水击理论与计算研究
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摘要
本论文首先简要介绍了当前水击计算的基本理论，包括水击数学模型和计算方法。指出了当前水击数学模型中的连续性方程不能满足恒定流条件、sinθ项存在的不合理性等问题，说明当前水击数学模型中的连续性方程是错误的。同时也指出了目前的计算方法也存在不严谨之处。接着，对这些问题存在的原因进行了详细分析，发现在当前推导水击压强公式的过程中没有考虑管道的倾斜度和摩擦阻力的影响，而在后面水击计算的连续性方程的推导过程中则考虑了管道的倾斜度，这就导致了在当前连续性方程的整个推导过程中前后矛盾的不合理现象。这也就是连续性方程不正确的根本原因。
本论文对水击数学模型中的连续性方程重新进行了严谨的推导，不仅得到了更加准确的水击压强和水击波速的计算公式
也建立了正确的水击数学模型
连续性方程
运动方程
当忽略次要因素以后，公式(1)和(2)即可转化为当前应用的水击压强计算公式和水击波速计算公式。
新的水击数学模型(3)完全满足恒定流条件。
本论文的另一个主要内容是，在正确的水击数学模型(3)的基础上，应用特征线法的原理，将微分方程组(3)转化成特征方程组，沿特征线对特征方程进行积分，并以其差分方程形式代替积分形式，以便利用计算机进行水击过程的数值计算。论文对各种边界条件也做了相应的推导。而且在上述中改善了当前水击计
郑州大学工学硕士论文
算的特征线法具体处理中的不严谨性，即改“用ds/g=士adt/g乘以特征方程后进
行积分”为“用ds/g二(。士a)dt/g乘以特征方程后进行积分”。原来的不严谨性不
仅影响计算精度，更重要的是将导致特征差分方程不满足恒定流条件。
对应于正确的水击数学模型(3)的特征差分方程形式如下
c，弓+吼川一C，唱一几弓扮几Rv另卜川=O
几代+吼川一几唱一吼嵘{一C:脚丸}唱}·“
本论文在最后的计算部分，通过对新老数学模型的数值计算比较，进一步论
证了当前水击数学模型的不正确性。并且应用改善了的特征线法对正确的数学模
型(3)进行了计算分析，研究了各种因素对水击压强值和水击现象衰减的影响，
指出在长管道系统中，沿程水头损失的分区计算对水击压强的计算结果影响较大，
建议在长管道系统的水击计算中应按分区进行沿程水头损失的计算。考虑进口及
多管道连接处的局部水头损失对短管道系统水击压强的计算结果影响较大。最后
考虑了实际电站水轮机组的运行特性，结合盘石头水库引水、发电、泄洪共用的
复杂引水系统，进行了电站甩负荷引起的非恒定过渡过程计算。
This paper, firstly, presents briefly the basic theories of current water hammer calculation including both water hammer mathematic model and calculative methods; points out continuity equation not meeting the conditions of steady flow, sin 0 being inherent illogically in current water hammer mathematic model, calculative methods of the equation being scarcely precise, etc, which account for the continuity equation is false in the current water hammer mathematic model. Secondly, detailedly analyzing reasons inducing these problems, author finds it is that not thinking of the slope of pipeline and the friction in the process of producing water hammer pressure functions, but, thinking of the effect of the slope of pipeline in the process of producing the consequent water hammer calculative continuity function, which results in the inconsequent illogicality in the whole process of producing. It is the fundamental reason that the continuity function faults.
The paper uses precise step to produce the continuity function of water hammer mathematic model, not only gains more precise water hammer pressure function and water hammer wave speed function
but also founds correct water hammer mathematic model
Continuity Equation
Movement Equation
After ignoring subordinate facts, function (1) and (2) translate into the current applied water hammer pressure function and water hammer wave speed function.
The new water hammer mathematic model (3) fully meets the conditions of steady
flow.
The other primary part is that based on the correct water hammer mathematic model (3), applying character line method, to translate the differential equation group (3) into character equation group, to count the character equation integral along with character line and at the same time to substitute the integral form for the difference form so as to make use of computer to carry through numerical value calculation of the water hammer pressure. The paper , too, does with the corresponding argumentation of all kinds of boundary conditions. The above content improves the no preciseness of disposing of the character line method of current water hammer calculation, namely translates " ds/g=+adt/g multiplies the character equation" into "ds/g = (v+a)dt/g multiplies the character equation". This no preciseness not only influence the calculative precision but also badly induces the character difference equation not meeting the conditions of steady flow.
Corresponding to the correct water hammer mathematic model (3), the character difference equation is
By comparing the new mathematic model with the old mathematic model, the last calculative part of paper argues the falseness of the current water hammer mathematic model, makes use of the improved character line method to analyze the correct mathematic model (3), studies all kinds of facts' impact on water hammer pressure value and water hammer phenomenon attenuation, points out that, in the long pipeline system, the subarea calculation of head loss along with flow rather influences the calculative results of water hammer pressure, advices to take the subarea calculation of head loss along with flow into account in the water hammer calculation of the long pipeline system. Ulteriorly, considering the local head loss in inlet opening and pipes junction plays more important role in the calculative results of water hammer pressure calculation of the short pipeline system. At last, considering the running trait of hydraulic turbine in true power stations, combining the complex pipe line system, generating electri
city, discharge flood all use of Pan Shi Tou reservoir compute the unsteady transition process.
本论文对水击数学模型中的连续性方程重新进行了严谨的推导，不仅得到了更加准确的水击压强和水击波速的计算公式
也建立了正确的水击数学模型
连续性方程
运动方程
当忽略次要因素以后，公式(1)和(2)即可转化为当前应用的水击压强计算公式和水击波速计算公式。
新的水击数学模型(3)完全满足恒定流条件。
本论文的另一个主要内容是，在正确的水击数学模型(3)的基础上，应用特征线法的原理，将微分方程组(3)转化成特征方程组，沿特征线对特征方程进行积分，并以其差分方程形式代替积分形式，以便利用计算机进行水击过程的数值计算。论文对各种边界条件也做了相应的推导。而且在上述中改善了当前水击计
郑州大学工学硕士论文
算的特征线法具体处理中的不严谨性，即改“用ds/g=士adt/g乘以特征方程后进
行积分”为“用ds/g二(。士a)dt/g乘以特征方程后进行积分”。原来的不严谨性不
仅影响计算精度，更重要的是将导致特征差分方程不满足恒定流条件。
对应于正确的水击数学模型(3)的特征差分方程形式如下
c，弓+吼川一C，唱一几弓扮几Rv另卜川=O
几代+吼川一几唱一吼嵘{一C:脚丸}唱}·“
本论文在最后的计算部分，通过对新老数学模型的数值计算比较，进一步论
证了当前水击数学模型的不正确性。并且应用改善了的特征线法对正确的数学模
型(3)进行了计算分析，研究了各种因素对水击压强值和水击现象衰减的影响，
指出在长管道系统中，沿程水头损失的分区计算对水击压强的计算结果影响较大，
建议在长管道系统的水击计算中应按分区进行沿程水头损失的计算。考虑进口及
多管道连接处的局部水头损失对短管道系统水击压强的计算结果影响较大。最后
考虑了实际电站水轮机组的运行特性，结合盘石头水库引水、发电、泄洪共用的
复杂引水系统，进行了电站甩负荷引起的非恒定过渡过程计算。
This paper, firstly, presents briefly the basic theories of current water hammer calculation including both water hammer mathematic model and calculative methods; points out continuity equation not meeting the conditions of steady flow, sin 0 being inherent illogically in current water hammer mathematic model, calculative methods of the equation being scarcely precise, etc, which account for the continuity equation is false in the current water hammer mathematic model. Secondly, detailedly analyzing reasons inducing these problems, author finds it is that not thinking of the slope of pipeline and the friction in the process of producing water hammer pressure functions, but, thinking of the effect of the slope of pipeline in the process of producing the consequent water hammer calculative continuity function, which results in the inconsequent illogicality in the whole process of producing. It is the fundamental reason that the continuity function faults.
The paper uses precise step to produce the continuity function of water hammer mathematic model, not only gains more precise water hammer pressure function and water hammer wave speed function
but also founds correct water hammer mathematic model
Continuity Equation
Movement Equation
After ignoring subordinate facts, function (1) and (2) translate into the current applied water hammer pressure function and water hammer wave speed function.
The new water hammer mathematic model (3) fully meets the conditions of steady
flow.
The other primary part is that based on the correct water hammer mathematic model (3), applying character line method, to translate the differential equation group (3) into character equation group, to count the character equation integral along with character line and at the same time to substitute the integral form for the difference form so as to make use of computer to carry through numerical value calculation of the water hammer pressure. The paper , too, does with the corresponding argumentation of all kinds of boundary conditions. The above content improves the no preciseness of disposing of the character line method of current water hammer calculation, namely translates " ds/g=+adt/g multiplies the character equation" into "ds/g = (v+a)dt/g multiplies the character equation". This no preciseness not only influence the calculative precision but also badly induces the character difference equation not meeting the conditions of steady flow.
Corresponding to the correct water hammer mathematic model (3), the character difference equation is
By comparing the new mathematic model with the old mathematic model, the last calculative part of paper argues the falseness of the current water hammer mathematic model, makes use of the improved character line method to analyze the correct mathematic model (3), studies all kinds of facts' impact on water hammer pressure value and water hammer phenomenon attenuation, points out that, in the long pipeline system, the subarea calculation of head loss along with flow rather influences the calculative results of water hammer pressure, advices to take the subarea calculation of head loss along with flow into account in the water hammer calculation of the long pipeline system. Ulteriorly, considering the local head loss in inlet opening and pipes junction plays more important role in the calculative results of water hammer pressure calculation of the short pipeline system. At last, considering the running trait of hydraulic turbine in true power stations, combining the complex pipe line system, generating electri
city, discharge flood all use of Pan Shi Tou reservoir compute the unsteady transition process.
引文
[1] 王树人等，水击理论与水击计算，清华大学出版社，1980
[2] 赵晓光等，简单管道水击计算程序的编制与应用，重庆工业高等专科学校学报，2001，16(4)
[3] 王树人等，水电站建筑物，清华大学出版社，1984
[4] E．B怀特等，瞬变流，水利电力出版社，1983
[5] 李进平，非恒定摩阻对管道水力过渡过程的影响，武汉大学学报，2002，35(2)13～17
[6] 周雪漪，计算水力学，清华大学出版社，1995
[7] [美]李文勋，水力学中的微分方程及其应用，上海科学技术出版社，
[8] [英]考蒂塔斯，计算水力学基础，水利电力出版社，1987
[9] [苏]基谢列夫，水力学流体力学原理，水利电办出版社，1983
[10] [荷]M．B阿包特，计算水力学，海洋出版社，1985
[1l] 华东水利学院，水力学，科学出版社，1979
[12] C．耶格尔，水力不稳定流，清华大学出版社，1983
[13] 武汉水利电力学院水力学教研室编，水利计算手册，1979
[14] Allievi,L.,The Theory of Water Hammer, English translation by Halmos,E.E.,ASME New York, 1925
[15] 杨景芳，微机计算水力学，大连理工大学出版社，1991
[16] 张晓宏，有泄洪支洞的压力引水系统中的非恒定流分析，水利学报，1998，1
[17] E.B.WYIE,V.L.STREETER, FLUID TRANSIENTS. McGraw Hill Book Co.,(1978)
[18] 慕希茂，输油管道水击过程分析，西安石油学院学报(自然科学版)，2001，16(5)
[19] 阎文周，电厂循环水系统饮水非恒定流分析计算，电力建设，1997
[20] MU Xi-mao，Analysis of the Water Hammer Process in Oil Pipeline，JXAPl2 0 01, V16, N. 5
[21] 蒋劲，小浪底电站技术供水回水系统水锤防护研究，华中科技大学学报(自然科学版)，2002，V．30，N．4
[22] 鞠小明，导叶分段关闭规律在电站非恒定流计算中的应用及问题分析，四川
水力发电，1994
[23] C.A.BREBBIA,A.J.FERRANTE.Computational Hydraulics[M].Butterworth &Co Ltd,1983,59～101
[24] 刘志勇，喷灌系统水锤及其防护，节水灌溉，2002
[25] 万五一，水击特征线计算中重分阻尼系数的时步处理方法，水利水电技术，2002，V．33
[26] V.L.STREETER/E.B.WYLIE,HYDRAULIC TRANSIENTS.McGraw Hill Book Co.,(1967)
[27] 魏占民，无分叉灌溉渠道系统非恒定流计算机模拟模型，内蒙古农牧学院学报，1997，18(2)
[28] M．A．莫斯特可夫著，水锤计算，王世泽译，燃料工业出版社，1985
[29] Gelfind,H,Solution if Equations in Integers(trans.L.F.Boron),Dover, New York, 1957
[30] Dooge,J.C.I,Linear Theory of Hydrologic Systems,Tech.Bull.,US Department od Agriculture,Washington,DC, 1973
[31] 吴子牛，计算流体力学基本原理，科学出版社，2001，2
[32] 白玉川，河网非恒定流数值模拟的研究进展，水利学报，2000
[33] G.K.Barchelor.An Introduction to Fluid Dynamics, lst,ed.,Camridge.Univ. Press, 197
[34] 万德华，孔口出流公式作为解水击连锁方程边界条件的局限性，长江科学院报，2000
[35] 杨玲霞，盘石头水库输水洞非恒定流过渡计算的几个问题，人民黄河，1999，V12．n6
[36] 鞠小明，水电站引水系统模型实验研究中若干问题的探讨，成都科技大学学报，1996，2
[37] 张煜辉，有压管路水击时的能量公式，流体机械，1998，V．21，N．11
[38] 成远楚，水电站水击通用计算程序设计，水电站设计，1997，V13，N2
[39] 李治勤，流速及管道特性对水击的影响，太原理工大学学报，2000，V．31，N．2
[40] 赵晓光，简单管道水击计算程序的编制与应用，重庆工业高等专科学校学报，2001，V16．，N．4
[2] 赵晓光等，简单管道水击计算程序的编制与应用，重庆工业高等专科学校学报，2001，16(4)
[3] 王树人等，水电站建筑物，清华大学出版社，1984
[4] E．B怀特等，瞬变流，水利电力出版社，1983
[5] 李进平，非恒定摩阻对管道水力过渡过程的影响，武汉大学学报，2002，35(2)13～17
[6] 周雪漪，计算水力学，清华大学出版社，1995
[7] [美]李文勋，水力学中的微分方程及其应用，上海科学技术出版社，
[8] [英]考蒂塔斯，计算水力学基础，水利电力出版社，1987
[9] [苏]基谢列夫，水力学流体力学原理，水利电办出版社，1983
[10] [荷]M．B阿包特，计算水力学，海洋出版社，1985
[1l] 华东水利学院，水力学，科学出版社，1979
[12] C．耶格尔，水力不稳定流，清华大学出版社，1983
[13] 武汉水利电力学院水力学教研室编，水利计算手册，1979
[14] Allievi,L.,The Theory of Water Hammer, English translation by Halmos,E.E.,ASME New York, 1925
[15] 杨景芳，微机计算水力学，大连理工大学出版社，1991
[16] 张晓宏，有泄洪支洞的压力引水系统中的非恒定流分析，水利学报，1998，1
[17] E.B.WYIE,V.L.STREETER, FLUID TRANSIENTS. McGraw Hill Book Co.,(1978)
[18] 慕希茂，输油管道水击过程分析，西安石油学院学报(自然科学版)，2001，16(5)
[19] 阎文周，电厂循环水系统饮水非恒定流分析计算，电力建设，1997
[20] MU Xi-mao，Analysis of the Water Hammer Process in Oil Pipeline，JXAPl2 0 01, V16, N. 5
[21] 蒋劲，小浪底电站技术供水回水系统水锤防护研究，华中科技大学学报(自然科学版)，2002，V．30，N．4
[22] 鞠小明，导叶分段关闭规律在电站非恒定流计算中的应用及问题分析，四川
水力发电，1994
[23] C.A.BREBBIA,A.J.FERRANTE.Computational Hydraulics[M].Butterworth &Co Ltd,1983,59～101
[24] 刘志勇，喷灌系统水锤及其防护，节水灌溉，2002
[25] 万五一，水击特征线计算中重分阻尼系数的时步处理方法，水利水电技术，2002，V．33
[26] V.L.STREETER/E.B.WYLIE,HYDRAULIC TRANSIENTS.McGraw Hill Book Co.,(1967)
[27] 魏占民，无分叉灌溉渠道系统非恒定流计算机模拟模型，内蒙古农牧学院学报，1997，18(2)
[28] M．A．莫斯特可夫著，水锤计算，王世泽译，燃料工业出版社，1985
[29] Gelfind,H,Solution if Equations in Integers(trans.L.F.Boron),Dover, New York, 1957
[30] Dooge,J.C.I,Linear Theory of Hydrologic Systems,Tech.Bull.,US Department od Agriculture,Washington,DC, 1973
[31] 吴子牛，计算流体力学基本原理，科学出版社，2001，2
[32] 白玉川，河网非恒定流数值模拟的研究进展，水利学报，2000
[33] G.K.Barchelor.An Introduction to Fluid Dynamics, lst,ed.,Camridge.Univ. Press, 197
[34] 万德华，孔口出流公式作为解水击连锁方程边界条件的局限性，长江科学院报，2000
[35] 杨玲霞，盘石头水库输水洞非恒定流过渡计算的几个问题，人民黄河，1999，V12．n6
[36] 鞠小明，水电站引水系统模型实验研究中若干问题的探讨，成都科技大学学报，1996，2
[37] 张煜辉，有压管路水击时的能量公式，流体机械，1998，V．21，N．11
[38] 成远楚，水电站水击通用计算程序设计，水电站设计，1997，V13，N2
[39] 李治勤，流速及管道特性对水击的影响，太原理工大学学报，2000，V．31，N．2
[40] 赵晓光，简单管道水击计算程序的编制与应用，重庆工业高等专科学校学报，2001，V16．，N．4