Jr. Chen et al., MODELING OF 2-PHASE BLOWDOWN FROM PIPELINES .1. A HYPERBOLIC MODEL-BASED ON VARIATIONAL-PRINCIPLES, Chemical Engineering Science, 50(4), 1995, pp. 695-713
In this paper, Geurst's variational principle for bubbly how is extend
ed to generalised multicomponent two-phase dispersions. The present va
riational principle allows both phases to be compressible in deriving
the momentum equations. A mixture energy equation is obtained using No
ether's invariant theorem and is shown to be comparable with the avera
ging formulation. The hyperbolicity of the equations is achieved by fo
rcing the flow to be marginally stable. Under the marginally stable co
ndition, all the information related to the structure of the flow is f
ound to be embedded in an inertial coupling constant and an expression
for this constant is obtained based on critical flow data. The margin
ally stability model gives correct sonic characteristics up to void fr
actions of 0.8. The clearly defined sonic characteristics make possibl
e the rigorous determination of the critical flow condition for rapid
depressurisation of pipelines.