As a reference power distribution for investigating power distribution flattening by a burnable poison design, and fuel loading and control rod patterns, the Haling distribution [19] may be used. It is based on the principle that if a power distribution can be kept constant through the operating cycle by proper man­agement of burnable poison and movable control rods, the peak-to-average value will be at a minimum. In derivation of the principle, it was assumed that the infinite multiplication factor of a fuel assembly is a decreasing function of burnup and variation in the flux-to-power ratio with burnup is small or a decreasing function of burnup. This assumption leads to a concludion that in comparison with the case of a constant power distribution through the operat­ing cycle, a slightly smaller power peaking for a period of the operating cycle will require fuel burning by reactor operation under a high power peaking for another period.

In a given fuel design, the Haling distribution of the fuel arrangement can be obtained from calculation of an initial power distribution shape and repeated calculations between the power distribution shape and burnup distribution. The repeated calculations finally give a consistent distribution between power and burnup. If this power distribution shape can be realized during the operating cycle by adjusting the burnable poison distribution in fresh fuel and the insertion amount and position of control rods, namely, the neutron absorber distribution, it will give a minimum power peaking.

This principle is useful in designing the control rod pattern during the operating cycle. For a given fuel arrangement, cycle length, and effective multiplication factor at EOC, a corresponding Haling distribution and the necessary infinite multiplication factor in each location of the core are obtained. The reactivity worth to be controlled by control rods and burnable poisons is found by taking the difference between the infinite multiplication factor distri­bution at BOC and the one necessary for the Haling distribution. The insertion location and depth of control rods are determined based on the difference. The insertion and withdrawn of control rods are actually discrete and the Haling distribution cannot be achieved strictly. The Haling distribution is, however, useful as a target plan for control rod operation.

A big advantage in using the Haling distribution for setting the control rod pattern is to be able to separately handle the fuel loading patterns over several cycles and the control rod pattern in the cycle of interest when the reactor is operated. In other words, when the fuel loading pattern is planned, the power distribution during reactor operation dose not need to be predicted based on a detailed control rod pattern, but is assumed to have a Haling distribution, in which the number of fresh fuel assemblies and the location change of reloading fuel assemblies are determined by evaluating the fuel burnup.

The nuclear design of the fuel assembly, namely, the design of the fuel enrichment zoning and burnable poison distribution in the fuel assembly, is optimized generally based on the fuel burnup distribution at an equilibrium cycle to exclude the singularity of a specific operating cycle. The Haling distribution has been used in design of the equilibrium cycle core and evalua­tion of fuel discharge burnup and required enrichment.

Burnable poison (burnable absorber) assemblies are constructed of boron — added absorber (borosilicate glass tube or Al2O3-B4C pellet) and corrosion — resistant cladding (stainless steel or zircaloy-4), as shown in Fig. 3.46.

Burnable poison rods are used to maintain a negative moderator temper­ature coefficient during reactor operation. As mentioned in the list [1](1) of Sect. 3.3.4, moderator temperature coefficients become less negative as soluble boron concentration increases. For a long cycle length, therefore, a high concentration of soluble boron to compensate for the excess reactivity may lead to a positive moderator temperature coefficient. Such an increase in soluble boron concentration should be restrained by using burnable poisons. From the viewpoint of reactivity control, thus, burnable poisons are used to compensate for a part of the excess reactivity corresponding to operating cycle length. The compensating reactivity amount depends on the operating cycle length and varies from 0 to 8 % Ak/k in the current operation. For a long cycle length, PWRs also adopt gadolinia-added fuel and the use of conventional burnable poisons is decreasing. Burnable poisons also play a role in flattening core radial power distribution by adjusting their location in the core.

D • Thimble Plug

: Burnable Poison Rod

Fig. 3.46 Burnable poison (burnable absorber) assembly of PWR (17 x 17 Type) [ ] (Copyright Mitsubishi Heavy Industries, Ltd., 2014 all rights reserved)

[1] Basic principles of thermal-hydraulic design

Thermal-hydraulic design of fast reactors is made so that the allowable thermal design limit is not exceeded at normal operation and abnormal operational occurrences and that fuel integrity is kept until the designed burnup. The basic principles are explained below.

Normal operation indicates the conditions where startup, shutdown, operation in power and refueling are intentionally carried out and the operational condition is within the limit. Anticipated operational occurrences indicate the conditions where the operation is disturbed due to a single failure of equipment or its malfunction, which are anticipated during its lifetime, or a single operator failure. A condition having similar frequency and leading to an unplanned state is also an anticipated operational occurrence. The allowable thermal design limit indicates the limit of allowing fuel damage for safety design and continuous operation of the nuclear reactor facility.

The basic principles of fast reactor thermal-hydraulic design are, at normal operation and anticipated operational occurrences: (i) prevent sodium from boiling and (ii) prevent fuel from reaching the allowable design limit.

Item (i) is followed because there is a possibility of positive reactivity insertion due to boiling and an excess increase in the fuel cladding temperature due to change in heat transfer characteristics. For satisfying the allowable thermal design limit, the maximum fuel centerline temperature and the fuel cladding temperature are limited from the viewpoint of thermal-hydraulic design. As for the maximum fuel centerline temperature, fuel melting is not allowed in the mainstream design in order to avoid failure of fuel cladding by excessive stress caused by thermal expansion of the fuel pellets. The design limit of the maximum fuel centerline temperature is determined by the melting limit test data with consideration of the design margin. As for the cladding temperature, the cladding temperature itself, which dominates the material properties, is limited instead of limiting the heat flux on the cladding surface because the heat transfer characteristic of sodium is better than that of water. For avoiding cladding failure by an increase in the cladding temperature for a short period at anticipated operational occurrences, the limit of maximum cladding temperature at anticipated operational occurrences is established. Stainless steel is generally used as the fuel cladding material of fast reactors. The limit of fuel cladding temperature at anticipated operational occurrences is determined based on out-of-pile rapid heat-up tests of irradiated target mate­rials. Since the internal pressure creep dominates the mechanical strength of the fuel cladding for ensuring fuel integrity until designed burnup, the limit of fuel cladding temperature at normal operation, which dominates the creep strength, is determined based on the creep test data of the target materials. This limit for sodium cooled reactors is set as 650-700 °C in many designs.

In the thermal-hydraulic design of fast reactors, the flow allocation among the fuel assemblies is provided according to the power distribution in order to satisfy the allowable design limits above and to efficiently remove the heat generated in the reactor. That is the important feature of fast reactors compared to LWRs.

In the burnup equations, the atomic number density N(r, t) and the neutron flux ф(~, t) are generally a function of space and time. Nuclear fuel does not uniformly burn at the location in actual nuclear reactors and neutron flux varies with time (neutron flux should be increased according to depletion of fissile nuclides to maintain a specified reactor power). For simplicity, the space-independent burnup equations are solved assuming a constant neutron flux with time.

In Eq. (1.1) for 235U, both sides are divided by N25 and this equation can be integrated from time 0 to t (separation of variables) to give Eq. (1.15).

N2Kt)=N2K0)e-^ (1.15)

As an example, the hypothetical case is considered for a pure 235U-fueled reactor operated at a constant neutron flux of 2.0 x 1014n/cm2s for 1 year. The depletion rate of 235U during the operation is calculated, using the cross section of Fig. 1.1, in the following.

Next, the burnup equation of 236U [Eq. (1.2)] is considered which can be solved in several ways. Here the term of N26(t) is transposed into the left-hand side and each term is multiplied by the integrating factor exp [сг%6фі] to obtain

JN26

Є °™фі +N2G{t) {of фе °™фі ) =<Tf0iV25 (t) e °™фі ot.

It should be noted that the left-hand side is a time-differentiated form of N26(t)exp [аТфі]. It follows therefore that

— IN26 (t) e =а2ЪфЫ2Ъ (t)e °™фі

dt.

Equation (1.16) is given by integrating both sides of the above expression from time 0 to t and substituting Eq. (1.15).

<r25

(1.16)

CJа (Уа

The burnup equations of 238U and 239Pu [Eqs. (1.5) and (1.14)] are identical to those of 235U and 236U. As a consequence, the solutions are given by the next expressions.

N2&(t)=N2S(0)e~a™*t (1.17)

sy 28

(1.18)

(7a (Ja

Continuing for the burnup equation of 240Pu, the term of N40(t) is transposed into the left-hand side and each term is multiplied by the integrating factor exp [аа°фь] to obtain

— IN40 (t) e =crc490iV49 (t) e а*°фі dt.

Equation (1.19) is obtained by integrating both sides of the above expression from time 0 to t and substituting Eq. (1.18).

Fig. 1.2 Depletion of 235U and buildup of Pu isotopes for a representative LWR fuel composition [4]

(1.19)

241 242

The same method can be applied to Pu, Pu, and the nuclides downstream in the burnup chain. Equations (1.17)—(1.19) can be perceived to have a regularity, and the general solution to them is known as the Bateman solution [3].

Figure 1.2 shows the depletion behavior of 235U and the production behavior of Pu isotopes for a representative LWR fuel. While 235U exponentially decreases, the neutron capture of U produces Pu, which in turn is converted by neutron capture into 240Pu and higher Pu isotopes. It is seen that the buildup of Pu isotopes is approaching an equilibrium state.

The function characterizing the energy dependence of neutron flux ф(г, E, t) is called the neutron spectrum and it varies with fuel enrichment, moderator density, void fraction, burnup, and so on. Figure 2.1 shows a neutron spectrum of a thermal reactor. The neutron spectrum of thermal reactors is divided into three distinct energy regions. In the high-energy region above 105 eV, since the prompt neutrons released by fission are dominant, the neutron spectrum is approximately

proportional to the fission spectrum x(E). In the energy region below several hundred of keV, the fast neutrons from fission lose their energies mainly through elastic scattering reaction with light moderator nuclides such as hydrogen.

According to neutron slowing-down theory [1], when fast neutron sources are in an infinite homogeneous medium which is an ideal moderator with negligible absorption, the neutron energy spectrum behaves as 1/E.

(2-6)

In the practical medium of fuel and moderator, the 1/E distribution is character­ized by the occurrence of fairly sharp depressions due to the resonance absorption of 238U, etc. as shown in Fig. 2.1. Moreover, if the resonance absorption is large, the neutron flux becomes somewhat smaller than the 1/E distribution in the low energy region.

If neutrons are moderated below several eV of kinetic energy, the kinetic energy by thermal vibration of nuclei cannot be ignored. In other words, if the kinetic energies of neutrons become appropriately small, the neutrons collide with ther­mally vibrating moderator nuclei and their kinetic energies become reversely large. This is called up-scattering against moderation (down-scattering). In this energy region, the neutron spectrum is characterized in a thermal equilibrium at a temper­ature T by a balance between down-scattering and up-scattering. Further, in the ideal infinite medium without absorption, the thermal equilibrium neutron spectrum is described by the following Maxwellian distribution function

(2.7)

where k is the Boltzmann constant. At room temperature (T = 300 K), фм is maximized at E = 0.0253 eV for which the corresponding velocity is 2,200 m/s.

On being absorbed, the thermal neutron spectrum deviates a little from фм (E) forward the high energy region because absorption cross sections are larger in lower energies. This is called absorption hardening. To compensate the Maxwellian distribution for the absorption hardening, neutron temperature, which is a little higher than moderator temperature, is used as T of Eq. (2.7).

The Boiling water reactor (BWR) concept was originally developed based on an early collaborative research between the General Electric Company (GE) and the ANL, and a series of the nuclear reactor experiments called the BORAX experi­ments. The first prototype BWR for electric power generation was Dresden Unit 1 (180 MWe) constructed near Chicago in 1960. The reactor was characterized by a dual cycle design of both direct and indirect cycles. After that, a forced circulation type of a single direct cycle has been used as a standard BWR design. The full-scale commercial BWR power plants began with Oyster Creek (650 MWe) which started operation in 1963. The GE also built an test reactor, Vallectios BWR (VBWR), in 1957 and used it in various improvements of BWR.

The first electricity from nuclear energy in Japan was generated by a 12.5 MWe — BWR, Japan Power Demonstration Reactor (JPDR), at the Japan Atomic Energy Institute (JAERI) in 1963. Later, the commercial BWRs started operation with Tsuruga Unit 1 (357 MWe) of the Japan Atomic Power Company in 1969 and Fukushima Daiichi Unit 1 (460 MWe) of the Tokyo Electric Power Company in 1970.

The history of BWR technology is summarized in Fig. 3.2 and Table 3.2. The main research and development of the BORAX series is shown in Table 3.3. In addition to USA and Japan, commercial BWRs are operated in Sweden, Germany, Mexico, India, etc.

[1] Fresh and spent fuel management [3]

Fuel management of nuclear power plants includes the tasks described next.

(1) Fresh fuel acquisition

Fuel assemblies manufactured in a nuclear fuel factory are transported to the power plant 3-4 months before the periodic inspection and then the acceptance inspection of fresh fuel is made to ensure there was no abnor­mality caused during the transport, and to confirm the fuel assembly appearance and size are as specified.

(2) Refueling during overhaul

Fresh fuel assemblies are stored in the fresh fuel storage after the accep­tance inspection and then moved to spent fuel storage pool before the periodic inspection. Alternatively, fresh fuel assemblies may be directly moved to the spent fuel storage pool after the acceptance inspection without being stored in fresh fuel storage.

In BWR refueling, usually not all fuel assemblies are moved to spent fuel storage pool as long as there is no large-scale construction in the core and reload fuel assemblies are shuffled in the core. Spent fuel assemblies are discharged to the spent fuel storage pool, and fresh fuel assemblies are loaded and shuffled in the core. After fuel loading, underwater TV cameras are used to confirm that the fuel assemblies are correctly loaded according to the fuel loading pattern.

The major features [37] of the Advanced PWR core design are the large-size core and introduction of neutron reflector in comparison with conventional PWRs. Table 3.13 summarizes the main core parameters of the Advanced PWR in comparison with the conventional 4-loop core. The core became large-sized, with 257 fuel assemblies. The radial power distribution oscillation by xenon should be noted with the enlargement of core, but such a large-size core still maintains the oscillation convergent.

Conventional 4-Coop PWR

Fig. 3.61 Structures of PWR reflector [38] (Copyright Mitsubishi Heavy Industries, Ltd., 2014 all rights reserved)

Another feature of the Advanced PWR core is the stainless steel neutron reflector installed around outmost fuel assemblies for improvement in neutron economy, reduction of neutron irradiation on the reactor vessel, and reduction in the number of parts by simplification of structures. The neutron reflector is constructed of stainless steel ring blocks piled up to eight stages, enclosing the fuel assemblies. Figure 3.61 depicts the neutron reflector structure in compar­ison with that of the conventional 4-loop core. While the conventional PWR had a stainless steel baffle and water in the reflector region outside core, the Advanced PWR introduces the stainless steel reflector and its cooling water which reduces the size of the water region and effectively reflects fast neutrons to the core inside without slowing down the neutrons.

Experiments in Japan using TCA, the light water critical assembly, have also confirmed that the steel reflector with the smaller sized water region gives excellent reactivity characteristics. In that experiment, the effect of the stainless steel reflector was estimated using iron reflector. The contribution of the iron

Fig. 3.62 Reactivity effect of reflector [38]

(Copyright Mitsubishi Heavy Industries, Ltd., 2014 all rights reserved)

• Measurement □ Calculation (PHOENIX-P) $ Calculation (MCNP) [Error Bar ± Sa]

20 40 60 80 100 120 140 160 180

Thickness of Iron Plate [mm]

reflector to reactivity was investigated with different thicknesses of the iron reflector installed at both ends of the fuel region with the 15 x 15 fuel rod arrangement. Figures 3.62 shows the result. It is seen that there is a reactivity gain of about 0.38 % Ak/k for the iron reflector thickness of about 150 mm. It is also noted that this gives a reactivity gain of about +1.8 % Ak/k from —1.4 % Ak/k at 22 mm in thickness. The 22 mm corresponds to the thickness of the stainless steel baffle. Thus, the experiments confirmed that the steel reflector reduces neutron leakage from core and significantly increases core reactivity.

The structure of the control rod is shown in Fig. 4.20. The “element” consists of B4C which is loaded in the refractory metal sleeve. The control rod (total length, about 3.1 m) is formed by axially connecting 10 elements using the connecting rod. The control rods are driven in pairs of two, and there are 16 pairs in total. The control rods is driven by hoisting the cable onto a drum using the control rod drive which is mounted in the stand pipe of the reactor pressure vessel. The control rods are inserted into the core from the top.

The reserve shutdown system is provided as backup to reactor shutdown system of the control rods. The reserve shut down system inserts negative reactivity into the core by dropping B4C pellets into the hole in the control rod guide column.

No optimization

Fuel temperature [ °С]

Fig. 4.21 Design of power distribution and fuel temperature distribution

In PWRs, the control rods for the 17 x 17 lattice fuel assembly are combined in clusters of 48 rods which are inserted from the top of the reactor vessel. Such a great number of rods with a relatively low reactivity worth keeps the neutron flux as
uniform as possible throughout the core. The control neutron absorber is an alloy of Ag-In-Cd, which features a somewhat weaker neutron absorption that produces less flux peaking and has a neutron absorption over a considerable range of neutron energies.

The control rods of BWRs consist of two crossed blades fitting into each corner between the fuel assemblies. The cruciform rods raise the surface-to-volume ratio of the control elements. Boron carbide (B4C) or hafnium (Hf) is employed as a control rod material. Hf loaded control rods absorb neutrons by resonance capture reactions of Hf isotopes. The control rods of BWRs are driven up from the bottom of the core. The bottom-entry arrangement makes the reactivity worth of control rods greater in the lower part of the core than in the upper part where the void ratio is high and the neutron spectrum is hard.

In fast reactors, the control assemblies composed of B4C rods, rather than the control rods inserted into fuel assemblies, replace some fuel assemblies in the core because the mean free path of neutrons is long.