基于有限体积法Godunov格式的管道泄漏检测模型研究

Research on Pipeline Leakage Detection Model Based on Finite Volume Method Godunov Scheme

摘要: 针对管道泄漏问题，采用有限体积法Godunov格式对其进行数值建模和计算分析。通过Riemann对水锤方程进行离散，采用MUSCL-Hancock方法进行重构得到二阶精度的Godunov格式，为了避免虚假振荡引入MINMOD斜率限制器，结合泄漏边界条件建立泄漏检测模型。二阶Godunov格式与特征线法的计算结果一致，从而验证了所建模型的正确性。计算分析表明，泄漏管道的压力曲线发生衰减和变形，完整管道的压力曲线不发生衰减和变形；泄漏流量影响曲线的衰减幅度，泄漏流量越大曲线衰减幅度越大；泄漏点的数量决定曲线峰值处拐点数量；泄漏点位置决定曲线的形状和第一个波峰发生拐点的时间，从而可以根据泄漏管道的压力曲线，判断管道是否发生泄漏、泄漏点的数量、泄漏发生位置。这对管道泄漏监测具有重要理论意义和实际指导价值。

Abstract: Finite volume method with first order and second order Godunov schemes is presented to simulate and analyze the pipeline leakage problem. The water hammer equation is discrete by Riemann, and the MUSCL-Hancock method is used to reconstruct the two-order precision Godunov format. In order to avoid the false oscillation, the MINMOD slope limiter is introduced, and the leakage detection model is established by combining the leakage boundary conditions. The two-order Godunov scheme is consistent with the result of the characteristic line method, thus verifying the correctness of the model. The calculation analysis shows that the pressure curve of the leakage pipe is attenuated and deformed, while the pressure curve of the whole pipe does not attenuate and deform; the leakage flux affects the attenuation amplitude of the curve, and the greater the leakage flow, the greater the attenuation amplitude of the curve; the number of leakage points determines the number of inflection points at the peak curve, and the location of the leakage point determines the curve. According to the pressure curve of the leakage pipe, the leakage, the number of leakage points and the location of the leakage can be judged by the time of the inflection point of the shape and the first wave peak. This has important theoretical significance and practical guidance value for pipeline leakage monitoring.