基于π定理的虹吸式出水管原型和模型虹吸形成时间的相似分析

Similarity analysis of siphon formation time of siphon pipes between the prototype and model based on the π theorem

基于π定理的量纲分析方法,对大型泵站虹吸式出水管虹吸形成过程中水力驱气阶段、水力挟气阶段和虹吸稳定流阶段水流特征量进行了量纲分析,分析了原、模型虹吸形成各阶段所应遵循的流体力学相似准则。结果表明:在重力相似条件下建立物理模型时,在虹吸形成过程的水力挟气阶段和虹吸稳定流阶段,模型的历时与原型相似;在水力驱气阶段,虹吸形成时间除受到Froude数影响,还受到Weber数和Euler数的影响。在进行虹吸式出水管模型试验研究时,仅保持重力相似的模型装置而不考虑Weber数及Euler数的影响,会引起原、模型间比尺效应问题,通过模型预测的虹吸形成时间将比原型的虹吸形成时间偏小。

Dimensional analysis of flow characteristics was made using the dimensional analysis method based on the π theorem for large scale pumping stations at the hydraulic air-driving stage,hydraulic air-carrying stage and siphon steady stage during siphon formation in the siphon pipes.The similarity criteria of fluid dynamics were investigated that the prototype and the model should obey at various stages.The results show that as for the physical model for the gravitational similarity conditions,the durations of the model are similar to those of the prototype during the hydraulic air-carrying stage and the siphon steady stage and that the siphon formation time is dominated by the Froude number,the Weber number and the Euler number during the hydraulic air-driving stage.The results also show that in model tests on siphon pipes,the model devices only with the gravitational similarity but without consideration of the Weber number and the Euler number effects may result in the scale effect in the prototype and the model,with the siphon formation time predicted by the model being shorter than that of the prototype.