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Eulerian 2-phase equilibrium drift model

This model accounts for the relative Celerity c between the vapor bubbles and the surrounding water .
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It applies principally to the flow regime in the SG core.
Both phases are supposed to be at saturation (equilibrium).
The model is valid for upwards vapor flow.
Since the fluid in the node is supposed homogeneous, the phases may be viewed as separated, and the relative vapor-to-mixture volume fraction α represents then as well the relative vapor-to-mixture area in any transverse cross-section of the node.

Accordingly, the vapor mass flow wv will be given by (1) where cv denotes the absolute vapor Celerity, vmv, the saturated vapor massic volume and sw, the transverse area of the node.
A corresponding relation (2) holds for the liquid flow wl.
(3) is the vapor-to-liquid relative celerity clv,
and (4) the total flow,
also expressed (5) in terms of α
(6) and (7) are generic relations relating α to vapor quality x,
which allow obtaining, after some transformations (6:14), a generic expression (15) which makes it clear that the h-flow wh is larger than the product of mass flow w and local enthalpy h, by an amount which vanishes with zero drift (clv=0) or when either water or vapor is saturated.
According to our implicit scheme convention, the enthalpy assigned to outlet section "s" during the whole δs is the, (still unknown), eos nodal enthalpy h2.
Hence the relation (16) will apply there.
On the other hand, the generic nodal balance relations (17) and (18) yield (20).
Comparing (16) and (20), accounting (21) for the assumed α-dependence of clv, and defining (23) a function y(x2) yields , as h2 = hl + x2 hlv, x2 as the root of the implicit equation (22).
Note that, for zero drift the homogenous eulerian solution h2 = mhe / me is recovered.
If the drift term in (22) is only a small correction, y(x2) (23) may be approximated by y(x1).
However, in order to avoid any instability, we prefer getting a quasi-exact solution by means of a Newton scheme (24:32).
Once m2 and h2 thus obtained, the outlet flows are taken from the global balances equations, which insures exact closure even if the calculated x2 is not the exact solution of (29).

We do not claim that the simple correlation (21) be a realistic model of the drift phenomena, which must also account for the type of flow, geometry, dynamic effects, non equilibrium between the phases,...
The main intent of this development is to make explicit that, if the relative celerity correlation can be factored into a pressure-only dependent factor clv0(p) and an α-only dependent analytical multiplier, how it can then be plugged into the balance equation to obtain an exact conservative solution.

The correlation (21) holds as long that vapor is the dispersed phase (bubbles).
From α > .5 we have assumed a constant liquid-to-vapor drop velocity clv0 .5.25

The installed drift model is intended to answer the questions:
has drift a sensible effect on the recirculation flow, on the mass and energy inventory in the SG core, on the secondary heat transfer, on the time-history of an accident such as the Steam Line Break?
In other words, is it a safety issue?
In order to allow drift sensitivity experiments, we have introduced as input a multiplier xclv to the calculated clv0.