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 引用本文: 陶智国, 周领, 邱海云, 李赟杰, 易昌宇. 复杂管道瞬变流的二阶GTS-MOC耦合求解方法. 力学学报, 待出版.
Tao Zhiguo, Zhou Ling, Qiu Haiyun, Li Yunjie, Yi Changyu. A coupled second-order GTS-MOC solution for transient flows in complex pipes. Chinese Journal of Theoretical and Applied Mechanics, in press.
 Citation: Tao Zhiguo, Zhou Ling, Qiu Haiyun, Li Yunjie, Yi Changyu. A coupled second-order GTS-MOC solution for transient flows in complex pipes. Chinese Journal of Theoretical and Applied Mechanics, in press.

## A COUPLED SECOND-ORDER GTS-MOC SOLUTION FOR TRANSIENT FLOWS IN COMPLEX PIPES

• 摘要: 经典的特征线法(method of characteristics, MOC)因其简单方便, 边界条件易于耦合求解, 常应用于有压管道瞬变流方程的数值求解. 对于复杂管道系统, 受库朗数限制, 该方法往往需要进行波速调整或插值求解, 可能出现严重的累积误差和数值耗散. 有限体积法Godunov格式(Godunov type scheme, GTS)对管道内部库朗数具有良好的鲁棒性, 但边界条件采用精确黎曼不变量方法, 处理复杂. 同时, 以往水锤计算通常仅考虑稳态摩阻, 低估了瞬变压力的衰减. 文章提出并推导了考虑动态摩阻的GTS-MOC耦合模型, 使用二阶GTS计算管道内部控制体, 在复杂边界处采用耦合GTS-MOC方法处理. 首先, 针对串联管和分叉管边界条件, 对精确黎曼不变量方法和MOC方法进行了理论分析. 推导结果表明, 在马赫数(Ma)较小的管道瞬变流求解中, 两种边界处理方法结果一致, 与实验结果对比分析, 验证了耦合格式求解的准确性. 最后, 将耦合格式分别与GTS和MOC进行比较. 结果证明, 耦合格式可以达到和GTS相同的精度, 同时, 串联管道系统中MOC线性插值法和波速调整法均存在数值耗散且随时间增加更明显, 耦合格式结果具有准确性和稳定性, 与精确解更吻合.

Abstract: The classical method of characteristics (MOC) is often applied to numerically solve the transient flow equations of pressurized pipelines because of its simplicity and convenience, and the boundary conditions are easy to be coupled and solved. For complex pipeline systems, limited by the Courant number, the method often requires wave velocity adjustment or interpolation for solving, which may result in serious cumulative errors and numerical dissipation. The finite volume method Godunov type scheme (GTS) has good robustness to the internal Coulomb number of the pipeline, but the boundary condition adopts the exact Riemann invariant method, which is complicated to handle. Meanwhile, previous water hammer calculations usually only consider the steady-state moiré resistance, which underestimates the attenuation of transient pressure. In this paper, a coupled GTS-MOC model considering unsteady friction is proposed and derived to compute the internal control body of the pipe using the second-order GTS, which is handled by the coupled GTS-MOC method at the complex boundary. First, the exact Riemann invariant method and the MOC method are theoretically analyzed for the tandem and bifurcated pipe boundary conditions. The derivation results show that the results of the two boundary treatments are consistent in the transient flow solution for pipes with small Mach number (Ma), and the accuracy of the coupled format solution is verified by comparing and analyzing with the experimental results. Finally, the coupled format is compared with GTS and MOC, respectively. The results prove that the coupled format can achieve the same accuracy as GTS, and at the same time, the numerical dissipation exists in both the MOC linear interpolation method and the wave velocity adjustment method in the series pipeline system and increases more obviously with time, and the results of the coupled format have the accuracy and stability, which are more consistent with the exact solution.

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