Modelling of two-phase blowdown from pipelines—I. A hyperbolic model based on variational principles

Abstract

In this paper, Geurst's variational priciple for bubbly flow is extended to generalised multicomponent two-phase dispersions. The present variational principle allows both phases to be compressible in deriving the momentum equations. A mixture energy equation is obtained using Noether's invariant theorem and is shown to be comparable with the averaging formulation. The hyperbolicity of the equations is achieved by forcing the flow to be marginally stable. Under the marginally stable condition, all the information related to the structure of the flow is found to be embedded in an inertial coupling constant and an expression for this constant is obtained based on critical flow data. The marginally stability model gives correct sonic characteristics up to void fractions of 0.8. The clearly defined sonic characteristics make possible the rigorous determination of the critical flow condition for rapid depressurisation of pipelines.