Unsteady compressible flow in long pipelines following a rupture

Abstract

AbstractThe unsteady frictional flow of a compressible fluid generated in a long pipeline after an accidental rupture is of considerable interest to the offshore gas industry. It answers several important questions concerning safety and pollution, e.g. the flow rate at the broken pipe end.Laboratory tests cannot simulate the rather complex phenomenon satisfactorily. The problem is highly non‐linear and no general analytical solution is yet known.In this study, based on computational fluid dynamics, the simplifying assumptions of isothermal and low Mach number flow often applied in the case of unsteady compressible flows in pipelines, have not been used.Owing to the choking condition (Ma=1) which prevails for some time at the broken end. and the cumulative effect of friction over the 145 km long pipeline, we obtain (∂p/∂x)t→−∞. This analytically established singularity leads to numerical difficulties which seriously affect the accuracy. For short tubes (such as shock tubes) this negative feature is much less severe. Special procedures were necessary to keep the accuracy within the chosen limit of 1 per cent.