AN UNEQUAL VELOCITY, UNEQUAL TEMPERATURE TWO-FLUID MODEL OF VAPOR-LIQUID FLOW AND SOLUTION OF A STANDARD BLOWDOWN PROBLEM

An unequal velocity, unequal temperature, equal bulk pressure (UVUTEBP) two-fluid model of vapor-liquid flow has been developed starting from the local, instantaneous conservation equations for the two phases via time-averaging and cross-sectional-averaging operations. This quasi-one-dimensional, time-dependent, six-equation model is hyperbolic in character and thus well-posed as initial-boundary value problem. In the present work, the hyperbolicity of the model equation set, as indicated by all-real characteristic roots, is preserved with the help of (i) two distribution parameters appearing naturally in the averaged phasic momentum equations due to nonuniform transverse profiles of phase axial velocities and of phase fractions, and (ii) the added mass term in the axial momentum equations. The UVUTEBP two-fluid model is then compared qualitatively to the multidomain, multiphase model of vapor-liquid mixture flow developed elsewhere.; A numerical solution scheme applicable only to hyperbolic equation systems, developed originally at Atomic Energy of Canada, has been extended in this work to the six-equation model and subsequently incorporated into a new computer program. The U.S. Nuclear Regulatory Commission Standard Problem No. 1, the Edwards-O'Brien blowdown problem, involving the depressurization of a horizontal pipe initially filled with subcooled, high pressure water has been solved by the afore-mentioned computer program. Our solution agrees well with the experimental results. The level to which the pressure near the closed end of the pipe recovers after the initial undershoot is compared to the value predicted by Lienhard, et. al. from semi-empirical considerations. The agreement is found to be quite good.