长距离输水有压-无压耦合水力瞬变的Godunov格式建模模拟

Simulation of long-distance water transportation system with a combination of free surface and pressurized flows based on Godunov scheme

针对含无压流、倒虹吸有压流联合的长距离输水系统,建立有限体积法Godunov格式的有压-无压耦合水力瞬变数学模型,并对运行水力特性进行模拟研究。对于无压流转变为有压流时,提出考虑有压流水锤效应的Preissmann狭缝法,实现有压流水力瞬变的模拟计算。基于有限体积法Godunov格式对控制方程进行离散求解,采用了虚拟边界法实现了边界与内部单元统一计算,简化了计算的繁琐。结合实际工程,针对稳态运行流态、糙率敏感性、水力过渡过程进行计算分析。结果表明:所建模型模拟结果与精确黎曼解数据基本一致;稳态运行情况下,运行流量越大、糙率越大、下游出水口水位越高,满管率、最大管道充满度、最小管道充满度越大,水面线越高。较高水面线时倒虹吸的惯性振荡可导致瞬变过程出现局部明满交替流波动。

In this paper,finite volume method Godunov scheme coupled hydraulic transient mathematical model is developed for a long-distance water transportation system with a combination of free surface and pressurized flows,and the operational hydraulic characteristics are simulated and studied.For the transition from free surface flow to pressurized flow,the Preissmann slot approach considering the hammer effect of pressurized flow is proposed to simulate the hydraulic transient of pressurized flow.Based on the finite volume method Godunov scheme,the governing equations are discretized.The virtual boundary method was proposed to achieve unified calculation of boundaries and internal cells,simplifying the complexity of calculation.The proposed model is used for actual engineering to calculate and analyze the steady-state operating flow regime,roughness sensitivity,and hydraulic transition process.The results show that the simulation results of the constructed model are basically consistent with the accurate Riemann solution data.Under steady-state operation,the higher the operating flow rate,roughness,and downstream outlet water level,the greater the full pipe rate,maximum pipeline filling,and minimum pipeline filling,while the higher the water surface line.The inertial oscillation of inverted siphon at a higher water surface can cause local alternating flow fluctuations in the transient process.