The experimental 30-MW(t), carbon dioxide—cooled, heavy water-moderated nuclear power station at Lucens, Switzerland, combined the fuel and coolant of the British Magnox reactors with a heavy-water moderator. The fuel element consisted of a graphite column with seven parallel longitudinal channels (Fig­ure 5.22a). Each channel contained fuel rods made from slightly enriched ura­nium metal clad in a finned magnesium alloy (Magnox) can (Figure 5.22 b). Each fuel element was placed in a Zircaloy pressure tube, closed at the bottom end so that the flow of high-pressure (60 bars) carbon dioxide was directed down the annulus between the graphite column and the pressure tube before passing upward to cool individual fuel rods. The heavy-water moderator was contained in an aluminum alloy calandria tank 3 m in diameter and 3 m high, through which the vertical pressure tubes passed (Figure 5.22c).

On January 21, 1969, an accident occurred that resulted in the destruction of one of the fuel elements and the rupturing of its pressure tube. The carbon dioxide expanded into the moderator tank and, after fracturing its rupture disks, entered the reactor containment, which in this case was an underground cav­ern, carrying with it fission products and a large fraction of the heavy-water moderator. The reactor was subsequently dismantled.

Postmortem. The investigations into the causes of the accident were com­plex and lasted about 10 years (Fritzsche, 1981). The initiating cause of the ac­cident was ingress of water into some of the fuel channels around the edge of the core. This was caused by water leaking from the shaft seals of the carbon dioxide gas circulators. Because the pressure tube was closed at the bottom end, a standing water level was formed in these edge fuel channels when the reactor was shut down. Corrosion at the water-air interface resulted in complete removal of the finning over a short length of the fuel rod.

When the reactor was started up on January 21, 1969, water and corrosion products were blown out of the fuel channel. However, due to the lack of any extended surface in the region of the corrosion damage, the magnesium alloy cladding started to melt (at 640°C). The molten cladding soon ran down the channel and solidified, causing a blockage that prevented coolant flow to that channel. The uranium metal soon reached its melting point (1130°C). The ura­nium and the magnesium alloy ignited in the carbon dioxide and the molten metals slumped down inside the graphite column. This column, however, was heated nonuniformly.

Figure 5.22: Layout of Lucens reactor and fuel element.

The column bowed and contacted the pressure tube, which in turn over­heated and burst open under the action of the coolant gas pressure. Only sec­onds earlier the reactor had been tripped because of the release of fission products into the coolant gas stream.

Immediately following the pressure tube rupture, the pressure in the moder­ator tank rose rapidly. At a pressure of 8 bars the bursting disks blew, 0.1 s after the pressure tube mpture, and the expanding C02 bubble forced about 1 ton of heavy water out of the moderator tank

When the pressure tube ruptured, the graphite column also burst apart and the superheated liquid uranium and magnesium metals contacted the pressure tube wall. The Zircaloy wall melted locally and the liquid metal was ejected into the moderator. About 2 kg of the finely dispersed material reacted explosively with the heavy-water moderator. The resulting jet of fire damaged an adjacent pressure tube, which, however, was quenched by returning heavy water before it ruptured. The pressure spike as a result of the chemical explosion reached 16-25 bars and expelled more D20 from the tank.

Perhaps the most significant aspect of this event was the fact that the ingress of water to the core was not identified. The susceptibility of Magnox cladding to corrosion by water is well known, but the very localized and extensive na­ture of the corrosion process in removing the finning from the fuel was crucial. The disadvantage of closed-end fuel channels and the separate parallel chan­nels is also to be noted. It was later determined that even if one of the seven flow channels in the graphite column was completely blocked, the flow to that fuel assembly decreased by only 2%.

As we saw above, the most important source of radioactive waste products is the fuel itself. We can illustrate the fuel cycle for a typical thermal reactor as shown in Figure 8.3. Essentially, there are two alternative routes for dealing with the spent fuel. In route A the fuel is passed through a reprocessing plant, which allows recycling of the plutonium and uranium and produces a highly active liquid waste stream. This latter stream may he passed to an interim liquid

Time after discharge— 5 years————————————————————————- 20 years

Figure 8.3: Options for management of high-level active wastes.

storage stage, followed by solidification in one form or another, before being passed to an engineered surface store, where it is kept for about 50 years. Ulti­mately the solidified waste material would be disposed of in suitable geological formations as discussed in Section 8.5. In route В the spent fuel is stored either at the reactor site or away from it in a specially engineered spent fuel store, be­fore ultimate geological disposal. As shown in Figure 8.2, the option of not re­processing fuel leads to a much longer period before the waste reaches the same level of hazard as the original uranium ore. The options presented by routes A and B are discussed in the next two sections.

To put energy production from uranium into context, it is interesting to com­pare the known recoverable resources and current use of uranium with the re­coverable resources and current use of fossil fuels (coal, oil, and natural gas). Figures provided from the 1992 World Energy Congress in Madrid are shown in Tables 1.1 to 1.3.

The estimated total fossil fuel resources (Table 1.2) are 209 x 1021 joules, of which 40.3 x 1021 joules are estimated to be recoverable.

Sources: WEC 1992 Su^rvey of Entergy ResourcesWEC 1989 Worid Entergy Horirnns 2000-2020; C. D. Masters et al., World* Resources of C^n. uk Oil and Natural Gas, 13th World Petroled Congress, 1991; C. D. [Masters et al., World* Res^ves of C^rude Oil, Natural Bitumen and Shale Oils, 12th World Petroled Confess, 1987.

Sources: OECD^/IAEA “Red Bok,” 1991;^^^, 1976.

Uranium resources can be similarly estimated, and the results are presented in Table 1.3.

The estimated “known” uranium resources are equivalent to 1.4 x 1021 joules if used in thermal reactors and 70 x 1021 joules if used in fast reactors (the dif­ference between these values is explained in Chapter 2). Taking account of speculative resources, the energy content for utilization in fast reactors is esti­mated to be between 175 and 285 x 1021 joules. Uranium resources would be greatly increased by extracting uranium from seawater, in which it occurs at a concentration of 3 parts per billion. This extraction is not likely to be economi­cally feasible in the foreseeable future, however.

Because “known” reserves will last only 76 years at present usage rates, it is important to utilize the uranium resources more efficiently than by simply burn­ing them in thermal reactors. Efficient utilization of these resources can be ob­tained by using fast reactors. An alternative approach might be to use thermal reactors in which the excess neutrons are employed to convert thorium (placed in the reactor core) to an alternative fissile material, uranium-233. ^thile such re­actors can be made self-sustaining (i. e., they can produce as much fissile material as they consume), they cannot be designed to breed efficiently, i. e., produce enough excess fissile material to start a new reactor within a reasonable time.

Primary energy usage from I960 to 1990 and estimated up to 2100 is given in Table 1.4 in Gtoe/year. It will be seen that nuclear power currently provides just

over 5% of world primary energy demand and this is predicted to grow to be­tween 8% and 30% by 2100.

REraRENCES

Armstead, H. C.H. (1978). Geothermal Energy, Chapman & Hall, London. Cowan, G. A. 0976). “A Natural Fission Reactor.” Sci. Am., July, 36-47.

Dorf, R. C. 0978). Energy Resources and Policy. Addison-Wesley, Reading, Mass.

Duffie, J. A., and W. A. Beckman 0980). Solar Engineering of Thermal Processes. Wiley, New York.

Gass, I. G. (1971). Understanding the Earth. Artemis Press.

Hawking, S. 0988). A BriefHistory of Time, Bantam, New York.

NEAIIAEA 0991). Uranium, Resources, Production and Demand. Joint report by OECD and IAEA.

Newson, H. E., and J. H. Jones 0990). Origin of the Earth OUP/Lunar and Planetary Institute, Houston.

U. K. Atomic Energy Authority 0976). Uraniumfrom Seawater.

Wetherill, G. W. 0990). “Formation of the Earth.” Ann. Rev. Earth Planet. Sci. 18:205-56.

——— (1980). “Formation of the Terrestrial Planets” Ann. Rev. Astron. Astrophys.

18:77-113.

World Energy Conference 0992). Survey of Energy Resources.

EXAMPLES ^AND PROBU-MS

1 Chemical energy release

Example: Liquid within a chemical reaction vessel releases chemical energy at the rate of 1.5 kW. The stirrer requires a further power input of 1 kW. If the vessel is cooled by water flowing in a jacket surrounding the vessel, what must the water flow rate be to limit the temperature rise across the jacket to 1 0°C?

Solution: The energy gained by the cooling water must equal that liberated by the chemical reaction and the heat put in by the stirrer. Let W be the water flow rate in kilograms per second. The specific heat of water is 4187 kJ/kg0C Therefore,

W X lOx 4187 = 1500 + 100OJ I s
W = 0.06kg /s

Problem: For the chemical reaction described in the above example, calculate the rise in cooling-water temperature that will occur if the flow rate of water in the cooling jacket is set at 0. 1 kg/s.

2 Pumped storage scheme

Example: A massive pumped storage scheme in North Wales has an upper reservoir containing 67 million m3 of water 500 m above the lower reservoir. The scheme can supply 1800 MW(e) to the electricity grid. Assuming there are no losses, how long can the plant remain in operation at maximum output?

Solution: The total mass of water in the upper reservoir is the volume of water (6.7 x 106 m3) multiplied by the density of water (100 kg! m3), or 6.7 x 109 kg. The total potential en­ergy is this mass times the head (in meters) times the acceleration due to gravity, or

Total potential energy = 6.7 x 109 x 500 x 9.81 = 32.8 X 1012 J

The power output is 1800 MW(e) = 1.8 x 109

= 1.8×109 J/s

Therefore, the plant can remain in operation for

= 5h

Problem. Suppose that the scheme described in the example is to be extended to sup­ply 2000 MW(e) for a period of 7 h. Assuming a conversion efficiency of 95%, calculate the volume of the upper reservoir now required.

3 National fast reactor policy

Example: It is sometimes stated that the introduction of the fast reactor allows a coun­uy to be independent of uranium imports. Why does this statement need considerable qualification? A country has a nuclear power program based on thermal reactors of 10GW by the year 2020. The demand for electric power is growing at 3% per year, and it is decided to introduce fast reactors capable of breeding sufficient plutonium for a further fast reactor in 40 years (the doubling time). What are the consequences? Solution. Let us assume that sufficient plutonium is available from the operation of the thermal reactors (for about 20 years) to allow 10 GW of fast reactors to be installed in 2020. However, the fast reactor capacity can then increase only at the rate at which plu­tonium becomes available to provide fuel for further fast reactors. This rate is 1/40 per year, or 2.5%/yr. Thus the rate at which fast reactors can be installed is lower than the electric power demand growth rate (3%/yr). The difference must (presumably) be made up by installing further thermal reactors, which will increase the counuy’s need for imported uranium. Even if a fast reactor with a shorter doubling time (say, 30 years) is available, a finite time will still be needed to replace thermal reactors by fast reactors. Thus it will take about twice the doubling time, i. e., 60 years, for the counuy to be free from uranium imports.

Problem. Suppose the counuy described in the example decided on an intensive pro­gram of energy conservation to reduce its growth in demand for electric power to 2%. How would this reduction affect the scenario for introducing fast reactors?

2

The stages in tea making are illustrated in Figure 4.2. The electric kettle (re­ferred to by our publisher as the “English samovar”) is first filled with water (a) and then connected to the main electricity supply (b). Ultimately, the water in the kettle boils (c), and the tea is brewed (d).

We may represent the stages illustrated in Figure 4.2 in more scientific terms by plotting graphs (as shown in Figure 4.3) of the following quantities:

1. The amount of water present in the kettle—the inventory.

2. The power input to the element

3. The temperature of the water

4. The surface temperature of the element

5. The temperature of the element windings

As will be seen, the kettle has many of the characteristics of a reactor system. Since it does not have any recirculating coolant, its temperature rises until the boiling point of the liquid is reached, at which point boil-off of the liquid oc­curs. ‘^ben the kettle is partially emptied (simulating a loss-of-coolant acci­dent), the temperature of the surface of the heating element increases. The

sequence of events shown in Figure 4.3 iUustrates the case of rewetting or quenching, which occurs when the kettle is returned to its normal position and the remaining water quenches the hot heating elements with a very audible hiss. Furthermore, modern kettles are equipped with engineered safety systems; for instance, kettles often have a device that ejects the plug by means of a spring actuated by a bimetallic strip if the kettle boils completely dry during the boil-off period. In fact, even newer kettles have a device that detects the emis­sion of vapor and switches the kettle off in a more easily reversible way when the water is boiled; this is another form of an engineered safety system.

The big difference between the kettle and a reactor system is that in the case of the kettle, the safety systems are able to switch off the power input com­pletely and any overheating occurs principally as a result of stored energy within the heating element. In a reactor, however, fission product heating con­tinues at a low rate relative to full power after the reactor has been shut down.

It is also interesting to compare the kettle with the reactor in the context of failure of the engineered safety systems. Plug ejection might occur several times during the lifetime of a kettle; reinstatement of the operation of the kettle can be achieved immediately afterward. However, should the plug fail to be ejected (due to, say, corrosion of the spring), then heating of the element will continue and can lead to its melting. Failure of the engineered safety systems leads to the need for a major repair of the kettle, and this would certainly also be the case in the nuclear reactor.

The final “defense in depth” barrier to the release ofradioactive materials to the environment is the containment building or system itself. The TMI-2 accident demonstrated the importance of the reactor containment in converting a very severe accident in the reactor itself into one that had very little public health im­pact. There has been much study of the integrity of containments, including ex­perimental research under simulated accident conditions, particularly for P^^s.

The main forms of reactor containment that have been employed are as follows:

• Large prestressed or reinforced concrete shells that are designed to withstand internal pressures of 3—4 bars above atmospheric.

• Spherical steel vessels (as used in German reactors) that are similar in concept to the concrete vessels and withstand about the same pressure.

• Steel or concrete vessels in which ice is used to condense any steam released from the reactor system (so-called ice-condenser plants). Here the design pressure can be lower, but such concepts are less popular than they used to be since the ice-condenser is of little help in containing, say, a hydrogen explosion.

• Pressure-suppression containments in which the system is arranged so that any steam escaping from the reactor circuit will bypass through vent tubes into a pool of cold water where it is condensed.

Advanced containment systems often involve a double wall containment with a steel or prestressed concrete inner wall and a reinforced concrete outer wall. A subatmospheric pressure is maintained in the interwall space. Alterna­tively it is possible to combine a pressure-suppression system inside a conven­tional dry-well containment.

The likelihood of an accident’s leading to a breach in the containment is low. As exemplified by the case of TMI-2, in the majority of severe accidents the containment will fulfill its function. Challenges, however, can come from over­heating or overpressurization, hydrogen explosion, or missile impacts. These could result in structural failure or damage to the liner or a penetration resulting in a high rate of leakage. In addition, failure to isolate the containment during an accident could allow the transfer of radioactivity to other parts of the plant or to the environment. The timing of any failure is also relevant. The longer the containment remains intact, the greater the opportunity to take action to protect the public from any release.

In the previous section we saw that if molten fuel reaches the reactor vessel lower head, then this may fail. If this failure occurs rapidly with the primary sys­tem still at high pressure, the molten fuel will be ejected into the reactor cavity and from there it can move into the containment building. Rapid heating and pressurization of the containment will result from

• molten debris particles heating the containment atmosphere

• chemical reactions between the debris and water-steam leading to additional heating

• hydrogen, produced by chemical reactions, burning or detonating

Tests have been carried out at the Sandia National Laboratories using one — tenth-scale containments modeling the geometric details of actual nuclear power plants. Iron/aluminium/chromium thermite was used to simulate the molten core. This was ejected by high-pressure steam from the scale pressure vessel bottom head. Pressures and temperatures inside the containment were measured. Water that might flood the reactor cavity or be on the containment basemat was present in some experiments.

The results demonstrated that heating of the containment is less if the debris is contained below the main operating deck. Water in the reactor cavity reduces the pressurization due to the steam released by quenching the melt. Water on the basemat has little or no effect. Hydrogen produced by the cavity interaction and dispersal processes burned with a diffusion flame in the upper dome and contributed about half to the pressurization. Any preexisting hydrogen burned slowly and had little effect. These experiments and modeling calculations sug­gest that a wide range of variables influence containment heating

• Primary circuit pressure prior to vessel failure

• Mass of molten core in pressure vessel lower head

• Temperature and composition of the molten core

• Particle-size distribution and entrapment of debris

• Impingement onto surfaces and freezing

• Chemical reaction of debris with steam

• Quenching by reactor cavity water

• Formation, transport, and burning of hydrogen

From a variety of studies it can be judged that containment integrity will be at risk only if a large fraction of the core is ejected and a hydrogen detonation occurs. In these circumstances, the containment may be subjected to continu­ous static pressures of 10-15 bars as well as a transient pressure pulse. How­ever, a major mitigating feature would be depressurization of the primary circuit prior to molten core ejection so as to limit debris dispersion. Depressurization to 15-25 bars is effective in this way (see Section 6.2.4).

Even if the containment survives the early containment heating and pressur­ization, there are still challenges to its integrity that occur later. These include

• hydrogen combustion

• gradual overpressurization

• basemat melt-through

Hydrogen formation and combustion are described in Section 6.3.3. Slow overpressurization may occur if there is no heat removal or venting of the con­tainment. Moreover, interaction of the core debris with concrete produces copi­ous amounts of noncondensible gases such as carbon monoxide and carbon dioxide to add to the pressurization.

The interaction between the molten core and the concrete depends on a number of factors including the presence of water. If the cavity is initially dry and the core debris forms a deep bed, then extensive interaction may occur. Flooding the debris may effectively cool the melt. Some comments about the coolability of debris beds are made in Section 6.3.2.

There remains a finite possibility that the molten core materials may attack the containment basemat. This scenario is discussed in Section 6.3.4. Com­plete melt-through of the basemat would take several days, but the conse­quences of failure are relatively small compared with the failure of the containment above ground.

Finally, the integrity of the containment building may be compromised by the failure to isolate the building. As explained in Chapter 4, once the emer­gency core cooling system in the P’^TC is initiated, the containment is isolated. In practice, a number of essential services must still be provided to the reactor (emergency feedwater, etc.), and this provides a number of routes for release from the containment. For example, rupture of the decay heat removal system outside the containment, coupled with failure of an isolation valve, could give a route out from the containment that bypasses the building itself. Proper se­curing of personnel and equipment airlocks is also essential. Two specific acci­dent sequences are important in this context:

The so-called interfacing systems LOCA in which important check (or nonre­turn) valves fail and low-pressure piping connected to the reactor coolant sys­tem fails outside the containment. This provides a bypass to the enviroment.

Failure of steam generator tubes during the course of an accident again may permit bypass to the enviroment via the secondary side steam relief valves

3.1 INTRODUCTION

As we saw in Chapter 2, a variety of liquids and gases have been used to cool nuclear reactors. The present chapter introduces some of the desired general features of a reactor coolant and discusses the actual processes of heat transfer from the fuel elements to the primary coolants and from the primary coolants to the steam generation system. It also reviews the various types of coolant (gaseous, liquid, and boiling) and concludes by giving some examples of the engineering features of cooling circuits used in various types of reactor.

1 LOCA in a PWR

Example: A major loss-of-coolant accident occurs in a P^^. The reactor is tripped and goes subcritical after I s; dryout (see Section 3.3) occurs after 4 s when the heat trans­fer coefficient from the fuel pin drops from 50,000 W/m2K to a very low value; the blowdown is complete in 30 s. The fuel pins consist of 10-mm U0 fuel pellets in an 11-mm outside diameter Zircaloy can. The maximum rating R is 40 kW/m. The coolant is initially at 300°C; the temperature drops through the can and across the fuel-pellet — to-can gap are initially 50 K and 300 K, respectively. What is the can temperature at the end of the blowdown phase?

After 30 s the ECCS system operates and provides water at 30°C. The heat transfer coefficient during the refill stage is 50 W/m2 K. What is the maximum temperature recorded during the refill stage, and when is it recorded?

Solution. There are four sources of energy that could make the can temperature rise.

(1) Delay in shutting down the reactor. We will assume that from the start of the transient to the time when the reactor goes subcritical at I s, normal cooling is provided and this component makes no contribution to can temperature rise.

(2) Internal energy stored in thefuel.

(a)

Fuel pellet temperatures equalize at a time t, given by s d/к, where s is a shape factor (equal to 0.2 in this case), K is the thermal diffusivity (= k/pc), and a the fuel pellet radius. For U02, k = 2.5 W/m K, (! = 10,000 kg/m3, and cp = 350 J/kg K. Therefore, к =0.7 x 10~—Dm2/s, and for a 5-mm fuel pellet temperatures equalize in

(b) The thermal capacity of the fuel per unit length (C) is given by Cf = 1ta2Qcp

= x25x 10-6 X 10- x 350 = 275 J/mK

The thermal capacity of the can (C) is given by

Cc = (b2 — a2 )e, cc

where b is the outer can radius, Qc is the can density (6500 kg/m3), and cc is the can material specific heat (350 J/kg K). Thus

Cc = X (0.001 Є -0.00102) X 6500 X 350 = 350J/kg K

(c) The energy stored in the fuel pin above the can surface temperature is made up of two parts: that in the fuel pellet and that in the can.

(3) Stored energy is thefuel pellet. is the product of the thermal capacity of the fuel

per unit meter and the mean temperature of the fuel pellet above the can surface temperature (T) Since the time (30 s) is long compared with the time for equaliza­tion across the fuel pellet, the fully equalized pellet temperature can be used and is

(= 40,000 J = 637 K

81tk I 8x7tx2.5 J

To this must be added the temperature drop across the can and across the pellet/can gap, 50 K + 300 K = 350 K.

Therefore, stored energy in the pellet above Ts = C, (637 + 350) = 2.71 X 105 J.

(4) Stored energy in the can. This is the product of the thermal capacity of the can per unit meter and the mean temperature of the can above the can surface temperature 77

We take the mean temperature as half the temperature rise across the can (= 50/2) = 25 K. Therefore, the stored energy in the can above 7 = Cc x 25 = 937 J (which can be neglected in relation to the stored energy of the fuel pellets).

(5) Residual fission heating—as the neutron chain reaction dies away. This can be taken as

I.6x R = 1.6 x 40,000 = 64,000 J

(6) Fission product decay heating. Integrating the fission product decay heating for 29 s, we have

1.5 X R = 1. 5 X 40, 000 = 60, 000 J

(7) But some heat is removed by good cooling between I and 4 s. This is estimated at 120,000 J. If we now add the various energy contributions, we have

(1) + (3) + (5) + (6)-(7)

0 + 271 kJ + 64 kJ + 60 kJ -120 kJ = 275 kJ/m

The thermal capacity of the fuel (pellet and can) per meter length is

275 + 37.5 = 312.5 J/m K

Therefore, the temperature rise is 880 K.
The initial can temperature is

So at the end of the blowdown phase the final can temperature is 880 K + 323.1°C = 1203.1°С. However, the cbolant temperature does not remain at 300°C, and during the blowdown the saturation temperature falls to that for I atm (~100°C). So the actual can temperature will be significantly less than 1203.1°C (by as much as 200°C, i. e., around 1000°C) (see also Figure 4.1 for an approximate solution to this problem).

At the end of the blowdown phase, the decay heating is 0.04 R or 1600 W/m. The heat removed by the ECCS is

X 0Ш1 X 50 X (1000-30) = 1676 W/m

So the heat removal is about the same as or slightly higher than the heat released, and the can temperature will be at a maximum of 1000°C at about 30 s and will start to fall as the decay heat falls.

Problem: Repeat the calculations described in the example, but assume that dryout of the fuel occurs after 1 s (simultaneous with the reactor trip). [2]

delay in shutting down the reactor is

35,000 J/ms x 4=140,000 J/m

(2) Internal energy stored in the fuel.

(a) The metal fuel temperatures equalize at a time t given by sa2/R where Ris the thermal diffusivity (=kQc), s a shape factor (= 0.2), and a the free radius. For uranium metal k = 32 W/m K, (! = 19,000 kg/m3, and cp = 170 J/kg K. There­fore, k = 9.8 x 10-6m2/s, and for a= 15 mm, metal fuel temperatures equalize in

0.2 X 225 X 10-6

t =——————— = 4.5 s

9.8 X 10-6

(b) The thermal capacity of the fuel per meter length Cj. is given by ndQcp. = x 225 x 10-6 x 1.9 x 104 x 170 = 2283 J/mK.

For the clad we are not told the mass or the dimensions of the can. From reference sources we established that the mass of clad per unit length is 1 kg/m and that cc is 1200 J/kg K. Therefore, the thermal capacity of the can=

1 X 1200=1200 J/m K

(c) The energy stored in the fuel pin above the clad surface temperature is made of two parts: that in the metal fuel and that in the cladding (which we neglect).

Tbe stored energy in the metal fuel is the product of the thermal capacity of the fuel per unit meter and the mean temperature of the metal fuel above the clad sur­face temperature. Since the time (50 — 5) s is long compared with the time for equalization across the fuel, the fully equalized metal temperature can be used and is

R = ( 35, 000 81tK |^8x 1tx32

We can neglect any other temperature drop in the fuel element; therefore, the stored energy in the fuel above the external clad temperature is

43.5 x 2283 = 99.310 J/m

(3) Residualfission heating—as the neutron chain reaction dies away. This can be taken as

1.6 X R = 1.6 X 35, 000 = 56, 000 J/m

(4) Fission product decay heating. Integrating the fission product decay heating for (50 — 5) s, we have

2.1 X R = 2.1 X 35,000 = 73,500 J/m

If we now add the various energy contributions, we have

(1) + (2) + (3) + (4) =

140,000 + 93,310 + 56, 000 + 73,500 = 362,810 J/m

The thermal capacity of the fuel (metal and cladding) per unit meter is

2283 + 1200 = 3843 J/m K

Therefore, the temperature rise is 104.1 K.

This is the temperature rise assuming no cooling of the fuel. Let us now calculate the effect of radiation of heat to the moderator. The moderator is assumed to be at a tem­perature of 350°C; the fuel element is assumed to be a cylinder of 50 mm (fin outside diameter) in a fuel channel of 100 mm.

The average clad temperature during the transient is

104

450 + — = 502° C 2

The heat lost by radiation may be calculated from the formula

where £ and £2 are the emissivities of the fuel and graphite, respectively, and are assumed to be 0.6 in each case. cr = 5.67 x 10—8 W/m2 K4 (Stefan’s constant), and the surface areas of the fuel element (Aj) and the graphite channel (A) per meter are

A = 0.157 m2 A2 = 0.314m2

(This assumes a 5-cm-diameter can in a 10-cm-diameter channel.) Heat lost by radia­tion is thus

5.67 x 10~8 X 0.157 (7754 — 6234)
1.98

The decay heat rate at (50 — 5) s is 0.038 of full power = 0.038 x 35,000 = 1330 W/m. So the heat lost by radiation is less than the decay heat rate, and in the absence of any other cooling the fuel element will heat up at

1330-945

3483

until the heat removed by radiation matches the decay heat rate.

The total heat removed during 50 s by radiation is

945 x 50 = 47, 250 J/m

corresponding to a reduction of 13.4 K compared with the no-cooling temperature rise of 104.1 K.

Therefore, the maximum cladding temperature is

450 + 104.1 — 13.5 = 540.6°C

Problem: A new Magnox fuel design is being considered in which the fuel element di­ameter is to be increased from 5 cm to 6.5 cm and the uranium metal fuel pin diame­ter is increased to 4 em. Repeat the calculations given in the example, and evaluate the effect of this design change on the temperatures reached in the specified accident.

3 Pumps on orpumps off?

Problem: There has been considerable controversy about whether the opera­tors should leave the main circulating pumps operating or stop them during a small break loss-of-coolant accident for a PWR. With the aid of the accompanying diagram, discuss the events that occur when the pumps are stopped (path I) or left operating (path 2).

Bffi

Bankoff, S. F., and N. H. Afgan (1982). Heat Transfer in Nuclear Reactor Safety. Proceed­ings of a Seminar on Nuclear Reactor Safety Heat Transfer, Dubrovnik, Yugoslavia, September 1-5, 1980. Hemisphere, Washington, D. C., 964 pp.

Barsell, A. W. (1981). A Study of the Risk Due to Accidents in Nuclear Power Plants. Ger­man Risk Study—Main Report, various pages.

Bergles, A. E., J. G. Collier., J. M. Delhaye, G. F. Hewitt, and F. Mayinger, (1981). Two — Phase Flow and Heat Transfer in the Power and Process Industries. Hemisphere, Washington, D. C., 719 pp.

Bowerman, J. M., and G. C. Dale, eds. (1982). The Safety of the AGR. CEGB and SSEB,

111 pp.

Fast Reactor Safety Technology. Proceedings of a Meeting, Seattle, August 19-23, 1979. American Nuclear Society, LaGrange Park, III., 5 vols.

Flowers, B. 0976). Nuclear Power and the Environment. Royal Conunission on Envi­ronmental Pollution, Sixth Report. HMSO, London, 237 pp.

Jones, O. C. (1981). Nuclear Reactor Safety Heat Transfer. Papers presented at the sum­mer school on nuclear reactor safety heat transfer, Dubrovnik, Yugoslavia, August 24-29, 1980. Hemisphere, Washington, D. C., 959 pp.

Judd, A. M. (1981). Fast Breeder Reactors: An Engineering Introduction. Pergamon, Elmsford, N. Y., 161 pp.

Menlo. M. (1983). Thermal-Hydraulics of Nuclear Reactors. Papers presented at the Second International Topical Meeting on Nuclear Reactor Thermal-Hydraulics, Santa Barbara, Calif., January 11-14, 1983, 1529 pp.

5

A basic decision in the design of any nuclear reactor is whether to remove and insert fuel while the reactor is operating (on-load refueling) or when the reac­tor is shut down (off-load refueling).

The choice between on-load and off-load refueling is dictated primarily by economic factors. On-load refueling is much more complex, and the cost of the equipment is high. On the other hand, total shutdown of the reactor system for a significant period to allow off-load refueling leads to a loss of electrical power output, and this in itself is very expensive. In general, reactors that have a large throughput of fuel, such as natural uranium reactors (Magnox and CANDU) op­erate with on-load refueling, whereas those with a lower throughput of en­riched fuel (e. g., P^^ and B^WR tend to use off-load refueling. The advanced gas-cooled reactor (AGR) is intermediate between these two cases; it has the ca­pability of on-load refueling, though this is only just being introduced into rou­tine operations Qenkins et al., 1995). For fast reactors, off-load refueling is necessary because of the veiy large changes in reactivity that would occur with any fuel movements during operation.

Molten (liquid) metals offer the possibility of much higher operating tempera­tures than can be obtained with water and have excellent heat transfer proper­ties. Only one metal, mercury, is liquid at room temperature, and in any case it has far too high a neutron absorption cross section for use in thermal reactors. It also has relatively high vapor pressures, and the vapor is toxic. However, it is interesting to note that mercury has been used in power generation cycles, and

several power stations in the United States were operated during the 1950s using mercury as a working fluid.

The only metals that combine the advantages of a relatively low melting point with low vapor pressure and low neutron absorption are sodium and potassium. Sodium and potassium are compatible with stainless steel at tem­peratures up to at least 800°C provided the liquid metal is kept free of oxygen. Sodium is the more abundant and cheaper to produce, and, furthermore, potas­sium can form compounds with oxygen that are explosive. In recent years, sodium has been the preferred liquid metal coolant, but in earlier reactors sodium-potassium mixtures (NaK) were frequently employed. The mixtures could be made liquid at room temperature and the pipework did not require heating in order to keep the coolant molten during periods of shutdown.

Sodium has been the primary choice as the coolant for fast breeder reactors. Referring to Table 3.1, we see that it has a higher thermal conductivity, though a lower specific heat, than water. For a given heat removal, the flow rate re­quired is five times higher for sodium than for water. However, the overriding advantage of sodium is its high boiling point, which allows sodium-cooled re­actors to operate near atmospheric pressure while maintaining a wide differ­ence between the operating temperature and the boiling point. The operating temperatures are sufficiently high for the sodium stream to evaporate water at high pressure to produce a high thermodynamic efficiency. However, there are a number of problems in using sodium as a coolant.

1. Because sodium is very reactive toward oxygen and water, contact must be avoided. An inactive cover gas such as argon is needed above all the sodium levels in the reactor system. This gas must be kept free of oxygen contami­nation. In the steam-generating system, the sodium heats tubes that contain the high-pressure evaporating water. These evaporators are one of the main sources of trouble in sodium-cooled reactors. Very small leaks can be toler­ated, but they cause contamination problems due to the formation of sodium hydroxide, which is corrosive. Large leaks can cause explosive interactions between the sodium and water, giving rise to hydrogen generation, and the hydrogen itself is explosive. Contamination of the reactor vessel can be min­imized by using an intermediate heat exchanger (Chapter 2); alternatively, some designs use double-walled tubes to enhance the separation between the two fluids in the steam generator. In the design of sodium-cooled reac­tors, provision is made to accommodate such sodium-water reactions safely. For instance, the steam generator can be isolated and its sodium content ejected through a special system that allows the hydrogen generated to be discharged through an outlet stack.

2. The primary coolant circuit becomes very radioactive through the formation of sodium-24, which has a 15-h half-life; the existence of this isotope in the primary coolant is another reason for having an intermediate exchanger be­tween the coolant and the steam generator. In practice, in view of the fairly short half-life, this isotope creates no particular difficulty associated with maintaining the reactor circuit, though sufficient time must be allowed for it to decay to a low level before the circuit is worked on.

To someone who has witnessed school chemistry laboratory experiments in which small pieces of sodium are dropped into water and has observed the dra­matic and explosive effects, the prospect of using this metal as a reactor coolant must seem rather horrifying. However, when contained within a reactor circuit, and with proper precautions taken to deal with any potential effects of its con­tact with the steam generator water, sodium is a surprisingly benign and ex­tremely efficient coolant.

The St. Laurent plant of Electricite de France is a 500-MW(t) Magnox reactor that was first brought into operation in January 1969. The reactor is fueled on load and the machine that carries this out is called a charging machine. We shall consider the use of these machines in Chapter 7 in discussing the handling of fuel elements subsequent to their period in the reactor core. The charging machine is a very large device that is computer-controlled to move about the top of the reactor and position itself properly over each access port to unload and load the fuel. Figure 5.23 illustrates the layout of the St. Laurent reactor.

During the midnight shift on October 17, 1969, with the reactor near full power, a normal loading and unloading operation was in progress. Graphite plugs that had been placed temporarily in one of the fuel channels in the core were being replaced by fuel. The charging machine had unloaded the graphite plugs from the core into its empty storage chambers and had loaded fuel into the core from two of its full chambers, but then it stopped. Three full chambers of fuel elements are required to load one fuel channel in the core completely, and each chamber contains four elements. When the charging machine stopped, the operator overrode the automatic system, and after a series of man­ual operations, he accidentally charged a flow restriction device into the chan­nel instead of a fuel element. These flow restrictors were used to control the gas flow to individual channels. The loading of a flow restrictor into this particular channel so reduced the flow that the fuel elements were inadequately cooled.

Some of the fuel elements in the affected channel heated up beyond their melting point, and the molten fuel flowed out of the channel onto the diagrid below (Figure 5.23). This released radioactive fission products, set off alarms, and activated a reactor trip. The molten fuel (about 50 kg) was still still con­tained within the massive concrete structure; hence, little, if any, radioactivity was released outside the structure and there were no injuries. However, a year was needed to complete the cleanup operations and restart the reactor. Modifi-

cations to the machine were made, and it is no longer so easy to override the automatic system and bring the machine into manual control.

This accident and a similar one at the British Chapelcross reactor in Scotland again demonstrate the importance of carefully matching the heat removal and heat input characteristics for the system as a whole and for each component part. Again, the scope for operator error is noted, and this has necessitated steps to reduce the scope.