In discussing heat transfer processes, it is usual to define a heat flux q from a surface, which is the rate of heat flow per unit surface area per unit time and has units joules per square meter per second or watts per square meter (a watt is a joule per second). The heat flux is commonly related to the temperature dif-

Source: Etherington 0958).

a Value of Ср2.8р2/р0,2 divided by that for sodium (hence value for sodium is unity).

ference or temperature drivingforce ДТ by the simple equation:

q = h!:lT

where h is a constant of proportionality commonly referred to as the heat trans­fer coefficient. The temperature difference Д T is defined as the difference be­tween the fuel element surface temperature Tw and the bulk coolant temperature TB

T= TW-TB

The temperature of the fluid is not uniform across the channel; the fluid ad­jacent to the wall is at the wall temperature. The bulk temperature TB is defined as the fluid temperature that would be obtained if the fluid were totally mixed within the channel. Figure 31 shows a typical temperature distribution across the fuel and coolant in a reactor. Heat is generated in the fuel pellets and is con­ducted to the pellet surface, then across the gas gap between the pellet and the can, then through the can wall, and finally out to the fluid.

The heat transfer processes in the reactor must be designed to prevent the system from exceeding two main temperature limits:

1. Maximum temperature of thefuel. If the fuel is made from uranium metal, its maximum temperature is around 650°C, where volume swelling occurs due to a crystal strncture change in the metal. For uranium oxide fuel, the maxi­mum temperature is around 2800°C, the melting point of the oxide. Despite its much lower maximum temperature, metal fuel may release heat from its surface at a higher rate than oxide fuel because of its much higher thermal conductivity. However, in modern reactors metal fuel is rarely used, since it undergoes chemical reaction with the coolant if the cladding is ruptured.

2. Maximum cladding temperature. The temperature of the cladding material is often the limiting factor. For instance, the commonly used Zircaloy cladding rapidly corrodes if its temperature is greater than about 5OO"C, and it reacts exothermically (i. e., generates heat, which can promote further reaction) with steam to form hydrogen at temperatures above 1 000°C. Stainless steel cladding is used in AGRs and liquid metal-cooled fast reactors; it is compat­ible with carbon dioxide and sodium at normal operating conditions (700-750°C) but oxidizes rapidly at higher temperature, the short-term ab­solute limit being the stainless steel melting point of about 1400°C.

In practice, it is not feasible to design a nuclear reactor system to work close to these maximum temperatures, since a margin must be provided for abnormal or accident conditions. Typical maximum cladding temperatures for steady op­eration of various reactor systems are as follows:

Magnesium alloy cladding (Magnox) 450oC

AGR stainless steel cladding 750°C

Pressurized-water reactor 320°C

Boiling-water reactor 300°C

Sodium-cooled fast reactor 750°C

The heat transfer coefficient h depends on the physical properties of the fluid, in­creasing with increasing fluid thermal conductivity, decreasing fluid viscosity, and increasing fluid density. It is also a strong function of the fluid velocity. Typical values of h for reactor coolants at the usual ranges of velocity are as follows:

Water

Boiling water

High-pressure carbon dioxide Liquid sodium

In a pressurized-water reactor the heat flux q is typically around 1.5 million W/m2, giving a cladding-to-fluid temperature difference of about 50°C. In a liq­uid metal-cooled fast reactor, the heat flux might be typically 2 million W/m2, giving a cladding-to-fluid temperature difference of about 35°C. Similarly, in a boiling-water reactor, a typical heat flux is 1 million W/m2, giving a temperature difference of around 15°C.

The values given above for heat transfer coefficients are those appropriate for smooth, plain surfaces. The values for carbon dioxide are very much lower than those for water and sodium. This means that the temperature difference would be unacceptably high, or the power output unacceptably low, for gas — cooled systems. It is thus necessary to enhance the heat transfer in some way in these systems. In Magnox reactors this is done by using external fins, typically of the form illustrated in Figure 2.4 and in more detail in Figure 3.2. The fins on the surface increase the area of cladding in contact with the gas, thus increasing the heat transfer rate for a given amount of fuel. The fins also promote intense

mixing of the gas, which also aids the heat transfer. By using external fins, the heat transfer rate is increased above that for a plain can by a factor of 5 to 6.

In the advanced gas-cooled reactor (AGR), enhancement of gas-phase heat transfer is achieved by quite different means. The can is machined to produce rectangular ribs on the surface as illustrated in Figure 3.3. These ribs add only slightly to the total surface area of the cladding, but they enhance the heat transfer coefficient by a factor of typically 2.5. By interrupting the flow of the hot gas along the surface and causing the hot gas to be mixed with the cooler gas in the bulk flow, they help bring the cooler gas to the surface, enhancing the heat transfer rate. However, this enhancement of heat transfer is achieved at the expense of increasing the frictional resistance to gas flow through the sys­tem, thus requiring more power to drive the circulators.

In nuclear electricity generation, it is necessary to boil water in order to pro­duce steam. In the boiling-water reactor, this is done directly in the reactor core (see Figure 2.10) In the other reactor types discussed in Chapter 2, boiling oc­curs in a separate steam generator, which is heated by the primary coolant: water (Р’^Ю, carbon dioxide (AGR), or sodium (fast reactor).

The phenomenon of boiling is encountered frequently in everyday life. Most British families have an electric kettle to produce boiling water for domestic purposes. In such kettles, bubbles of steam are produced at the heating element surface and rise through the water, initially condensing but later escaping from

the surface of the water and out through the kettle spout, at which time most people remember to switch off the kettle. In a typical kettle, the heat flux would be around 150,000 W/m2. For such a domestic kettle, the heat transfer coeffi­cient would be around 10,000 W/m2 °C, giving a temperature difference be­tween the surface of the element and boiling water of about 15°C. The electric kettle provides a useful analogy in discussing safety issues and accident condi­tions in Chapter 4. Note that the heat transfer coefficient for a typical domestic kettle is approximately one-sixth of that observed for boiling in a boiling-water reactor, because the heat transfer coefficient in boiling increases with increasing pressure and with increasing heat flux, both of which are higher in the B^WR

A further complication in the B^^ is that the steam generated flows along with the remaining water, resulting in a two-phase flow (the two phases being water vapor and water liquid). Two-phase flows are highly complex in nature and have higher flow resistance (higher pressure drop through the reactor) than equivalent single-phase flows. The development of two-phase flow in a heated channel is illustrated for the case of a simple heated tube in Figure 3.4. At the bottom of the channel, heat transfer is to the liquid alone (i. e., a single phase). At a certain point along the channel, bubbles start to form at the wall, and we enter the bubbly two-phase flow regime. Initially, the bubbles are formed at the wall and condense rapidly when they move toward the center of the tube. However, when the liquid heats up to its boiling point the bubbles can no longer condense. As the flow proceeds farther up the tube, more and more of the fluid is in the form of steam. A parameter commonly used to describe the extent of evaporation is the steam quality x, which is the fraction of the total mass flow in the form of vapor. The quality increases along the channel as vapor is generated as a result of the transfer of heat to the fluid. When the pop­ulation of bubbles is sufficiently high, they begin to coalesce and form very large bullet-shaped bubbles, which characterize the slug flow regime. Eventu­ally, these slug flow bubbles all join together, and we enter the annular flow regime, where there is a liquid film on the heated surface with the vapor flow­ing in the center of the channel (Figure 3.4). The surface of this liquid film is highly disturbed by ripples and waves, and liquid is picked up from the wave tips in the form of droplets and flows with the steam.

Farther along the channel, the liquid film is gradually thinned by the process of evaporation and droplet formation and finally dries up. Here, the drop flow regime is entered, with the liquid phase flowing totally as droplets. The transi­tion from the annular flow (wetted wall) to the drop flow (dry wall) region is often referred to as dryout or burnout. This is a particularly important transition since it results in a large decrease in the heat transfer coefficients. In the annu­lar flow regime, the coefficient is typically many tens of thousands of watts per square meter per degree centigrade. Beyond the transition, in the drop flow regime, the coefficient can fall to a small fraction of this value, typically 2000 W/m2 °С This large decrease in heat transfer coefficient results in an increase in heating surface temperarure if the heat flux is maintained constant. As a result, the heating surface may become unacceptably hot. It is important to avoid the dryout-burnout transition in the reactor core situation, where the heat flux is governed mainly by the neutron population. As shown in Section 2.2, the tern-

Figure 3.4: Flow patterns in a vertical heated channel.

perature of the fuel in an operating nuclear reactor is determined by the rate of heat transfer into the coolant. If the heat transfer coefficient falls by a factor of, say, 30, from 60,000 to 2,000 W/m2 °C, then the temperature difference between the fuel and the coolant will rise by an equivalent factor, namely, from 15°C to 450°C, which would exceed the permissible operating temperature for Zircaloy cladding. It is thus vety important to operate nuclear reactors under conditions at which dtyout-burnout does not occur.

Referring to Figure 3.4, we see that the droplets persist for long distances be­yond the dtyout point. This occurs because the droplets evaporate slowly, even if the steam is heated well above the boiling point or saturation temperature. Heat transfer in the region beyond dryout-burnout is vety important in consid­ering accident conditions and will be discussed in Chapter 4

In contrast to the situation in the reactor core, where the heat flux is con­trolled by the neutron population, boiling in the steam generators of indirect — cycle reactors (AGR, P^WR fast reactor) is controlled by the temperature of the primacy coolant fluid. Thus, if and when the dtyout-burnout transition is tra­versed, the heat flux itself will decrease commensurate with the decreased heat transfer coefficient. In one design of P^^ steam generator (the “once-through” steam generator design of Babcock & Wilcox), the dtyout-burnout transition is deliberately traversed. This is also the case in the steam generators of the AGR and in some steam generator designs for fast reactors.

5.1.1 The SL-1 Accident

A small (thermal capacity, 3 ^MW) experimental boiling-water reactor called SL — 1 (Stationary Low-Power Plant No. 1), installed at the U. S. National Reactor Test­ing Station (NRTS) in Idaho, was destroyed on January 3, 1961, as a result of the manual withdrawal of a control rod while the reactor was shut down. The re­actor had been shut down for maintenance and to install additional instrumen­tation. This work was completed during the day shift on January 3, and it was the job of the three-man crew of the 4-12 p. m. shift to reconnect the control rods. The installation of the additional instrumentation required disconnecting the control rods, leaving them fully immersed in the reactor. However, when they were disconnected, the rods could be lifted out manually. Lifting the con­trol rods by about 40 cm (16 in.) was sufficient to make the reactor critical.

At 9:01 p. m. onJanuary 3, alarms sounded at the fire stations and security head­quarters of the NRTS, which was located some distance from the SL-1 facility. Upon investigation it was found that two operators had been killed (a third died later) and that high radiation levels were present in the building. The exact reason for the accident has never been discovered; the removal of the control rod could have been accidental or deliberate, but no one will ever know.

Based on a careful examination of the remains of the core and the vessel during the cleanup phase, it was concluded that the control rod had been with ■
drawn by about 50 cm (20 in.), sufficient for a very large increase in reactivity. The resulting power surge caused the reactor power to reach 20,000 MW in about 0.01 s. This caused the plate-type fuel to melt. The molten fuel interacted with the water in the vessel, and the explosive formation of steam caused the water above the core to rise with such force that when it hit the lid of the pres­sure vessel, the vessel itself rose 3 m (9 ft) in the air and then dropped back ap­proximately to its original position.

Two main lessons were learned from this incident:

1. It is unsatisfactory to have any reactor system (even a small experimental re­actor of this kind) in which removal of control rods is not prevented by a suitable series of interlocks. Removal of a control rod as in the SL-1 accident would be impossible in a modern power reactor.

2. Ejection of water from the core normally leads to a decrease in reactivity, which automatically shuts down the reactor by additional void formation. However, as the SL-1 accident showed, a very fast increase in reactivity can melt the fuel before significant voids are formed to shut down the fission re­action. This effect was demonstrated deliberately in another U. S. reactor test: the so-called BORAX reactor was deliberately brought into this condition and destroyed in 1954.

Explosions arising from the interaction of molten fuel and liquid coolant will be discussed further in Chapter 6.

The diagram of the CANDU in Figure 3.6 shows the positioning of the two re­fueling machines at either end of one of the horizontal channels. Each machine is a pressure vessel that can be connected to the ends of the horizontal channel, becoming pressurized to system pressure when a plug at the end of the chan-

NEW IRRADIATED IRRADIATED FUEL FUEL FUEL ASSEMBLY DISMANTLING BUFFER STORE Figure 7.3: Fuel-refuel sequence for AGRs.

nel is removed. Each refueling machine contains a magazine that can hold ei­ther spent fuel (at the discharge end) or fresh fuel (at the inlet end). A ram is used to push the fuel bundles through the channel. The success of these refu­eling machines has contributed significantly to the very high load factor (pro­portion of time for which the reactor is at power) achieved in the C^NDU reactors as a result of on-load refueling. For a typical 600-^W(e) reactor, ap­proximately 70 fuel bundles are changed each week. The fuel in the machines is cooled by means of a flow of heavy water taken from the main reactor coolant circuit and passed through the machines back into the fuel channels.

To the First Edition

The decision to write this book was made several years ago against a back­ground of general unease that we both felt about the level of public under­standing of nuclear power and its associated technologies. There is no doubt that there are currently considerable fears in the minds of many people about nuclear power generation. Unless these fears are dispelled through a deeper and more widespread understanding of the technologies and other issues in­volved, the development of nuclear power, which has a vital contribution to make to the world’s energy requirements, may be jeopardized.

In preparing this book we have tried our utmost to present nuclear power in simple terms as it really is. Thus, we have discussed real and actual accident scenarios in detail, just as we have discussed the problems of disposal of nu­clear waste. Our aim has been to give a factual and unemotional presentation of what is now a relatively mature technology. This book was in production when news of the Chernobyl reactor accident in the USSR emerged. We have in­cluded some material on this reactor type and, as best as we can, the informa­tion available about the accident itself. The worldwide concern following this accident has illustrated again very directly the need for better and simpler in­formation to be available to the public about nuclear power.

One of the major difficulties in writing a general introductory book of this kind is that of deciding the level and type of audience to which it should be ad­dressed. Our overall aim has been to produce a text thai is as free of jargon as is possible and that demands the minimum possible basic scientific knowledge, while at the same time presenting descriptions and facts at a level of detail suf­ficient to make them generally useful. Thus, the text should be of interest to a variety of readers, including the following:

1. The intelligent general reader, interested in science and technology, who wishes to brief him or herself in greater depth about nuclear power.

2. The undergraduate or graduate student pursuing introductory courses on en­ergy in general and nuclear power in particular. It was with this student au­dience in mind that we have given a number of worked examples and problems at the end of each chapter; these are designed to increase the depth of understanding of the concepts described and to provide an aid to the use of the text in presenting such courses.

3. The industrial technologist wishing to obtain an overview of the nuclear in­dustry. It is perhaps typical of the pressures of modern life that many tech­nologists, even within the nuclear industry itself, do not have a full general appreciation of the overall basis of nuclear power. This book should, we hope, help fill that gap.

Both of us were trained as chemical engineers QGC at University College, London, and GFH at UMIST, Manchester), and we have both specialized in the thermal aspects of nuclear power. It is from this viewpoint that the book has mainly been written. We make no apologies for this; the generation and dissi­pation of heat have a dominant position in nuclear power. Heat generation is important not only during the time of operation of the nuclear reactor but also in considering what happens to the nuclear fuel once it is removed from the re­actor. Because of the fission products, heat generation continues at a significant rate for decades after the fuel is taken out of the reactor. Careful consideration must, therefore, be given to cooling the fuel at all stages, and this will be the theme that forms a consistent thread throughout the book.

We gratefully acknowledge the considerable assistance we had from a num­ber of people in preparing the final manuscript. In particular, we thank Sonya Crowe and Mary Phillips Born, who read the manuscript from the nonspecialist viewpoint. They, and several other readers, helped us identify unnecessary jar­gon in the original manuscript and pinpoint parts of the text where the expla­nations were less clear than they ought to be. We are also very grateful to our colleagues at Harwell and in the CEGB for assistance in the preparation of the diagrams, checking of the examples, and typing and preparing the manuscript, although we stress that any views and opinions are our own. Finally, we would like to thank our wives (Ellen and Shirley) for their support and patience. De­spite their good efforts to keep us apart, we fear that (by continuing our inces­sant conversations on nuclear power and two phase heat transfer) we have not given them the support that we should at many a cocktail and dinner party! The objective of this book is to introduce nuclear power in a factual and un­

emotional manner. However, in all fairness to the reader, we must close this preface by stating our own position quite unequivocally. Notwithstanding fluc­tuations caused by recessions, supply difficulties, oil price rises and slumps, etc., there is a continuous underlying increase in humanity’s demand for en­ergy. This will continue and accelerate as the underdeveloped countries begin to demand standards that we now take for granted in the industrialized nations. The fossil fuels (coal, gas, and oil) are finite and, as we all realize, recovery may ultimately prove uneconomic or their use unacceptable as the demand for global environmental protection grows. Alternative energy sources (tidal, solar, geothermal, and wind) all have their place and deserve continuing support and development; however, even the most optimistic of their proponents, cannot see them becoming the major component of the growing bulk energy require­ment. Energy conservation, too, is vitally important and must be encouraged with the maximum attention. However, neither alternative sources nor energy conservation is likely to bridge the gap between demand and supply over the next century, and nuclear power is the important and growing energy source for the future. It is a clean and efficient power source, both economic and com­pact, with a minimum of environmental impact. Accidents like Three Mile Is­land and Chernobyl need to be put firmly into context with other industrial accidents and particularly those related to the energy industry. However, like any other technology, nuclear power must be developed responsibly and the facts about it clearly understood and accepted by the public and also by those in government who make decisions on technology policy. That is why we wrote this book.

John G. Collier Geoffrey F. Hewitt

1

Water is the most commonly used boiling coolant, and about 30% of the world’s nuclear reactors are boiling-water reactors (BWRs). These reactors were de­scribed in Section 2.4.

Many of the features of water as a boiling coolant are identical to those of water as a liquid coolant, which were described in Section 3 5. It should be noted that BWRs operate at much lower pressures than PWRs (7 rather than

15.5 MPa, 1000 rather than 2300 psia).

Using water as a boiling rather than a liquid coolant entails the additional im­portant problem of radiolysis, whereby the water is decomposed into its con­stituent elements, hydrogen and oxygen, which are released into the vapor during the boiling process. The rate of recombination of the hydrogen and oxy­gen is much slower than in a system operated purely in the liquid phase, lead­ing to higher concentrations of oxygen in the circuit fluid. Since the circuit is under stress due to the high pressure, a form of corrosion called stress corrosion cracking can occur, and this has presented a major difficulty in the operation of BWRs. It can be overcome by using more resistant materials, but replacing pipework in existing reactors is obviously an expensive process.

The advanced gas-cooled reactors are designed to be refueled while in opera­tion. Initial on-load refueling operations with the first two AGRs at Hunterston and Hinkley Point were confined to the charging of fuel into channels in which dummy fuel assemblies had been loaded when the reactor was first charged with fuel. By November 1978, some 15 fuel assemblies at Hinkley and 20 at Hunterston had been charged on-load into these so-called vacancy channels.

On November 19, 1978, a fuel assembly was being withdrawn from channel 4K05 on Hinkley Point B reactor R4. The assembly was raised about 10 ft and then snagged, and the charge machine hoist tripped out on overload. Subse­quently, it was successfully raised into the charge machine. Visual examination of the connected string of fuel elements withdrawn from this reactor channel (the stringer) showed the graphite sleeves surrounding the third, fourth, and fifth elements to be severely damaged. Damage to the graphite sleeve resulted in the fuel elements above the damaged sleeve being starved of coolant and thus overheating, resulting in failure of some of the fuel “pins” that made up the element. Subsequently, a large portion of graphite sleeve from element 4 was recovered from the reactor during a statutory in-reactor inspection. The level of radiation from the sleeve suggested that it was never in the reactor core and that the damage occurred during the loading process. The damaged assembly had been loaded into a vacancy channel at 82% power earlier in the year. The incident caused doubts about the safety of refueling AGRs at power, and an em­bargo was placed on on-load refueling. A program of investigations was begun to establish the cause of the problem.

When the fuel is being lowered into the reactor, it receives considerable buf­feting from the very high gas flow through the empty channel. It is believed that small cracks may have been present in a number of fuel element sleeves and that the sleeve of element 4 cracked further due to the pressure differential across the sleeve during on-load refueling. Techniques have been developed to detect cracks in sleeves, and these and other improvements have been incor­porated into the AGRs. On-load refueling has been resumed at low power.

Geological storage involves the placement of the canisters containing spent fuel elements in a stable stratum typically 1 km below the surface. Such rocks can be assumed to contain water, since the depth would be well below the water table. However, the water is not expected to play a large role in the heat trans­fer from the blocks, and the store would be designed to maintain the surface temperature of the canisters at no more than 100°C or so. However, the pres­ence of groundwater means that material that is leached from the storage blocks may be transported through the stratum in the water. and this is an im­portant consideration in the design of such systems. Circulation of water through the rock as a result of density differences induced hv temperature gr:i-

dients over long periods (the thermal buoyancy or thermal circulation effect) is important in determining the migration of the fission products. This is a very slow process and is not expected to present a serious hazard, but it must be very carefully taken into account for long-term disposal systems. We discuss such systems further in considering the disposal of fission products from repro­cessing plants in the next section.

The choice among the various methods of disposal will be dictated by the availability of suitable storage sites. More geological data will be required be­fore optimum choices can be made. However, studies in many countries indi­cate that spent fuel can be managed and disposed of without undue risk to humans or the environment.

Although other coolants have been proposed, nearly all practical thermal power reactors are cooled with carbon dioxide (Magnox and AGR) or with light water (BWR and PWR as well as the Russian RB^K type) or heavy water (CANDU). We shall restrict the descriptions of reactors to these more common systems.

The classical design basis accident for a pressurized-water reactor is the large-break loss-of-coolant accident (LOCA). It is assumed that in this accident one of the inlet pipes from the circulating pump to the reactor vessel is com-

pletely broken and moved apart to allow free discharge of the primary coolant from both broken ends. This kind of break is called a “double-ended guillotine” break or a “200%” break. Because this break is commonly believed to represent about the worst accident that could happen to a water reactor circuit, it has been chosen as the basis for the design of the emergency response systems.

The sequence of events following the break is shown in Figures 4.13 to 4.17, which illustrate the situation in the whole reactor circuit. A more detailed illus­tration of the events within the reactor vessel itself is given in Figure 4.18. The main phases are as follows:

1. Blowdown phase. Under normal operation (Figures 4.4 and 4.18a), water flows through the inlet pipes (the cold legs) to the reactor vessel, down the annular space around the core, up through the core, and out through the vessel outlet pipes (hot legs) to the steam generator. When a large break oc­curs in one of the cold legs, the contents of the reactor vessel and primary loops are blown down through the break as illustrated in Figure 4.13 and 4.18b. After a very rapid initial depressurization, the pressure falls more slowly due to the creation of a two-phase steam-water mixture in the vessel and circuit, the mass flow of such a mixture through a break being much lower than that for a single-phase liquid. After about 10 s, the pressure has

Refill phase time = 30-40 seconds

Fi^^e 4.16: Large LOCA: reflood phase (40-250 s).

fallen to that for initiation of flow from the high-pressure injection system and the accumulators into the ECCS line in the cold legs.

2. Bypass phase. After the initiation of the ECCS, starting with the HPIS and the accumulators, there is still a significant upward flow of steam in the down­comer annulus through which the cooling water normally flows. This steam flow prevents the accumulator ECCS water from entering the region of the vessel below the core (the lowerplenum), and the water simply bypasses the

upper part of the inlet annulus and flows out through the break, as illustrated in Figures 4.14 and 4.18c.

3. Refill phase. Filling of the lower plenum (the refill phase—Figures 4.15 and 4.18c) begins after further depressurization, when the steam flow up the an­nulus has dropped to a sufficiently low value that it can no longer restrict the ingress of ECCS water. By this stage, the LPIS system will also have been ini­tiated. In a typical PWR, refilling of the lower plenum starts about 23 s after the initial break, and it takes 17 s to fill the lower plenum with liquid, ending this refill phase of the accident.

4. Reflood phase. At a very early stage in the blowdown phase, the core has dried out and the fuel element temperatures rise rapidly, after which they fall relatively slowly due to the existence of substantial steam flows in the core. Typically, the fuel element temperatures rise to around 1000°C. This leads to rupture of the fuel elements, which release gaseous fission products into the primary circuit and, via the break, into the containment vessel. The behavior of typical fuel elements as a function of temperature is shown in Table 4.2. When the lower plenum is filled, the reflood phase begins (Figures 4.16 and 4.184), with the fuel elements beihg rewetted from the bottom upward. Es­sentially, a constant liquid head is Maintained in the inlet annulus during this phase, with excess ECCS water overflowing through the break as illustrated. As the fuel elements rewet, a considerable volume of steam is formed and entrained liquid droplets flow before the rewetting front and pass into the upper plenum. The steam-droplet mixture passes from the upper plenum, through the steam generator, through the circulating pump, and back into the cold leg, flowing out through the break. The water droplets tend to evap­orate in the steam generator due to the backflow of heat from the secondary — side (still hot) fluid. The resistance presented by the outflow route causes a back pressure in the upper plenum, which restricts the rate at which the re­flood can take place. This phenomenon is often referred to as steam bind­ing. The highest resistance of the upper plenum, through the steam generator and circulating pump, to the break would occur when all of the droplets issuing from the core passed to the steam generator and the circu­lating pump rotor was locked stationary. However, the resistance is much re­duced, and the flooding rate greatly increased, if the droplets deposit out on the upper plenum structures and thus are not carried out of the vessel, and if the pump rotor is still rotating.

5. Long-term cooling. In the long term, the situation is as illustrated in Figure 4.17. Water is passed to the unbroken cold leg from the LPIS injection pump and maintains a head of liquid that drives water through the core by natural circulation. Steam maybe generated in the core and may escape with the overflow water through the break as illustrated. This generated steam is condensed by sprays in the containment, which are also fed from the LPIS pump.

In carrying out the design of a P^WR two types of calculations are usually em­ployed, based on an evaluation model or on best-estimate methods. With an evaluation model, the various phenomena are represented by equations and as­sumptions that are postulated to give the worst conceivable result. For instance, it is normally assumed that there is no penetration of ECCS water during the blowdown phase. In best-estimate methods, the best available physical models are used for the various phenomena and an attempt is made to calculate the sys­tem behavior on the basis of these models. It should be pointed out, however, that the calculation of two-phase flows, particularly for the rapid transient condi­tions and large pipe sizes encountered in reactors, is still at an uncertain stage. As explained in Chapter 3, two-phase flows are very complex and in many re­spects poorly understood. It would be unsatisfactory to rely on two-phase mod­eling as a basis for reactor design. Some critics claim that the uncertainties in two-phase flow predictions imply that the reactor is unsafe. We do not share this view. From our long experience, we would agree with the assessment of the current state of modeling of two-phase flows but disagree that the reactor design is based on the results of such modeling. This design must satisfy very conserv­ative criteria that do not depend on knowing about the details of two-phase flow behavior.

Figure 4.19 shows the variation of peak clad temperature as a function of time calculated from the evaluation and best-estimate models, respectively. The con­tinuous line was calculated by using the conservative evaluation approach; the best-estimate values are shown as error bars.

I

When a liquid comes into contact with another liquid and the first liquid is at a temperature much greater than the boiling point of the second liquid, rapid vaporization of the second liquid may occur as the first liquid cools. Under some circumstances, this rapid vaporization may cause a detonation. Such det­onations have been observed in metal foundries where vats of molten metal have been accidentally poured into vessels of water, or vice versa. They may also occur if room-temperature water is brought into contact with liquid natural gas; in this case, the detonation may be followed by a fire as the gas cloud burns. The potential for an energetic interaction between molten uranium fuel and the water coolant may also exist if molten fuel is jetted into water. This can occur as

• molten fuel is ejected into the coolant when the cladding fails during a

severe power excursion (cf. Chernobyl).

• the lower core support plate fails and molten fuel is jetted into a pool of water in the vessel lower head

• the lower head of the pressure vessel fails and molten fuel falls into a water-filled reactor cavity

The circumstances arising in a fuel-coolant interaction and leading to a vapor explosion are illustrated in Figure 6.3. The molten fuel is initially above the pool of coolant (Figure 6.3a) and then falls into it (Figure 6.3h), giving rise to coarse mixing between the fuel and the coolant with a dispersion of large elements of the molten fuel as illustrated. These elements might be 1 cm in diameter. They transfer heat relatively slowly to the water, since a thin vapor film forms around them and insulates them from the water coolant. The third stage is that of trig­gering a shock wave. This is often postulated to occur at the surface of the ves­sel (Figure 6.3c) and might be caused by a small, localized vapor explosion or impact. This shock wave then passes through the coarse fuel-coolant mixture and breaks up the fuel into small elements, which may transfer their stored en-

ergy rapidly to the coolant. This energy release strengthens the shock wave, which continues to propagate through the mixture in an explosive manner (Fig­ure 6.3d).

The energy stored by the molten fuel on release into the coolant pool is partly converted to energy in the shock wave. The extent of this conversion is obviously very important in considering the effects of the resultant shock wave on the reactor system. Experimental studies indicate that the efficiency of con­version from the stored energy in the fuel to the energy within the explosion is about 1.5%.

This would result in an explosion of roughly 1 GJ (or 200 kg TNT equivalent) if all the fuel in a P’^TC, say, reacted simultaneously.

There is still considerable discussion about the precise mechanism by which the shock wave propagates through the fuel-coolant mixture. One theory sug­gests that associated with the shock, there is spontaneous formation of vapor bubbles, giving rise to rapid transfer of energy from the fuel to the coolant. An­other theory suggests that in the shock itself the mechanism of heat transfer is quite different, with the fuel being shredded to small elements by the shear forces in the shock and these elements transferring their energy rapidly to the coolant behind the shock. As we have discussed earlier, a high-pressure im­pulse resulting from a steam explosion is transmitted into the coolant pond. This accelerates a slug of coolant, which impacts the upper head of the vessel and might induce failure. The influence of steam explosions in reactor systems is still a subject of debate, and no final judgments can be made at this time.