调压室涌浪的随机数学模型

水电站有压引水系统中的水击与调压室涌浪的发生条件及各种影响因素的随机性决定了它们的随机本质。本文在综合研究以前的研究成果的基础上,主要从理论上对调压室涌浪和水击的随机分析进行了一系列的研究,得出了一些结论,并且通过了算例验证。算例结果表明本文的结论与蒙特卡罗模拟法模拟的结论完全一致。主要内容如下: 1.在综述了国内外研究现状的基础上,给出了调压室涌浪和水击的随机模型及各随机参变量的分布假设。 2.在将管道糙率和初始带负荷程度系数考虑为随机变量时对调压室涌浪进行了随机分析。利用管道糙率和初始带负荷程度系数的分布严格推导出了水头损失的密度函数表达式和最大相对涌浪值的密度函数计算公式;从数学上严格证明了调压室涌浪随机模型存在唯一均方解;最后利用刘维尔方程求解了调压室涌浪解过程的联合密度函数及其相应的概率信息。 3.在将库水位、初始带负荷程度系数和阀门关闭历时均考虑为随机变量时,对简单水力系统的水击进行了随机分析。利用线性关闭历时推导出了水头的幂级数表达式;利用库水位、初始带负荷程度系数和阀门关闭历时的分布给出了最大水击压力和极限水击压力的密度积分计算公式;从理论上给出了第一相水击升压、极限水击升压、最大水击压力和极限水击压力的敏感性分析表达式,并利用该表达式进行了敏感性分析;引进了分布类型拟合法,确定了水击升压和最大水击压力的分布类型。得到了水击升压应该服从对数正态分布,而最大水击压力应该服从正态分布;利用库水位、初始带负荷程度系数和阀门关闭历时的分布给出了求解水击均值过程的矩特征线法。 4.利用具体算例验证了本文所给方法的正确性。
工业羊毛毡
The randomness of conditions under which waterhammer and surge occur and the factors that influence the magnitudes of watherhammer pressures and surge levels result in the stochasticism of waterhammer and surge. Based on a comprehensive study of the former research results, this dissertation makes a range of theoretical research on stochastic analysis of waterhammer and surge, and puts forward several conclusions that have been successfully verified by the results from computational examples, which agree completely with the results from the Monte-Carlo method.The dissertation reads as follows:1. The random model of waterhammer and surge and the distribution assumption of various random parameters are given on the basis of a summary of the existing research results both at home and abroad.2. The stochastic analysis of surge is made with pipe roughness and original load regarded as random variables. By use of the distributions of pipe roughness and original load, this dissertation draws the following conclusions: the formula for probability density function of hydraulic head-loss is rigidly deduced; the computational formula for probability density function of maximum value of relative surge level is rigidly deduced; the existence of the only mean square solution to the random model of surge is rigidly verified in mathematics; and the joint probability density function in solution processing of surge is solved with Liouville Equation.3."The stochastic analysis of waterhammer in a single system is made with water level of reservoir, original load, and valve closing regarded as random variables. By use of the valve closure linear relationship, the power series formula for the solution to the waterhammer pressure in a single system is derived. By use of the distributions of water level, original load and valve closure time, the integral formulas for probability density function of pressures of first interval type waterhammer and limit type waterhammer in a single hydraulic system are provided. The theoretical formulas for sensitivity analysis for waterhammer in a single system are given and, with these formulas, sensitivity analysis is made through examples. The method of distribution type fitting is introduced to determine the distribution of waterhammer pressures in single systems. Thereby conclusions are drawn that the distribution of increasing pressures of waterhammer in single systems is log-normal type and that of maximum pressures is normal type. By use of the distributions of water level, original load and valve closure time, moment characteristic method is presented for the solution to the mean value of waterhammer pressures in a single system.4. Computational examples are given to verify all the methods involved.