Void fraction predictions in forced convective subcooled boiling of water between 10 and 18 MPa

A new heat balance for flow boiling

“…A large number of correlations1–6 have been proposed for the evaluation of the cross‐sectional average volumetric fraction or void fraction of vapor bubbles α, which is of central interest to power and process industries because void fraction significantly affects neutron absorption, heat transfer, and pressure drop in flow boiling 1–6. Unfortunately, the complex nonequilibrium subcooled region, in which saturated vapor bubbles steadily coexist with subcooled bulk liquid, has prevented to define a coherent expression of the heat balance for subcooled flow boiling 1–6…”

“…So, for void fraction calculation, the standard expression for the heat balance for this zone, and also for the full boiling region, is the definition of an “equilibrium” quality1–6 x eq as where q ′ is the uniform heat per unit mass and per unit inlet length (kJ/kg m), z is the axial distance along the heated wall (m), h L,i is the inlet liquid enthalpy (assuming only liquid at the inlet) (kJ/kg), and h F and h G are the saturated liquid and saturated vapor enthalpies at the inlet pressure, respectively (kJ/kg). Usually, the kinetic and gravity terms are neglected 1–6…”

“…To relate this “equilibrium” quality with the unknown true local vapor weight fraction, Levy4 postulated an exponential function. Recently, Delhaye et al5 have postulated a hyperbolic tangent function. Then, the vapor volumetric fraction is obtained from this true local vapor weight fraction and accepted relationships between vapor weight and volumetric fractions, which were based mainly on the “drift flux” model of Zuber and Findlay 6.…”

“…Then, the vapor volumetric fraction is obtained from this true local vapor weight fraction and accepted relationships between vapor weight and volumetric fractions, which were based mainly on the “drift flux” model of Zuber and Findlay 6. The “drift flux” model, which is considered complex and empirical,5 treats the different velocities of the two phases defining the so‐called “weighted drift” velocity 5, 6…”

“…The shaded tests, although repeated, are included to analyze the influence of heat flux, mass velocity, and pressure in the model. Recently, Delhaye et al5 have used the same MPI data as reference to validate some extrapolations from R12 void fraction data to water at high pressure, due to the high expense of such experiments.…”