As mentioned before, BWRs have the feature that the sets of a cruciform control rod and four surrounding assemblies are regularly arranged in the core. In the case of no large change in dimensions of fuel assemblies and fuel rods, the main investigation point in core design set-up is to determine how many fuel assemblies to load. When altering the dimensions of fuel assemblies or fuel rods in order to improve the core performance, it is important to investigate the relationships of each design param­eter to the core performance and to other design parameters.

[1] Fuel inventory

Technical terms and their definitions [7] concerning fuel loading amount in

core are as follows.

(i) Fuel inventory (W): total mass amount of fissionable materials in reactor core [kg or ton].

(ii) Specific power (Ps): the thermal power produced per unit fuel inventory [kW/kg or MW/t].

(iii) Fuel discharge burnup (Bd): the total energy produced per unit mass of initial fuel until the fuel materials are discharged from the core [MWd/t]; there is a restriction from the viewpoint of mechanical design of fuel.

(iv) Operating cycle length (D): the length of the cycle of continuous opera­tion after refueling [days or months].

(v) Fuel batch size (n): the reciprocal of the discharged fuel fraction in one refueling.

For a reactor thermal power of Q, the fuel batch size n and the specific power PS are given by Eqs. (3.1) and (3.2).

Ps = Q/W=Bd/(nxD) (3.2)

The fuel batch size is deeply related to the fuel economy. A large batch size leads to a small number of fuel assemblies to be discharged in refueling. The fuel assemblies remain in the core for a long period and reach a high burnup. Therefore, the fuel cycle cost is reduced. On the other hand, a small batch size shortens the burning period of fuel assemblies in the core and leads to a low burnup. Hence, the fuel cycle cost is increased. The typical batch size of BWRs is about 4, namely, about one of four fuel assemblies is discharged and replaced in one refueling.

If a small amount of fuel is loaded in the core, that is, if a high specific power is intended, the fuel batch size becomes small. For a given fuel discharge burnup and operating cycle length, it is necessary to set the specific power so that the fuel batch size does not become extremely small. Since the specific power is equivalent to the measure of energy produced per unit volume of pellets, it is related to the linear heat generation rate of fuel rods and the heat flux density on the fuel rod surface as well. Therefore, the specific power is designed considering fuel integrity and coolant heat removal.

Based on the discussions above, the specific power of a BWR is set roughly as 25 kW/kgU as a criterion. The specific power and fuel batch size are important indicators in estimating the fuel inventory for a given reactor power or in evaluating the validity of the fuel inventory estimated from the specifications of fuel rods and assemblies.

PWR cores are designed to assure complete core shutdown capability at the hot temperature condition even with the most reactive rod cluster control assembly (RCCA) stuck in the fully withdrawn position. They are also designed to maintain the core shutdown capability even at the cold tem­perature condition by boric acid injection using the chemical and volume control system.

Natural uranium contains only 0.7 % 235U. The remaining 99.3 % is non-fissile material. Light water reactors (LWRs), operated under the thermal spectrum, mainly utilize 235U as nuclear fuel.

A U nuclide is converted to a 9Pu nuclide by capturing a neutron. 9Pu is a new nuclear fuel. The 239Pu nuclide is further converted to 241Pu through 240Pu by capturing a neutron twice. 241Pu is also a new nuclear fuel. By utilizing those

Y. Oka (ed.), Nuclear Reactor Design, An Advanced Course in Nuclear Engineering 2, DOI 10.1007/978-4-431-54898-0_4, © Authors 2014

Fig. 4.1 Neutron yields per absorption (n) [1]

239 241

conversions, breeder reactors where production of Pu and Pu is larger than their consumption have been developed.

The configuration of a nuclear reactor, which pursues breeding of nuclear fuel, is determined by fundamental phenomena: nuclear reactions. The neutron yield per absorption n becomes

(4.1)

where v, oc, Of, a are neutron yield per fission, capture cross section, fission cross section and the ratio oc/of. Among n neutrons, one neutron is absorbed by a fissile nuclide to keep the fission chain reaction going. L neutrons are consumed by being absorbed by structures and coolant or leaking to the outside of the reactor. The remaining n~ (1 + L) neutrons are captured by fertile materials ( U, Pu)

239 241

and produce new fissile materials ( Pu, Pu). For breeding the fissile materials, condition (4.2) is necessary.

П -(1 + L)> 1 (4.2)

As L cannot be zero, breeding is fundamentally impossible unless n is over 2. Figure 4.1 shows n. It depends on neutron energy. Among fissile materials, 239Pu gives the highest n for fast neutrons and hence the highest breeding perfor­mance. A nuclear reactor that breeds nuclear fuel by utilizing fast neutrons is called a fast breeder reactor (FBR) [2, 3]. On the other hand, a nuclear reactor where fission reactions are mainly caused by thermal neutrons is called a thermal reactor such as a LWR. Figure 4.2 shows neutron spectra of typical fast and thermal reactors.

For the reactor core concept of a fast reactor, the following conditions are essential.

(a) Remove materials that moderate fast neutrons.

(b) Make the fraction of fissile fuel and fertile materials in the core as large as possible in order to efficiently utilize neutrons for breeding.

The breeding ratio (BR) and doubling time (DT) indicate the characteristics of a fast reactor.

Fissile materials produced per unit time Fissile material destroyed per unit time

DT = Time for doubling mass of fissile materials

Initialloadingmassoffissile materials (44)

(BR — 1) x (Reactorpower)

As BR becomes higher or the specific power, which is the ratio of the reactor power and the initial loading mass of fissile materials, becomes higher, DT is shorter [3, 5].

Liquid metal fast breeder reactors (LMFBRs) have been developed by giving shape to the fast reactor concept described above. The liquid metal (mainly sodium) was selected in consideration of the following conditions.

(a) Moderation of neutrons is as little as possible.

(b) The breeding ratio is kept as high as possible.

(c) Cooling performance is very high in order to realize a high power density.

Despite not satisfying(c), gas cooled fast reactors have also been researched

because their characteristics associated with (a) and (b) are good [3].

In the following subsections, core design mainly for the LMFBR is introduced.

In order to realize the core design, the mechanical design must be realized as well as the nuclear and thermohydraulic designs. In this section, the mechanical design of the fuel rod and the fuel block is described [52].

[1] Fuel rod

The fuel rod design must ensure integrity considering production and release of FPs, thermal expansion, irradiation creep, etc. The following conditions must be satisfied at normal operation and anticipated operational occurrences.

(i) The failure fraction of the coating layers at fabrication must be made below a certain limit in order to avoid the release of FPs from the coated particle fuels. In the HTTR design, the limit is set as 0.2 % and the fraction of through-damaged particles of 2 x 10~4 % is achieved in the actual fabrication [53].

(ii) In order to avoid failure of the coating layers, corrosion of the SiC layer caused by palladium, and degradation of the coating layers caused by migration of the fuel kernel, the maximum fuel temperature is kept below 1,600 °C. As already shown in Fig. 4.19, the failure fraction of the coating layers increases when the fuel temperature exceeds 1,800 °C. Migration of the fuel kernel is caused by its encroaching upon the coating layers along the temperature gradient; this is called the amoeba effect. The cross section of a coated particle fuel exhibiting the amoeba effect is shown in Fig. 4.42 [54]. Its mechanism is based on the following chemical formula.

2CO ) CO2 + C (4.30)

At high temperature, the excess oxygen in the fuel kernel produces CO by reacting with the carbon in the low density PyC layer (first layer). At low temperature, the CO decomposes into C and CO2, so that C accumulates there. Through the products of these reactions, the fuel kernel is pushed towards cracks formed at high temperature. The coated particle fuels are designed so that the fuel kernel does not reach the SiC layer.

(iii) Cracking of the fuel rod by thermal expansion or irradiation deformation, which may threaten its structural integrity by mechanical interaction between the fuel compact and the graphite sleeve, is avoided. To do that, an adequate gap between the fuel compact and the graphite sleeve is provided in their fabrication.

[2] Fuel block

The following conditions must be satisfied for the fuel block.

(i) The integrity of the fuel block must be maintained against loads during normal operation and anticipated operational occurrences. The sum of the loads to the graphite block and the stresses caused by the temperature gradient and irradiation deformation must be below the allowable stress of graphite.

(ii) The gap between the fuel blocks needs to be as small as possible in order to reduce the coolant flow rate which is not contributing to fuel cooling. At the same time, the layout of the fuel blocks needs to be designed so that the refueling space is ensured.

The moderator temperature coefficient of the thermal utilization factor can be approached in the same way. A variation in the moderator atomic density due to an increase in the moderator temperature (the moderator volume fraction is constant) can be described with the linear expansion coefficient of the moderator and also by considering the moderator temperature dependence of the thermal disadvantage factor. In addition, the thermal absorption cross sections of both the fuel and moderator change in order to shift the thermal neutron spectrum due to an increase in the moderator temperature. The moderator temperature coefficient can be therefore obtained by Eq. (1.68).

The temperature dependence of the thermal cross sections is given by Eq. (1.69) [18].

o — (Tn) = f<? (TO (2f )1/2 a (To) (1 -69)

This equation can be obtained by integrating a 1/u cross section for the thermal neutron spectrum in a Maxwellian distribution characterized by effective neutron temperature Tn of the system. g(Tn), called the non-1/u factor (Westcott factor), represents the extent of the difference from the 1/u behavior of resonance cross sections in the range of thermal neutron energies. The non-1/u factor depends on the neutron temperature because the thermal neutron spectrum and resonance cross section vary with tem­perature. a(T0) is the cross section at the neutron speed of и = 2200 m/s and it is employed as a reference mark. The corresponding neutron energy and temperature (T0) are 0.0253 eV and 293.61 K, respectively.

The neutron temperature Tn may be considered to be the same as the moderator temperature TM to determine the thermal neutron spectrum. However, since the thermal neutron spectrum is practically hardened by thermal neutron absorption (absorption hardening), the neutron tempera­ture is somewhat different from the moderator temperature. The neutron temperature can be regarded as approximately proportional to the moder­ator temperature by using a proportionality constant a, given by

Tn = aTM (1.7°)

where a is about 1.2-1.3 for a light water-moderated reactor [14, 19].

Thus the moderator temperature coefficient of the thermal cross section can be written as

JL = JL дд дТп _ 1 дТп = 9 _ 1 d 71)

* ^

Applying Eq. (1.71) to Eq. (1.68) gives the moderator temperature coeffi­cient concerning the thermal utilization factor

a£v=(l— f)(36M—а^+ааф (172)

where the temperature coefficient of the non-1/u factor was removed for a 1/u absorber such as the light water moderator. The first term in the second parenthesis on the right-hand side is positive. Physically, this results from the effect to raise the absorption probability of thermal neutrons in the fuel due to a decrease in moderator density caused by a moderator temperature increase. Its magnitude is large, about 10~4Ak/k/K for liquid moderators. For the second term in the second parenthesis on the right-hand side, let us consider a special case in which the fuel and moderator temperatures uniformly change; then the moderator temperature coefficient of the dis­advantage factor in Eq. (1.72) can be summed with the fuel temperature coefficient of the disadvantage factor in Eq. (1.65), that is,

CCt=CCtf~^~(Xtm, (1:73)

It turns out that aT is always negative [14]. This is due to the fact that the thermal diffusion length increases with temperature. As the diffusion length increases, the neutron flux in the lattice fuel cell tends to flatten, that is, the depression of the flux across the cell becomes less pronounced, and this leads to a smaller value of the disadvantage factor. As a result, there is a positive reactivity effect on the temperature coefficient of the thermal utilization factor. Further details are not discussed here.

The third term in the second parenthesis on the right-hand side of Eq. (1.72) is the effect of the non-1/u absorption cross section of fuel.

Table 1.3 n values of major fuel nuclides [18]

The temperature coefficient is generally quite small, on the order of 10_6AklklK for 233U and 235U. However, 239Pu has a high dependence of its non-1/u factors on the neutron temperature, as shown in Table 1.2, and the moderator temperature coefficient of f has a large positive reactivity effect (order of 10_4AklklK). Hence, this effect should not be neglected as 239Pu builds up with fuel burnup.

Since the time variation of nuclear characteristics in the core is relatively slow with burnup, the normal N-TH coupled core calculation is carried out using the time-independent equation at each time step as shown in Fig. 2.26.

*N = *0 + ^

—

}— HUn)

H : Historical Parameters I : Instantaneous Parameters

Fig. 2.26 Renewal of historical parameters in core burnup calculation

~(t0) represents the distribution of historical parameters in the core at time t0. The burnup E(r, t0) and the historical moderator density p(r, t0) are the typical historical parameters, and other ones can be used depending on reactor design code. The burnup in conventional LWRs is usually expressed in the unit of (MWd/t), which is measured as the energy (MWd) produced per metric ton of heavy metal initially contained in the fuel. That is, the burnup is the time — integrated quantity of the thermal power.

For the historical moderator density, a spatial distribution of burnup E(r, t0) at time t0 and a spatial distribution of thermal power density q //0(r, t0) obtained from the N-TH coupled core calculation are considered next. The thermal power density is assumed not to change much through the interval to the next time step (t0 < t < t0+ ^t). Then, the burnup distribution at time tN (=t0 + ^t) can be given by

E(r, tN)~E(?, to)+C’q"'(r, to)At (2-101)

where C is a constant for unit conversion.

Next, the distribution of the historical moderator density is recalculated. Since it is the burnup-weighted average value of the instantaneous moderator density, the historical moderator density at time tN is given by

where E0 and EN are abbreviations of E(r, t0) and E(r, tN), respectively. Here, if the distribution of instantaneous moderator density obtained from the N-TH coupled core calculation at time t0 remains almost constant during the time interval (t0 < t < tN), ~(r, tN) can be expressed as Eq. (2.103).

Hence, the historical moderator density at the next time step tN can be calculated using the historical moderator density and the instantaneous mod­erator density obtained from the N-TH coupled core calculation, at time t0. Thus, the core burnup calculation can proceed until the target burnup by renewing the historical parameters with the burnup step.

[8] Space-dependent kinetics calculation

A space-dependent transient analysis for a short time is made using the time— dependent diffusion equation as

(2.104)

where в is the delayed neutron fraction, Xg is the prompt neutron spectrum, and jdp is the neutron spectrum of delayed neutron group i. Ci is the precursor concentration of delayed neutron group i and Xi is its decay constant. Com­parison with the normal multi-group diffusion equation [see Eq. (2.90)] shows that the time derivative term in the LHS is added and a different expression of the fission source is given by the fourth and fifth terms of the RHS. Both terms represent the prompt and delayed neutron sources which are classified by time behavior. The precursor concentration balance equation can be given by

(2.105)

For an extremely short time difference of 10 4 to 10 3 (t = told + ^t), the following approximations are introduced.

і дф„ ^ і /ф„-ф^

Vg dt VgV At /

The macroscopic cross section in Eq. (2.104) is the feedback cross section similar to that in the N-TH coupled core calculation. Since At is very short, the macroscopic cross section at time t can be substituted by the macroscopic cross section corresponding to the instantaneous parameters at t = told.

Zx, g(r, *)~Х*,Др(г, tM Tm(r, tMX Tf(r, tM -) (2-108)

Substitution of Eqs. (2.106) and (2.107) into Eqs. (2.104) and (2.105) gives Eq. (2.109).[6]

V’DgVtpg (sr, j,+ J фд ^ Xy—y фд

VgAt / д’фд

(2-109)

І і 1+XiAt )Xj ko It 1 +kiAt VgAt J

=0

This is in the same form as that of the steady-state multi-group diffusion equation for a fixed-source problem and it can be solved for фя (r, t) by the numerical solutions mentioned until now. Then, the thermal-hydraulic calcu­lation is performed and the instantaneous parameters are recalculated, simi­larly to the steady-state N-TH coupled calculation. The feedback cross section at the next time step is in turn prepared from Eq. (2.108) and the diffusion equation of Eq. (2.109) is solved again. These repeated calculations give the neutron flux distribution and its corresponding thermal power distribution at each time step.

Since it is hard to use a fine time interval less than 10_3 s in a practical code for the space-dependent kinetics calculation, a large number of considerations have been introduced for high-speed and high-accuracy calculation within a practical time [19]; two examples are the method to express the time variation in neutron flux as an exponential function and the method to describe the neutron flux distribution as the product of the amplitude component with fast time-variation and the space component with relatively smooth variation (the improved quasi-static method). The fast nodal diffusion method is a general solution in the analysis code for LWRs.

The point kinetics model widely used is in principle based on the first order perturbation theory where it is assumed that the spatial distribution of neutron flux does not change much even though the cross section varies by some external perturbation. Hence, when the neutron flux distribution is consider­ably distorted due to such an event as a control rod ejection accident, the space-dependent kinetics analysis must accurately predict the time behavior of the reactor.

Since the BWR core has a low void fraction in the lower part and a high void fraction in the upper part due to steam being directly generated in the core, this leads to an axial distribution of void fraction in the core. The axial void distribution causes a difference in the moderation effect between the core lower and upper parts and the lower part, with the large moderation effect, has a relatively high multiplication factor compared with the upper part. This, therefore, gives rise to power peaking in the lower part. The mitigation of the axial power peaking is an important challenge to improve the plant capacity

Power

Distribution

(Bottom) Core Height (Top)

Fig. 3.16 Improvement in flattening of axial power distribution

1.5 —

И 0.5

Fig. 3.17 Improvement in axial power distribution at EOC

factor in considering an increase of operating easiness as well as maintaining the core thermal margin.

As shown in Fig. 3.16, control rods were shallowly inserted from the core bottom and gadolinia was added to the lower part of the fuel rods to suppress the distortion of axial power distribution in early BWR designs. However, this strategy caused high power peaking in the lower part of the core, as shown in Fig. 3.17, because the core excess reactivity decreases with burnup and control

rods are withdrawn to compensate for the decrement near the end of the operating cycle.

As a solution of this problem, the uranium enrichment in the core upper part can be increased a little more than that in the lower part to compensate for the decrease of the infinite multiplication factor due to the void in the core upper part. This strategy balances the infinite multiplication factor between the core upper and lower parts, and is practically employed to flatten the core axial power distribution; it is referred to as the axially two-zoned fuel concept [10, 11]. Figure 3.18 shows an example of an axially two-zoned fuel core design [10]. The enrichment of upper pellets of some fuel rods is higher by about 0.2-0.5 wt% than that of lower ones and the cross-sectional average enrichment of the fuel assembly upper part is higher by about 0.2 wt% to give a balance of infinite multiplication factors between the upper and lower parts. While control rods are withdrawn and the effect of burnable poisons is decreas­ing with burnup, the effect of the axially two-zoned fuel on the flat axial power distribution can be maintained with burnup even at the end of the operating

Fig. 3.19 Comparison of control rod pattern between (a) Previous core and (b) Control cell core

cycle [14] as shown in Fig. 3.17. The axially two-zoned BWR core consider­ably improves the plant capacity factor by decreasing the maximum linear heat generation rate by 20 % compared with the previous core and by simplifying the control rod operation [12—14].

Thus, different axial enrichments, independent of the core reactivity control, are applied to control of the axial power distribution in the axially two-zoned BWR core. This makes it easy to optimize the axial power distribution and makes it possible to use burnable poisons in core reactivity control separately from control of the axial power distribution.

(i) Structure of Rod Cluster Control Assembly (RCCA)

A RCCA consists of a set of control rods arranged by spider connecting fingers as shown in Fig. 3.39. Each RCCA moves up and down through inside the control rod guide tube (thimble).

Control rods are made of an alloy (Ag 80 %-In 15 %-Cd 5 %) as a neutron absorbing material enclosed by stainless steel cladding and end plugs are welded at both ends. This alloy is widely used because of its excellent properties regarding neutron absorption, metallurgy,

and ease of manufacture. Cd has a large thermal neutron absorption cross section and Ag and In have suitable thermal neutron absorption cross sections and resonance absorption cross sections as well. Thus, the alloy has overall good neutron absorption properties. Also, from the viewpoint of metallurgy, it has excellent stability as a single-phase solid solution and excellent corrosion resistance. Finally, the alloy produces no gaseous element, i. e. helium gas through the (n, a) reaction

as is the case with B4C. A hybrid type of Ag-In-Cd alloy and B4C, or Hf is used as a neutron absorber for control rods in some PWRs.

The control rod drive mechanism is mounted on the reactor vessel head and drives RCCAs which are inserted from the core top and moved in about 1.6 cm increments (one step) in the magnetic jack type mechanism. At a reactor trip, all RCCAs are inserted at once by free fall by a power cutoff.

(ii) Pattern and control of Rod Cluster Control Assemblies (RCCAs)

The number and pattern of RCCAs are determined to control the following three reactivities.

• Power defect: The power defect is the reactivity difference from full power to zero power. This is the sum of reactivity changes by fuel temperature variation (Doppler defect), moderator temperature variation (moderator temperature detect), and neutron flux distribu­tion variation (neutron flux redistribution effect), from full power to zero power.

A­B — C — D — E — F — G — 180° H — J — K— L — M — N — P­R —

A : Control Bank A В : Control Bank В C • Control Bank C D • Control Bank D Sa : Shutdown Bank Sa Sb : Shutdown Bank Sb Sc : Shutdown Bank Sc Sd : Shutdown Bank Sd

Fig. 3.40 Arrangement of control rod cluster (4-Loop PWR) [32] (Copyright Mitsubishi Heavy Industries, Ltd., 2014 all rights reserved)

• Void disappearance: Voids assumed in a small fraction of core disappear with power decrease and then the corresponding reactivity is inserted.

• Shutdown margin: A negative reactivity margin should be secured at shutdown. This is set based on the evaluation of overcooling tran­sients and accidents (abnormal depressurization of the secondary system or main steam line break, etc.). In other words, overcooling transients and accident may lead to a decrease in moderator temper­ature, a reduction in reactivity shutdown margin, and re-criticality of core. The reactivity shutdown margin is assumed as the initial condition of the analysis in evaluating such a transient and accident.

Rod Cluster Control Assemblies (RCCAs) are uniformly located in the core as shown in Fig. 3.40. RCCAs are divided into two groups according to

their main purpose: the control group for power control and the shutdown group for shutdown margin. The groups are divided again into smaller groups, called banks, to reduce the effect on the power distribution and to avoid the too large reactivity change in control rod insertion. In particular, the control group is usually divided into four banks, considering control characteristics during reactor operation. In Fig. 3.40, both control and shutdown groups have four banks each which are withdrawn in the order of SA, SB, SC, SD, A, B, C, D and inserted in the reverse order. This order of withdrawal and insertion is not changed during an operating cycle.

Figure 3.41 presents differential control rod worth (reactivity change per one step) of a single bank. The differential control rod worth is zero at core top and bottom. In actual operation, however, control bank D is positioned not at full withdrawal but at about 5 % insertion and it correspondingly provides an appropriate differential control rod worth. An overlapping method, in which insertion of control bank C begins when control bank D is inserted about 60 % (usually at 100-step position), is employed to avoid zero differential control rod worth at the core bottom. This method reduces the fluctuation of differential control rod worth as shown in Fig. 3.42.

If RCCAs are deeply inserted during reactor operation, the remaining reactivity worth of RCCAs for shutdown becomes small. Control rod insertion depth is limited, as shown in Fig. 3.43, to reduce the decrement of reactivity worth and to secure shutdown margin. This is referred to as the control rod insertion limit and it is monitored by the shutdown margin monitoring system during reactor operation. An evaluation of reactivity shutdown margin is given in Table 3.12.

Since control rods are almost completely withdrawn during reactor power operation, there is almost no decline in control rod worth by

depletion of neutron absorbing nuclides. Control rod lifetime depends on mechanical integrity such as wear of control rod cladding rather than nuclear depletion.

Nuclear reactors are designed to have inherent power controllability, i. e. to have a negative power reactivity coefficient. Nuclear reactors are also designed to have excess reactivity for controlling the core against changes in the power as well as the burnup reactivity to allow its operation for the designed period. The excess reac­tivity is adequately designed so that the reactor is safely operated and shut down.

[1] Reactivity coefficients

The reactivity coefficients indicate the change in the reactivity against the

temperatures of fuel, structure and coolant, and the coolant void fraction etc.

They depend on the plutonium content, uranium content and burnup condition.

(a) Doppler coefficient: This is the ratio of the reactivity change and the change in the effective fuel temperature. The value is negative as long as the fissile enrichment is not too high. When the fuel temperature rises due to the increase in the power or other causes, thermal motions of nuclei become stronger and the apparent width of the resonance absorption cross section curve of U and Pu is expanded. This increases resonance absorption of neutrons by those nuclei. Since the Doppler effect is mainly provided by the resonance absorptions of U and Pu, it gets stronger for the core with more neutrons at the resonance energy. The Doppler effect dominates the reactivity feedback against the change in the reactor condi­tions. Thus, the power reactivity coefficient, which is obtained by combin­ing all the reactivity effects, is always kept negative for all the operating regions and hence the reactor has an inherent safety feature.

(b) Fuel temperature coefficient excluding the Doppler effect: This is the ratio of the reactivity change by thermal expansion of fuel elements mainly in the axial direction to the change in the fuel temperature causing the thermal expansion.

(c) Structure temperature coefficient: This is the ratio of the reactivity change by thermal expansion of structures to the change in the structure tempera­ture causing the thermal expansion.

(d) Coolant temperature coefficient: This is the ratio of the reactivity change by a decrease in the coolant density to the change in the coolant temperature causing the density change.

(e) Core support plate temperature coefficient: This is the ratio of the reactivity change by enlarging the fuel assembly gap caused by thermal expansion of the core support plate to the change in the temperature of the core support plate.

(f) Void reactivity: This is the reactivity change when a void is generated in the coolant. Fast reactors are designed so that the coolant does not evaporate at normal operation, anticipated abnormal occurrences and even design basis accidents, and that gas bubbles are not formed. For the purpose of defining and calculating the void reactivity, the following assumptions are made.

• Gas bubbles formed in the primary system due to a certain cause pass through the core.

• The coolant evaporates although it is technically not possible.

During reactor operation, neutron interactions with fuel give rise to various nuclear reactions such as fission of fissile nuclides, conversion of fertile nuclides into fissile ones, and production of FPs. This section solves the burnup equation to determine atomic number densities of fissile and fertile nuclides in fuel, and considers the changes with fuel burnup. Fission products are mainly treated in Sect. 1.2.

Y. Oka (ed.), Nuclear Reactor Design, An Advanced Course in Nuclear Engineering 2, DOI 10.1007/978-4-431-54898-0_1, © Authors 2014