Particle Reynolds Number Research Articles

Shear-induced oil separation from a sand particle moving in water

Removing oil attached to fine solid particles in water purification presents challenging technical, economic, and ecological issues. The present work numerically investigates the shear effect on oil that contains a 100-μm-diameter sand particle in a water medium. In this research, we employ the coupled level set and volume of fluid method to track interface evolution accurately. An adaptive mesh refinement technique allows us to resolve an interface down to 60 nm. Computations at various particle Reynolds numbers (Rep=2−200) and oil film thicknesses (5%, 10%, 20%, and 40% of the diameter) reveal four coating behaviour scenarios: deformation, tail formation, partial separation, and full separation. The oil film negligibly deforms at Rep≤5 at most film thicknesses. The separation occurs in full or partial regimes at higher Rep and thicker films. A thinner film forms a tail that periodically fluctuates. The analysis shows that these fluctuations uniquely reshape the oil tail at each time period.

Particle response to oscillatory flows at finite Reynolds numbers

The response of spherical particles to oscillatory fluid flow forcing at finite Reynolds numbers exhibits significant deviations from classical analytical predictions due to nonlinear convective contributions. This study employs finite element simulations to explore the long-term (stationary) behavior of such particles across a wide range of conditions, including various external and particle Reynolds numbers, Strouhal numbers, and fluid-to-particle density ratios. Key contributions of this work include determining the range of validity of Tchen's equation of motion for infinitesimal and finite Reynolds numbers and correlating particle response for a wide range of density ratios and flow conditions at high frequency oscillations. This work introduces a modified form of the history drag term in a newly proposed Lagrangian equation of motion. The new equation incorporates a parameter-dependent fractional-order derivative tailored to accommodate nonlinearities due to convective effects. These novel correlations not only extend the operational range of existing model equations but also provide accurate estimates of particle response under a range of external flow conditions, as validated by comparison with numerical solutions of the Navier–Stokes flow around the particles.

Study on the motion characteristics of Janus based on the squirmer model in the flow

The motion characteristics of Janus in the flow are studied numerically using the lattice Boltzmann method based on the squirmer model. The effects of velocity ratio J on the right and left hemisphere surface of Janus, particle Reynolds number Rep, flow Reynolds number Rec, initial orientation angle φ0 on Janus trajectory, and lateral equilibrium position yeq/H are analyzed. The results showed that, for the motion of Janus in stationary power-law fluids in a channel, Janus moves randomly in a small space in shear-thickening fluids when Rep is low and exhibits three motion modes at Rep = 5. The larger the J value, the easier it is for Janus to reach yeq/H. The higher the Rep, the closer the yeq/H is to the lower wall. In shear-thinning fluids, the motion of Janus exhibits significant randomness at Rep = 0.5 and 1, reaches the same yeq/H at Rep = 2 and 3, and tends toward yeq/H near the centerline and along the upper wall, respectively, at Rep = 4 and 5. For the motion of Janus particles in a channel flow of power-law fluids, in shear-thinning fluids, no matter what value J is, Janus reaches yeq/H on the centerline. The lower the Rep, the closer the yeq/H is to the wall. Two particles move toward yeq/H when Rep ≥ 1. The higher the Rep, the closer the yeq/H is to the centerline. The two particles will exhibit the upstream mode at Rep = 2. Two particles eventually reach yeq/H at different Rec. When φ0 > 0°, the two particles first eventually tend toward yeq/H = 0.2 and 0.8. When the value of φ0 is negative, the larger the absolute value of φ0 and higher the Rep, the more likely particles are to exhibit upstream mode.

Quantifying the Wind‐Induced Bias of Rainfall Measurements for the Thies CLIMA Optical Disdrometer

AbstractThe wind‐induced bias of rainfall measurements obtained from non‐catching instruments is addressed in this work with reference to the Laser Precipitation Monitor (LPM) optical disdrometer manufactured by Thies CLIMA. A numerical simulation approach is adopted to quantify the expected bias, involving three different models with increasing complexity. Computational Fluid‐Dynamics simulation of the airflow field around the instrument with an embedded Lagrangian particle‐tracking module to obtain raindrop trajectories are performed by solving the Unsteady Reynolds Averaged Navier‐Stokes (URANS) equations and a Large Eddy Simulation (LES) model. URANS‐uncoupled, LES‐uncoupled, and LES‐coupled approaches are tested to assess the impact of modeling the airflow turbulent fluctuations in detail. Due to the non‐radially symmetric external shape of the instrument, various combinations of the wind speed and direction are considered. Catch ratios for monodisperse rain are obtained as a function of the particle Reynolds number and the wind direction and fitted to obtain site‐independent curves to support application of the simulation results. Based on literature expressions to link the drop size distribution of real rainfall events with the rainfall intensity (which instead depend on the local rainfall climatology at the measurement site), sample collection efficiency curves are obtained from the catch ratios of monodisperse rain. The resulting adjustment curves allow rainfall measurements to be corrected using either a real‐time or post‐processing approach. However, at high wind speed and assuming that the wind blows parallel to the instrument sensing area, the instrument may fail to report precipitation altogether.

A Numerical Study on the Influence of Confining Walls on Drag and Heat Transfer Coefficients in Single‐Particle Lab‐Scale Reactors

AbstractSingle‐particle reactors in lab‐scale are a promising technology to gain an in‐depth understanding of the intricate reaction and transport processes that occur in catalyst particles under operando conditions. It is not described whether the effect of the bounding walls in such narrow flow channels influence the processes at the particle. Therefore, this work applies three‐dimensional (3D) computational fluid dynamics (CFD) simulations to analyze the drag coefficient CD alongside the local and average particle Nusselt number Nup as characteristic local and integral quantities in the range of particle Reynolds numbers 10 ≤ Rep ≤ 103. An equation is derived to correct for the wall effects on CD and Nup and assist the experimenter in the interpretation of measured results.

Physically consistent immersed boundary method: A framework for predicting hydrodynamic forces on particles with coarse meshes

In the present paper, a fluid-particle coupling method is directly derived from the Navier-Stokes equations (NSE) by applying the concept of volume-filtering, yielding a physically consistent methodology to incorporate solid wall boundary conditions in the volume-filtered flow solution, thereby allowing to solve the governing flow equations on non-body conforming meshes. The resulting methodology possesses similarities with a continuous forcing immersed boundary method (IBM) and is, therefore, termed physically consistent IBM (PC-IBM). Based on the recent findings of Hausmann et al. [1], the closures arising in the volume-filtered NSE are closed by suitable models or even expressed analytically. The PC-IBM is fully compatible with the large eddy simulation framework, as the volume-filtered NSE converge to the filtered NSE away from solid boundaries. The potential of the PC-IBM is demonstrated by means of different particle-laden flow applications, including a dense packing of fixed particles and periodic settling of 500 particles. The new methodology turns out to be capable of accurately predicting the fluid forces on particles with relatively coarse mesh resolutions. For the flow around isolated spheres, a spatial resolution of six fluid mesh cells per diameter is sufficient to predict the drag force with less than 10% deviation from highly resolved simulation for the investigated particle Reynolds numbers ranging from 10 to 250.

Numerical investigation of different transverse Rib shapes on thermal convection in a channel filled with nanofluid

With the growing interest in energy optimization, corrugated surfaces are arguably an excellent choice, finding applications in areas as diverse as heat exchangers, automobiles, building energy efficiency, and chemical reactors. However, due to the poor thermal properties of conventional fluids, heat transfer is limited. The introduction of nanoparticles into fluids is a promising solution to improve their thermal performance. This paper does a detailed numerical analysis of how different factors affect the forced convection heat transfer in a two-dimensional ribed channel. The shape of the ribs is one of the factors that are looked at, along with some new parameters like e/H, which is the ratio of rib height to channel height, and L2/P, which is the test section to the pitch between the ribs. The aim is to determine the optimum geometry that maximizes the Nusselt number while minimizing the pressure drop. The study also examines the effects of nanoparticle type and concentration on heat transfer and fluid flow characteristics. To this end, the continuity, momentum, and energy equations were solved with the finite volume method using the SIMPLE scheme with the k-ε turbulence model at different Reynolds numbers ranging from 4000 – 14,000. The results indicate that triangular ribs with ratios e/H = 0.15 and L2/P = 4 increase the Nusselt number by 63.3 % while reducing the pressure drop by 22 % compared with the other cases. The improvement in heat transfer in the water-SiO2 case was the greatest compared with the other nanofluids tested. Particle size fraction and Reynolds number increased the Nusselt number in ribbed channels by 20.7 % compared with water.

Advancing particle forces and motion dynamics in centrifugal concentrator based on flow field simulation

ABSTRACT The forces and motion state of particles within the fluid domain of the Knelson concentrator have long been a focal point for researchers. Presently, Stokes’ flow laws are commonly employed as the basis for theoretical calculations. However, this approach somewhat deviates from reality due to challenges in determining the Reynolds number of particles in the centrifugal force field during practical work. Additionally, the relationship between the Reynolds number and the drag coefficient remains undetermined in certain ranges. This study presents a high predictive relationship curve, obtained using fitting software, to supplement and rectify the limitations in the existing relationship. Leveraging fluid simulation software, this research determines the Reynolds number of particles of different sizes and densities within the fluid, offering a methodological reference for similar flow field problems. A new drag coefficient function is proposed and validated for the Reynolds number range of 1 to 20, addressing a gap in existing theoretical models. The simulation results indicate that under the suitable separation conditions of −0.074 + 0.02 mm particles, the concentrate particles overcome the flushing effect of the reverse washing water and move in the opposite direction to the fluid. This advancement not only improves the theoretical framework but also offers significant academic and practical value by enhancing the efficiency of particle separation in the Knelson concentrator.

Synthesis of agro-industrial wastes/sodium alginate/bovine gelatin-based polysaccharide hydrogel beads: Characterization and application as controlled-release microencapsulated fertilizers

Synthesis of novel agro-industrial wastes/sodium alginate/bovine gelatin-based polysaccharide hydrogel beads, micromeritic/morphometric characteristics of the prepared formulations, greenhouse trials using controlled-release microencapsulated fertilizers, and acute fish toxicity testing were conducted simultaneously for the first time within the scope of an integrated research. In the present analysis, for the first time, 16 different morphometric features, and 32 disinct plant growth traits of the prepared composite beads were explored in detail within the framework of a comprehensive digital image analysis. The hydrogel beads composed of 19 different agro-industrial wastes/materials were successfully synthesized using the ionotropic external gelation technique and CaCl2 as cross-linker. According to micromeritic characteristics, the ionotropically cross-linked beads exhibited 77.86 ± 3.55 % yield percentage and 2.679 ± 0.397 mm average particle size. The dried microbeads showed a good swelling ratio (270.02 ± 80.53 %) and had acceptable flow properties according to Hausner's ratio (1.136 ± 0.028), Carr's index (11.94 ± 2.17 %), and angle of repose (25.03° ± 5.33°) values. The settling process of the prepared microbeads was observed in the intermediate flow regime, as indicated by the average particle Reynolds numbers (169.17 ± 82.81). Experimental findings and non-parametric statistical tests reveal that dried fertilizer matrices demonstrated noteworthy performance on the cultivation of red hot chili pepper plant (Capsicum annuum var. fasciculatum) according to the results of greenhouse trials. Surface morphologies of the best-performing fertilizer matrices were also characterized by Scanning Electron Microscopy. Moreover, the static fish bioassay experiment confirmed that no abnormalities and acute toxic reactions occurred in shortfin molly fish (Poecilia sphenops) fed with dried leaves of red hot chili pepper plants grown with formulated fertilizers. This study showcased a pioneering investigation into the synthesis of microcapsules using synthesized hydrogel beads along with digital image processing for bio-waste management and sustainable agro-application.

Flow-induced erosion modelling of cohesive material with coupled CFD-DEM approach

Erosion is one of the continuous wear mechanisms in cohesive materials caused by the shear stress applied by the fluid flow at the liquid–solid interface. The erosion resistance of cohesive materials is significantly influenced by the strength of the cohesive bonds that hold the particles together, increasing the complexity of the mechanism. The erosion rate of cohesive materials depends on the critical shear stress (CSS) and the erodibility coefficient at the surface. The current understanding of the relationship among the inter-particle bond strength, CSS, erodibility coefficient, and their respective contributions to the flow-induced erosion process is still lacking; therefore, it cannot be adequately described mathematically. The present research offers a coupled computational fluid dynamics (CFD)–discrete element method (DEM) approach to visualize and quantitatively analyze the flow-induced erosion in cohesive materials. The capability and accuracy of the developed model were validated using experimental data available in the literature. A cohesion model was then employed to describe the strength of the cohesive bond, and the effects of the cohesion energy density (CED) on the CSS and erodibility coefficient were investigated. The analysis indicated that for cohesive materials, the non-dimensional CSS not only is affected by the particle Reynolds number but also strongly depends on CED. The simulation results indicated that by increasing the CED value from 500 to 900kJ/m3, the CSS increased by 25 %, and the erodibility coefficient decreased by 62 %. The proposed CFD–DEM approach can effectively estimate the erosion initiation and erosion rate of cohesive materials in different applications and geometries.

Experimental analysis of ice crystal size–velocity correlation in icing wind tunnel with digital holographic particle tracking velocimetry

The ice crystal icing in aero-engines poses a significant threat to aircraft flight safety, and investigating the correlation between ice crystal size and velocity in icing wind tunnels is essential for correlating ground tests with flight conditions. In this paper, a digital holographic particle tracking velocimetry system is developed and integrated with an icing wind tunnel, and the ice crystal size and velocity are simultaneously measured in experiments at four different wind speeds. The velocity difference between the ice crystal and wind has been experimentally observed, and it increases with both the ice crystal size and wind speed. The normalized velocities of the ice crystals by the wind speeds decrease with size, and the maximum velocity difference in the experiments reaches 28% of the wind speed. Additionally, quantitative correlations between ice crystal size and normalized velocity based on the power function and polynomial model are established. The relationship between the particle Reynolds number of ice crystal and size is also analyzed, resulting in the development of a model based on the power function, and the power index ranges from 1.51 to 1.64. These findings will provide valuable assistance in the calibration and commissioning of the ice crystal simulation system in icing wind tunnels, as well as in exploring the correlation between ground icing tests and flight and in developing corresponding models.

Turbulent pipe flow with spherical particles: Drag as a function of particle size and volume fraction

Suspensions of finite-size solid particles in a turbulent pipe flow are found in many industrial and technical flows. Due to the ample parameter space consisting of particle size, concentration, density and Reynolds number, a complete picture of the particle–fluid interaction is still lacking. Pressure drop predictions are often made using viscosity models only considering the bulk solid volume fraction. For the case of turbulent pipe flow laden with neutrally buoyant spherical particles, we investigate the pressure drop and overall drag (friction factor), fluid velocity and particle distribution in the pipe. We use a combination of experimental (MRV) and numerical (DNS) techniques and a continuum flow model. We find that the particle size and the bulk flow rate influence the mean fluid velocity, velocity fluctuations and the particle distribution in the pipe for low flow rates. However, the effects of the added solid particles diminish as the flow rate increases. We created a master curve for drag change compared to single-phase flow for the particle-laden cases. This curve can be used to achieve more accurate friction factor predictions than the traditional modified viscosity approach that does not account for particle size.

Model construction of the suction force of high-sphericity particles based on the PI theorem

Spheroid particles with high-sphericity are more common in particle absorption's applications than spherical particles, and their suction force (Fs) is a crucial mechanical factor in the particle absorption process, which is significantly affected by the spatial position of the particle concerning to the suction hole. Therefore, in this work, a combination of the PI theorem and the idealized model method was employed to establish an Fs model of spheroid particles with high-sphericity. More specifically, the spatial coordinates of the particle relative to the suction hole were introduced, rendering the model more applicable in practical engineering scenarios. Through the validation process, the proposed model exhibited excellent applicability for predicting Fs on spheroid particles of sphericity exceeding 90.24% within conditions of diameter ratio 0.571–1, diameter-distance ratio 0.5–0.786, particle center-tilt ratio 0–0.207, RPp−1 (reciprocal of particle Reynolds number under pressure condition) 3.29–4.25, and the prediction error can be controlled in 10%. Moreover, valuable insights were derived regarding the effective suction domain and constraints associated with the PI theorem in constructing unknown models during the subsequent analysis of the experimental data.

A Study of the Relationship between Sand Movement and Flow Field Distribution and Wear Causes in a Multiphase Pump

The Rosin–Rammler function is used in this paper to model the diameter distribution of sand particles. It investigates the characteristics of sand distribution and identifies the primary factors contributing to wear on flow components in a blade-type multiphase pump, considering varying particle sizes. The result of research shows that the blade head of the impeller and the middle section of the flow passage in the diffuser domain represent primary areas prone to sand particle accumulation. The concentration of sand particles within the diffuser surpasses that within the impeller, yet wear severity and extent are more pronounced in the impeller domain compared to the diffuser domain. Meanwhile, the movement trajectory of sand particles is linked to both shear flow and vortex flow. The wear of the front section of the impeller blade is more severe than the second half. On the pressure surface of the blade, particle Reynolds number emerges as a primary factor influencing wear, while on the suction surface, sand particle concentration plays a dominant role in determining wear. The particle concentration in the diffuser domain is the primary factor influencing wear on both the suction and pressure surfaces. The wear rate in the impeller is primarily influenced by the sand particle Reynolds number, whereas the wear rate in the diffuser domain is affected by a combination of sand particle diameter, sand particle concentration, and sand particle Reynolds number. The research findings possess significant engineering value in terms of enhancing the operational lifespan of multiphase pumps.

Experimental Investigation of Spherical Particles Settling in Annulus Filled with Rising-Bubble-Containing Newtonian Fluids

During the drilling of ultra-deep wells, gas kick often occurs, influenced by the complex void pressure profile. The accurate description of particle settling behavior in the gas–liquid mixture is of great significance to effectively deal with gas kicks and ensure drilling safety. In this study, the gas–liquid two-phase annulus flow with different gas volume fractions is created through the transparent annular pipe, constant pressure air pump, and gas flowmeter. High-speed photography is used to record and analyze the sedimentation of particles in gas–liquid mixtures. This study is based on 288 tests. The main parameters in this experiment include the particle Reynolds number, the gas fraction, and liquid viscosity. The effects of wall and gas fraction on the drag coefficient were analyzed. The correlation of particle terminal settling velocity was established. The results obtained show a correlation with average absolute errors (AAE) of 10.7%. This study reveals the settling characteristics of particles in the annular gas–liquid mixed flow, provides an accurate terminal settling velocity prediction explicit formula, and provides guidance for the calculation of bottom hole pressure under the condition of gas kick.

Resolving Flow Structures Inside Three Dimensional Packed Beds With Gas Flow By Ray Tracing Particle Image Velocimetry

Two different configurations are investigated in this study by ray tracing Particle Image Velocimetry to access the interior of different spherical packing structures. Configuration 1 consists of a regular bidisperse packed bed of 10mm and 40mm spheres based on a body-centered cubic arrangement. Ray tracing Particle Image Velocimetry was performed behind two spheres in the 40mm layer for particle Reynolds numbers from 200 to 700. The averaged velocity flow fields show the jet structures according to the pores between the underlying smaller spheres and the influence of the large spheres. Since ray-tracing Particle Image Velocimetry suffers from experimental and numerical limitations, planar 2D Particle Image Velocimetry measurements are performed to obtain spatially highly resolved validation data in the optically accessible void pores. These measurements were performed at different height positions in the bed showcasing that similar flow fields appear in the different pores. Configuration 2 deals with the jet flow (Re=5900) around an individual sphere, part of a body-centred cubic arrangement of d=40mm spheres. The emphasis lays on the temporally resolved snapshot data of the turbulent jet flow obtained by ray tracing Particle Image velocimetry. Data obtained from both configurations is used for a comprehensive discussion of the chances and challenges of ray tracing Particle Image Velocimetry. Limitations appear on the experimental side, like generation of depth of field, illumination and reflections, sufficient measurement signal, and accuracy of the geometry, but also on the numerical side, like the reproduction of the geometry, material properties, and real-world conditions. Since all these phenomena are interlinked, performing the ray tracing method in more complex systems is questionable.

Laboratory investigations of wave-induced transport of plastic debris over a rippled bottom

Laboratory experiments are conducted in a wave flume to investigate the effect of water waves on the transport of plastic pellets over a rippled bottom. The horizontal velocities of plastic debris are analyzed over the rippled bottom for different wave conditions and plastic elements with different properties. Laboratory investigations determined the characteristic transport patterns of wave-induced plastic debris with a density of ∼2.0g/cm3 moving along the rippled bottom. In the first, swing-type motion, the grains move only in the ripple trough with velocities lower than 0.10 m/s. For sliding-type movement, the grains move along the entire rippled surface with velocities in the range of 0.10–0.13 m/s. For higher velocities in the range of 0.15–0.20 m/s, a saltation-type motion becomes dominant. The results show that plastic grains may move up to 2–3 cm above the ripple crest depending on hydrodynamic conditions. The analysis shows that for velocity-skewed flows, sliding-type motion and onshore transport dominate. For acceleration-skewed flows, saltation-type motion and offshore transport dominate, which is attributed to higher boundary layer thickness and phase lag effects. The analysis of the relationship between the particle Reynolds number and the thickness of the turbulent boundary layer reveals that for values of Rep≥1000 and a boundary layer thicknessδ≥50 mm saltation-type motion becomes dominant. The direction of transport is affected not only by the density of the sediment and the wave skewness coefficients but also by the dimensions of the bottom ripples. The laboratory investigations also provide insight into the hydrodynamic conditions affecting the transport of plastic debris along the bottom covered with ripples in oscillating nonlinear water flows.

A general drag coefficient model for a spherical particle incorporating rarefaction and particle-to-gas temperature ratio effects

A concept and model of two critical Reynolds numbers Rep,cr1 and Rep,cr2 corresponding respectively to onsets of drag crisis and recovery are proposed. A drag model at limits of zero particle Mach and Knudsen numbers is constructed. On this basis, we develop a general drag coefficient model applicable for a spherical particle traveling in a gas by using a large number of available data derived from the previous experiments, direct numerical simulations and direct simulation Monte-Carlo methods. The scope of applicability of the proposed drag model covers all flow regimes relative to the particle characterized by particle Reynolds and Mach (or Knudsen) numbers and different particle-to-gas temperature ratios. Its comparison with two latest general drag models shows the significantly smaller relative error. Furthermore, quasi-one dimensional simulations against two supersonic nozzle gas-particle flow experiments are conducted with an in-house code to validate its accuracy in comparison with the two drag models.

Drag, lift, and torque correlations for axi-symmetric rod-like non-spherical particles in linear wall-bounded shear flow

This paper presents novel correlations to predict the drag, lift, and torque coefficients of axi-symmetric non-spherical rod-like particles in a wall-bounded linear shear flow. The particle position and orientation relative to the wall are varied to systematically investigate the influence of the wall on the hydrodynamic forces. The newly derived correlations for drag, lift, and torque on the particle depend on various parameters, including the particle Reynolds number, the orientation angle between the major axis of the particle and the main local flow direction, the aspect ratio of the particle, and the dimensionless distance from the particle centre to the wall. The impact of the wall on the hydrodynamic forces is accounted for as a function of a multiplication factor on the drag force in case of locally uniform flow, and an additional force contribution for the lift and the torque, modifying the resultant forces experienced by a particle in a locally uniform flow. The changes in the hydrodynamic forces prove to be substantial, emphasizing the necessity of accounting for wall effects across all particle types and flow conditions investigated in this study. The coefficients of the correlations are determined through a fitting process utilizing the data generated from our previous study on the interaction forces between a locally uniform flow and an axi-symmetric non-spherical rod-like particles, as well as from data of novel direct numerical simulations (DNS) performed in this work of flow past axi-symmetric rod-like particles near a wall. The proposed correlations exhibit a good agreement compared to the DNS results, with median errors of 2.89%, 5.37%, and 11.00%, and correlation coefficients of 0.99, 0.99, and 0.96 for the correlations accounting for the drag, lift, and torque coefficients of a non-spherical particle in wall-bounded linear shear flow profile, respectively. These correlations can be used in large-scale simulations using an Eulerian–Lagrangian or a CFD/DEM framework to predict the behaviour of axi-symmetric rod-like non-spherical particles in wall-bounded shear flow to locally uniform flow conditions.

Experimental and numerical investigation on the effect of surface roughness on the drag coefficient of a spherical particle

The drag coefficient (CD) for particles has a significant effect on the gas–solid fluidization characteristics. However, it is unclear whether the particle surface roughness (Rap) can notably affect CD at relatively low particle Reynolds numbers (Rep). Herein, the CD for several single near-spherical particles with different Rap and density were determined using high-speed videography in conjunction with the image analysis method. In addition, a quasi-direct numerical simulation (q-DNS) method was applied to further resolve the flow field surrounding the particle. Both experimental and simulation results suggest that within a low Rep range (<500), there is no evident difference in CD. However, if the Rep exceeds 500, CD gradually decreases with the increase in Rap. Since the separation point of the particle boundary layer moves downstream, the rough sphere experiences lower pressure in the wake vortex region. This study provides a valuable conclusion: the Rap is a non-negligible factor in studying hydrodynamic behaviors of two-phase flow, especially at high fluidization velocity.