Modeling fluid–particle interaction in dilute-phase turbulent liquid–particle flow simulation

The present work examines the predictive capability of a two-fluid CFD model that is based on the kinetic theory of granular flow in simulating dilute-phase turbulent liquid–particle pipe flows in which the interstitial fluid effect on the particle fluctuating motion is significant. The impacts of employing different drag correlations and turbulence closure models to describe the fluid–particle interactions (i.e. drag force and long-range interaction) are examined at both the mean and fluctuating velocity l...     

High-order resolution Eulerian–Lagrangian simulations of particle dispersion in the accelerated flow behind a moving shock

This paper presents a computational study of the two-dimensional particle-laden flow developments of bronze particle clouds in the accelerated flow behind a moving normal shock. Particle clouds with a particle volume concentration of 4% are arranged initially in a rectangular, triangular and circular shape. Simulations are performed with a recently developed high-order resolution Eulerian–Lagrangian method that approximates the Euler equations governing the gas dynamics with the improved high order weighted essentially non-oscillatory (WENO-Z) scheme, while individual particles are traced in the Lagrangian frame using high-order time integration schemes. Reflected shocks form ahead of all the cloud shapes. The detached shock in front of the triangular cloud is weakest. At later times, the wake behind the cloud becomes unstable, and a two-dimensional vortex-dominated wake forms. Separated shear layers at the edges of the clouds pull particles initially out of the clouds that are consequently transported along the shear layers. Since flows separated trivially at sharp corners, particles are mostly transported out of the cloud into the flow at the sharp front corner of the rectangular cloud and at the trailing corner of the triangular cloud. Particles are transported smoothly out of the circular cloud, since it lacks sharp corners. At late times, the accelerated flow behind the running shock disperses the particles in cross-stream direction the most for the circular cloud, followed by the rectangular cloud and the triangular cloud.     

Improvement,validation and application of CFD/DEM model to dense gas–solid flow in a fluidized bed

Dense gas–solid flow with solid volume fraction greater than 10% and at moderate Reynolds number is important in many industrial facilities such as fluidized beds. In this work, the Euler–Lagrange approach in combination with a deterministic collision model is applied to a laboratory-scale fluidized bed. The fluid–particle interaction is studied using a new procedure called the offset method, which results in several numbers of spatial displacements of the fluid grid. The proposed method is highly precise in determining porosity and momentum transfer, thus improving simulation accuracy. A validation study was carried out to assess the results using this in-house CFD/DEM code against 5-s operation of a Plexiglas spouted-fluidized bed, showing good qualitative correlation of solid distribution in the bed and acceptable quantitative agreement of pressure drops at different positions in the bed. In view of high computing cost, special emphasis is placed on effective program design, such as application of advanced detection algorithm for particle–particle/wall collisions, the multi-grid method and parallel calculation. In this context, the influence of increasing the processor number, up to 36, on calculation efficiency was investigated.     

Implementation and efficiency analysis of parallel computation using OpenACC: a case study using flow field simulations

The Open Accelerator (OpenACC) application programming interface is a relatively new parallel computing standard. In this paper, particle-based flow field simulations are examined as a case study of OpenACC parallel computation. The parallel conversion process of the OpenACC standard is explained, and further, the performance of the flow field parallel model is analysed using different directive configurations and grid schemes. With careful implementation and optimisation of the data transportation in the parallel algorithm, a speedup factor of 18.26× is possible. In contrast, a speedup factor of just 11.77× was achieved with the conventional Open Multi-Processing (OpenMP) parallel mode on a 20-kernel computer. These results demonstrate that optimised feature settings greatly influence the degree of speedup, and models involving larger numbers of calculations exhibit greater efficiency and higher speedup factors. In addition, the OpenACC parallel mode is found to have good portability, making it easy to implement parallel computation from the original serial model.     

A LBM–DEM solver for fast discrete particle simulation of particle–fluid flows

The lattice Boltzmann method (LBM) for simulating fluid phases was coupled with the discrete element method (DEM) for studying solid phases to formulate a novel solver for fast discrete particle simulation (DPS) of particle–fluid flows. The fluid hydrodynamics was obtained by solving LBM equations instead of solving the Navier–Stokes equation by the finite volume method (FVM). Interparticle and particle–wall collisions were determined by DEM. The new DPS solver was validated by simulating a three-dimensional gas–solid bubbling fluidized bed. The new solver was found to yield results faster than its FVM–DEM counterpart, with the increase in the domain-averaged gas volume fraction. Additionally, the scalability of the LBM–DEM DPS solver was superior to that of the FVM–DEM DPS solver in parallel computing. Thus, the LBM–DEM DPS solver is highly suitable for use in simulating dilute and large-scale particle–fluid flows.     

Segregation of particulate solids＂ Experiments and DEM simulations

Segregation of granular materials is a complex phenomenon, difficult to measure quantitatively and to predict. Discrete element method （DEM） can be a useful tool to predict segregation effects and to support the industrial design. In this context, a very challenging idea is the characterization of the granular solids to provide the key parameters needed for a successful DEM simulation of segregation processes. Rolling friction, sliding friction and the coefficient of restitution are the critical parameters to be studied. These microscopic simulation parameters are calibrated by comparing the macroscopic behavior of granular matter in standard bulk experiments, which have the advantage of being highly repeatable and reliable. An experimental method is presented to characterize free surface segregation. The effects of different particle properties, particularly, shape and size, on segregation of cohesionless materials were investi- gated. From the experiments, particle size demonstrated a stronger effect on segregation than particle shape. Finally, the corresponding DEM simulations of the segregation experiments were presented. The parameters obtained by calibration were validated by the comparison of the modeled segregation behav- ior with the experimental results. Thus, calibrated DEM simulations are capable of predicting segregation effects.     

Numerical simulation of a dense solid particle flow inside a cyclone separator using the hybrid Euler–Lagrange approach

This paper presents a numerical simulation of the flow inside a cyclone separator at high particle loads. The gas and gas–particle flows were analyzed using a commercial computational fluid dynamics code. The turbulence effects inside the separator were modeled using the Reynolds stress model. The two phase gas–solid particles flow was modeled using a hybrid Euler–Lagrange approach, which accounts for the four-way coupling between phases. The simulations were performed for three inlet velocities of the gaseous phase and several cyclone mass particle loadings. Moreover, the influences of several submodel parameters on the calculated results were investigated. The obtained results were compared against experimental data collected at the in-house experimental rig. The cyclone pressure drop evaluated numerically underpredicts the measured values. The possible reason of this discrepancies was disused.     

Onset velocity of circulating fluidization and particle residence time distribution: A CFD–DEM study

Until now, the onset velocity of circulating fluidization in liquid–solid fluidized beds has been defined by the turning point of the time required to empty a bed of particles as a function of the superficial liquid velocity, and is reported to be only dependent on the liquid and particle properties. This study presents a new approach to calculate the onset velocity using CFD–DEM simulation of the particle residence time distribution (RTD). The onset velocity is identified from the intersection of the fitted lines of the particle mean residence time as a function of superficial liquid velocity. Our results are in reasonable agreement with experimental data. The simulation indicates that the onset velocity is influenced by the density and size of particles and weakly affected by riser height and diameter. A power-law function is proposed to correlate the mean particle residence time with the superficial liquid velocity. The collisional parameters have a minor effect on the mean residence time of particles and the onset velocity, but influence the particle RTD, showing some humps and trailing. The particle RTD is found to be related to the particle trajectories, which may indicate the complex flow structure and underlying mechanisms of the particle RTD.     

Influence of a homogeneous axial magnetic field on Taylor–Couette flow of ferrofluids with low particle–particle interaction

Experimental results concerning the stability of Couette flow of ferrofluids under magnetic field influence are presented. The fluid cell of the Taylor–Couette system is subject to a homogeneous axial magnetic field and the axial flow profiles are measured by ultrasound Doppler velocimetry. It has been found that an axial magnetic field stabilizes the Couette flow. This effect decreases with a rotating outer cylinder. Moreover, it could be observed that lower axial wave numbers are more stable at a higher axial magnetic field strength. Since the used ferrofluid shows a negligible particle–particle interaction, the observed effects are considered to be solely based on the hindrance of free particle rotation.     

One-way coupled fluid–structure interaction of gas–liquid slug flow in a horizontal pipe: Experiments and simulations

Pipelines conveying a multiphase mixture must withstand the cyclic induced stresses that occur due to the alternating motion of gas pockets and liquid slugs. Few previous studies have considered gas–liquid slug flow and the associated fluid–structure interaction problems. In this study, experimental and numerical techniques were adopted to simulate and analyze the two-phase slug flow and the associated stresses in the pipe structure. In the numerical simulation, a one-way coupled fluid–structure framework was developed to explore the slug flow interaction with a horizontal pipe assembly under various superficial gas and liquid velocities. A modified Volume of Fluid and finite element methods were utilized to model the fluid and structure domains. The file-based coupling technique was adopted to execute the coupling mechanism. By contrast, slug characteristics were measured experimentally, while Bi-axial strain gauges were used to capture time-varying strain signals. Excellent agreements between the predicted and measured stress results were achieved with a maximum error of 10.2 %. It was found that at constant superficial liquid velocity, the maximum induced stresses on the pipe wall increased with increasing the slug length and slug velocity. While for the slug frequency, the maximum principal stresses decreased with increasing the slug frequency.     

Measurement on particle rotation speed in gas–solid flow based on identification of particle rotation axis

When a two-dimensional (2D) imaging system is used to visualize particle motion in a 3D gas–solid flow, the particle rotation speed was found extremely difficult to be accurately measured due to the fact that the direction of rotation axis was usually random and hard to be distinguished. The paper presents a method to calculate the particle rotation speed from particle images based on the identification of its rotation axis using two or more characteristic points on its surface. The idea was analyzed and realized in a mathematical way and based on which a calculation program was given. The measurement method was verified with an experiment using a small sphere with known rotation axis and rotation speed. The effects of several factors, including the direction of the particle rotation axis, the particle image resolution, the types and positions of characteristic points, etc., on the measurement error are discussed. The error is found to be acceptable for most cases. The measurement method was finally applied to those small glass beads in a real 3D gas–solid flow inside a cold circulating fluidized bed (CFB) riser, which indicates that the problems of 2D imaging system applying to 3D particulate system could be solved by using this mathematical method.     

Two-phase co-current flow simulations using periodic boundary conditions in horizontal, 4, 10 and 90° inclined eccentric annulus,flow prediction using a modified interFoam solver and comparison with experimental results

Two-phase oil and gas flow were simulated in an entirely eccentric annulus and compared with experimental data at horizontal, 4, 10, and 90° inclination. The gas-phase was sulphur hexafluoride and the liquid phase a mixture of Exxsol D60 and Marcol 82 for the inclined cases (5–16), and pure Exxsol D60 for the horizontal cases (1–4). The diameter of the outer and inner cylinders was 0.1 and 0.04 m, respectively, for the inclined domains and 0.1 and 0.05 m for the horizontal domain. The cases studied consist of liquid phase fractions between 0.3 and 0.65 and mixture velocities from 1.2 to 4.25 m/s. The mean pressure gradient is within 33% of the expected experimental behavior for all inclined cases. In contrast, the low-velocity horizontal domains exhibit significant deviation, with a drastic over-prediction of the mean pressure gradient by as much as 200–335% for cases 1 and 2. The two remaining horizontal cases (3 and 4) are within 22% of the expected mean pressure gradient. Cases 13–16 are a replication of cases 5–8 at an increased inclination; the mean pressure gradient is within 6.5% of the expected increase due to the increase in hydrostatic pressure. By comparing cases 1–4 to previous published simulations at a lower eccentricity, we found a decrease of the mean pressure gradient by 30–40%, which is in line with existing literature, although for single-phase flows. The simulated and experimental liquid holdup profiles are in good agreement when comparing the fractional data; wave and slug frequencies match to within 0.5 Hz; however, at closer inspection, it is apparent that there is a decrease in the amount of phase-mixing of the simulations compared to the experiments. When increasing the mesh density from 115 k cells/m to 2 million cells/m, the simulations exhibit significantly more phase mixing, but are still unable to produce conventional slugs. In a simplified case, conventional slugs are observed at grid sizing of 1 × 1 × 1 mm, whereas the cells of the 2 million cells/m mesh are roughly 1.5 × 1.5 × 1.5 mm.     

Accelerating CFD–DEM simulation of processes with wide particle size distributions

Size-reduction systems have been extensively used in industry for many years. Nevertheless, reliable engineering tools to be used to predict the comminution of particles are scarce. Computational fluid dynamics(CFD)–discrete element model(DEM) numerical simulation may be used to predict such a complex phenomenon and therefore establish a proper design and optimization model for comminution systems.They may also be used to predict attrition in systems where particle attrition is significant. Therefore,empirical comminution functions(which are applicable for any attrition/comminution process), such as:strength distribution, selection, equivalence, breakage, and fatigue, have been integrated into the threedimensional CFD–DEM simulation tool. The main drawback of such a design tool is the long computational time required owing to the large number of particles and the minute time-step required to maintain a steady solution while simulating the flow of particulate materials with very fine particles.The present study developed several methods to accelerate CFD–DEM simulations: reducing the number of operations carried out at the single-particle level, constructing a DEM grid detached from the CFD grid enabling a no binary search, generating a sub-grid within the DEM grid to enable a no binary search for fine particles, and increasing the computational time-step and eliminating the finest particles in the simulation while still tracking their contribution to the process.The total speedup of the simulation process without the elimination of the finest particles was a factor of about 17. The elimination of the finest particles gave additional speedup of a factor of at least 18.Therefore, the simulation of a grinding process can run at least 300 times faster than the conventional method in which a standard no binary search is employed and the smallest particles are tracked.     

Accelerating CFD–DEM simulation of processes with wide particle size distributions

Size-reduction systems have been extensively used in industry for many years. Nevertheless, reliable engineering tools to be used to predict the comminution of particles are scarce. Computational fluid dynamics (CFD)–discrete element model (DEM) numerical simulation may be used to predict such a complex phenomenon and therefore establish a proper design and optimization model for comminution systems. They may also be used to predict attrition in systems where particle attrition is significant. Therefore, empirical comminution functions (which are applicable for any attrition/comminution process), such as: strength distribution, selection, equivalence, breakage, and fatigue, have been integrated into the three-dimensional CFD–DEM simulation tool. The main drawback of such a design tool is the long computational time required owing to the large number of particles and the minute time-step required to maintain a steady solution while simulating the flow of particulate materials with very fine particles.The present study developed several methods to accelerate CFD–DEM simulations: reducing the number of operations carried out at the single-particle level, constructing a DEM grid detached from the CFD grid enabling a no binary search, generating a sub-grid within the DEM grid to enable a no binary search for fine particles, and increasing the computational time-step and eliminating the finest particles in the simulation while still tracking their contribution to the process.The total speedup of the simulation process without the elimination of the finest particles was a factor of about 17. The elimination of the finest particles gave additional speedup of a factor of at least 18. Therefore, the simulation of a grinding process can run at least 300 times faster than the conventional method in which a standard no binary search is employed and the smallest particles are tracked.     

Fluid–solid interaction simulation of flow and stress pattern in thoracoabdominal aneurysms: A patient-specific study

Thoracoabdominal aneurysm (TA) is a pathology that involves the enlargement of the aortic diameter in the inferior descending thoracic aorta and has risk factors including aortic dissection, aortitis or connective tissue disorders. Abnormal flow patterns and haemodynamic stress on the diseased aortic wall are thought to play an important role in the development of this pathology and the internal wall stress has proved to be more reliable as a predictor of rupture than the maximum diameter for abdominal aortic aneurysms; but this assumption has not been validated yet for aneurysms involving the thoracic aorta. In the present study, three patients with TAs of different maximum diameters were scanned using magnetic resonance imaging (MRI) techniques. Realistic models of the aneurysms were reconstructed from the in vivo MRI data acquired from the patients, and subject-specific flow conditions were applied as boundary conditions. The wall and thrombus were modelled as hyperelastic materials and their properties were derived from the literature. A normal descending aorta was also simulated to provide data for comparison. Fully coupled fluid–solid interaction (FSI) simulations as well as solid static simulations were performed using ADINA 8.2. The results show that the wall stress distribution and its magnitude are strongly dependent on the 3-D shape of the aneurysm and the distribution of thrombus. Maximum wall stresses in all TA models are higher than in the normal aorta, and values of maximum wall stress are not directly related to the maximum aneurysm diameter. Comparisons between the FSI and solid static simulation results showed no significant difference in maximum wall stress, supporting those previous studies which found that FSI simulations were not necessary for wall stress prediction.     

A Novel Relative Permeability Model Based on Mixture Theory Approach Accounting for Solid–Fluid and Fluid–Fluid Interactions

A novel model is presented for estimating steady-state co- and counter-current relative permeabilities analytically derived from macroscopic momentum equations originating from mixture theory accounting for fluid–fluid (momentum transfer) and solid–fluid interactions (friction). The full model is developed in two stages: first as a general model based on a two-fluid Stokes formulation and second with further specification of solid–fluid and fluid–fluid interaction terms referred to as \(R_{{i}}\) (i =  water, oil) and R, respectively, for developing analytical expressions for generalized relative permeability functions. The analytical expressions give a direct link between experimental observable quantities (end point and shape of the relative permeability curves) versus water saturation and model input variables (fluid viscosities, solid–fluid/fluid–fluid interactions strength and water and oil saturation exponents). The general two-phase model is obeying Onsager’s reciprocal law stating that the cross-mobility terms \(\lambda _\mathrm{wo}\) and \(\lambda _\mathrm{ow}\) are equal (requires the fluid–fluid interaction term R to be symmetrical with respect to momentum transfer). The fully developed model is further tested by comparing its predictions with experimental data for co- and counter-current relative permeabilities. Experimental data indicate that counter-current relative permeabilities are significantly lower than corresponding co-current curves which is captured well by the proposed model. Fluid–fluid interaction will impact the shape of the relative permeabilities. In particular, the model shows that an inflection point can occur on the relative permeability curve when the fluid–fluid interaction coefficient \(I>0\) which is not captured by standard Corey formulation. Further, the model predicts that fluid–fluid interaction can affect the relative permeability end points. The model is also accounting for the observed experimental behavior that the water-to-oil relative permeability ratio \(\hat{{k}}_{\mathrm{rw}} /\hat{{\mathrm{k}}}_{\mathrm{ro}} \) is decreasing for increasing oil-to-water viscosity ratio. Hence, the fully developed model looks like a promising tool for analyzing, understanding and interpretation of relative permeability data in terms of the physical processes involved through the solid–fluid interaction terms \(R_{{i}}\) and the fluid–fluid interaction term R.     

Modeling of oil–water flow using energy minimization concept

A new model is developed to predict flow behaviors including flow pattern, pressure gradient and holdup for oil–water flow in horizontal and slightly inclined pipes. The model is based on the universal principle that a system stabilizes to its minimum total energy. The structural configurations observed in two-phase flow systems can be interpreted in terms of total energy minimization. Performance of the developed model is tested against several experimental data, and comparisons with existing models are presented. It is evident from the results and comparisons that the model estimates the pressure gradient and flow pattern very well. The model provides extensive information about oil–water flow characteristics.     

Viscoelastic flow past confined objects using a micro–macro approach

This paper is concerned with the numerical prediction of viscoelastic flow past a cylinder in a channel and a sphere in a cylinder using molecular-based models. The basis of the numerical method employed is a micro–macro model in which the polymer dynamics is described by the evolution of an ensemble of Brownian configuration fields. The spectral element method is used to discretize the equations in space. Comparisons are made between the macroscopic simulations based on the Oldroyd B constitutive model and microscopic simulations based on Hookean dumbbells, and excellent agreement is found. The micro–macro approach can be used to simulate models, such as the finitely extensible nonlinear elastic (FENE) dumbbell model, which do not possess a closed-form constitutive equation. Numerical simulations are performed for the FENE model. The influence of the model parameters on the flow is described and, in particular, the dependence of the drag as a function of the Weissenberg number.