Recent work is directed toward deriving a model for energy transfer to the sodium by considering high energy fuel particles being ejected from the core. These are presumed to transfer energy to the sodium through which they pass, leaving a trail of vaporized sodium along their flight paths (see Fig. 5.13).

Such a model would include the three conservation equations for mass, momentum, and energy and an equation of state for the vaporization of the sodium.

Conservation of mass

dmjdt = —dmv/dt (5.20)

Conservation of momentum

(mh + m{ + |ttjv + mg) dvb/dt = A(PV — Pg) — (mL + mt + mv + mg)g

(5.21)

Conservation of energy

— (»V — »l) dmv/dt = (mv duv/dt) + (mt дщ/dt) + vbA(Pv — Pg) (5.22) Equation of state

Hl = ub{T) (5.23)

In these equations m is mass, и is internal energy, P is pressure, v is velocity, A is the cross-sectional area of motion, and the subscripts L, f, v and g refer to the liquid sodium, fuel, sodium vapor, and cover gas (see Fig. 5.14).

Fig. 5.14. Sodium hammer model, including the sodium vapor driving force.

The analysis requires a fuel model in order to compute the heat transferred from the fuel (m{du{jdt). It assumes that incompressible sodium is being driven, by the pressure of the sodium vapor produced, against the cover gas. Such a model also needs an allowance for direct momentum transfer, since the previous driving force considered in Section 5.5.2.1 is also a driving force here. It should take account of the fact that fuel particle populations of differing sizes may be shot into the sodium in different times and the

final driving force is an integrated effect of sodium vapor produced by a large number of individual energy transfer events.

Such a model could be included into a larger hydrodynamic model and could be expanded to include the effect of vessel internals. Table 5.13 shows some sample results from such a model, results which show a very moderate sodium hammer behavior, for in one case it did not even reach the vessel plug before the sodium vapor condensed. Later improved versions of this analysis included waves of particles reaching the sodium thus resulting in much larger slug energies up to 20 or 30 MW-sec (27b).