Elliptical tanks were used as an alternative to circular tanks in order to improve mixing efficiency and reduce mixing time in unbaffled stirred tanks(USTs). Five different aspect ratios of elliptical vessels were des...Elliptical tanks were used as an alternative to circular tanks in order to improve mixing efficiency and reduce mixing time in unbaffled stirred tanks(USTs). Five different aspect ratios of elliptical vessels were designed to compare their mixing time and flow field. Computational fluid dynamics(CFD) simulations were performed using the k–ε model to calculate the mixing time and simulate turbulent flow field features, such as streamline shape, velocity distribution, vortex core region distribution, and turbulent kinetic energy(TKE) transfer. Visualization was also carried out to track the tinctorial evolution of the liquid phase. Results reveal that elliptical stirred tanks can significantly improve mixing performance in USTs. Specifically, the mixing time at an aspect ratio of 2.00 is only 45.3% of the one of a circular stirred tank. Furthermore, the secondary flow is strengthened and the vortex core region increases with the increase of aspect ratio. The axial velocity is more sensitive to the aspect ratio than the circumferential and radial velocity. Additionally, the TKE transfer in elliptical vessels is altered. These findings suggest that elliptical vessels offer a promising alternative to circular vessels for enhancing mixing performance in USTs.展开更多
Efficiently modulating the velocity distribution and flow pattern of non-Newtonian fluids is a critical challenge in the context of dual shaft eccentric mixers for process intensification,posing a significant barrier ...Efficiently modulating the velocity distribution and flow pattern of non-Newtonian fluids is a critical challenge in the context of dual shaft eccentric mixers for process intensification,posing a significant barrier for the existing technologies.Accordingly,this work reports a convenient strategy that changes the kinetic energy to controllably regulate the flow patterns from radial flow to axial flow.Results showed that the desired velocity distribution and flow patterns could be effectively obtained by varying the number and structure of baffles to change kinetic energy,and a more uniform velocity distribution,which could not be reached normally in standard baffle dual shaft mixers,was easily obtained.Furthermore,a comparative analysis of velocity and shear rate distributions is employed to elucidate the mechanism behind the generation of flow patterns in various dual-shaft eccentric mixers.Importantly,there is little difference in the power number of the laminar flow at the same Reynolds number,meaning that the baffle type has no effect on the power consumption,while the power number of both unbaffle and U-shaped baffle mixing systems decreases compared with the standard baffle mixing system in the transition flow.Finally,at the same rotational condition,the dimensionless mixing time of the U-shaped baffle mixing system is 15.3%and 7.9%shorter than that of the standard baffle and the unbaffle mixing system,respectively,which shows the advantage of the U-shaped baffle in stirring rate.展开更多
Large eddy simulations (LES) of mixing process in a stirred tank of 0.476m diameter with a 3-narrow blade hydrofoil CBY impeller were reported. The turbulent flow field and mixing time were calculated using LES with S...Large eddy simulations (LES) of mixing process in a stirred tank of 0.476m diameter with a 3-narrow blade hydrofoil CBY impeller were reported. The turbulent flow field and mixing time were calculated using LES with Sma-gorinsky-Lilly subgrid scale model. The impeller rotation was modeled using the sliding mesh technique. Better agree-ment of power demand and mixing time was obtained between the experimental and the LES prediction than that by the traditional Reynolds-averaged Navier-Stokes (RANS) approach. The curve of tracer response predicted by LES was in good agreement with the experimental. The results show that LES is a reliable tool to investigate the unsteady and quasi-periodic behavior of the turbulent flow in stirred tanks.展开更多
Based on the two-phase fluid （Eulerian-Eulerian） model, a mathematical model about the gas-liquid flow and mixing behavior was developed to investigate the effect of the offset of dual plugs, the included angle of d...Based on the two-phase fluid （Eulerian-Eulerian） model, a mathematical model about the gas-liquid flow and mixing behavior was developed to investigate the effect of the offset of dual plugs, the included angle of dual plugs with a center point, and gas flow rate on the mixing time in a ladle with dual plugs. Numerical results indicate that two types of recirculation zones exist in the ladle. One is the middle recirculation between gas and liquid plumes, and the other is the sidewall recirculation between plumes and the ladle sidewall. The correction shows that the mixing time is in proportion to -0.2676 power of gas flow rate. There is a unique optimum offset of dual plugs with a particular included angle, in turn, a unique optimum included angle of dual plugs exits with a particular offset.展开更多
Peirce-Smith copper converting involves complex multiphase flow and mixing.In this work,the flow zone distribution and mixing time in a Peirce-Smith copper converter were investigated in a 1:5 scaled cold model.Flow f...Peirce-Smith copper converting involves complex multiphase flow and mixing.In this work,the flow zone distribution and mixing time in a Peirce-Smith copper converter were investigated in a 1:5 scaled cold model.Flow field distribution,including dead,splashing,and strong-loop zones,were measured,and a dimensionless equation was established to determine the correlation of the effects of stirring and mixing energy with an error of<5%.Four positions in the bath,namely,injection,splashing,strong-loop,and dead zones,were selected to add a hollow salt powder tracer and measure the mixing time.Injecting a quartz flux through tuyeres or into the backflow point of the splashing wave through a chute was recommended instead of adding it through a crane hopper from the top of the furnace to improve the slag-making reaction.展开更多
The Issue of mixing efficiency in agitated tanks has drawn serious concern in many industrial processes. The turbulence model is very critical to predicting mixing process in agitated tanks. On the basis of computatio...The Issue of mixing efficiency in agitated tanks has drawn serious concern in many industrial processes. The turbulence model is very critical to predicting mixing process in agitated tanks. On the basis of computational fluid dynamics（CFD） software package Fluent 6.2, the mixing characteristics in a tank agitated by dual six-blade-Rushton-turbines（6-DT） are predicted using the detached eddy simulation（DES） method. A sliding mesh（SM） approach is adopted to solve the rotation of the impeller. The simulated flow patterns and liquid velocities in the agitated tank are verified by experimental data in the literature. The simulation results indicate that the DES method can obtain more flow details than Reynolds-averaged Navier-Stokes（RANS） model. Local and global mixing time in the agitated tank is predicted by solving a tracer concentration scalar transport equation. The simulated results show that feeding points have great influence on mixing process and mixing time. Mixing efficiency is the highest for the feeding point at location of midway of the two impellers. Two methods are used to determine global mixing time and get close result. Dimensionless global mixing time remains unchanged with increasing of impeller speed. Parallel, merging and diverging flow pattern form in the agitated tank, respectively, by changing the impeller spacing and clearance of lower impeller from the bottom of the tank. The global mixing time is the shortest for the merging flow, followed by diverging flow, and the longest for parallel flow. The research presents helpful references for design, optimization and scale-up of agitated tanks with multi-impeller.展开更多
The mixing time of impact zone in liquid-continuous impinging streams reactor(LISR) is theoretically calculated by empirical model and modern micromixing model of the fluid mixing process, and the variation laws of ma...The mixing time of impact zone in liquid-continuous impinging streams reactor(LISR) is theoretically calculated by empirical model and modern micromixing model of the fluid mixing process, and the variation laws of macromixing time and micromixing time are quantitatively discussed. The results show that under a continuous and stable operating condition, as the paddle speed increases, the macromixing time and micromixing time calculated by the two models both decrease, even in a linkage equilibrium state. Simultaneously, as the paddle speed increases, the results figured by the two models tend to be consistent. It indicates that two models both are more suitable for calculation of mixing time in high paddle speed. Compared with the existing experimental results of this type of reactor, the mixing time computed in the speed of 1500 r/min is closer to it. These conclusions can provide an important reference for systematically studying the strengthening mechanism of LISR under continuous mixing conditions.展开更多
This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solve...This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.展开更多
In molten phase metallurgical processes,mixing via gas injection has a vital role in obtaining a homogeneous product.The efficiency of mixing depends on operational variables such as gas flow rate and slag height as w...In molten phase metallurgical processes,mixing via gas injection has a vital role in obtaining a homogeneous product.The efficiency of mixing depends on operational variables such as gas flow rate and slag height as well as physical properties of the molten phases.A numerical simulation is conducted to study the above parameters in the flow behavior of a bottom-blown bath.The molten metal and the slag are modeled by water and oil,respectively.The numerical results,particularly the mixing time,are validated against experimental data.The results show that mixing time increases as the slag height increases and decreases as the density of the slag material increases.The mixing time decreases with an increase in the density of the primary phase;however,it increases as the surface tension between air and water increases.A case with properties close to a real molten metal is also modeled.The performance of the system is influenced by the momentum rather than the dissipative forces.Thus,the effect of the density of the molten phase on the mixing process is more pronounced compared to the effect of the surface tension between the air and the molten phase.展开更多
Glycidyl methacrylate (GMA) was grafted onto poly (lactic acid) (PLA) by melt mixing in internal mixer using dicumyl peroxide (DCP) as an initiator. The results from proton nuclear magnetic resonance (1H-NMR) and Four...Glycidyl methacrylate (GMA) was grafted onto poly (lactic acid) (PLA) by melt mixing in internal mixer using dicumyl peroxide (DCP) as an initiator. The results from proton nuclear magnetic resonance (1H-NMR) and Fourier transform infrared (FTIR) spectroscopy indicated that the grafting reaction of GMA onto PLA took place successfully. The impact strength of PLA-g-GMA was significantly higher than that of pure PLA. The crystallinity of PLA, obtained from differential scanning calorimetry (DSC), decreased after grafting. In order to obtain the optimal mixing conditions, the mixing time was varied into 7, 10 and 14 min. The optimum mixing time of 10 min was found to give the optimum mechanical properties of glycidyl methacrylate grafted poly (lactic acid) (PLA-g- GMA). However, the mixing time played no important role in impact behavior of PLA-g-GMA. In addition, the highest crystallinity was obtained with the PLA-g-GMA prepared with the mixing time of 7 min.展开更多
We study waiting time problems for first-order Markov dependent trials via conditional probability generating functions. Our models involve α frequency cells and β run cells with prescribed quotas and an additional ...We study waiting time problems for first-order Markov dependent trials via conditional probability generating functions. Our models involve α frequency cells and β run cells with prescribed quotas and an additional γ slack cells without quotas. For any given and , in our Model I we determine the waiting time until at least frequency cells and at least run cells reach their quotas. For any given τ ≤ α + β, in our Model II we determine the waiting time until τ cells reach their quotas. Computer algorithms are developed to calculate the distributions, expectations and standard deviations of the waiting time random variables of the two models. Numerical results demonstrate the efficiency of the algorithms.展开更多
This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of suff...This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.展开更多
The mixed l1/H2 optimization problem for MIMO (multiple input-multiple output) discrete-time systems is considered. This problem is formulated as minimizing the l1-norm of a closed-loop transfer matrix while maintaini...The mixed l1/H2 optimization problem for MIMO (multiple input-multiple output) discrete-time systems is considered. This problem is formulated as minimizing the l1-norm of a closed-loop transfer matrix while maintaining the H2-norm of another closed-loop transfer matrix at prescribed level. The continuity property of the optimal value in respect to changes in the H2-norm constraint is studied. The existence of the optimal solutions of mixed l1/H2 problem is proved. Because the solution of the mixed l1/H2 problem is based on the scaled-Q method, it avoids the zero interpolation difficulties. The convergent upper and lower bounds can be obtained by solving a sequence of finite dimensional nonlinear programming for which many efficient numerical optimization algorithms exist.展开更多
Considering that the vehicle routing problem （VRP） with many extended features is widely used in actual life, such as multi-depot, heterogeneous types of vehicles, customer service priority and time windows etc., a ...Considering that the vehicle routing problem （VRP） with many extended features is widely used in actual life, such as multi-depot, heterogeneous types of vehicles, customer service priority and time windows etc., a mathematical model for multi-depot heterogeneous vehicle routing problem with soft time windows （MDHVRPSTW） is established. An improved ant colony optimization （IACO） is proposed for solving this model. First, MDHVRPSTW is transferred into different groups according to the nearest principle, and then the initial route is constructed by the scanning algorithm （SA）. Secondly, genetic operators are introduced, and crossover probability and mutation probability are adaptively adjusted in order to improve the global search ability of the algorithm. Moreover, the smooth mechanism is used to improve the performance of the ant colony optimization （ACO）. Finally, the 3-opt strategy is used to improve the local search ability. The proposed IACO was tested on three new instances that were generated randomly. The experimental results show that IACO is superior to the other three existing algorithms in terms of convergence speed and solution quality. Thus, the proposed method is effective and feasible, and the proposed model is meaningful.展开更多
By establishing equivalent fixed point theorem, the boundary value problems of p Laplace equations with finite time delay are studied. It’s the first time that the functional differential equation is discussed w...By establishing equivalent fixed point theorem, the boundary value problems of p Laplace equations with finite time delay are studied. It’s the first time that the functional differential equation is discussed with p Laplacian. The topological degree and fixed point theorem on cone are used to prove the existence of solution and positive solution. The conditions are all easy to check.展开更多
An optimal dimension-down iterative algorithm （DDIA） is proposed for solving a mixed （continuous/ discrete） transportation network design problem （MNDP）, which is generally expressed as a mathematical programmin...An optimal dimension-down iterative algorithm （DDIA） is proposed for solving a mixed （continuous/ discrete） transportation network design problem （MNDP）, which is generally expressed as a mathematical programming with equilibrium constraints （MPEC）. The upper level of the MNDP aims to optimize the network performance via both the expansion of existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium （UE） model. The idea of the proposed DDIA is to reduce the dimensions of the problem. A group of variables （discrete/continuous） are fixed to altemately optimize another group of variables （continuous/discrete）. Some continuous network design problems （CNDPs） and discrete network design problems （DNDPs） are solved repeatedly until the optimal solution is obtained. A numerical example is given to demonstrate the efficiency of the proposed algorithm.展开更多
A novel chaotic search method is proposed,and a hybrid algorithm combining particle swarm optimization(PSO) with this new method,called CLSPSO,is put forward to solve 14 integer and mixed integer programming problems....A novel chaotic search method is proposed,and a hybrid algorithm combining particle swarm optimization(PSO) with this new method,called CLSPSO,is put forward to solve 14 integer and mixed integer programming problems.The performances of CLSPSO are compared with those of other five hybrid algorithms combining PSO with chaotic search methods.Experimental results indicate that in terms of robustness and final convergence speed,CLSPSO is better than other five algorithms in solving many of these problems.Furthermore,CLSPSO exhibits good performance in solving two high-dimensional problems,and it finds better solutions than the known ones.A performance index(PI) is introduced to fairly compare the above six algorithms,and the obtained values of(PI) in three cases demonstrate that CLSPSO is superior to all the other five algorithms under the same conditions.展开更多
The time dependent vehicle routing problem with time windows（TDVRPTW） is considered. A multi-type ant system（MTAS） algorithm hybridized with the ant colony system（ACS）and the max-min ant system（MMAS） algorithm...The time dependent vehicle routing problem with time windows（TDVRPTW） is considered. A multi-type ant system（MTAS） algorithm hybridized with the ant colony system（ACS）and the max-min ant system（MMAS） algorithms is proposed. This combination absorbs the merits of the two algorithms in solutions construction and optimization separately. In order to improve the efficiency of the insertion procedure, a nearest neighbor selection（NNS） mechanism, an insertion local search procedure and a local optimization procedure are specified in detail. And in order to find a balance between good scouting performance and fast convergence rate, an adaptive pheromone updating strategy is proposed in the MTAS. Computational results confirm the MTAS algorithm＇s good performance with all these strategies on classic vehicle routing problem with time windows（VRPTW） benchmark instances and the TDVRPTW instances, and some better results especially for the number of vehicles and travel times of the best solutions are obtained in comparison with the previous research.展开更多
Without applying any stable element techniques in the mixed methods, two simple generalized mixed element(GME) formulations were derived by combining the minimum potential energy principle and Hellinger–Reissner(H–R...Without applying any stable element techniques in the mixed methods, two simple generalized mixed element(GME) formulations were derived by combining the minimum potential energy principle and Hellinger–Reissner(H–R) variational principle. The main features of the GME formulations are that the common C0-continuous polynomial shape functions for displacement methods are used to express both displacement and stress variables, and the coefficient matrix of these formulations is not only automatically symmetric but also invertible. Hence, the numerical results of the generalized mixed methods based on the GME formulations are stable. Displacement as well as stress results can be obtained directly from the algebraic system for finite element analysis after introducing stress and displacement boundary conditions simultaneously. Numerical examples show that displacement and stress results retain the same accuracy. The results of the noncompatible generalized mixed method proposed herein are more accurate than those of the standard noncompatible displacement method. The noncompatible generalized mixed element is less sensitive to element geometric distortions.展开更多
基金supported by the National Key Research and Development Project(2022YFB3504305,2019YFC1905802)National Natural Science Foundation of China(22078030)+2 种基金Joint Funds of the National Natural Science Foundation of China(U1802255)Key Project of Independent Research Project of State Key Laboratory of Coal Mine Disaster Dynamics and Control(2011DA105287-zd201902)Three Gorges Laboratory Open Fund of Hubei Province(SK211009,SK215001).
文摘Elliptical tanks were used as an alternative to circular tanks in order to improve mixing efficiency and reduce mixing time in unbaffled stirred tanks(USTs). Five different aspect ratios of elliptical vessels were designed to compare their mixing time and flow field. Computational fluid dynamics(CFD) simulations were performed using the k–ε model to calculate the mixing time and simulate turbulent flow field features, such as streamline shape, velocity distribution, vortex core region distribution, and turbulent kinetic energy(TKE) transfer. Visualization was also carried out to track the tinctorial evolution of the liquid phase. Results reveal that elliptical stirred tanks can significantly improve mixing performance in USTs. Specifically, the mixing time at an aspect ratio of 2.00 is only 45.3% of the one of a circular stirred tank. Furthermore, the secondary flow is strengthened and the vortex core region increases with the increase of aspect ratio. The axial velocity is more sensitive to the aspect ratio than the circumferential and radial velocity. Additionally, the TKE transfer in elliptical vessels is altered. These findings suggest that elliptical vessels offer a promising alternative to circular vessels for enhancing mixing performance in USTs.
基金supported by the National Natural Science Foundation of China(22078030,52021004)Natural Science Foundation of Chongqing(2022NSCO-LZX0014)+1 种基金Fundamental Research Funds for the Central Universities(2022CDJQY-005,2023CDJXY-047)National Key Research and Development Project(2022YFC3901204)。
文摘Efficiently modulating the velocity distribution and flow pattern of non-Newtonian fluids is a critical challenge in the context of dual shaft eccentric mixers for process intensification,posing a significant barrier for the existing technologies.Accordingly,this work reports a convenient strategy that changes the kinetic energy to controllably regulate the flow patterns from radial flow to axial flow.Results showed that the desired velocity distribution and flow patterns could be effectively obtained by varying the number and structure of baffles to change kinetic energy,and a more uniform velocity distribution,which could not be reached normally in standard baffle dual shaft mixers,was easily obtained.Furthermore,a comparative analysis of velocity and shear rate distributions is employed to elucidate the mechanism behind the generation of flow patterns in various dual-shaft eccentric mixers.Importantly,there is little difference in the power number of the laminar flow at the same Reynolds number,meaning that the baffle type has no effect on the power consumption,while the power number of both unbaffle and U-shaped baffle mixing systems decreases compared with the standard baffle mixing system in the transition flow.Finally,at the same rotational condition,the dimensionless mixing time of the U-shaped baffle mixing system is 15.3%and 7.9%shorter than that of the standard baffle and the unbaffle mixing system,respectively,which shows the advantage of the U-shaped baffle in stirring rate.
文摘Large eddy simulations (LES) of mixing process in a stirred tank of 0.476m diameter with a 3-narrow blade hydrofoil CBY impeller were reported. The turbulent flow field and mixing time were calculated using LES with Sma-gorinsky-Lilly subgrid scale model. The impeller rotation was modeled using the sliding mesh technique. Better agree-ment of power demand and mixing time was obtained between the experimental and the LES prediction than that by the traditional Reynolds-averaged Navier-Stokes (RANS) approach. The curve of tracer response predicted by LES was in good agreement with the experimental. The results show that LES is a reliable tool to investigate the unsteady and quasi-periodic behavior of the turbulent flow in stirred tanks.
基金supported by the National High-tech Research and Development Program of China (No.2009AA03Z530)the National Natural Science Foundation of China and Shanghai Baosteel (No.50834010)the Key Project of the Ministry of Education of China (No.108036)
文摘Based on the two-phase fluid （Eulerian-Eulerian） model, a mathematical model about the gas-liquid flow and mixing behavior was developed to investigate the effect of the offset of dual plugs, the included angle of dual plugs with a center point, and gas flow rate on the mixing time in a ladle with dual plugs. Numerical results indicate that two types of recirculation zones exist in the ladle. One is the middle recirculation between gas and liquid plumes, and the other is the sidewall recirculation between plumes and the ladle sidewall. The correction shows that the mixing time is in proportion to -0.2676 power of gas flow rate. There is a unique optimum offset of dual plugs with a particular included angle, in turn, a unique optimum included angle of dual plugs exits with a particular offset.
基金This work was financially supported by the National Nat-ural Science Foundation of China(No.51974018)the Guangxi Innovation-Driven Development Project(No.AA18242042-1)the Fundamental Research Funds for the Central Universities(No.FRF-TP-19-016A3).
文摘Peirce-Smith copper converting involves complex multiphase flow and mixing.In this work,the flow zone distribution and mixing time in a Peirce-Smith copper converter were investigated in a 1:5 scaled cold model.Flow field distribution,including dead,splashing,and strong-loop zones,were measured,and a dimensionless equation was established to determine the correlation of the effects of stirring and mixing energy with an error of<5%.Four positions in the bath,namely,injection,splashing,strong-loop,and dead zones,were selected to add a hollow salt powder tracer and measure the mixing time.Injecting a quartz flux through tuyeres or into the backflow point of the splashing wave through a chute was recommended instead of adding it through a crane hopper from the top of the furnace to improve the slag-making reaction.
基金Supported by Key Scientific Research Project of Sichuan Provincial Education Department(Grant No.15ZA0107)Doctor Foundation of Southwest University of Science and Technology(Grant No.11zx7162)
文摘The Issue of mixing efficiency in agitated tanks has drawn serious concern in many industrial processes. The turbulence model is very critical to predicting mixing process in agitated tanks. On the basis of computational fluid dynamics（CFD） software package Fluent 6.2, the mixing characteristics in a tank agitated by dual six-blade-Rushton-turbines（6-DT） are predicted using the detached eddy simulation（DES） method. A sliding mesh（SM） approach is adopted to solve the rotation of the impeller. The simulated flow patterns and liquid velocities in the agitated tank are verified by experimental data in the literature. The simulation results indicate that the DES method can obtain more flow details than Reynolds-averaged Navier-Stokes（RANS） model. Local and global mixing time in the agitated tank is predicted by solving a tracer concentration scalar transport equation. The simulated results show that feeding points have great influence on mixing process and mixing time. Mixing efficiency is the highest for the feeding point at location of midway of the two impellers. Two methods are used to determine global mixing time and get close result. Dimensionless global mixing time remains unchanged with increasing of impeller speed. Parallel, merging and diverging flow pattern form in the agitated tank, respectively, by changing the impeller spacing and clearance of lower impeller from the bottom of the tank. The global mixing time is the shortest for the merging flow, followed by diverging flow, and the longest for parallel flow. The research presents helpful references for design, optimization and scale-up of agitated tanks with multi-impeller.
基金Project(51276131)supported by the National Natural Science Foundation of ChinaProject(ZRZ0316)supported by the Natural Science Foundation of Hubei Province,ChinaProject(2013070104010025)supported by the Morning Glory Project of Wuhan Science and Technology Bureau,China
文摘The mixing time of impact zone in liquid-continuous impinging streams reactor(LISR) is theoretically calculated by empirical model and modern micromixing model of the fluid mixing process, and the variation laws of macromixing time and micromixing time are quantitatively discussed. The results show that under a continuous and stable operating condition, as the paddle speed increases, the macromixing time and micromixing time calculated by the two models both decrease, even in a linkage equilibrium state. Simultaneously, as the paddle speed increases, the results figured by the two models tend to be consistent. It indicates that two models both are more suitable for calculation of mixing time in high paddle speed. Compared with the existing experimental results of this type of reactor, the mixing time computed in the speed of 1500 r/min is closer to it. These conclusions can provide an important reference for systematically studying the strengthening mechanism of LISR under continuous mixing conditions.
基金the National Science and Tech-nology Council,Taiwan for their financial support(Grant Number NSTC 111-2221-E-019-048).
文摘This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.
文摘In molten phase metallurgical processes,mixing via gas injection has a vital role in obtaining a homogeneous product.The efficiency of mixing depends on operational variables such as gas flow rate and slag height as well as physical properties of the molten phases.A numerical simulation is conducted to study the above parameters in the flow behavior of a bottom-blown bath.The molten metal and the slag are modeled by water and oil,respectively.The numerical results,particularly the mixing time,are validated against experimental data.The results show that mixing time increases as the slag height increases and decreases as the density of the slag material increases.The mixing time decreases with an increase in the density of the primary phase;however,it increases as the surface tension between air and water increases.A case with properties close to a real molten metal is also modeled.The performance of the system is influenced by the momentum rather than the dissipative forces.Thus,the effect of the density of the molten phase on the mixing process is more pronounced compared to the effect of the surface tension between the air and the molten phase.
文摘Glycidyl methacrylate (GMA) was grafted onto poly (lactic acid) (PLA) by melt mixing in internal mixer using dicumyl peroxide (DCP) as an initiator. The results from proton nuclear magnetic resonance (1H-NMR) and Fourier transform infrared (FTIR) spectroscopy indicated that the grafting reaction of GMA onto PLA took place successfully. The impact strength of PLA-g-GMA was significantly higher than that of pure PLA. The crystallinity of PLA, obtained from differential scanning calorimetry (DSC), decreased after grafting. In order to obtain the optimal mixing conditions, the mixing time was varied into 7, 10 and 14 min. The optimum mixing time of 10 min was found to give the optimum mechanical properties of glycidyl methacrylate grafted poly (lactic acid) (PLA-g- GMA). However, the mixing time played no important role in impact behavior of PLA-g-GMA. In addition, the highest crystallinity was obtained with the PLA-g-GMA prepared with the mixing time of 7 min.
文摘We study waiting time problems for first-order Markov dependent trials via conditional probability generating functions. Our models involve α frequency cells and β run cells with prescribed quotas and an additional γ slack cells without quotas. For any given and , in our Model I we determine the waiting time until at least frequency cells and at least run cells reach their quotas. For any given τ ≤ α + β, in our Model II we determine the waiting time until τ cells reach their quotas. Computer algorithms are developed to calculate the distributions, expectations and standard deviations of the waiting time random variables of the two models. Numerical results demonstrate the efficiency of the algorithms.
文摘This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.
基金This project was supported by the National Nature Science Foundation of China (60374009)Nature Science Foundation of Guangdong Province of China (990795).
文摘The mixed l1/H2 optimization problem for MIMO (multiple input-multiple output) discrete-time systems is considered. This problem is formulated as minimizing the l1-norm of a closed-loop transfer matrix while maintaining the H2-norm of another closed-loop transfer matrix at prescribed level. The continuity property of the optimal value in respect to changes in the H2-norm constraint is studied. The existence of the optimal solutions of mixed l1/H2 problem is proved. Because the solution of the mixed l1/H2 problem is based on the scaled-Q method, it avoids the zero interpolation difficulties. The convergent upper and lower bounds can be obtained by solving a sequence of finite dimensional nonlinear programming for which many efficient numerical optimization algorithms exist.
基金The National Natural Science Foundation of China(No.61074147)the Natural Science Foundation of Guangdong Province(No.S2011010005059)+2 种基金the Foundation of Enterprise-University-Research Institute Cooperation from Guangdong Province and Ministry of Education of China(No.2012B091000171,2011B090400460)the Science and Technology Program of Guangdong Province(No.2012B050600028)the Science and Technology Program of Huadu District,Guangzhou(No.HD14ZD001)
文摘Considering that the vehicle routing problem （VRP） with many extended features is widely used in actual life, such as multi-depot, heterogeneous types of vehicles, customer service priority and time windows etc., a mathematical model for multi-depot heterogeneous vehicle routing problem with soft time windows （MDHVRPSTW） is established. An improved ant colony optimization （IACO） is proposed for solving this model. First, MDHVRPSTW is transferred into different groups according to the nearest principle, and then the initial route is constructed by the scanning algorithm （SA）. Secondly, genetic operators are introduced, and crossover probability and mutation probability are adaptively adjusted in order to improve the global search ability of the algorithm. Moreover, the smooth mechanism is used to improve the performance of the ant colony optimization （ACO）. Finally, the 3-opt strategy is used to improve the local search ability. The proposed IACO was tested on three new instances that were generated randomly. The experimental results show that IACO is superior to the other three existing algorithms in terms of convergence speed and solution quality. Thus, the proposed method is effective and feasible, and the proposed model is meaningful.
文摘By establishing equivalent fixed point theorem, the boundary value problems of p Laplace equations with finite time delay are studied. It’s the first time that the functional differential equation is discussed with p Laplacian. The topological degree and fixed point theorem on cone are used to prove the existence of solution and positive solution. The conditions are all easy to check.
基金The National Natural Science Foundation of China(No. 50908235 )China Postdoctoral Science Foundation (No.201003520)
文摘An optimal dimension-down iterative algorithm （DDIA） is proposed for solving a mixed （continuous/ discrete） transportation network design problem （MNDP）, which is generally expressed as a mathematical programming with equilibrium constraints （MPEC）. The upper level of the MNDP aims to optimize the network performance via both the expansion of existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium （UE） model. The idea of the proposed DDIA is to reduce the dimensions of the problem. A group of variables （discrete/continuous） are fixed to altemately optimize another group of variables （continuous/discrete）. Some continuous network design problems （CNDPs） and discrete network design problems （DNDPs） are solved repeatedly until the optimal solution is obtained. A numerical example is given to demonstrate the efficiency of the proposed algorithm.
基金Projects(50275150,61173052) supported by the National Natural Science Foundation of ChinaProject(14FJ3112) supported by the Planned Science and Technology of Hunan Province,ChinaProject(14B033) supported by Scientific Research Fund Education Department of Hunan Province,China
文摘A novel chaotic search method is proposed,and a hybrid algorithm combining particle swarm optimization(PSO) with this new method,called CLSPSO,is put forward to solve 14 integer and mixed integer programming problems.The performances of CLSPSO are compared with those of other five hybrid algorithms combining PSO with chaotic search methods.Experimental results indicate that in terms of robustness and final convergence speed,CLSPSO is better than other five algorithms in solving many of these problems.Furthermore,CLSPSO exhibits good performance in solving two high-dimensional problems,and it finds better solutions than the known ones.A performance index(PI) is introduced to fairly compare the above six algorithms,and the obtained values of(PI) in three cases demonstrate that CLSPSO is superior to all the other five algorithms under the same conditions.
文摘The time dependent vehicle routing problem with time windows（TDVRPTW） is considered. A multi-type ant system（MTAS） algorithm hybridized with the ant colony system（ACS）and the max-min ant system（MMAS） algorithms is proposed. This combination absorbs the merits of the two algorithms in solutions construction and optimization separately. In order to improve the efficiency of the insertion procedure, a nearest neighbor selection（NNS） mechanism, an insertion local search procedure and a local optimization procedure are specified in detail. And in order to find a balance between good scouting performance and fast convergence rate, an adaptive pheromone updating strategy is proposed in the MTAS. Computational results confirm the MTAS algorithm＇s good performance with all these strategies on classic vehicle routing problem with time windows（VRPTW） benchmark instances and the TDVRPTW instances, and some better results especially for the number of vehicles and travel times of the best solutions are obtained in comparison with the previous research.
基金supported by the National Natural Science Foundation of China (Grant 11502286)
文摘Without applying any stable element techniques in the mixed methods, two simple generalized mixed element(GME) formulations were derived by combining the minimum potential energy principle and Hellinger–Reissner(H–R) variational principle. The main features of the GME formulations are that the common C0-continuous polynomial shape functions for displacement methods are used to express both displacement and stress variables, and the coefficient matrix of these formulations is not only automatically symmetric but also invertible. Hence, the numerical results of the generalized mixed methods based on the GME formulations are stable. Displacement as well as stress results can be obtained directly from the algebraic system for finite element analysis after introducing stress and displacement boundary conditions simultaneously. Numerical examples show that displacement and stress results retain the same accuracy. The results of the noncompatible generalized mixed method proposed herein are more accurate than those of the standard noncompatible displacement method. The noncompatible generalized mixed element is less sensitive to element geometric distortions.
