Casting experiments and macro-micro numerical simulations were conducted to examine the microstructure characteristics of K439B nickel-based superalloy casting with varying cross-sections during the gravity investment...Casting experiments and macro-micro numerical simulations were conducted to examine the microstructure characteristics of K439B nickel-based superalloy casting with varying cross-sections during the gravity investment casting process.Firstly,microstructure analysis was conducted on the casting using scanning electron microscopy(SEM)and electron backscatter diffraction(EBSD).Subsequently,calculation of the phase diagram and differential scanning calorimetry(DSC)tests were conducted to determine the macro-micro simulation parameters of the K439B alloy,and the cellular automaton finite element(CAFE)method was employed to develop macro-micro modeling of K439B nickel-based superalloy casting with varying cross-sections.The experimental results revealed that the ratio of the average grain area increased from the edge to the center of the sections as the ratio of the cross-sectional area increased.The simulation results indicated that the average grain area increased from 0.885 to 0.956 mm^(2)as the ratio of the cross-sections increased from 6꞉1 to 12꞉1.The experiment and simulation results showed that the grain size became more heterogeneous and the grain shape became more irregular with an increase in the ratio of the cross-sectional area of the casting.CAFE modeling was an effective method to simulate the microstructure evolution of the K439B alloy and ensure the accuracy of the simulation.展开更多
Microporosity formed in the solidification process of Al alloys is detrimental to the alloy properties.A two-dimensional cellular automaton(CA)model was developed to simulate the microstructure and microporosity forma...Microporosity formed in the solidification process of Al alloys is detrimental to the alloy properties.A two-dimensional cellular automaton(CA)model was developed to simulate the microstructure and microporosity formation in Al-Cu alloys,considering variations in Cu content and solidification rate.The results indicate that the Cu content primarily influences the growth of microporosity.To validate the model,directional solidification experiments were conducted on Al-Cu alloys with varing Cu contents and withdrawal rates.The experimental results of dendrites and microporosity characteristics agree well with the predictions from the developed model,thus confirming the validity of the model.The alloy’s liquidus temperature,dendrite morphology,and hydrogen saturation solubility arising from different Cu contents have significant effects on microporosity morphology.The withdrawal rate primarily affects the nucleation of hydrogen microporosity by altering cooling rates and dendritic growth rates,resulting in different microporosity characteristics.展开更多
The microstructure formed during solidification has a significant impact on the mechanical properties of materials.In this study,a two-dimensional(2D)cellular automaton(CA)-finite difference(FD)-CALPHAD model was deve...The microstructure formed during solidification has a significant impact on the mechanical properties of materials.In this study,a two-dimensional(2D)cellular automaton(CA)-finite difference(FD)-CALPHAD model was developed to simulate the formation of microstructure and solute segregation in the solidification processes of ternary alloys.In the model,dendritic growth is simulated using the CA technique,while solute diffusion is solved by the FD method,and the CALPHAD method is employed to calculate thermodynamic phase equilibrium during solidification.The CA-FD-CALPHAD coupled model is capable of reproducing the evolution of continuous nucleation and growth of grains as well as the evolution of the microstructure and solute distribution during solidification of ternary alloys.In this study,Al–Zn–Mg ternary alloy is taken as an example to simulate the growth of equiaxed and columnar grains and the columnar-to-equiaxed transition(CET)under different solidification conditions.The simulation results are compared with experimental data from the literature,showing a good agreement.Besides,the study also investigates the evolution of temperature and multicomponent solute fields during solidification and the effects of alloy composition and cooling rate on the microstructure morphology.The results reveal that the initial alloy composition and cooling rate significantly affect dendritic morphology and solute segregation.Higher initial alloy concentrations promote the growth of side branches in equiaxed grains,leading to more pronounced solute segregation between dendrites.As the cooling rate increases,the average grain size of the equiaxed grains decreases accordingly.Additionally,a higher cooling rate accelerates the columnar-to-equiaxed transition,leading to a finer grain structure.展开更多
Accurately tailoring microstructures,especially grain size,during thermomechanical processing is crucial for achieving the desired strengthductility synergy of wrought magnesium alloys.This study establishes a multile...Accurately tailoring microstructures,especially grain size,during thermomechanical processing is crucial for achieving the desired strengthductility synergy of wrought magnesium alloys.This study establishes a multilevel cellular automaton(CA)model to predict the microstructure evolution of wrought magnesium alloys undergoing both dynamic recrystallization(DRX)and dynamic precipitation(DP),surpassing the capabilities of traditional DRX models.Multiple physical metallurgical mechanisms,including variations in dislocation with work hardening(WH)and dynamic recovery(DRV),DRX,DP,and solute diffusion,are integrated and interconnected by their mutual effects.To facilitate the CA modeling,a novel local pinning model is proposed to reflect the uneven retardation of a precipitate to grain boundary migration and the virtual intersections of precipitates and grain boundaries based on their distribution,and its rationality is verified by simulations for grain coarsening.Considering the substantial difference in grain size and precipitate size,a multilevel cellular space is constructed,with a coarse parent cellular space for DRX and a sub-cellular space discretized from parent cells for DP,to balance computational efficiency and accuracy.The simulation successfully captures the microstructure evolution with multiscale characteristics,specifically the refinement of grains from hundreds of micros to a few micros through DRX,aided by dynamically precipitated second-phase particles in the submicron(hundreds of nanometers)range.The high degree of agreement between simulated and experimental results in terms of kinetics for microstructure evolution and microstructure after deformation at various temperatures and strain rates attests to the sound rationality and strong predictive capability of the established multilevel CA model.A comparison between the simulated results of the traditional CA model exclusively for DRX and those obtained from the multilevel CA model that incorporates both DRX and DP highlights the necessity of considering the interaction between these two phenomena for accurate grain size prediction.展开更多
A novel deceleration traffic flow model is established based on the oscillatory congested states and the slow-tostart rule.The novel model considers human overreaction and mechanical restrictions as limited decelerati...A novel deceleration traffic flow model is established based on the oscillatory congested states and the slow-tostart rule.The novel model considers human overreaction and mechanical restrictions as limited deceleration capacity,effectively avoiding the unrealistic deceleration behavior found in most existing traffic flow models.In order to consider that the acceleration of a stationary vehicle is slower than that of a moving vehicle due to reasons such as driver inattention,the slow-to-start rule is introduced.In actual traffic,the driver will take different deceleration measures according to local traffic conditions,divided into ordinary and emergency deceleration.The deceleration setting in the deceleration model with only ordinary deceleration is modified.Computer simulations show that the novel model can achieve smooth,comfortable acceleration and deceleration behavior.Introducing the slow-to-start rule can realize the first-order transition from free flow to synchronized flow.The oscillatory congested states enable a first-order transition from synchronized flow to wide moving jam.Under periodic boundary conditions,the novel model can reproduce three traffic flow phases(free flow,synchronized flow,and wide moving jam)and two first-order transitions between three phases.In addition,the novel model can reproduce empirical results such as linear synchronized flow and headway distribution of free flow below 1 s.Under open boundary conditions,different congested patterns caused by on-ramps are analyzed.Compared with the classic deceleration model,this model can better reproduce the phenomenon and characteristics of actual traffic flow and provide more accurate decision support for daily traffic management of expressways.展开更多
提出一种基于确定的有穷状态自动机(deterministic finite automaton,简称DFA)的正则表达式压缩算法.首先,定义了膨胀率DR(distending rate)来描述正则表达式的膨胀特性.然后基于DR提出一种分片的算法RECCADR(regular expressions cut a...提出一种基于确定的有穷状态自动机(deterministic finite automaton,简称DFA)的正则表达式压缩算法.首先,定义了膨胀率DR(distending rate)来描述正则表达式的膨胀特性.然后基于DR提出一种分片的算法RECCADR(regular expressions cut and combine algorithm based on DR),有效地选择出导致DFA状态膨胀的片段并隔离,降低了单个正则表达式存储需求.同时,基于正则表达式的组合关系提出一种选择性分群算法REGADR(regular expressions group algorithm based on DR),在可以接受的存储需求总量下,通过选择性分群大幅度减少了状态机的个数,有效地降低了匹配算法的复杂性.展开更多
A cellular automaton（CA） modeling of discontinuous dynamic recrystallization（DDRX） of a near-α Ti-6Al-2Zr-1Mo-1V（TA15） isothermally compressed in the β single phase field was presented.In the CA model,nucleati...A cellular automaton（CA） modeling of discontinuous dynamic recrystallization（DDRX） of a near-α Ti-6Al-2Zr-1Mo-1V（TA15） isothermally compressed in the β single phase field was presented.In the CA model,nucleation of the β-DDRX and the growth of recrystallized grains（re-grains） were considered and visibly simulated by the CA model.The driving force of re-grain growth was provided by dislocation density accumulating around the grain boundaries.To verify the CA model,the predicted flow stress by the CA model was compared with the experimental data.The comparison showed that the average relative errors were10.2%,10.1%and 6%,respectively,at 1.0,0.1 and 0.01 s^-1 of 1020 ℃,and were 10.2%,11.35%and 7.5%,respectively,at 1.0,0.1and 0.01 s^-1 of 1050 ℃.The CA model was further applied to predicting the average growth rate,average re-grain size and recrystallization kinetics.The simulated results showed that the average growth rate increases with the increasing strain rate or temperature,while the re-grain size increases with the decreasing strain rate;the volume fraction of recrystallization decreases with the increasing strain rate or decreasing temperature.展开更多
Based on the cellular automaton （CA） method, a numerical model was developed to simulate the dendritic growth of magnesium alloy with HCP crystal structure. The growth kinetics was calculated from the complete solut...Based on the cellular automaton （CA） method, a numerical model was developed to simulate the dendritic growth of magnesium alloy with HCP crystal structure. The growth kinetics was calculated from the complete solution of the transport equations. By defining a special neighborhood configuration with the square CA cell, and using a set of capturing rules which were proposed by BELTRAN-SANCHEZ and STEFANESCU for the dendritic growth of cubic crystal metals during solidification, modeling of dendritic growth of magnesium alloy with different growth orientations was achieved. Simulation of equiaxed dendritic growth and columnar dendritic growth under directional solidification was carried out, and validation was performed by comparing the simulated results with the experimental results and those in the previously published works.展开更多
Highlighting the Time,Culture and Identity cross-disciplinary project conducted between the Science Museum in London,the Palace Museum in Beijing,academics at Beijing Jiaotong University and the Institute for the Hist...Highlighting the Time,Culture and Identity cross-disciplinary project conducted between the Science Museum in London,the Palace Museum in Beijing,academics at Beijing Jiaotong University and the Institute for the History of Natural Sciences,and creative industries practitioners in China and the UK,this introduction highlights the key impacts of the research.As well as creating the practical output of a digital museum experience focused on the workings of the Country Scene clock,the research brought a range of wider impacts,including a change in understanding between collaborators,capacity-building skills,research process development and a change in attitude.The papers of this supplementary issue reflect some of the range of impacts of the work of our collaborators.展开更多
Digital media offer unique opportunities for museums to bring to life the secrets and stories of their historical collections.To bring insight into the process of developing digital media exhibits,this paper presents ...Digital media offer unique opportunities for museums to bring to life the secrets and stories of their historical collections.To bring insight into the process of developing digital media exhibits,this paper presents the perspective of a creative practitioner in approaching technology-and media-based interpretation for collection objects.It follows the Time,Culture and Identity digital workshop held in Beijing in October 2019,which explored and shared ideas about collaborative research and interdisciplinary practice in digital interpretation between academics,institutions,creative practitioners,and developers.Following the direction of the workshop,the paper takes as its focus the clocks and automatons of the imperial collection at the Palace Museum in Beijing.Observations are based on the author’s practice-led experience in running a design studio,Harmonic Kinetic,developing new media exhibits using digital technology and audiovisual media for museums,galleries,and exhibitions in the UK,including the Science Museum,V&A,Barbican,Tate,and the Tower of London.Taking a broad interaction-design-led outlook,the paper explores a personal design perspective for developing interpretive content and considers the particular opportunities and approaches these historical devices suggest.The paper concludes with a final section that reviews the process and reflects on outcomes from the Time,Culture and Identity digital workshop.This explored possibilities for an interpretive exhibit on the Country Scene clock from the Palace Museum collection.展开更多
It was analyzed that the finite element-cellular automaton （CAFE） method was used to simulate 3D-microstructures in solidification processes. Based on this method, the 3D-microstructure of 9SMn28 free-cutting steel ...It was analyzed that the finite element-cellular automaton （CAFE） method was used to simulate 3D-microstructures in solidification processes. Based on this method, the 3D-microstructure of 9SMn28 free-cutting steel was simulated in solidification processes and the simulation results are consistent with the experimental ones. In addition, the effects of Gaussian distribution parameters were also studied. The simulation results show that the higher the mean undercooling, the larger the columnar dendrite zones, and the larger the maximum nucleation density, the smaller the size of grains. The larger the standard deviation, the less the number of minimum grains is. However, the uniformity degree decreases first, and then increases gradually.展开更多
基金supported by the National Science and Technology Major Project of China(No.J2019-VI-0004-0117)。
文摘Casting experiments and macro-micro numerical simulations were conducted to examine the microstructure characteristics of K439B nickel-based superalloy casting with varying cross-sections during the gravity investment casting process.Firstly,microstructure analysis was conducted on the casting using scanning electron microscopy(SEM)and electron backscatter diffraction(EBSD).Subsequently,calculation of the phase diagram and differential scanning calorimetry(DSC)tests were conducted to determine the macro-micro simulation parameters of the K439B alloy,and the cellular automaton finite element(CAFE)method was employed to develop macro-micro modeling of K439B nickel-based superalloy casting with varying cross-sections.The experimental results revealed that the ratio of the average grain area increased from the edge to the center of the sections as the ratio of the cross-sectional area increased.The simulation results indicated that the average grain area increased from 0.885 to 0.956 mm^(2)as the ratio of the cross-sections increased from 6꞉1 to 12꞉1.The experiment and simulation results showed that the grain size became more heterogeneous and the grain shape became more irregular with an increase in the ratio of the cross-sectional area of the casting.CAFE modeling was an effective method to simulate the microstructure evolution of the K439B alloy and ensure the accuracy of the simulation.
基金financially supported by the National Natural Science Foundation of China(Grant No.51875211)the Beijing Natural Science Foundation(Grant No.L223001)。
文摘Microporosity formed in the solidification process of Al alloys is detrimental to the alloy properties.A two-dimensional cellular automaton(CA)model was developed to simulate the microstructure and microporosity formation in Al-Cu alloys,considering variations in Cu content and solidification rate.The results indicate that the Cu content primarily influences the growth of microporosity.To validate the model,directional solidification experiments were conducted on Al-Cu alloys with varing Cu contents and withdrawal rates.The experimental results of dendrites and microporosity characteristics agree well with the predictions from the developed model,thus confirming the validity of the model.The alloy’s liquidus temperature,dendrite morphology,and hydrogen saturation solubility arising from different Cu contents have significant effects on microporosity morphology.The withdrawal rate primarily affects the nucleation of hydrogen microporosity by altering cooling rates and dendritic growth rates,resulting in different microporosity characteristics.
基金supported by the National Natural Science Foundation of China(Grant No.52301035)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20230844)the National Key Research and Development Program of China(Grant No.2023YFB3710202).
文摘The microstructure formed during solidification has a significant impact on the mechanical properties of materials.In this study,a two-dimensional(2D)cellular automaton(CA)-finite difference(FD)-CALPHAD model was developed to simulate the formation of microstructure and solute segregation in the solidification processes of ternary alloys.In the model,dendritic growth is simulated using the CA technique,while solute diffusion is solved by the FD method,and the CALPHAD method is employed to calculate thermodynamic phase equilibrium during solidification.The CA-FD-CALPHAD coupled model is capable of reproducing the evolution of continuous nucleation and growth of grains as well as the evolution of the microstructure and solute distribution during solidification of ternary alloys.In this study,Al–Zn–Mg ternary alloy is taken as an example to simulate the growth of equiaxed and columnar grains and the columnar-to-equiaxed transition(CET)under different solidification conditions.The simulation results are compared with experimental data from the literature,showing a good agreement.Besides,the study also investigates the evolution of temperature and multicomponent solute fields during solidification and the effects of alloy composition and cooling rate on the microstructure morphology.The results reveal that the initial alloy composition and cooling rate significantly affect dendritic morphology and solute segregation.Higher initial alloy concentrations promote the growth of side branches in equiaxed grains,leading to more pronounced solute segregation between dendrites.As the cooling rate increases,the average grain size of the equiaxed grains decreases accordingly.Additionally,a higher cooling rate accelerates the columnar-to-equiaxed transition,leading to a finer grain structure.
基金financially supported by the National Natural Science Foundation of China(Project No.52075288)。
文摘Accurately tailoring microstructures,especially grain size,during thermomechanical processing is crucial for achieving the desired strengthductility synergy of wrought magnesium alloys.This study establishes a multilevel cellular automaton(CA)model to predict the microstructure evolution of wrought magnesium alloys undergoing both dynamic recrystallization(DRX)and dynamic precipitation(DP),surpassing the capabilities of traditional DRX models.Multiple physical metallurgical mechanisms,including variations in dislocation with work hardening(WH)and dynamic recovery(DRV),DRX,DP,and solute diffusion,are integrated and interconnected by their mutual effects.To facilitate the CA modeling,a novel local pinning model is proposed to reflect the uneven retardation of a precipitate to grain boundary migration and the virtual intersections of precipitates and grain boundaries based on their distribution,and its rationality is verified by simulations for grain coarsening.Considering the substantial difference in grain size and precipitate size,a multilevel cellular space is constructed,with a coarse parent cellular space for DRX and a sub-cellular space discretized from parent cells for DP,to balance computational efficiency and accuracy.The simulation successfully captures the microstructure evolution with multiscale characteristics,specifically the refinement of grains from hundreds of micros to a few micros through DRX,aided by dynamically precipitated second-phase particles in the submicron(hundreds of nanometers)range.The high degree of agreement between simulated and experimental results in terms of kinetics for microstructure evolution and microstructure after deformation at various temperatures and strain rates attests to the sound rationality and strong predictive capability of the established multilevel CA model.A comparison between the simulated results of the traditional CA model exclusively for DRX and those obtained from the multilevel CA model that incorporates both DRX and DP highlights the necessity of considering the interaction between these two phenomena for accurate grain size prediction.
基金supported by the National Natural Science Foundation of China(Grant No.71671109)the National Key Research and Development Program of China(Grant No.2020YFB1600500)the Key Research and Development Program of Heilongjiang Province,China(Grant No.GZ20220089)。
文摘A novel deceleration traffic flow model is established based on the oscillatory congested states and the slow-tostart rule.The novel model considers human overreaction and mechanical restrictions as limited deceleration capacity,effectively avoiding the unrealistic deceleration behavior found in most existing traffic flow models.In order to consider that the acceleration of a stationary vehicle is slower than that of a moving vehicle due to reasons such as driver inattention,the slow-to-start rule is introduced.In actual traffic,the driver will take different deceleration measures according to local traffic conditions,divided into ordinary and emergency deceleration.The deceleration setting in the deceleration model with only ordinary deceleration is modified.Computer simulations show that the novel model can achieve smooth,comfortable acceleration and deceleration behavior.Introducing the slow-to-start rule can realize the first-order transition from free flow to synchronized flow.The oscillatory congested states enable a first-order transition from synchronized flow to wide moving jam.Under periodic boundary conditions,the novel model can reproduce three traffic flow phases(free flow,synchronized flow,and wide moving jam)and two first-order transitions between three phases.In addition,the novel model can reproduce empirical results such as linear synchronized flow and headway distribution of free flow below 1 s.Under open boundary conditions,different congested patterns caused by on-ramps are analyzed.Compared with the classic deceleration model,this model can better reproduce the phenomenon and characteristics of actual traffic flow and provide more accurate decision support for daily traffic management of expressways.
文摘提出一种基于确定的有穷状态自动机(deterministic finite automaton,简称DFA)的正则表达式压缩算法.首先,定义了膨胀率DR(distending rate)来描述正则表达式的膨胀特性.然后基于DR提出一种分片的算法RECCADR(regular expressions cut and combine algorithm based on DR),有效地选择出导致DFA状态膨胀的片段并隔离,降低了单个正则表达式存储需求.同时,基于正则表达式的组合关系提出一种选择性分群算法REGADR(regular expressions group algorithm based on DR),在可以接受的存储需求总量下,通过选择性分群大幅度减少了状态机的个数,有效地降低了匹配算法的复杂性.
基金Projects (50935007,51175428) supported by the National Natural Science Foundation of ChinaProject (2010CB731701) supported by the National Basic Research Program of China+2 种基金Project (NPU-FFR-JC20100229) supported by the Foundation for Fundamental Research of Northwestern Polytechnical University in ChinaProject (27-TZ-2010) supported by the Research Fund of the State Key Laboratory of Solidification Processing,ChinaProject (B08040) supported by the Program of Introducing Talents of Discipline to University,China
文摘A cellular automaton（CA） modeling of discontinuous dynamic recrystallization（DDRX） of a near-α Ti-6Al-2Zr-1Mo-1V（TA15） isothermally compressed in the β single phase field was presented.In the CA model,nucleation of the β-DDRX and the growth of recrystallized grains（re-grains） were considered and visibly simulated by the CA model.The driving force of re-grain growth was provided by dislocation density accumulating around the grain boundaries.To verify the CA model,the predicted flow stress by the CA model was compared with the experimental data.The comparison showed that the average relative errors were10.2%,10.1%and 6%,respectively,at 1.0,0.1 and 0.01 s^-1 of 1020 ℃,and were 10.2%,11.35%and 7.5%,respectively,at 1.0,0.1and 0.01 s^-1 of 1050 ℃.The CA model was further applied to predicting the average growth rate,average re-grain size and recrystallization kinetics.The simulated results showed that the average growth rate increases with the increasing strain rate or temperature,while the re-grain size increases with the decreasing strain rate;the volume fraction of recrystallization decreases with the increasing strain rate or decreasing temperature.
基金Projects (2010DFA72760, 2011BAE22B02, 2011ZX04014-052, 2011ZX04001-071) supported by the Ministry of Science and Technology of China
文摘Based on the cellular automaton （CA） method, a numerical model was developed to simulate the dendritic growth of magnesium alloy with HCP crystal structure. The growth kinetics was calculated from the complete solution of the transport equations. By defining a special neighborhood configuration with the square CA cell, and using a set of capturing rules which were proposed by BELTRAN-SANCHEZ and STEFANESCU for the dendritic growth of cubic crystal metals during solidification, modeling of dendritic growth of magnesium alloy with different growth orientations was achieved. Simulation of equiaxed dendritic growth and columnar dendritic growth under directional solidification was carried out, and validation was performed by comparing the simulated results with the experimental results and those in the previously published works.
基金the UK Arts and Humanities Research Councilthe Newton Fund
文摘Highlighting the Time,Culture and Identity cross-disciplinary project conducted between the Science Museum in London,the Palace Museum in Beijing,academics at Beijing Jiaotong University and the Institute for the History of Natural Sciences,and creative industries practitioners in China and the UK,this introduction highlights the key impacts of the research.As well as creating the practical output of a digital museum experience focused on the workings of the Country Scene clock,the research brought a range of wider impacts,including a change in understanding between collaborators,capacity-building skills,research process development and a change in attitude.The papers of this supplementary issue reflect some of the range of impacts of the work of our collaborators.
文摘Digital media offer unique opportunities for museums to bring to life the secrets and stories of their historical collections.To bring insight into the process of developing digital media exhibits,this paper presents the perspective of a creative practitioner in approaching technology-and media-based interpretation for collection objects.It follows the Time,Culture and Identity digital workshop held in Beijing in October 2019,which explored and shared ideas about collaborative research and interdisciplinary practice in digital interpretation between academics,institutions,creative practitioners,and developers.Following the direction of the workshop,the paper takes as its focus the clocks and automatons of the imperial collection at the Palace Museum in Beijing.Observations are based on the author’s practice-led experience in running a design studio,Harmonic Kinetic,developing new media exhibits using digital technology and audiovisual media for museums,galleries,and exhibitions in the UK,including the Science Museum,V&A,Barbican,Tate,and the Tower of London.Taking a broad interaction-design-led outlook,the paper explores a personal design perspective for developing interpretive content and considers the particular opportunities and approaches these historical devices suggest.The paper concludes with a final section that reviews the process and reflects on outcomes from the Time,Culture and Identity digital workshop.This explored possibilities for an interpretive exhibit on the Country Scene clock from the Palace Museum collection.
基金supported by the National Natural Science Foundation of China (No.50874007, 50774109)
文摘It was analyzed that the finite element-cellular automaton （CAFE） method was used to simulate 3D-microstructures in solidification processes. Based on this method, the 3D-microstructure of 9SMn28 free-cutting steel was simulated in solidification processes and the simulation results are consistent with the experimental ones. In addition, the effects of Gaussian distribution parameters were also studied. The simulation results show that the higher the mean undercooling, the larger the columnar dendrite zones, and the larger the maximum nucleation density, the smaller the size of grains. The larger the standard deviation, the less the number of minimum grains is. However, the uniformity degree decreases first, and then increases gradually.
