Investigation of unsteady friction effects in transient two-phase pipe flow

Abstract

Water hammer and transient cavitating flow may induce large pressure fluctuations in pipelines. Transient events in pipeline may cause a drop in pressure large enough to break liquid homogeneity and continuity (liquid column separation, distributed vaporous cavitation). Trapped air pockets in liquid may be a major problem in piping systems. The paper deals with mathematical tools for modelling unsteady skin friction, transient vaporous cavitation (liquid column separation) and transient gaseous cavitation (trapped air pockets). The method of characteristics transformation of the unsteady liquid pipe flow equations gives the water hammer solution procedure. A convolution-based unsteady skin friction model is explicitly incorporated into the staggered grid of the method of characteristics. Incorporating discrete cavities into the water hammer model leads to the discrete cavity model. An advanced discrete gas cavity model (DGCM) with consideration of unsteady pipe flow friction effects is presented in the paper. The DGCM is capable to simulate vaporous and gaseous cavitation at the same time. Pipeline apparatus for measurement of transient liquid flow (water hammer) and transient two-phase flow (vaporous and gaseous cavitation) is briefly described. The paper concludes with two distinct case studies showing profound effects of unsteady skin friction on pressure histories.