Liquid metals are used as coolants because they are very good media for heat transfer. The high thermal conductivity is due to the motion of the electrons in the conduction energy band, which are much more mobile than the positive ions. Being so light the electrons transport energy but little momentum so the thermal conductivity is high but the viscosity is not. As a result the Prandtl number Pr = лc/K (where ц is the viscosity, c the specific heat capacity and K the thermal con­ductivity), which for most fluids is of the order of one because energy and momentum are both transported by the diffusion of molecules, is very small for liquid metals. For sodium at 600 °C, Pr = 4.2 x 10-3 and K = 62.3 Wm-1K-1, whereas for water at 100 °C, Pr = 1.72 and K = 0.68 Wm-1K-1.

This does not mean, however, that the heat is transferred 100 times more readily to sodium than to water because in a flowing liquid

the bulk motion as well as the diffusion of molecules or electrons is important. The higher the Reynolds number the smaller the advantage of a liquid metal over a nonmetallic fluid.

The heat transfer coefficient h between a heated surface and a fluid is defined by h = Q/AT, where Q is the local heat flux (Wm-2) and AT is the difference between the local temperature of the heated surface and the mixed mean fluid temperature. For fluid flowing in a channel h can be nondimensionalised conveniently in the Nusselt number Nu = hDH/K, where DH, is the hydraulic diameter of the channel. Dimensional analysis then shows that for a liquid metal, in which turbulence does not make a significant contribution to heat transfer so that h is independent of л, Nu = Nu (Pe), where Pe is the Peclet number pcvDH/K, p is the fluid density and v is the mean fluid velocity.

Figure 3.4 shows the variation of Nu with Pe for sodium flowing in a cylindrical tube. As Pe ^ 0, Nu tends to a constant value. If the liquid velocity were uniform across the tube and heat transfer were purely by conduction Nu would be 8. The effect of the variation of velocity across the tube is to reduce Nu, whereas turbulence increases Nu at high Pe. A good fit to the experimental data is

Nu = 5 + 0.025Pe08.

For flow at high Reynolds numbers parallel to a triangular array of cylindrical rods various correlations such as

Nu = 4.0 + °.°°63ai■8Pe0M + 0.16a50, (3.8)

where a is the pitch-to-diameter ratio P/D, have been proposed. Nu increases with a as shown in Figure 3.5, but h does not increase in the same way because DH also increases with a.

The experimental heat transfer data for liquid metals, especially for arrays of tubes, are in most cases very scattered, and the experimental values of Nu usually lie below, and sometimes a factor of two below, the theoretical predictions. This is due in part to the difficulty of doing the experiments. If for example Nu = 8 for sodium flowing in a tube 1° mm in diameter, then h = 5 x 104 Wm-2 K-1. Even if the heat flux is as high as 10° kWm-2 the temperature difference is only 2 K and cannot be measured accurately. In addition the temperature differ­ence can be affected considerably by even very slight contamination of the heater surface. The presence of oxide films may explain why experimental values of Nu for sodium are frequently lower than those for mercury, for example.

What is true for the experiment is also true for the reactor, and in many cases uncertainty in Nu is not important because the temperature difference is so small. If the linear rating q of a fuel element at the
centre of a sodium-cooled reactor core is 50 kW m-1 and the outer radius of the cladding is 3 mm the surface heat flux Q is 5 MWm-2. If the mean coolant velocity is 10 ms-1 and a = 1.25, then Pe = 353 and equation 3.8 gives Nu = 6.8, h = 1.0 x 105 Wm-2K-1 and AT = 14 K. This is the peak value of the temperature difference between the cladding and the coolant at the most highly rated point in the core and it is clear that even a 20% error in h is not very important.

The same is not true for gas coolant. In a non-ionised fluid heat is transferred by the turbulent motion of the fluid, viscosity is import­ant, and heat transfer depends strongly on the Reynolds number Re = pvDh/p.. The Nusselt number is usually given by an empirical relationship, a simple example of which is

Nu = 0.023 Re08 Pr °’4. (3.9)

Taking again the example of CO2 at 20 MPa, if it were flowing at 60ms-1 over fuel elements of diameter 6 mm with P/D = 1.3, Re would be about 106 and Nu about 1.3 x 103, giving a heat transfer coefficient h of 1.7 x 104 Wm-2K-1. This, with Q = 5 MWm-2, would give a temperature difference between the cladding and the coolant AT of about 300 K, compared with 14 K for sodium under comparable conditions.

3.2.2 Coolant and Cladding Temperatures

The mean coolant temperature Tc(z) at a height z above the bottom of the core, neglecting heat generated in the axial breeder, is

Tc (z) = Tci + q(z)dx/Avp c, (3.10)

0

where Tci is the coolant inlet temperature. The mean cladding surface temperature Ts(z) is

Ts (z) = Tc (z) + q(z)/2n Rsh,

where Rs is the outer radius of the cladding. Typical variations of Ts and Tc with z for sodium and gas coolants are shown in Figure 3.6. For liquid metal coolants Ts follows Tc closely and the maximum value of Ts occurs at the top of the core, but for gas for which h is much smaller Ts reaches its maximum near the centre of the core.

The maximum cladding temperature is a very important limit on the design of the reactor. It is set principally by the creep strength that the cladding has to have, and in turn it sets the coolant outlet temperature and hence influences the thermodynamic efficiency of the generating plant. The maximum cladding temperature is, however, not the same as the maximum value of Ts because for a number of reasons there are, or may be, local variations that give locally high cladding temperatures or “hot spots”. There are many possible causes of the irregularities in the heat transfer that give rise to hot spots, of which the most important are as follows.

The variation of coolant temperature across the coolant channel between three adjacent fuel elements is significant and is reflected as a variation of the cladding temperature round a fuel element. Ts is higher at a point near a neighbouring element and lower opposite a gap between elements, as shown in Figure 3.7.

The variation is larger for close-packed arrays and for fluids with low Prandtl numbers. This is because heat transfer within the coolant

(i. e. from the intensely heated gap between two fuel elements to the centre of the subchannel between three fuel elements where most of the coolant flows) is strongly affected by the coolant velocity and is therefore relatively insensitive to Pr. Heat transfer across the boundary layer depends mainly on conduction and therefore varies strongly with Pr. If Pr is high (i. e. close to 1), boundary-layer heat transfer is poor and the cladding surface is in effect partially insulated from the temperature variation in the coolant. The temperature variation around a fuel element in a gas-cooled reactor is thus less severe than in a liquid-metal-cooled reactor with the same linear heat rating.

The coolant channels near the wrapper are often larger than those in the rest of the subassembly so that the edge fuel elements are overcooled. Coolant and cladding temperatures in the edge channels are lower than average, implying that the cladding temperatures in the centre of the subassembly are higher than average, giving another form of hot spot.

Except at the centre of the core the power density varies across a subassembly and may be some 10% higher on one side than the other.

As a result coolant and cladding temperatures on the hot side are higher than the average. The coolant temperature distribution across the outlet of a typical subassembly is shown in Figure 3.8 which illus­trates the effects of “power tilt”, the overcooling of edge fuel elements, and the variation of temperatures across each coolant channel.

The fuel elements are held in position by grids or wire wraps as explained in section 3.4.1. Either form of support modifies the coolant flow in places and although the effect is usually to increase the turbu­lence locally and hence increase h and decrease Ts there is a possibility of a region of poor cooling. Other hot spots occur at random because of variations of the dimensions and composition of various components within the manufacturing tolerances.

Cumulatively the allowances that have to be made for all these effects are very significant and may amount to as much as half the mean coolant temperature rise through the core, something in the range of 70-100 K. Thus if the cladding temperature Ts has to be limited to 700 °C to make sure that it retains its integrity, it is likely to be necessary to limit the coolant outlet temperature to 600 °C.

Heat transfer and fluid flow within the core are discussed at length by Tang, Coffield, and Markley (1978).

The instrumentation needed to detect an incipient accident can be divided into two classes: one for accidents that affect the whole of the core (such as reactivity changes or primary coolant pump failure), and one for accidents that affect initially only part of the core (such as a coolant flow failure in one subassembly). The latter is discussed in section 5.2.3.

It is relatively easy to detect an accident affecting the whole core by means of the instruments used to control the reactor in normal operation. The condition to be guarded against is overheating, so it is necessary to monitor the reactor power and the coolant temperature and flow-rate.

The reactor power is determined by measuring the neutron flux at convenient points. The flux-measuring instruments are normally fission chambers or boron trifluoride chambers. The main difficulty is that neutron flux has to be measured over the range from full power (maybe 3000 MW) to the shutdown level of 100 mW or less — a range of more than 1010. This cannot be done by any single instrument. If the flux is high it is possible to measure the overall ionisation current, but when it is low it is necessary to count individual pulses and determine the average count rate.

Even with these two modes of operation it may not be possible to cover the entire range with a single instrument. It is frequently necessary to have two or more sets of fission chambers in positions of different sensitivity. At low power instruments close to the core are used, whereas at high power other instruments in the neutron shield or outside the reactor vessel are brought into operation.

The high gamma flux from the radioactive primary sodium has to be allowed for. At the highest powers it may be possible to ignore it in comparison with the neutron flux because the energy of a fission event is so much greater than that of a gamma from the sodium. However, at lower powers, when the sodium activity (with a half-life of 15 hours) may correspond to earlier high-power operation, it is necessary to compensate for the ionisation caused by gammas or to discriminate against them if the pulse-counting mode is in use.

Several measuring stations round the core are necessary, partly for reasons of reliability and partly to allow for changes in the flux shape due to the movement of control rods or irregularities in the pattern of loading new fuel into the core. As burnup proceeds the sensitivity of the instruments changes as the flux at the periphery of the core and in the breeder increases relative to that at the core centre. For this reason a high power trip based on neutron flux cannot be very precise, but it is very reliable.

The signal from the neutron flux instrumentation is also used to determine the inverse period dC/Cdt, where C is the indicated flux level. The inverse period is closely (but indirectly) related to the net reactivity, and the reactor is tripped when it becomes too large. This trip system is of little importance when the reactor is operating at power because feedback keeps the net reactivity close to zero, but when the power is very low and very little heat is being generated there is no feedback. Under these conditions an inverse-period trip is a protection against accidental increases in reactivity.

Coolant temperature can be measured by thermocouples at the core outlet. The main difficulty is to ensure that a thermocouple meas­ures the mean temperature correctly, for the coolant temperature is not uniform. Coolant from the edge of a subassembly is cooler than the rest and unless the flow is mixed by some device to enhance the turbu­lence a thermocouple may be exposed to a stream of unrepresentative coolant; moreover as the coolant flow-rate changes the flow pattern at the outlet may change possibly bringing coolant from a different unrepresentative part of the subassembly to the thermocouple.

Other difficulties are caused by changes in the power generated in a subassembly by the movement of nearby control rods, and by burnup of the fuel. It is thus usually necessary to measure the temperature at a number of positions at the top of the core and use an average for the control and trip systems. The alternative of measuring the temperature farther from the core where the coolant has become more thoroughly mixed is less satisfactory because the delay allows more of the structure to experience a temperature change before corrective action is taken.

Coolant flow-rate can be monitored by flowmeters at the core outlet or by observing the rotation of the circulating pumps. The flow-rate in a pipe can be measured conveniently by an electromag­netic flowmeter, which makes use of the electromotive force induced when a conductor (the sodium) moves through a magnetic field.

It is normal to trip the reactor if the pumps stop or if the flow out of the core falls below a set value. If the reactor is to be operated efficiently at less than its full power, however, either the trip level on coolant flow has to be set low (at say 10% of the full flow-rate) or the trip level has to be altered according to the power required. This disadvantage can be avoided if the ratio of measured power to measured flow-rate is used as a trip signal.

Transport theory and diffusion theory are based on equations that describe the average behaviour of large numbers of neutrons as they interact with large numbers of nuclei. As the preceding paragraphs show the equations are complex and their solution by numerical means even more so. This is in contrast to the actual behaviour of individual neutrons, which is quite simple: they travel in straight lines between nuclei and they interact with the nuclei in a limited number of ways the probabilities of which are known. The transport equation has the effect of turning a large number of simple problems into a single complex problem. The alternative, which is to solve the simple problems, is the “Monte Carlo” method (Brown, 2012).

The basis of the method is to track neutrons one by one. The outcome of each event in the history of each neutron is chosen at random in accordance with the known probabilities. This is done for large numbers of different neutron histories, so large a number that when they are all put together they make up an estimate of the actual neutron distribution.

The method depends on a random number generator that produces a sequence of numbers Rn distributed uniformly at random in the range (0,1). For a “source-type” calculation (for example a subcritical reactor driven by a neutron source) the procedure is straightforward. A neutron is assumed to emerge from the source travelling in a direction (в, f) chosen at random (which is ensured by setting f = 4nR1 and в = cos-1 (1 — 2R2)) and with an energy E given by R3 = jf s(E’)dE’, s being the spectrum of source neutrons normalised to 1. The reactor is assumed to be made up of discrete regions (fuel, coolant, structure, etc.) each of which has a uniform composition and uniform nuclear properties. The neutron is assumed to travel in its initial direction for a number m = — ln R4 of mean free paths to its first interaction with a nucleus. In its course it may well cross one or more boundaries from region to region. The actual distance travelled is given by m = x1E(1 + x2£(2 + … Хі^і where x1 is the distance travelled in the region in which it was born, x2 the distance through the next region, and so on, and xi is the distance travelled in the region i in which it finally interacts with a nucleus.

What happens when it interacts is then decided by the use of further random numbers to select the type of nuclide it interacts with and the interaction (elastic scattering, inelastic scattering, capture or fission) that takes place, the choices being weighted by the various macroscopic cross-sections. In the case of elastic or inelastic scattering the neutron continues on its way in a different direction and with a different energy, again chosen at random taking account of any possible anisotropy of elastic scattering and the probabilities of exciting different nuclear energy levels in the case of inelastic scattering. In the case of capture the neutron disappears. In the case of fission it is replaced by one or more new neutrons, their number and energies chosen at random in accordance with data on v and x for the fissile nuclide concerned. These new neutrons are then tracked as before and the tracking continues until all daughter neutrons are captured or have travelled out of the reactor.

The same procedure is followed for many neutrons and accounts are kept of the numbers and locations of the different interactions. For example reaction rates can be estimated by keeping account of the number of reactions taking place in an element of volume, and the power density can be deduced from the rate at which fissions take place. Neutron flux can be estimated by keeping account of the total path-length traversed by neutrons in the volume element, and neutron current by noting the number of neutrons that pass through an element of area. An estimate of one of these quantities is given by limN^TO (Nq/N), where Nq is the number of records of event q and N is the total number of neutron histories that have been calculated. Additional neutrons are tracked until a statistical test shows that the variance of the estimates of q is small enough to give confidence that

the limit has been approached sufficiently closely. The most intricate part of the calculation is the determination of which regions a neutron passes through and where it crosses the inter-region boundaries.

The procedure for a critical reactor is a little more complicated than that for one driven by a neutron source because as well as the fluxes and reaction rates the eigenvalue ke has to be estimated. It can be done as follows. A number N1 of neutrons, sometimes called a “batch”, are tracked up to the point at which they are captured, leak out of the reactor, or cause fissions. If a total of N2 new neutrons are born in these fissions, N2/N1 = ke1 is a first estimate of ke. All values of v are then divided by this estimate and the N2 new neutrons from the fissions caused by the first batch, which become the second batch, are tracked until they in turn cause fissions that give rise to N3 further neutrons. (N3/N2)ke1 = ke2 is then a new estimate of ke, the v are modified again, a third batch of neutrons are tracked, and so on. In due course the estimates cluster around a limit, which is the required value of ke, and the process continues until the variance is small enough. In making the final estimate of ke it is normal to reject the values produced by the initial batches of neutrons as they converge towards the final value. The process is shown diagrammatically in Figure 1.4. The neutron fluxes generated in the course of this process are of course meaningless because they relate to a reactor with artificial values of v. It is necessary to iterate by adjusting its composition or dimensions until ke = 1.

To obtain reliable estimates of ke or the critical composition it is necessary to track large numbers of neutrons. For a large power reactor a batch would consist of 104 or 105 neutrons and several hun­dred batches would be calculated with possibly the first 50 or so being rejected as the estimates converged. In all tens of millions of neutron histories are likely to be followed to give an estimate of ke with a stand­ard deviation of 0.0001 or better. No doubt the numbers of neutron histories will increase and the ke estimates will improve as computing facilities become more powerful. (The numbers can be put in perspect­ive by remembering that a 2500 MW (heat) reactor is producing some 2 x 1020 fission neutrons per second.)

The variance of the estimate of a quantity such as the flux at a certain point in the reactor depends on the number of neutron histor­ies that contribute to it. This implies that more histories have to be calculated for a reliable estimate of the flux in a low-flux region than for the flux at the centre of the core. Since the variance is roughly inversely proportional to the square root of the number of histories this implies that if it is necessary to calculate N histories to attain a satisfactory estimate of the flux at the core centre, 100 N histories will be required for an equally reliable estimate of the flux in a region, such as a breeder or a reflector, where it is a tenth of that at the centre. This consideration would, in principle, make it impossible to use a Monte Carlo method to calculate the performance of a reactor shield, which may be required to attenuate the flux by a factor of 1012 or more, but the difficulty can be avoided by “splitting” neutrons.

For example if a neutron crosses the outer boundary of the reactor core and enters the shield it can be replaced by two neutrons each of which has half the “weight” of the original neutron and is then allowed to have an independent history. The process can be repeated at other boundaries in the outer parts of the shield so that there are statistically

significant numbers of neutrons throughout the shield but the atten­uation is accounted for by their diminished weights. The process is shown diagrammatically in Figure 1.5.

2.4.1 Recrystallisation

During irradiation the crystal structure of the fuel is changed almost completely. Figure 2.7 shows a polished and etched cross-section of typical pellet fuel after irradiation and Figure 2.8 shows a similar axial cross-section of vipac fuel. Throughout most of the cross-section the

original particulate structure of the vipac fuel has completely disap­peared.

The most striking change is that a hole appears in the centre. It is surrounded by a region of high density in which the grains are

Un restructured Equiaxial Columnar

grains grains grains

long and narrow and lie along radii of the cylinder. This is known as the “columnar grain” region. Outside it is a region where the grains are larger than in the original material but are oriented at random. This is called the “equiaxial grain” region. Finally, in the outermost part of the fuel it retains its original structure, and this is called the “unrestructured” region. These three distinct regions are shown in Figure 2.9.

Observations made after various periods of irradiation show that this basic structure is set up very quickly — within an hour of achiev­ing the full power density. Thereafter the pattern of equiaxial and columnar grains spreads outwards from the centre but at a rate that decreases very rapidly. The higher the linear rating the greater the radii of the restructured regions, and for most of the life of the fuel it is a fair approximation to regard the outer edge of the columnar grain region as being close to the 1800 °C isotherm, and that of the equiaxial region close to the 1600 °C isotherm.

As far as is known the restructuring takes place as follows. At intermediate temperatures the sintering that started during manufac­ture continues. The pores between the grains tend to coalesce and the individual grains grow to form the equiaxial grain region.

At higher temperatures the pores become mobile and move up the temperature gradient. There are two mechanisms for this process: surface diffusion whereby atoms of fuel move round the pore from the hot to the cold side, and volume diffusion whereby atoms evap­orate from the hot side and condense on the cold. The result is that the pore moves towards the region of higher temperature and at the same time the fuel is recrystallised as the pore moves through it. The atoms deposited on the cold side of the pore form a single new crystal, relatively free from imperfections and occupying the volume swept out by the pore as it moves.

The pores move to the centre — the hottest part — of the fuel and there form the central void, while the density of the columnar grain region increases to something close to the theoretical value, which is that of a single crystal. The speed with which the pores move depends strongly on temperature so the outer boundary of the columnar region moves quickly to start with and then very slowly. Initially it is the pores incorporated in the material when it is manufactured that move in this way but later it is the bubbles formed by the accumulation of fission — product gas on the grain boundaries (section 2.3.1). As a result the columnar grain region is continually being recrystallised.

1.1 INTRODUCTION

1.1.1 Choice of Coolant

This chapter describes the engineering of the remainder of the plant in a fast reactor electricity-generating station, apart from the reactor core that is the subject of Chapter 3. The nature of the plant depends primarily on the coolant, which is the heat-transfer medium. The main considerations determining the choice of the coolant were explained in sections 3.2.3 and 3.2.4. The most important is that the high power density of a fast reactor core demands a high-density coolant and high coolant velocities. The relative advantages and disadvantages of the various possible coolants can be summarised in terms of the choices available to a reactor designer, as follows.

Liquid or Gas. Helium has the advantage that it is chemically inert and is therefore appropriate for use in a high-temperature reactor. CO2 has the advantage that there is extensive experience of its use in thermal reactors. Neither presents significant problems of corrosion or erosion. However any gas coolant has to be pressurised to make it dense enough to transport heat out of the core without unreas­onably high velocities. The major consequent disadvantage is that it is then very hard to guarantee that decay heat could be removed safely in the event of an accidental loss of pressure. It would be

necessary either to accept relatively low power density in the core (compared with what is possible if a liquid coolant is used) or to provide elaborate emergency cooling equipment for use in the event of a major breach of the primary coolant system. For this reason no gas-cooled power-producing fast reactor has, at the time of writing, been built and thus there is no operating experience, but that does not mean that gas coolant may not at some time in the future become attractive.

Water or Liquid Metal. Water is almost inevitably ruled out as a coolant for a fast reactor because the moderating effect of the hydro­gen would degrade the neutron energy spectrum to the extent that its advantages — either as a breeder of fissile material or as a consumer of radioactive waste — would be lost or at least drastically reduced. A fast reactor cooled with supercritical water (“supercritical” in the thermo­dynamic sense, at a pressure above the critical pressure of 22.12 MPa) has been suggested but never taken beyond the stage of an outline design.

All liquid metals have the major advantage that they do not have to be pressurised so the reactor structure can be relatively light. In the case of an accident the decay heat can be removed by ensuring that the fuel stays immersed in the coolant, and it may be possible to arrange the primary coolant circuit so that even if the pumps fail natural convection cooling is adequate.

An important disadvantage of liquid metals is that they are opaque, which makes inspection of the core and coolant circuit structures and components difficult.

Light or Heavy Liquid Metal. The alkali metals lithium, sodium and potassium all suffer from the major disadvantage that they react chemically with air and water. They have the advantage that they are light, and they are not corrosive. They have low melting temperatures so that it is relatively easy to avoid freezing, but also low boiling temperatures so that there is a possibility that the cooling may be impaired under extreme accident conditions. They are all moderators.

Sodium and potassium are cheap. Lithium is too expensive and too much of a moderator to be considered.

Heavy liquid metals such as lead or bismuth have the major dis­advantages that they corrode steel and that at more than moderate velocities they cause erosion and cavitation damage, particularly in pump rotors. In addition they are heavy and expensive and they have high melting temperatures. Their advantages are that they do not react chemically with water, they have high boiling temperatures, and they are poor moderators (so they do not degrade the neutron energy) while having high scattering cross-sections (so they reduce neutron leakage from the core).

Mercury was the coolant for very early experimental fast react­ors in the United States and the Former Soviet Union but has never been used since. It would not be contemplated now because it is too expensive and too toxic.

Sodium or Potassium. Although both are chemically reactive potassium is rather more hazardous than sodium. Compared with potassium, sodium has the disadvantage that it becomes radioactive by the 23Na(n, y)24Na reaction. The resulting 24Na decays with a 15- hour half-life. While the reactor is operating the specific activity of the sodium primary coolant may exceed 30 GBq/kg.

It has never proved possible to eliminate the possibility of a leak in a sodium-heated steam generator, and in fact such leaks have occurred quite frequently. A large steam-generator leak generates large volumes of steam and hydrogen accompanied by tens or hun­dreds of kilograms of NaOH, and the only way to protect the reactor is to vent these reaction products to the atmosphere. This cannot be contemplated if they are radioactive. Therefore the steam gener­ators cannot be heated directly by the radioactive primary sodium, and intermediate nonradioactive secondary sodium circuits have to be interposed.

Sodium, being lighter, has a greater moderating effect than potassium. This is a disadvantage not only in that it degrades the neutron energies but also because removal of sodium from the centre of the core causes a positive reactivity change. This gives an undesir­able positive contribution to the temperature coefficient of reactivity and, in a severe accident that causes the sodium to boil, a substantial reactivity increase.

However sodium has the overwhelming advantage that it is cheap and readily available, and for this reason, in spite of its disadvantages, it has been used almost universally as the coolant for fast power reactors.

Pure potassium has never been used as a reactor coolant but in a few cases sodium-potassium alloy, usually referred to as “NaK”, has proved attractive. Pure sodium melts at 97.8 °C so care has to be taken to avoid freezing, but the admixture of potassium reduces the melting point. Eutectic NaK (77%K, 23%Na) freezes at -12.6 °C.

Lead or Lead-Bismuth Alloy. The melting point of pure lead is 327 oC so extensive reliable trace heating of the primary coolant circuit has to be employed to avoid freezing. However, as in the case of NaK, the addition of bismuth can reduce the requirement substantially. Eutectic Pb-Bi (55%Bi, 45%Pb) freezes at 123.5 °C.

The main disadvantage of lead-bismuth alloy is the reaction 209Bi(n, y)210Po. The resulting 210Po is а-active with a half-life of 3.5 x 106 years and constitutes a major hazard in reactor maintenance and refuelling. In addition bismuth is expensive. In spite of these disad­vantages lead-bismuth was chosen as the coolant for the fast reactor power plants of the innovative — but secret — USSR “Alpha”-class submarines, and their deployment has provided many reactor-years of operating experience. When in the 1990s the Russian authorities began to release this information lead-bismuth came to be regarded as a serious alternative to sodium as a coolant for fast reactors.

Best estimate transition-phase calculations, supported by the results of small-scale experiments, indicate that, after a core-disruptive acci­dent, the fuel would be in the form of a mass of debris dispersed in the primary coolant. The internal structure of the reactor vessel (in the case of a pool reactor, the inner vessel, the primary pumps, the intermediate heat exchangers and the decay-heat rejection heat exchangers) would be damaged and probably inoperable but the ves­sel itself would be intact and would retain the primary coolant. The coolant would continue to serve to remove the decay heat from the fuel and would circulate by natural convection. The coolant itself would lose heat to the emergency cooling equipment, probably the RVACS system (see section 5.2.4). There would be plenty of time to ensure the correct operation of the RVACS (see Figure 5.1).

If the coolant is sodium the fuel debris would fall towards the bottom of the reactor vessel. To eliminate the possibility of it accumu­lating and forming a critical mass it may be necessary to put in place a structure in the form of a tray shaped to catch the fragments in a sub­critical layer. A tray of this type is usually known as a “core-catcher”. It might be made of neutron-absorbing material to reduce the chance of criticality.

Provided it was porous the mass of debris would be cooled by sodium circulating within it. If the fuel were to coagulate in some way so that the sodium could not circulate it might become hot enough to damage the structure on which it rested, so the core-catcher has to be arranged in such a way that the coolant is able to circulate underneath it to keep it cool. The core-catcher would also act to protect the reactor vessel itself from the risk of being damaged and even melted by the hot fuel. In this way the core debris would be retained safely and

ess steel

[1] in the proportions 56:20:15:9. If plutonium of this isotopic com­position is substituted for pure 239Pu in the reference reactor there is very little change in the spectrum but there is a large effect on the enrichment, which goes from 26% to 30%. However this is rather mis­leading because the enrichment is defined as (total Pu)/(Pu+U), and “total Pu” now contains a significant amount of fertile material. The actual ratio fissile/(fissile + fertile) falls to 22%. This is because 241Pu has a higher fission cross-section than 239Pu and a higher value of v.

Thorium. Figure 1.11 compares reactors utilising the uranium and thorium cycles by showing the effect of replacing 239Pu and 238U with

Early in 1939 Meitner and Frisch suggested that the correct interpreta­tion of the results observed when uranium is bombarded with neutrons is that the uranium nuclei undergo fission. Within a few months two very important things became clear: that fission releases a large amount of energy, and that fission of a nucleus by one neutron liberates usually two or three new neutrons. These discoveries immediately disclosed the possibility of a chain reaction that would produce power.

There was a difficulty, however, in making a chain reaction work. Natural uranium consists of two isotopes: 235U (with an abundance of 0.7%) and 238U (99.3%). Of the two only 235U is “fissile”, meaning that fission can be induced in it by neutrons of any energy. On the other hand 238U undergoes fission only if the neutrons have an energy greater than about 1.5 MeV, and even then they are more likely to be captured or scattered inelastically.

Figure 1 shows the fission cross-sections of 235U and 238U and the capture cross-section of 238U as functions of neutron energy. Because 238U is so abundant in natural uranium capture it dominates over fission in 235U except at energies below about 1 eV.

Neutrons generated in fission have average energies of about 2 MeV and at that energy cannot sustain a chain reaction in natural uranium. If a neutron survives many scattering interactions, however, its kinetic energy decreases until it is in thermal equilibrium with the atoms by which it is being scattered. It is then known as a “thermal” neutron and its most probable energy is about 0.025 eV.

If a chain reaction is to take place, therefore, either the fission neutrons have to be reduced in energy to near the thermal level, in which case natural uranium can be used, or the proportion of 235U has to be increased substantially. Both of these routes were followed in the early work on nuclear reactors. The first led to the development of “thermal” reactors and the second to “fast” reactors, so called because the neutrons causing fission are fast as opposed to thermal.

Temperature affects reactivity in a number of ways. The temperat­ure of the structure affects the dimensions of the reactor core and sometimes the relative position of the various parts: the densities of all the materials depend on temperature (but the most important effects arise from changes in the density of the coolant), and the temperature of the fuel affects the resonance self-shielding in the fuel materials. The various effects are discussed in detail by Hummel and Okrent (1970).

If the temperature changes are small the resulting changes in dimensions, density and self-shielding are also small in most cases and proportional to the temperature changes. First-order perturba­tion theory is valid and the resulting reactivity changes are, approxim­ately at least, linear and independent. As a result it is useful to express temperature-induced reactivity changes as reactivity coefficients of the form dp/dTi, where T is the temperature in question (the coolant inlet temperature, for example, or the mean fuel temperature) and dp/dT can be taken to be constant and independent of all the Ti.

This approximation breaks down in some cases. It may not be true in normal operation if there is intermittent contact between bowing fuel elements, and it is certainly untrue in the extreme conditions that may be encountered in an accident — if the coolant boils, for example, or if the fuel temperature rises very high.

2.6.1 Carbide

Extensive work has been done on mixed carbide fuel in India in con­nection with the thorium-based breeder cycle. To initiate this cycle reactors fuelled with 239Pu but with 232Th rather than 238U as the fertile material are needed. In such reactors uranium is essentially redund­ant, so mixed oxide, which as indicated in section 2.3.3 is limited to about 40% plutonium, or ternary metal alloy with a large uranium

content, are not attractive options. In several respects mixed carbide has superior properties, particularly its high density and high thermal conductivity.

The properties of mixed carbide depend strongly on the stoi­chiometry. Mixtures of UC and PuC at any ratio form solid solutions. The melting points of UC and PuC are around 2780 °C and 1875 °C respectively, but those of the sesquicarbides U2C3 and Pu2C3, which are present to a varying degree in a hyperstoichiometric mixture, are 2100 °C and 2285 °C respectively. As a result the melting point varies over a wide range depending on the contents of the mixture.

Figure 2.23 shows the conductivity of UC and its integral. Both are much higher than the corresponding properties of oxide fuel (see Figure 2.1). However the conductivity of PuC is much lower, rising from 10 Wm-1 K-1 at 700 °C to 20 Wm-1 K-1 at 1100 °C, and the influence of stoichiometry and impurities such as oxygen on the con­ductivity is complex. As a result the effective conductivity of a partic­ular fuel material is much lower than that of pure UC, and values of about 7 Wm-1 K-1 at 500 °C rising to 11 Wm-1 K-1 at 1000 °C have been reported for (U1-aPua)C fuel with a in the range 0.55-0.7. Nev­ertheless the conductivity is still much higher than that of oxide, and with a surface temperature of 1000 °C (assuming the gap between fuel and cladding is filled with gas) and a linear heat rating q of 50 kWm-1 carbide fuel would have a central temperature of around 1380 °C, well below the melting point. Thus higher values of q without central melt­ing are possible in principle. (It may, however, be that this potential cannot be exploited because of limitations to the rate at which heat can be transported out of the reactor core — see section 3.2.3.)

A disadvantage of carbide fuel is that it carries the risk of carbur­isation of the steel cladding. The risk depends on the stoichiometry because the carbon activity of (U, Pu)2C3 is high. Carbide is chemic­ally compatible with sodium so it is possible to fill the gap between fuel and cladding with sodium to provide a good thermal bond. The sodium however tends to transport carbon to the cladding, so helium bonding is usually preferred.

Carbide fuel has a higher density than oxide (because each heavy atom is accompanied by only one light atom rather than two), so it swells more on irradiation. As with metal fuel the swelling is accom­modated mainly by a low smear density. At the start of irradiation the fuel pellets form extensive cracks. Swelling closes the gap between fuel and cladding and eventually eliminates the as-manufactured poros­ity in the pellets. The stress on the cladding from further swelling is relieved, to some extent, by creep of the fuel material. This is particu­larly important for high-plutonium mixtures, which are softer because the melting temperature is lower.

Because the temperatures are so much lower carbide suffers much less restructuring than oxide (see section 2.4.1) and a smaller fraction of the fission-product gas is released.

Carbide is usually produced by carbothermic reduction of oxide. Oxide and carbon powders are mixed, formed into pellets and heated, and the oxygen is driven off in the form of carbon monoxide. Further heating in a hydrogen atmosphere can control the stoichiometry and remove residual oxide and other impurities. A significant disadvantage of carbide is that it is pyrophoric, so the manufacturing process and all fuel-handling activities have to be carried out in an inert atmosphere.

4.3.1 Steam Generator Design

The secondary sodium gives up its heat to raise steam in steam gen­erators that are normally shell-and-tube heat exchangers with water or steam in the tubes. These have to be larger than the intermediate heat exchangers because of the poorer heat transfer on the steam side. They also differ in that they are stressed by the high-pressure steam as well as by thermal expansion. The overriding concern in design and operation is to prevent leaks, because of the consequences of the chemical reaction between water and sodium.

Many older fast reactors had evaporators and superheaters in sep­arate vessels, and some had separate sodium-heated reheaters as well. The flow of hot secondary sodium was divided between superheater and reheater and then recombined before flowing to the evaporator. Austenitic stainless steel cannot be used in evaporators because of the risk of chloride stress corrosion. Although the chloride concentra­tion in the feedwater can be controlled by ion-exchange units there is a danger of an accidental increase, particularly if the condenser is cooled with seawater. Evaporator tubes can be made of ferritic steel, such as 2.25 Cr 1 Mo with about 0.4% niobium added to stabilise the carbon, or of a steel with a higher chromium content such as 9 Cr 1 Mo that resists decarburisation. Separate superheaters and reheaters can be made either of austenitic steel (provided they can be kept free from droplets of water from the evaporators) or of a ferritic steel.

Figure 4.9 Steam plant with recirculating boilers.

Some reactors used a Lamont-type boiler in which the evapor­ator produced a mixture of water and steam that were separated in a steam drum, the water being recirculated to the evaporator and the saturated steam being passed to the superheater. Figure 4.9 shows a steam plant with recirculating evaporators and sodium-heated super­heaters and reheaters. The main advantage of this arrangement is that the evaporator tube walls are always covered with water. The flow of the two-phase mixture of water and steam is either “bubbly” (near the water inlet and where the steam is in bubbles dispersed throughout the water) or “annular” (near the outlet where the steam bubbles coalesce to form a continuous vapour region in the centre of the tube and most of the water is in a film on the wall). The boiling water on the wall gives a high heat transfer coefficient so that the wall temperature stays close to the saturation temperature. It also has the advantage that the mass of steam and water in the steam drums tends to decouple the reactor and sodium coolant circuits from rapid changes in demand for steam caused by fluctuations in the electrical load, so that control of

Figure 4.10 Steam plant with once-through boilers.

the plant is easier. But it has the disadvantage of being complex and expensive.

A “once-through” steam generator as shown in Figure 4.10 is much simpler and cheaper because it does not require steam drum or boiler circulating pumps. The feedwater enters a single heat exchanger in which it is heated to saturation, evaporated and then superheated. The disadvantage is that somewhere along the tube the wall ceases to be covered with water. (This is either the point of “departure from nucleate boiling” (DNB), where nucleate boiling gives way to film boiling, or the “dryout” point, where annular flow gives way to dis­persed flow (Collier 1972).) At this point the heat transfer coefficient falls substantially (see section 4.3.3).

It is very difficult to engineer sodium-heated reheaters with a once — through steam generator. The absence of reheat by sodium is a disad­vantage, both because, both because it reduces the thermal efficiency of the plant by reducing the mean temperature at which heat is trans­ferred to the steam, and also because the wetness at the low-pressure end of the turbine is increased. There is little that can be done about
the reduced efficiency, but the wetness can be reduced by means of moisture separators between the turbine stages or by employing bled — steam reheat as shown in Figure 4.9. Some of the steam is taken from the high-pressure turbine and used to heat the main flow of steam after further expansion. The bled steam is partly condensed in the reheater but is still hot enough to be used in a feed heater. There is a loss of thermal efficiency because of the entropy increase in the reheater, but this may be offset by the increased efficiency of the final turbine stages due to the lower wetness.