Particle Wall Restitution Coefficient Research Articles

Multiphase flow and nozzle wear with CFD-DEM in high-pressure abrasive water jet

The issue of wear failure in High-Pressure Abrasive Water Jet (HP-AWJ) nozzles is an unavoidable challenge, and studying methods to enhance and predict the effective lifetime of nozzles is worth deep exploration. This paper employs a CFD-DEM coupling numerical approach to investigate wear phenomena inside the HP-AWJ nozzle, aiming to capture the realistic particle wear and erosion failure issues at the focusing tube region, which is a high-wear area of the HP-AWJ nozzle. Furthermore, the study considers realistic particles and nozzle wall constitutive models, incorporating material properties into the physical model, and employs computer-aided design methods to reflect wear failure conditions at different time intervals in the inner wall of the focusing tube at the nozzle. The results demonstrate that the number of realistic particles and initial inlet velocity has no impact on the particle exit kinetic energy. However, the particle-wall restitution coefficient affects the average particle kinetic energy at the outlet in the AWJ nozzle. The equivalent model of the realistic particles reflects the influence of the particle roundness on particle kinetic energy, acceleration, and stress concentration variations in the nozzle. These variations further affect the particle erosion rate on the nozzle wall and the actual wear failure problems on the wall surface. Finally, by combining the proposed erosion and wear model, a representative erosion profile at the AWJ focusing tube location comparable to experimental results is obtained, and the wear depth of the focusing tube changing with time is also studied. The results and methodologies presented in this paper provide valuable guidance for controlling the effective service lifetime of the AWJ nozzle, improving machining efficiency, and extending the lifespan of the AWJ nozzle.

The effect of collision parameters on the 3D Eulerian simulation of a thin rectangular bubbling fluidized bed

It is well known that the hydrodynamics of dense gas–particle flows depends heavily on inter-particle and particle–wall collisions; however, the subtleties of these interactions are not always fully recognized or appreciated. In this study, the two-fluid model is used to systematically examine the effects of collision parameters, i.e., particle–particle restitution coefficient, particle–wall restitution coefficient, and wall specularity coefficient, on simulations of the hydrodynamics of a pseudo two-dimensional bubbling fluidized bed.The utilization of high-resolution Eulerian simulations facilitates the representation of meso-scale structures without the use of a sub-grid scale model, while qualitatively reflecting the experimental data. To ensure statistically robust results and increase confidence in the simulations, a careful assessment of the time-averaging interval was first undertaken to smooth out the fluctuations that persist even after the bed reaches steady state.A quantitative analysis was then performed to analyze important facets of the flow, including bubble characteristics, particle velocity fields, and granular temperature. The underlying physical formulation was employed to elucidate how collision parameters impact the hydrodynamics of the flow.The notable findings of this study are threefold. First, the specific details of the collisions between particles are shown to significantly influence the bubble characteristics and overall flow pattern. However, the effect of the particle–particle restitution coefficient turns out to be minimal on the bed circulation time except in the limit of particle elastic collisions. It is also found that the elastic collision of particles highly affects the bubble count and unexpectedly changes the role of the wall from a source to a sink of granular temperature. Second, the effect of the particle–wall restitution coefficient is appreciable on the granular temperature while having a minimal effect on the flow hydrodynamics. Third, the effect of the wall specularity coefficient is felt across the bed such that an increase in this parameter increases the bed circulation time. The results of this systematic study enhance the understanding of how collision parameters impact flow characteristics while also providing insight into the selection of their values in simulations.

The Use of Optimized Restitution Coefficients to Improve Residence Time Prediction in Computational Fluid Dynamics-Discrete Parcel Method Models for Counter-Current Spray Dryers

This work studies the dispersion of solids in the cold isothermal operation of swirl counter current spray dryers. Residence time distributions (RTDs) of glass beads and detergent powder are obtained in a semi-industrial unit under varying Reynolds and injection positions and validated with the results of a novel Reynolds average Navier Stokes-discrete parcel method (DPM) framework. The simulations stress that the particle RTD is governed to a large extent by the interaction of the solids with the walls, which is usually simplified with the assumption of a particle-wall restitution coefficient. Since this is often unavailable experimentally, here, we propose an alternative combined model that integrates the computational fluid dynamics (CFD)-DPM model with reinforcement learning using a training set of experimental RTDs to extract an “effective pair of wall restitution coefficients”. The method improves the accuracy of existing CFD platforms, reducing the errors in the mean residence time from 30–100% to <25%.

Validation and sensitivity analysis of an Eulerian-Eulerian two-fluid model (TFM) for 3D simulations of a tapered fluidized bed

In the present work, the hydrodynamics behavior of a 3D small-scale cold flow modeling of a gas-solid tapered fluidized bed is evaluated with the Eulerian-Eulerian two-fluid modeling (TFM) approach. The sensitivity of different modeling parameters, including lift and virtual mass forces, viscous force, gas-solid drag force, granular temperature, granular viscosity, granular pressure, particle-wall specularity coefficient, particle-particle restitution coefficient, and particle-wall restitution coefficient, are systematically investigated to optimize the performance of the present numerical model. The results from different sensitivity analyses reveal that the gas-particle drag force is a more important force to resolve the correct time-averaged axial and radial solids holdup profiles of the tapered fluidized bed than the other investigated parameters. The highest accuracy possible from simulations is achieved from the Gibilaro drag model followed by the Arastoopour and EMMS/bubbling models. In contrast, all other drag models over-predict the gas-particle interaction force. The assessment of the lift and virtual mass forces, viscous force, granular temperature, granular viscosity, granular pressure, and particle-wall restitution coefficient results reveal that these parameters are less critical for the numerical simulations of the tapered fluidized bed than the gas-solid drag force. However, the assessment of particle-wall specularity coefficient and particle-particle restitution coefficient reveals that adjusting these parameters in the numerical simulations is helpful to achieve a better agreement between the experimental data and model results. For the higher gas flow rate, the current work shows that a better agreement can be achieved by tuning the parameter values in the standard sub-models than the previously published TFM studies. Meanwhile, for the lower gas flow rate, the accuracy of the present work is slightly lower than the previously published work but acceptable with the experimental measurements. The current work has an advantage over the previously published work in terms of lower computational effort by using the simplified geometry and mean particle diameter assumptions.

CFD simulation and experimental validation of nanoparticles fluidization in a conical spouted bed

In the present study, hydrodynamic parameters of micro/nanoparticles in a conical spouted bed were investigated using experimental and computational fluid dynamics (CFD) techniques. The Eulerian–Eulerian approach, in conjunction with the kinetic theory of granular flow (KTGF) has been used, and the effects of solid wall boundary condition parameters such specularity coefficient (φ), and particle-wall restitution coefficient (ew), on the hydrodynamics of the bed were studied. The effect of drag force on the fluidization behavior of nanoparticles was investigated using Gidaspow and RUC drag models, and the results showed the superiority of the RUC model. Experiments were carried out for measuring the pressure drop in a lab-scale conical spouted bed. The CFD predictions were in good agreement with the experimental data in terms of pressure drop and particle distribution.

Segregation behavior of a ternary mixture of titanium dioxide particles in a pseudo two-dimensional fluidized bed

The segregation behavior of a mixture of silica-coated titanium dioxide (TiO2) particles of three different sizes in a pseudo two-dimensional fluidized bed was studied experimentally by the freeze–sieving method and numerically by the multi-fluid model (MFM). Three-dimensional computational fluid dynamics (CFD) simulations were carried out to evaluate the effects of the solid wall boundary conditions on particle segregation in terms of specularity and particle–wall restitution coefficients. The quantitative indexes of segregation tendency and segregation degree were used to determine the axial segregation of the mixture in triangular coordinates. The simulation results revealed that the axial segregation increased with the specularity coefficient, whereas the particle–wall restitution coefficient had a minor effect on axial segregation. Comparison of the simulation results with experimental data showed that the appropriate value of the specularity coefficient used in the CFD model depended on superficial gas velocity. The study of the effects of superficial gas velocity on segregation behavior demonstrated that the greatest segregation was obtained at minimum fluidization velocity and the segregation decreased as the gas velocity gradually increased.

Optimisation of interaction parameters for CFD modelling of multiphase flow using NR method

Accurate modelling of fluid and particle flow is essential for reliable predictions of gas–solid reactions in the multiphase reactor. Due to the promising features such as short contact time, less back mixing of solids and low residence time, downer column has been used in industries than conventional riser configuration. However, the effective simulation and validation of the hydrodynamic characteristics have been scarce. A RANS model with an appropriate Eulerian-Eulerian approach poses a challenging task of choosing the hydrodynamic simulation parameters, such as i) particle-particle restitution coefficient, ii) particle-wall restitution coefficient and iii) specularity coefficient. The objective of the present study was to optimise these model parameters to obtain close validation with experimental data so that accurate downer hydrodynamics can be predicted. The error obtained from validating the experimental data with the CFD simulation output is our function which needs to be minimised. Newton Raphson multi-parameter root finding method was used for this purpose. The Jacobian evaluation required multiple CFD simulations at each iteration. A 61% reduction in error was achieved after 3 iterations. Thus, the optimised model parameters of hydrodynamics used for further modelling study in predicting hydrodynamic characteristics of a 200 mm diameter 8 m column. Highlights Validation of hydrodynamics of multiphase flow in downer employing Eulerian-Eulerian Approach Optimisation of hydrodynamic interactive model parameters viz., Restitution and Specularity coefficient coupled with Newton Raphson multi-parameter root finding and Jacobian Method. Agreement between experimental and simulation with optimised modelling parameters

Calibration of parameters for DEM simulations of solar particle receivers by bulk experiments and surrogate functions

Bauxite particles known as proppants from the fracking industry are an emerging heat transfer medium for solar thermal power plants. The discrete element method (DEM) has just recently been applied to these systems and the information on parameters for contact force models is scarce; calibrated parameters cannot be found. In this work a novel, three-stage calibration approach based on multiple bulk experiments and surrogate functions is presented. The experiments comprise the angle of repose, the residence time on a horizontal conveyor and the impact on an inclined plate. Particle-particle and particle-wall parameters for the Hertz contact force model and the modified linear spring dash-pot rolling friction model are determined for five different proppants and two wall materials. The assumptions of the calibration procedure and the calibration results themselves are checked and discussed on the basis of a sensitivity analysis. It is shown that almost all parameters can be constricted to unique values by the approach and that most parameters only gradually differ between particle types. Additionally, the influence of coarse graining on the parameters is examined. The behavior of the restitution coefficients is explained in detail by kinetic gas theory. It is found that only the particle-wall restitution coefficient is invariant to coarse graining, but not the particle-particle restitution coefficient, which must decrease with coarse-graining factor.

CFD simulations of a full-loop CFB reactor using coarse-grained Eulerian–Lagrangian dense discrete phase model: Effects of modeling parameters

The hydrodynamics of a 3D full-loop circulating fluidized bed (CFB) reactor were investigated using a coarse-grained dense discrete phase model (DDPM). The effects of changes in key modeling parameters such as the drag force, particle number per parcel, and particle–particle/particle–wall restitution coefficients were thoroughly investigated. Previous experimental data were used as a benchmark for validating the numerical results. In terms of the drag force, the simulation results show that the effect of mesoscale structures on drag force must be considered in the DDPM approach. Regarding the number of particles per parcel, the predictions indicate parcel-independent behavior at all of the coarse-graining ratios tested (dcl/dp = 55, 95, and 125), which is further proof that parcel-independent results can be achieved when the parcel diameter is in the size range of clusters. The effect of energy dissipation from particle–particle (epp) collisions shows that better results are generated when epp is in the non-ideal range (0.1–0.9) than for the ideal case (epp = 1.0). However, the particle–wall restitution coefficient (epw) has little effect on hydrodynamic behavior in either the ideal or non-ideal collision range. In addition, the effect of the particle size distribution on the full-loop hydrodynamics was investigated. The predicted results are similar to those from mean particle diameter simulations, but the distributions for different particles in the CFB are different. This would certainly affect the heat and mass transfer and reactions, and will be further investigated in our ongoing simulations of combustion in CFBs.

The effects of collisional parameters on the hydrodynamics and heat transfer in spouted bed: A CFD-DEM study

An accurate prediction of particle collisions is of great importance to the success of modeling in fluidized beds, which depends on proper selection of collisional parameters. The present study aims to clarify the effects of collisional parameters on the hydrodynamics and heat transfer in a slot-rectangular spouted bed based on CFD-DEM simulations. We find that the macroscopic characteristics (i.e., the fountain height, solid velocity profiles and kinetic energy of solid phase) of the spouted bed are very sensitive to different collisional parameters, except the particle-wall restitution coefficient. It is observed that the increase of inter-particle restitution coefficient tends to suppress the translational movements of solid phase, and new insight is provided on the control mechanism of inter-particle restitution coefficient in the spouted bed. The results show that the raise in friction coefficient and rolling friction coefficient leads to decreased translational movements of solid phase. The effects of collisional parameters on the solid rotational movements are also analyzed. Moreover, the results demonstrate that heat transfer behaviors in the spouted bed are greatly affected by the area of dead zone, which is very sensitive to the friction and rolling friction coefficients. In comparison, the variation of collisional parameters mainly influences the conductive heat transfer and has minor impact on the convective heat transfer.

Choice of model parameters in turbulent gas-solid flow simulations of particle classifiers

Comprehensive numerical simulations of particle laden gas flows are complex in general and its complexity increases dramatically when real world equipment are modelled. In this study, several model parameters required to simulate such a flow are tested. Initially, single-phase numerical results from a static classifier are validated against published experimental data. The Reynolds Stress Turbulence Model is demonstrated to be capable of accurate predictions for classifier airflow. The model is further extended by the addition of a particle Lagrangian phase. Several particle parameters are investigated and compared with published experimental data. It is found that the particle separation accuracy is improved with the inclusion of turbulence dispersion. Particle rough wall model and wall restitution coefficients influence the flow of coarse particles alone. The model is extended to simulate gas flow in a dynamic classifier with rotor. Physics involved in the flow inside a dynamic separator are explained.

CFD modeling of heat transfer and hydrodynamics in a draft tube conical spouted bed reactor under pyrolysis conditions: Impact of wall boundary condition

In the present study, the hydrodynamics and heat transfer parameters of a conical spouted bed with a draft tube were investigated under the pyrolysis conditions using computational fluid dynamics (CFD) technique. The Eulerian-Eulerian approach in conjunction with the kinetic theory of granular flow (KTGF) was applied, and some important parameters, such as pressure drop, solid volume fraction, particle velocity, and heat transfer coefficients between the wall and the bed were evaluated. The impact some solid-wall boundary conditions, such as specularity coefficient (φ), and particle-wall restitution coefficient (ew), have on the heat transfer and hydrodynamics of the bed were studied. The CFD predictions were in close quantitative agreement with measurements in terms of heat transfer coefficients and pressure drop. It was found that both specularity and particle-wall restitution coefficient have a significant influence on the pressure drop and heat transfer coefficients, with the effect on pressure drop being higher than on heat transfer coefficients.

Impacts of solid-phase wall boundary condition on CFD simulation of conical spouted beds containing heavy zirconia particles

The gas–solid flow behavior of a conical spouted bed including heavy particles, zirconia, with density of 6050kg/m3 that typically encountered in chemical vapor deposition (CVD) was studied by the CFD technique. An Eulerian–Eulerian two-fluid model (TFM) in conjunction with the kinetic theory of granular flows (KTGF) was used in a full 3D computational framework. To reduce the computational time, while maintaining the accuracy of the results, polyhedral mesh structure was utilized. Parametric studies of the specularity coefficient and particle–wall restitution coefficient were also performed. The hydrodynamics parameters including particle velocity and solid volume fraction profiles at different bed levels were evaluated, and the overall behavior of particles in the bed was studied. The simulation results showed that the specularity coefficient significantly affects the CFD results, while the impact of small changes in the particle–wall restitution coefficient is not noticeable. Furthermore, a small specularity coefficient of 0.05 provides suitable predictions that are in agreement of the experimental data. Incoherent spouting was also properly predicted by the present CFD model, which was shown to be in agreement with the experimental observations. It was also found that both the no-slip boundary condition and the specularity of φ=1 wall boundary condition predict roughly the same results. Finally, the influences of the drag function and particle–particle restitution coefficient on the CFD results were studied, and the new findings were discussed.

Influences of geometric factors on CFD results of a draft tube cylindrical spouted bed

The effect of some geometric factors, namely, draft tube diameter and entrainment height was investigated by the two-fluid model (TFM) applying the kinetic theory of granular flow. The model proposed was found to be in a good agreement with the experimental measurements in a wide range of gas velocities and different draft tube diameters as well as entrainment heights. The influence of particle-wall restitution coefficient in the small and large draft tube diameters was examined. Accordingly, different values of ew were evaluated in the draft tubes. It was observed that the model predictions for particle behaviour through the small draft tube are sensitive to the values of ew, while the sensitivity declines and disappears for large draft tube. The particle behaviour for various geometric factors was predicted by the model.

Hydrodynamics studies of a pseudo 2D rectangular spouted bed by CFD

A Eulerian–Eulerian two-fluid model in conjunction with the kinetic theory of granular flows (KTGF) was used for simulation of a pseudo 2D rectangular spouted bed. The thin thickness of the rectangular spouted bed was included in the analysis. To save the computational time, symmetry framework was used in all simulations. Comparisons were made for particle velocity distributions along the bed axis and in the radial direction, as well as, the time-averaged particle velocity vectors for 2D and 3D modeling. Different values of the specularity and particle–wall restitution coefficients, which are important parameters of the solid wall boundary condition, were used in these simulations. The simulation results showed that the 3D computational fluid dynamic (CFD) model is more sensitive to the specularity coefficient and the particle–wall restitution coefficient compared to the 2D model. In addition, the 3D model was more significantly affected by the variation of the specularity coefficient when compared with changes in the particle–wall restitution coefficient. It was also found that the 3D model gives more accurate results in comparison with the 2D Cartesian frame for spouted bed with low thickness.

CFD simulation via conventional Two-Fluid Model of a circulating fluidized bed riser: Influence of models and model parameters on hydrodynamic behavior

A two-dimensional (2D) numerical simulation of gas–solids flow in a circulating fluidized bed riser was performed based on the Two-Fluid Model (TFM). In this model, the kinetic theory of granular flows (KTGF) was used to solve gas–solids flow behavior. Despite several published studies, the selection of proper wall boundary conditions (BC) and the appropriate closure model to simulate riser flow remains inconclusive. In this study, a number of simulations were performed to understand the influence of the wall boundary condition, solid shear viscosity model and particle–particle restitution coefficient. At first, we systematically evaluated the influence of the combined effect of the specularity and particle–wall restitution coefficients based on Johnson and Jackson [1] BC. The key point we observed was that the effect of high specularity coefficient (φ=0.001) was less at low particle–wall restitution coefficients (ew=0.8, 0.9) on the axial solid holdup profile. At lower specularity coefficient (φ=0.00001 & 0.0001) value, different particle–wall restitution coefficients (ew=0.8, 0.9, 0.99) did not show any significant effect. Moreover, the effect of the elasticity of particle collisions showed that the low particle–particle restitution coefficients gave good quantitative agreement. The effects of solid shear viscosity models on flow predictions were investigated under different solid circulation rates (Gs=39.14kg/m2s, 51.05kg/m2s, 73.21kg/m2s). Both Syamlal et al. [2] and Gidaspow [3] models gave good qualitative agreement with the experimental results. The Syamlal et al. solid viscosity model demonstrated fairly consistent results in the dilute region, whereas transition from lower to higher solid holdup was reasonably well predicted by the Gidaspow model.

CFD study of particle velocity profiles inside a draft tube in a cylindrical spouted bed with conical base

The hydrodynamics of a cylindrical spouted bed with a draft tube were studied using the two-fluid model (TFM) incorporating the kinetic theory of granular flow. The effect of some essential parameters, namely, particle–wall restitution coefficient (ew), specularity coefficient (φ), and minimum frictional solid volume fraction (αs,min), was examined. Different values of ew and φ were evaluated in the draft tube. The CFD results show that the accuracy of model predictions depends on the proper evaluation of the frictional stress as well as on the values chosen for ew and φ. In particular, model predictions for particle behavior through the draft tube are sensitive to the values of these parameters. A series of CFD simulations for gas–solid flow in spouted beds were performed. Particular attention was given to the solid-phase boundary condition on the draft tube. The model proposed was found to be in close quantitative agreement with the experimental measurements in a wide range of gas flow rates and values of design parameters, such as draft tube diameter and entrainment height.

Modeling on the hydrodynamics of pressurized high-flux circulating fluidized beds (PHFCFBs) by Eulerian–Lagrangian approach

A novel Eulerian–Lagrangian approach based on the multi-phase particle-in-cell (MP-PIC) methodology was applied in the simulation of the hydrodynamic behavior of pressurized high-flux circulating fluidized beds (DHFCFBs) in this work. The sensitivities of key model (i.e. the drag model) and modeling parameters (particle–particle restitution coefficient, normal particle–wall restitution coefficient, and tangential particle–wall restitution coefficient) on the predictions have been tested systematically. Experimental results of Richtberg et al. [Powder Technol. 2005, 155(2), 145–152] and Yin et al. [Chem. Eng. Technol.2012, 35(5), 904–910] were used as a numerical benchmark to assess the simulations quantitatively. The results show that the Gidaspow drag model displays better agreement with both the axial profiles of pressure drop and the radial distributions of particle volume fraction. Compared with the perfectly elastic particle collision (ep=1.0), the non-ideal particle–particle interaction could get more reasonable prediction results. The particle–wall restitution coefficient has somewhat of an effect on the simulated gas–solid flow behaviors in the risers. However, no critical changes of simulated flow characteristic in the trends of pressure drop and solid volume fraction distribution have been found. Based on the comparison of simulation results with experiments, a suitable model (i.e., Gidaspow drag model) and a group of modeling parameters, namely a particle–particle restitution coefficient (ep=0.9), a normal particle–wall restitution coefficient (ewn=0.1) and a free-slip boundary condition (i.e. the tangential particle–wall restitution coefficient, ewτ=1.0) for modeling the hydrodynamic behavior in the DHFCDB riser were determined and verified.

Evaluation of the effect of wall boundary conditions on numerical simulations of circulating fluidized beds

A computational fluid dynamics (CFD) modeling of the gas–solids two-phase flow in a circulating fluidized bed (CFB) riser is carried out. The Eularian–Eularian method with the kinetic theory of granular flow is used to solve the gas–solids two-phase flow in the CFB riser. The wall boundary condition of the riser is defined based on the Johnson and Jackson wall boundary theory (Johnson & Jackson, 1987) with specularity coefficient and particle–wall restitution coefficient. The numerical results show that these two coefficients in the wall boundary condition play a major role in the predicted solids lateral velocity, which affects the solid particle distribution in the CFB riser. And the effect of each of the two coefficients on the solids distribution also depends on the other one. The generality of the CFD model is further validated under different operating conditions of the CFB riser.

Effect of wall boundary condition on CFD simulation of CFB risers

The effect of solid-phase wall boundary condition on the numerical simulation of gas–solid flow in CFB risers containing FCC particles was investigated using the two-fluid model incorporating the kinetic theory of granular flow. Both the Gidaspow drag model and the EMMS-based drag model were used. The Johnson and Jackson (1987) wall boundary condition was applied to describe the interaction between particles and wall. Based on the experimental system of Li and Kwauk (1994), parametric studies of specularity coefficient (φ=1.0, 0.6, 0.0005, 0.00005, 0) and particle–wall restitution coefficient (ew=0.6, 0.9, 0.95, 0.99, 0.999) were performed to evaluate their effects on axial voidage profile, solids flux, meso-scale and heterogeneous structures. Simulation results showed that solid-phase wall boundary condition had little effect on axial voidage profile when the Gidaspow drag model was used. However, the specularity coefficient φ had a pronounced influence on flow behavior when the EMMS-based drag model was used, and a small specularity coefficient (φ=0.00005, 0) could result in better agreement with experimental data. The particle–wall restitution coefficient ew plays but a minor role in the holistic flow characteristics.