CFD–DEM simulation of turbulence modulation in horizontal pneumatic conveying

A study is presented to evaluate the capabilities of the standard k–ε turbulence model and the k–ε turbulence model with added source terms in predicting the experimentally measured turbulence modulation due to the presence of particles in horizontal pneumatic conveying, in the context of a CFD–DEM Eulerian–Lagrangian simulation. Experiments were performed using a 6.5-m long, 0.075-m diameter horizontal pipe in conjunction with a laser Doppler anemometry (LDA) system. Spherical glass beads with two sizes, 1.5 and 2 mm, were used. Simulations were performed using the commercial discrete element method software EDEM, coupled with the computational fluid dynamics package FLUENT. Hybrid source terms were added to the conventional k–ε turbulence model to take into account the influence of the dispersed phase on the carrier phase turbulence intensity. The simulation results showed that the turbulence modulation depends strongly on the model parameter C_ε3. Both the standard k–ε turbulence model and the k–ε turbulence model with the hybrid source terms could predict the gas phase turbulence intensity trend only generally. A noticeable discrepancy in all cases between simulation and experimental results was observed, particularly for the regions close to the pipe wall. It was also observed that in some cases the addition of the source terms to the k–ε turbulence model did not improve the simulation results when compared with those of the standard k–ε turbulence model. Nonetheless, in the lower part of the pipe where particle loading was greater due to gravitational effects, the model with added source terms performed somewhat better.     

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.     

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.     

Experimental and numerical study of installing a dune model in a 90° bend in the horizontal-vertical pneumatic conveying system

In the pneumatic conveying process, particles move to the bend under the influence of inertia to form a particle rope, which will cause serious wear between the particles and the pipe wall, and then the dune model is designed and installed in the 90° bend to reduce energy consumption and wear in this study. Firstly, the minimum pressure drop velocity of particles transported by different size dune models was obtained through experimental study. Then the energy saving mechanism of the dune model is studied by CFD-DEM coupling. The experimental results show that the installation of the dune model reduces the minimum pressure drop velocity. The numerical simulation results show that the number of collisions between the particles and the tube wall in the vertical tube decreases after the installation of the dune model, which reduces the energy loss. Moreover, the increasing of tail size of the dune model is beneficial to the diffusion and acceleration of the particles in the vertical tube.     

Fluid dynamics of horizontal air–water slug flows through a dividing T-junction

Experimental data from horizontal air–water slug flows were obtained in a test facility which was a 34 mm internal diameter, 10 m long Plexiglas pipe connected to the 90° branch arms from a T-junction. The test points were located on the flow pattern map in the proximity of the transition lines which separates different flow patterns. Capacitive probes with helical and concave plate sensors were used to quantify the dynamic liquid holdup in each branch. They were combined with Venturi nozzles + differential pressure transmitters in each outlet branch for measuring the two-phase mass flow rates. The dynamic characteristics of the slug flow splitting in a T-junction were studied from the acquired signals. Diaphragm straight-through type valves were used in the run and in the lateral branch arms to imitate equipments consuming the two-phase flow after the T-junction. This assembly can also be used as a gas–liquid separation system. The results showed different mechanisms acting on the slug flow division phenomenon. Liquid accumulation into the run branch, between the TJ and the control valve, caused more gas to come to the lateral branch.     

Exploring the undrained cyclic behavior of methane-hydrate-bearing sediments using CFD–DEM

Based on the mechanical experimental results of methane hydrate (MH), a bond contact model considering the rate-dependency of MH is proposed. A CFD–DEM scheme considering fluid compressibility is used to simulate a series of undrained cyclic shear tests of numerical methane-hydrate-bearing sediment (MHBS) samples. The dynamic behavior, including stress–strain relationship, dynamic shear modulus, and damping ratio, is investigated. In addition, the force chains, contact fabric and averaged pure rotation rate (APR) are examined to investigate the relationships between micromechanical variables and macromechanical responses in the DEM MH samples. The effects of temperature, confining pressure and MH saturation are also analyzed. Due to the micro-structural strengthening by the MH bonds, no obvious change in microscopic quantities is observed, and the samples remain at the elastic stage under the applied low-shear stress level. When confining pressure and MH saturation increase, the dynamic elastic modulus increases, while the damping ratio decreases. An increasing temperature (leading to weakening of MH bonds) can lower the dynamic elastic modulus, but has almost no impact on the damping ratio. On the contrary, an increasing cyclic shear stress level lowers the damping ratio, but has almost no effect on the dynamic elastic modulus.     

CFD simulation of a gas–solid fluidized bed with two vertical jets

A computational fluid dynamics (CFD) model is used to investigate the hydrodynamics of a gas–solid fluidized bed with two vertical jets. Sand particles with a density of 2660 kg/m³ and a diameter of 5.0 × 10^?4 m are employed as the solid phase. Numerical computation is carried out in a 0.57 m × 1.00 m two-dimensional bed using a commercial CFD code, CFX 4.4, together with user-defined Fortran subroutines. The applicability of the CFD model is validated by predicting the bed pressure drop in a bubbling fluidized bed, and the jet detachment time and equivalent bubble diameter in a fluidized bed with a single jet. Subsequently, the model is used to explore the hydrodynamics of two vertical jets in a fluidized bed. The computational results reveal three flow patterns, isolated, merged and transitional jets, depending on the nozzle separation distance and jet gas velocity and influencing significantly the solid circulation pattern. The jet penetration depth is found to increase with increasing jet gas velocity, and can be predicted reasonably well by the correlations of Hong et al. (2003) for isolated jets and of Yang and Keairns (1979) for interacting jets.     

CFD–DEM simulation of particle deposition characteristics of pleated air filter media based on porous media model

In this study, the three-dimensional physical model of pleated air filtration media was simplified to porous media model, and the calculation parameters of porous media were obtained based on experimental data. The model of V-shaped pleated air filter media is constructed, the height of the media pleat is 50 mm and the pleat thickness is 4 mm, the pleat angle is 3.7°. The Hertz-Mindlin contact model was modified by Johnson Kendall Roberts (JKR) adhesion contact model. The deposition process of particles in media was simulated based on computational fluid dynamics (CFD) theory and discrete element method (DEM). Results show that the CFD–DEM coupling method can be effectively applied to the macro research of pleated air filter media. The particles will form dust layer and dendrite structure on the fiber surface, and the dust layer will affect the subsequent air flow organization, and the dendrite structure will eventually form a “particle wall”. The formation of the “particle wall” will prevent the particles from moving further in the fluid domain, which makes area of pleated angle become the “low efficiency” part about the particle deposition. Compared with area of pleated angle, the particles are concentrated in the opening area and the middle area of the pleated to agglomerate and deposit.     

Transport modeling of sedimenting particles in a turbulent pipe flow using Euler–Lagrange large eddy simulation

A volume-filtered Euler–Lagrange large eddy simulation methodology is used to predict the physics of turbulent liquid–solid slurry flow through a horizontal periodic pipe. A dynamic Smagorinsky model based on Lagrangian averaging is employed to account for the sub-filter scale effects in the liquid phase. A fully conservative immersed boundary method is used to account for the pipe geometry on a uniform cartesian grid. The liquid and solid phases are coupled through volume fraction and momentum exchange terms. Particle–particle and particle–wall collisions are modeled using a soft-sphere approach. Three simulations are performed by varying the superficial liquid velocity to be consistent with the experimental data by Dahl et al. (2003). Depending on the liquid flow rate, a particle bed can form and develop different patterns, which are discussed in light of regime diagrams proposed in the literature. The fluctuation in the height of the liquid-bed interface is characterized to understand the space and time evolution of these patterns. Statistics of engineering interest such as mean velocity, mean concentration, and mean streamwise pressure gradient driving the flow are extracted from the numerical simulations and presented. Sand hold-up calculated from the simulation results suggest that this computational strategy is capable of predicting critical deposition velocity.     

CFD–DEM study of effect of bed thickness for bubbling fluidized beds

The effect of bed thickness in rectangular fluidized beds is investigated through the CFD–DEM simulations of small-scale systems. Numerical results are compared for bubbling fluidized beds of various bed thicknesses with respect to particle packing, bed expansion, bubble behavior, solids velocities, and particle kinetic energy. Good two-dimensional (2D) flow behavior is observed in the bed having a thickness of up to 20 particle diameters. However, a strong three-dimensional (3D) flow behavior is observed in beds with a thickness of 40 particle diameters, indicating the transition from 2D flow to 3D flow within the range of 20–40 particle diameters. Comparison of velocity profiles near the walls and at the center of the bed shows significant impact of the front and back walls on the flow hydrodynamics of pseudo-2D fluidized beds. Hence, for quantitative comparison with experiments in pseudo-2D columns, the effect of walls has to be accounted for in numerical simulations.     

Experimental study and numerical simulation of the characteristics of a percussive gas–solid separator

The presence of solid particles in the flow of hypersonic wind tunnels damages the appearance of the experiment models in the wind tunnel and influences the accuracy of experimental results. The design of a highly efficient gas–solid separator was therefore undertaken. Particle trajectory imaging methods were used to measure trajectories under different conditions. The flow field and particle movement characteristics for different head angles (HAs) and separation tooth angles (STAs), inlet velocities, and the exhaust gas outlet pressures in the separator, were calculated using simulations based on the discrete phase model. The particle separation efficiency, pressure loss, and flow loss resulting from different structural parameters were also studied. In line with experimental observations, the characteristic angle of particle movements in the separator and the separation efficiency of the separator were found to increase with decreasing HA and with increasing STA. Separation efficiency improves with increasing inlet velocity and with increasing negative pressure of the exhaust gas outlet; however, the corresponding pressure loss and the flow rate of the waste gas also increased.     

Numerical simulation of a compressible vortex–wall interaction

The wall interaction of isolated compressible vortices generated from a short driver section shock tube has been simulated numerically by solving the Navier–Stokes equations in axisymmetric form. The dynamics of shock-free (incident shock Mach number \(M = 1.36\)) and shock-embedded \((M = 1.57)\) compressible vortices near the wall has been studied in detail. The AUSM+ scheme with a fifth-order upwind interpolation formula is used for the convective fluxes. Time integration is performed using a low dissipative and dispersive fourth-order six-stage Runge–Kutta scheme. The evolution of primary and wall vortices has been shown using the velocity field, vorticity field, and numerical schlierens. The vortex impingement, shocklets, wall vortices, and their lift-off are clearly identified from the wall pressure time history. It has been observed that the maximum vorticity of the wall vortices reaches close to 30 % of the primary vortex for \(M = 1.36\) and it reaches up to 60 % for \(M = 1.57\). The net pressure force on the wall due to incident shock impingement is dominant compared to the compressible vortex impingement and their evolution.     

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.     

Special issue on conveying and handling of particulate solids–Challenges of discrete element simulation,application and calibration

<正>A series of international Conveying and Handling of Particulate Solids(CHoPS)conferences was initiated in Herzliya,Israel in 1995and has since proceeded with six successive conferences held in Jerusalem(1997),the Dead Sea(2000),Budapest(2003),Sorrento(2006),Brisbane(2009)and Friedrichshafen(2012).The conference series covers processes involving particulate solids,for example     

Two and three dimensional modeling of fluidized bed with multiple jets in a DEM–CFD framework

Fluidized beds with multiple jets have widespread industrial applications. The objective of this paper is to investigate the jet interactions and hydrodynamics of a fluidized bed with multiple jets. Discrete element modeling coupled with in-house CFD code GenIDLEST has been used to simulate a bed with nine jets. The results are compared with published experiments. Mono dispersed particles of size 550 μm are used with 1.4 times the minimum fluidization velocity of the particles. Both two and three dimensional computations have been performed. To the best of our knowledge, the results presented in this paper are the first full 3D simulations of a fluidized bed performed with multiple jets. Discrepancies between the experiment and simulations are discussed in the context of the dimensionality of the simulations. The 2D solid fraction profile compares well with the experiment close to the distributor plate. At higher heights, the 2D simulation over-predicts the solid fraction profiles near the walls. The 3D simulation on the other hand is better able to capture the solid fraction profile higher up in the bed compared to that near the distributor plate. Similarly, the normalized particle velocities and the particle fluxes compare well with the experiment closer to the distributor plate for the 2D simulation and the freeboard for the 3D simulation, respectively. A lower expanded bed height is predicted in the 2D simulation compared to the 3D simulation and the experiment. The results obtained from DEM computations show that a 2D simulation can be used to capture essential jetting trends near the distributor plate regions, whereas a full scale 3D simulation is needed to capture the bubbles near the freeboard regions. These serve as validations for the experiment and help us understand the complex jet interaction and solid circulation patterns in a multiple jet fluidized bed system.     

Heterogeneous nucleation in CFD simulation of flashing flows in converging–diverging nozzles

Flashing flow is an important phenomenon in many industrial contexts; however simulation of these flows remains difficult. CFD simulations are able to describe the distribution and evolution of 3D structures in the flow but are dependent on good closure relations for interphase transfer. Nucleation during flashing flow is often neglected in CFD simulation where a minimum starting vapour fraction and a constant bubble number density are given. Models that include nucleation have used wall nucleation terms from 1D system code models, averaged over the domain. In this work, three models for wall nucleation are tested and compared with experimental data from a converging–diverging nozzle. Nucleation is applied at the walls of the domain, and various models are investigated. Good agreement with the critical flow rate and axial profiles are found, but agreement with the radial void fraction data is not satisfactory. Methods of addressing this are explored, and it is found that including a small bulk heterogeneous nucleation term gives the best agreement with the radial profiles, with negligible impact on the axial average properties.     

On the use of generalized Hamilton׳s principle for the derivation of the equation of motion of a pipe conveying fluid

In this paper, first, some pertinent studies are reviewed, undertaken to extend Hamilton׳s principle or Lagrange׳s equations to open systems, and continua including so-called non-material volumes; then, the corresponding mathematical formulations are reproduced and discussed using a uniform nomenclature. A typical flexible pipe conveying fluid system is considered next, and it is shown that the expression given by McIver for Hamilton׳s principle remains valid even in the presence of non-material volumes; the extra term due to the flux of kinetic energy through the control surface in the expression obtained by Casetta and Pesce vanishes.     

A study of the vibration of a horizontal U-bend subjected to an internal upwards flowing air–water mixture

U-bends are a common geometry in heat exchangers. In this paper, a U-bend in the vertical plane connected to horizontal straight pipes is considered. An initially stratified water/air flow moves upwards against gravity. The aim of this research is to investigate the internal flow profile and resulting force when the U-bend is subjected to a stratified air–water flow at the inlet. This is done numerically, i.e. by solving the unsteady Reynolds-averaged Navier–Stokes equations. For low mass flow rates, large gas bubbles are naturally formed at the entrance of the bend. The transient force on the tube allows to determine precisely the time instants of bubble initiation and thus to quantify the bubble frequency. Firstly, the tube is assumed to be rigid and the dependence of force oscillation on the inlet conditions is investigated. Secondly, the influence of the viscosity, wall wetting and the mass flow rate is analyzed. Finally, a fluid–structure interaction calculation is performed in order to quantify the vibration characteristics of the tube.     

On the response spectrum of Euler–Bernoulli beams with a moving mass and horizontal support excitation

In this study, the response spectrum of a time-varying system such as a beam subjected to moving masses under a harmonic and earthquake support excitations is explored. The excitations are supposed to act on the horizontal directions of the beam axis. The inertial effect of the moving masses on the natural frequencies of the beam for different cases of loading is investigated and a critical value of a so called parameter “mass staying time” is presented to avoid dynamic instability of the system. Finally, some 3D response spectra for different supports excitations as well as the beam natural frequencies are depicted.     

Numerical simulation of counter-current flow field in the downcomer of a liquid–solid circulating fluidized bed

A comprehensive study on the hydrodynamics in the downcomer of a liquid–solid circulating fluidized bed (LSCFB) is crucial in the control and optimization of the extraction process using an ion exchange LSCFB. A computational fluid dynamics model is proposed in this study to simulate the counter-current two-phase flow in the downcomer of the LSCFB. The model is based on the Eulerian–Eulerian approach incorporating the kinetic theory of granular flow. The predicted results agree well with our earlier experimental data. Furthermore, it is shown that the bed expansion of the particles in the downcomer is directly affected by the superficial liquid velocity in downcomer and solids circulation rate. The model also predicts the residence time of solid particles in the downcomer using a pulse technique. It is demonstrated that the increase in the superficial liquid velocity decreases the solids dispersion in the downcomer of the LSCFB.