Entrainment rate of droplets in the ripple-annular regime for small vertical tubes Page: 4 of 28
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Introduction:
The state-of-the-art correlations to predict dryout in boiling water reactors are
empirical interpolations of full scale steam/water experimental data. A mechanistic two-
fluid model for dryout would reduce the need for full scale experiments and would also be
valid in transient situations associated with reactor safety. However there are large
uncertainties in the constitutive relations. The difficulty is two-fold: many of the two-
phase transport mechanisms are not completely understood and there are not sufficient
separate effects data to validate the models for typical reactor operating conditions.
The dryout of the liquid film attached to the wall in annular-mist flow is the
mechanism that leads to the critical heat flux limit in many nuclear reactor situations. A
three field two-fluid model is the most suitable for the topology of annular-mist flow. The
liquid phase is divided into two fields: film and droplets. The mechanisms of entrainment
rate, e, and deposition of droplets, d, are essential parts of this model. The one-
dimensional three-field conservation of mass equations are:
" Droplet Continuity Equation:
t9 0
p, ad + apf adud=e , -d)+ r (1
The first term on the right hand side is the liquid mass transfer due to entrainment
and deposition of droplets, and the last term is the mass source term due to phase change.
" Liquid Film Continuity Equation:
apf a + ep a u =-a, ( -d)+ F. (2)
" Vapor Continuity Equation:
p, ag + pg a, ug= - rd -- ;ff (3)
Here ud, ur and ug are the area averaged axial velocities for entrained droplets, liquid film
and vapor, p. and pg are the densities of liquid and gas and a is the volume fraction of
each field. The entrainment and deposition are the exchanges of liquid mass between the
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Lopez de Bertodano, M.A.; Assad, A. & Beus, S.G. Entrainment rate of droplets in the ripple-annular regime for small vertical tubes, article, June 1, 1998; West Mifflin, Pennsylvania. (https://digital.library.unt.edu/ark:/67531/metadc706213/m1/4/: accessed March 28, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.