Solid Velocity Research Articles

Numerical prediction of near-wall flow field of dense slurry flow in pipe bends

Abstract Dense particulate slurry flow field through 90O circular pipe bends is numerically investigated in the present work. The dense slurry is modelled using Eulerian-Eulerian approach treating the phases as co-existing continua that exchange mass, momentum and energy with each other. Finite volume technique as implemented in ANSYS-FLUENT has been employed to numerically compute the flow field. Mono-size slurry with particle size of 16 µm and 50 µm is simulated at different flow Reynolds number at two solids efflux concentration (by volume) of 10% and 22%. Results have been validated partially with grid independence tests and with available experimental data. Within the range of operating parameters considered, it is found that with increase in flow velocity, and with increase in efflux concentration, the local solids concentration increases near the extrados of the bend, while local solids velocity shows higher values near the intrados region.

Eulerian Multiphase Simulation of the Particle Dynamics in a Fluidized Bed Opposed Gas Jet Mill

The compressible and turbulent gas–solid multiphase flow inside a fluidized bed opposed jet mill was systematically investigated through numerical simulations using the Euler–Euler approach along with the kinetic theory of granular flow and frictional models. The solid holdup and nozzle inlet air velocity effects on the gas–solid dynamics were assessed through a detailed analysis of the time-averaged volume fraction, the time-averaged velocity, the time-averaged streamlines, and the time-averaged vector field distributions of both phases. The simulated results were compared with the experimental observations available in the literature. The numerical simulations contributed to a better understanding of the particle–flow dynamics in a fluidized bed opposed gas jet mill which are of fundamental importance for the milling process performance.

The Basal Friction Coefficient of Granular Flows With and Without Excess Pore Pressure: Implications for Pyroclastic Density Currents, Water‐Rich Debris Flows, and Rock and Submarine Avalanches

AbstractNumerous large‐scale geophysical flows propagate with low‐apparent basal friction coefficients, but the source of such phenomenology is poorly known. Motivated by scarce basal friction data from natural flows, we use numerical methods to investigate the interaction of granular flows with their substrate under idealized conditions. Here we investigate 3‐D monodisperse and polydisperse fluid‐particle granular flow rheology and flow‐substrate interaction using discrete element modeling and coarse‐graining techniques. This combination allows us to calculate the continuum fields of solid fraction, velocity, shear stress, and solid pressure and compare it with force measurements on the substrate. We show that the wall/basal friction coefficient is not constant. Instead, it is a function of the nondimensional slip defined as the ratio of the slip velocity over the slip velocity fluctuations. The scaling of the wall friction with nondimensional slip is independent of air viscosity and density and presence of excess pore pressure. Therefore, the reduction of the basal stress that must occur in mobile natural flows with excess pore pressure is not ascribed to the lowering of wall friction coefficient. Instead, lowering of the normal stress by fluid drag in flows with elevated pore fluid pressure justifies the definition of effective wall and internal friction coefficients to capture the geophysical flow rheology and the forcing on its substrate. These results are fundamental to understand the dynamics of geophysical mass flows including pyroclastic density currents, water‐rich debris flows, and rock and submarine avalanches.

The impact of swirling on the dynamics of a spouted bed

This work is devoted to a numerical study of inflow swirl on the flow field in a spouted bed. The Eulerian-Eulerian multiphase model was used to simulate the hydrodynamics of a gas-solid flow in a 2D axisymmetric spouted bed under an unsteady laminar regime. The results of the simulations are validated with the experimental data obtained by He et al. (Can. J. Chem. Eng. Vol. 72, pp. 229–234 and pp. 561–568, 1994). The comparison of the results shows that the numerically obtained profiles of the time-averaged axial solid velocity agree well with the experimentally measured values. The results of the simulations revealed that the slightly increase in the swirling ratio of the inlet flow leads to an enhanced spouting process, while a strong swirling ratio has an adverse effect on the mixing between gas and solid particles. Thus, the use of the inflow swirl enables control of dynamics of spouted beds.

Parametric study of particles homogenization in cold-flow riser reactors

Fluid Catalytic cracking (FCC) process are frequently used for the upgrading of heavy crude oil into more valuable products. Traditionally, the FCC process occurs in a riser reactor, where both vaporised hydrocarbon feed-stock and solid catalyst flow in the direction against gravity. This kind of reactor presents heterogeneous flow distributions that affect the axial and radial flow structures, as well as the product quality. To understand the effect of operational variables over riser flow distribution, a numerical study of the two-phase cold-flow in the pre-acceleration zone of a riser reactor fed with catalyst particles used in this kind of reactors is presented in this work considering a two-dimensional model. The Computational Fluids Dynamics (CFD) software ANSYS® Fluent® is used to study two-dimensional gas (air) and solid (catalyst particle) flow in a riser section of a cold-flow Circulation Fluidized Bed (CFB) system under different flow inlet conditions (i.e., either for the gas and solid flux), as well the particle diameter size. An Eulerian-Eulerian approach, including the turbulence ( κ − ε model) and the Kinetic Theory of Granular Flow (KTGF) models, are solved for the gas phase and the solid particles treated as a dispersed phase. The implemented computational model is validated by comparing numerical results for solid velocity and volume fraction distribution to values reported by peers. As expected, a higher concentration towards the axis of the reactor is obtained for the solid volume fraction values. The R N I index estimated for gas velocities of 3 m/s and 4 m/s are significantly lower than the others, indicating that as the inlet gas velocity is reduced, a more homogeneous profile is obtained. Finally, the numerical results obtained shown closer to the experimental data used for the validation as the steady-state is attained.

Pore-resolved simulations of porous media combustion with conjugate heat transfer

Porous media combustion (PMC) is an active field of research with a number of potential advantages over free-flame combustors. A key contributor to these phenomena is the interphase heat exchange and heat recirculation from the products upstream to the reactants. In this paper, we present a network model that captures the conjugate heat transfer in pore-resolved 2D simulations of PMC. A series of simulations are presented with varying solid conduction and inlet velocity to isolate the role of conjugate heat transfer on the salient features of the burner, including flame stability, axial temperature profiles, and flame structure. We show that both the flame stabilization and the propagation behavior are strongly related to the conjugate heat transfer, and the flame stability regime is shifted to higher velocities as the conductivity of the solid material is increased.

CFD-PBM simulation of gas–solid bubbling flow with structure-dependent drag coefficients

Bubble size distribution resulted from bubble coalescence and breakup has significant effects on the effective interphase drag in gas–solid bubbling fluidized beds, which was however not taken into account in previous coarse-grid simulations. In this study, the population balance model (PBM) was used to describe the dynamic evolution of gas bubbles in gas–solid bubbling fluidization, wherein the coalescence and breakup kernels were derived by considering the effects of bubble velocity difference, wake capture and bubble instability. An improved energy-minimization multi-scale (EMMS) bubbling model was developed to calculate the effective interphase drag in sub-grid scale. By incorporating both the PBM and the EMMS drag into an Eulerian continuum model, a CFD-PBM-EMMS coupled scheme was further proposed to predict the hydrodynamics of bubbling fluidized beds. The scheme was validated through comparison of simulated results with experimental data. The bed expansion characteristics and the lateral profiles of solids velocities were reasonably predicted at acceptable computational cost. Satisfactory agreement was also achieved between the measured and simulated bubble size distributions. The proposed sub-grid drag model and coupled simulation scheme can facilitate capturing the salient features of the hydrodynamics of gas–solid bubbling fluidized beds.

2D Hydro‐Mechanical‐Chemical Modeling of (De)hydration Reactions in Deforming Heterogeneous Rock: The Periclase‐Brucite Model Reaction

AbstractDeformation at tectonic plate boundaries involves coupling between rock deformation, fluid flow, and metamorphic reactions, but quantifying this coupling is still elusive. We present a new two‐dimensional hydro‐mechanical‐chemical numerical model and investigate the coupling between heterogeneous rock deformation and metamorphic (de)hydration reactions. We consider linear viscous compressible and power‐law viscous shear deformation. Fluid flow follows Darcy's law with a Kozeny‐Carman type permeability. We consider a closed isothermal system and the reversible (de)hydration reaction: periclase and water yields brucite. Fluid pressure within a circular or elliptical inclusion is initially below the periclase‐brucite reaction pressure and above in the surrounding. Inclusions exhibit a shear viscosity thousand times smaller than for the surrounding. For circular inclusions, solid deformation has a minor impact on the evolution of fluid pressure, porosity, and reaction front. For elliptical inclusions and far‐field shortening, rock pressure inside the inclusion is higher compared to circular inclusions, and reaction‐front propagation is faster. The reaction generates a large change in porosity (∼0.1%–55%) and in solid density (∼2,300–3,500 kg m−3), and the reaction front exhibits steep gradients of fluid pressure and porosity. Reaction‐front propagating increases the weak inclusion's surface and causes an effective, reaction‐induced weakening of the heterogeneous rock. Weakening evolves nonlinear with progressive strain. Distributions of fluid and rock pressure as well as magnitudes and directions of fluid and solid velocities are significantly different. The models mimic basic features of shear zones and show the importance of coupling deformation and metamorphism. The applied MATLAB algorithm is provided.

Analytical model for coupled consolidation and diffusion of organic contaminant transport in triple landfill liners

A triple-layer composite liner consisting of a geomembrane liner (GMB), a geosynthetic clay liner (GCL) and a compacted clay liner (CCL) is commonly used at the landfill bottom liner system to isolate the contaminated leachates. In this paper, one-dimensional quasi-steady-state small deformation model (SDSS) was developed to investigate the behavior of organic chemicals transport in landfill composite liner system considering coupled effect of consolidation, diffusion and degradation. The first and second type bottom boundary conditions are used to derive the analytical solutions. The generalized integral transform technique (GITT) is adopted to derive the analytical solutions. The effect of consolidation on the performance of GMB/GCL/CCL with intact or leaking GMB is investigated. The triple liner under double drainage boundary condition (DDBC) has better performance compared to the case under single drainage boundary condition (SDBC). This is because the velocity induced by consolidation under DDBC is lower than that under SDBC. The effect of GCL consolidation shows an opposite trend compared to CCL consolidation. Considering GCL consolidation can increase the breakthrough time. The effective diffusion coefficient of GCL can be two magnitude orders smaller after consolidation, which provides a better diffusion barrier for the chemical transport. The effects of adsorption and degradation have been analyzed as well. Increasing the adsorption capacity of a deforming composite liner can increase the steady-state bottom flux, which shows the opposite tendency compared to the case without considering consolidation. This is due to the fact that for the case of a deforming composite liner, the advection induced by consolidation includes a new term due to the solid velocity. This velocity will result in the increase the mass of chemical migration through the composite liner.

Verification and validation of the DDPM-EMMS model for numerical simulations of bubbling, turbulent and circulating fluidized beds

Compared with the traditional Eulerian-Eulerian two-fluid modeling (TFM) approach, dense discrete phase model (DDPM) is potentially promising for industrial-scale applications of fluidized bed reactors, due to its capability of tracking the trajectories of particle parcels and resolving the particle size distributions (PSD). However, DDPM is yet at its early stage of mature implementation. Hence, verification and validation of the DDPM approach is still required for future applications of different gas-solid fluidization regimes.In the present work, verification and validation of the DDPM is systematically investigated for the first time, with regards to bubbling, turbulent and circulating fluidized beds. The sensitivity of the drag force, a key modeling parameter in gas-solid fluidized bed reactors is investigated with two different drag models i.e., Gidaspow and EMMS/bubbling. Numerical results of bubbling, turbulent and circulating fluidization regimes are presented in terms of discrete particle distributions, axial and radial solid concentrations and radial solid velocity profiles distributions. The results indicate that the sub-grid correction based on the EMMS approach is essential for the DDPM to correctly account for the effects of dissipative structures in all three fluidization regimes. While, the DDPM with the conventional Gidaspow drag failed to do so. Further, validations of the numerical results with the experimental data also prove that the DDPM approach with EMMS/bubbling drag model can resolve the time-averaged axial and radial solid concentrations and radial solid velocity profiles better than the conventional Gidaspow drag model.

Numerical analysis of the effects of gas-phase properties on the internal characteristics and wear in a centrifugal pump

Centrifugal pumps are indispensable in aquaculture engineering. The existence of bubbles is inevitable in a centrifugal pump and may affect the performance of the pump which delivers solid-liquid two-phase flow. Thus, this study aims to analyze the effects of gas-phase properties on the internal characteristics of a centrifugal pump by using a computational fluid dynamic code based on Eulerian multiphase mode and a standard k–ε two-equation turbulence model. Results show that gas-phase properties, such as concentration and diameter, affect the absolute pressure and the phase distribution in the centrifugal pump. The gas-phase distribution on the working faces of blades is greater than forces on the back face of the blades. The larger the diameter of the gas-phase is, the easier it is to be concentrated; Thus, the working face of the blades is prone to cavitation and corrosion, and with the increase of the bubble size, the cavitation corrosion of the back surface of the impeller becomes more serious. The solid-phase velocity and static pressure distribution increase with increasing concentration or diameter of gas-phase. The solid-phase is more easily leave the impeller area and enter the volute because of the existence of gas-phase, which may lead to abrasion of volute. The existence of gas makes the solid velocity distribution in the centrifugal pump more uneven, which may cause uneven wear of the centrifugal pump. The obtained results by this method can reveal the effects of gas-phase properties and wear on the internal characteristics in centrifugal pumps and are helpful for improvement and empirical correction in the hydraulic design of centrifugal pumps.

Scaling of amplitude and pitch of surface ripples after welding solidification

The average amplitude and pitch of surface ripples after solidification are exploratorily interpreted from scale analysis and numerical computation of transport variables and free surface deformation in a molten pool. Rippling influences welding, additively manufacturing and nano-technologies. By accounting for solid speed and oscillation of fluid velocity, the results find that amplitude is proportional to the difference in surface pressures and mechanical energy losses between edge and centre regions. Pitch is determined by the product of solid speed with timescale for surface displacement. The ratios between solid speed and liquid velocity near the central and pool edge regions, respectively, determine amplitude and pitch. Rather than pitch, oscillating flow is insensitive to amplitude. Transport fields solved by COMSOL code confirm scaled results.

CFD investigation of the flow characteristics of liquid–solid slurry in a large-diameter horizontal pipe

As an efficient and environmentally friendly method of delivering solid particles, the transport of liquid–solid slurry through a pipeline has attracted considerable attention. However, the flow characteristics of the slurry in large-diameter pipes, especially multi-sized slurry, are far from fully understood. In this study, an Eulerian multiphase model is applied to investigate single- and multi-sized slurry flows in horizontal pipes. The results show that the pipe diameter has a distinct effect on the particle distribution and that the flow properties of multi-sized slurry are different from those of single-sized slurry. In the 900-mm pipe, the variations in the solid concentration and velocity distributions of single-sized slurry are significantly affected by the particle size and efflux concentration but display weak dependence on the mixture velocity. The total particle concentration profile of the multi-sized slurry becomes relatively symmetric in the upper half of the pipe and highly asymmetric in the lower half with increasing mean particle size. The pressure drop per meter of the single-sized slurry first decreases and then increases with increasing particle size, and the pressure drop of the multi-sized slurry containing coarse particles is much higher than that of the single-sized slurry under the same working conditions.

Discrete particle simulation of heterogeneous gas-solid flows in riser and downer reactors

The heterogeneous structures of the gas-solid flow in riser and downer reactors determine reactor performance but are not fully understood. This paper presents a numerical study of the hydrodynamic characteristics of cohesive particles in a riser and a downer. This is done by the combined approach of discrete element method (DEM) for particles and computational fluid dynamics (CFD) for the gas phase. The numerical results show that this CFD-DEM model can reproduce different annular dense distributions of particles in the fully developed sections of the riser and downer. This realization requires suitable periodic boundary conditions applied to both the gas and solid phases in the flow direction as well as adequately fine meshes. The flow behaviors are analyzed in detail in terms of particle flow pattern, cluster behaviors, gas and solid velocities and forces acting on particles. Also, the dependence of the dense solid ring in the downer on some pertinent variables related to pipe geometries, material properties, and operational conditions is examined.

Simulating the ultrafiltration of whey proteins isolate using a mixture model

Ultrafiltration (UF) is widely used in the fractionation and concentration of milk proteins. During this process, proteins concentrate at the membrane surface, increasing the resistance of the membrane system, and decreasing permeate flux leaving the process unit. In this study we use Computational Fluid Dynamics (CFD) to examine the UF of whey proteins. Specifically we employ a multiphase mixture model to predict the solid concentration and velocity distributions near the membrane, under both dead-end and crossflow modes. As whey proteins have a fairly compact globular structure we use hard sphere theory to model the suspension permeability and osmotic pressure: Notably these properties depend only on parameters that can be independently measured, such as protein size and concentration. Model predictions are found to be in good agreement with experimental flux data for both flow modes, significantly in the absence of any additional resistance models representing (for example) pore blockage, surface adsorption or gel/cake formation. We find that during dead-end filtration, the extent of flux decline is logically dependent on the concentration film thickness and maximum solids concentration attained at the membrane surface. Under crossflow conditions suspension advection from the bulk towards the membrane increases the permeate flux, particularly along any upstream membrane area edges. Simulating the system using simplified 2D geometries produces qualitative, rather than quantitative agreement with experiment, highlighting the need to capture the system geometry accurately when modelling concentration polarisation (CP) effects. This work shows that industrially relevant whey protein filtration can be predicted via the multiphase modelling of hard sphere suspensions, using as-measured particle sizes, and points to more accurate methods for optimising and designing whey UF systems.

Role of lattice trapping for sliding friction

Using molecular dynamics we study the dependence of the friction force on the sliding speed when an elastic slab (block) is sliding on a rigid substrate with a surface height profile. The friction force is nearly velocity independent due to phonon emission at the closing and opening crack tips, where rapid atomic snap-in and -out events occur during sliding. The rapid events result from lattice trapping and are closely related to the velocity gap and hysteresis effects observed in model studies of crack propagation in solids. This indicates that the friction force is dominated by processes occurring at the edges of the contact area, which is confirmed by calculations showing that the friction force is independent of the normal force. The friction force increases drastically when the sliding velocity approaches the solid transverse sound velocity, as expected from the theory of cracks.

3D CPFD simulation of gas-solids flow in the high-density downer with FCC particles

The gas-solids flow in high-density downers with FCC particles was simulated by Computational Particle Fluid Dynamics (CPFD) approach. A drag model was proposed based on the equivalent diameter of cluster with the analysis of force balance on particle cluster. A global sensitivity analysis method was used to analyze the influencing factors of cluster size. The drag model was incorporated into the three-dimensional (3D) CPFD approach to simulate the gas-solids flow in two different downers operating at various conditions. 3D CPFD simulation provided detailed trajectories and distributions of solids. Good agreements of the predicted solids holdup and velocity with experimental data were achieved at both low and high-density conditions, which verified the rationality and applicability of the present drag model considering the characteristics of particle cluster in the downer. Finally, the flow and clustering behavior in the high-density downer were adequately analyzed and compared with that in low-density downer.

Solid-liquid flow in stirred tanks: Euler-Euler/RANS modeling

Stirred tanks are widely used equipment in process engineering. CFD simulations of such equipment on industrial scales are feasible within the Euler-Euler/RANS approach. In this approach, phenomena on particle scale are not resolved and, accordingly, suitable closure models are required. The present work applies a set of closure relations that originates from a comprehensive review of existing results. Focus is on the modeling of interfacial forces which include drag, lift, turbulent dispersion, and virtual mass. Specifically, new models for the drag and lift forces are considered based on the best currently available description. To validate the model a comprehensive set of experimental data including solid velocity and volume fraction as well as liquid velocity and turbulence has been assembled. The currently proposed model compares reasonably well with this dataset and shows generally better prediction compared with other model variants that originate from different combinations of force correlations.

Numerical simulation and comparative analysis of pressure drop estimation in horizontal and vertical slurry pipeline

Transportation of solids with water as a carrier in the form of slurry through long length pipelines is widely used by many industries and power plants. The transportation of slurry through vertical pipeline is a challenging task and require modification to overcome the pressure loss and power consumption requirements. In this perspective, numerical simulation of three-dimensional horizontal slurry pipeline (HSPL) and vertical slurry pipeline (VSPL) carrying glass beads solid particulates of spherical diameter 440 µm and density 2,470 kg/m3 is carried out. The 3D computational model for horizontal and vertical slurry pipeline is developed for a pipe of 0.0549 m diameter and analyzed in available commercial software ANSYS Fluent 16. The simulation is conducted by using Eulerian multiphase model with RNG k-ɛ turbulence closure at solid concentration range 10 – 20% (by volume) for mean flow velocities ranging from 1-4 ms-1. It is found that the pressure drop rises for both HSPL and VSPL with escalation in mean flow velocity and solid concentration. The predicted pressure drop in VSPL is found to follow the same pattern as with HSPL but higher in magnitude for all chosen velocity and solid concentration range. The obtained results of predicted pressure drop in HSPL are validated with the available experimental data in the literature. A parametric study is conducted with the aim of visualizing and understanding the slurry flow behavior in HSPL and VSPL. Finally, the results of solid concentration contour, velocity contour, solid concentration profiles, velocity profiles and pressure drop are predicted for both the slurry pipelines.

Numerical modelling of a bubbling fluidized bed combustion: A simplified approach

Biomass combustion in a bubbling fluidized bed has become a competitive technology due to its unique advantages of fuel flexibility and less pollutant emission. Numerical modelling of bubbling fluidized bed is a complex issue and recent models can’t describe the fuel movement and conversion due to the complicated combustion phenomena. In this work, a simplified comprehensive three dimensional numerical model is used to study different biomass combustion process in a bubbling fluidized bed combustor including all necessary steps to define solid movement and conversion using CFD software AVL Fire. The hydrodynamic behaviour and combustion of the solid fuel is observed under different working conditions. Two different biomass fuels, wood pellet and olive stone are used to study the combustion phenomena. Solid conversion process is modelled comprehensively including evaporation, devolatilization, homogeneous and heterogeneous char reactions with a detailed heat transfer process. Eulerian-Eulerian approach is used to represent the transport of mass exchange, momentum and energy for solid and gas phases through different user defined subroutines. Various scalers are used to optimize the solid volume fraction, bed temperature distribution, solid velocity, heat transfer coefficients, gas species concentration and reaction rates for the solid phase as well as for the gas phase. Numerical results are compared with the existing results available in the literature and found reasonable agreement. High combustion rate is observed due to vigorous agitation of the solid bed. Two solid high temperature regions are located along the height of the combustor and they exist separately at the inlet and dilute zone.