Considering two-phase flow, homogenous flow assumes that the gas and liquid phases are flowing at the same velocity, while other models for two-phase flow, such as drift-flux assume a separated flow model with the phases allowed to flow at different velocities. Generally the vapor flow is faster in upward flow because of the density difference.

3.3.1 The homogenous equilibrium model

Homogenous Equilibrium Model (HEM) treats the two-phase flow as finely mixed and homogeneous in density and temperature with no difference in velocity between the gas and liquid phases.

A general expression for void fraction a, is given in (Feentra et al., 2000).

where pG and pL are the gas and liquid densities respectively and S is the velocity ratio of the gas and liquid phase (i. e. S = UG / UL ). The quality of the flow x is calculated from energy balance, which requires measurement of the mass flow rate, the temperature of the liquid entering the heater, the heater power, and the fluid temperature in the test section. The HEM void fraction aH is the simplest of the two-phase fluid modeling, whereby the gas and liquid phases are assumed to be well mixed and velocity ratio S in Equation 36 is assumed to be unity. The average two-phase fluid density p is determined by Equation 37.

P = apG + (1 — a)pL (37)

The HEM fluid density pH is determined using Equation 32 by substituting aH in place of a. The HEM pitch flow velocity VP is determined by

Vp = Gp / pH

Where Gp=Pitch mass flux