Leidenfrost [204] in 1756 reported that water droplets can endure for several seconds on a sufficiently hot metal surface as a result of an intervening vapor film that inhibits heat transfer. With decreasing surface temperature the vapor film could no longer be sustained and the droplet quickly boiled away. The minimum surface temperature for the existence of a vapor film became known as the Leidenfrost Point. However, later experiments and theoretical analyses in the twentieth century showed that the Leidenfrost Point is not just a property of the liquid and surface temperature. Specifically, particulate impurities or surface roughness are found to reduce the formation energy [205] of an embryonic vapor bubble and so precipitate nucleation. Indeed with extreme liquid purity, stillness and surface purity, boiling on a wetted surface can be inhibited until temperatures are well above normal and towards the limiting homogeneous nucleation temperature [205].

The destabilization of a vapor film (triggering) to initiate an MFCI in a Severe Accident differs radically from the collapse of a Leidenfrost vapor film. First, liquid corium temperatures are orders of magnitude larger (> 3500 K) so an enormous radiant heat flux component[81] [82] enters the liquid interface. Secondly, a film would contain non-condensable hydrogen11 or fission product gases that can modify its thermodynamic states and thermal conductivity [3,210]. Finally, an explosive liquid to liquid heat transfer over m-seconds is induced by external shock waves: rather than spontaneous passive nucleation over seconds. Preliminary aluminum-water experiments at AEEW confirm the necessity of a shock wave to destabilize otherwise quiescent film boiling. These tests in Rig A repeatedly created a detonable coarse mixture like that in Figure 5.1 without an MFCI. Later, a small chemical explosive was used to initiate a weak shock wave which then consistently triggered an MFCI. On the other hand, subsequent urania-water experiments in Rig A and MFTF were consistently triggered just by the injection of melt. Accordingly, to achieve greater understanding for reactor safety assess­ments, experimental [207] and theoretical [206] research was under­taken into shock wave destabilization of vapor films.

As can be readily visualized from Figure 5.1, a realistic three­dimensional simulation of triggering is presently intractable. Never­theless by characterization of the pertinent physical processes useful insight can be gained from the one-dimensional model in Figure 5.4. Due to their widely different acoustic impedances a trigger pressure wave in the liquid propagates only weakly into the vapor. Also many reflections of this transmitted wave occur in the relatively thin vapor before the next stress wave in the liquid arrives back at the interface.[83] Consequently, as inferred from Figure 5.5, vapor pressure can be considered spatially uniform at any instant. Moreover, because thermodynamic relaxation times [211] are of order

I ns and film destabilization requires [207] some 20 ms, classical thermodynamic state variables can describe each point in a film. However, by increasing fugacity [3], permanent gases in a vapor film during a Severe Accident alter these states from those of the pure substance. For example, if the partial pressure of a permanent gas is

dPsat = (tlSAt/tGSAt) • p0

where

vLSAT, vGSAT — specific volume of saturated liquid and vapor, respectively.

Table 5.1 presents the specific volume ratio vLSAT/vGSAT and the fraction of undissociated steam as a function of pressure at 3500 K [208,209]. Because the fission product pressure for locally rupturing a fast reactor fuel pin is of order 2 MPa, the change in the saturation vapor pressure of sodium is seen to be largely negligible. Accordingly, it is inferred that all other thermodynamic states in a film mixture remain essentially those of its separate constituents. In the case of a water reactor, the corresponding specific volume ratio is seen to increase slowly enough for the permanent gases to have a negligible effect on the saturated steam pressure: especially as increasing pressure inhibits its dissociation. It is again concluded that all thermodynamic states in a film mixture are those of its separate constituents.

The extreme temperatures in a vapor film significantly affect its local thermal conductivity. Available data [209] for superheated sodium vapor appear restricted to temperatures no greater than 1500 K. Never­theless, it can be assumed to behave as a perfect gas at higher temperatures. On this basis kinetic theory [210] suggests a two-fold increase in thermal conductivity across a sodium vapor film to the obvious benefit of its stability. In the case of superheated steam, thermal conductivities in Table 5.2 exceed kinetic theory predictions by virtue of more mobile hydrogen molecules created by its partial dissociation.

Accordingly, film stability considerations should involve a distributed model of heat diffusion in the vapor, but too many mesh points would clearly aggravate numerical problems as a film collapses.

If water is in thermal equilibrium with its vapor at 60 °C, the evaporation and condensation mass fluxes derived from kinetic theory

are about 2kg/m2 — s or 6.7 x 1026 molecules/m2 — s. Despite this chaotic interchange at an interface, experiments [214,215] show that it remains plane to within 1 or 2 molecular diameters due to inter­molecular attraction. When a shock wave accelerates the liquid into its vapor, Rayleigh-Taylor waves [216,217] are suppressed so the inter­face remains locally plane. On the other hand if an interface deceler­ates close to a hot melt, these waves could conceivably distort an originally plane interface element. No analysis is apparently pub­lished that engrosses both surface tension and viscosity, but larger predicted oscillatory amplitudes would patently obtain without vis­cous damping. Assuming a uniform deceleration over half the typical 20 ms destabilization period [207] of a 100 mm vapor film by a 10 MPa trigger, then with just surface tension the fastest growing wavelength l* and its time constant t* are shown in Table 5.3 from calculations

where

€ — uniform deceleration of liquid phase

sL — surface tension of the liquid

pL, po — density of liquid and vapor, respectively

Though it appears that Rayleigh-Taylor waves could grow significantly during film destabilization, the large viscous shear forces associated with such rapid micron-sized wavelengths would (in the author’s opinion) strangle their growth. Moreover, experiments [207] confirm a later analysis that the collapse of a vapor film is hardly resisted, so it is therefore reasonable to conclude that a liquid-vapor interface remains essentially locally plane during its destabilization.