基于图论的环状管网慢变流的计算研究

管网负荷变动的水力过程可以抽象成非恒定流中的慢变流进行研究,这是大量管网运行中的现实现象.对基于图论的环状管网慢变流模型进行分析,利用矩阵论导出了采用链支流量矩阵计算慢变流过程的解析表达式,并在此基础上得到了适于数值模拟的离散求解模型.通过实际算例计算了管段流量和节点水头等水力要素随时间的演化过程.慢变流理论不仅对分析管网系统的水力工况有很大作用,还由于其时间过程所包含的丰富信息使其在管网的水力摩阻识别及漏失故障诊断中具有重要意义.由于引入链支流量矩阵作为因变量,在很大程度上简化了定量计算,将会非常有利于对上述系统识别问题的搜索求解.

Analysis and calculation of the slow transient flow in the multi-loops network based on graph theory

The actual hydraulic process of the variableload in pipe networks can be treated as the slow transient flow.This paper analyzed the multi-loops network slow transient model based on graph theory and obtained analytical formulas expressed by link discharge matrix which are deduced by using matrix theory.The discrete model which was suitable for the numerical simulation was established.Taking one actual pipe network as an example,the changing process of the pipe discharges,nodal pressures and other hydraulic factors with time was calculated and illustrated.It is obvious that the slow transient theory is not only useful on analyzing the hydraulic state of the network,but also on identifying hydraulic resistance coefficients of pipes and diagnosing leakage detection in networks because transient processes offer much more information than a steady process.Furthermore,the introduction of link discharge matrix as the variable greatly simplifies the calculation of slow transient flow,and benefits the solution of system identification.