管道内水流冲击滞留气团的二阶Godunov数学模型

长距离输水、城市供排水等工程管道系统中常存在水流冲击滞留气团的现象,极可能产生异常压力波动,严重时甚至发生爆管事故。对此,提出将一种准确高效的非恒定摩阻模型引入水流冲击滞留气团的计算中,建立了考虑非恒定摩阻的二阶Godunov模型;并采用"虚拟单元"处理上游入口边界及下游水气交界面,实现了边界通量和内部单元通量的统一计算,避免了以往分别计算两种通量的繁琐,以及追踪水气交界面时数值插值的复杂求解。将该模型计算结果与恒定摩阻模型计算结果及试验数据进行比较分析,结果表明考虑非恒定摩阻的二阶Godunov有限体积模型能准确预测瞬变过程中压力波动和能量衰减情况。

A Second Order Godunov Model of Transient Flow with Trapped Air

Transient flow with entrapped air pockets often arises in urban water supply and drainage systems,which easily causes abnormal pressure surge and even induces pipeline damage accidents.In this paper,an accurate and efficient model considering unsteady friction is introduced into the calculation of transient flow with entrapped air pockets,and a second order Godunov model with unsteady friction is established.The " virtual units" is used to deal with the upstream entrance boundary and downstream air-water interface,which realizes the unified calculation of the boundary fluxes and internal fluxes,and avoids the tedious calculation of the two fluxes separately in the past.In addition,the application of "virtual units" also avoids the complex of numerical interpolation when dynamic tracking the air-water interface.The results obtained by the proposed model are compared to the model without considering the influence of unsteady friction and the experimental data measured.It shows that the new presented second order Godunov finite volume model with considering unsteady friction can accurately predict the pressure fluctuation and energy attenuation of air pockets.