Particle-laden Fluid Flow Research Articles

Research on particle migration in fractures driven by gas-liquid two-phase flow during deep energy storage and extraction

Particle-laden fluid flow in fracture encompasses various deep geo-energy projects, including but not limited to hydraulic fracturing, mud and water inrush, and sand production. The migration of particles under fluid flow seriously affects the stability of geo-energy engineering and understanding the mechanisms is of great importance. This study presents a numerical investigation of particle-laden fluid flow in rock fractures under two-phase flow. A coupled approach of resolved computational fluid dynamics (CFD) and discrete element method (DEM) is employed to capture the particle movements and variations in hydraulic properties, with the volume of fluid (VOF) method to reproduce the two-phase flow. The results indicate that the model with gas injection exhibits higher particles migration velocity compared to that without gas due to the increase in fluid velocity and fluctuation in drag force. Particles migration velocity presents an initial increase followed by a subsequent decrease as the gas fraction increases, which can be attributed to the initial rise followed by a subsequent decline in the drag force. In addition, the sensitive analysis shows that the particle migration velocity decreases with the increase of liquid viscosity and fracture roughness in the fluid, and further accelerates with the increase of particle size and hydraulic gradient. Our results have important implications for understanding the mechanisms of particle migration in rock fractures driven by the multiphase flow during deep energy storage and extraction.

A Short Review on the Preferential Concentration of Particles in Fluid Flow

Particle laden fluid flows are important in many fields of application such as environmental, chemical, astrophysical, and biological flows. They are examples of multicomponent fluid flow where the dispersed component is transported within a carrier fluid, and the dynamics of the flow are mostly dictated by the carrier fluid. The dispersed phase generally consists of particles such as droplets, bubbles, sediments, or nanoparticles while the carrier phase is typically water, oil, and chemical and biological liquids. Preferential concentration is an important characteristic of such multicomponent fluid flow which is defined by a higher density of particles in local regions of flow based on local acceleration, vorticity, strain, and pressure. Due to the intrinsic challenges of dealing with turbulence, mixing, particle tracking, and inter-and intra-component interactions, these flows are complicated to model. Based on the mass ratio of the particles to the fluid, the particles exhibit different preferential concentration patterns. In this article, experimental and numerical works on the preferential concentration of dispersed particles in different fluid flow problems are reviewed and discussed.

Finite volume simulations of particle-laden viscoelastic fluid flows: application to hydraulic fracture processes

Accurately resolving the coupled momentum transfer between the liquid and solid phases of complex fluids is a fundamental problem in multiphase transport processes, such as hydraulic fracture operations. Specifically we need to characterize the dependence of the normalized average fluid–particle force $$\langle F \rangle$$ on the volume fraction of the dispersed solid phase and on the rheology of the complex fluid matrix, parameterized through the Weissenberg number Wi measuring the relative magnitude of elastic to viscous stresses in the fluid. Here we use direct numerical simulations (DNS) to study the creeping flow ( $$Re\ll 1$$ ) of viscoelastic fluids through static random arrays of monodisperse spherical particles using a finite volume Navier–Stokes/Cauchy momentum solver. The numerical study consists of $$N=150$$ different systems, in which the normalized average fluid–particle force $$\langle F \rangle$$ is obtained as a function of the volume fraction $$\phi$$ $$(0 < \phi \le 0.2)$$ of the dispersed solid phase and the Weissenberg number Wi $$(0 \le Wi \le 4)$$ . From these predictions a closure law $$\langle F(\phi,Wi) \rangle$$ for the drag force is derived for the quasi-linear Oldroyd-B viscoelastic fluid model (with fixed retardation ratio $$\beta = 0.5$$ ) which is, on average, within $$5.7\%$$ of the DNS results. In addition, a flow solver able to couple Eulerian and Lagrangian phases (in which the particulate phase is modeled by the discrete particle method (DPM)) is developed, which incorporates the viscoelastic nature of the continuum phase and the closed-form drag law. Two case studies were simulated using this solver, to assess the accuracy and robustness of the newly developed approach for handling particle-laden viscoelastic flow configurations with $$O(10^5-10^6)$$ rigid spheres that are representative of hydraulic fracture operations. Three-dimensional settling processes in a Newtonian fluid and in a quasi-linear Oldroyd-B viscoelastic fluid are both investigated using a rectangular channel and an annular pipe domain. Good agreement is obtained for the particle distribution measured in a Newtonian fluid, when comparing numerical results with experimental data. For the cases in which the continuous fluid phase is viscoelastic we compute the evolution in the velocity fields and predicted particle distributions are presented at different elasticity numbers $$0\le El \le 30$$ (where $$El=Wi/Re$$ ) and for different suspension particle volume fractions.

Data-driven closure model for the drag coefficient of the creeping flow past a translating sphere in a shear-thinning viscoelastic fluid

A drag force closure model for particle-laden viscoelastic fluid flows is the key to describing the ensemble-averaged behavior of the mixture. The effects of fluid rheological properties on the flow dynamics of a spherical particle in viscoelastic fluids in the creeping flow regime are parameterized using the Giesekus rheological model. Direct numerical simulations are performed within a large range of Deborah number(0−10).The drag force of a sphere in unbounded Giesekus fluids decreases monotonically with the increase of Deborah number. The negative wake may occur when the viscosity ratio is larger than 0.6 in Giesekus fluids but is absent in Oldroyd-B fluids in all conditions. An explicit closure model for the drag coefficient of a sphere in Giesekus fluids is established using the backpropagation artificial neural network. The drag closure model provides a method for explicitly formulating the momentum exchange model for dilute suspensions of solid particles in shear-thinning viscoelastic fluids.

A numerical study of particle-laden flow around an obstacle: flow evolution and Stokes number effects

Three-way coupled numerical simulations of particle-laden fluid flow around a square obstacle are performed by a coupled finite-volume and discrete-element method, taking account of the collisions between particles. The fluid flow is described by the Eulerian formalism, while the Lagrangian formalism is used for the solid particles. The dynamics of each phase and the modulation mechanism of the flow field by the inertial particles are explored. The Reynolds number based on the side length of the obstacle is 100, which leads to a typical periodic flow pattern of vortex shedding. Under the action of particles, the flow tends to be chaotic even in the upstream region, and the vortex shedding occurs earlier. The intensity of the vortex is attenuated due to particle dissipation. At sufficiently small Stokes numbers, the particles exhibit flow tracer behavior with relatively high fidelity. However, as the Stokes number and mass loading increase, the interaction between the particles and fluid becomes important, especially in the core region of the channel. With the increase of the particle response time, the spanwise velocity fluctuation is attenuated, while the influence on the streamwise velocity fluctuation seems complicated. No particles are observed to hit the rear surface of the obstacle or deposit in the domain during the flow. When the Stokes number and mass loading are elevated from 0.0036 and 0.065 to 0.5 and 9.024, respectively, the distribution of the particles near the channel centerline varies from being filled in the shedding vortices to surrounding them. Meanwhile, the particle-free zones centered on these vortices become larger. For the Stokes number and mass loading up to 1.5 and 27.073, respectively, the particles are scattered in the downstream area, and the flow pattern of the Kármán vortex street is modified. Within the range of the Stokes number considered, the drag and lift coefficients, and the Strouhal number also show a certain trend of variation.

Genesis of electric field assisted microparticle assemblage in a dielectric fluid

Abstract

The effect of particle shape on discharge and clogging

Granular flow is common across different fields from energy resource recovery and mineral processing to grain transport and traffic flow. Migrating particles may jam and form arches that span constrictions and hinder particle flow. Most studies have investigated the migration and clogging of spherical particles, however, natural particles are rarely spherical, but exhibit eccentricity, angularity and roughness. New experiments explore the discharge of cubes, 2D crosses, 3D crosses and spheres under dry conditions and during particle-laden fluid flow. Variables include orifice-to-particle size ratio and solidity. Cubes and 3D crosses are the most prone to clogging because of their ability to interlock or the development of face-to-face contacts that can resist torque and enhance bridging. Spheres arriving to the orifice must be correctly positioned to create stable bridges, while flat 2D crosses orient their longest axes in the direction of flowlines across the orifice and favor flow. Intermittent clogging causes kinetic retardation in particle-laden flow even in the absence of inertial effects; the gradual increase in the local particle solidity above the constriction enhances particle interactions and the probability of clogging. The discharge volume before clogging is a Poisson process for small orifice-to-particle size ratio; however, the clogging probability becomes history-dependent for non-spherical particles at large orifice-to-particle size ratio and high solidities, i.e., when particle–particle interactions and interlocking gain significance.

A correction scheme for wall-bounded two-way coupled point-particle simulations

The accuracy of Euler-Lagrange point-particle models employed in particle-laden fluid flow simulations depends on accurate estimation of the particle force through closure models. Typical force closure models require computation of the slip velocity at the particle location, which in turn requires accurate estimation of the undisturbed fluid velocity. Such an undisturbed velocity is not readily available when the fluid and particle phases are two-way coupled, due to the disturbance created by the particle's force in the nearby fluid velocity field. A common practice is to use the disturbed velocity to compute the particle force which can result in errors as much as 100% in predicting the particle dynamics. In this work, a correction scheme is developed that facilitates accurate estimation of the undisturbed fluid velocity in particle-laden fluid flows with and without no-slip walls. The model is generic and can handle particles of different size and density, arbitrary interpolation and projection functions, anisotropic grids with large aspect ratios, and wall-bounded flows. The present correction scheme is motivated by the recent work of Esmaily & Horwitz (JCP, 2018) on unbounded particle-laden flows. Modifications necessary for wall-bounded flows are developed such that the undisturbed fluid velocity at any wall distance is accurately recovered, asymptotically approaching the result of unbounded schemes for particles far away from walls. A detailed series of verification tests was conducted on settling velocity of a particle in parallel and perpendicular motions to a no-slip wall. A range of flow parameters and grid configurations; involving anisotropic rectilinear grids with aspect ratios typically encountered in particle-laden turbulent channel flows was considered in detail. When the wall effects are accounted for, the present correction scheme reduces the errors in predicting the near-wall particle motion by one order of magnitude smaller values compared to the unbounded correction schemes.

Fluid flow and heat transfer for a particle-laden gas modeled as a two-phase turbulent flow

PurposeThe purpose of this study is to examine the physical processes experienced by a particle-laden gas due to various types of collisions, different heat transfer modalities and jet axis switching. Here, attention is focused on a particle-laden gas subjected to jet axis switching while experiencing fluid flow and heat transfer.Design/methodology/approachThe methodology used to model and solve these complex problems is numerical simulation treated here as a two-phase turbulent flow in which the gas and the particles keep their separate identities. For the turbulent flow model, validation was achieved by comparisons with appropriate experimental data. The considered interactions between the fluid and the particles include one-way fluid–particle interactions, two-way fluid–particle interactions and particle–particle interactions.FindingsFor the fluid flow portion of the work, emphasis was placed on the particle collection efficiency and on independent variables that affect this quantity and the trajectories of the fluid and of the particles as they traverse the space between the jet orifice and the impingement plate. The extent of the effect depended on four factors: particle size, particle density, number of particles and the velocity of the fluid flow. The major effect on the heat transferred to the impingement plate occurred when direct heat transfer between the impinging particles and the plate was taken into account.Originality/valueThis paper deals with issues never before dealt with in the published literature: the effect of jet axis switching on the fluid mechanics of gas-particle flows without heat transfer and the effect of jet axis switching and the presence of particles on jet impingement heat transfer. The overall focus of the work is on the impact of jet axis switching on particle-laden fluid flow and heat transfer.

Coupled CFD-DEM simulation of oscillatory particle-laden fluid flow through a porous metal foam heat exchanger: Mitigation of particulate fouling

A coupled finite volume-discrete element (FVM-DEM) numerical method is developed to investigate oscillating multiphase foulant-laden air (solid-gas) flow and particulate fouling in a porous heat exchanger channel comprising an array of circular cylinders. Oscillatory fluids serve as a steppingstone to advance existing conventional anti-fouling techniques and to yield optimum energy consumption. A performance evaluation criteria based on various amplitudes of pulsation and foulant injection rates is established. The fouling characteristics and pressure drop is compared against a non-oscillating steady flow. For the solid foulant particles considered in this study, the results show that the time-averaged deposition fraction is sensibly invariant with increasing foulant injection rate; however, the same observation is not realized for steady-flow cases. The 1 Hz case showed no significant disparity in terms of deposition fraction at high injection rates compared with the non-oscillating steady flow case. In addition, the 1 Hz case showed miniscule reduction of low-density foulants. The higher-frequency spectrum has superior fouling mitigation capabilities although comparatively higher pressure drop is generated. The 6-pore configuration outperforms the 3-pore under certain oscillatory flow conditions. An optimum frequency of 5 Hz exhibits superior fouling mitigation performance while achieving a low time-averaged pressure drop.

Two- and four-way coupling of cohesive poly-disperse particulate foulants on a metal foam fibre immersed in quiescent fluid

The ubiquity and complexity of the unsteadiness of fouling and multiphase flows in various engineering systems signify the need to develop advanced numerical methods to study the underlying phenomena of two-phase particle-laden fluid flows in heat exchanger systems such as, compact electronics cooling (i.e. heat sinks) and HVAC&R systems. Fouling is omnipresent in many industries such as power generation, chemical, petroleum, among others. The mechanisms governing fouling coupled with multiphase foulant-laden fluid flow in porous heat exchangers, such as metal foams, are very complex and poorly understood. This investigation forms the basis for addressing the implications of fouling for a myriad of industrial processes. This study will discuss the development of a coupled finite volume method and discrete element method (FVM-DEM) numerical framework to investigate the mechanisms governing particulate fouling in an idealized metal foam heat exchanger. This study resolves four-way and two-way coupled interactions based on poly-disperse cohesive foulants in fluid-saturated foam. The significance stems from the inclusion of cohesiveness between particle-particle and particle-wall contacts which play a decisive role in the foulant aggregation process prevalent in particles with a diameter smaller than 50μm. The present results show that the cohesive foulants exhibit strong tendency to aggregate with time and form chain-like projections. A rigid aggregate stack is formed which alters the fluid velocity of the fluid-filled foam. Quantitative analysis of the foulant count and time-averaged aggregate count is discussed. The presented results and the numerical framework could potentially be used to optimize heat exchanger designs by considering operating conditions and foam morphology (i.e. pore diameter, ligament thickness, porosity) that is most susceptible to particulate fouling.

A theoretical model of Lorentz force particle analyzer: a potential flow perspective

A Lorentz force particle analyzer (LFPA) is a device for the contactless measurement of micron-sized particles in electrically conducting fluids. The LFPA is based on the measurement of either force or torque changes acting upon a magnetic-generating system when the particle passes near a magnetic field. In this paper, we first formulate the theory of the LFPA using a magnetic dipole with a magnetic field penetrating a particle-laden thin fluid flow layer. The disturbed electromagnetic quantities in the presence of a particle are analytically solved using an approach analogous to that for potential flow, providing a relationship between the measured physical quantities, i.e., force, torque and induced magnetic field, and the particle size. A detailed investigation of physical properties and operating parameters provides a rational framework for predicting the sensitivity of LFPAs in laboratory experiments and in industrial practice.

Analysis of particle-laden fluid flows, tortuosity and particle-fluid behaviour in metal foam heat exchangers

Tortuosity and porosity are critical parameters for characterizing fluid flow in porous media. These parameters are of paramount importance in the design of porous compact heat exchangers, packed bed reactors, and catalysis supports; however, in the context of heat exchangers, these parameters are generally formulated for single-phase fluid flow under steady-state conditions. However, most industrial flows in a porous medium such as metal foams comprise of transient particle-laden fluid flow. A coupled finite volume and discrete element method (FVM-DEM) is developed to examine transient particle-laden Stokesian flow, particulate fouling (deposition), and fluid flow patterns in an idealized porous metal foam. This work presents a comparative analysis of the analytical and numerical pressure drop profiles. The solid-gas suspension in a porous media is discussed. Secondly, a new time-dependent pore-level fluid tortuosity relation is established which is linked with a modified porosity-based Darcy-Forchheimer equation. Fluid disturbance attributable to the inception of particle deposition is quantified by the tortuosity and instantaneous shift in streamline angle ratio. It is shown that the streamline angle ratio and the meandering of fluid flow paths vary with changing porosity and tortuosity. Moreover, the Reynolds number and particle density play a critical role in the alteration of the resistance to fluid flow and permeability which is related to the tortuosity and variation in fluid flow behaviour. The results and numerical method serves as a steppingstone to better optimize various heat exchangers while taking into account complex multiphase flow behaviour and the tortuous flow paths of porous structures.

Accurate calculation of Stokes drag for point–particle tracking in two-way coupled flows

In this work, we propose and test a method for calculating Stokes drag applicable to particle-laden fluid flows where two-way momentum coupling is important. In the point-particle formulation, particle dynamics are coupled to fluid dynamics via a source term that appears in the respective momentum equations. When the particle Reynolds number is small and the particle diameter is smaller than the fluid scales, it is common to approximate the momentum coupling source term as the Stokes drag. The Stokes drag force depends on the difference between the undisturbed fluid velocity evaluated at the particle location, and the particle velocity. However, owing to two-way coupling, the fluid velocity is modified in the neighborhood of a particle, relative to its undisturbed value. This causes the computed Stokes drag force to be underestimated in two-way coupled point-particle simulations. We develop estimates for the drag force error as function of the particle size relative to the grid size. We then develop a correction method that estimates the undisturbed fluid velocity from the computed disturbed velocity field. The correction scheme is tested for a particle settling in an otherwise quiescent fluid and is found to reduce the error in computed settling velocity by an order of magnitude compared with common interpolation schemes.

On Necessary Pumping Pressures for Industrial Process-Driven Particle-Laden Fluid Flows

Due to increasing demands for faster and faster manufacturing of new complex materials, such as casting of particulate composites, the determination of pumping pressures needed for particle-laden fluids through channels is critical. In particular, the increase in viscosity as a function of the particle volume fraction can lead to system malfunction, due to an inability to deliver necessary pressures to pump the more viscous fluid through the system. This paper studies the pressure gradient needed to maintain a given flow rate, explicitly as a function of the volume fraction of particles present in the fluid. It is also crucial to control voids in the casted products, which can be traced to air-entrainment, spurious internal reactions, dewetting, etc., which can be traced to high Reynolds numbers. Accordingly, an expression for the resulting Reynolds number as a function of the particle volume fraction and flow rate is also developed. Numerical examples are provided to illustrate the practical use of the derived relations to characterize the necessary pumping pressures for process-driven, particle-laden fluid flows.

Experimental investigation of the effect of obstacles on the behavior of turbidity currents

Turbidity current is produced when a particle-laden fluid flows under lighter ambient fresh fluid. The streaming of particle-laden fluid is called a turbidity current and this kind of current is an important mechanism for sediment transportation in lakes and oceans. In the present research, the main concentration is on the effect of obstacle with an isosceles right triangular cross section on the behavior of turbidity current. A series of laboratory experiments were carried out with various obstacle heights and different inlet densimetric Froude numbers. In each experiment, velocity profiles upstream and downstream of the obstacle were measured, using an acoustic Doppler velocimeter. Kaolin was used as the suspended material. Experiments showed that the density current with lower inlet Froude number, reacts to the presence of the obstacle more rapidly compared to the currents with higher values of inlet Froude number. At the upstream section of the obstacle, an increase in the height of the obstacle resulted in a reduction in the current inertia and the maximum velocity. Also the local Froude numbers had an abrupt increase when the dense layer passed the obstacle.

Computational Aspects of Multiscale Simulation with the Lumped Particle Framework

AbstractFirst introduced in, the lumped particle framework is a flexible and numerically efficient framework for the modelling of particle transport in fluid flow. In this paper, the framework is expanded to simulate multicomponent particle-laden fluid flow. This is accomplished by introducing simulation protocols to model particles over a wide range of length and time scales. Consequently, we present a time ordering scheme and an approximate approach for accelerating the computation of evolution of different particle constituents with large differences in physical scales. We apply the extended framework on the temporal evolution of three particle constituents in sandladen flow, and horizontal release of spherical particles. Furthermore, we evaluate the numerical error of the lumped particle model. In this context, we discuss the Velocity-Verlet numerical scheme, and show how to apply this to solving Newton’s equations within the framework. We show that the increased accuracy of the Velocity-Verlet scheme is not lost when applied to the lumped particle framework.

An OpenMP-enabled parallel simulator for particle transport in fluid flows

By using C/C++ programming and OpenMP parallelization, we implement a newly developed numerical strategy for simulating particle transport in sparsely particle-laden fluid flows. Due to its highly dynamic property of the chosen numerical framework, the implementation needs to properly handle the moving, merging and splitting of a large number of particle lumps. We show that a careful division of the entire computational work into a set of distinctive tasks not only produces a clearly structured code, but also allows taskwise parallelization through appropriate use of OpenMP compiler directives. The performance of the OpenMP-enabled parallel simulator is tested on representative architectures of multicore-based shared memory, by running a large case of particle transport in a pipe flow. Attention is also given to a number of performance-critical features of the simulator.

Simultaneous measurement of particle and fluid velocities in particle-laden flows

For the velocity measurement in a particle-laden fluid flow, the fluid velocity and the inherently dispersed particle velocity can be analyzed by using PIV and PTV, respectively. Since the PIV result statistically represents the average displacement of all the particles in a PIV image, it is inevitable that the PIV result includes the influence of the dispersed particles’ displacement if a single CCD camera is used to simultaneously measure the fluid velocity and the dispersed particle velocity. The influence of dispersed particles should be excluded before the PIV analysis in order to evaluate the fluid velocity accurately. In this study, the optimum replacement brightness of dispersed particles to minimize the false influence of dispersed particles on the PIV analysis was theoretically derived. Simulation results show that the modification of dispersed particle brightness can significantly reduce the PIV error caused by the dispersed particles. This modification method was also verified in the analysis of an actual experimental case of the particle-laden fluid flow in a triangular grooved channel.

A computational framework for agglomeration in thermochemically reacting granular flows

A computational framework is developed which couples a series of models, each describing vastly different physical events, in order to characterize particle growth (agglomeration) in thermochemically reacting granular flows. The modelling is purposely simplified to expose the dominant mechanisms which control agglomeration. The overall system is comprised of relatively simple coupled submodels describing impact, heat production, bonding and fragmentation, each of which can be replaced by more elaborate descriptions, if and when they are available. Inverse problems, solved with a genetic algorithm, are then constructed to ascertain system parameters which maximize agglomeration likelihood within a range of admissible data.