Gas-solid Drag Force Research Articles

Sensitivity analysis of a dense discrete phase model for 3D simulations of a tapered fluidized bed

This study aims to conduct a sensitivity analysis of closure models and modeling parameters for the Dense Discrete Phase Modeling (DDPM) approach in order to investigate the hydrodynamics of a 3D lab-scale Tapered Fluidized Bed (TFB). The closure models and model parameters under investigation include the gas-solid drag force, viscous models, particle-particle interaction models, restitution coefficient, specularity coefficient, and rebound coefficient. The primary objective of this sensitivity analysis is to optimize the numerical model's performance. The numerical results, in terms of axial and lateral Solid Volume Fraction (SVF) profiles obtained from the sensitivity analysis, indicate that the drag force and restitution coefficient significantly influence the hydrodynamics of the TFB. Properly selecting these parameters could result in the improved performance of the numerical model. However, the sensitivity of turbulence models, particle-particle interaction models, specularity coefficient, and rebound coefficient has a lesser impact on the hydrodynamics results. This work concludes with the recommendation of a set of closure models and modeling parameters that offer the most accurate prediction of the hydrodynamics of the TFB.

Euler multiphase‐CFD simulation on a bubble‐driven gas–liquid–solid fluidized bed

AbstractAn integrated flow model was developed to simulate the fluidization hydrodynamics in a new bubble‐driven gas–liquid–solid fluidized bed using the computational fluid dynamic (CFD) method. The results showed that axial solids holdup is affected by grid size, bubble diameter, and the interphase drag models used in the simulation. Good agreements with experimental data could be obtained by adopting the following parameters: 5 mm grid, 1.2 mm bubble diameter, the Tomiyama gas–liquid model, the Schiller–Naumann liquid–solid model, and the Gidaspow gas–solid model. At full fluidization state, an internal circulation of particles flowing upward near the wall and downward in the centre is observed, which is in the opposite direction compared with the traditional core‐annular flow structure in a gas–solid fluidized bed. The simulated results are very sensitive to bubble diameters. Using smaller bubble diameters would lead to excessive liquid bed expansions and more solid accumulated at the bottom due to a bigger gas–liquid drag force, while bigger bubble diameters would result in a higher solid bed height caused by a smaller gas–solid drag force. Considering the actual bubble distribution, population balance model (PBM) is employed to characterize the coalescence and break up of bubbles. The calculated bubble diameters grow up from 2–4 mm at the bottom to 5–10 mm at the upper section of the bed, which are comparable to those observed in experiments. The simulation results could provide valuable information for the design and optimization of this new type of fluidized system.

Modeling of dynamic characteristic of particle in transient gas–solid flow via a machine learning approach

Based on a reliable dataset of particle dynamics from DNS, a R–CNN model combining the functional structures of RNN and CNN was proposed to systematically learn both the temporal and spatial inhomogeneities of particulate flow and predict the particle dynamic. The particle pattern matrix sequence with length of 10 ( ms ) and β after a specific period of 1 ms were selected as the input and output. The matrix size was set as 25×25 according to the particle size of 0.5 mm and the proportion of particle size to the sampling domain of 1:25. Through validation and final testing, the R–CNN model maintained good predictive accuracy and robustness (validation: δ ¯ = 0.13 , R 2 = 0.63; testing: δ ¯ = 0.12 , R 2 = 0.64). The model was proven to be effective with an appropriate input sequence length of 3 ( ms ) and in an appropriate time span of 4 ms . The model performance is affected by the comprehensiveness of local particle pattern. The particle resolution corresponding to the best performance of the model was 0.8–1. Additionally, adding the feature ( u r ) that do not have a high correlation with the target is not necessarily effective in improving the model's performance. Overall, the feasibility of a physical–meaning–oriented R–CNN model with an optimizable combination of functional architecture and parameters was confirmed. • A coupled R–CNN model was proposed to predict gas–solid drag force based on true DNS. • R–CNN model was proved to be more accurate and robust than pure RNN and pure CNN model. • Accuracy can be guaranteed under a proper range of temporal variables in R–CNN model. • Proper resolution to capture particles' pattern can lead to an optimal performance. • Enriching the feature with low correlation is not necessarily effective.

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.

Evaluation of sorption-enhanced reforming of biodiesel by-product in fluidized beds by means of CFD approach

The sorption-enhanced glycerol steam reforming (SE-GSR) provides a promising high-efficient means for hydrogen production. Fluidized bed reactors have their own potential on the heat transfer and sorbent regeneration. To gain a deep insight into the SE-GSR process in fluidized bed reactors, a computational fluid dynamics (CFD) approach is employed in this study. The multi-fluid model is implemented with chemical kinetics of glycerol steam reforming and CO2 absorption. The bubble effect on gas-solid drag force is considered via a bubble-based EMMS drag model. A three-dimensional simulation is carried out to investigate the flow characteristics and interaction mechanic of binary mixture with catalyst and sorbent particles. The predictions with and without sorption reactions are compared. The effects of operating velocity and sorbent size on the performance are also discussed. The results reveal that reducing operating velocity and sorbent diameter can improve the hydrogen yield and fuel conversion.

Influence of solids outlets and the gas inlet design on the generation of a gas-solids rotating fluidized bed in a vortex chamber for different types of particles

Two design aspects of vortex chambers for the generation of gas-solids rotating fluidized beds are experimentally studied for different types of particles: the solids outlet(s) and the gas inlets. Efficient solids retention and minimal solids losses via the chimney are aimed at so that the gas and solids residence times can be controlled independently. The importance of a strong vortex in the central particle bed freeboard region is demonstrated. It is shown that separate, well-dimensioned and -positioned solids outlets prevent a significant presence of particles in the freeboard region, increasing the vortex strength in this region. This is found to be particularly important when fluidizing small/light particles. The ratio centrifugal force-to-radial gas-solid drag force that is generated by the gas injection is shown to also have an important impact. Theoretically it is shown that this ratio strongly depends on the particle characteristics and to what extent it can be increased by increasing the gas injection velocity, preferentially by reducing the gas inlet slot size and otherwise the number of gas inlet slots. Experiments with different vortex chambers and particles qualitatively confirm the theoretical expectations, but show that limitations are encountered. A very high gas injection velocity prevents efficient penetration of especially fine/light particles in the gas inlet jets which is detrimental for the transfer of tangential momentum between the gas and the particle bed. Slots smaller than the particle size are also shown to be inefficient, as they generate rotational motion of the particles around their own center of gravity.

Effect of granular temperature and solid concentration fluctuation on the gas-solid drag force: A CFD test

Recent studies have shown that the expanded bed heights of bubbling fluidized beds obtained from direct numerical simulations (DNS) are higher than those obtained from CFD-DEM method. In this study, we show that the consideration of the effect of either granular temperature using the model proposed by Tang et al. (AIChE Journal, 2016, 62: 1958–1969) or solid concentration fluctuation on the interphase drag force can significantly improve the agreement with the DNS results. This study highlights the importance of the fluctuation of state variables on the accurate CFD simulation of gas fluidization.

A Lagrangian-Eulerian hybrid model for the simulation of poly-disperse fluidized beds: Application to industrial-scale olefin polymerization

We present a generalization of the Lagrangian-Eulerian hybrid model for the numerical assessment of poly-disperse gas-solid flows (Schneiderbauer et al., Pow. Tech., 2016) to olefin polymerization fluidized beds. The main idea of such a modeling strategy is to use a combination of a Lagrangian discrete phase model (DPM) and a coarse-grained two-fluid model (TFM) to take advantage of the benefits of those two different formulations. On the one hand, the DPM model unveils additional information such as the local particle size distribution, which is not covered by TFM. On the other hand, the TFM solution deflects the DPM trajectories due to the inter-particle stresses. Moreover, sub-grid drag corrections are applied to account for the impact of the small unresolved scales on the gas-solid drag force. This hybrid approach further enables the efficient evaluation of gas-solid reactions at a particle level using DPM. In particular, at each DPM trajectory we consider the olefin polymerization accounting for the catalyst profile (activity over time), the pressure driven solubility of the reaction gases in the polymer particles, the particles crystallinity and the corresponding reaction masses and reaction heat. These, in turn, are mapped to the TFM approach, where they appear as additional mass and energy source terms. The predictive capability and numerical efficiency of this reactive hybrid modeling approach is demonstrated in the case of (i) an inert bi-disperse fluidized bed and (ii) in the case of an industrial-scale olefin polymerization fluidized bed. The results show that the model is able to correctly predict segregation in poly-disperse gas-solid flows. In addition, the model is able to predict the particle growth in a fluidized bed reactor as well as its impact on the hydrodynamics of the bed. The results further give a closer insight about the temperatures and the crystallinity of the polymer particles.

A Lagrangian-Eulerian hybrid model for the simulation of industrial-scale gas-solid cyclones

We present a generalization of the Lagrangian-Eulerian hybrid model for the numerical assessment of poly-disperse gas-solid flows (Pirker and Kahrimanovic, Acta Mechanica 204, 2009) [1] to industrial-scale cyclones. The main idea of this hybrid model is to use a combination of a Lagrangian discrete phase model (DPM) and a two-fluid model (TFM) to take advantage of the benefits of those two different formulations. On the one hand, the local distribution of the different particle diameters, which is required for the gas-solid drag force, can be obtained by tracking statistically representative particle trajectories for each particle diameter class. On the other hand, the contribution from the inter-particle stresses, i.e. inter-particle collisions, can be deduced from the TFM solution. These then appear as additional body force in the force balance of the tracer particles. Furthermore, we apply sub-grid modifications to the TFM to account for the small unresolved scales in the case of coarse grids required for industrial-scale applications. The numerical model is applied to an industrial-scale gas-solid cyclone separator, where the impact of an apex cone is studied. Furthermore, we investigate the effect of agglomeration on the separation efficiency of the cyclone. The results show (i) that the apex cone increases the separation efficiency of the sub-micrometer particles but yields an considerable increase of the cyclone's pressure drop and (ii) an adequate modeling of agglomeration is required to correctly predict the separation efficiency of the sub-micrometer particles. Finally, the presented model requires considerably less computational resources compared to multi-fluid models, where each particle diameter class is represented by its own transport equations.

CFD simulation of a fluidized bed using the EMMS approach for the gas-solid drag force

Drag force is one of the main contributing factors in describing the hydrodynamics of gas-solid flow systems. In fact, the drag force is the primary coupling force between the fluid and particulate phases. Therefore, accurate prediction of the drag is the goal of the present study. Flow of particulate solids in gas-solid flow systems is inherently heterogeneous due to different attraction and repulsion forces between the particles. The assumption of a homogeneous system leads to unrealistic predictions of system characteristics for different gas-solid regimes, e.g., bubbling fluidized beds and circulating fluidized beds. In the literature, several approaches have been developed to encounter the effect of heterogeneities inside the system, e.g., EMMS (Energy Minimization Multi-Scale) and subgrid filtering approaches. In this study, an EMMS approach was applied to a fluidized bed operating at the ranges between the bubbling regime and packed bed. The result of 2D simulations in a fluidized bed was compared with both experimental data and homogeneous models. Simulation results using the EMMS approach showed very good agreement with the Krishna [20] bed expansion experimental data, while the modeling using homogeneous drag force diverged considerably from the experimental data.

Eulerian simulation of a circulating fluidized bed with a new flow structure-based drag model

The heterogeneous flow in a circulating fluidized bed (CFB) deteriorates momentum, combined with its heat and mass transfer between gas and solid, have been confirmed by several experiments. Due to no consideration of this heterogeneous flow in Euler–Eluer two phase flow model, there are the significant deviation of average voidage between the simulating results and experimental data. Therefore, we developed a new model to evaluate the local heterogeneous flow parameters, based on which gas–solid drag force coefficient in calculating mesh was calculated. This drag coefficient based on these local heterogeneous flow structure parameters improves the Euler–Eluer two phase flow model greatly, which further is confirmed by better description of average voidage in experiments. With this drag force coefficient model, the nature of axial S-shape and radial core-annular distribution of solid concentration in CFB can be captured.

CFD simulation of hydrodynamics of gas–liquid–solid three-phase bubble column

A 3D time dependent numerical study was performed to study the gas–liquid–solid three-phase flow dynamics in bubble columns by employing the Eulerian–Eulerian–Eulerian three-fluid approach. The three-phase bubble column of Gandhi et al. (Powder Technol. 1999, 103 (2), 80–94), Rampure et al. (Can. J. Chem. Eng. 2003, 81 (3–4), 692–706) and our previous study (Powder Technol. 2014, 260, 27–35) were studied. A mathematical model of a gas–liquid–solid three-phase flow was built. The effect of numerical schemes (wall boundary conditions, momentum discretization schemes and time steps) was discussed. CFD simulations were performed to study the sensitivity of the interphase drag models (different liquid–solid, gas–solid and gas–liquid drag models), and the predictions were compared with the experiments. The results showed that no-slip conditions for the wall boundary conditions, 0.001s for the calculation time step and second-order Upwind for momentum discretization, had better prediction results. The appropriate interphase drag forces to describe the three phase flow found in this study were the Zhang–Vanderheyden model, which was used as a gas–liquid drag model, Schiller–Naumann model, used as a liquid–solid drag model, and gas–solid drag force, which was not considered. The appropriate numerical schemes and interphase drag models were utilized to simulate the hydrodynamic parameters (time-averaged gas holdup, solid holdup, liquid axial velocity) in a gas–liquid–solid bubble column. The effects of superficial gas velocity, particle volume fraction, particle size and density were analysed and discussed. Four flow regimes of a gas–liquid–solid bubble column were simulated; the CFD results were compared with the experimental flow structures, and it was found that the bubble coalescence regime was better depicted. Superficial gas velocity had a large effect on the gas holdup of the bed, and the effect of solid volume fraction (Vs=0.03–0.30) and particle size (dp=75μm–270μm) on the distributions of time-averaged solid holdup and liquid axial velocity was greater than that of particle density (ρp=2500kg/m3–4800kg/m3). When particle size dp≥150μm and solid volume fraction Vs≥0.09, the hydrodynamic parameters had a strong dependency on dp and Vs. The larger the values of the Vs, dp and ρp were, the larger the axial solid concentration gradient was.

Analysis of the time-averaged gas–solid drag force based on data from transient 3D CFD simulations of fluidized beds

In the present work, a qualitative analysis of the time-averaged gas–solid drag force in gas–solid fluidized beds is carried out. The analysis is based on a large number of transient Eulerian–Eulerian 3D CFD simulations of small bubbling, turbulent and circulating fluidized beds. The obtained results significantly differ from corresponding data previously obtained from 2D simulations, especially at high solid concentrations. This confirms that to accurately model the gas–solid drag force in a steady state 3D simulation, the drag model should not be based on data from transient 2D simulations. In the present work, the average drag force is expressed as the product of the drag force calculated from time-averaged velocities and volume fractions and a correction coefficient. The study shows that even when the third dimension is described in the mesh with only three nodes, the 3D character of the flow is captured in the drag correction coefficient. Thus, a large number of parametric studies could be carried out in a reasonable time frame. In the paper, the parameters affecting the time-averaged drag force are identified and the nature of the effects are analyzed. The analysis shows that solid volume fraction, particle size, solid density, gas viscosity, the slip velocity between gas and solids and the lateral distance to a wall have significant effects on the drag correction coefficient. At high gas densities typical e.g. of pressurized fluidization even the gas density has significant effects. A closure relation for the time-averaged drag force for a wide range of fluidization conditions should include these seven variables as inputs.

CFD modeling of gas–solids flow in a large scale circulating fluidized bed furnace

A Eulerian multiphase model was used to study the hydrodynamics of the gas–solids flow in a circulating fluidized bed (CFB) furnace. Alternative modeling approaches were tried to evaluate their effects on the predicted solids distribution in the furnace. Due to high computational costs, large scale calculations are commonly performed by using a coarse mesh, which leads to too uniform solids flow field and an overestimated gas–solid drag force. Thus, a suitable form of correction of the gas–solid drag is needed for coarse mesh simulations. This study presents fluid dynamics simulations of a 235MWe CFB furnace by two sets of interphase momentum exchange coefficients: the model based on the homogeneous flow condition and the model based on the energy-minimization multi-scale (EMMS) approach. The calculations with one solid phase included studies with two mesh resolutions and different particle sizes. Additional simulations were performed using two solid phases and four solid phases to analyze the effect of polydispersity of particles. The model results were compared with the measured vertical pressure profile of the furnace and the locally measured solid concentration and velocity profiles. The results show that with a homogeneous model, the model matches better with measurements if the mesh resolution is finer. The EMMS approach can be used to improve the calculations in a coarse mesh if the average particle size can be determined correctly for the model. With multiple solid phases, the vertical and horizontal segregation could be simulated. However, increasing the number of solid phases did not change the total solid concentration and pressure profiles if the Sauter mean diameter of the total system was constant. The results indicate that with a coarse mesh, similar drag corrections would be necessary between the solid phases that have been developed for gas–solid drag.

Numerical Study of a Bi-disperse Gas-solid Fluidized Bed Using an Eulerian and Lagrangian Hybrid Model

In this paper, we present a hybrid model for the numerical assessment of poly-disperse gas-solid fluidized beds. The main idea of such a modeling strategy is to use a combination of a Lagrangian discrete phase model (DPM) and a kinetic theory based TFM to take advantage of the benefits of those two different formulations. On the one hand, the local distribution of the different particle diameters, which is required for the gas-solid drag force, can be obtained by tracking statistically representative particle trajectories for each particle diameter class. On the other hand, the contribution from the inter-particle stresses, i.e. inter-particle collisions, can be deduced from the TFM solution. These then appear as additional body force in the force balance of the DPM. Note that in a first step we solely consider diameter averaged solids stresses since the drag force is at least on order of magnitude higher than the solids stresses in fluidized beds. Finally, the numerical model is applied to a fluidized bed of a bi-disperse mixture of glass particles (0.5mm and 2.5mm particles) and with a cross-section of 0.15 m x 0.02 m. The results are then analyzed with respect to experimental data of Puttinger et al [1]. This comparison demonstrates that the computed bed hydrodynamics is in fairly good agreement with the experiment. However, the results also suggest that sub-grid drag corrections [2–4] for poly-disperse fluidized beds are required to make the numerical investigation of industrial scale fluidized bed units accessible.

CFD simulations of gas–solid flow in an industrial-scale circulating fluidized bed furnace using subgrid-scale drag models

Mesoscale flow structures such as clusters and streamers of particles are characteristic features of gas–solid flow in fluidized beds. Numerical simulations of gas–solid flows for industrial-scale fluidized beds are often performed using the Eulerian description of phases. An accurate prediction of this type of flow structure using the Eulerian modeling approach requires a sufficiently fine mesh resolution. Because of the long computational time required when using fine meshes, simulations of industrial-sized units are usually conducted using coarse meshes, which cannot resolve the mesoscale flow structures. This leads to an overestimation of the gas–solid drag force and a false prediction of the flow field. For these cases, a correction must be formulated for the gas–solid drag. We have simulated a large-scale circulating fluidized bed furnace using different gas–solid drag models and compared the model results with measurements.

Multifluid Modeling of Mixing and Segregation of Binary Gas–Solid Flow in a Downer Reactor for Coal Pyrolysis

The mixing and segregation characteristics of different types of solid particles in a downer reactor are of fundamental importance in the pyrolysis of low-rank coals where sand particles are used as the heat carrier. However, relevant fundamental studies are seldom reported. This work presents a computational investigation of the hydrodynamic behavior of binary gas–solid flows in a downer using an Eulerian-Eulerian method with a modified gas–solid drag force model, taking the effect of mesoscale particle clustering structures into consideration. Three-dimensional CFD simulations were carried out and the results obtained were compared with the experimental data available in literature. It was shown that a reasonable agreement with experimental data can be obtained with the proposed drag modification. The segregation/mixing behavior in the downer was then analyzed with two popular methods, which results in the conclusion that the solid particles in the downer reactor can mix reasonably well, therefore offer...

Modeling of the time-averaged gas–solid drag force in a fluidized bed based on results from transient 2D Eulerian–Eulerian simulations

In the present paper, the possibilities to cover all fluidization states by a single drag law in steady-state CFD multiphase flow modeling are evaluated. The time-averaged drag force is expressed as the product of the drag force calculated from the traditional drag laws for homogeneous conditions, and a correction function. Closure correlations for the correction function are developed by nonlinear regression modeling based on data collected from 69 transient 2D simulations of bubbling, turbulent and circulating fluidized beds. The correlations are given as functions of eight variables: the solid volume fraction, the distance from the nearest wall, the height above the air distributor, the slip velocity between the phases, the gas velocity, the particle size, the solid density and the gas viscosity. The results indicate that covering all fluidized bed conditions in a single drag correlation is feasible, although fully satisfactory results were not obtained for the surface and freeboard regions of a bubbling fluidized bed (BFB) with correlations that were acceptable in circulating fluidized bed (CFB) conditions. A correlation that covers the whole range of fluidized states is complicated and thus the modeling task could be divided into development of separate correlations for different regions that could be combined into a single correlation by means of blending functions. The validity of this approach was demonstrated by developing a separate correlation for the dilute conditions above a height of 1.5m in CFB risers. Results show that the accuracy of the predictions significantly improved in dilute CFB conditions where a much simpler correlation with six input variables could be used. The modeling approach is a good starting point for the development of a general drag law for CFD simulations of fluidized beds.

Parametric study of the time-averaged gas–solid drag force in circulating fluidized bed conditions

Steady state modeling based on time-averaged transport equations is a computationally efficient method for CFD simulation of large industrial-scale circulating fluidized beds. The feasible alternative for steady state modeling is to carry out transient simulations in a coarse mesh, which would require mesh resolution dependent closure laws and lead to long simulations in order to characterize the average process behavior. These closures could be avoided by simulations with adequate spatial and temporal resolutions, but the required computational effort renders such simulations unfeasible in industrial scale applications in near future. Equation closures for steady state modeling can be developed by time-averaging results from transient simulations. One of the largest terms to be modeled is the time-averaged drag force. In the present work, parameters that need to be accounted for in a model for the time-averaged drag force were studied by analyzing time-averaged results from a number of transient 2D simulations carried out with fairly fine spatial resolution. The analysis was limited to Geldart B particles. In the literature, the solid volume fraction, distance to the wall and the gas–solid slip velocity have been included as parameters in drag correction functions developed for transient coarse-mesh simulations. In the present work, the same parameters are found to have significant effects on the time-averaged gas–solid drag force. Additionally, solid density, particle size and gas phase laminar viscosity are shown to have significant effects on the average drag force. Thus process conditions, which significantly vary inside a CFB, need to be accounted for in the model.

A modified correlation to calculate solid friction factor for horizontal dilute phase pneumatic conveying

The calculation accuracy of solid friction factor ( f p ) is important for the prediction of pressure drop, gas–solid drag force and particle velocity in a horizontal dilute phase pneumatic conveying system. In this study, some modifications were applied to the commonly-used f p correlation developed by Yang. First, the data processing to implicitly correlate f p was improved. Unlike the method used Yang's derivation, the solid volumetric concentration, the ratio of the particle's radial velocity to axial velocity and the ratio of inertial force to gravity force of the fluid were separately used instead of combining together. In addition, the sphericity of the particles was considered such that the correlation can be valid for the non-spherical particles. Experiments were also conducted to validate the correction of the modified correlation. Compared with the experimental data, the modified correlation has remarkably better accuracy on f p prediction than the existing correlation. Moreover, the correlations of solid velocity and pressure drop based on the newly proposed f p correlation were derived. The predictions of the derived correlations agree well with the present and literature experimental data.