Nuclear Steam Generators and Waste Heat Boilers

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…”

“…Alternatively, the difference of velocity between the phases has been classically quantified through the slip ratio S ,1–3 which is defined as the cross‐sectional area mean vapor velocity c G (m/s) divided by the cross‐sectional area mean liquid velocity c L (m/s). Its standard expression1–3 in function of “flow” quality x flow (so S would be a “flow” slip), void fraction α, and saturated liquid and vapor densities ρ F and ρ G , respectively, is Unfortunately, the better‐known correlations for void fraction, which include the calculation of this slip ratio, may show1 a standard deviation for the prediction of S flow ranging from 30 to 70–80%.…”

“…The main novelty of this work is to use classic thermodynamic relationships between vapor weight and volumetric fractions, i.e., to deal with the well known “thermodynamic” quality x th , classically defined as3 where ρ m is the standard mixture density1–3 of the vapor‐liquid mixture (kg/m 3 ) and ρ L is the density of the liquid (kg/m 3 ), which might be subcooled or saturated.…”

“…First, we neglect pressure drop, so assuming a constant pressure along the channel equal to the inlet pressure p i . For the liquid enthalpy at subcooling, we assume the classic approach1, 2 of considering it practically equal to the “flow” mixture enthalpy, i.e., Eq. 1, So, the axial location of the saturation point z sat can be readily calculated.…”