Explosive Interactions of Core Debris with Water
Steam explosions, also known as “fuel-coolant interactions (FCI),” arise when high temperature molten materials interact with water to produce a shock wave. The phenomena entered the considerations of containment integrity during the preparation of the Reactor Safety Study  as a result of explosive magma interactions with ocean water in Iceland . Steam explosions have plagued the ferrous and nonferrous metals industries for a very long time . Buxton and Nelson  provide a review of the history of steam explosions including accidents in industrial settings.
An example of an explosive melt interaction with water is shown in Fig. 7.8. The explosion shown in this photograph was produced by dropping a 5-kg mass of molten iron and aluminum oxide produced by a ther- mitic reaction into a pool of cold water contained within a Plexiglas receiver.
The concern that arose originally in connection with accident progression under severe accident conditions dealt with molten core debris interactions with residual water in the reactor pressure vessel. The concern was that explosive interactions could either rupture the reactor pressure vessel head or generate missiles that would penetrate the reactor containment. Such a containment penetration early in the course of a reactor accident could result in very large releases of radioactivity into the environment. This immediate failure of containment as a result of core debris interactions with water became known as an “alpha-mode containment failure.”
STEAM EXPLOSION PRODUCED BY 5 KG OF MOLTEN IRON AND ALUMINUM OXIDE FALLING INTO A LARGE POOL OF WATER
Core debris that penetrates the reactor vessel will cascade into the reactor cavity which may contain water. There is, then, the possibility of steam explosions outside the reactor coolant system. There is less concern about the structural consequences of ex-vessel steam explosions because the reactor cavities are typically robust and numerous obstacles exist along pathways missiles might take to impact the reactor containment structure. Some concern remained that steam explosions might damage the pedestal supports for the reactor vessels in boiling water reactor containments. Collapse of the vessel could fail the containment and lead to release paths for radionuclides from the containment to the environment .
Following publication of the Reactor Safety Study, a period of intense investigations of steam explosions was undertaken by the nuclear community . These investigations paralleled those undertaken especially by the aluminum and copper industry following steam explosions in industrial situations that damaged property and in a few cases resulted in the loss of life. Two configurations for molten core debris and water were considered. Most of the research attentions focused on the explosive interactions that were possible when high temperature melts were poured into liquid water. Much less attention was devoted to the so-called alternate contact mode or stratified contact mode  in which a water pool overlays a pool of molten core debris. It was established, however, that this alternate contact mode could lead to explosive interactions of molten material and water.
The research established the general phases of melt interactions with water. Photographs in Fig. 7.9 show some of these important phases. High temperature melts streaming into water break into droplets as a result of hydrodynamic instability. The breakup is into droplets that are on the order of 0.01 m in diameter. The droplets are surrounded by a film of steam since droplet temperatures are well into the film-boiling regime for liquid water. Visual evidence indicates that droplets vibrate and oscillate vigorously during this phase of mixing with the larger body of coolant. Of course, heat removal from the droplets by film boiling is low compared to nucleate boiling. Furthermore, radiant heat loss is limited by high temperature sources of the cloud of surrounding droplets also in film boiling. Consequently, this coarsely mixed configuration of large droplets in film boiling can persist as droplets settle to the bottom of a water pool, accumulate, and coalesce into a melt pool.
The course mixing phase of melt interactions with water can be interrupted. A pressure pulse passing through the system can cause the steam film surrounding a droplet to collapse. Much of the current
FIG. 7.9 MAJOR STAGES OF THE STEAM EXPLOSION PROCESS
understanding of what happens following collapse of the steam film comes from experiments with single molten droplets [40, 41] and models of these experiments . Once the steam film collapses, there is intimate contact between the molten surface and liquid water. The resulting rapid heat transfer leads to rapid steam generation and causes melt to solidify at the surface. The solidified material is not structurally sound. It fragments and exposes more molten material to liquid water. This leads to further, rapid, steam production. The sudden generation of steam produces a pressure pulse that can trigger collapse of steam films on adjacent droplets. These adjacent droplets also quench, fragment and produce large amounts of steam and additional pressure pulses. Individual pressure pulses combine and accumulate at a propagation front to produce a shock wave. A plot of pressure against time recorded during a steam explosion experiment is shown in Fig. 7.10. Quite clearly, the sharp pressure rise is indicative of a shock wave.
The exact nature of the pressure pulse to trigger the energetic steam explosion process initially is not well understood . Pressure pulses can be produced artificially to cause steam explosions once some level of coarse mixing of melt with water has been achieved. Magnitudes of the pressure pulses required for triggering are similar to pressure pulses expected to occur naturally during the course of severe accident progression by collapses of equipment and structures. Rarefaction as the settling coarse mixture of droplets approaches the bottom of the water pool often appears in experiments to be sufficient to initiate a steam explosion. Triggering of explosive interactions of molten material with water under pressurized conditions is more difficult because the pressurized steam film surrounding molten droplets is “stiffer.” Stiffening the vapor blanket can also occur when steam surrounding the droplet reacts to produce hydrogen  which does not condense under conditions of interest.
Triggering indubitably introduces a stochastic character into the steam explosion process. One of the singular frustrations of the experimental investigations of steam explosion phenomena is that replicate experiments with boundary conditions as nearly identical as possible will yield quite different results. In addition to this undiagnosed variability, there is variability in the probability of steam explosions with the composition of the melt material. Molten aluminum, aluminum oxide, and molten iron appear to be quite likely to produce steam explosions when mixed with water. On the other hand, molten uranium dioxide, despite a much higher melting temperature, does not readily undergo explosive interactions with water unless some external pressure pulse is applied to initiate the interaction. This variability in explosiveness with melt composition may well have to do with formation of a solidified crust at the melt-vapor interface during the coarse mixing phase of melt interactions with water. Hot solid materials even when finely divided prior to addition to water do not cause explosive interactions. Slow heat transfer and consequent slow steam generation when water interacts with hot solids may not lead to pressure pulses adequate to propagate the vapor film collapse throughout the mixture. A crust at the interface of melt and vapor of sufficient thickness to maintain integrity during vapor collapse may also retard heat transfer and steam generation enough to retard the propagation of the vapor
PRESSURE AS A FUNCTION OF TIME DURING A STEAM EXPLOSION EXPERIMENT collapse process. Current thinking is that crusts on the order of 2 x 10-4 m thick may be sufficient to prevent steam explosions. Of course, thick crusts are most likely to form on low thermal conductivity, high melting point materials such as uranium dioxide.
The development and propagation of the shock wave during steam explosions remains a topic of research. Early models were based on an analogy to shock fronts produced in the detonation of gas mixtures . The idealized configuration assumed a steady shock wave moving through a homogeneous mixture. Mechanical and thermal equilibrium were assumed to be reached in a narrow zone behind the shock wave. Such modeling predicted shock pressures and propagation velocities well in excess of those observed in experiments. Critical assumptions made in the model included rapid droplet fragmentation and complete mixing of the hot and cold fluids in the reaction zone.
Current modeling of the propagation phase of steam explosions is still based roughly on an analogy to gas detonations, but some of the original assumptions have been relaxed. The essential challenge faced by modelers is that there is no equivalent to Schlieren photography for imaging the shock front propagating through the melt-water mixture as can be done for combustible gases. Details of both the mechanisms and the rates of droplet fragmentation and steam production remain topics of discussion.
A vast number of experiments to investigate steam explosion for purposes of nuclear reactor safety has been done. Corradini et al.  provide an extensive list of tests and conditions. Melt masses have varied from very small for single droplet experiments to in excess of 100 kg. The testing has been largely heuristic in nature. Variables such as melt composition, melt-water volume ratio, water depth, water subcooling and the like have been studied. The stochastic nature of the steam explosion process has greatly complicated development of an informative data base.
An important issue for the analysis of steam explosion consequences is the efficiency with which thermal energy in the high temperature melt is converted into mechanical work. There is, of course, a thermodynamic limit known as the Hicks-Menzies limit  of about 29%. Measured conversion efficiencies are always much lower than this thermodynamic limit. Some typical values for experiments of the type shown in Fig. 7.8 are plotted in Fig. 7.11 against the ratio of the water mass divided by melt mass. Results shown in this figure illustrate also the variability of data obtained in steam explosion experiments. Conversion efficiencies shown in the figure are
THERMAL TO MECHANICAL EFFICIENCIES DETERMINED IN STEAM EXPLOSION EXPERIMENTS VARYING THE MASS RATIO OF COOLANT AND MELT less than two percent. The largest conversion efficiency reported in experiments pertinent to reactor accident analyses is about 12% in a test with a single droplet. It does appear that conversion efficiency can be increased by system pressurization though this may well inhibit triggering of steam explosions.
Though the efficiencies with which thermal energy is converted to mechanical energy in steam explosions are low, there is a large amount of thermal energy available in reactor core melts. Consequently, much attention has been paid to identifying the limits on the total mechanical energy that could be released during steam explosion processes. Limits to the extent of coarse mixing have been examined [36, 47]. The reliability of triggering by rarefaction at the water pool base so that only melt suspended in water can participate in an explosion has been examined . Computer models of the complicated three or four phase hydrodynamic and heat transfer situation are being developed to assess limitations on the phenomenon of steam explosions .
The likelihood that steam explosions would threaten the integrities of the reactor pressure vessel and the reactor containment was examined both in the aftermath of publication of the Reactor Safety Study and as part of the preparation of the NUREG-1150 study of severe reactor accidents in representative US nuclear power plants . In the Reactor Safety Study, the alpha containment failure mode was assigned somewhat arbitrarily a probability of 1% given the occurrence of a severe accident initiating event. Expert judgments used for analyses in the preparation of the NUREG-1150 study assigned lower conditional probabilities when core degradation and melt relocation took place within a pressurized reactor pressure vessel. Subsequent expert opinion elicitations  led to a consensus that conditional probabilities for reactor pressure vessel rupture by steam explosions were exceptionally low even if the system was not pressurized. This same expert panel did note that small steam explosions are quite likely to occur. Though they are not likely to be either large enough or involve sufficiently efficient thermal to mechanical energy conversion to threaten structural integrity of either the reactor pressure vessel or the reactor containment, they could affect the continued progression of a severe accident.
The steam explosion process quenches and finely fragments the melt that interacts with water. The size distribution of debris produced by steam explosions is compared in Fig. 7.12 with the size distribution of debris produced by simple, nonexplosive quenching of a similar melt. More than 96% of the mass of debris from the simple quenching process has particles sizes in excess of 0.5 mm based on simple sieve analysis.
SIZE DISTRIBUTION OF SOLID DEBRIS COLLECTED FOLLOWING A STEAM EXPLOSION AND FOLLOWING A SIMPLE, NONEXPLOSIVE MELT QUENCHING EVENT
Only 37% of the debris collected following a steam explosion has such a large particle size. Most of the debris from the steam explosion is less than 0.1 mm in size.
The debris produced by a steam explosion is fine enough that sufficient accumulations of the debris within areas of either the reactor pressure vessel or the reactor containment will not be coolable even if submerged in water . Flooding limits the ability of liquid water to penetrate deeply into beds of fine particulate. Because water is unable to penetrate the bed, the bed will dry; the debris will reheat and eventually melt. The hot debris will then interact with the substrate which for many reactor containments will be concrete. The interactions of core debris with structural concrete are discussed in Section 7.5. Included in these discussions are the effects of water on core debris interacting with concrete.
A concern at the time steam explosions were identified as a potential hazard to containment integrity was that steam explosions could loft finely divided reactor core materials into the containment atmosphere. Air might chemically react with the debris particles. Such air reactions were expected to release large fractions of the radioactive inventory of ruthenium which had not been considered to be a major cause of reactor accident consequences. This contention has largely been refuted by more detailed analyses .
Steam explosions, even ones that do not threaten the structural integrity of either the reactor pressure vessel or the reactor containment but do affect the progression of the reactor accident, are not routinely considered in reactor accident analyses. Computer models of the steam explosion process are not now viewed as predictive in capability. There are, then, ongoing investigations of steam explosions within the nuclear community. Experimental studies are underway in Italy  and in Korea . Because of the poorly resolved status of the technical issues of steam explosions, safety analyses rely heavily on expert opinion  and uncertainty analyses [37, 54].