Stirred gas–solid fluidized bed reactors are commercially employed in polyolefin manufacturing, but the complex gas–solid contacting dynamics pose challenges in design, scale-up, and operation. In this study, the influence of agitation on the fluidization performance of Geldart B particles was investigated experimentally by X-ray imaging and pressure drop measurements and numerically by Computational Fluid Dynamics (CFD) - Discrete Element Method (DEM) - Immersed Boundary Method (IBM). The experimentally obtained minimum fluidization curve and time-averaged pressure drop show good qualitative agreement with the simulation results. Visual observations underscore that an increase in the angular velocity of the agitator results in reduced bubble size and improved bed homogeneity, as further evidenced by reduced pressure fluctuations. Furthermore, the simulations reveal that while the impeller enhances solids agitation, a proper design study is imperative, considering that static immersed bodies, such as the stirrer shaft, can adversely impact solids motion.@en

In this work, we perform simulations of particle laden flow in a wide and long narrow channel in a Newtonian fluid. Simulations are performed for mono-sized and equal density spheres with varying Archimedes and Reynolds number. In the simulations, different phases of particle transport - rolling, saltation and suspension are observed. During simulations the average bed height is monitored and its steady state value is used for proposing a correlation between solids volume fraction (ϕ), shear Reynolds number (Re_s) and Archimedes number (Ar). This correlation is used to predict the critical shear Reynolds number for particle lift-off and a condition at which particles would occupy the whole channel at a given Archimedes number. The value of this critical Reynolds number is compared with the critical Reynolds number for single particle lift-off.

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In this work, we investigate the influence of channel structure and fluid rheology on non-inertial migration of non-Brownian polystyrene beads. Particle migration in this regime can be found in biomedical, chemical, environmental and geological applications. However, the effect of fluid rheology on particle migration in porous media remains to be clearly understood. Here, we isolate the effects of elasticity and shear thinning by comparing a Newtonian fluid, a purely elastic (Boger) fluid, and a shear-thinning elastic fluid. To mimic the complexity of geometries in real-world application, a random porous structure is created through a disordered arrangement of cylindrical pillars in the microchannel. Experiments are repeated in an empty channel and in channels with an ordered arrangement of pillars, and the similarities and differences in the observed particle focusing are analyzed. It is found that elasticity drives the particles away from the channel walls in an empty microchannel. Notably, particle focusing is unaffected by curved streamlines in an ordered porous microchannel and particles stay away from pillars in elastic fluids. Shear-thinning is found to reduce the effect of focusing and a broader region of particle concentration is observed. It is also noteworthy that the rheological characteristics of the fluid are not important for the particle distribution in a randomly arranged pillared microchannel and particles have a uniform distribution for all suspending fluids. Moreover, discussion on the current discrepancy in the literature about the equilibrium positions of the particles in a channel is extended by analyzing the results obtained in the current experiments.

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In this paper, an accurate and stable sharp interface immersed boundary method(IBM) is presented for the direct numerical simulation of particle laden flows. The current IBM method is based on the direct-forcing method by incorporating the ghost-cell approach implicitly. An important feature of this IBM is the sharp representation of the solid surface, contrary to other variants of IBM for freely moving particles in which the solid surface is diffuse. Moreover, a correction of the diameter is not necessary for obtaining accurate results. The current ghost-cell IBM is stable because spurious oscillations incurred due to discontinuity in the pressure and velocity field in moving particle simulations is avoided. An algorithm for accurate torque computation is developed. The proposed algorithm is verified by comparison to an analytical expression and is shown to give a substantial improvement over the existing method. Finally, the present IBM is validated for various test cases of single and multi-particle systems and is shown to be accurate and robust for a wide range of flow conditions.@en

Hypothesis Multiphase flow through porous media is important in a number of industrial, natural and biological processes. One application is enhanced oil recovery (EOR), where a resident oil phase is displaced by a Newtonian or polymeric fluid. In EOR, the two-phase immiscible displacement through heterogonous porous media is usually governed by competing viscous and capillary forces, expressed through a Capillary number Ca, and viscosity ratio of the displacing and displaced fluid. However, when viscoelastic displacement fluids are used, elastic forces in the displacement fluid also become significant. It is hypothesized that elastic instabilities are responsible for enhanced oil recovery through an elastic microsweep mechanism. Experiments In this work, we use a simplified geometry in the form of a pillared microchannel. We analyze the trapped residual oil size distribution after displacement by a Newtonian fluid, a nearly inelastic shear thinning fluid, and viscoelastic polymers and surfactant solutions. Findings We find that viscoelastic polymers and surfactant solutions can displace more oil compared to Newtonian fluids and nearly inelastic shear thinning polymers at similar Ca numbers. Beyond a critical Ca number, the size of residual oil blobs decreases significantly for viscoelastic fluids. This critical Ca number directly corresponds to flow rates where elastic instabilities occur in single phase flow, suggesting a close link between enhancement of oil recovery and appearance of elastic instabilities.

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It is known that viscoelastic fluids exhibit elastic instabilities in simple shear flow and flow with curved streamlines. During flow through a straight microchannel with pillars, we found strikingly strong hydrodynamic instabilities characterized by very large transversal excursions, even leading to a complete change in lanes, and the presence of fast and slowmoving lanes. Particle image velocimetry measurements through a pillared microchannel provide experimental evidence of these instabilities at a very low Reynolds number (< 0.01). The instability is characterized by a rapid increase in spatial and temporal fluctuations of velocity components and pressure at a critical Deborah number. We characterize under which conditions these strong instabilities arise.

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We investigate creeping flow of a viscoelastic fluid through a three dimensional random porous medium using computational fluid dynamics. The simulations are performed using a finite volume methodology with a staggered grid. The no slip boundary condition on the fluid-solid interface is implemented using a second order finite volume immersed boundary (FVM-IBM) methodology [1]. The viscoelastic fluid is modeled using a FENE-P type model. The simulations reveal a transition from a laminar regime to a nonstationary regime with increasing viscoelasticity. We find an increased flow resistance with increase in Deborah number even though shear rheology is shear thinning nature of the fluid. By choosing a length scale based on the permeability of the porous media, a Deborah number can be defined, such that a universal curve for the flow transition is obtained. A study of the flow topology shows how in such disordered porous media shear, extensional and rotational contributions to the flow evolve with increased viscoelasticity. We correlate the flow topology with the dissipation function distribution across the porous domain, and find that most of the mechanical energy is dissipated in shear dominated regimes instead, even at high viscoelasticity.@en

We investigate creeping flow of a viscoelastic fluid through a three dimensional random porous medium using computational fluid dynamics. The simulations are performed using a finite volume methodology with a staggered grid. The no slip boundary condition on the fluid-solid interface is implemented using a second order finite volume immersed boundary (FVMIBM) methodology [1]. The viscoelastic fluid is modelled using a FENE-P type constitutive relation. The simulations reveal a transition of flow structure from a laminar Newtonian regime to a nonstationary non-Newtonian regime with increasing viscoelasticity. We find that the flow profiles are mainly governed by the porous microstructure. By choosing a proper length scale a universal curve for the flow transition can be obtained. A study of the flow topology shows how in such disordered porous media shear, extensional and rotational contributions to the flow evolve with increased viscoelasticity.@en

We investigate the flow of unsteadfy three-dimensional viscoelastic fluid through an array of symmetric and asymmetric sets of cylinders constituting a model porous medium. The simulations are performed using a finite-volume methodology with a staggered grid. The solid-fluid interfaces of the porous structure are modeled using a second-order immersed boundary method [S. De et al., J. Non-Newtonian Fluid Mech. 232, 67 (2016)]. A finitely extensible nonlinear elastic constitutive model with Peterlin closure is used to model the viscoelastic part. By means of periodic boundary conditions, we model the flow behavior for a Newtonian as well as a viscoelastic fluid through successive contractions and expansions. We observe the presence of counterrotating vortices in the dead ends of our geometry. The simulations provide detailed insight into how flow structure, viscoelastic stresses, and viscoelastic work change with increasing Deborah number De. We observe completely different flow structures and different distributions of the viscoelastic work at high De in the symmetric and asymmetric configurations, even though they have the exact same porosity. Moreover, we find that even for the symmetric contraction-expansion flow, most energy dissipation is occurring in shear-dominated regions of the flow domain, not in extensional-flow-dominated regions.@en

An efficient and accurate model for the direct numerical simulations (DNS) of liquid-solid flows is presented in this work. In this numerical model, fluid-solid coupling is achieved by implementing the no-slip boundary condition at the particles’ surfaces by using a second order ghost-cell immersed boundary method, allowing for a fixed Cartesian grid to be used for solving the fluid equations. The particle-particle and particle-wall interactions are implemented using the soft sphere collision model. Lubrication forces are included through a sub-grid scale model because of its range of influence on a scale smaller than the grid size.
After the validation of the model, the transport of solid particles in a narrow channel is simulated to mimic the proppant transport in rock fractures in fracking process. The simulations are performed for solids volume fractions ranging from 1.7 to 20 % with the range of Reynolds and Archimedes number: 100-400 and 0-7848, respectively.@en

We investigate creeping viscoelastic fluid flow through two-dimensional porous media consisting of random arrangements of monodisperse and bidisperse cylinders, using our finite volume-immersed boundary method introduced in S. De, et al., J. Non-Newtonian Fluid Mech., 2016, 232, 67–76. The viscoelastic fluid is modeled with a FENE-P model. The simulations show an increased flow resistance with increase in flow rate, even though the bulk response of the fluid to shear flow is shear thinning. We show that if the square root of the permeability is chosen as the characteristic length scale in the determination of the dimensionless Deborah number (De), then all flow resistance curves collapse to a single master curve, irrespective of the pore geometry. Our study reveals how viscoelastic stresses and flow topologies (rotation, shear and extension) are distributed through the porous media, and how they evolve with increasing De. We correlate the local viscoelastic first normal stress differences with the local flow topology and show that the largest normal stress differences are located in shear flow dominated regions and not in extensional flow dominated regions at higher viscoelasticity. The study shows that normal stress differences in shear flow regions may play a crucial role in the increase of flow resistance for viscoelastic flow through such porous media.@en

We report on simulations of an unsteady three dimensional viscoelastic fluid flow through a model porous medium, employing a finite volume methodology (FVM) with a staggered grid. Boundary conditions at the walls of the porous structures are imposed using a second order immersed boundary method (IBM), allowing for accurate simulations using a relatively coarse grid. We compare the viscoelastic stresses obtained using this new IBM technique with those published in literature and find good correspondence. Next, we applied this methodology to model viscoelastic fluids with a FENE-P constitutive model flowing through closely spaced cylinders. Using periodic boundary conditions, we modeled the flow behavior for Newtonian and viscoelastic fluids for successive contractions and expansions. We observe the presence of counter-rotating vortices in between the closely spaced cylinders. The viscoelastic flow structure is symmetric for lower Deborah (De) number, but onset of an asymmetry occurs after a critical De for an infinite array of cylinders. In the presence of side walls, we observe that the onset of flow asymmetry happens at a much lower De, which can be related to higher viscoelastic stresses normal to the flow direction and larger extensional viscosities which affect the curved streamlines. The three-dimensional flow characteristics for viscoelastic flow at higher De number are quite different in comparison with Newtonian flow behavior.

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The large-scale hydrodynamic behavior of relatively dense dispersed multiphase flows, such as encountered in fluidized beds, bubbly flows, and liquid sprays, can be predicted efficiently by use of Euler-Lagrange models. In these models, grid-averaged equations for the continuous-phase flow field are solved, where the grid size is larger than the discrete phase size, while the discrete phase is explicitly tracked and experiencing forces in a Lagrangian fashion. In this chapter, we provide a summary of our own efforts in this field, including details which we deem necessary for a novice to be aware of. We start with a theoretical introduction to Euler-Lagrange models, emphasizing the importance of the availability of high-quality correlations for the interphase momentum transfer and the outcome of binary interactions between members of the discrete phase. Then, in three topical sections, we discuss implementations of the methods which are used intensely in our group: the computational fluid dynamics/discrete element method (CFD-DEM), discrete bubble method (DBM), and direct simulation Monte Carlo (DSMC). CFD-DEM is most suitable for solid particles moving in a gas. The interplay between hydrodynamic flow and dissipative collisions between these particles leads to inhomogeneities at meso- and larger scale. DBM applies to bubbly flows, where the additional complication of coalescence and splitting of bubbles needs to be taken into account accurately. DSMC is suitable for not-too-dense systems of particles or droplets in a gas (dispersed volume fraction less than 10%). Collisions between the discrete phase elements are detected stochastically from the local number density, relative velocities, and sizes of neighboring dispersed elements, leading to a considerable saving of computer time. We end with an outlook into directions of research which would lead to an even more comprehensive use of Euler-Lagrange models in the future.

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This paper reviews the use of direct numerical simulation (DNS) models for the study of mass, momentum and heat transfer phenomena prevailing in dense gas-solid flows. In particular, we consider the DNS models as the first important step in a multiscale modeling strategy. Both the merits and the limitations of different DNS methods are discussed, in particular for the field of fluidized bed modeling. The importance of the closures for interfacial transfer of mass, momentum and heat, obtained from DNS and applied in coarser scale models, is demonstrated with illustrative examples. Finally, we present our view on required future developments of DNS models for the investigation of various chemical engineering problems.

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