There are various possible cladding materials but most if not all are steel alloys containing at least a few percent of chromium. After the start of irradiation the inside surface of the cladding is quickly covered with a thin layer of oxide, mainly Cr2O3. Further oxidative corrosion involves reactions in the matrix of the metal crystals, often preceded by intergranular attack at the interfaces between crystals.

Fission products are involved particularly in the intergranular attack. The mechanisms are not understood in detail but it is clear that caesium and tellurium, possibly in the form of Cs2Te, are import­ant. The Cs2Te appears to react with chromium and the tellurium released then attacks the steel by dissolving iron and nickel.

Intergranular corrosion is facilitated by a high power rating (imply­ing high fuel temperatures) and the presence of an open gap between the fuel and the cladding. High temperature is important because it enhances the mobility of volatile species, allowing the caesium to move out of the fuel matrix to the cladding (see Figure 2.16). The gap between fuel and cladding is open early in the life of the fuel element, but then closes, only to reopen later (see section 2.4.4).

Corrosion at the start of irradiation of a new fuel element, which can occur within a few days, is sometimes known as “corrosion dejeun — esse”. In later life, when the gap has reopened, intergranular corrosion is sometimes seen at the top of the fuel column, where the surface temperature of the fuel is highest, and is sometimes called “reaction interface fissile-fertile”, or RIFF.

In spite of uncertainty about the details of the mechanisms of cor­rosion it is clear that corrosion increases with burnup, temperature gradients, and oxygen content. The last is most important and is the principal reason for making the oxygen content of new fuel signific­antly sub-stoichiometric, x being typically -0.02 or -0.03. And in spite of the propensity for intergranular corrosion experience has shown that it rarely leads to loss of integrity of the cladding, even though it is stressed by the pressure of the fission-product gases. Many tens of thousands of oxide fuel elements have been irradiated to burnups as high as 25% or more, with failure rates of the order of 0.1% or less.

If two turbulent streams of sodium at different temperatures meet and mix together the temperature in the resulting stream will fluctu­ate initially, although the fluctuations will be smoothed eventually by conduction. However if the sodium flows over a component of the structure the temperature fluctuations may be transferred to it and cause fluctuating thermal stresses. Over the lifetime of a reactor the number of such fluctuations may be very high indeed and there may be a possibility of high-cycle fatigue damage.

(In the context of sodium-cooled reactors the phenomenon of high- cycle thermal strain is sometimes known as “thermal striping”. This name derives from a conceptual image of streams of coolant at dif­ferent temperatures emerging from different fuel subassemblies of a reactor core. These are envisaged as giving rise to “stripes” of coolant at different temperatures twisting around each other in the region above the core and impinging on the structure. This concept is neither physically accurate nor helpful. It is more accurate to think of streams of coolant at different temperatures flowing side by side and mixing by the formation of eddies. The structure is then exposed at differ­ent times to hot eddies in an otherwise cold flow or cold eddies in a hot flow. The term “thermal striping” is misleading and should be avoided.)

The potential for damage can be illustrated simply as follows. If the surface of a fully restrained structural member is subjected to temperature fluctuations with a peak-to peak amplitude of AT the resulting thermal strain range is roughly a AT. For an austenitic steel with a = 18 x l0-6 K-1, if AT exceeds about 110 K, the strain range exceeds 0.002. If the temperature fluctuates with a frequency of order 1 Hz, then over a 40-year life at 80% load factor there will be 109

such cycles, which is enough to cause significant damage. If to avoid this damage the reactor is designed with a safety factor of 2 on strain, temperature fluctuations in excess of 55 K would have to be avoided. In a reactor where the core temperature rise may be 150 K or more this places severe restrictions on design, particularly for structures above the core outlet where temperature differences are greatest, both at the outlets of adjacent subassemblies and at the boundary of the core.

The component most likely to be at risk is the above-core struc­ture. If for example there are two adjacent subassemblies from which coolant is emerging at different temperatures there will be temperat­ure fluctuations in the region where the coolant streams mix. Figure 4.4 illustrates the situation. If the coolant velocity is ~3 ms-1 and the dia­meter of the subassembly outlets is ~0.1 m, eddies of -0.03 m might be expected, with a frequency of -1 Hz. The thermal diffusivity of sodium is about 6 x 10-5 m2 s-1, so the temperature difference in a typical eddy would last for 10 s or more, long enough for it to be trans­ported anywhere in the hot pool and certainly for it to impinge on the above-core structure. Other components may also be at risk, not only in the main primary and secondary circuits but also in auxiliary circuits such as plugging meter loops or cold traps (see section 4.2.7).

Oxide, however, is far from perfect as a fuel material. The oxygen acts as a partial moderator, reducing the mean neutron energy and therefore decreasing the breeding ratio. The low thermal conductivity of the oxide is another disadvantage because it means that the fuel elements have to be very slender and the cost of manufacturing them is high.

There are on the other hand compensating advantages apart from the ability of oxide to withstand high burnup. The low mean neutron energy means that there are enough neutrons in the 238U resonance region to make the Doppler effect important. This results in a prompt negative temperature coefficient of reactivity, which in some cases offsets the positive sodium temperature coefficient due to the large size of the core of a high-power reactor. These effects are described in Chapter 1.

Oxide fuel can be operated at a higher temperature than metal, and it can be clad in stainless steel, which is cheaper than the refract­ory metals used in metal-fuelled reactors. Above all there is a lot of experience about it because it is widely used as a fuel for thermal reactors.

This last is the reason why oxide is preferred to carbide. A mixture of UC and PuC would have important advantages (higher thermal conductivity, higher density, less moderating effect), but because it is not so well understood caution dictated that oxide should be preferred. It is possible that carbide fuels will be used widely at some time in the future.

Other fuels have been tried. Experiments were done on cermets, consisting of a sintered mixture of stainless steel and oxide powders. This had the advantage of high thermal conductivity and a por­ous structure that can accommodate fission products. It was rejected because absorption of neutrons in the steel was very detrimental to the breeding ratio. Molten fuel was tried in the LAMPRE experiment. This reactor had molten plutonium fuel clad in tantalum. The problems of corrosion and of the accumulation of bubbles of fission-product gas in the molten fuel were so severe that this line of development was not pursued.

So by 1970 mixed oxide fuel, stainless steel cladding and structure, and sodium coolant became accepted almost universally as the route for the development of fast breeder reactors. These materials restrict the designers’ choice of variables such as the dimensions of the fuel elements and the core and as a result all fast breeder reactors of the period, from whatever country, showed marked similarities. The British Prototype Fast Reactor (PFR), French Phenix, Russian BN — 350, German SNR-300, Japanese Monju, and the proposed Clinch River Breeder Reactor (CRBR) in the United States were, as far as the design of the reactor core is concerned, very much alike. They were all prototypes intended to be followed by full-scale production reactors for commercial generation of electricity such as Super-Phenix in France, the Commercial Fast Reactor (CFR) in Britain, and BN-600 in Russia.

A reactor designed to consume plutonium rather than breed it inev­itably has less 238U in the core, so the negative component of the Doppler coefficient is reduced, but it is not lost. Table 1.5 shows the various components of the Doppler effect of losing all the sodium from the fuel subassemblies in a 2500 MW (thermal) core with fuel enriched to 45%. The plutonium is assumed to have been recycled once in a thermal reactor. The enrichment is the maximum for which (U, Pu)O2 is soluble for reprocessing.

It will be seen that even with this low concentration the negative effect of capture in 238U dominates the Doppler coefficient. Moreover even if there were no 238U at all the coefficient, for this highly irradi­ated plutonium, would still be slightly negative mainly because of the contribution of the 240Pu. However for “high-grade” plutonium rich in 239Pu it would be positive. As in the case of a breeder the Doppler coef­ficient can be made more negative by incorporating solid moderating material in the core.

In a consumer core compared with a breeder the reduced effect of fission in 238U makes the neutron importance spectrum flatter and thus the moderation component of the sodium coefficient smaller. However the effect of increasing the concentrations of the higher plutonium isotopes in a consumer reactor is the opposite of that in a burner. Although in both case the fertile-to-fissile ratio increases the fact that the fast-neutron fission cross-section of 240Pu is higher than that of 238U makes the importance spectrum steeper and the moderating component larger.

3.1 INTRODUCTION

Having described the neutron physics of a fast reactor in Chapter 1 and the behaviour of the fuel elements in Chapter 2, in this chapter we discuss the engineering of the core of a power-producing fast reactor. The three following sections deal with heat transfer, materials and structure.

Heat transfer comes first because the dimensions of the fuel ele­ments and of the core are determined mainly by the demands of heat transfer. The fuel elements have to be of the right dimensions to trans­fer heat to the coolant at the required rate without overheating. The core has then to be large enough to allow enough coolant to flow through it to take the heat away. This section deals mainly with liquid metal coolants.

Once the main dimensions are fixed the form of the core is determ­ined by the properties of the materials of which it is made, and in particular by the way these properties are affected by neutron irradi­ation and exposure to the coolant. The structure of the core has then to be designed within these constraints to hold the fuel in place, to allow it to be changed when necessary, to distribute the coolant flow correctly, and to provide for the control rods.

There is a range of abnormal events that befall power stations so frequently that they cannot be thought of as accidents even though they interrupt ordinary operation. It goes without saying that such events cannot be allowed to hazard the operating staff or the public, and in addition the control system has to be designed so that they do not cause damage to the plant.

Examples of these abnormal events are failures of the connection to the power distribution system, which might be due to storm dam­age to a power line, and would cause a sudden loss of the alternator load. Failure of pieces of auxiliary equipment such as the bearing lub­rication system or the alternator cooling system would demand rapid shutdown of the turbine. Failure of the feed pumps or the primary or secondary sodium pumps would prevent full-power operation of the plant and probably require complete shutdown. Perhaps the most important sources of such events are failures of the reactor and plant protective system itself. The protective system is designed to be “fail­safe”, so that for example if an ionisation chamber measuring neutron flux goes wrong it gives an indication of high flux. If two or more ionisation chambers fail the protective system takes action as if the flux were really too high and trips the reactor down (i. e. shuts it down automatically).

The control system has to be designed so that the plant or the affected part of it can be shut down safely and without damage if one of these abnormal, or “upset”, events happens. The design of the turbine and alternator trip system can follow conventional lines, but tripping the reactor and the sodium coolant circuits involves special considerations, the two most important of which are the removal of the decay heat and the avoidance of thermal shock.

Even if the reactor is shut down the fuel continues to generate heat by the decay of radioactive fission products. Emergency cooling systems are provided to remove this heat under accident conditions (section 5.2.4), but it may be preferable not to rely on them in an upset event. It may be better to maintain operation of the primary and secondary sodium circuits in case of a reactor trip and to reject the decay heat to the condenser by maintaining the supply of feedwater to the evaporators. In the event of a turbine trip it may be best to open a bypass so that steam can flow directly to the condenser. If one primary or secondary sodium pump fails it may be decided to trip the reactor but keep the other pumps operating to remove the decay heat.

It is more difficult to avoid thermal shock. If the turbine trips either the full flow of steam has to be diverted to a very large standby “dump” condenser (which is expensive), or the reactor has to be tripped or reduced in power very quickly. If the latter course is taken the sodium flow-rates have to be matched to the power if rapid changes in temper­ature of the above-core structure and the intermediate heat exchangers are to be avoided.

Considerations such as these impose considerable demands on the control system, especially as the time constants for temperature changes in the reactor core and the steam generators are quite short.

REFERENCES FOR CHAPTER 4

Anderson, C. A. (1978) Optimization of the Westinghouse / Stone and Webster Prototype Large Breeder Reactor, pp 247-259 in Optimisation of Sodium — Cooled Fast Reactors, British Nuclear Energy Society, London Aubert, M., J. M. Chaumont, M. Mougniot, M. Recolin and M. Acket (1978) Temperature Conditions in an LMFBR Power Plant from Primary Sodium to Steam Circuits, pp 305-310 in Optimisation of Sodium-Cooled Fast React­ors, British Nuclear Energy Society, London Broomfield, A. M. and J. A. Smedley (1979) Operating Experience with Tube to Tubeplate Welds in PFR Steam Generators, pp 3-18 in Welding and Fabrication in Nuclear Industry, British Nuclear Energy Society, London Campbell, R. H. (1973) Primary Systems Design of Sodium-Cooled Fast Reactors, Journal of the British Nuclear Energy Society, 12, 357-365 Claxton, K. T. (1976) Solubility of Oxygen in Liquid Sodium — Effects on Interpretation of Corrosion Data, pp 407-414 in Liquid Metal Technology in Energy Production, Volume 1, American Nuclear Society, Hinsdale, Illinois, USA

Collier, J. G. (1972) Convective Boiling and Condensation, McGraw Hill, New York

Eickhoff, K. G., J. Allen and C. Boorman (1967) Engineering Development for Sodium Systems, pp 873-895 in Fast Breeder Reactors (BNES Conference proceedings), Pergamon, Oxford

Evans, P. B. F, E. J. Burton, E. Duncombe, D. Harrison, G. O. Jackson and N. T. C. McCaffer (1967) Control and Instrumentation of the Prototype Fast Reactor, pp 765-782 in Fast Breeder Reactors (BNES Conference pro­ceedings), Pergamon, Oxford

Frame, A. G., W. G. Hutchinson, J. M. Laithwaite and H. F. Parker (1967) Design of the Prototype Fast Reactor, pp 291-315 in Fast Breeder Reactors (BNES Conference proceedings), Pergamon, Oxford Hans, R. andK. Dumm, (1977) Leak Detection of Steam or Water into Sodium in Steam Generators of LMFBRs, Atomic Energy Review, 15, 611-699 Hayden, O. (1976) Design and Construction of Past and Present Steam Gen­erators for the UK Fast Reactors, Journal of the British Nuclear Energy Society, 15, 129-145

Haywood, R. W. (1975) Analysis of Engineering Cycles (Second Edition), Pergamon, Oxford

Horst, K. M. (1978) General Electric / Bechtel Prototype Large Breeder Reactor, pp 175-184 in Optimisation of Sodium-Cooled Fast Reactors, British Nuclear Energy Society, London IAEA (2012) Liquid Metal Coolants for Fast Reactors Cooled by Sodium, Lead, and Lead-Bismuth Eutectic IAEA Nuclear Energy Series No. NP-T — 1.6 International Atomic Energy Agency, Vienna Knowles, J. B. (1976) Principles of Nuclear Power Station Control, Journal of the British Nuclear Energy Society, 15, 225-236 Lewins, J. (1978) Nuclear Reactor Kinetics and Control Pergamon, Oxford Lillie, A. F. (1978) Design of the Clinch River Breeder Reactor Steam Gen­erators, pp 557-571 in Design, Construction and Operating Experience of Demonstration LMFBRs, International Atomic Energy Agency, Vienna Smith, C. A., P. A. Simm and G. Hughes (1979) Analysis of Hydride and Oxide Deposition and Resolution in Relation to Plugging Meter Behaviour, Nuclear Energy, 18, 201-214

Tang, Y. S., R. D. Coffield and R. A. Markley (1978) Thermal Analysis of Liquid-Metal Fast Reactors American Nuclear Society, Hinsdale, Illinois, USA

Tattersall, J. O., P. R. P. Bell and E. Emerson (1967) Large Commercial Sodium-Cooled Fast Reactors, pp 352-372 in Fast Breeder Reactors (BNES Conference proceedings), Pergamon, Oxford Whittingham, A. C. (1976) An Equilibrium and Kinetic Study of the Liquid Sodium-Hydrogen Reaction and Its Relevance to Sodium-Water Leak Detection in LMFBR Systems, Journal of Nuclear Materials, 60, 119-131

Although it is always possible to solve equations 1.9 to find the eigen­value k of a system it is very useful to have a means of estimating the effect of small changes. This is particularly so in the case of temperature coefficients. For example, as explained later, a change in temperature makes small alterations to certain group cross-sections by means of the Doppler effect. A method of estimating the resultant change in k is needed, and this is provided by perturbation theory.

Suppose the perturbation in which we are interested results in an increase S £cg in the capture cross-section for group g in a small region dV at a point r in the reactor. The increased rate of capture of group g neutrons is then pg = (r)S£cgdV. The resulting effect on k depends on g and r; that is to say neutrons in some parts of the reactor and at some energies are more important than others. For example neutrons captured at the edge of the core, which were anyway quite likely to have
leaked out and been lost, are less important than neutrons captured at the centre, which were more likely to cause another fission. This distinction can be represented by assigning an importance, ф*, to each neutron. ф* depends on energy and position, so ф* = ф*(г). ф* can be defined in a simple physical way as follows (although it should be remembered that this is not the only way of interpreting it).

If a reactor with no source of neutrons apart from fission is exactly critical and operating at a certain mean power P, and a single neutron in group g is artificially introduced into it at a point r, the power will, after a time, settle down to a new mean value P + SP, where SP is a random quantity. If it was possible to repeat the experiment many times the average change in power due to the introduction of one new neutron could, in principle, be found. This we call фg (r), the importance of the neutron in group g at г.

With this definition in mind it can be seen that the rate of change of power due to the increased capture S£cg at г is

Iі = — фg (r’№g(r)8ZcgdV.

To determine the effect on к we have also to know what the actual power is in terms of ф*. The rate at which new group g neutrons are being generated in dV is sgdV, where

(1.21)

If the mean lifetime of these neutrons is X the number of group g neutrons in dV is Xsg dV and their contribution to the reactor power is Xф*sgdV. The total reactor power is therefore

and the time constant is т = P/P.

Elementary reactor kinetics using the point kinetics model shows that t is related to reactivity p by т = k/p, where p is defined as (k — 1)/k. Thus we have finally

p = — ф; (r)(pg(r)S’LcgdV/C, (1.23)

where

the integral being taken to run over the whole of the reactor.

This treatment glosses over a lot of difficulties, chiefly that k is different for neutrons in different groups, but it illustrates the principle. A rigorous treatment is given by Duderstadt and Hamilton (1976), for example, and shows that in the general case of perturbations to any of the group constants the change Sp in reactivity is given by

E {&£^Фф + SDgVФІ-ЧФЇ)

In the case of a fundamental mode calculation the requirement that the reactor is exactly critical (k = 1) and that the total flux is normalised (equation 1.11) implies that the importance of neutrons born in fission is also normalised so that

N

ЕхпФі =1 (1.26)

n=1

1.2.3 Matrix Notation

The complicated expression of equation 1.25, and indeed much of multigroup diffusion theory, can be written much more easily in matrix

form. In this notation equations 1.9 become

Мф = 1 Бф,

к

Фі

Мтф* = 1 Бтф*,

к

where Мт and FT are the transposes of M and F (i. e. the i, j element of MT is the j, i element of M etc.). MT and FT are actually the “adjoints” of М and F, but because М and F are real the adjoint (which is the transpose of the complex conjugate) is the same as the transpose. ф* is often called the “adjoint flux”, but this is misleading because it does not have the properties of a flux. In particular if two adjacent groups g and g + 1 are combined to form a new group g, ф^ = фg + ф^, but in contrast ф* is not additive and фg, is an average between фg and ф*+1.

Equation 1.25, which is the basic result of first-order perturbation theory, in matrix notation is

(1.31)

This is called “first-order” for two reasons. The first is that second — order small quantities have been neglected in the usual way. The second is that ф and ф* both refer to the unperturbed reactor. If in equation 1.30 ф were the flux after the reactor had been perturbed the equation would be exactly right and the result would be that of exact perturbation theory. It would not be nearly so useful, however, because equation 1.30 makes it possible to estimate the effect of any small perturbation using the results of just two multigroup calcula­tions, one to find ф from equations 1.26, the other to find ф* from equations 1.29.

Design and manufacture of the fuel have to take account of the way it is to be reprocessed after discharge from the reactor (assuming it is not to be consigned to long-term storage as waste material). Oxide fuel is usually reprocessed by the “Purex” process, which involves dissolving it in nitric acid. However (U, Pu)O2 containing more than about 40% plutonium does not dissolve readily. It is therefore necessary to ensure that the fuel is mixed uniformly during manufacture, because particles of fuel with a high plutonium content might not dissolve and would cause difficulty at some later stage in the process. It is not difficult to ensure uniformity of co-precipitated fuel but if pellets are formed from mixed UO2 and PuO2 powders care has to be taken that the grains are very small and are mixed thoroughly. In vipac fuel all the plutonium may be in the larger granules so their plutonium concentration has to be greater than the average for the fuel as a whole, and if after irradiation (when the plutonium concentration is still higher) it exceeds 40% difficulty will be experienced in dissolution.

Purex is a solvent extraction process that separates first uranium and plutonium from the fission products, and then uranium and plutonium from each other. The separation depends on differences between solubility in water and in an organic solvent, and these differ­ences depend on acidity. The feed for the process is the aqueous stream of fuel dissolved in nitric acid, containing the uranium, plutonium and fission products as nitrates, which is brought into contact with a stream of the organic solvent tributyl phosphate (TBP). TBP and water are not mutually soluble. Under acid conditions uranium and plutonium are more soluble in TBP whereas the fission products are more soluble in water, so when the aqueous and organic phases are agitated together the heavy metals are transferred to the TBP while the fission products remain in the water. The two phases are then separated and the TBP stream is brought into contact with water of neutral acidity where the heavy metals go back into the water. The process can be repeated in a second cycle to remove any residual fission products. With two cycles a decontamination factor (the ratio of the fission-product concentration in the final heavy metal product to that in the initial feed) of 10-6 can be achieved.

Plutonium can be separated from uranium by making use of the different valency states it can take. Tri-valent plutonium in the form of Pu(NO3)3 is not soluble in TBP, so by adding a reagent that reduces Pu(IV) to Pu(III), uranium can be taken into the organic phase, leaving plutonium in the aqueous. Separation factors of 10-4 can be achieved.

These solvent extraction processes take place in contactors that agitate the immiscible aqueous and organic streams together in such a way as to make the area of the interface between them as large as possible. The contactors may be horizontal “mixer-settler” tanks fitted with alternating agitated and quiescent compartments, but more usually are vertical packed columns. In a “pulsed column” the effect of the packing or perforated plates in the column as they break up the streams of TBP (flowing upwards) and water (flowing down) is enhanced by pulsing the feed flow.

Whatever the form of the contactors they have to be designed to avoid criticality. This can be done by means of the geometry (for example by minimising the diameter of a pulsed column) and by incor­porating structural materials that contain thermal neutron absorbers such as boron or gadolinium.

3.4.1 Fuel Subassemblies

The design of fuel elements is discussed in Chapter 2. Each element, or “fuel pin” as it is sometimes called, consists of a steel tube, 6 to 8 mm in diameter and usually some 2.5 to 3 m long. It contains about 1 m or more of core fuel, in the case of a breeder reactor 0.3 to 0.5 m of axial breeder fuel both above and below the core fuel, and a void or plenum up to 1 m long to contain the fission-product gases released from the fuel as explained in section 2.3.6. The plenum can be situated either below or above the core and axial breeders. A typical fuel element for a breeder reactor is shown in Figure 2.6.

Unlike those of thermal reactors the fuel elements of a fast reactor are usually arranged in a triangular array. This is better than a square array because, for the same ratio of coolant and fuel volumes, it allows greater clearances between the fuel elements and therefore smaller variations of cladding temperature round each element.

As shown in section 3.2.2 a reactor core may contain some 105 fuel elements, which obviously cannot be inserted and removed one by one. They are assembled into subassemblies each consisting of 200­300 fuel elements surrounded by a hexagonal tube or “wrapper”. In addition to facilitating handling this arrangement enables the coolant flow-rate to each part of the core to be regulated so that the outlet temperature is approximately uniform across the core. This is done by means of adjustable flow restrictors or “gags” at the bottom of each subassembly.

The use of subassembly wrappers underlines another important difference between fast and thermal reactors. In a thermal reactor the incorporation of large amounts of structural material in the reactor core would have an adverse effect on the neutron economy, but in a fast reactor in which the neutron cross-sections are much lower it has little effect. In addition the choice of the structural material is hardly constrained by neutronic considerations: there is no need to resort to zirconium; steel is entirely acceptable.

The choice of subassembly size is a matter of compromise. Large subassemblies make for easier fuel handling and lower manufacturing costs. Small subassemblies have the advantages of smaller transverse temperature variation (and therefore less severe hot spots), easier removal of decay heat when the irradiated fuel is removed from the reactor, and less serious consequences of an accident confined to one subassembly. (This point is explained more thoroughly in Chapter 5.)

There are two possible methods of locating the fuel elements within the wrapper. In one a wire is wrapped helically around each element with a pitch of the order of 0.2 m. The diameter of the wire is equal to the required distance between elements so that each element is located with respect to each of its six nearest neighbours at two points in each pitch of the helix. Wire wraps tend to induce helical distortion of the fuel elements because they cause a slight asymmetry of the cladding temperature, and they introduce a considerable quantity of metal into the core, but they have the advantage that the helical shape tends to promote mixing of the coolant between the various subchannels. In spite of this the edge subchannels adjacent to the wrapper are larger than the rest so the fuel elements at the edge of the bundle are slightly over-cooled (as shown in Figure 3.8).

An alternative to wire wraps is to locate the fuel element by means of transverse grids every 0.1 m or so along their length. Grids use less material and do not distort the elements as much as wire wraps, and they allow the possibility of reducing the over-cooling of the edge fuel elements. However they are expensive and have the disadvantage that the fine clearances between grids and elements may be prone to blockage by any foreign material present in the coolant. They also tend to have a high resistance to coolant flow, which increases the pressure drop through the core.

As well as fuel elements a subassembly may also contain shield­ing material, usually in the form of steel rods or a steel block, both above and below the fuel elements. The shield serves to protect the permanent structure on which the core rests, and equipment such as heat exchangers and the roof of the reactor vessel, from neutron and y radiation from the core. There is also usually a coolant filter at the inlet end. Figure 3.20 shows a typical fuel subassembly. Radial breeder fuel is usually contained in larger diameter fuel elements in sub-assemblies similar to those in the core.

It is pointed out earlier in section 5.2.3 that it is necessary to detect a single subassembly accident and prevent it from spreading to damage the rest of the core. As an illustration of how the protective systems described in section 5.2.3 do this we trace in outline the development of an accident initiated by a partial blockage of the coolant flow in the core region of one subassembly. A complete analysis would be much more detailed but would follow these general lines.

There is of course a very high probability that the protective sys­tems would operate, but the possible sequence of events if they did not is as follows: the blockage would cause overheating, which might

Blockage Failed Coolant

Formed Fuel Boils

Trip

Operates

Figure 5.10 An event tree for a subassembly blockage accident.

boil the coolant and then melt the fuel, and this might cause a vapour explosion (see section 5.1.2), which in turn might damage the rest of the core. Figure 5.10 is a very simple form of an event tree describing this sequence. It can be used to determine the frequency with which the undesirable outcome (damage beyond the initially affected sub­assembly) can be expected.

First we have to assess the frequency of the initiating event — the occurrence of the blockage. Subassembly inlets are fitted with filters, so a blockage within the subassembly cannot be formed by material from outside. The only source of blockage material inside the subassembly would be cladding or fuel from one or more failed fuel elements. It might be supposed that fragments of fuel might come out of a crack in the cladding into the coolant and be trapped between the fuel pins to form the blockage. It has been shown that this is very unlikely if not impossible. Experiments in which fuel elements have been made to fail in an operating reactor have shown that large cladding fail­ures have not caused blockages (Kramer et al., 1979; Smith et al., 1978). Data like these show that the frequency of the initiating event is very low.

Since the only source of blockage material is failed fuel a blockage must be accompanied by a substantial failed fuel detection signal. It
can be shown that a blockage can cause damage only if it escapes detection either because the failed fuel detection system is inoperative or it happens so quickly that the damage is caused before the detection system has time to initiate a trip (i. e. within a few seconds). Because the detection system may well consist of three separate independent subsystems either possibility is very unlikely, so the probability of failure (the “no” branch at the first branch point in Figure 5.10) is very small.

If the “no” branch is taken, the blockage might become large enough to make the coolant boil. (A more detailed analysis would analyse the growth of a blockage and there would be more branch points in the event tree.) Experiments have determined the temperat­ure distribution in the recirculating wake of a blockage (Kirsch, 1974; Schleisiek, 1974). If the blockage is large enough the coolant will boil (“yes” at the second branch point in Figure 5.10). This is unlikely because the boiling point is some 400 K above the normal coolant temperature, so the blockage has to be quite large.

If the coolant boils it will be detected by the boiling detection system, if one is fitted (see section 5.2.3). Only if this fails can the accident progress. Experiments in reactors (Smith et al., 1978) and test rigs (Schleisiek, 1974) have shown that even if the coolant does boil the fuel is cooled adequately by the two-phase coolant. The blockage has to grow still more before the two-phase flow becomes unstable and the surface of the fuel elements dries out. If this lasts for more than a few seconds (which is unlikely) the affected fuel is uncooled and will melt.

The last two branch points in Figure 5.10 ask whether a vapour explosion takes place and then whether it is violent enough to damage the rest of the core. At present these points have not been resolved experimentally, but the available data (Briggs, Fishlock, and Vaughan, 1979) suggest that the probability of “yes” is low at both branches. It can be shown (Smidt and Schleisiek, 1977) that if a vapour explosion is to be severe enough to disrupt the subassembly wrapper it must involve a large amount of fuel (the amount depends on the design of the wrapper). This in itself makes the probability of “yes” at the last branch point small.

For illustrative purposes the frequency of the initiating event — the formation of a large coolant flow blockage by release of fuel debris from a cladding breach — might be taken to be 10-1 per year. The probability that the failed fuel detection system will then fail to initiate a trip might be 10-2. A pessimistic assumption might be that there is then a 50% chance that the coolant will boil within the mass of the blockage or in its wake. A boiling detection system might have a 20% chance of failing. Even if the coolant boils the blockage has to be large before it will cause the fuel to melt, so the probability of fuel melting might be 10-2. If the fuel melts the paucity of experimental evidence of a vapour explosion might be taken to indicate a probability of 10-1 that it would occur, and a further probability of 10-1 that it would be severe enough to propagate damage through the subassembly wrapper. Thus, as shown in Figure 5.10, the frequency of damage to the rest of the core caused by blockages in single subassemblies would be assessed to be 10-8 per year.

It must be emphasised that this is only an illustration of the way an event tree can be used: an analysis for the purposes of a reactor safety case would be based on detailed statistical assessment of the performance of the instrumentation and trip systems and on the avail­able experimental evidence about the various phenomena involved, such as blockage formation, coolant boiling and vapour explosions.