Flow Regimes in Bubble Columns with and without Internals: A Review

Hydrodynamics characterization in terms offlow regime behavior is a crucial task to enhance the design of bubble column reactors and scaling up related methodologies.This review presents recent studies on the typicalflow regimes established in bubble columns.Some effort is also provided to introduce relevant definitions pertaining to thisfield,namely,that of“void fraction”and related(local,chordal,cross-sectional and volumetric)variants.Experimental studies involving different parameters that affect design and operating conditions are also discussed in detail.In the second part of the review,the attention is shifted to cases with internals of various types(perfo-rated plates,baffles,vibrating helical springs,mixers,and heat exchanger tubes)immersed in the bubble columns.It is shown that the presence of these elements has a limited influence on the global column hydrodynamics.However,they can make the homogeneousflow regime more stable in terms of transition gas velocity and transi-tion holdup value.The last section is used to highlight gaps which have not beenfilled yet and future directions of investigation.

Consolidation of high replacement ratio stone column-reinforced ground:Analytical solutions incorporating clogging effect

The utilization of stone columns has emerged as a popular ground improvement strategy,whereas the drainage performance can be adversely hampered by clogging effect.Despite the ample progress of calculation methods for the consolidation of stone column-improved ground,theoretical investigations into the clogging effect have not been thoroughly explored.Furthermore,it is imperative to involve the column consolidation deformation to mitigate computational error on the consolidation of composite ground with high replacement ratios.In this context,an analytical model accounting for the initial clogging and coupled time and depth-dependent clogging of stone columns is established.Then,the resulting governing equations and analytical solutions are obtained under a new flow continuity relationship to incorporate column consolidation deformation.The accuracy and reliability of the proposed model are illustrated by degradation analysis and case studies with good agreements.Subsequently,the computed results of the current study are juxtaposed against the existing models,and an in-depth assessment of the impacts of several crucial parameters on the consolidation behavior is conducted.The results reveal that ignoring column consolidation deformation leads to an overestimate of the consolidation rate,with maximum error reaching up to 16%as the replacement ratio increases.Furthermore,the initial clogging also has a significant influence on the consolidation performance.Additionally,the increment of depth and time-clogging factors a and b will induce a noticeable retardation of the consolidation process,particularly in the later stage.

Visual experimental study of nanofluids application to promote CO_(2) absorption in a bubble column

The addition of dispersed-phase nanoparticles in the liquid phase can enhance the gas-liquid transfer process as the suspended nanoparticles affect the transfer process inside the fluid through microdisturbance or micro-convection effects.In this article,a high-speed digital camera was used to visualize the bubble behavior of CO_(2) in pure water and nanofluids to examine the effects of CO_(2) gas flow rate,nanoparticle solid content and type on the bubble behavior in the fluids.The CO_(2) absorption performance in three water-based nanofluids were compared in a bubbler.And the mass transfer characteristics during CO_(2) bubble absorption and the reasons for the enhanced gas-liquid mass transfer effect of nanoparticles were analyzed.The results showed that the presence of nanoparticles affected the formation process of bubbles in the fluid,shortened the bubble detachment time,reduced the detachment diameter,effectively increased the gas-liquid contact area,and improved the bubbles detachment frequency.The system with MCM-41 corresponded to a higher overall mass transfer coefficient.Uncalined MCM-41 contained surfactant that enhanced foaming behavior in water.This prevented the transfer of CO_(2) to some extent,and the CO_(2) absorption by uncalined MCM-41/H_(2)O was 5.34%higher than that by pure water.Compared with SiO_(2) nanoparticles with the same particle size and the same composition,MCM-41 had a higher adsorption capacity and better hydrophilicity due to its larger specific surface area and rich porous structure,which was more favorable to accelerate the collision between nanoparticles and CO_(2) bubbles to cause micro-convection.Under the condition of 0.1%(mass)solid content,the enhancement of CO_(2) absorption process by MCM-41 nanoparticles was more significant and improved by 16.9%compared with pure water.

Comparative impact behaviours of ultra high performance concrete columns reinforced with polypropylene vs steel fibres

Polypropylene(PP) fibres have primarily used to control shrinkage cracks or mitigate explosive spalling in concrete structures exposed to fire or subjected to impact/blast loads, with limited investigations on capacity improvement. This study unveils the possibility of using PP micro-fibres to improve the impact behaviour of fibre-reinforced ultra-high-performance concrete(FRUHPC) columns. Results show that the addition of fibres significantly improves the impact behaviour of FRUHPC columns by shifting the failure mechanism from brittle shear to favourable flexural failure. The addition of steel or PP fibres affected the impact responses differently. Steel fibres considerably increased the peak impact force(up to 18%) while PP micro-fibres slightly increased the peak(3%-4%). FRUHPC significantly reduced the maximum midheight displacement by up to 30%(under 20°impact) and substantially improved the displacement recovery by up to 100%(under 20° impact). FRUHPC with steel fibres significantly improved the energy absorption while those with PP micro-fibres reduced the energy absorption, which is different from the effect of PP-macro fibre reported in the literature. The optimal fibre content for micro-PP fibres is 1% due to its minimal fibre usage and low peak and residual displacement. This study highlights the potential of FRUHPC as a promising material for impact-resistant structures by creating a more favourable flexural failure mechanism, enhancing ductility and toughness under impact loading, and advancing the understanding of the role of fibres in structural performance.

Experimental Study on the Axial Compression Performance of Bamboo Scrimber Columns Embedded with Steel Reinforcing Bars

In this paper,a new type of bamboo scrimber column embedded with steel bars(rebars)was proposed,and the compression performance was improved by pre-embedding rebars during the preparation of the columns.The effects of the slenderness ratio and the reinforcement ratio on the axial compression performance of reinforced bamboo scrimber columns were studied by axial compression tests on 28 specimens.The results showed that the increase in the slenderness ratio had a significant negative effect on the axial compression performance of the columns.When the slenderness ratio increased from 19.63 to 51.96,the failure mode changed from strength failure to buckling failure,and the maximum bearing capacity decreased by 43.03%.The axial compression performance of the reinforced bamboo scrimber columns did not significantly improve at a slenderness ratio of 19.63,but the opposite was true at slenderness ratios of 36.95 and 51.96.When the reinforcement ratio increased from 0%to 4.52%,the bearing capacity of those with a slenderness ratio of 51.96 increased by up to 16.99%,and the stiffness and ductility were also improved.Finally,based on existing specifications,two modification parameters,the overall elastic modulus Ec and the combined strength fcc,were introduced to establish a calculation method for the bearing capacity of the reinforced bamboo scrimber columns.The calculation results were compared with the test results,and the results showed that the proposed calculation models can more accurately predict the bearing capacity.

A Two-Stage Scenario-Based Robust Optimization Model and a Column-Row Generation Method for Integrated Aircraft Maintenance-Routing and Crew Rostering

Motivated by a critical issue of airline planning process,this paper addresses a new two-stage scenario-based robust optimization in operational airline planning to cope with uncertainty and possible flight disruptions.Following the route network scheme and generated flight timetables,aircraft maintenance routing and crew scheduling are critical factors in airline planning and operations cost management.This study considers the simultaneous assignment of aircraft fleet and crew to the scheduled flight while satisfying a set of operational constraints,rules,and regulations.Considering multiple locations for airline maintenance and crew bases,we solve the problem of integrated Aircraft Maintenance Routing and Crew Rostering(AMRCR)to achieve the minimum airline cost.One real challenge to the efficiency of the planning results is the possible disruptions in the initial scheduled flights.Due to the fact that disruption scenarios are expressed discretely with a specified probability,and we provide adjustable decisions under disruption to deal with this disruption risk,we provide a Two-Stage Scenario-Based Robust Optimization(TSRO)model.In this model,here-and-now or first-stage variables are the initial resource assignment.Furthermore,to adapt itself to different disruption scenarios,the model considers some adjustable variables,such as the decision to cancel the flight in case of disruption,as wait-and-see or second-stage variables.Considering the complexity of integrated models,and the scenario-based decomposable structure of the TRSO model to solve it with better computational performance,we apply the column and row generation(CRG)method that iteratively considers the disruption scenarios.The numerical results confirm the applicability of the proposed TSRO model in providing the AMRCR problem with an integrated and robust solution with an acceptable level of computational tractability.To evaluate the proposed TSRO model,which solves the AMRCR problem in an integrated and robust manner,five Key Performance Indicators(KPIs)like Number of delayed/canceled flights,Average delay time,and Average profit are taken into account.As key results driven by conducting a case study,we show the proposed TSRO model has substantially improved the solutions at all indicators compared with those of the sequential/non-integrated and nominal/non-robust models.The simulated instances used to assess the performance of the proposed model and CRG method reveal that both CPLEX and the CRG method exhibit comparable and nearly optimal performance for small-scale problems.However,for large-scale instances the proposed TSRO model falls short in terms of computational efficiency.Conversely,the proposed CRG method is capable of significantly reducing computational time and the optimality gap to an acceptable level.

Numerical Analysis of Cold-Formed Thin-Walled Steel Short Columns with Pitting Corrosion during Bridge Construction

Pitting corrosion is harmful during bridge construction,which will lead to uneven roughness of steel surfaces and reduce the thickness of steel.Hence,the effect of pitting corrosion on the mechanical properties of cold-formed thin-walled steel stub columns is studied,and the empirical formulas are established through regression fitting to predict the ultimate load of web and flange under pitting corrosion.In detail,the failure modes and load-displacement curves of specimens with different locations,area ratios,and depths are obtained through a large number of non-linear finite element analysis.As for the specimens with pitting corrosion on the web,all the specimens are subject to local buckling failure,and the failure mode will not change with pitting corrosion,but the failure location will change with pitting corrosion location;the size,location,and area ratio of pitting corrosion have little influence on the ultimate load of cold-formed thin-walled steel short columns,but the loss rate of pitting corrosion section area has a greater impact on the ultimate bearing capacity.As for the specimen with flange pitting corrosion,the location and area ratio of pitting corrosion have less influence on the ultimate load of cold-formed thin-walled steel short columns,and the section area loss rate has greater influence on the ultimate bearing capacity;the impact of web pitting corrosion on the ultimate load is greater than that of flange pitting corrosion under the same condition of pitting corrosion section area.The prediction formulas of limit load which are suitable for pitting corrosion of web and flange are established,which can provide a reference for performance evaluation of corroded cold-formed thin-walled steel.

An Affordable and Easily Accessible Approach for Acrylonitrile Monomer Purification through a Simple Column Technique

This manuscript presents a dataset detailing a method for purifying monomers. Purification plays a crucial role in every chemical process, as it leads to an improvement in product quality through the removal of impurities. The primary method for monomer purification, like acrylonitrile (AN), is the distillation technique. However, this technique is unsafe and hard to set up or handle. A straightforward, risk-free, low-cost method like the column technique resolves these issues. A simple column technique demonstrated the successful execution of purifying AN. Fourier transform infrared (FTIR) and nuclear magnetic resonance (NMR) analyses confirmed that AN was successfully purified, with purity reaching 99.8%. FTIR spectra revealed changes in the position and intensity of the stretching vibration peaks after purification. Also, the functional groups of the inhibitor monomethyl ether of hydroquinone (MeHQ) were undetected after purification. Furthermore, after purification, NMR spectra revealed the absence of aromatic protons and carbons associated with MeHQ. In conclusion, the column technique is a successful and inexpensive way to purify AN monomers. This makes it useful for a wide range of applications, especially in polymerization reactions where MeHQ needs to be removed to prevent self-polymerization during the initiation process.

Comprehensive analysis of phenolic composition and antioxidant mechanisms in Gymnema sylvestre extracts using LC-MS and column chromatography

Recent studies have highlighted the potential of plant extracts as therapeutic agents for managing oxidative stress and related disorders.This study aims to elucidate the phenolic composition and antioxidant properties of Gymnema sylvestre extracts.Ethanolic reflux extraction followed by column chromatography was employed to isolate phenolic compounds.The total phenolic and flavonoid contents were quantified using the Folin–Ciocalteu and aluminum chloride colorimetric methods,respectively.Antioxidant activities were assessed by DPPH,ABTS scavenging assays and the ferric reducing antioxidant power(FRAP)assay.High-Performance Liquid Chromatography(HPLC)with a C18 column and Thermo TSQ Quantum Access Max(LC-MS)were used to determine the levels of gymnemic acid and identify other potential phenolic compounds.The analysis revealed significant antioxidant activities in the fractions.Fraction A showed the highest DPPH and ABTS scavenging activities,and Fraction C demonstrated the highest ferric reducing power.LC-MS analysis identified several phenolic compounds,indicating that these are major contributors to the antioxidant efficacy of the extract.This study provides a detailed phenolic profile and confirms the strong antioxidant potential of Gymnema sylvestre leaf extract,supporting its therapeutic use and further investigation.

Modelling and Sizing of a Floor Reinforced by Ballasted Columns Intended to Support a Tank

This work aims to study the modeling and sizing of a floor reinforced by ballasted columns. We are studying the system of reinforcement by ballasted columns because this technique is able to replace deep foundations that are technically difficult to realize and their cost is higher. The modelling and dimensioning of foundations on a ballasted column will be an important contribution to the state of the art of this method because it will highlight the mode of transfer of loads, and will expose the induced deformations by also allowing to verification criteria of bearing capacity and allowable settlement according to geometric information of the model. The columns on a substrate located at 9 m have a length of 9 m and a diameter of 40 cm and were obtained by incorporating ballast of granular class 0/31.5 of internal friction angle of 38˚ and a density weight of 21 kN/m3. The choice of this method is based on the geotechnical characteristics of the initial soil. Thus, identification and characterization tests were carried out to estimate the bearing capacity and the settlement giving respectively 125 kPa and 57 cm. These results show the ground does not have sufficient mechanical properties to withstand the loads transmitted by the tank. By adopting the reinforcement of the soil with ballasted columns, numerical calculations show that after applying a load equal to 265.1 KPa, 20 cm vertical settlement and 17 cm horizontal displacement were obtained. This is in the tolerable deformation range for our tank, namely, less than 20 cm. Analytically, in addition to reducing settlement, ballasted columns, Due to their high stiffness, they have effectively contributed to the increase of the permissible soil stress up to 257 kPa.

Simultaneous Adsorption of Aqueous Pb2+, Cu2+, Zn2+, and Cd2+ Using Surfactant-Modified and Unmodified Activated Carbon in a Fixed Bed Column

The goal of this work is to improve the simultaneous removal of Pb2+, Cu2+, Zn2+, and Cd2+ ions from synthetic wastewater in a fixed bed column by incorporating sodium dodecyl sulfate (SDS) onto the surface of activated carbon made from coconut shells. The activated carbons were characterized using Fourier transform infrared spectroscopy (FT-IR) and scanning electron microscopy-energy dispersive x-ray (SEM-EDX). The adsorption column dynamics were studied by varying the flow rates (5, 10 and 15 mL/min), bed heights (10, 15 and 20 cm), and initial concentrations (50, 150, and 250 mg/L). The activated carbon has a pore volume of 0.715 cm3/g and a BET-specific surface area of 1410 m2/g. Sodium dodecyl sulfate (SDS) surfactant incorporation onto the surface of the activated carbon enhances its capacity for simultaneous adsorption of Pb2+, Cu2+, Zn2+, and Cd2+ from the aqueous medium. The affinity of the heavy metals to both unmodified (AC) and modified (AC-SDS) activated carbons followed the order of Pb2+ > Cu2+ > Zn2+ > Cd2+. The dynamic adsorption of the column depends on the flow rate, bed height, initial metal concentration, and SDS surface modification. With a 5 mL/min flow rate, a 20 cm bed height, and a 50 mg/L initial metal concentration, a maximum break-through time of 150 minutes for the unmodified activated carbon (AC) and 180 minutes for the SDS-modified activated carbon (AC-SDS) was reached.

Nonlinear Time History Analysis for the Different Column Orientations under Seismic Wave Synthetic Approach

The significant impact of earthquakes on human lives and the built environment underscores the extensive human and economic losses caused by structural collapses. Over the years, researchers have focused on improving seismic design to mitigate earthquake-induced damages and enhance structural performance. In this study, a specific reinforced concrete (RC) frame structure at Kyungpook National University, designed for educational purposes, is analyzed as a representative case. Utilizing SAP 2000, the research conducts a nonlinear time history analysis to assess the structural performance under seismic conditions. The primary objective is to evaluate the influence of different column section designs, while maintaining identical column section areas, on structural behavior. The study employs two distinct seismic waves from Abeno (ABN) and Takatori (TKT) for the analysis, comparing the structural performance under varying seismic conditions. Key aspects examined include displacement, base shear force, base moment, joint radians, and layer displacement angle. This research is anticipated to serve as a valuable reference for seismic restraint reinforcement work on RC buildings, enriching the methods used for evaluating structures through nonlinear time history analysis based on the synthetic seismic wave approach.

An optimization method for enhancement of gas–liquid mass transfer in a bubble column reactor based on the entropy generation extremum principle

In this study,an optimization method is proposed to enhance the gas–liquid mass transfer in bubble column reactor based on the entropy generation extremum principle.The mass transfer–induced entropy generation can be maximized with the increase of mass transfer rate,based on which the velocity field can be optimized.The oxygen gas–liquid mass transfer is the major rate–limiting step of the toluene emissions biodegradation process in bubble column reactor,so the entropy generation due to oxygen mass transfer is used as the objective function,and the conservation equations of the gas–liquid flow and species concentration are taken as constraints.This optimization problem is solved by the calculus of variations,the optimal liquid flow pattern is obtained and the relationship of the maximum mass transfer enhancement on viscous dissipation is revealed,which can be used to improve the design of internal structure of the bubble column reactor.

Bubble size modeling approach for the simulation of bubble columns

The constant bubble size modeling approach(CBSM)and variable bubble size modeling approach(VBSM)are frequently employed in Eulerian–Eulerian simulation of bubble columns.However,the accuracy of CBSM is limited while the computational efficiency of VBSM needs to be improved.This work aims to develop method for bubble size modeling which has high computational efficiency and accuracy in the simulation of bubble columns.The distribution of bubble sizes is represented by a series of discrete points,and the percentage of bubbles with various sizes at gas inlet is determined by the results of computational fluid dynamics(CFD)–population balance model(PBM)simulations,whereas the influence of bubble coalescence and breakup is neglected.The simulated results of a 0.15 m diameter bubble column suggest that the developed method has high computational speed and can achieve similar accuracy as CFD–PBM modeling.Furthermore,the convergence issues caused by solving population balance equations are addressed.

Rapid Analysis of Four Alkaloids in Uncaria rhynchophylla by Core-Shell Column HPLC and Quantitative Analysis of Multi-Components by Single Marker(QAMS)

As a traditional herbal medicine,the major alkaloids in Uncaria rhynchophylla have been proven to have blood pressure-lowering and sedative effects.It is essential to develop an effective method for the determination of the major alkaloids in U.rhynchophylla.In this research,a rapid quantitative analysis involving multi-components analysis by a single marker strategy coupled with core-shell column HPLC was adopted to analyse four alkaloids(corynoxeine,isocorynoxeine,isorhynchophylline,rhynchophylline)in U.rhynchophylla.Isorhynchophylline was selected as the internal reference substance,the content of which was determined by the traditional external standard method.Relative correction factors(RCF)between isorhynchophylline and the other three alkaloids were calculated respectively.The results showed that the QAMS method had good robustness under different HPLC instruments.Nineteen batches of U.rhynchophylla were tested.No significant difference was observed between the results by QAMS and EMS(Correlation coefficient>0.99,p>0.05).The QAMS method could be employed as a rapid,effective technique for the quality control of U.rhynchophylla.

Different efficiency toward the biomimetic aerobic oxidation of benzyl alcohol in microchannel and bubble column reactors: Hydrodynamic characteristics and gas–liquid mass transfer

The selective aerobic oxidation of benzyl alcohol to benzaldehyde has attracted considerable attention because benzaldehyde is a high value-added product. The rate of this typical gas–liquid reaction is significantly affected by mass transfer. In this study, CoTPP-mediated(CoTPP: cobalt(II) mesotetraphenylporphyrin) selective benzyl alcohol oxidation with oxygen was conducted in a membrane microchannel(MMC) reactor and a bubble column(BC) reactor, respectively. We observed that 83% benzyl alcohol was converted within 6.5 min in the MMC reactor, but only less than 10% benzyl alcohol was converted in the BC reactor. Hydrodynamic characteristics and gas–liquid mass transfer performances were compared for the MMC and BC reactors. The MMC reactor was assumed to be a plug flow reactor,and the dimensionless variance was 0.29. Compared to the BC reactor, the gas–liquid mass transfer was intensified significantly in MMC reactor. It could be ascribed to the high gas holdup(2.9 times higher than that of BC reactor), liquid film mass transfer coefficient(8.2 times higher than that of BC reactor), and mass transfer coefficient per unit interfacial area(3.8 times higher than that of BC reactor). Moreover,the Hatta number for the MMC reactor reached up to 0.61, which was about 15 times higher than that of the BC reactor. The computational fluid dynamics calculations for mass fractions in both liquid and gas phases were consistent with the experimental data.

A benzenesulfonic acid-modified organic polymer monolithic column with reversed-phase/hydrophilic bifunctional selectivity for capillary electrochromatography

Here,a styrene-based polymer monolithic column poly(VBS-co-TAT-co-AHM)with reversed-phase/hydrophilic interaction liquid chromatography(RPLC/HILIC)bifunctional separation mode was success-fully prepared for capillary electrochromatography by the in situ polymerization of sodium p-styrene sulfonate(VBS)with cross-linkers 3-(acryloyloxy)-2-hydroxypropyl methacrylate(AHM)and 1,3,5-triacryloylhexahydro-1,3,5-triazine(TAT).The preparation conditions of the monolith were optimized.The morphology and formation of the poly(VBS-co-TAT-co-AHM)monolith were confirmed by scanning electron microscopy(SEM)and Fourier transform infrared spectroscopy(FT-IR).The separation perfor-mances of the monolith were evaluated systematically.It should be noted that the incorporation of VBS functional monomer can provideπ-πinteractions,hydrophilic interactions,and ion-exchange in-teractions.Hence,the prepared poly(VBS-co-TAT-co-AHM)monolith can achieve efficient separation of thiourea compounds,benzene series,phenol compounds,aniline compounds and sulfonamides in RPLC or HILIC separation mode.The largest theoretical plate number for N,N0-dimethylthiourea reached 1.7×10^(5)plates/m.In addition,the poly(VBS-co-TAT-co-AHM)monolithic column showed excellent reproducibility and stability.This novel monolithic column has great application value and potential in capillary electrochromatography(CEC).

Prediction of column failure modes based on artificial neural network

To implement the performance-based seismic design of engineered structures,the failure modes of members must be classified.The classification method of column failure modes is analyzed using data from the Pacific Earthquake Engineering Research Center(PEER).The main factors affecting failure modes of columns include the hoop ratios,longitudinal reinforcement ratios,ratios of transverse reinforcement spacing to section depth,aspect ratios,axial compression ratios,and flexure-shear ratios.This study proposes a data-driven prediction model based on an artificial neural network(ANN)to identify the column failure modes.In this study,111 groups of data are used,out of which 89 are used as training data and 22 are used as test data,and the ANN prediction model of failure modes is developed.The results show that the proposed method based on ANN is superior to traditional methods in identifying the column failure modes.

Reliability assessment for serviceability limit states of stiffened deep cement mixing column-supported embankments

The reliability and deterministic analyses of wood-cored stiffened deep cement mixing and deep cement mixing column-supported embankments(referred to as WSCSE and DCSE,respectively)considering serviceability limit state requirements are presented in this paper.Random field theory was used to simulate the spatial variability of soil
cement mixing(SCM)material in which the adaptive Kriging Monte Carlo simulation was adopted to estimate the failure probability of a column
supported embankment(CSE)system.A new method for stochastically generating random values of unconfined compressive strength(qu)and the ratio(Ru)between the undrained elastic modulus and qu of SCM material based on statistical correlation data is proposed.Reliability performance of CSEs concerning changes in the mean(μ),coefficient of variation(CoV),and vertical spatial correlation length(θv)of qu and Ru are presented and discussed.The obtained results indicate that WSCSE can provide a significantly higher reliability level and can tolerate more SCM material spatial variability than DCSE.Some performance of DCSE and WSCSE,which can be considered satisfactory in a deterministic framework,cannot guarantee an acceptable reliability level from a probabilistic viewpoint.This highlights the importance and necessity of employing reliability analyses for the design of CSEs.Moreover,consideration of only μ and CoV of qu seems to be sufficient for reliability analysis of WSCSE while for DCSE,uncertainties regarding the Ru(i.e.both μ and CoV)and θv of qu cannot be ignored.

Numerical simulation of gas–liquid flow in the bubble column using Wray–Agarwal turbulence model coupled with population balance model

In this paper,an improved computational fluid dynamic(CFD)model for gas-liquid flow in bubble column was developed using the one-equation Wary-Agarwal(WA)turbulence model coupled with the population balance model(PBM).Through 18 orthogonal test cases,the optimal combination of interfacial force models,including drag force,lift force,turbulent dispersion force.The modified wall lubrication force model was proposed to improve the predictive ability for hydrodynamic behavior near the wall of the bubble column.The values simulated by optimized CFD model were in agreement with experimental data,and the errors were within±20%.In addition,the axial velocity,turbulent kinetic energy,bubble size distribution,and the dynamic characteristic of bubble plume were analyzed at different superficial gas velocities.This research work could provide a theoretical basis for the extension of the CFD-PBM coupled model to other multiphase reactors..