In this study,based on the Luo bubble coalescence model,a model correction factor C_e for pressures according to the literature experimental results was introduced in the bubble coalescence efficiency term.Then,a coup...In this study,based on the Luo bubble coalescence model,a model correction factor C_e for pressures according to the literature experimental results was introduced in the bubble coalescence efficiency term.Then,a coupled modified population balance model(PBM) with computational fluid dynamics(CFD) was used to simulate a high-pressure bubble column.The simulation results with and without C_e were compared with the experimental data.The modified CFD-PBM coupled model was used to investigate its applicability to broader experimental conditions.These results showed that the modified CFD-PBM coupled model can predict the hydrodynamic behaviors under various operating conditions.展开更多
On the basis of population balance a mathematical model is developed to describe the formation of polymer particle in styrene suspension polymerization. The characteristics of coalescence and breakage of droplets and ...On the basis of population balance a mathematical model is developed to describe the formation of polymer particle in styrene suspension polymerization. The characteristics of coalescence and breakage of droplets and the gel effect are analyzed in particular. Parameters of the models are estimated by experimental data on reaction conversion and particle size distribution. The results show that the model is suitable for predicting polymerization processes.展开更多
A new multivariate population balance modeling for the homogenous nucleation from bismuth vapor is tested against experimental results. However, the small differences of some key parameters could lead to the ill-posed...A new multivariate population balance modeling for the homogenous nucleation from bismuth vapor is tested against experimental results. However, the small differences of some key parameters could lead to the ill-posed problem, such as the surface tension. In this study, the parameter fluctuations set according to the response surface method are employed in the population balance simulation to identify their importance. Subsequently, the quadratic polynomials are established to replace the simulation and the fluctuations are evaluated with the characteristic parameters of particle evolution. It is found that the surface tension tends to be the most significant factor determining the particle evolution, which is also influenced by the coefficient in condensation rates and fractal dimension in the coagulation. To get more accurate modeling and key parameters, the comprehensive sum of mean square error is calculated based on all the fluctuations and the appropriate value for the surface tension is 0.466 N/m.展开更多
In multiphase pumps transporting gas-liquid two-phase flows,the high-speed rotation of the impeller induces complex deformations in bubble shapes within the flow domain,making the prediction of gasliquid two-phase dra...In multiphase pumps transporting gas-liquid two-phase flows,the high-speed rotation of the impeller induces complex deformations in bubble shapes within the flow domain,making the prediction of gasliquid two-phase drag forces highly challenging in numerical simulations.To achieve precise prediction of the drag forces on irregular bubbles within multiphase pumps,this study modifies the existing bubble drag force model and applies the revised model to the prediction of gas-liquid two-phase flow within multiphase pumps.The research findings indicate that the modified drag force model significantly enhances the accuracy of predicting flow characteristics within the pump,particularly under high gas volume fraction conditions.The simulation results for gas phase distribution and vorticity exhibit strong agreement with experimental data.The modified drag model better captures the accumulation of the gas phase at the suction side of the impeller outlet.It also accurately predicts the vortex characteristics induced by bubble backflow from the trailing edges of the diffuser.Additionally,the adjustment of the drag coefficient enhances the model’s ability to represent local flow field characteristics,thereby optimizing the performance simulation methods of multiphase pumps.Compared to traditional drag force models,the modified model reduces prediction errors in head and efficiency by 36.4%and 27.5%,respectively.These results provide important theoretical foundations and model support for improving the accuracy of gas-liquid two-phase flow simulations and optimizing the design of multiphase pumps under high gas volume fraction conditions.展开更多
It is the fact that several process parameters are either unknown or uncertain. Therefore, an optimal control, profile calculated with developed process models with respect to such process parameters may not give an o...It is the fact that several process parameters are either unknown or uncertain. Therefore, an optimal control, profile calculated with developed process models with respect to such process parameters may not give an optimal performance when implemented to real processes. This study proposes a batch-to-batch optimization strategy for the estimation of uncertain kinetic.par.ameters in a batch crystallization process of potassium sulfate production. The knowledge of a crystal size distribution of the product at the end of batch operation is used in the proposed methodology. The updated kinetic parameters are applied for determining an optimal operating temperature policy for the next batch run.展开更多
Rapid dewatering and thickening of whole-tailings with ultrafine particles is one of the most important processes for the whole-tailings paste preparation. Deep-cone thickener, a kind of such process for the flocculat...Rapid dewatering and thickening of whole-tailings with ultrafine particles is one of the most important processes for the whole-tailings paste preparation. Deep-cone thickener, a kind of such process for the flocculation and settling of whole-tailings, is particularly necessary to study. However, there exist many problems in observing the flocculation and settling process of whole-tailings, as well as the particle size distribution(PSD) of whole-tailings floccules in deep-cone thickener. Population balance model(PBM) is applied to predict the PSD in deep-cone thickener, and LUO model and GHADIRI model are employed to study the aggregation and fragmentation mechanism of the whole-tailings particles, respectively. Through three-dimensional numerical simulation on the whole-tailings flocculation and settling in deep-cone thickener using computational fluid dynamics(CFD)-PBM, the distribution of density and turbulent kinetic energy in deep-cone thickener were obtained, at the same time the spatio-temporal changes of whole-tailings floccules particle size distribution are analyzed. Finally, the major flocculation position in deep-cone thickener is found and the flocculation settling rules of whole-tailings are achieved.展开更多
The computational fluid dynamics （CFD）-population balance equations （PBE） coupled model is employed to investigate the hydrodynamics in a gas-slurry internal loop reactor with external slurry circulation. The pred...The computational fluid dynamics （CFD）-population balance equations （PBE） coupled model is employed to investigate the hydrodynamics in a gas-slurry internal loop reactor with external slurry circulation. The predicted radial profiles of local gas holdup and bubble diameter are in good agreement with the corresponding experimental data. The spatio-temporal velocity profile of the gas phase reveals that the upward movement of gas is slowed down and the residence time of gas is prolonged by the downward momentum of the slurry, introduction of the external slurry can greatly improve the uniformity of gas holdup distribution in the reactor, especially in the downcomer-tube action region. Moreover, the interaction between the downward slurry and upward gas can lead to small bubble size and high interfacial area as well as good mass and heat transfer. The above results suggest the function of external slurry circulation for the internal loop reactor and would be helpful for optimizing the design and scale up of reactors.展开更多
Thickeners are important units for water recovery in various industries. In this study, a semi-industrial pilot plant thickener similar to the tailing thickener of the Sarcheshmeh Copper Mine was simulated by CFD mode...Thickeners are important units for water recovery in various industries. In this study, a semi-industrial pilot plant thickener similar to the tailing thickener of the Sarcheshmeh Copper Mine was simulated by CFD modeling. The population balance was used to describe the particle aggregation and breakup. In this population balance, 15 particle sizes categories were considered. The Eulerian-Eulerian approach with standard k-e turbulence model was applied to describe two phases of slurry flow in the thickener under steady-state condition. The simulation results have been compared with the experimental measurements to validate the accuracy of the CFD modeling. After checking the numerical results, the effect of important parameters such as, feed flow rate, solid percentage in the feed, and solid particle size on the thickener performance was studied. The thickener residence time distribution were obtained by the modeling and also compared with the experimental data. Finally, the effects of feedwell feeding on the average diameter of aggregate and turbulent intensity were evaluated.展开更多
In this paper,a cell average technique(CAT)based parameter estimation method is proposed for cooling crystallization involved with particle growth,aggregation and breakage,by establishing a more efficient and accurate...In this paper,a cell average technique(CAT)based parameter estimation method is proposed for cooling crystallization involved with particle growth,aggregation and breakage,by establishing a more efficient and accurate solution in terms of the automatic differentiation(AD)algorithm.To overcome the deficiency of CAT that demands high computation cost for implementation,a set of ordinary differential equations(ODEs)entailed from CAT based discretized population balance equation(PBE)are solved by using the AD based high-order Taylor expansion.Moreover,an AD based trust-region reflective(TRR)algorithm and another interior-point(IP)algorithm are established for estimating the kinetic parameters associated with particle growth,aggregation and breakage.As a result,the estimation accuracy can be further improved while the computation cost can be significantly reduced,compared to the existing algorithms.Benchmark examples from the literature are used to illustrate the accuracy and efficiency of the AD-based CAT,TRR and IP algorithms in comparison with the existing algorithms.Moreover,seeded batch cooling crystallization experiments ofβform L-glutamic acid are performed to validate the proposed method.展开更多
Bubble columns are widely used in chemical and biochemical processes due to their excellent mass and heat transfer characteristics and simple construction.However,their fundamental hydrodynamic behaviors,which are ess...Bubble columns are widely used in chemical and biochemical processes due to their excellent mass and heat transfer characteristics and simple construction.However,their fundamental hydrodynamic behaviors,which are essential for reactor scale-up and design,are still not fully understood.To develop design tools for engineering purposes,much research has been carried out in the area of computationalfluid dynamics(CFD)modeling and simulation of gas-liquidflows.Due to the importance of the bubble behavior,the bubble size distribution must be considered in the CFD models.The population balance model(PBM)is an effective approach to predict the bubble size distribution,and great efforts have been made in recent years to couple the PBM into CFD simulations.This article gives a selective review of the modeling and simulation of bubble column reactors using CFD coupled with PBM.Bubble breakup and coalescence models due to different mechanisms are discussed.It is shown that the CFD-PBM coupled model with proper bubble breakup and coalescence models and interphase force formulations has the ability of predicting the complex hydrodynamics in differentflow regimes and,thus,provides a unified description of both the homo-geneous and heterogeneous regimes.Further study is needed to improve the models of bubble coalescence and breakup,turbulence modification in high gas holdup,and interphase forces of bubble swarms.展开更多
The aggregation behavior of submicron-sized particles of praseodymium-doped zirconium silicate, a ceramic pigment, in aqueous suspension was predicted by a modified population balance model, In the model, the collisio...The aggregation behavior of submicron-sized particles of praseodymium-doped zirconium silicate, a ceramic pigment, in aqueous suspension was predicted by a modified population balance model, In the model, the collision frequencies were selected to describe evolution of the particle size distribution of the suspension. The collision efficiency was estimated as a function of interaction potential between particles based on Derjaguin-Landau-Verwey-Overbeek theory. The population balance model was modified to predict the stable state of the aggregation by introducing the volume mean size of aggregate to stability ratio. In addition, aggregation of the particles in aqueous suspension in the presence of sodium dodecyl benzene sulfonate or potassium chloride was experimentally investigated. The predicted data （i.e., the final aggregate size, aggregation rate, and particle size distribution） were similar to the experimentalresults.展开更多
The novel circulating turbulent fluidized bed(CTFB)technology has found wide applications in various processes owing to its high solid circulation rate and low backmixing.However,up to now,only a limited number of CFD...The novel circulating turbulent fluidized bed(CTFB)technology has found wide applications in various processes owing to its high solid circulation rate and low backmixing.However,up to now,only a limited number of CFD simulation studies on this type of reactor can be found in the literature.Moreover,there is currently no guidance available for selecting appropriate subgrid drag models that take into account the impact of mesoscale structures.In this work,a two-fluid model incorporating seven different drag models include homogeneous drag models,filtered models,and EMMS-based drag models was employed to conduct a systematic investigation into the hydrodynamics of CTFB reactors.It was found that the flow structure in the CTFB reactor differs significantly from conventional fast fluidized beds,exhibiting relatively weaker radial heterogeneity and attenuated near-wall particle downward flows.Comparative analysis demonstrates that the homogeneous drag models fail to predict reasonable hydrodynamics consistent with the experiments.In contrast,the mesoscale drag models show satisfactory performance in reproducing solid concentration profiles,while additional marker variables should be considered in the drag models to enhance the prediction accuracy of particle velocity.The EMMS-based drag model with an advanced conservation equation for cluster size achieves better accuracy in predicting both solid concentration and velocity distributions.Nevertheless,future model development should address wall boundary effects to enhance mesoscale drag applicability in CTFB simulations.展开更多
A dynamic two-zone model is proposed to address the formation of granulation and drying zones in fluidized bed layering granulation processes with internal product classification. The model assumes a constant volume f...A dynamic two-zone model is proposed to address the formation of granulation and drying zones in fluidized bed layering granulation processes with internal product classification. The model assumes a constant volume for the granulation zone, but a variable overall volume for the fluidized bed to account for classified product removal. The model is used to study the effect of various process parameters on dynamics and process stability. Stability is shown to depend on the separation diameter of product removal and the flow rate of the injected liquid. A lower and upper range of separation diameters with stable process behavior are found. In an intermediate range instability in the form of self-sustained oscillations is observed. The lower stability boundary is in qualitative agreement with recent experimental observations （Schmidt, Bück, ＆ Tsotsas, 2015）; the upper boundary was reported in a theoretical paper by Vreman, Van Lare, and Hounslow （2009） based on a single zone model.展开更多
Pigment nanoparticles with a size range of 10~100 nm were produced from large agglomerates via a stirred media mill operating in the wet-batch mode and using polymeric media. The effects of several operating variables...Pigment nanoparticles with a size range of 10~100 nm were produced from large agglomerates via a stirred media mill operating in the wet-batch mode and using polymeric media. The effects of several operating variables such as the surfactant concentration, polystyrene media loading, and media size on the pigment size distribution of the product were studied. The process dynamics was also investigated. Dynamic light scattering and electron microscopy were used as the characterization techniques. The polymeric grinding media are found to be effective for the production of pigment nanoparticles. The experimental results suggest the existence of an optimum media size and surfactant concentration. A population balance model of the process reveals a transition from first-order breakage kinetics for rela-tively coarse particles to non-first-order kinetics, with a delay period, for the smaller particles. The model implies that large agglomerates split in a first-order fashion whereas the breakage of individual nanoparticles may depend on induced fatigue of the particles.展开更多
This paper presents a thorough study of particle impact breakage in selection function with a unified breakage criterion.The impact mode and breakage pattern for particulate materials are classified based on a signifi...This paper presents a thorough study of particle impact breakage in selection function with a unified breakage criterion.The impact mode and breakage pattern for particulate materials are classified based on a significant review of well-established impact testers.It was found that the lack of a unified breakage criterion to determine the breakage probability disables a direct comparison of particle breakage propensity from different impact loading testers.The literature breakage models to describe the breakage probability are reviewed where the advantage and drawback of these models are scrutinized.The sourced literature breakage models are compared with the zeolite breakage datasets in a unified breakage criterion to evaluate the model performance.A novel computational modelling workflow for a milling process is proposed to provide a guidance in implementing the digital twin in milling process prediction.The breakage probability models,i.e.the selection functions are comprehensively assessed in population balance model to examine the model serviceability.The model simplicity and fidelity in the model assessment are specifically discussed and the value of digital twin in substantially reducing the experimental trials is highlighted.展开更多
Operating conditions strongly affect the yield and quality of polysilicon in a polysilicon fluidized bed.In this study,a new model of polysilicon fluidized bed was established using the Euler-Euler model coupled with ...Operating conditions strongly affect the yield and quality of polysilicon in a polysilicon fluidized bed.In this study,a new model of polysilicon fluidized bed was established using the Euler-Euler model coupled with population balance model(PBM),which was combined with fluid flow,heat,and mass transfer models,while considering the scavenging effect of silicon fines.The effects of different operating conditions on the deposition and formation rates of silicon fines were investigated.Results show that the model can correctly describe the particle growth process in the fluidized bed of polysilicon.The silicon fines and the interphase velocity difference show"N"-and"M"-shaped distributions along the axial direction,respectively.The particle temperature and concentration near the wall are higher than those in the central region.The decomposition of silane in the bottom region of the bed is dominated by het-erogeneous deposition.The scavenging of silicon fines occurs in the dilute-phase region.The effects of operating conditions,i.e.inlet gas temperature,silane composition,and gas velocity,on the reactor performance were also explored comprehensively.Increasing the inlet gas composition and velocity enhances the formation rates of solid silicon and fines.Increasing the inlet gas temperature promotes the growth of solid silicon and inhibits the formation of silicon fines.High fluidization ratio,low inlet silane concentration,and high inlet gas temperature enhance the selectivity of silicon growth.展开更多
Aggregation of fine ash into larger particles benefits fly ash removal in an electrostatic precipitator.Thermal aggregation,turbulent aggregation,and electrical aggregation of fine ash (derived from co-firing of bioma...Aggregation of fine ash into larger particles benefits fly ash removal in an electrostatic precipitator.Thermal aggregation,turbulent aggregation,and electrical aggregation of fine ash (derived from co-firing of biomass fuel and anthracite coal) was simulated under different conditions in an electrostatic precipitator.A population balance model and user-defined function in Fluent were assumed to obtain aggregation kernel functions and calculate the aggregation effects on the co-combusted particles.The results show that electrical aggregation had an obvious effect on both micron-and submicron-sized particles.For submicron particles,the effect of thermal aggregation is about ten times greater than turbulent aggregation.Meanwhile,for micron-sized particles,turbulent aggregation is about seven times greater than thermal aggregation.Therefore,particle aggregation in the electrostatic precipitator mainly occurs because of electrical aggregation,supplemented by thermal aggregation and turbulent aggregation.When the flow velocity is 1.0 m/s,particle volume fraction is 1.4%,and biomass co-firing ratio is 10%,the effects of all three aggregation processes on ash particles are optimized.展开更多
The technique state to design counter-current extraction columns is based on the performance of pilot plant experiments. The modelling is then either with the equilibrium or dispersion model, whereas in the latter the...The technique state to design counter-current extraction columns is based on the performance of pilot plant experiments. The modelling is then either with the equilibrium or dispersion model, whereas in the latter the dispersion coefficient accounts for all hydrodynamic non-idealities. A new approach uses single droplet experiments to obtain the basic laws and functions governing droplet breakage, coalescence, relative velocity, and axial dispersion when using droplet populance balance models （DPBM）. The hydrodynamics simulation results show that the mean Sauter diameter, hold-up, and concentration profiles could be well predicted, which promotes the use of DPBM models for further applications in industrial scale.展开更多
基金Supported by the National Natural Science Foundation of China(91634101)The Project of Construction of Innovative TeamsTeacher Career Development for Universities and Colleges under Beijing Municipality(IDHT20180508)
文摘In this study,based on the Luo bubble coalescence model,a model correction factor C_e for pressures according to the literature experimental results was introduced in the bubble coalescence efficiency term.Then,a coupled modified population balance model(PBM) with computational fluid dynamics(CFD) was used to simulate a high-pressure bubble column.The simulation results with and without C_e were compared with the experimental data.The modified CFD-PBM coupled model was used to investigate its applicability to broader experimental conditions.These results showed that the modified CFD-PBM coupled model can predict the hydrodynamic behaviors under various operating conditions.
文摘On the basis of population balance a mathematical model is developed to describe the formation of polymer particle in styrene suspension polymerization. The characteristics of coalescence and breakage of droplets and the gel effect are analyzed in particular. Parameters of the models are estimated by experimental data on reaction conversion and particle size distribution. The results show that the model is suitable for predicting polymerization processes.
基金supported by the National Natural Science Foundation of China(grant Nos.U2330204 and 52025063)the German Research Foundation(DFG)within the research group 2284(project No.262219004).
文摘A new multivariate population balance modeling for the homogenous nucleation from bismuth vapor is tested against experimental results. However, the small differences of some key parameters could lead to the ill-posed problem, such as the surface tension. In this study, the parameter fluctuations set according to the response surface method are employed in the population balance simulation to identify their importance. Subsequently, the quadratic polynomials are established to replace the simulation and the fluctuations are evaluated with the characteristic parameters of particle evolution. It is found that the surface tension tends to be the most significant factor determining the particle evolution, which is also influenced by the coefficient in condensation rates and fractal dimension in the coagulation. To get more accurate modeling and key parameters, the comprehensive sum of mean square error is calculated based on all the fluctuations and the appropriate value for the surface tension is 0.466 N/m.
基金funded by Sichuan Natural Science Foundation Outstanding Youth Science Foundation(No.2024NSFJQ0012)Key project of Regional Innovation and Development Joint Fund of National Natural Science Foundation(No.U23A20669)Sichuan Science and Technology Program(2022ZDZX0041).
文摘In multiphase pumps transporting gas-liquid two-phase flows,the high-speed rotation of the impeller induces complex deformations in bubble shapes within the flow domain,making the prediction of gasliquid two-phase drag forces highly challenging in numerical simulations.To achieve precise prediction of the drag forces on irregular bubbles within multiphase pumps,this study modifies the existing bubble drag force model and applies the revised model to the prediction of gas-liquid two-phase flow within multiphase pumps.The research findings indicate that the modified drag force model significantly enhances the accuracy of predicting flow characteristics within the pump,particularly under high gas volume fraction conditions.The simulation results for gas phase distribution and vorticity exhibit strong agreement with experimental data.The modified drag model better captures the accumulation of the gas phase at the suction side of the impeller outlet.It also accurately predicts the vortex characteristics induced by bubble backflow from the trailing edges of the diffuser.Additionally,the adjustment of the drag coefficient enhances the model’s ability to represent local flow field characteristics,thereby optimizing the performance simulation methods of multiphase pumps.Compared to traditional drag force models,the modified model reduces prediction errors in head and efficiency by 36.4%and 27.5%,respectively.These results provide important theoretical foundations and model support for improving the accuracy of gas-liquid two-phase flow simulations and optimizing the design of multiphase pumps under high gas volume fraction conditions.
文摘It is the fact that several process parameters are either unknown or uncertain. Therefore, an optimal control, profile calculated with developed process models with respect to such process parameters may not give an optimal performance when implemented to real processes. This study proposes a batch-to-batch optimization strategy for the estimation of uncertain kinetic.par.ameters in a batch crystallization process of potassium sulfate production. The knowledge of a crystal size distribution of the product at the end of batch operation is used in the proposed methodology. The updated kinetic parameters are applied for determining an optimal operating temperature policy for the next batch run.
基金Project(51174032)supported by the National Natural Science Foundation of ChinaProject(NCET-10-0225)supported by the Program for New Century Excellent Talents in University,ChinaProject(FRF-TP-09-001A)supported by the Fundamental Research Funds for the Central Universities,China
文摘Rapid dewatering and thickening of whole-tailings with ultrafine particles is one of the most important processes for the whole-tailings paste preparation. Deep-cone thickener, a kind of such process for the flocculation and settling of whole-tailings, is particularly necessary to study. However, there exist many problems in observing the flocculation and settling process of whole-tailings, as well as the particle size distribution(PSD) of whole-tailings floccules in deep-cone thickener. Population balance model(PBM) is applied to predict the PSD in deep-cone thickener, and LUO model and GHADIRI model are employed to study the aggregation and fragmentation mechanism of the whole-tailings particles, respectively. Through three-dimensional numerical simulation on the whole-tailings flocculation and settling in deep-cone thickener using computational fluid dynamics(CFD)-PBM, the distribution of density and turbulent kinetic energy in deep-cone thickener were obtained, at the same time the spatio-temporal changes of whole-tailings floccules particle size distribution are analyzed. Finally, the major flocculation position in deep-cone thickener is found and the flocculation settling rules of whole-tailings are achieved.
基金Financial support from the National Natural Science Foundation of China(51076043 and 51061130538)Program for New Century Excellent Talents in University(NCET-09-0342)+1 种基金Central Universities(12QN02)111 Project(B12034)
文摘The computational fluid dynamics （CFD）-population balance equations （PBE） coupled model is employed to investigate the hydrodynamics in a gas-slurry internal loop reactor with external slurry circulation. The predicted radial profiles of local gas holdup and bubble diameter are in good agreement with the corresponding experimental data. The spatio-temporal velocity profile of the gas phase reveals that the upward movement of gas is slowed down and the residence time of gas is prolonged by the downward momentum of the slurry, introduction of the external slurry can greatly improve the uniformity of gas holdup distribution in the reactor, especially in the downcomer-tube action region. Moreover, the interaction between the downward slurry and upward gas can lead to small bubble size and high interfacial area as well as good mass and heat transfer. The above results suggest the function of external slurry circulation for the internal loop reactor and would be helpful for optimizing the design and scale up of reactors.
文摘Thickeners are important units for water recovery in various industries. In this study, a semi-industrial pilot plant thickener similar to the tailing thickener of the Sarcheshmeh Copper Mine was simulated by CFD modeling. The population balance was used to describe the particle aggregation and breakup. In this population balance, 15 particle sizes categories were considered. The Eulerian-Eulerian approach with standard k-e turbulence model was applied to describe two phases of slurry flow in the thickener under steady-state condition. The simulation results have been compared with the experimental measurements to validate the accuracy of the CFD modeling. After checking the numerical results, the effect of important parameters such as, feed flow rate, solid percentage in the feed, and solid particle size on the thickener performance was studied. The thickener residence time distribution were obtained by the modeling and also compared with the experimental data. Finally, the effects of feedwell feeding on the average diameter of aggregate and turbulent intensity were evaluated.
基金supported in part by the National Natural Science Foundation of China(61633006)the Fundamental Research Funds for the Central Universities of China(DUT2018TB06)National Key Research and Development Program of China(2017YFA0700300)。
文摘In this paper,a cell average technique(CAT)based parameter estimation method is proposed for cooling crystallization involved with particle growth,aggregation and breakage,by establishing a more efficient and accurate solution in terms of the automatic differentiation(AD)algorithm.To overcome the deficiency of CAT that demands high computation cost for implementation,a set of ordinary differential equations(ODEs)entailed from CAT based discretized population balance equation(PBE)are solved by using the AD based high-order Taylor expansion.Moreover,an AD based trust-region reflective(TRR)algorithm and another interior-point(IP)algorithm are established for estimating the kinetic parameters associated with particle growth,aggregation and breakage.As a result,the estimation accuracy can be further improved while the computation cost can be significantly reduced,compared to the existing algorithms.Benchmark examples from the literature are used to illustrate the accuracy and efficiency of the AD-based CAT,TRR and IP algorithms in comparison with the existing algorithms.Moreover,seeded batch cooling crystallization experiments ofβform L-glutamic acid are performed to validate the proposed method.
基金gratefully acknowledged the financial supports by the National Natural Science Foundation of China(Grant No.20606021)Foundation for the Author of National Excellent Doctoral Dissertation of China(No.200757)the State Key Development Program for Basic Research Project of China(Grant No.2007CB714302).
文摘Bubble columns are widely used in chemical and biochemical processes due to their excellent mass and heat transfer characteristics and simple construction.However,their fundamental hydrodynamic behaviors,which are essential for reactor scale-up and design,are still not fully understood.To develop design tools for engineering purposes,much research has been carried out in the area of computationalfluid dynamics(CFD)modeling and simulation of gas-liquidflows.Due to the importance of the bubble behavior,the bubble size distribution must be considered in the CFD models.The population balance model(PBM)is an effective approach to predict the bubble size distribution,and great efforts have been made in recent years to couple the PBM into CFD simulations.This article gives a selective review of the modeling and simulation of bubble column reactors using CFD coupled with PBM.Bubble breakup and coalescence models due to different mechanisms are discussed.It is shown that the CFD-PBM coupled model with proper bubble breakup and coalescence models and interphase force formulations has the ability of predicting the complex hydrodynamics in differentflow regimes and,thus,provides a unified description of both the homo-geneous and heterogeneous regimes.Further study is needed to improve the models of bubble coalescence and breakup,turbulence modification in high gas holdup,and interphase forces of bubble swarms.
文摘The aggregation behavior of submicron-sized particles of praseodymium-doped zirconium silicate, a ceramic pigment, in aqueous suspension was predicted by a modified population balance model, In the model, the collision frequencies were selected to describe evolution of the particle size distribution of the suspension. The collision efficiency was estimated as a function of interaction potential between particles based on Derjaguin-Landau-Verwey-Overbeek theory. The population balance model was modified to predict the stable state of the aggregation by introducing the volume mean size of aggregate to stability ratio. In addition, aggregation of the particles in aqueous suspension in the presence of sodium dodecyl benzene sulfonate or potassium chloride was experimentally investigated. The predicted data （i.e., the final aggregate size, aggregation rate, and particle size distribution） were similar to the experimentalresults.
基金supported by the“Low-carbon transformation technologies and demonstrations in chemical engineering and metallurgical processing”,Strategic Priority Research Program of the Chinese Academy of Sciences(grant No.XDA0390501)the National Natural Science Foundation of China(grant Nos.22378396,22008240)+1 种基金the Youth Innovation Promotion Association of the Chinese Academy of Sciences(grant No.2022046)the Fund of State Key Laboratory of Mesoscience and Engineering(grant No.Meso-23-A02).
文摘The novel circulating turbulent fluidized bed(CTFB)technology has found wide applications in various processes owing to its high solid circulation rate and low backmixing.However,up to now,only a limited number of CFD simulation studies on this type of reactor can be found in the literature.Moreover,there is currently no guidance available for selecting appropriate subgrid drag models that take into account the impact of mesoscale structures.In this work,a two-fluid model incorporating seven different drag models include homogeneous drag models,filtered models,and EMMS-based drag models was employed to conduct a systematic investigation into the hydrodynamics of CTFB reactors.It was found that the flow structure in the CTFB reactor differs significantly from conventional fast fluidized beds,exhibiting relatively weaker radial heterogeneity and attenuated near-wall particle downward flows.Comparative analysis demonstrates that the homogeneous drag models fail to predict reasonable hydrodynamics consistent with the experiments.In contrast,the mesoscale drag models show satisfactory performance in reproducing solid concentration profiles,while additional marker variables should be considered in the drag models to enhance the prediction accuracy of particle velocity.The EMMS-based drag model with an advanced conservation equation for cluster size achieves better accuracy in predicting both solid concentration and velocity distributions.Nevertheless,future model development should address wall boundary effects to enhance mesoscale drag applicability in CTFB simulations.
文摘A dynamic two-zone model is proposed to address the formation of granulation and drying zones in fluidized bed layering granulation processes with internal product classification. The model assumes a constant volume for the granulation zone, but a variable overall volume for the fluidized bed to account for classified product removal. The model is used to study the effect of various process parameters on dynamics and process stability. Stability is shown to depend on the separation diameter of product removal and the flow rate of the injected liquid. A lower and upper range of separation diameters with stable process behavior are found. In an intermediate range instability in the form of self-sustained oscillations is observed. The lower stability boundary is in qualitative agreement with recent experimental observations （Schmidt, Bück, ＆ Tsotsas, 2015）; the upper boundary was reported in a theoretical paper by Vreman, Van Lare, and Hounslow （2009） based on a single zone model.
文摘Pigment nanoparticles with a size range of 10~100 nm were produced from large agglomerates via a stirred media mill operating in the wet-batch mode and using polymeric media. The effects of several operating variables such as the surfactant concentration, polystyrene media loading, and media size on the pigment size distribution of the product were studied. The process dynamics was also investigated. Dynamic light scattering and electron microscopy were used as the characterization techniques. The polymeric grinding media are found to be effective for the production of pigment nanoparticles. The experimental results suggest the existence of an optimum media size and surfactant concentration. A population balance model of the process reveals a transition from first-order breakage kinetics for rela-tively coarse particles to non-first-order kinetics, with a delay period, for the smaller particles. The model implies that large agglomerates split in a first-order fashion whereas the breakage of individual nanoparticles may depend on induced fatigue of the particles.
基金The corresponding author would like to acknowledge the startupfunding from University College Cork.The authors appreciate many helpful discussions with Dr.Jianfeng Lifrom Process Systems Enterprise,New Jersey Office,USA.
文摘This paper presents a thorough study of particle impact breakage in selection function with a unified breakage criterion.The impact mode and breakage pattern for particulate materials are classified based on a significant review of well-established impact testers.It was found that the lack of a unified breakage criterion to determine the breakage probability disables a direct comparison of particle breakage propensity from different impact loading testers.The literature breakage models to describe the breakage probability are reviewed where the advantage and drawback of these models are scrutinized.The sourced literature breakage models are compared with the zeolite breakage datasets in a unified breakage criterion to evaluate the model performance.A novel computational modelling workflow for a milling process is proposed to provide a guidance in implementing the digital twin in milling process prediction.The breakage probability models,i.e.the selection functions are comprehensively assessed in population balance model to examine the model serviceability.The model simplicity and fidelity in the model assessment are specifically discussed and the value of digital twin in substantially reducing the experimental trials is highlighted.
基金support by the Science and Technology Planning Project of the Science and Technology Department of Yunnan Province (grant No.202002AB080002 and 202202AB080014).
文摘Operating conditions strongly affect the yield and quality of polysilicon in a polysilicon fluidized bed.In this study,a new model of polysilicon fluidized bed was established using the Euler-Euler model coupled with population balance model(PBM),which was combined with fluid flow,heat,and mass transfer models,while considering the scavenging effect of silicon fines.The effects of different operating conditions on the deposition and formation rates of silicon fines were investigated.Results show that the model can correctly describe the particle growth process in the fluidized bed of polysilicon.The silicon fines and the interphase velocity difference show"N"-and"M"-shaped distributions along the axial direction,respectively.The particle temperature and concentration near the wall are higher than those in the central region.The decomposition of silane in the bottom region of the bed is dominated by het-erogeneous deposition.The scavenging of silicon fines occurs in the dilute-phase region.The effects of operating conditions,i.e.inlet gas temperature,silane composition,and gas velocity,on the reactor performance were also explored comprehensively.Increasing the inlet gas composition and velocity enhances the formation rates of solid silicon and fines.Increasing the inlet gas temperature promotes the growth of solid silicon and inhibits the formation of silicon fines.High fluidization ratio,low inlet silane concentration,and high inlet gas temperature enhance the selectivity of silicon growth.
基金the National Natural Science Foundation of China(Grant No.51376063).
文摘Aggregation of fine ash into larger particles benefits fly ash removal in an electrostatic precipitator.Thermal aggregation,turbulent aggregation,and electrical aggregation of fine ash (derived from co-firing of biomass fuel and anthracite coal) was simulated under different conditions in an electrostatic precipitator.A population balance model and user-defined function in Fluent were assumed to obtain aggregation kernel functions and calculate the aggregation effects on the co-combusted particles.The results show that electrical aggregation had an obvious effect on both micron-and submicron-sized particles.For submicron particles,the effect of thermal aggregation is about ten times greater than turbulent aggregation.Meanwhile,for micron-sized particles,turbulent aggregation is about seven times greater than thermal aggregation.Therefore,particle aggregation in the electrostatic precipitator mainly occurs because of electrical aggregation,supplemented by thermal aggregation and turbulent aggregation.When the flow velocity is 1.0 m/s,particle volume fraction is 1.4%,and biomass co-firing ratio is 10%,the effects of all three aggregation processes on ash particles are optimized.
基金Supported by the AiF (Arbeitsgemeinschaft Industrieller Forschungsvereinigungen, "Otto von Guericke" e.V.), the BMWA (Bundesministerium für Wirtschaft und Arbeit) and the DFG (Deutsche Forschungsgemeinschaft)
文摘The technique state to design counter-current extraction columns is based on the performance of pilot plant experiments. The modelling is then either with the equilibrium or dispersion model, whereas in the latter the dispersion coefficient accounts for all hydrodynamic non-idealities. A new approach uses single droplet experiments to obtain the basic laws and functions governing droplet breakage, coalescence, relative velocity, and axial dispersion when using droplet populance balance models （DPBM）. The hydrodynamics simulation results show that the mean Sauter diameter, hold-up, and concentration profiles could be well predicted, which promotes the use of DPBM models for further applications in industrial scale.
