Fluid-particle Systems Research Articles

An efficient framework for particle-fluid interaction using Discrete Element Lattice Boltzmann Method: Coupling scheme and periodic boundary condition

Discrete modeling of particle-fluid interaction was of great importance for its wide applications in chemical, petroleum and geotechnical engineering. Using Immersed Boundary Method (IBM) to couple Discrete Element Method (DEM) with Lattice Boltzmann Method (LBM) was adopted by many researchers to study particle-fluid systems. However, to accurately simulate the behavior of a large number of particles in the fluid, a huge computational power wasrequired to fully resolved the motion of each particle and an intensive search of particles’ contacts was needed to account for the collision between particles. In this paper, a periodic boundary was proposed for coupling DEM with LBM using IBM and an efficient particle contact detection algorithm was developed to further reduce the computation cost. The model was validated by several well-defined benchmark including: a single particle settling in a box, particle spinning in a channel and the well-known ‘Drafting, Kissing and Tumbling’ (DKT) effect of two settling disks. The model's applicability was exhibited in the simulation of sediments movement in a channel, which agreed well with previous experiments. These results showed the potential usage of present numerical model to investigate in particle-fluid interaction systems.

Blowup Mechanism for a Fluid-Particle Interaction System in $\mathbb{R}^{3}$

We study the Cauchy problem and the mixed initial boundary value problem of a fluid-particle interaction system in $\mathbb{R}^{3}$ . A Serrin type criterion for the strong solution of the Cauchy problem is established in terms of $\|\rho \|_{L^{\infty }_{t}L^{\infty }_{x}}$ and $\|u\|_{L^{s}_{t}L^{r}_{x}}$ , where $2/s+3/r\le 1$ and $3< r\le \infty $ . In view of some useful integral inequalities, we prove the life span estimates of the regular solution.

Generalized models for predicting the drag coefficient and settling velocity of rigid spheres in viscoelastic and viscoinelastic power-law fluids

The design and optimization of several fluid-particle transport systems often require the determination of particle settling velocity in non-Newtonian fluids. These fluid-particle transport systems are encountered in a wide variety of industrial processes including drill cuttings transport in oil and gas well drilling operations and proppant transport in hydraulic fracturing operations. Current conventional approaches to estimate settling velocity in these non-Newtonian fluids often exclude the effect of elasticity on particle settling which can lead to erroneous estimation. It is therefore imperative to devise an accurate means to mathematically account for the fluid elasticity in particle settling in viscoelastic fluids. An experimental study was conducted to measure the settling velocity of spherical particles in viscoelastic and viscoinelastic power-law type fluids. Using a semi-mechanistic approach, explicit mathematical models were developed for estimating drag coefficient and particle settling velocity in viscoelastic fluids and viscoinelastic fluids. The main objectives of the study were: i.) To measure the terminal settling velocity of particles in various viscoelastic and viscoinelastic power-law type fluids intended at augmenting the present corpus of experimental data in literature. ii.) To develop new drag coefficient and particle Reynolds number correlations that are applicable to viscoelastic and viscoinelastic power-law type fluids and, iii.) To present a general explicit approach for predicting settling velocities of particles in viscoelastic and viscoinelastic fluids.Particle Image Shadowgraphy (PIS) was used to measure the settling velocities of the spherical particles (Specific gravity 2.5–7.7; Diameters: 0.71–4.00 mm) in Hydrolyzed Polyacrylamide and Tylose solutions of varying elastic properties. Rheological characterization of the fluids was carried out using the C-VOR Bohlin Rheometer. Experimental results from this study were combined with various data published in the literature to create an extensive database and widen the scope for empirical analysis. The database had a consistency index (k) range of 0.012–6.773 Pa.sn and a fluid behavior index (n) range of 0.370–0.940. New drag coefficient and Reynold number correlations for particles settling in viscoelastic and viscoinelastic power-law fluids were developed by using a semi-mechanistic approach, which also included the fluid elasticity effect quantified in terms of the longest relaxation time. The newly developed correlations and an advanced statistical modeling program (OriginPro 9.0) were used to mathematically create explicit models that can be used for predicting particle settling velocity in viscoelastic and viscoinelastic fluids.Comparative analysis showed that an increase in the fluid elasticity gave a corresponding decrease in the particle Reynolds number and dampened the particle settling velocity in viscoelastic fluids. This dampening effect can be attributed to the unique ability of elastic fluids to partially or fully regain their original structure after deformation. Furthermore, statistical analysis showed that the presented new models predict settling velocity accurately with a very low with a Percentage Mean Absolute Error of about 7.5% and 30% for viscoinelastic and viscoelastic fluids respectively. The proposed models also exhibited Root Mean Square Error (RMSE) values of 0.04 m/s and 0.009 m/s for viscoinelastic and viscoinelastic fluids respectively.

Acoustical Studies on Beryllium Oxide/Silicone Oil Nanofluids

Molecular interactions of Silicone oil based Beryllium oxide nanofluids have been studied using ultrasonic parameters at room temperature. BeO nanoparticles synthesized by chemical precipitation method was used to prepare silicone oil based BeO nanofluids. BeO nanofluids were prepared by dispersing synthesized BeO nanoparticles in the Silicone Oil base fluid with the help of sonication. Ultrasonic velocity for particle-fluid mixtures of Silicone oil with BeO has been carried out for different volume fraction (0 to 0.003) at 0.0005 intervals at room temperature. The data experimentally measured has been used to estimate the various acoustical and thermodynamical parameters. The behavior of these parameters in this particle fluid system has been discussed in terms of inter/intramolecular interactions with respect to concentration. The particle base fluid molecular interactions in the nanofluids cause an increment in velocity value of Silicone oil based nanofluids. The propagation of ultrasonic waves causes impedance which increases the intermolecular distance between the molecules. The transmission and reflection modes of sound waves in the nanoparticle and base fluid molecules are noted by the specific acoustic impedance. It is noted that the acoustic impedance value increases with rise in concentration owing to the molecular interaction between BeO and silicone oil fluid molecules affecting the structural arrangement.

Simulation of Multiscale Hydrophobic Lipid Dynamics via Efficient Integral Equation Methods

In this paper, a mathematical model for long-range, hydrophobic attraction between amphiphilic particles is developed to quantify the macroscopic assembly and mechanics of a lipid bilayer membrane in solvents. The nonlocal interactions between amphiphilic particles are obtained from the first domain variation of a hydrophobicity functional, giving rise to forces and torques (between particles) that dictate the motion of both particles and the surrounding solvent. The functional minimizer (that accounts for hydrophobicity at molecular-aqueous interfaces) is a solution to a boundary value problem of the screened Laplace equation. We reformulate the boundary value problem as a second-kind integral equation (SKIE), discretize the SKIE using a Nyström discretization and Quadrature by Expansion (QBX), and solve the resulting linear system iteratively using GMRES. We evaluate the required layer potentials using the GIGAQBX fast algorithm, a variant of the Fast Multipole Method (FMM), yielding the required particle interactions with asymptotically optimal cost. A mobility problem formulation supplies the motion for the rigid particles in a viscous fluid. The simulated fluid-particle systems exhibit a variety of multiscale behaviors over both time and length. Over short time scales, the numerical results show self-assembly for model lipid particles. For large system simulations, the particles form realistic configurations like micelles and bilayers. Over long time scales, the bilayer shapes emerging from the simulation appear to minimize a form of bending energy.

Particle-fluid flow and transport within rough fractures

Proppant injection is an important part of a hydraulic fracturing programs in which fluid-particle slurry is injected into rock fractures. Injected particles are lodged between fracture surfaces during wall close-in thereby propping open the fracture, improving connectivity and production. This paper investigates behaviour of proppant particles within artificially generated rock fractures, providing insight into transport behavioural differences caused by realistic surface roughness. Better understanding of proppant behaviour within more realistic rough fracture conditions provides greater understanding of proppant transport as compared to past works where smooth walled fracture configurations were utilized. A clearer understanding is important in providing more accurate evaluation of realistic proppant flow and distribution and improving injection design. In this study a roughened surface, analogues to actual rock fracture surface, is artificially generated based on a rock surface’s fractal dimension and asperity height standard deviation. Computational representation of the rock surfaces and flow domain is generated. Resolved Discrete Element Method coupled with computational fluid dynamics (DEM-CFD) is implemented in this study to evaluate proppant particle transport behaviour within the fractures. This work highlights importance of considering fracture surface roughness in evaluating proppant flow and transport and more generally the impact of rough boundary conditions of particle-fluid systems.

Numerical investigations for a chain of particles settling in a channel

The present work deals with the numerical investigation for a chain-like formation of suspended particles of circular shape in fluid flow. An explicit volume integral approach for the calculation of hydrodynamic forces acting on the particle’s surface is used. A collision strategy proposed by Glowinski, Singh, Joseph and coauthors for the treatment of colliding or approaching particles is used. The direct simulation technique (fictitious boundary method) achieves the solution of incompressible flow along with moving rigid bodies. The Eulerian based approach which is independent of particle size, particle shape and number of particles is adopted to solve the fluid-particle phenomena in the computational domain. The fluid domain consisting of a multigrid finite element background is considered and the whole numerical process is carried out through open source code FEATFLOW. Numerical experiments for settling particles which are close together forming chain like formations are performed and analyzed. The study is carried out using different configurations of particle positions resulting in different chain patterns. Consequences of such patterns on particles’ motion and on the fluid-particle system is discussed.

A smoothed particle hydrodynamics (SPH) formulation of a two-phase mixture model and its application to turbulent sediment transport

A Smoothed Particle Hydrodynamics (SPH) formulation and implementation of the classical two-phase mixture model are reported, with a particular focus on the turbulent sediment transport and the sediment disturbances generated by moving equipment operating near or on the seabed. In the mixture model, the fluid-particle system is considered to be an equivalent medium whose evolution is described by a set of equations for the mixture continuity and momentum conservation, with the particle volume fraction being tracked by a transport equation. The governing equations are adapted to a Lagrangian, weakly-compressible SPH framework, the turbulence is modeled by a Reynolds-averaged Navier-Stokes approach, and adaptive boundary conditions for shear stress and turbulent quantities are implemented to account for laminar or turbulent local flow conditions. The complex rheological behavior of clay sediment/water mixtures is modeled using a volume fraction, shear rate-dependent viscosity which accounts for the existence of a yield stress. Hence, the proposed work encompasses several challenging modeling aspects: turbulence, non-Newtonian fluid behavior, sediment transport, and fluid-structure interactions. It is then illustrated on diverse cases of interest: a fluid-particle mixture column release, its subsequent turbulent transport and return to a hydrostatic equilibrium, the settling of particle clouds and two cases of particle-driven gravity currents, and their comparisons with available results. Finally, SPH simulation results for the disturbance of a bed of clay sediment/water mixture induced by a moving plate are reported and compared with experiments performed in our laboratory. The proposed SPH two-phase mixture model agrees well with the existing results considered in this study.

An approach to distribute the marker points on non-spherical particle/boundary surface within the IBM-LBM framework

IBM-LBM-DEM (immersed boundary method – lattice Boltzmann method – discrete element method) is a powerful tool to solve the particle-fluid interaction problems, and the super-ellipsoids can model particles of various shapes in DEM. To lay the foundation of IBM-LBM-DEM for particles with arbitrary shapes, the super-ellipsoid model is introduced to describe non-spherical particles. For the successful simulation of particle-fluid systems by IBM-LBM-DEM based on super-ellipsoids, adopting an appropriate method to distribute the discrete marker points on the surface of a super-ellipsoid within the IBM and DEM frameworks is indispensable. In light of this, a strip approach originally proposed for sphere is extended to super-ellipsoid to discretize the particle surface. For the surface discretization of arbitrary solid shapes, the multi-super-ellipsoid model is further proposed in this paper that a particle is composed of two or more super-ellipsoids. The IBM-LBM simulations of the flow over a stationary particle with different shapes, including spherical, cuboidal, ellipsoidal, cylindrical and spherocylindrical particles, are subsequently carried out to validate the capability of the proposed approaches. The fairly good agreement between the current simulation results and the relevant literature results demonstrates its feasibility in discretizing the particle surface. The comparisons between different shape-approximation accuracies for cuboidal and cylindrical particles modeled by super-ellipsoids further reveal that adopting the relatively low shape-approximation accuracy is also acceptable.

Fully-coupled pressure-based two-fluid solver for the solution of turbulent fluid-particle systems

A fully-coupled pressure-based two-fluid solver for the solution of turbulent fluid-particle flows is presented. The numerical framework details several crucial aspects: implicit treatment of the phase-velocity-pressure coupling, the implicit treatment of inter-phase momentum transfer and finally the solution algorithm. The two-fluid solver is implemented within the open source tool-box foam-extend which is a community driven fork of OpenFOAM. The coupled solver is verified against a standard segregated implementation of the two-fluid solution algorithm and validated against benchmark experimental data. The coupled solver shows marked improvements in convergence, stability and solution time. The coupled implementation is capable of solving to a tolerance that is six orders of magnitude smaller in residual error and 1.7 times quicker than the segregated solver. Additionally, the sequentially solved system of phase-energies experienced performance improvements when solved in conjunction with the coupled solver.

Bridging functional nanocomposites to robust macroscale devices.

At the intersection of the outwardly disparate fields of nanoparticle science and three-dimensional printing lies the promise of revolutionary new "nanocomposite" materials. Emergent phenomena deriving from the nanoscale constituents pave the way for a new class of transformative materials with encoded functionality amplified by new couplings between electrical, optical, transport, and mechanical properties. We provide an overview of key scientific advances that empower the development of such materials: nanoparticle synthesis and assembly, multiscale assembly and patterning, and mechanical characterization to assess stability. The focus is on recent illustrations of approaches that bridge these fields, facilitate the design of ordered nanocomposites, and offer clear pathways to device integration. We conclude by highlighting the remaining scientific challenges, including the critical need for assembly-compatible particle-fluid systems that ultimately yield mechanically robust materials. The role of domain boundaries and/or defects emerges as an important open question to address, with recent advances in fabrication setting the stage for future work in this area.

Geometric universality and anomalous diffusion in frictional fingers

Frictional finger trees are patterns emerging from non-equilibrium processes in particle-fluid systems. Their formation share several properties with growth algorithms for minimum spanning trees (MSTs) in random energy landscapes. We propose that the frictional finger trees are indeed in the same geometric universality class as the MSTs, which is checked using updated numerical simulation algorithms for frictional fingers. We also propose a theoretical model for anomalous diffusion in these patterns, and discuss the role of diffusion as a tool to classify geometry.

Fully resolved simulations of thermal convective suspensions of elliptic particles using a multigrid fictitious boundary method

In particulate flows, particle-particle collisions play a very important role in determining the flow behavior of the fluid-particle two-phase systems. Thus, it is very important in the numerical simulations of particulate flows to treat the particle-particle interactions with a felicitous method. In this paper, a recently developed direct numerical simulation (DNS) technique, the Finite Element Fictitious Boundary Method (FEM-FBM), for thermal convective particulate flows is used for the simulations of dense particulate suspensions of elliptic shaped particles. The momentum and temperature flow fields are coupled with the aid of Boussinesq approximation. The thermal and momentum interactions between solid and fluid phases are handled by using the Fictitious boundary method (FBM). The continuity, momentum, and energy equations are solved on a fixed Eulerian mesh which is independent of flow features by using a multi-grid finite element scheme. A modified collision model is proposed that can handle not only the interactions between the circular particles but also effectively treat the collisions between the elliptic shaped particles. Firstly, we validate the newly developed collision model for isothermal circular particles together with a comparative study of “drafting, kissing and tumbling” (DKT) motion of both elliptic and circular shaped isothermal particles. Then we investigated the DKT motions of the hot and cold elliptic particles with energy exchange and studied the lateral behavior of the particles in numerous settings. Further, we studied the DKT motion of catalyst particles and investigate the particles behavior at different Grashof numbers. Numerical tests are performed to show that the present method is robust and provides an efficient approach for the simulations of particulate flows with a large number of elliptic particles.

Direct numerical simulation of fluid flow and dependently coupled heat and mass transfer in fluid-particle systems

In this paper, an efficient ghost-cell based immersed boundary method (IBM) is used to perform direct numerical simulation (DNS) of reactive fluid-particle systems. With an exothermic first order reaction proceeding at the exterior particle surface, the solid temperature rises and consequently increases the reaction rate via an Arrhenius temperature dependence. In other words, the heat and mass transport is dependently coupled through the particle thermal energy equation and the Arrhenius equation, and they offer dynamic boundary conditions for the fluid phase thermal energy equation and species equation respectively. The fluid-solid coupling is enforced at the exact position of the particle surface by implicit incorporation of the boundary conditions into the discretized momentum, species and thermal energy conservation equations of the fluid phase. Different fluid-particle systems are studied with increasing complexity: a single sphere, three spheres and a dense array consisting of hundreds of randomly generated particles. In these systems the mutual impacts between heat and mass transport processes are investigated.

Numerical simulation of proppant transport in propagating fractures with the multi-phase particle-in-cell method

In this work, the proppant transport process in large-scale propagating fractures is simulated using an Eulerian–Lagrangian method. Fracture propagation is solved using the Perkins–Kern–Nordgren(PKN) model, while the fluid-particle system is solved with the multi-phase particle-in-cell (MP-PIC) method. The fluid motion is governed by volume-averaged Navier–Stokes equations, and solved using the finite volume method, and the particle motion is solved by applying Newton’s second law in a Lagrangian manner. Based on the original MP-PIC method, an extended 2D system of governing equations for fluid-particle flow is derived to solve the moving boundary problems associated with fracture propagation. By means of this method, the fluid-particle interaction is fully coupled, and the propagating fracture is considered as a prior-known boundary for the fluid and particle phases. Several numerical experiments are performed to validate the method for simulating fluid motion and proppant settling behaviors in a fracture through comparison with results in the literature. The simulation results of the 2D framework are also compared with those of 3D framework and show a good agreement. Large-scale problems of proppant transport in propagating fractures for different proppant and fracturing fluid properties, including the leak-off effect, are then simulated using this method. The Lagrangian feature of the MP-PIC method allows for flexible design of proppant injection, such as injection of proppant with multi-densities and/or multi-sizes.

Coupling the fictitious domain and sharp interface methods for the simulation of convective mass transfer around reactive particles: Towards a reactive Sherwood number correlation for dilute systems

We suggest a reactive Sherwood number model for convective mass transfer around reactive particles in a dilute regime. The model is constructed with a simple external-internal coupling and is validated with Particle-Resolved Simulation (PRS). The PRS of reactive particle-fluid systems requires numerical methods able to handle efficiently sharp gradients of concentration and potential discontinuities of gradient concentrations at the fluid-particle interface. To simulate mass transfer from reactive catalyst beads immersed in a fluid flow, we coupled the Sharp Interface Method (SIM) to a Distributed Lagrange Multiplier/Fictious Domain (DLM/FD) two-phase flow solver. We evaluate the accuracy of our numerical method by comparison to analytic solutions and to generic test cases fully resolved by boundary fitted simulations. A previous theoretical model that couples the internal diffusion-reaction problem with the external advection-diffusion mass transfer in the fluid phase is extended to the configuration of three aligned spherical particles representative of a dilute particle-laden flow. Predictions of surface concentration, mass transfer coefficient and chemical effectiveness factor of catalyst particles are validated by DLM-FD/SIM simulations. We show that the model captures properly the effect of an internal first order chemical reaction on the overall respective reactive Sherwood number of each sphere depending on their relative positions. The proposed correlation for the reactive Sherwood number is based on an existing non-reactive Sherwood number correlation. The model can be later used in Euler/Lagrange or Euler/Euler modelling of dilute reactive particle-laden flows.

A novel approach to rigid spheroid models in viscous flows using operator splitting methods

Calculating cost-effective solutions to particle dynamics in viscous flows is an important problem in many areas of industry and nature. We implement a second-order symmetric splitting method on the governing equations for a rigid spheroidal particle model with torques, drag and gravity. The method splits the operators into a vector field that is conservative and one that takes into account the forces of the fluid. Error analysis and numerical tests are performed on perturbed and stiff particle-fluid systems. For the perturbed case, the splitting method greatly improves the solution accuracy, when compared to a conventional multistep method, and the global error behaves as $\mathcal {O}(\varepsilon h^{2})$ for roughly equal computational cost. For stiff systems, we show that the splitting method retains stability in regimes where conventional methods blow up. In addition, we show through numerical experiments that the global order is reduced from $\mathcal {O}(h^{2}/\varepsilon )$ in the perturbed regime to $\mathcal {O}(h)$ in the stiff regime.

A supervised machine learning approach for predicting variable drag forces on spherical particles in suspension

CFD-DEM simulations have been used extensively to study dense fluid-particle systems. In the point mass representation of particles in DEM, the modeled drag force plays an important role in the dynamics. Current state-of-the-art methodologies use the mean drag correlations based on the superficial Reynolds number and void fraction. In this work, as proof-of-concept, a new data-driven approach for drag force model development is presented using Particle Resolved Simulations (PRS). The key idea in the proposed framework is the use of supervised machine learning to build higher fidelity drag force models for CFD-DEM simulation based on data obtained by PRS. Results show that a trained artificial neural network (ANN) improves the accuracy of drag force prediction by accounting for the relative neighbor particle locations as inputs to the model along with the existing Reynolds number and void fraction information. The ANN trained prediction are within 15% of PRS predictions for 68% of particles, whereas only 46% of particles lie in the same error range if the mean drag is used. This work highlights the viability and potential of using machine learning to develop accurate drag models for particles in suspension.

Detecting Particle Clusters in Particle-Fluid Systems by a Density Based Method

Detecting Particle Clusters in Particle-Fluid Systems by a Density Based Method

Evaluation of physics based hard-sphere model with the soft sphere model for dense fluid-particle flow systems

In this paper we present the application of a physics-based three dimensional hard-sphere impact model to many-particle systems. The hard sphere model is used with conventional time-advancement which is not event driven. A particle relocation technique based on using both pre- and post-collision velocities is developed and validated for dense systems. Also developed is a parallelization scheme which overcomes the inherent sequential nature of processing collisions with the hard sphere model. The relocation technique is tested in a one-dimensional stack of particles and in the three-dimensional settling of a bed of particles. The technique demonstrates its ability to prevent excessive overlaps and maintaining stable stacks of particles at coefficients of restitutions ranging from 0.0 to 0.98. The model is validated in a bubbling fluidized bed and shows no discernable differences with the soft sphere model but at a computational cost about 23 times less than that of the soft sphere model. The model is used to investigate particle agglomeration of 20 µm size particles in a turbulent ribbed duct flow using LES. It was found that the 20 µm particles were prone to agglomerate in regions of low velocity at the upstream and downstream corners of the rib-wall junction. The hard sphere model enabled time steps an order of magnitude larger than that permissible for the soft sphere model which resulted in DEM speedups of more than 20 times.