The Euler-Euler model is less effective in capturing the free surface of flow film in the spiral separator,and thus a Eulerian multi-fluid volume of fluid(VOF)model was first proposed to describe the particulate flow ...The Euler-Euler model is less effective in capturing the free surface of flow film in the spiral separator,and thus a Eulerian multi-fluid volume of fluid(VOF)model was first proposed to describe the particulate flow in spiral separators.In order to improve the applicability of the model in the high solid concentration system,the Bagnold effect was incorporated into the modelling framework.The capability of the proposed model in terms of predicting the flow film shape in a LD9 spiral separator was evaluated via comparison with measured flow film thicknesses reported in literature.Results showed that sharp air–water and air-pulp interfaces can be obtained using the proposed model,and the shapes of the predicted flow films before and after particle addition were reasonably consistent with the observations reported in literature.Furthermore,the experimental and numerical simulation of the separation of quartz and hematite were performed in a laboratory-scale spiral separator.When the Bagnold lift force model was considered,predictions of the grade of iron and solid concentration by mass for different trough lengths were more consistent with experimental data.In the initial development stage,the quartz particles at the bottom of the flow layer were more possible to be lifted due to the Bagnold force.Thus,a better predicted vertical stratification between quartz and hematite particles was obtained,which provided favorable conditions for subsequent radial segregation.展开更多
n the area of naval architecture and ocean engineering,the research about the underwater xplosion problem is of great significance.To achieve prolonged simulation of near-free surface underwater explosion,the underwat...n the area of naval architecture and ocean engineering,the research about the underwater xplosion problem is of great significance.To achieve prolonged simulation of near-free surface underwater explosion,the underwater explosion transient numerical model is established in this paper based on compressible Eulerian finite element method(EFEM).Compared with Geers Hunter formula,EFEM is availably validated by simulating the free-field underwater xplosion case.Then,the bubble pulsation and flow field dynamic characteristics of the cases with different underwater explosive depth are compared in this work.Lastly,the height of the water hump and the pressure of flow flied are analyzed quantitatively through the simulation results.展开更多
The Eulerian？Lagrangian method（ELM） has been used by many ocean models as the solution of the advection equation,but the numerical error caused by interpolation imposes restriction on its accuracy.In the present st...The Eulerian？Lagrangian method（ELM） has been used by many ocean models as the solution of the advection equation,but the numerical error caused by interpolation imposes restriction on its accuracy.In the present study,hybrid N-order Lagrangian interpolation ELM（Li ELM） is put forward in which the N-order Lagrangian interpolation is used at first,then the lower order Lagrangian interpolation is applied in the points where the interpolation results are abnormally higher or lower.The calculation results of a step-shaped salinity advection model are analyzed,which show that higher order（N=3？8） Li ELM can reduce the mean numerical error of salinity calculation,but the numerical oscillation error is still significant.Even number order Li ELM makes larger numerical oscillation error than its adjacent odd number order Li ELM.Hybrid N-order Li ELM can remove numerical oscillation,and it significantly reduces the mean numerical error when N is even and the current is in fixed direction,while it makes less effect on mean numerical error when N is odd or the current direction changes periodically.Hybrid odd number order Li ELM makes less mean numerical error than its adjacent even number order Li ELM when the current is in the fixed direction,while the mean numerical error decreases as N increases when the current direction changes periodically,so odd number of N may be better for application.Among various types of Hybrid N-order Li ELM,the scheme reducing N-order directly to 1st-order may be the optimal for synthetic selection of accuracy and computational efficiency.展开更多
A difference scheme in curvilinear coordinates is put forward for calculation of salinity in estuaries and coastal waters, which is based on Eulerian-Lagrangian method. It combines first-order and second-order Lagrang...A difference scheme in curvilinear coordinates is put forward for calculation of salinity in estuaries and coastal waters, which is based on Eulerian-Lagrangian method. It combines first-order and second-order Lagrangian interpolation to reduce numerical dispersion and oscillation. And the length of the curvilinear grid is also considered in the interpolation. Then the scheme is used in estuary, coast and ocean model, and several numerical experiments for the Yangtze Estuary and the Hangzhou Bay are conducted to test it. These experiments show that it is suitable for simulations of salinity in estuaries and coastal waters with the models using curvilinear coordinates.展开更多
A two-dimensional finite element （FE） model for the high speed turning operations when orthogonally machining AISI H13 tool steel at 49HRC using poly crystalline cubic boron nitride （PCBN） is described. An arbitra...A two-dimensional finite element （FE） model for the high speed turning operations when orthogonally machining AISI H13 tool steel at 49HRC using poly crystalline cubic boron nitride （PCBN） is described. An arbitrary Lagrangian Eulerian （ALE） method has been adopted which does not need any chip separation criteria as opposed to the traditional Lagrangian approach. Through FE simulations temperature and stresses distributions are presented that could be helpful in predicting tool life and improving process parameters. The results show that high temperatures are generated along the tool rake face as compared to the shear zone temperatures due to high thermal conductivity of PCBN tools.展开更多
An Arbitrary Lagrangian-Eulerian(ALE) method was employed to simulate the sheet metal extrusion process,aiming at avoiding mesh distortion and improving the computational accuracy.The method was implemented based on M...An Arbitrary Lagrangian-Eulerian(ALE) method was employed to simulate the sheet metal extrusion process,aiming at avoiding mesh distortion and improving the computational accuracy.The method was implemented based on MSC/MARC by using a fractional step method,i.e.a Lagrangian step followed by an Euler step.The Lagrangian step was a pure updated Lagrangian calculation and the Euler step was performed using mesh smoothing and remapping scheme.Due to the extreme distortion of deformation domain,it was almost impossible to complete the whole simulation with only one mesh topology.Therefore,global remeshing combined with the ALE method was used in the simulation work.Based on the numerical model of the process,some deformation features of the sheet metal extrusion process,such as distribution of localized equivalent plastic strain,and shrinkage cavity,were revealed.Furthermore,the differences between conventional extrusion and sheet metal extrusion process were also analyzed.展开更多
Eulerian method is a main numerical simulation method in elastoplastic hydrodynamics, which is suitable for the problems with multi-component and large deformation. As the feature of the problems to be simulated, such...Eulerian method is a main numerical simulation method in elastoplastic hydrodynamics, which is suitable for the problems with multi-component and large deformation. As the feature of the problems to be simulated, such as detonation and penetration, the dynamic parallel method （DPM） is designed to adjust the computational domain dynamically to get better load balance. Dynamic parallel method can be separated into two parts： one is division of initial computational domain and location of the data, the other is expansion of the computational domain and adjustment of the data location. DPM program can greatly shorten computational time and be preferable in simulating actual problems. The speedup of the DPM program is linear in parallel test. DPM can be popularized to parallel program of other multi-component high dimension Eulerian methods naturally.展开更多
A new flux-based hybrid subcell-remapping algorithm for staggered multimaterial arbitrary Lagrangian-Eulerian (MMALE) methods is presented. This new method is an effective generalization of the original subcell-remapp...A new flux-based hybrid subcell-remapping algorithm for staggered multimaterial arbitrary Lagrangian-Eulerian (MMALE) methods is presented. This new method is an effective generalization of the original subcell-remapping method to the multi-material regime (LOUBERE, R. and SHASHKOV,M. A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods. Journal of Computational Physics, 209, 105–138 (2005)). A complete remapping procedure of all fluid quantities is described detailedly in this paper. In the pure material regions, remapping of mass and internal energy is performed by using the original subcell-remapping method. In the regions near the material interfaces, remapping of mass and internal energy is performed with the intersection-based fluxes where intersections are performed between the swept regions and pure material polygons in the Lagrangian mesh, and an approximate approach is then introduced for constructing the subcell mass fluxes. In remapping of the subcell momentum, the mass fluxes are used to construct the momentum fluxes by multiplying a reconstructed velocity in the swept region. The nodal velocity is then conservatively recovered. Some numerical examples simulated in the full MMALE regime and several purely cyclic remapping examples are presented to prove the properties of the remapping method.展开更多
This paper provides the number of combinatorially distinct general rooted Eulerian planar maps with the number of edges and the valency of rooted vertex of the maps as. two parameters. It is also an answer to open pro...This paper provides the number of combinatorially distinct general rooted Eulerian planar maps with the number of edges and the valency of rooted vertex of the maps as. two parameters. It is also an answer to open problem 7.1 in [1]. Meanwhile, the case of three variables can be derived by using Lagrangian inversion.展开更多
A numerical model based on the Eulerian–Eulerian two-fluid approach is used to simulate the gasification of coal char inside an entrained flow gasifier. In this model, effects of thermophoresis of coal char particles...A numerical model based on the Eulerian–Eulerian two-fluid approach is used to simulate the gasification of coal char inside an entrained flow gasifier. In this model, effects of thermophoresis of coal char particles are thoroughly investigated. The thermophoresis is due to the gas temperature gradient caused by absorpted heat of coal char gasification. This work, firstly, calculates the gas temperature gradient and thermophoretic force at1100 °C,1200 °C,1300 °C and 1400 °C wall temperatures. Then, the changes of particle volume fraction and velocity in the gasifier are studied in the simulation with thermophoresis or not. The results indicate that considering the particle thermophoresis has some effects on the calculation of particle volume fraction in the gasifier, especially at wall temperature of 1400 °C, and the maximum particle volume fraction variance ratio reaches up to 1.38% on wall surface of the gasifier. These effects are mainly caused by large gas temperature gradient along the radial direction of the gasifier. For the particle velocity, the changes are small but can be observable along radial direction of the gasifier, which has good agreement with the distributions of radial gas temperature gradient and thermophoretic force. These changes above may have certain effects on gasification reaction rates in this Eulerian model. So the change of gasification reaction rates in the simulation with thermophoresis or not is studied finally.展开更多
Wet steam condensing flow in low-pressure steam turbine leads to efficiencylosses and blade erosions. In order to investigate this problem by numerical approach, anEulerian/Eulerian model has been developed, in which ...Wet steam condensing flow in low-pressure steam turbine leads to efficiencylosses and blade erosions. In order to investigate this problem by numerical approach, anEulerian/Eulerian model has been developed, in which the wet steam is regarded as mixture comprisingtwo coupled systems: the vapor phase and the liquid phase. These two systems are both described byconservation equations. High resolution TVD scheme is employed to capture condensing phenomena inwet steam flow. This model has been validated by numerical simulations of condensing flows in 1D and2D nozzles. Compared with experimental data, a good agreement is observed. This Eulerian/Eulerianmodel can be extended to 3D calculation of condensing flow.展开更多
基金the National Natural Science Foundation of China(Nos.51974065 and 52274257)the Open Foundation of State Key Laboratory of Mineral Processing(No.BGRIMMKJSKL-2020-13)the Fundamental Research Funds for the Central Universities(Nos.N2201008 and N2201004).
文摘The Euler-Euler model is less effective in capturing the free surface of flow film in the spiral separator,and thus a Eulerian multi-fluid volume of fluid(VOF)model was first proposed to describe the particulate flow in spiral separators.In order to improve the applicability of the model in the high solid concentration system,the Bagnold effect was incorporated into the modelling framework.The capability of the proposed model in terms of predicting the flow film shape in a LD9 spiral separator was evaluated via comparison with measured flow film thicknesses reported in literature.Results showed that sharp air–water and air-pulp interfaces can be obtained using the proposed model,and the shapes of the predicted flow films before and after particle addition were reasonably consistent with the observations reported in literature.Furthermore,the experimental and numerical simulation of the separation of quartz and hematite were performed in a laboratory-scale spiral separator.When the Bagnold lift force model was considered,predictions of the grade of iron and solid concentration by mass for different trough lengths were more consistent with experimental data.In the initial development stage,the quartz particles at the bottom of the flow layer were more possible to be lifted due to the Bagnold force.Thus,a better predicted vertical stratification between quartz and hematite particles was obtained,which provided favorable conditions for subsequent radial segregation.
基金The authors would like to acknowledge the support of the National Natural Science Foundation of China(Grant 11672081)the Industrial Technology Development Program(Grants JCKY2018604C010 and JCKY2017604C002).Finally,Thanks for the help of Zu-Hui Li during writing the paper.
文摘n the area of naval architecture and ocean engineering,the research about the underwater xplosion problem is of great significance.To achieve prolonged simulation of near-free surface underwater explosion,the underwater explosion transient numerical model is established in this paper based on compressible Eulerian finite element method(EFEM).Compared with Geers Hunter formula,EFEM is availably validated by simulating the free-field underwater xplosion case.Then,the bubble pulsation and flow field dynamic characteristics of the cases with different underwater explosive depth are compared in this work.Lastly,the height of the water hump and the pressure of flow flied are analyzed quantitatively through the simulation results.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.40906044 and 41076048)the Fundamental Research Funds for the Central Universities Project(Grant No.2011B05714)
文摘The Eulerian？Lagrangian method（ELM） has been used by many ocean models as the solution of the advection equation,but the numerical error caused by interpolation imposes restriction on its accuracy.In the present study,hybrid N-order Lagrangian interpolation ELM（Li ELM） is put forward in which the N-order Lagrangian interpolation is used at first,then the lower order Lagrangian interpolation is applied in the points where the interpolation results are abnormally higher or lower.The calculation results of a step-shaped salinity advection model are analyzed,which show that higher order（N=3？8） Li ELM can reduce the mean numerical error of salinity calculation,but the numerical oscillation error is still significant.Even number order Li ELM makes larger numerical oscillation error than its adjacent odd number order Li ELM.Hybrid N-order Li ELM can remove numerical oscillation,and it significantly reduces the mean numerical error when N is even and the current is in fixed direction,while it makes less effect on mean numerical error when N is odd or the current direction changes periodically.Hybrid odd number order Li ELM makes less mean numerical error than its adjacent even number order Li ELM when the current is in the fixed direction,while the mean numerical error decreases as N increases when the current direction changes periodically,so odd number of N may be better for application.Among various types of Hybrid N-order Li ELM,the scheme reducing N-order directly to 1st-order may be the optimal for synthetic selection of accuracy and computational efficiency.
基金This project was supported by the Major State Basic Research Program under Contract Grant No. G1999043803the University Fund for Mainstay Teachers of State Ministry of Education and the Opening Fund of Open Laboratory of Marine Dynamic Process and Sa
文摘A difference scheme in curvilinear coordinates is put forward for calculation of salinity in estuaries and coastal waters, which is based on Eulerian-Lagrangian method. It combines first-order and second-order Lagrangian interpolation to reduce numerical dispersion and oscillation. And the length of the curvilinear grid is also considered in the interpolation. Then the scheme is used in estuary, coast and ocean model, and several numerical experiments for the Yangtze Estuary and the Hangzhou Bay are conducted to test it. These experiments show that it is suitable for simulations of salinity in estuaries and coastal waters with the models using curvilinear coordinates.
基金This project is supported by National Natural Science Foundation of China (No.50505003).
文摘A two-dimensional finite element （FE） model for the high speed turning operations when orthogonally machining AISI H13 tool steel at 49HRC using poly crystalline cubic boron nitride （PCBN） is described. An arbitrary Lagrangian Eulerian （ALE） method has been adopted which does not need any chip separation criteria as opposed to the traditional Lagrangian approach. Through FE simulations temperature and stresses distributions are presented that could be helpful in predicting tool life and improving process parameters. The results show that high temperatures are generated along the tool rake face as compared to the shear zone temperatures due to high thermal conductivity of PCBN tools.
基金Project(50505027) supported by the National Natural Science Foundation of ChinaProject(20070248056) supported by the Research Fund for the Doctoral Program of Higher Education of China
文摘An Arbitrary Lagrangian-Eulerian(ALE) method was employed to simulate the sheet metal extrusion process,aiming at avoiding mesh distortion and improving the computational accuracy.The method was implemented based on MSC/MARC by using a fractional step method,i.e.a Lagrangian step followed by an Euler step.The Lagrangian step was a pure updated Lagrangian calculation and the Euler step was performed using mesh smoothing and remapping scheme.Due to the extreme distortion of deformation domain,it was almost impossible to complete the whole simulation with only one mesh topology.Therefore,global remeshing combined with the ALE method was used in the simulation work.Based on the numerical model of the process,some deformation features of the sheet metal extrusion process,such as distribution of localized equivalent plastic strain,and shrinkage cavity,were revealed.Furthermore,the differences between conventional extrusion and sheet metal extrusion process were also analyzed.
基金Sponsored by State Key Laboratory of Computational Physics Fundation(9140C690101070C69)
文摘Eulerian method is a main numerical simulation method in elastoplastic hydrodynamics, which is suitable for the problems with multi-component and large deformation. As the feature of the problems to be simulated, such as detonation and penetration, the dynamic parallel method （DPM） is designed to adjust the computational domain dynamically to get better load balance. Dynamic parallel method can be separated into two parts： one is division of initial computational domain and location of the data, the other is expansion of the computational domain and adjustment of the data location. DPM program can greatly shorten computational time and be preferable in simulating actual problems. The speedup of the DPM program is linear in parallel test. DPM can be popularized to parallel program of other multi-component high dimension Eulerian methods naturally.
基金Project supported by the China Postdoctoral Science Foundation(No.2017M610823)
文摘A new flux-based hybrid subcell-remapping algorithm for staggered multimaterial arbitrary Lagrangian-Eulerian (MMALE) methods is presented. This new method is an effective generalization of the original subcell-remapping method to the multi-material regime (LOUBERE, R. and SHASHKOV,M. A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods. Journal of Computational Physics, 209, 105–138 (2005)). A complete remapping procedure of all fluid quantities is described detailedly in this paper. In the pure material regions, remapping of mass and internal energy is performed by using the original subcell-remapping method. In the regions near the material interfaces, remapping of mass and internal energy is performed with the intersection-based fluxes where intersections are performed between the swept regions and pure material polygons in the Lagrangian mesh, and an approximate approach is then introduced for constructing the subcell mass fluxes. In remapping of the subcell momentum, the mass fluxes are used to construct the momentum fluxes by multiplying a reconstructed velocity in the swept region. The nodal velocity is then conservatively recovered. Some numerical examples simulated in the full MMALE regime and several purely cyclic remapping examples are presented to prove the properties of the remapping method.
文摘This paper provides the number of combinatorially distinct general rooted Eulerian planar maps with the number of edges and the valency of rooted vertex of the maps as. two parameters. It is also an answer to open problem 7.1 in [1]. Meanwhile, the case of three variables can be derived by using Lagrangian inversion.
文摘A numerical model based on the Eulerian–Eulerian two-fluid approach is used to simulate the gasification of coal char inside an entrained flow gasifier. In this model, effects of thermophoresis of coal char particles are thoroughly investigated. The thermophoresis is due to the gas temperature gradient caused by absorpted heat of coal char gasification. This work, firstly, calculates the gas temperature gradient and thermophoretic force at1100 °C,1200 °C,1300 °C and 1400 °C wall temperatures. Then, the changes of particle volume fraction and velocity in the gasifier are studied in the simulation with thermophoresis or not. The results indicate that considering the particle thermophoresis has some effects on the calculation of particle volume fraction in the gasifier, especially at wall temperature of 1400 °C, and the maximum particle volume fraction variance ratio reaches up to 1.38% on wall surface of the gasifier. These effects are mainly caused by large gas temperature gradient along the radial direction of the gasifier. For the particle velocity, the changes are small but can be observable along radial direction of the gasifier, which has good agreement with the distributions of radial gas temperature gradient and thermophoretic force. These changes above may have certain effects on gasification reaction rates in this Eulerian model. So the change of gasification reaction rates in the simulation with thermophoresis or not is studied finally.
基金This project is supported by National Natural Science Foundation of China (No.50176035)Doctorate Foundation of Xi'an Jiaotong University,China (No.DFXJU2000-18)
文摘Wet steam condensing flow in low-pressure steam turbine leads to efficiencylosses and blade erosions. In order to investigate this problem by numerical approach, anEulerian/Eulerian model has been developed, in which the wet steam is regarded as mixture comprisingtwo coupled systems: the vapor phase and the liquid phase. These two systems are both described byconservation equations. High resolution TVD scheme is employed to capture condensing phenomena inwet steam flow. This model has been validated by numerical simulations of condensing flows in 1D and2D nozzles. Compared with experimental data, a good agreement is observed. This Eulerian/Eulerianmodel can be extended to 3D calculation of condensing flow.
