This numerical simulation investigates the two⁃phase flow under the condition of supercooled large droplets impinging on the aircraft surface.Based on Eulerian framework,a method for calculating supercooled water drop...This numerical simulation investigates the two⁃phase flow under the condition of supercooled large droplets impinging on the aircraft surface.Based on Eulerian framework,a method for calculating supercooled water droplet impingement characteristics is established.Then,considering the deformation and breaking effects during the movement,this method is extended to calculate the impingement characteristics of supercooled large droplets,as well as the bouncing and splashing effects during impingement.The impingement characteristics of supercooled large droplets is then investigated by this method.The results demonstrate that the deformation and breaking effects of supercooled large droplets have negligible influence on the impingement characteristics under the experimental conditions of this paper.In addition,the results of the impingement range and collection efficiency decrease when considering the bouncing and splashing effects.The bouncing effect mainly affects the mass loss near the impingement limits,while the splashing effect influences the result around the stagnation point.This investigation is beneficial for the analysis of aircraft icing and the design of anti⁃icing system with supercooled large droplet conditions.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
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
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
The study of mesoscale eddies is generally categorized in Eulerian or Lagrangian frameworks.We employed the eddy identification techniques in both frameworks in the South China Sea(SCS),examining the differential char...The study of mesoscale eddies is generally categorized in Eulerian or Lagrangian frameworks.We employed the eddy identification techniques in both frameworks in the South China Sea(SCS),examining the differential characteristics of mesoscale eddies ascertained through each approach,and attempting to identify factors influencing eddy lifetime.The findings suggest that eddies identified via the sea surface height(SSH)method in the Eulerian framework typically have larger spatial extents compared to those identified using the Lagrangian Average Vorticity Deviation(LAVD)method.The latter is characterized by a greater number of vortices with smaller average values of characteristic parameters.SSH eddies exhibited more remarked seasonal variations than LAVD vortices,and the seasonal variations of their respective cyclonic and anticyclonic eddies showed opposite trends.Analysis in both frameworks indicates that eddy lifetime is positively correlated with various eddy characteristic parameters,including radius,vorticity,kinetic energy,amplitude,EKE/MKE(ratio of boundary to spatial mean kinetic energy),and U/c(max rotation speed to mean propagation speed ratio).A subsequent comparison between SSH eddies with LAVD cores(SSH eddy with LAVD vortex inside)and those without reveals a greater likelihood of extended lifetime in the former.Compared to the characteristic parameters of eddies,the presence of LAVD cores emerges as a critical factor in determining the lifetime of SSH eddies.展开更多
We present a simple and efficient strategy for the acceleration of explicit Eulerian methods for multidimensional hyperbolic systems of conservation laws.The strategy is based on the Galilean invariance of dynamic equ...We present a simple and efficient strategy for the acceleration of explicit Eulerian methods for multidimensional hyperbolic systems of conservation laws.The strategy is based on the Galilean invariance of dynamic equations and optimization of the reference frame,in which the equations are numerically solved.The optimal reference frame moves(locally in time)with the average characteristic speed of the system,and,in this sense,the resulting method is quasi-Lagrangian.This leads to the acceleration of the numerical computations thanks to the optimal CFL condition and automatic adjustment of the computational domain to the evolving part of the solution.We show that our quasi-Lagrangian acceleration procedure may also reduce the numerical dissipation of the underlying Eulerian method.This leads to a significantly enhanced resolution,especially in the supersonic case.We demonstrate a great potential of the proposed method on a number of numerical examples.展开更多
In this paper, we incorporate fuzzy mathematics approach into the Eulerian method to simulate three dimensional multi-material interfaces. In particular, we propose a fuzzy interface treatment for describing interface...In this paper, we incorporate fuzzy mathematics approach into the Eulerian method to simulate three dimensional multi-material interfaces. In particular, we propose a fuzzy interface treatment for describing interfaces, designing transport plans, and computing transport quantities. Using a set of three-dimensional inviscid isothermal elastic-plastic hydrodynamic equations, we simulate shaped charge jet in different filled dynamite structures. Strain and stress have been under consideration in simulations. Numerical results demonstrate that the fuzzy interface treatment is correct and efficient for three-dimensional multi-material problems.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
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
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 computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as th...A computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as the free surface motion, the arbitrary Lagrangian-Eulerian formulation is employed as the basis of the finite element spatial discretization. For numerical integration in time, the fraction,step method is used. This method is useful because one can use the same linear interpolation function for both velocity and pressure. The method is applied to the nonlinear interaction of a structure and a tuned liquid damper. All computations are performed with a personal computer.展开更多
We develop computational teractions subject to thermal fluctuations geometry. The methods take into account methods for the study of fluid-structure in- when confined within channels with slit-like the hydrodynamic co...We develop computational teractions subject to thermal fluctuations geometry. The methods take into account methods for the study of fluid-structure in- when confined within channels with slit-like the hydrodynamic coupling and diffusivity of microstructures when influenced by their proximity to no-slip walls. We develop stochas- tic numerical methods subject to no-slip boundary conditions using a staggered finite volume discretization. We introduce techniques for discretizing stochastic systems in a manner that ensures results consistent with statistical mechanics. We show how an exact fluctuation-dissipation condition can be used for this purpose to discretize the stochastic driving fields and combined with an exact projection method to enforce incompressibil- ity. We demonstrate our computational methods by investigating how the proximity of ellipsoidal colloids to the channel wall affects their active hydrodynamic responses and passive diffusivity. We also study for a large number of interacting particles collective drift-diffusion dynamics and associated correlation h/actions. We expect the introduced stochastic computational methods to be broadly applicable to applications in which con- finement effects play an important role in the dynamics of microstructures subject to hydrodynamic coupling and thermal fluctuations.展开更多
A new method called mixed Lagrangian and Eulerian method （MILE method） was used to simulate the thermomechanical behavior during continuous casting process of steel YF45MnV. The simulation results are basically in a...A new method called mixed Lagrangian and Eulerian method （MILE method） was used to simulate the thermomechanical behavior during continuous casting process of steel YF45MnV. The simulation results are basically in agreement with the measured data. The delaying period at the beginning of solidification is about 0.1. in square root of solidification time which is agreement with the data in literatures, and shell thickness increases in linear relation to square root of solidification time. The bloom surface temperature decreases gradually as the casting proceeds. The effective stress in the comer is much larger than that in the mid-face. The comer area is the dangerous zone of cracking. The effects of mold flux break temperature on the air gap and hot tearing indicator were also modeled. The model predicts that the bloom surface temperature increases with the increase of the mold flux break temperature, but the heat flux decreases with the increase of the mold flux break temperature. ,The hot tearing indicator is much smaller when the mold flux break temperature is higher.展开更多
基金supported in part by the National Natural Science Foundation of China(No.51806008)the Open Fund of Key Laboratory of Rotor Aerodynamics Key Laboratory(No.RAL202104-2)。
文摘This numerical simulation investigates the two⁃phase flow under the condition of supercooled large droplets impinging on the aircraft surface.Based on Eulerian framework,a method for calculating supercooled water droplet impingement characteristics is established.Then,considering the deformation and breaking effects during the movement,this method is extended to calculate the impingement characteristics of supercooled large droplets,as well as the bouncing and splashing effects during impingement.The impingement characteristics of supercooled large droplets is then investigated by this method.The results demonstrate that the deformation and breaking effects of supercooled large droplets have negligible influence on the impingement characteristics under the experimental conditions of this paper.In addition,the results of the impingement range and collection efficiency decrease when considering the bouncing and splashing effects.The bouncing effect mainly affects the mass loss near the impingement limits,while the splashing effect influences the result around the stagnation point.This investigation is beneficial for the analysis of aircraft icing and the design of anti⁃icing system with supercooled large droplet conditions.
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(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.
基金Supported by the National Natural Science Foundation of China(No.41906021)the Guangdong Ocean University Scientific Research Start-up Fund(No.060302112312)。
文摘The study of mesoscale eddies is generally categorized in Eulerian or Lagrangian frameworks.We employed the eddy identification techniques in both frameworks in the South China Sea(SCS),examining the differential characteristics of mesoscale eddies ascertained through each approach,and attempting to identify factors influencing eddy lifetime.The findings suggest that eddies identified via the sea surface height(SSH)method in the Eulerian framework typically have larger spatial extents compared to those identified using the Lagrangian Average Vorticity Deviation(LAVD)method.The latter is characterized by a greater number of vortices with smaller average values of characteristic parameters.SSH eddies exhibited more remarked seasonal variations than LAVD vortices,and the seasonal variations of their respective cyclonic and anticyclonic eddies showed opposite trends.Analysis in both frameworks indicates that eddy lifetime is positively correlated with various eddy characteristic parameters,including radius,vorticity,kinetic energy,amplitude,EKE/MKE(ratio of boundary to spatial mean kinetic energy),and U/c(max rotation speed to mean propagation speed ratio).A subsequent comparison between SSH eddies with LAVD cores(SSH eddy with LAVD vortex inside)and those without reveals a greater likelihood of extended lifetime in the former.Compared to the characteristic parameters of eddies,the presence of LAVD cores emerges as a critical factor in determining the lifetime of SSH eddies.
基金The work of A.Kurganov was supported in part by NSF grants DMS-0310585 and DMS-0610430.
文摘We present a simple and efficient strategy for the acceleration of explicit Eulerian methods for multidimensional hyperbolic systems of conservation laws.The strategy is based on the Galilean invariance of dynamic equations and optimization of the reference frame,in which the equations are numerically solved.The optimal reference frame moves(locally in time)with the average characteristic speed of the system,and,in this sense,the resulting method is quasi-Lagrangian.This leads to the acceleration of the numerical computations thanks to the optimal CFL condition and automatic adjustment of the computational domain to the evolving part of the solution.We show that our quasi-Lagrangian acceleration procedure may also reduce the numerical dissipation of the underlying Eulerian method.This leads to a significantly enhanced resolution,especially in the supersonic case.We demonstrate a great potential of the proposed method on a number of numerical examples.
基金the National Natural Science Foundation of China (Grant No.10272023).
文摘In this paper, we incorporate fuzzy mathematics approach into the Eulerian method to simulate three dimensional multi-material interfaces. In particular, we propose a fuzzy interface treatment for describing interfaces, designing transport plans, and computing transport quantities. Using a set of three-dimensional inviscid isothermal elastic-plastic hydrodynamic equations, we simulate shaped charge jet in different filled dynamite structures. Strain and stress have been under consideration in simulations. Numerical results demonstrate that the fuzzy interface treatment is correct and efficient for three-dimensional multi-material problems.
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.
文摘A computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as the free surface motion, the arbitrary Lagrangian-Eulerian formulation is employed as the basis of the finite element spatial discretization. For numerical integration in time, the fraction,step method is used. This method is useful because one can use the same linear interpolation function for both velocity and pressure. The method is applied to the nonlinear interaction of a structure and a tuned liquid damper. All computations are performed with a personal computer.
基金Project supported by the Applied Mathematics Program within the Department of Energy(DOE)Office of Advanced Scientific Computing Research(ASCR)as part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials(CM4)(No.DOE ASCR CM4 DE-SC0009254)the DOE National Laboratory Directed Research Development(No.LDRD69738)the National Science Foudation of the United States(Nos.DMS-0956210,DMS-1616353,DMR-1121053,and NSF CNS-0960316)
文摘We develop computational teractions subject to thermal fluctuations geometry. The methods take into account methods for the study of fluid-structure in- when confined within channels with slit-like the hydrodynamic coupling and diffusivity of microstructures when influenced by their proximity to no-slip walls. We develop stochas- tic numerical methods subject to no-slip boundary conditions using a staggered finite volume discretization. We introduce techniques for discretizing stochastic systems in a manner that ensures results consistent with statistical mechanics. We show how an exact fluctuation-dissipation condition can be used for this purpose to discretize the stochastic driving fields and combined with an exact projection method to enforce incompressibil- ity. We demonstrate our computational methods by investigating how the proximity of ellipsoidal colloids to the channel wall affects their active hydrodynamic responses and passive diffusivity. We also study for a large number of interacting particles collective drift-diffusion dynamics and associated correlation h/actions. We expect the introduced stochastic computational methods to be broadly applicable to applications in which con- finement effects play an important role in the dynamics of microstructures subject to hydrodynamic coupling and thermal fluctuations.
基金Project(51174020) supported by the National Natural Science Foundation of China
文摘A new method called mixed Lagrangian and Eulerian method （MILE method） was used to simulate the thermomechanical behavior during continuous casting process of steel YF45MnV. The simulation results are basically in agreement with the measured data. The delaying period at the beginning of solidification is about 0.1. in square root of solidification time which is agreement with the data in literatures, and shell thickness increases in linear relation to square root of solidification time. The bloom surface temperature decreases gradually as the casting proceeds. The effective stress in the comer is much larger than that in the mid-face. The comer area is the dangerous zone of cracking. The effects of mold flux break temperature on the air gap and hot tearing indicator were also modeled. The model predicts that the bloom surface temperature increases with the increase of the mold flux break temperature, but the heat flux decreases with the increase of the mold flux break temperature. ,The hot tearing indicator is much smaller when the mold flux break temperature is higher.
