the flow is solved by a one-fluid formulation of the incompressible Navier-Stokes equations, where the pressure-velocity coupling is provided by an algebraic augmented Lagrangian method and particles presence is modeled by an implicit penalty fictitious domain method, a sub-grid scale lubrication force and soft-sphere collision model. The simulated fluidized bed is a 8 cm diameter, 64 cm height cylindrical column containing 2133 6 mm glass particles fluidized by a low viscosity liquid (3.8x10-3 Pa.s). Particle Reynolds and Stokes number based on terminal velocity are 530 and 7.7 respectively. Simulation results show that homogeneous fluidization regime is obtained for all fluidization velocities investigated, and exhibit large-scale coherent structures in the particle motion. Main features of the Lagrangian velocity signal of the particles are well reproduced by the simulations. Predicted fluidization law nicely fits the experimental curve. Despite the limited time of simulation runs, particle velocity variance is also well predicted as well as the value of the anisotropy coefficient, which is found to be independent of bed concentration. The fluid velocity variance is larger than that of the particles at all bed concentration investigated, following the same trend as Aguilar Corona’s data (2008).
8th International Conference on Multiphase Flow, International Conference on Multiphase Flow (ICMF): Jeju, South Korea. 2013.; 06/2013
[show abstract][hide abstract] ABSTRACT: We investigate in this article the macroscopic behavior of sheared suspensions of spherical particles. The effects of the fluid inertia, the Brownian diffusion, and the gravity are neglected. We highlight the influence of the solid-phase inertia on the macroscopic behavior of the suspension, considering moderate to high Stokes numbers. Typically, this study is concerned with solid particles O (100 microns) suspended in a gas with a concentration varying from 5% to 30%. A hard-sphere collision model (with elastic or inelasic rebounds) coupled with the particle Lagrangian tracking is used to simulate the suspension dynamics in an unbounded periodic domain. We first consider the behavior of the suspension with perfect elastic collisions. The suspension properties reveal a strong dependence on the particle inertia and concentration. Increasing the Stokes number from 1 to 10 induces an enhancement of the particle agitation by three orders of magnitude and an evolution of the probability density function of the fluctuating velocity from a highly peaked (close to the Dirac function) to a Maxwellian shape. This sharp transition in the velocity distribution function is related to the time scale which controls the overall dynamics of the suspension flow. The particle relaxation (resp. collision) time scale dominates the particulate phase behavior in the weakly (resp. highly) agitated suspensions. The numerical results are compared with the prediction of two statistical models based on the kinetic theory for granular flows adapted to moderately inertial regimes. The suspensions have a Newtonian behavior when they are highly agitated similarly to rapid granular flows. However, the stress tensors are highly anisotropic in weakly agitated suspensions as a difference of normal stresses arises. Finally, we discuss the effect of energy dissipation due to inelastic collisions on the statistical quantities. We also tested the influence of a simple modeling of local hydrodynamic interactions during the collision by using a restitution coefficient which depends on the local impact velocities.
[show abstract][hide abstract] ABSTRACT: We propose a theoretical prediction of the self-diffusion tensor of inertial particles embedded in a viscous fluid. The derivation of the model is based on the kinetic theory for granular media including the effects of finite particle inertia and drag. The self-diffusion coefficients are expressed in terms of the components of the kinetic stress tensor in a general formulation. The model is valid from dilute to dense suspensions and its accuracy is verified in a pure shear flow. The theoretical prediction is compared to simulations of discrete particle trajectories assuming Stokes drag and binary collisions. We show that the prediction of the self-diffusion tensor is accurate provided that the kinetic stress components are correctly predicted.
[show abstract][hide abstract] ABSTRACT: Particle shear-induced self-diffusion is investigated at low Reynolds and variable Stokes (St) numbers. We simulated the suspension hydrodynamics for St<<1 by using the Force Coupling Method. For suspensions with finite particle inertia (finite St), we proposed a new Eulerian prediction based on the kinetic theory for granular flows which have been validated by discrete particle simulations assuming Stokes drag and binary collisions (for low to moderate solid concentration). On the microscopic level, the particle velocity fluctuations have a Gaussian distribution shape for both high and vanishing St, whereas they show a highly peaked distribution for suspensions characterized by St~O(1) and low solid volume fractions. On the macroscopic level, the self-diffusion tensor is strongly anisotropic and the diffusive behavior becomes more prominent when the particle inertia increases. The self-diffusion coefficients decrease with concentration at high St. The results will be analyzed in terms of analogies and differences between the two regimes investigated (hydrodynamic interactions or collisional effects).
[show abstract][hide abstract] ABSTRACT: In this work we investigate numerically the dynamics of sheared suspensions in the limit of vanishingly small fluid and particle inertia. The numerical model we used is able to handle the multi-body hydrodynamic interactions between thousands of particles embedded in a linear shear flow. The presence of the particles is modeled by momentum source terms spread out on a spherical envelop forcing the Stokes equations of the creeping flow. Therefore all the velocity perturbations induced by the moving particles are simultaneously accounted for. The statistical properties of the sheared suspensions are related to the velocity fluctuation of the particles. We formed averages for the resulting velocity fluctuation and rotation rate tensors. We found that the latter are highly anisotropic and that all the velocity fluctuation terms grow linearly with particle volume fraction. Only one off-diagonal term is found to be non zero (clearly related to trajectory symmetry breaking induced by the non-hydrodynamic repulsion force). We also found a strong correlation of positive/negative velocities in the shear plane, on a time scale controlled by the shear rate (direct interaction of two particles). The time scale required to restore uncorrelated velocity fluctuations decreases continuously as the concentration increases. We calculated the shear induced self-diffusion coefficients using two different methods and the resulting diffusion tensor appears to be anisotropic too. The microstructure of the suspension is found to be drastically modified by particle interactions. First the probability density function of velocity fluctuations showed a transition from exponential to Gaussian behavior as particle concentration varies. Second the probability of finding close pairs while the particles move under shear flow is strongly enhanced by hydrodynamic interactions when the concentration increases.
Chemical Engineering Research and Design 01/2007; 8(6):778-791. · 1.93 Impact Factor
[show abstract][hide abstract] ABSTRACT: Sedimenting and sheared bidisperse homogeneous suspensions of non-Brownian particles are investigated by numerical simulations in the limit of vanishing small Reynolds number and negligible inertia of the particles. The numerical approach is based on the solution of the three-dimensional Stokes equations forced by the presence of the dispersed phase. Multi-body hydrodynamic interactions are achieved by a low order multipole expansion of the velocity perturbation. The accuracy of the model is validated on analytic solutions of generic flow configurations involving a pair of particles. The first part of the paper aims at investigating the dynamics of monodisperse and bidisperse suspensions embedded in a linear shear flow. The macroscopic transport properties due to hydrodynamic and non hydrodynamic interactions (short range repulsion force) show good agreement with previous theoretical and experimental works on homogeneous monodisperse particles. Increasing the volumetric concentration of the suspension leads to an enhancement of particle fluctuations and self-diffusion. The velocity fluctuation tensor scales linearly up to 15% concentration. Multi-body interactions weaken the correlation of velocity fluctuations and lead to a diffusion like motion of the particles. Probability density functions show a clear transition from Gaussian to exponential tails while the concentration decreases. The behavior of bidisperse suspensions is more complicated, since the respective amount of small and large particles modifies the overall response of the flow. Our simulations show that, for a given concentration of both species, when the size ratio varies from 1 to 2.5, the fluctuation level of the small particles is strongly enhanced. A similar trend is observed on the evolution of the shear induced self-diffusion coefficient. Thus for a fixed and total concentration, increasing the respective volume fraction of large particles can double the velocity fluctuation of small particles. In the second part of the paper, the sedimentation of a single test particle embedded in a suspension of monodisperse particles allows the determination of basic hydrodynamic interactions involved in a bidisperse suspension. Good agreement is achieved when comparing the mean settling velocity and fluctuations levels of the test sphere with experiments. Two distinct behaviors are observed depending on the physical properties of the particle. The Lagrangian velocity autocorrelation function has a negative region when the test particle has a settling velocity twice as large as the reference velocity of the surrounding suspension. The test particle settles with a zig-zag vertical trajectory while a strong reduction of horizontal dispersion occurs. Then, several configurations of bidisperse settling suspensions are investigated. Mean velocity depends on concentration of both species, density ratio and size ratio. Results are compared with theoretical predictions at low concentration and empirical correlations when the assumption of a dilute regime is no longer valid. For particular configurations, a segregation instability sets in. Columnar patterns tend to collect particles of the same species and eventually a complete separation of the suspension is observed. The instability threshold is compared with experiments in the case of suspensions of buoyant and heavy spheres. The basic features are well reproduced by the simulation model.
Physics of Fluids 01/2006; 18. · 1.94 Impact Factor
[show abstract][hide abstract] ABSTRACT: The dynamics of macroscopically homogenous sheared suspensions of neutrally buoyant, non-Brownian spheres is investigated in the limit of very small Reynolds and Stokes numbers using the Force Coupling Model (Lomholt & Maxey1). In this numerical approach, the velocity disturbance is obtained by a low order multipole expansion (particle forcing on the flow is represented by monopole and dipole terms spread on a finite volume envelop related to particle radius).