基于Euler-Lagrange的发泡成型射料过程的数值模拟
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摘要
干砂负压消失模铸造技术中模样是消失模铸造成败的关键,而泡沫珠粒的充填是获得优质泡沫模样的关键工序之一。泡沫珠粒在模具中充填不均或不密实会使模样出现残缺不全或融合不充分等缺陷,影响产品的表面质量。因此利用计算机对泡沫珠粒射料充填过程的流动场进行数值模拟,定量地了解射料过程的影响因素,有利于优化射料工艺、提高效率和减少废品。
本文建立了基于欧拉-拉格朗日模型的考虑可压缩性影响的密相气固两相流的模型,比较全面系统地推导出含有10个未知变量的密相可压气固两相流的封闭的偏微分方程组,其中考虑了变密度的影响,为流场的数值分析奠定了坚实的理论基础。
本文建立了基于欧拉-拉格朗日模型的适用于密相可压气固两相流的数值解法。在建立压力修正方程时考虑了气相的可压缩性,使得这种修正方法可适用于变密度的各种情况。
基于欧拉-拉格朗日模型,采用计算流体分析软件Fluent对发泡模具射料充填过程进行数值模拟。与物理模拟对比表明,数值模拟结果中的泡沫珠粒的流动趋势与实际情况基本上是一致的。
In lost foam casting ,the foam pattern is the key qualification, and the filling process is one of the crucial processes to ensure the high quality of the foam pattern. Filling without uniformity and denseness will cause various defects and affect the quality of the surface. The influential factors of filling process are realized .And optimizing filling process, enhancing efficiency, decreasing waster and so on are obtained by the numerical simulation of filling process .
The partial differential equations which is based on Euler-Lagrange model containing 10 variables are established systematically to control dense gas-solid two-phase turbulent flow in which variable density in two-phase turbulent flow have been taken into account, and the foundation is thus laid for numerical analysis.
A new algorithm is proposed to solve dense compressible gas-solid two-phase flow. The pressure correction equations of gas pressure is established in which correction of gas concentration is considered so that it can be applied to variable density case.
Based on Euler-Lagrange method, the filling process is simulated by Fluent, an analysis software of the computation fluid dynamics. By comparing the result of numerical simulation with the examinations, it is found that the fluid trend of foam beads in the numerical simulation is accordant to the actual process.
本文建立了基于欧拉-拉格朗日模型的考虑可压缩性影响的密相气固两相流的模型,比较全面系统地推导出含有10个未知变量的密相可压气固两相流的封闭的偏微分方程组,其中考虑了变密度的影响,为流场的数值分析奠定了坚实的理论基础。
本文建立了基于欧拉-拉格朗日模型的适用于密相可压气固两相流的数值解法。在建立压力修正方程时考虑了气相的可压缩性,使得这种修正方法可适用于变密度的各种情况。
基于欧拉-拉格朗日模型,采用计算流体分析软件Fluent对发泡模具射料充填过程进行数值模拟。与物理模拟对比表明,数值模拟结果中的泡沫珠粒的流动趋势与实际情况基本上是一致的。
In lost foam casting ,the foam pattern is the key qualification, and the filling process is one of the crucial processes to ensure the high quality of the foam pattern. Filling without uniformity and denseness will cause various defects and affect the quality of the surface. The influential factors of filling process are realized .And optimizing filling process, enhancing efficiency, decreasing waster and so on are obtained by the numerical simulation of filling process .
The partial differential equations which is based on Euler-Lagrange model containing 10 variables are established systematically to control dense gas-solid two-phase turbulent flow in which variable density in two-phase turbulent flow have been taken into account, and the foundation is thus laid for numerical analysis.
A new algorithm is proposed to solve dense compressible gas-solid two-phase flow. The pressure correction equations of gas pressure is established in which correction of gas concentration is considered so that it can be applied to variable density case.
Based on Euler-Lagrange method, the filling process is simulated by Fluent, an analysis software of the computation fluid dynamics. By comparing the result of numerical simulation with the examinations, it is found that the fluid trend of foam beads in the numerical simulation is accordant to the actual process.
引文
[1] 黄乃瑜, 罗吉荣. 面向 21 世纪的消失模铸造技术[J]. 特种铸造及有色合金, 1998(4): 37~40
[2] 黄乃瑜, 叶升平, 樊自田. 消失模铸造原理及质量控制[M]. 武汉: 华中科技大学出版社, 2004
[3] 胡国良. 消失模铸造用共聚物泡沫模样的成型及控制技术[D], 武汉: 华中科技大学材料学院, 2002
[4] 王文琪. 两相流动[M]. 北京: 水利电力出版社, 1989
[5] M.A. Rizk, S.E. Eloghobshi. A two-equation turbulence model for dispersed dilute confined two-phase flows [J]. Int J Multiphase Flow, 1989, 15(1) 119~133
[6] 周力行. 湍流两相流动与燃烧的数值模拟[M]. 北京: 清华大学出版社, 1991
[7] Dukowicz, J.K.. A particle-fluid numerical model for liquid sprays[J]. J. Comput. Phys. 1980(35), 229-253,
[8] 刘大有. 两相流体动力学[M]. 北京: 高等教育出版社, 1993
[9] 周力行. 湍流两相流动与燃烧的数值模拟[M]. 北京: 清华大学出版社, 1991
[10] Smoot, L.D., Pratt, D.T. .Pulverized coal combustion and gasification[M]. New York: Plenum, 1979
[11] Gauvin, W.H., Katta, S., Knelman, F.H., 1975.Drop trajectory predictions and their importance in the desigh of spray dryers[J]. Int. J.Multiphase Flow, 1993(20), 793-816
[12] Crowe, C.T., Sharma, M.P. , Stock, D.E., 1977. The particle-source-in cell(PSI-CELL) model for gas-droplet flows[J]. Trans, ASME J. Fluids Eng. 99, 325-332
[13] Andrews, M.J.,O’Rourke, P. J.,The Multiphase Particle-In-Cell(MP-PIC) Method for Dense Particulate Flows[J]. Int. J. Multiphase Flow. 1996, 22:379-402
[14] O’Rourke, P.J. Collective drop effects on vaporizing liquid sprays[D]. Princeton University, NJ. 1981
[15] D.M. Snider, P. J. O’Rourke, and M. J. Andrews. Sediment flow in inclined vessels calculated using multiphase particle-in-cell model for dense particle flow[J], Int. J. Multiphase Flow.1998, 24: 1359-1382
[16] N.A. Patankar, D.D. Joseph. Lagrangian numerical simulation of particulate flows[J]. Int J Numerical methods Fluids, 1999, 29(8): 201- 217
[17] Golafshani, H.T. Loh. Computation of two phase viscous flow in solid rocket motor using a flux-split Eulerian-Lagrangian technique[J]. AIAA-89-2985
[18] R Madabhushi, J Sabnois, F Jong and H Gibeling. Calculation of the two-phase aft-dome flowfield in solid rocket motors[J]. J propulsion, 1991, 7(2): 178-184
[19] T Jachandra, R C Mehta.A fast algorithm to stove viscous two-phase flow in an axisymmetric rocket nozzle[J]. Int J Numerical methods Fluids, 1998, 26(5): 501- 517
[20] T.J. Coakly, J M. Champeny. Numerical simulation of compressible turbulent two-phase flow[J]. AIAA-85-1666
[21] H.T. Chang, L.W. Hourng, L.C. Chien. Application of flux-vector-splitting scheme to a dilute gas-particle JPL nozzle flow[J].Int J Numerical Methods Fluids, 1996, 22(10): 921-935
[22] 侯晓. 固体火箭喷管两相湍流的数值模拟[D] , 西安: 西北工业大学航天工程学院, 1990
[23] 李江. 固体火箭发动机内颗粒运动模式的研究[D]. 西安: 西北工业大学航天工程学院,1998
[24] Hiroyasu Makino, Yasuhiro Maeda, Hiroyuki Nomura.Force analysis in air-flowpress moulding using the distinct element method[J].Int.J.Cast Metal Res, 1997, 10: 171~175
[25] Sahm,Pelzer M, Meiser L, Pro. Simulation of the Core shooting Process [R].CIATF Technical Forum 99
[26] 美国 Arena-Flow 公司的介绍光盘[CD]. 堪萨斯城: 美国铸造博览会, 2002, 5
[27] 陈代海, 崔怡, 王海, 吴浚郊. 射砂过程气砂两相运动的研究[J]. 中国铸造装备与技术, 2001(4): 12~13
[28] 王涛, 崔怡, 陈代海, 李文珍. 射砂紧实过程的试验研究[J]. 中国铸造装备与技术, 2001(2): 9~11
[29] 崔怡, 李文珍, 吴浚郊, 张涛. 射砂紧实机理的研究[J]. 中国铸造装备与技术, 2001(1): 17~19
[30] 崔怡, 李文珍, 吴浚郊. 射砂过程初始条件的试验研究[J]. 中国铸造装备与技术, 2000(5): 11~13
[31] 崔怡, 李文珍, 吴浚郊.射砂过程的数值模拟[J].特种铸造及有色合金, 2001(2): 34~36
[32] 陈代海, 崔怡, 吴浚郊.芯盒设计对射砂过程的影响[J].铸造, 2001(7), 342~345
[33] 崔怡, 李文珍, 吴浚郊.利用两相流模型模拟射砂过程的进展[J].铸造技术, 2000(6): 8~10
[34] 崔怡, 李文珍, 吴浚郊. 芯盒结构对射砂过程的影响[J].特种铸造及有色合金, 2000(3): 4~6
[35] 崔怡, 李文珍, 吴浚郊, 张涛.冷芯盒射砂工艺参数的研究[J].铸造, 2000(9): 527~532
[36] 李宏亮, 崔怡, 吴浚郊.射砂过程数值模拟的技术现状[J].铸造, 2002(11): 737~740
[37] 崔怡, 李宏亮,吴浚郊. 射沙过程数值模拟的应用[J]. 铸造, 2003(6): 415-419
[38] 姜俊侠. 发泡模具射料过程充填过程的数值模拟[J]. 铸造, 2005(5): 479-483
[39] 陈尧剑. 消失模珠粒射料充填过程的数值模拟[J], 清华大学学报, 2005(8): 106-109
[40] H.K. Versteeg, W. Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method. Wiley, New York, 1995
[41] 施学贵, 徐旭常, 冯俊凯. 颗粒在湍流中的运动受力分析[J].工程热物理学报, 1989, 10(3): 320~325
[42] Harris, S.E., Crighton D.G..Solitons, Solitary waves and voidage disturbances in gas-fluidized beds[J]. J.Fluid Mech. 1994, 243-276
[43] W. Malalasekera .An Introduction to CFD: The Finite Volume Method. Wiley, New York, 1994
[44] T. Hayase, J.A.C.Humphrey,A.Greif,A consistently formulated QUICK schcme for fast and stable convergence using finite-volume iterative calculation procedures[J]. Joumal of Computational Physics,1992, 98:108-118,
[45] S V Patankar. 传热与流体流动的数值计算[M], 北京: 科学技术出版社. 1984
[46] Rhie, W.L. Chow. Numerical study of the turbulent flow past an airfoil with trailing edge seperation[J]. AIAA(J), 1983, 21(9): 1525-1532.1
[47] D.B. Spalding. Numerical computation of multiphase fluid flow and heat transfer[M]. In recent advances in numerical methods in fluids, 1980(1): 139-167
[48] 王长安, 密相液固两相三维湍流流动的研究及其在泵叶轮内流场计算与数值分析中的应用[D]. 西安: 西安交通大学能源与动力工程学院, 1996
[49] 魏进家, 密相液固两相湍流 KET 模型和数值计算及离心泵叶轮内两相流场实验研究[D]. 西安: 西安交通大学能源与动力工程学院, 1998
[50] 曾卓雄, 密相可压气固两相湍流流动[D], 西安交通大学能源与动力工程学院, 2002
[51] Hui. Boundary conditions for high shear grain flows[J], J Fluid Mech, 1984, 145(223)
[52] 李勇, 刘志友, 安亦然. 介绍计算流体力学通用软件—Fluent. 水动力学研究与进展[J], 2001(6): 254~258
[2] 黄乃瑜, 叶升平, 樊自田. 消失模铸造原理及质量控制[M]. 武汉: 华中科技大学出版社, 2004
[3] 胡国良. 消失模铸造用共聚物泡沫模样的成型及控制技术[D], 武汉: 华中科技大学材料学院, 2002
[4] 王文琪. 两相流动[M]. 北京: 水利电力出版社, 1989
[5] M.A. Rizk, S.E. Eloghobshi. A two-equation turbulence model for dispersed dilute confined two-phase flows [J]. Int J Multiphase Flow, 1989, 15(1) 119~133
[6] 周力行. 湍流两相流动与燃烧的数值模拟[M]. 北京: 清华大学出版社, 1991
[7] Dukowicz, J.K.. A particle-fluid numerical model for liquid sprays[J]. J. Comput. Phys. 1980(35), 229-253,
[8] 刘大有. 两相流体动力学[M]. 北京: 高等教育出版社, 1993
[9] 周力行. 湍流两相流动与燃烧的数值模拟[M]. 北京: 清华大学出版社, 1991
[10] Smoot, L.D., Pratt, D.T. .Pulverized coal combustion and gasification[M]. New York: Plenum, 1979
[11] Gauvin, W.H., Katta, S., Knelman, F.H., 1975.Drop trajectory predictions and their importance in the desigh of spray dryers[J]. Int. J.Multiphase Flow, 1993(20), 793-816
[12] Crowe, C.T., Sharma, M.P. , Stock, D.E., 1977. The particle-source-in cell(PSI-CELL) model for gas-droplet flows[J]. Trans, ASME J. Fluids Eng. 99, 325-332
[13] Andrews, M.J.,O’Rourke, P. J.,The Multiphase Particle-In-Cell(MP-PIC) Method for Dense Particulate Flows[J]. Int. J. Multiphase Flow. 1996, 22:379-402
[14] O’Rourke, P.J. Collective drop effects on vaporizing liquid sprays[D]. Princeton University, NJ. 1981
[15] D.M. Snider, P. J. O’Rourke, and M. J. Andrews. Sediment flow in inclined vessels calculated using multiphase particle-in-cell model for dense particle flow[J], Int. J. Multiphase Flow.1998, 24: 1359-1382
[16] N.A. Patankar, D.D. Joseph. Lagrangian numerical simulation of particulate flows[J]. Int J Numerical methods Fluids, 1999, 29(8): 201- 217
[17] Golafshani, H.T. Loh. Computation of two phase viscous flow in solid rocket motor using a flux-split Eulerian-Lagrangian technique[J]. AIAA-89-2985
[18] R Madabhushi, J Sabnois, F Jong and H Gibeling. Calculation of the two-phase aft-dome flowfield in solid rocket motors[J]. J propulsion, 1991, 7(2): 178-184
[19] T Jachandra, R C Mehta.A fast algorithm to stove viscous two-phase flow in an axisymmetric rocket nozzle[J]. Int J Numerical methods Fluids, 1998, 26(5): 501- 517
[20] T.J. Coakly, J M. Champeny. Numerical simulation of compressible turbulent two-phase flow[J]. AIAA-85-1666
[21] H.T. Chang, L.W. Hourng, L.C. Chien. Application of flux-vector-splitting scheme to a dilute gas-particle JPL nozzle flow[J].Int J Numerical Methods Fluids, 1996, 22(10): 921-935
[22] 侯晓. 固体火箭喷管两相湍流的数值模拟[D] , 西安: 西北工业大学航天工程学院, 1990
[23] 李江. 固体火箭发动机内颗粒运动模式的研究[D]. 西安: 西北工业大学航天工程学院,1998
[24] Hiroyasu Makino, Yasuhiro Maeda, Hiroyuki Nomura.Force analysis in air-flowpress moulding using the distinct element method[J].Int.J.Cast Metal Res, 1997, 10: 171~175
[25] Sahm,Pelzer M, Meiser L, Pro. Simulation of the Core shooting Process [R].CIATF Technical Forum 99
[26] 美国 Arena-Flow 公司的介绍光盘[CD]. 堪萨斯城: 美国铸造博览会, 2002, 5
[27] 陈代海, 崔怡, 王海, 吴浚郊. 射砂过程气砂两相运动的研究[J]. 中国铸造装备与技术, 2001(4): 12~13
[28] 王涛, 崔怡, 陈代海, 李文珍. 射砂紧实过程的试验研究[J]. 中国铸造装备与技术, 2001(2): 9~11
[29] 崔怡, 李文珍, 吴浚郊, 张涛. 射砂紧实机理的研究[J]. 中国铸造装备与技术, 2001(1): 17~19
[30] 崔怡, 李文珍, 吴浚郊. 射砂过程初始条件的试验研究[J]. 中国铸造装备与技术, 2000(5): 11~13
[31] 崔怡, 李文珍, 吴浚郊.射砂过程的数值模拟[J].特种铸造及有色合金, 2001(2): 34~36
[32] 陈代海, 崔怡, 吴浚郊.芯盒设计对射砂过程的影响[J].铸造, 2001(7), 342~345
[33] 崔怡, 李文珍, 吴浚郊.利用两相流模型模拟射砂过程的进展[J].铸造技术, 2000(6): 8~10
[34] 崔怡, 李文珍, 吴浚郊. 芯盒结构对射砂过程的影响[J].特种铸造及有色合金, 2000(3): 4~6
[35] 崔怡, 李文珍, 吴浚郊, 张涛.冷芯盒射砂工艺参数的研究[J].铸造, 2000(9): 527~532
[36] 李宏亮, 崔怡, 吴浚郊.射砂过程数值模拟的技术现状[J].铸造, 2002(11): 737~740
[37] 崔怡, 李宏亮,吴浚郊. 射沙过程数值模拟的应用[J]. 铸造, 2003(6): 415-419
[38] 姜俊侠. 发泡模具射料过程充填过程的数值模拟[J]. 铸造, 2005(5): 479-483
[39] 陈尧剑. 消失模珠粒射料充填过程的数值模拟[J], 清华大学学报, 2005(8): 106-109
[40] H.K. Versteeg, W. Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method. Wiley, New York, 1995
[41] 施学贵, 徐旭常, 冯俊凯. 颗粒在湍流中的运动受力分析[J].工程热物理学报, 1989, 10(3): 320~325
[42] Harris, S.E., Crighton D.G..Solitons, Solitary waves and voidage disturbances in gas-fluidized beds[J]. J.Fluid Mech. 1994, 243-276
[43] W. Malalasekera .An Introduction to CFD: The Finite Volume Method. Wiley, New York, 1994
[44] T. Hayase, J.A.C.Humphrey,A.Greif,A consistently formulated QUICK schcme for fast and stable convergence using finite-volume iterative calculation procedures[J]. Joumal of Computational Physics,1992, 98:108-118,
[45] S V Patankar. 传热与流体流动的数值计算[M], 北京: 科学技术出版社. 1984
[46] Rhie, W.L. Chow. Numerical study of the turbulent flow past an airfoil with trailing edge seperation[J]. AIAA(J), 1983, 21(9): 1525-1532.1
[47] D.B. Spalding. Numerical computation of multiphase fluid flow and heat transfer[M]. In recent advances in numerical methods in fluids, 1980(1): 139-167
[48] 王长安, 密相液固两相三维湍流流动的研究及其在泵叶轮内流场计算与数值分析中的应用[D]. 西安: 西安交通大学能源与动力工程学院, 1996
[49] 魏进家, 密相液固两相湍流 KET 模型和数值计算及离心泵叶轮内两相流场实验研究[D]. 西安: 西安交通大学能源与动力工程学院, 1998
[50] 曾卓雄, 密相可压气固两相湍流流动[D], 西安交通大学能源与动力工程学院, 2002
[51] Hui. Boundary conditions for high shear grain flows[J], J Fluid Mech, 1984, 145(223)
[52] 李勇, 刘志友, 安亦然. 介绍计算流体力学通用软件—Fluent. 水动力学研究与进展[J], 2001(6): 254~258