Models for Analysis of Water Hammer in Piping With Entrapped Air

Water hammer transients in a pipe line with an entrapped air pocket are analyzed with three one-dimensional models of varying complexity. The most simple model neglects the influence of gas-liquid interface movement on wave propagation through the liquid region and assumes uniform compression of the entrapped noncondensable gas. In the most complex model, the full two-region wave propagation problem is solved for adjoining gas and liquid regions with time varying domains. An intermediate model which allows for time variation of the liquid domain, but assumes uniform gas compression, is also considered. Calculations are carried out for a wide range of initial system pressure ranging from 0.101 MPa (14.7 psia) to 6.89 MPa (1000 psia). A step increase in pressure equal to 5 times the initial system pressure is imposed at the pipe inlet and the pressure response of the system is investigated. Results show that time variation of the liquid domain and nonuniform gas compression can be neglected for initial air volumes comprising 5% or less of the initial pipe volume. The uniform compression model with time-varying liquid domain captures all of the essential features predicted by the full two-region model for the entire range of pressure and initial gas volume considered in the study, and it is the recommended model for analysis of waterhammer in pipe lines with entrapped air.