相场法模拟对流对枝晶生长的影响
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摘要
采用计算机建模和数值模拟建立材料微观组织与材料加工工艺、材料性能间的联系,实现对材料性能的预测和改善具有重要的工程意义和理论价值。对流影响凝固微观组织形貌已是不容质疑的事实。本文利用相场法微观组织数值模拟技术,对强迫对流作用下的过冷纯金属凝固过程单枝晶、多枝晶的生长进行模拟,研究了不同模拟条件下的枝晶生长方式,探讨了过冷纯金属熔体枝晶生长机制。
本文基于Tong相场模型发展得到的单相场控制多晶粒相场模型,采用相场、流场及温度场三场耦合的方法对纯金属镍凝固过程中的枝晶生长进行了数值模拟。采用Visual C++6.O实现程序的计算,为了提高计算效率和节省计算时间,应用直接差分去求解两场方程,然后以.TXT方式输出计算结果,最后利用Tecplot9.0实现模拟结果的可视化。
首先,通过分析比较有无强迫对流情况下单枝晶形貌的不同,得出对流作用下上游尖端生长速度最快,水平方向次之,下游尖端生长速度最慢;研究了单枝晶在不同择优生长方向有无对流时的枝晶形貌和尖端速度。
其次,研究了强迫对流无扰动情况下对流速度、各向异性系数、过冷度及耦合系数对晶粒形貌的影响,计算了不同情况下的尖端生长速度。结果表明:对流作用下枝晶各尖端生长速率表现为对流速度越大,整个枝晶体积也越大,上游枝晶生长速度的优势越明显;各向异性越大,各向主枝越细,当各向异性大于0.07时,枝晶形貌发生变异失真;过冷度在纯金属枝晶生长过程中起着决定性的作用,随着过冷度的增大,枝晶尖端速率是呈线性增大趋势的;随着耦合系数的增大,形貌由肥大枝晶状-瘦长枝晶状,当人为放大时,晶粒形貌失真,因此,耦合系数的选取应由材料的热物性参数决定。
再次,模拟了纯金属有无对流时多晶粒在不同择优方向上的生长形貌,结果表明,当晶粒彼此相向生长时,生长会彼此影响,不同晶粒的主枝会彼此抑制,使得某个晶粒的某一主枝长度比其他主枝长度小,而且主枝生长弯曲。另外加入噪声的情况下,促进二次枝晶的生长。本文的计算效率大大提高,能较真实的模拟凝固过程枝晶的生长过程。
Computer modeling and numerical simulations of dendritic crystal growth plays an important role in prediction and improving material properties to establish the relationship of material properties and material processing with material microstructure.Convection influence on the organization in solidifying is already the fact which allows of no to query. In this paper aimed at simulating single grain and multiple grains growth under the role of forced convective during solidifieation of undercooled melt of pure metal under different condition by using phase-field method.The mechanism of dendritic growth in undercooled melt is diseussed.
Based on the coupling of flow and temperature,phase field of phase-field model, proposed by Tong, develops the model which consists of a single-phase control of many grains of dendritic growth, and studies pure nickel metal in solidification process of dendritic growth for the numerical simulation.In the process of simulation, the Visual C++ 6.0 was used to calculate the program and the Tecplot 9.0 was used to achieve the vision of results. In order to save time of calculation and improve the efficiency, an interpolative method is used to achieve the coupling of the macro field and the micro field.
First of all, through the analysis of whether or not forced convection case compared dendrite morphology,The growth speeds of each tip in a forced flow are different, the upstream tip is highest,the tip in a horizontal direction normal to the flow comes next, and the downstream tip is slowest. studies of a single dendrite at the preferred growth orientation whether or not convection case dendrite morphology and the speeds of tip.
Secondly, studies the influence of forced convection velocity U, the undercooling△, anisotropic coefficientγand the coupling coefficientλon the grain morphologies, calculated under different circumstances the speeds of tip. The results showed that: with the fast of the convection velocity, the growth speeds of the dendrite become larger ,the more obvious advantagest of the speed upstream dendrites ; the larger the anisotropic coefficient y , the thinner the branching are ,when anisotropy is greater than 0.07, the variation of dendrite morphology distortion happened; undercooling in the pure metal dendrite growth process plays a very decisive role, when the undercooling is great, dendrite tip velocity is increased linearly the general trend; coupling coefficient with the increase of crystal morphology by mast～slender sticks crystal, when the artificial amplification, the grain morphology of distortion, Therefore, the value of coupling coefficient is detemined by physical properties .
Third, whether or not the convection of pure metal is simulated when many grains in different directions at the preferred growth orientation morphology, The results show that the opposite to each other,when the grains growth will be affected each other, different grains with one another and inhibit the main branch, making a grain length of a main branch length shorter than the other, and its main branch the growth of bending. Also add the case of noise, and promote the growth of secondary dendrites.In this paper, greatly improve the computational efficiency, and the model could present the true solidification process of dendritic growth.
本文基于Tong相场模型发展得到的单相场控制多晶粒相场模型,采用相场、流场及温度场三场耦合的方法对纯金属镍凝固过程中的枝晶生长进行了数值模拟。采用Visual C++6.O实现程序的计算,为了提高计算效率和节省计算时间,应用直接差分去求解两场方程,然后以.TXT方式输出计算结果,最后利用Tecplot9.0实现模拟结果的可视化。
首先,通过分析比较有无强迫对流情况下单枝晶形貌的不同,得出对流作用下上游尖端生长速度最快,水平方向次之,下游尖端生长速度最慢;研究了单枝晶在不同择优生长方向有无对流时的枝晶形貌和尖端速度。
其次,研究了强迫对流无扰动情况下对流速度、各向异性系数、过冷度及耦合系数对晶粒形貌的影响,计算了不同情况下的尖端生长速度。结果表明:对流作用下枝晶各尖端生长速率表现为对流速度越大,整个枝晶体积也越大,上游枝晶生长速度的优势越明显;各向异性越大,各向主枝越细,当各向异性大于0.07时,枝晶形貌发生变异失真;过冷度在纯金属枝晶生长过程中起着决定性的作用,随着过冷度的增大,枝晶尖端速率是呈线性增大趋势的;随着耦合系数的增大,形貌由肥大枝晶状-瘦长枝晶状,当人为放大时,晶粒形貌失真,因此,耦合系数的选取应由材料的热物性参数决定。
再次,模拟了纯金属有无对流时多晶粒在不同择优方向上的生长形貌,结果表明,当晶粒彼此相向生长时,生长会彼此影响,不同晶粒的主枝会彼此抑制,使得某个晶粒的某一主枝长度比其他主枝长度小,而且主枝生长弯曲。另外加入噪声的情况下,促进二次枝晶的生长。本文的计算效率大大提高,能较真实的模拟凝固过程枝晶的生长过程。
Computer modeling and numerical simulations of dendritic crystal growth plays an important role in prediction and improving material properties to establish the relationship of material properties and material processing with material microstructure.Convection influence on the organization in solidifying is already the fact which allows of no to query. In this paper aimed at simulating single grain and multiple grains growth under the role of forced convective during solidifieation of undercooled melt of pure metal under different condition by using phase-field method.The mechanism of dendritic growth in undercooled melt is diseussed.
Based on the coupling of flow and temperature,phase field of phase-field model, proposed by Tong, develops the model which consists of a single-phase control of many grains of dendritic growth, and studies pure nickel metal in solidification process of dendritic growth for the numerical simulation.In the process of simulation, the Visual C++ 6.0 was used to calculate the program and the Tecplot 9.0 was used to achieve the vision of results. In order to save time of calculation and improve the efficiency, an interpolative method is used to achieve the coupling of the macro field and the micro field.
First of all, through the analysis of whether or not forced convection case compared dendrite morphology,The growth speeds of each tip in a forced flow are different, the upstream tip is highest,the tip in a horizontal direction normal to the flow comes next, and the downstream tip is slowest. studies of a single dendrite at the preferred growth orientation whether or not convection case dendrite morphology and the speeds of tip.
Secondly, studies the influence of forced convection velocity U, the undercooling△, anisotropic coefficientγand the coupling coefficientλon the grain morphologies, calculated under different circumstances the speeds of tip. The results showed that: with the fast of the convection velocity, the growth speeds of the dendrite become larger ,the more obvious advantagest of the speed upstream dendrites ; the larger the anisotropic coefficient y , the thinner the branching are ,when anisotropy is greater than 0.07, the variation of dendrite morphology distortion happened; undercooling in the pure metal dendrite growth process plays a very decisive role, when the undercooling is great, dendrite tip velocity is increased linearly the general trend; coupling coefficient with the increase of crystal morphology by mast～slender sticks crystal, when the artificial amplification, the grain morphology of distortion, Therefore, the value of coupling coefficient is detemined by physical properties .
Third, whether or not the convection of pure metal is simulated when many grains in different directions at the preferred growth orientation morphology, The results show that the opposite to each other,when the grains growth will be affected each other, different grains with one another and inhibit the main branch, making a grain length of a main branch length shorter than the other, and its main branch the growth of bending. Also add the case of noise, and promote the growth of secondary dendrites.In this paper, greatly improve the computational efficiency, and the model could present the true solidification process of dendritic growth.
引文
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[2]Steinbach I,Beckermann C.Three -dimensional modeling of equiaxed dendritic growth on a mesoscopic scale.Acta Mater,1999,47(3):971-982
[3]于艳梅.过冷熔体中枝晶生长的相场法数值模拟.西北工业大学博士学位论文.西安:西北工业大学,2002,6
[4]Rappaz M,Gandin C A.Probabilostic Modelling of Microstructure Formation in Solidification Processes.Acta Metall,1993,41(2):350-361
[5]Gandin C A,Rappaz M.A coupled Finite Element-Celluar Automation Model for the prediction of dendritic grain structures on solidification processes.Acta Metall,1994,42(7):2233-2246
[6]Wang C Y,Beckermann C.Prediction of Columnar to Equiaxed Transition during Diffusion-Controlled Dendritic Alloy Solidification.Metall.Mater.Trans.A,1994,25A:1081-1093
[7]Oldfield W.A qualitative approach to casting solidification.Freezing of Cast Iron,ASM Trans,1996,59:945-960
[8]Hunt J D.Steady State Columnar and Equiaxed Growth of Dendrites and Eutectic.Mater.Sci.Eng,1984,65:75-83
[9]Thevoz Ph,Desbiolies J L,Rappaz M.Modeling of Equiaxed Microstructure Formation in Casting.Metall.Trans.A,1989,20A:311-321
[10]Rappaz M,Thevoz Ph.Solute Diffusion Model for Exquiaxed Dendritic Growth.Acta Metall,1987,35(7):1487-1497
[11]Rappaz M,Thevoz Ph.Solute Diffusion Model for Exquiaxed Dendritic Growth:Analytical Solution.Acta Metall,1987,35(12):2929-2933
[12]Wang C Y,Beckermann C.Prediction of Columnar to Equiaxed Transition during Diffusion-Controlled Dendritic Alloy Solidification.Metall.Mater.Trans.A,1994,25A:1081-1093
[13]Wang C Y,Beckermann C.Equiaxed Dendritic Solidification with Convection Multiscale/Multiphase Modeling.Metall.Mater.Trans,1996,27A(9):2754-2764
[14]Wang C Y,Beckermann C.Equiaxed Dendritic Solidification with Convection Numerical Simulations for an A1-4wtpctCuAlloy.Metall.Mater.Trans.A,1996, 27A(9): 2765-2783
[15] D.罗伯.计算材料学.北京.化学工业出版社.2003
[16] Spittle J A ,Brown S G R. Computer Simulation of the Effects of Alloy Variables on the Grain Structures of Castings. Acta Metall, 1989,37 (7):1803-1810
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