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
In this paper,we derive rigorously a non-local cross-diffusion system from an interacting stochastic many-particle system in the whole space.The convergence is proved in the sense of probability by introducing an inte...In this paper,we derive rigorously a non-local cross-diffusion system from an interacting stochastic many-particle system in the whole space.The convergence is proved in the sense of probability by introducing an intermediate particle system with a mollified interaction potential,where the mollification is of algebraic scaling.The main idea of the proof is to study the time evolution of a stopped process and obtain a Gronwall type estimate by using Taylor's expansion around the limiting stochastic process.展开更多
The breakage of brittle particulate materials into smaller particles under compressive or impact loads can be modelled as an instantiation of the population balance integro-differential equation.In this paper,the emer...The breakage of brittle particulate materials into smaller particles under compressive or impact loads can be modelled as an instantiation of the population balance integro-differential equation.In this paper,the emerging computational science paradigm of physics-informed neural networks is studied for the first time for solving both linear and nonlinear variants of the governing dynamics.Unlike conventional methods,the proposed neural network provides rapid simulations of arbitrarily high resolution in particle size,predicting values on arbitrarily fine grids without the need for model retraining.The network is assigned a simple multi-head architecture tailored to uphold monotonicity of the modelled cumulative distribution function over particle sizes.The method is theoretically analyzed and validated against analytical results before being applied to real-world data of a batch grinding mill.The agreement between laboratory data and numerical simulation encourages the use of physics-informed neural nets for optimal planning and control of industrial comminution processes.展开更多
Fluent version 6.2 computational fluid dynamics environment has been enhanced with a population balance capability that operates in conjunction with its multiphase calculations to predict the particle size distributio...Fluent version 6.2 computational fluid dynamics environment has been enhanced with a population balance capability that operates in conjunction with its multiphase calculations to predict the particle size distribution within the flow field. The population balance is solved by the quadrature method of moments （QMOM）. Fluent＇s prediction capabilities are tested by using a 2-dimensional analogy of a constantly stirred tank reactor with a fluid flow compartment that mixes the fluid quickly and efficiently using wall movement and has a feed stream and a product stream. The results of these Fluent simulations using QMOM population balance solver are compared to steady state analytical solutions for the population balance in a stirred tank where 1） growth, 2） aggregation, and 3） breakage, take place separately and 4） combined nucleation and growth and 5） combined nucleation, growth and aggregation take place. The results of these comparisons show that the moments of the population balance are accurately predicted for nucleation, growth, aggregation and breakage when the flow field is turbulent. With laminar flow the mixing is not ideal and as a result the steady state well mixed solutions are not accurately simulated.展开更多
For many processes of industrial significance, due to the strong coupling between particle interactions and fluid dynamics, the population balance must be solved as part of a computational fluid dynamics （CFD） simul...For many processes of industrial significance, due to the strong coupling between particle interactions and fluid dynamics, the population balance must be solved as part of a computational fluid dynamics （CFD） simulation. In this work, a CFD based population balance model is tested using a batch crystallization reactor. In this CFD model, the population balance is solved by the standard method of moments （SMOM） and the quadrature method of moments （QMOM）. The results of these simulations are compared to analytical solutions for the population balance in a batch tank where 1） nucleation, 2） growth, 3） aggregation, and 4） breakage are taking place separately. The results of these comparisons show that the first 6 moments of the population balance are accurately predicted for nucleation, growth, aggregation and breakage at all times.展开更多
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funding from the European Research Council (ERC)under the European Union's Horizon 2020 research and innovation programme,ERC Advanced Grant No.101018153support from the Austrian Science Fund (FWF) (Grants P33010,F65)supported by the NSFC (Grant No.12101305).
文摘In this paper,we derive rigorously a non-local cross-diffusion system from an interacting stochastic many-particle system in the whole space.The convergence is proved in the sense of probability by introducing an intermediate particle system with a mollified interaction potential,where the mollification is of algebraic scaling.The main idea of the proof is to study the time evolution of a stopped process and obtain a Gronwall type estimate by using Taylor's expansion around the limiting stochastic process.
基金supported in part by the Ramanujan Fellowship from the Science and Engineering Research Board,Government of India(Grant No.RJF/2022/000115)。
文摘The breakage of brittle particulate materials into smaller particles under compressive or impact loads can be modelled as an instantiation of the population balance integro-differential equation.In this paper,the emerging computational science paradigm of physics-informed neural networks is studied for the first time for solving both linear and nonlinear variants of the governing dynamics.Unlike conventional methods,the proposed neural network provides rapid simulations of arbitrarily high resolution in particle size,predicting values on arbitrarily fine grids without the need for model retraining.The network is assigned a simple multi-head architecture tailored to uphold monotonicity of the modelled cumulative distribution function over particle sizes.The method is theoretically analyzed and validated against analytical results before being applied to real-world data of a batch grinding mill.The agreement between laboratory data and numerical simulation encourages the use of physics-informed neural nets for optimal planning and control of industrial comminution processes.
文摘Fluent version 6.2 computational fluid dynamics environment has been enhanced with a population balance capability that operates in conjunction with its multiphase calculations to predict the particle size distribution within the flow field. The population balance is solved by the quadrature method of moments （QMOM）. Fluent＇s prediction capabilities are tested by using a 2-dimensional analogy of a constantly stirred tank reactor with a fluid flow compartment that mixes the fluid quickly and efficiently using wall movement and has a feed stream and a product stream. The results of these Fluent simulations using QMOM population balance solver are compared to steady state analytical solutions for the population balance in a stirred tank where 1） growth, 2） aggregation, and 3） breakage, take place separately and 4） combined nucleation and growth and 5） combined nucleation, growth and aggregation take place. The results of these comparisons show that the moments of the population balance are accurately predicted for nucleation, growth, aggregation and breakage when the flow field is turbulent. With laminar flow the mixing is not ideal and as a result the steady state well mixed solutions are not accurately simulated.
文摘For many processes of industrial significance, due to the strong coupling between particle interactions and fluid dynamics, the population balance must be solved as part of a computational fluid dynamics （CFD） simulation. In this work, a CFD based population balance model is tested using a batch crystallization reactor. In this CFD model, the population balance is solved by the standard method of moments （SMOM） and the quadrature method of moments （QMOM）. The results of these simulations are compared to analytical solutions for the population balance in a batch tank where 1） nucleation, 2） growth, 3） aggregation, and 4） breakage are taking place separately. The results of these comparisons show that the first 6 moments of the population balance are accurately predicted for nucleation, growth, aggregation and breakage at all times.
