汽轮机汽缸二维温度场理论研究
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摘要
为了研究汽缸热膨胀,本文在二维圆筒壁非稳态导热微分方程的基础上,得到了内部蒸汽沿轴向线性分布、随时间非线性变化、外壁绝热和外壁对流换热的温度场迭代计算公式。通过与有限元计算结果进行对比,表明所得模型计算精度高、速度快。在此基础上,针对不同结构的汽缸,经过一些合理假设,将汽缸复杂的结构分解成简单的子结构,就能得到汽缸轴向膨胀的计算模型。该模型还可用于汽缸轴向膨胀的实时监测,所采用的推导方法和得到的膨胀计算公式亦可用于其它具有类似边界条件的厚壁圆筒部件的相关分析。
In order to studying the thermal expansion of turbine casing ,the analytics of the cylinder temperature field has been obtained from deduction, which starting from unstable differential equation of heat conduction for a two-dimentional(2-D) cylindrical wall, in which the internal steam is linearly distributing along the axial direction, and varying along with the time, and external wall is adiabatic and convective,and a comparison with the result from finite-element calculation being carried out. It shows that the obtained model has high precision and rapid calculation. Directing against steam cylinders with different structure, and through some reasonable assumptions, a complicated cylinder structure can be decomposed into simple sub-structures, and a cylinder model of axial expansion has been obtained. The said model can also be used for real-time monitoring of axial expansion for the steam cylinder. The deducting method applied and the expansion calculating formula obtained can also be used for other correlative analysis of cylindrical components with thick wall having similar boundary conditions.
In order to studying the thermal expansion of turbine casing ,the analytics of the cylinder temperature field has been obtained from deduction, which starting from unstable differential equation of heat conduction for a two-dimentional(2-D) cylindrical wall, in which the internal steam is linearly distributing along the axial direction, and varying along with the time, and external wall is adiabatic and convective,and a comparison with the result from finite-element calculation being carried out. It shows that the obtained model has high precision and rapid calculation. Directing against steam cylinders with different structure, and through some reasonable assumptions, a complicated cylinder structure can be decomposed into simple sub-structures, and a cylinder model of axial expansion has been obtained. The said model can also be used for real-time monitoring of axial expansion for the steam cylinder. The deducting method applied and the expansion calculating formula obtained can also be used for other correlative analysis of cylindrical components with thick wall having similar boundary conditions.
引文
[1]梅志农.汽轮机高压内缸变形问题的探讨.浙江电力,2001,3:37-39
[2]孟繁娟,何光新.汽缸热膨胀的计算方法.汽轮机技术,1998,30(3):219-221
[3]顾卫东,等.亚临界300MW汽轮机高中压内缸热应力分析.汽轮机技术,2003,35(3),137-138
[4]张恒良,谢诞梅,熊扬恒,等. 600MW汽轮机转子高精度热应力在线监测模型研制[J].中国电机工程学报, 2006, 26(1): 21-25.
[5]任庆民.一种计算瞬态汽缸热膨胀的新方法.现代电力,2002,19(5):1-7
[6]邱爱玲,刘启民.俄制500MW汽轮机中压缸膨胀及胀差问题研究.华北电力技术,2000,9:22-23
[7]哈尔滨汽轮机厂.20万千瓦汽轮机的结构.北京,水利电力出版社,1992:11-12
[8]甘肃省电力工业局,河南省电力工业局,合编.汽轮机设备运行技术.中国电力出版社,1995:282-289
[9]王林,顾卫东等.汽轮机高中压外缸温度场分析.汽轮机技术,2007年2月第49卷第1期
[10]张乃强.汽轮机高压内缸径向碰磨.华北电力大学硕士学位论文,2005年3月
[11]в.п.伊萨琴科.传热学.(王丰,冀守礼,等).北京,高等教育出版社,1981:16-21
[12]童恩超.大功率汽轮机快速冷却时汽缸壁温度的计算方法.热能动力工程, 1995年7月第10卷
[13]葛晓霞.汽轮机汽缸壁温及胀差全工况仿真数学模型.中国电机工程学报, 1995年9月第15卷第5期
[14] M.N.奥齐西克.热传导.(俞昌铭).北京,高等教育出版社,1983:96-106
[15]邓博.汽轮机汽缸温度场理论研究.华北电力大学硕士论文.2006.3
[16]洪荣华,徐剑锋,胡亚才.长圆筒壁热学传递函数建模研究.大连理工大学学报,2001年11月第41卷增刊1
[17]杜森,叶春等.电站汽轮机高压内缸的二维在线计算方法.动力工程,2007年2月第27卷第1期
[18]鲁超,杨爱萍.N200-12.7/535/535型汽轮机胀差变化规律与控制.江苏电机工程,2003,23(3):22-23
[19]刘式适,刘式达.特殊函数.北京,气象出版社,2002:386-327
[20]数学手册编写组.数学手册.北京,高等教育出版社,1979:627-631
[21]李益民,李中华,王华,陈强,陈聪智.某电厂50MW汽轮机汽缸温度场及热应力有限元分析.热力发电,2003,9:21-23
[22]喻刚.国产四缸四排汽300MW汽轮机本体结构改造设计.汽轮机技术,2003,35(1):25-26
[23]丁有余,等.汽轮机强度计算.北京,水利水电出版社,1985
[24]于圣波,赵君,孟晓曦.200MW汽轮机最佳启动工况寻优的研究.东北电力学院学报,2002,22(3):39-52
[25] M.M. Yanovich. Heat transfer in electronic packaging[A].Hewitt G F, ed.Proceeding of the 10th International Heat Transfer Conference[C]. Brighton:1993.93-103
[26] A.D. Krans, A. Bar-cohen. Thermal analysis and control of electronic equipment[M]. Washington, Hemisphere Publishing Corporation, 1993.303-600
[27] J. P. Holman. Heat transfer 8th ed[M].New York: McGraw Hill Book Company,1997.5-20
[28] Xin R C, Tao W Q. Analytical solution for transient heat conduction in two semi-infinite bodies in contact[J].ASME J Heat Transfer,1993,116(1) :223-228
[29]上海电力学院,山东电力工业局,合编.大型汽轮机安装.水利水电出版社,1987
[30]朱佳生.透平机械制造工艺学.机械工业出版社,1979
[31]吴季兰.汽轮机设备及系统.中国电力出版社,1996
[32]陈桂杰.高压汽轮机胀差与动静叶轮相磨的关系及对策.汽轮机技术,1999.10
[33]黄润泽,李强.国产200MW汽轮机组极热态启动实践.东北电力技术,1998.9
[34]姜求志,王金瑞,等.火力发电厂金属材料手册.北京,中国电力出版社,2001:900-901
[35]竹内洋一朗.热应力.科学出版社,1982
[36]汤云柯.汽轮机转子应力分析与机组运行寿命研究.清华大学工学博士学位论文,1992
[37] J.H. Daniels. Dynamic Representation of a large Boiler-Turbine Unit.ASME Pape, 1961
[38]刘钧朴,等.核电汽轮机高压缸三维有限元热应力分析.动力工程,1995, 15(2):35-31
[39]黄晓齐,龚德鸿,李环.非均匀内热源圆筒壁稳态导热微分方程的热流分流和叠加.贵州工业大学学报(自然科学版),2001,30(3):9-12
[40]王照亮,张克舫,李华玉,梁金国.一种求解复合圆筒壁非稳态导热问题的新方法.石油大学学报(自然科学版),2005,29(2):89-92
[41]田禾.关于二维非稳态导热的可视化研究.天津师范大学硕士学位论文,2003
[42] Hwankee Cho. Elastodynamic Thermal Shock Stresses in Orthotropic Thick Cylindrical Shells. A thesis Presented to The Academic Faculty, in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in Aerospace Engineering. Georgia Institute of Technology, 1997.1-21
[43] V. Birman. Thermal Dynamic Problems of Reinforced Composite Cylinders. ASME Journal of Applied Mechanics, 1990,57:931-937
[44] H.S. Carslw, J.C. Jaeger. Conduction of Heat in Solids, 2nd ed. Clarendon Press, 1959
[45] H. Cho, C.S. Valle, G.A. Kardomateas. Elastodynamic Solution for the Thermal Shock Stresses in an Orthotropic Thick Cylindrical Shell. ASME Journal of Applied Mechanics,1997
[46] G. Cinelli. Dynamic Vibrations and Stresses in Elastic Cylinders and Spheres. ASME Journal of Applied Mechanics, 1966.825-830
[47] J.E. Greenspon. Vibrations of a Thick-Walled Cylindrical Shell- Comparison of the Exact Theory with Approximate Theories. The Journal of the Acoustical Society of America, 1960,32(5):571-578
[48] T. Hata. Reconsideration of the Stress Focusing Effect in a Uniformly Heated Solid Cylinder. ASME Journal of Applied Mechanics, 1993,61:676-680
[49] A.M. Velez Garcia. Temperature Field Due to Conduction Heat Transfer In Thin Circular Plates, Infinitely Long Cylinders and Spheres With Discrete Heat Generation Sources Using Green’s Functions Techniques. Master of Science in Mechanical Engineering University of Puerto Rico Mayaguez Campus, 2003.51-61
[50]蔡睿贤,张娜.柱坐标下变热物性非定常轴对称导热方程的解析解.自然科学进展,2002,12(11):1155-1161
[51]蔡睿贤,蔡档.工程热物理学科中的若干解析解.西安交通大学学报,2000, 33(2):1-5
[52]沈佩华.引进型300MW汽轮机内缸法兰螺栓的有限元应力分析.中国电力,2003 ,37(10):32-35
[53]张娜,蔡睿贤.考虑中心孔影响的汽轮机转子不定常温度场显式解析解[J].中国电机工程学报, 1999, 19(7): 38-40.
[54]张光,张保衡.监测汽轮机转子热应力的二维离散模型[J].中国电机工程学报, 1996, 16(1): 38-40.
[55]姚学诗,周传荣.转子的热膨胀与横向振动[J].应用力学学报, 2003,20(1): 118-120.
[56] Morita A, Kagawa H, Sugawara M. Evaluation of corrosion fatigue crack propagation life at low-pressure steam turbine rotor groove[J]. Engineering Fracture Mechanics, 2006, 73(12): 1615-1628.
[57] Mukhopadhay N K, Dutta B K, Kushwaha H S. On-line fatigue-creep monitoring system for high-temperature components of power plants[J]. International Journal of Fatigue, 2001, 23(6): 549-560.
[58] Kiyoshi saito, Akira sakuma, Masataka fukuda. Recent life assessment technology for existing steam turbines[J]. JSME International Journal Series B: Fluids and Thermal Engineering, 2006, 49(2): 192-197.
[59] Stubbs T. The role of NDE in the life management of steam turbine rotors[J]. Insight, 2004, 46(9): 529-532.
[60]史进渊,杨宇,邓志成,张兆鹤.超临界超超临界汽轮机汽缸传热系数的研究.动力工程,2006年2月第26卷第1期
[61]周兰欣等125MW汽轮机低压缸体温度场计算华北电力大学学报.Vol.28, No.3 July,2001
[2]孟繁娟,何光新.汽缸热膨胀的计算方法.汽轮机技术,1998,30(3):219-221
[3]顾卫东,等.亚临界300MW汽轮机高中压内缸热应力分析.汽轮机技术,2003,35(3),137-138
[4]张恒良,谢诞梅,熊扬恒,等. 600MW汽轮机转子高精度热应力在线监测模型研制[J].中国电机工程学报, 2006, 26(1): 21-25.
[5]任庆民.一种计算瞬态汽缸热膨胀的新方法.现代电力,2002,19(5):1-7
[6]邱爱玲,刘启民.俄制500MW汽轮机中压缸膨胀及胀差问题研究.华北电力技术,2000,9:22-23
[7]哈尔滨汽轮机厂.20万千瓦汽轮机的结构.北京,水利电力出版社,1992:11-12
[8]甘肃省电力工业局,河南省电力工业局,合编.汽轮机设备运行技术.中国电力出版社,1995:282-289
[9]王林,顾卫东等.汽轮机高中压外缸温度场分析.汽轮机技术,2007年2月第49卷第1期
[10]张乃强.汽轮机高压内缸径向碰磨.华北电力大学硕士学位论文,2005年3月
[11]в.п.伊萨琴科.传热学.(王丰,冀守礼,等).北京,高等教育出版社,1981:16-21
[12]童恩超.大功率汽轮机快速冷却时汽缸壁温度的计算方法.热能动力工程, 1995年7月第10卷
[13]葛晓霞.汽轮机汽缸壁温及胀差全工况仿真数学模型.中国电机工程学报, 1995年9月第15卷第5期
[14] M.N.奥齐西克.热传导.(俞昌铭).北京,高等教育出版社,1983:96-106
[15]邓博.汽轮机汽缸温度场理论研究.华北电力大学硕士论文.2006.3
[16]洪荣华,徐剑锋,胡亚才.长圆筒壁热学传递函数建模研究.大连理工大学学报,2001年11月第41卷增刊1
[17]杜森,叶春等.电站汽轮机高压内缸的二维在线计算方法.动力工程,2007年2月第27卷第1期
[18]鲁超,杨爱萍.N200-12.7/535/535型汽轮机胀差变化规律与控制.江苏电机工程,2003,23(3):22-23
[19]刘式适,刘式达.特殊函数.北京,气象出版社,2002:386-327
[20]数学手册编写组.数学手册.北京,高等教育出版社,1979:627-631
[21]李益民,李中华,王华,陈强,陈聪智.某电厂50MW汽轮机汽缸温度场及热应力有限元分析.热力发电,2003,9:21-23
[22]喻刚.国产四缸四排汽300MW汽轮机本体结构改造设计.汽轮机技术,2003,35(1):25-26
[23]丁有余,等.汽轮机强度计算.北京,水利水电出版社,1985
[24]于圣波,赵君,孟晓曦.200MW汽轮机最佳启动工况寻优的研究.东北电力学院学报,2002,22(3):39-52
[25] M.M. Yanovich. Heat transfer in electronic packaging[A].Hewitt G F, ed.Proceeding of the 10th International Heat Transfer Conference[C]. Brighton:1993.93-103
[26] A.D. Krans, A. Bar-cohen. Thermal analysis and control of electronic equipment[M]. Washington, Hemisphere Publishing Corporation, 1993.303-600
[27] J. P. Holman. Heat transfer 8th ed[M].New York: McGraw Hill Book Company,1997.5-20
[28] Xin R C, Tao W Q. Analytical solution for transient heat conduction in two semi-infinite bodies in contact[J].ASME J Heat Transfer,1993,116(1) :223-228
[29]上海电力学院,山东电力工业局,合编.大型汽轮机安装.水利水电出版社,1987
[30]朱佳生.透平机械制造工艺学.机械工业出版社,1979
[31]吴季兰.汽轮机设备及系统.中国电力出版社,1996
[32]陈桂杰.高压汽轮机胀差与动静叶轮相磨的关系及对策.汽轮机技术,1999.10
[33]黄润泽,李强.国产200MW汽轮机组极热态启动实践.东北电力技术,1998.9
[34]姜求志,王金瑞,等.火力发电厂金属材料手册.北京,中国电力出版社,2001:900-901
[35]竹内洋一朗.热应力.科学出版社,1982
[36]汤云柯.汽轮机转子应力分析与机组运行寿命研究.清华大学工学博士学位论文,1992
[37] J.H. Daniels. Dynamic Representation of a large Boiler-Turbine Unit.ASME Pape, 1961
[38]刘钧朴,等.核电汽轮机高压缸三维有限元热应力分析.动力工程,1995, 15(2):35-31
[39]黄晓齐,龚德鸿,李环.非均匀内热源圆筒壁稳态导热微分方程的热流分流和叠加.贵州工业大学学报(自然科学版),2001,30(3):9-12
[40]王照亮,张克舫,李华玉,梁金国.一种求解复合圆筒壁非稳态导热问题的新方法.石油大学学报(自然科学版),2005,29(2):89-92
[41]田禾.关于二维非稳态导热的可视化研究.天津师范大学硕士学位论文,2003
[42] Hwankee Cho. Elastodynamic Thermal Shock Stresses in Orthotropic Thick Cylindrical Shells. A thesis Presented to The Academic Faculty, in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in Aerospace Engineering. Georgia Institute of Technology, 1997.1-21
[43] V. Birman. Thermal Dynamic Problems of Reinforced Composite Cylinders. ASME Journal of Applied Mechanics, 1990,57:931-937
[44] H.S. Carslw, J.C. Jaeger. Conduction of Heat in Solids, 2nd ed. Clarendon Press, 1959
[45] H. Cho, C.S. Valle, G.A. Kardomateas. Elastodynamic Solution for the Thermal Shock Stresses in an Orthotropic Thick Cylindrical Shell. ASME Journal of Applied Mechanics,1997
[46] G. Cinelli. Dynamic Vibrations and Stresses in Elastic Cylinders and Spheres. ASME Journal of Applied Mechanics, 1966.825-830
[47] J.E. Greenspon. Vibrations of a Thick-Walled Cylindrical Shell- Comparison of the Exact Theory with Approximate Theories. The Journal of the Acoustical Society of America, 1960,32(5):571-578
[48] T. Hata. Reconsideration of the Stress Focusing Effect in a Uniformly Heated Solid Cylinder. ASME Journal of Applied Mechanics, 1993,61:676-680
[49] A.M. Velez Garcia. Temperature Field Due to Conduction Heat Transfer In Thin Circular Plates, Infinitely Long Cylinders and Spheres With Discrete Heat Generation Sources Using Green’s Functions Techniques. Master of Science in Mechanical Engineering University of Puerto Rico Mayaguez Campus, 2003.51-61
[50]蔡睿贤,张娜.柱坐标下变热物性非定常轴对称导热方程的解析解.自然科学进展,2002,12(11):1155-1161
[51]蔡睿贤,蔡档.工程热物理学科中的若干解析解.西安交通大学学报,2000, 33(2):1-5
[52]沈佩华.引进型300MW汽轮机内缸法兰螺栓的有限元应力分析.中国电力,2003 ,37(10):32-35
[53]张娜,蔡睿贤.考虑中心孔影响的汽轮机转子不定常温度场显式解析解[J].中国电机工程学报, 1999, 19(7): 38-40.
[54]张光,张保衡.监测汽轮机转子热应力的二维离散模型[J].中国电机工程学报, 1996, 16(1): 38-40.
[55]姚学诗,周传荣.转子的热膨胀与横向振动[J].应用力学学报, 2003,20(1): 118-120.
[56] Morita A, Kagawa H, Sugawara M. Evaluation of corrosion fatigue crack propagation life at low-pressure steam turbine rotor groove[J]. Engineering Fracture Mechanics, 2006, 73(12): 1615-1628.
[57] Mukhopadhay N K, Dutta B K, Kushwaha H S. On-line fatigue-creep monitoring system for high-temperature components of power plants[J]. International Journal of Fatigue, 2001, 23(6): 549-560.
[58] Kiyoshi saito, Akira sakuma, Masataka fukuda. Recent life assessment technology for existing steam turbines[J]. JSME International Journal Series B: Fluids and Thermal Engineering, 2006, 49(2): 192-197.
[59] Stubbs T. The role of NDE in the life management of steam turbine rotors[J]. Insight, 2004, 46(9): 529-532.
[60]史进渊,杨宇,邓志成,张兆鹤.超临界超超临界汽轮机汽缸传热系数的研究.动力工程,2006年2月第26卷第1期
[61]周兰欣等125MW汽轮机低压缸体温度场计算华北电力大学学报.Vol.28, No.3 July,2001