The temperature coefficient aTp at fuel temperature TF is considered. The Doppler effect is shown through the resonance escape probability p and the fuel expansion effect is shown through f and p.

(1) Fuel temperature coefficient of resonance escape probability The resonance escape probability can be given by [14, 15]

(1.58)

where Nf and VF are the atomic density and volume fraction of the fuel, and Zm^sm and VM are the moderating power and volume fraction of the moderator. I is the resonance integral for the normalized moderated neutron flux which behaves as 1/E beyond the resonance, given by the following.

I =f <J„F (E) ф(Е)clE

An experimental formula [16] for the temperature dependence I of is known as

I ( Tf)=I(300K) [ 1+іЗ’Ш-М)]

/ (300K)=11.6+22.8 77- MF

238U02 : /Ґ’=61Х 10-4+47X 10-4-^7“

MF

232Th02 : /?"=97 X10-4+120 X 10-4

where TF is the fuel temperature (unit: K), and SF and MF are, respectively, the surface area (unit: cm2) and mass (unit: g) of the fuel element. Thus, the temperature dependence of I indeed shows the Doppler effect. That is, since the vibration of the nuclei increases with the fuel temperature, the relative velocity of the interacting neutron to the nucleus changes and hence the neutron energy range for the resonance reaction is broadened. Then, the Doppler effect mitigates the depression of the neutron flux due to large resonance absorption cross sections of a large amount of nuclides in the reactor (the energy self-shielding effect) and increases the resonance absorption reaction.

The temperature coefficient aTFDoppler) of the resonance escape probability p due to the Doppler effect can be obtained by differentiating I with TF as the following.

(1.61)

Since p < 1, ln(l/p) > 0 and a^Doppler) becomes negative. It can be noted that the magnitude of the absolute value is about 10_4-10_5^k/k/K.

Next, the effect of the fuel expansion is considered assuming the ratio of the fuel volume fraction is constant. Suppose that the fuel will axially expand causing a decrease in the fuel atomic density. The temperature coefficient of the atomic density can be represented by the coefficient of linear expansion as Eq. (1.62).

(1.62)

The linear expansion coefficient of a material in the cube of length l is generally defined as

Equation (1.62) is derived from the relation between axial length and atomic density

The temperature coefficient of the resonance escape probability due to the fuel expansion can be given by taking note of the variation in fuel atomic density due to a temperature change and by using Eq. (1.62) as

Since ln(1/p) > 0, aTFExpansion) is positive. The magnitude of the absolute value is small, about 10_5dk/k/K for a solid fuel. This shows physically that the decrease in the density of resonance nuclides leads to the increase in the resonance escape probability.

The diffusion equation of the eigenvalue problem by the one-group theory [Eq. (2.67)] can be extended to an equation based on the multi-group theory and its numerical solutions are discussed here.

In the eigenvalue problem of the multi-group theory, it is necessary to describe the fission source term (и£ф in the multi-group form as well as the loss and production terms due to the neutron slowing-down. Since the fission reaction occurs in all energy groups, the total production rate of fission neutrons in the unit volume is given by Eq. (2.70).

P=v’LfA<l>1+v’Lf,2<l>2+v’Lf,3<l)3—=%v’Zf. g<l>!i’ (2.70)

The probability that a fission neutron will be born with an energy in group g is given by

(2.71)

where x(E) is the fission neutron spectrum normalized to unity and therefore the sum ofxg is the same unity.

Xz»=l-0

Hence, the fission source of group g can be expressed as Eq. (2.73).

ХдЕ Хд^У^д’Фд’

g

For the three-group problem (fixed-source problem) of Fig. 2.20, replace­ment of the external source by the fission source is considered. If Sg is substituted by xgP/keff in Eqs. (2.57), (2.58), and (2.59), then the following diffusion equations are given for three-group eigenvalue problem:

9 X2P

Group 2: — D2V202 + (Га2ф2 + Г2->3Фг) = т— + ^і^2Фі

Keff

Group 3: — D3V203 + (£а, зФз)

7Г—- ^ і^зФі + ^г^гФі)

K-eff

where

P — vZf гфг + 202 + [4] [5]^/,303 (2.77)

In the three-group fixed-source problem, it was seen that the diffusion equations are solved in consecutive order from group 1. However, Eqs. (2.74), (2.75), and (2.76) have the fission source P which includes 01, 02, and 03, and moreover kef is unknown. Hence, iterative calculations are performed as the next sequence.

(i) Guess kf for kef, and 010), 020), and 03°for determining P. It is common

to begin with an initial guess of k^f = 1.0 and a flat distribution of the neutron fluxes (constant values).

(ii) Since neutron fluxes are relative and arbitrary values in eigenvalue problems, normalize the initial neutron fluxes to satisfy Eq. (2.78).

k{$ =fcore vZf. і фТ+vlLf, 2 (pf+vZf, з фТ<Ж (2.78)

Since fission source terms are divided by keff in eigenvalue diffusion equations, Eq. (2.78) indicates that the total neutron source in the system is normalized to a value of 1 to fit into the next diffusion equation.

(iii) Provide P(0) of Eq. (2.79) with the RHS of Eq. (2.80) and then solve this

for 011).

P(0) = v£/дф1(0) + v2>,20<o) + v2>>3^0) (2.79)

У p(°)

(2.80)

keff

Substitute again the solutions 0^ and 021) from Eqs. (2.80) and (2.81) for the RHS of Eq. (2.82) and then solve this for 031).

Y P

(2.82)

ke/f

(vi) Recalculate kejf by ф^, , and ф^ obtained in (iii) to (v) like

Eq. (2.83)

=fcore VLf, і фГ+ vXf, 2 (jW+v-Lf, з tffdV (2.83)

Here, keff is interpreted as the number of neutrons that will be born in the next generation finally, considering moderation and transport in the whole core, when assuming that one neutron is given as a fission source to the whole core. This is the definition of the effective multiplication factor.

Those solutions are not the correct ones yet because they are based on the initial guesses. The calculations from (iii) to (vi) are iteratively performed until keff and all of the group fluxes converge. This iterative calculation is known as the outer iteration calculation. The outer iteration test for convergence is done by comparing values at an iteration (n) with those at its previous iteration (n — 1):

where ek and Єф are the convergence criteria of the effective multiplication factor and neutron flux, respectively.

The relative neutron flux distribution ф^ (r) has absolute values due to the thermal power Q of the reactor. The normalization factor A of ф^ (r) to an absolute neutron flux distribution Og(r) can be determined by

Фд(г)=Афд(г) (2.86)

Q=Kfcore Zf-e ^ ФЄ ^dV=KAfcore ъг-и (r)dV (287)

where к is the energy released per fission (about 200 MeV). Finally, the absolute neutron flux distribution for the thermal power can be given as the following.

(2:88)

The distribution of the thermal power within the reactor core is

(2.89)

9

which is used as a heat source for the thermal-hydraulic calculation.

A general form of the multi-group diffusion equation in the case of the eigenvalue problem is given by Eq. (2.90), which can be solved in the same way considering the balance between neutron production and loss in group g as shown in Fig. 2.21. It is seen that Eqs. (2.74), (2.75), and (2.76) are also represented by the general form.

(2.90)

Cruciform control rods are employed for BWRs as shown in Fig. 3.14, and boron carbide (B4C) or hafnium is usually used as a neutron absorber. The control rods are inserted from the bottom of the reactor pressure vessel into the cruciform region formed between four fuel assemblies. There are two types of control rod drive mechanisms: hydraulic pressure piston drive and electric motor drive. Most of BWRs use the hydraulic pressure-driven system to move the control rods in 15.2 cm increments (one notch). The control rods in the advanced BWR (ABWR) design are driven in 1.8 cm increments (one step) by electric fine motion motors which make it possible to simultaneously move the maximum 26 control rod groups. For B4C control rods, stainless steel tubes, which are arranged in a blade sheath, are filled with B4C powder. For hafnium control rods, metal hafnium plates or rods are inserted into the sheath.

All control rods are inserted at reactor shutdown and control rods of about 5-10 % are inserted to control the excess reactivity during reactor operation at the rated power.

An inherent feature of power and reactivity control of BWRs is to control reactivity by changing the coolant flow rate in the core, which can be controlled by changing the pumping speed of the coolant recirculation pumps. BWR cores
have a coolant void and its value decreases as the coolant flow rate increases from the normal condition. Since the coolant also serves as a moderator in the core, the reduction in void fraction leads to a large effect on neutron moderation and results in progression of neutron spectrum softening. Therefore, the reactivity and reactor power increase. This leads to an increase in the void fraction again and results in an equilibrium state of the reactor power level corresponding to the void fraction at reactivity balance. On the other hand, a decrease in the coolant flow rate leads to a reactivity decrease and then the reactor power equilibrates at a lower level. Another feature of BWR cores is that the core power distribution hardly changes before and after a variation in core coolant flow rate.

This capability for reactivity control by coolant flow rate can be applied to compensate for the reactivity variation during reactor operation; fissile mate­rials are consumed and reactor power gradually drops with reactor operation. Control rods can be withdrawn little by little to maintain the reactor power and to control the reactivity, but it gives rise to a distortion of the core power distribution. The change in coolant flow rate makes it possible to control the reactivity without distorting the core power distribution and moreover change in coolant flow rate is relatively easy to implement.

Nuclear reactors are designed to have inherent characteristics of power suppression, namely, to have negative reactivity coefficients for temperature variation. There­fore, an excess reactivity to accommodate temperature variation is required to operate the reactor during a given cycle length. Reactors are designed to be shut down safely by properly controlling the excess reactivity.

[1] Reactivity Coefficients

PWR cores have almost no voids and therefore the void coefficient is not significant (only a small void fraction is assumed in evaluating shutdown margin in core design). Important reactivity coefficients in self-controllability of the reactor core are moderator temperature coefficient and Doppler coefficient.

(1) Moderator Temperature Coefficient

The moderator temperature coefficient is defined as a reactivity variation by the moderator temperature rise of 1 °C. In PWRs, water density decreases as moderator temperature increases, and reactivity varies correspondingly.

Boron in the moderator, used as a means of reactivity control, makes the moderator temperature coefficient less negative because the moderator temperature rise results in a decrease in boron concentration as well as water density. Figure 3.35 shows the dependence of the moderator temper­ature coefficient on boron concentration. A high boron concentration can cause a positive moderator temperature coefficient. Burnable poison rods and gadolinia-added fuel rods can be employed to lower boron concentra­tion and maintain a negative moderator temperature coefficient. Thus, reactor cores are designed to have a negative moderator coefficient during power operation and therefore a moderator temperature rise leads to the nuclear feedback to decrease reactivity.

Rod Cluster Control Assemblies insertion gives a more negative moder­ator temperature coefficient because neutrons with a longer mean free path due to the moderator temperature rise are more easily absorbed in control rods.

The moderator temperature coefficient shifts to more negative values with increasing burnup, as shown in Fig. 3.36. The main reason is the decline of critical boron concentration as burnup proceeds and the produc­tion of plutonium and FPs also contribute to the more negative moderator temperature coefficient as burnup proceeds.

[1] Design of fuel element

(1) Operating environment features for fast reactor fuel

Fast reactor fuel has a different operating environment from LWR fuel has. That difference needs to be considered in fuel design. As an example, general features and special points to note for consideration are summa­rized below for MOX fuel, which has acquired much operating experience as fast reactor fuel.

(a) High fast neutron flux and fast neutron exposure enhance swelling and creep deformation of the fuel clad and wrapper tube. Measures should be taken for them.

(b) High operating temperatures of coolant and materials lead to changes of the materials, and care should be taken for them, including especially corrosion-caused changes.

(c) The high pellet temperature of MOX fuel leads to significant restructuring of the pellet and increases the FP gas release rate.

(d) The temperature gradients in the radial and axial directions of the pellet are large causing cracking and relocation (slipping of the cracked pellet fragment), and also causing redistribution of the O/M (oxygen-metal ratio) and migration (movement inside the pellet) of plutonium and FPs such as cesium. Those pellet behaviors during irradiation should be taken into account in the design.

(e) High burnup enhances pellet swelling and FP gas release.

(f) Due to the high burnup and low coolant pressure compared to LWRs (especially PWRs), the fuel cladding internal pressure is higher than its external pressure. Thus, creep rupture of the fuel cladding by the high internal pressure is selected as the major failure mode of fast reactor fuel to be considered.

(2) Major design principles of fast reactor fuel element

Based on the above operating environment features, the major design

principles of the fast reactor fuel element are summarized as the following.

(a) The fuel element must not fail at normal operation and anticipated operational occurrences. Concretely, creep rupture by internal pressure is avoided and pellet cladding mechanical interaction (PCMI) is miti­gated. To avoid creep rupture by internal pressure, an adequate length of the gas plenum, optimization of the cladding thickness and limitation of the cladding temperature must be provided. For mitigating PCMI, optimization of the fuel density and adequate initial pellet-cladding gap must be provided.

(b) Cladding deformation must not be excessive. Since excess deformation of the cladding blocks the coolant flow path, deteriorating the cooling performance, the cladding deformation by swelling and creep needs to be kept small. For that purpose, the fuel internal pressure must be reduced as much as possible, materials with small swelling and creep must be used, and interaction between the fuel bundle and wrapper tube must be mitigated.

(c) Fuel pellets must not melt at anticipated operational occurrences. (It should be noted that most fast reactor fuel designs do not allow fuel melting even at design basis accidents.) A melting limit of linear heat rate based on power to melting experiments and an adequate design criterion must be set up.

(3) Structure of fast reactor fuel element

According to the design principles above, the structure of fast reactor core fuel element is outlined here. Many MOX pellets along with the depleted UO2 pellets as the axial blanket are inserted into a stainless steel fuel cladding. The plenum spring is inserted into the upper part of the fuel element to prevent the pellets from moving. The fuel element is sealed by welding the stainless steel end plugs into the top and bottom of the cladding. An adequate pellet-cladding initial gap is arranged and the gas plenum is provided, so that excess stress is avoided on the cladding or welds of the end plugs; this stress is due to the internal pressure of released FP gas and the cladding deformation caused by the difference of thermal expansion and swelling between the cladding and the pellet. Figure 4.3 showed the concept of the core fuel element.

In the blanket fuel element, many depleted UO2 pellets are inserted into the stainless steel fuel cladding. In order to increase the fuel volume fraction for high breeding ratio, the diameter of the blanket fuel element is a little bit larger than that of the core fuel element. The shape and structure of the blanket fuel element are almost the same as those of the core fuel element.

(4) Major evaluation items in fuel element design

(a) Evaluation of cumulative damage fraction (CDF)

FP gas accumulates with burnup of fuel and that increases the cladding internal pressure. CDF is the evaluation item of cladding integrity associated with creep rupture and is defined below.

(4-8)

t : Time

tR: Creep rupture time (time to creep rupture under constant tempera­ture and stress)

T: Cladding temperature a : Stress.

In the evaluation of CDF, cumulative fatigue fraction by thermal transients is added.

According to the definition of CDF, the fuel element ruptures when CDF reaches 1.0. In the design, the CDF limit is set taking an adequate margin to 1.0. Fuel integrity is assessed by ensuring that the evaluated CDF, considering various uncertainties, is below the limit.

(b) Evaluation of melting limit of linear heat rate and fuel temperature In order to avoid fuel melting, the melting limit of the linear heat rate is identified by power to melting experiments. Based on the melting limit, the allowable design limit of the linear heat rate is set by considering various uncertainties and the operational overpower coefficient (ratio of the scram setpoint and rated power). In the core neutronics design,

By integrating this equation,

dT r2 rkTr+c> T=c‘

(4.10)

is obtained. By providing the boundary conditions as

dT at r = 0 (pellet center), T dr

Ts at r = Rs (pellet surface)

C1 = 0 is obtained. By integrating Eq. (4.10),

(4.11) is obtained. By integrating from the pellet surface to the pellet center and assuming T = T0 at r = 0,

/Тт;к(т)сіт=^-я

(4.12)

is obtained. By using, x = QnRs2 the relation between the power density and the linear heat rate is written as Eq. (4.13).

X=4xf£k(.T)dT

(4.13)

X : Linear heat rate k : Thermal conductivity of fuel pellet T : Temperature T0: Pellet centerline temperature Ts: Pellet surface temperature

The maximum fuel centerline temperature is estimated for normal operation and overpower conditions based on the cladding inner sur­face temperature and using the heat transfer coefficient between the pellet and cladding (gap conductance) and the thermal conductivity of the fuel pellet. In the case of overpower condition, the overpower coefficient is applied.

The gap conductance used for fuel design is based on irradiation test results from experimental reactors in Japan and overseas. The empirical correlations of the pellet thermal conductivity have been prepared by researchers in Japan and overseas as well. The thermal conductivity of MOX pellet, which has extensive operating experience as fast reactor fuel, is arranged as a function of the pellet density, O/M ratio and temperature.

It is known from the irradiation data that the MOX pellet structure is changed by irradiation under high temperature and high heat flux conditions. After being irradiated at high temperature, the internally fabricated pores in the pellet move towards the fuel center which has the peak temperature, so that the structure inside the pellet changes from that at the time of fabrication. In the post-irradiation examinations of fuel pellets which had been irradiated at high temperature, the following features have been observed: an unchanged region remained at the external layer of the pellet; an equiaxial crystal region was present inside the unchanged layer; a columnar crystal region existed inside the equiaxial crystal region; and a void was formed at the pellet center. The temperatures at the boundaries between the two regions and the densities of those structures have also been evaluated by post­irradiation examinations.

In the fuel element design, those data and correlations are installed into the fuel temperature evaluation model. The fuel temperature is calculated by solving the thermal conduction equation in consideration of the fuel restructuring.

It is convenient to begin with the multi-group diffusion equation in a steady state.

(1.84)

Dg diffusion coefficient in energy group g

Ъ1д: macroscopic total cross section in group g

£sg’g: macroscopic scattering cross section from group g’ to group g

v: average number of neutrons released per fission

ILfg. macroscopic fission cross section in group g

Xg. fission spectrum in group g

фд. neutron flux in group g

k: effective multiplication factor

Equation (1.84) can be represented in the matrix form expanded in the energy group as

(1.85)

where the matrix elements of M and F, and the elements of vector ф are given by the followings.

(1.86)

Wgg^XgVg’Zfg’ (1-87)

(Ф)д = Фд (1-88)

Since M and F are matrices and the former includes differential operators, the

product order is not commutative. M and F are called the operators on ф and the effective multiplication factor k is called the eigenvalue.

The inner product between two arbitrary functions / and g which are vectors in the energy group is defined as

(Л д>Ліії(?)д,(г)<і*г (1-89)

9

where fg denotes the complex conjugate of fg. Since physical quantities used in nuclear reactor physics are normally real numbers, the complex conjugate need not actually to be considered (although necessary in mathematics).

The inner product to define the operator M{ adjoint to the operator M is used as Eq. (1.90).

(MV, g) = (J, Mg) (1.90)

The adjoint operator of F can be defined in the same way.

In general, there is a corresponding solution ф{ (the adjoint neutron flux) to the adjoint equation

(1.91)

Here, it is noted that the eigenvalue is the same as that in Eq. (1.85). This can be found as the following. First, Eq. (1.91) is written as

(Ю

The inner product of Eq. (1.85) is taken with the adjoint flux ф{ as

From the definition of the adjoint operator in Eq. (1.90), the following is given.

(MVf- 0)=НгЧрУ. )

ft

Applying Eq. (Й0 to the left-hand side gives

-^-(FV, ф)=± )

and it is found that k = k{*. Since the eigenvalue in the multi-group diffusion equation is a real number, k = k{, therefore it is evident that the eigenvalue in Eq. (1.85) agrees with that in its adjoint equation.

Next, it is necessary to discuss some characteristics of the adjoint operator. An inner product for one-group macroscopic cross section can be written as

if, !g)=/vf*I, gd3r=fvil, f)*gd3r = (‘Zf, g) (1-92)

It is found that = £ and thus the operator and its adjoint operator are identical. Such operators are said to be self-adjoint.

Then, the spatial derivatives in the leakage term of the multi-group diffusion equation are considered, that is,

where the Integration by Parts formula was used to move the operand function of the differential operator from g to /. The first term on the right-hand side can be converted into an integral over the surface using Gauss’ theorem. Since the func­tions / and g are regarded as zero on the surface, the surface integral vanishes. Repeating this procedure for the second term gives

if, ^•D%’>=-/v(^f*>D%dar

=-fvV — [( Vf*)Dg]d

=fvtf-D^f)*gd3r = (V-DVf, g) .

V • DV and thus the leakage term is also self-adjoint.

From Eqs. (1.92) and (1.93), it is apparent that the operators in the static one-group diffusion equation are self-adjoint. In the one-group theory, the diffusion equation and adjoint equation are identical, namely, the neutron flux and its adjoint flux are identical except for the normalization factor.

Not being self-adjoint is encountered in multi-group operators or the time differential operators, that is,

(1.94)

where T implies the transpose matrix. Equation (1.94) is derived in the following. Since the time differential operators are out of the scope of this book, the references [23—25] should be consulted for Eq. (1.95).

The relation between the multi-group operator M and its adjoint operator M{, which meets the definition of the adjoint operator in Eq. (1.90), can be determined to find Eq. (1.94). It can be readily expressed with the matrix elements in energy group. Disregarding the spatial dependence of the operators for simplicity, the right-hand side of Eq. (1.90) is rewritten as

(Л Mflf)=2 f* (M 9=lfg*Mgg gg’ =£ f’Yg,

9 9,9 9, 9′

and the left-hand side is rewritten as

(му, g)=1j(M Y)^ =ЪШ}„ feTg,■

9 9,9 .

Hence,

м},=м*я- мг=мг*.

The matrix elements of the adjoint operators M{ and F{ are concretely represented by the next two equations.

№)gg — = И • Dj + Ztg)8gg’ — Zsgg. (1.96)

Wgg^VahgXg’ (1.97)

As mentioned above, the multi-group diffusion equation was represented in the form of a matrix and the adjoint operators were introduced. These are very useful in deriving the perturbation theory to calculate reactivity changes.

LOCA analysis is composed of two parts: blowdown phase and reflood phase. As an example of SCWR, the blowdown analysis model is shown in Fig. 2.47 in which valves and systems able to simulate cold-leg break and hot-leg break are implemented into the abnormal transient and accident analysis model of Fig. 2.46.

The reflood phase can be analyzed by modeling the LPCI in the calculation code as shown in Fig. 2.48. In the practical analysis of plant safety, general — purpose codes are used to describe more detailed models and to calculate the blowdown and reflood phases as one body.

Stretch types of power uprates can be typically introduced up to around 7 % of the original licensed power levels without major plant modification by using conservative measures built into the plant.

(2) Extended type

Extended types of power uprates can increase the original rated thermal power by up to 20 % with high performance fuel, but require significant modifications to major plant machinery such as the steam turbine and main electric generator.

The following effects are expected in BWR power uprates.

• Nuclear and thermal margin (core and fuel)

• Neutron flux increase (reactor vessel)

• Decay heat increase (containment vessel)

• Steam flow rate increase (turbine system)

• Load factor increase (turbine system and electric generator)

• Turbine exhaust heat increase (condenser)

• Condenser flow rate increase (feedwater pipe and feedwater heater)

Those effects of power uprates have been evaluated as to whether they are allowable within the design criteria or not, considering reactor operation and maintenance experience and operation data. The range of improvements and facility modifications are determined based on the evaluation results.

As discussed before, the fuel lattice design of BWRs is easily changed. An increase in the number of fuel rods is one of the leading core and fuel technologies to secure the nuclear and thermal margin in uprating reactor power and to improve plant economy. As using a large number of fuel rods improves critical power characteristics and reduces average linear heat gener­ation rate of fuel rods, therefore a lattice design with more rods can be applied to a high burnup long-operating cycle core and a high power density core.

On the other hand, it causes an increase in pressure drop within a fuel assembly and reduces thermal-hydraulic stability. Hence, a practical 10 x 10 type fuel has been introduced coupled with measures against the pressure drop such as partial length fuel rod.

Negative power coefficients keep the PWR cores stable against core power oscillation. The stability of PWR cores is focused on the core power spatial oscillation induced by xenon, which tends to become larger and gives a less convergence for a larger core and a flatter power distribution.

(1) Radial Power Distribution Oscillation

A radial power distribution oscillation may occur by abnormal operation of rod cluster control assemblies (for example, only one rod cluster control assembly works in an abnormality). Core equivalent diameter is smaller than one causing an oscillation divergence and the radial power distribution oscillation has an inherent convergence feature due to the feedback effect of moderator temperature coefficient. Therefore, it is not necessary to suppress the radial power distribution oscillation which can be continu­ously monitored and detected by quadrant core power tilt (a symmetry index of core four-quadrant powers) through the coolant outlet temperature distribution and ex-core neutron detectors.

4.2.1 Overview

The technologies of the high temperature gas-cooled reactors (HTGRs) are based on the designs and operating experiences with Magnox reactors and Advanced Gas-cooled Reactors (AGRs). In AGRs, the outlet coolant temperature could not be elevated due to chemical reaction of the CO2 coolant with the graphite structures. Thus, helium gas having high chemical stability is adopted as the coolant of the HTGRs, which enables high reactor outlet coolant temperature. Various gas-cooled reactors are compared in Table 4.5 [18—20]. Since metals could not be used as the fuel clad under the high temperature condition, coated particle fuel using ceramics coating was developed [21]. The coated particle fuel consists of spherical fuel kernels coated with pyrolytic carbon (PyC) and SiC. Utilization of the helium

Table 4.5 Compassion of various gas-cooled reactors Magnox reactor (COo cooled reactor) Advanced gas—cooled reactor (AGR) High-temperature gas-cooled reactor (HTGR) Gas-cooled fast reactor PWR as reference Reactor Tokai NPP unit 1 Hinkley Point-B THTR-300 Conceptual design by JAEA Ooi NPP unit 1 etc (587 MWt) [19] (1,500 MWt) [19] (750 MWt) [19] (2,400 MWt) [20] (3,411 MWt) [21] Moderator Graphite Graphite Graphite Light water Coolant C02 gas C02 gas Helium gas Helium gas Light water Fuel Metal natural uranium (with Magnox alloy clad) UOo (with stainless steel clad) Coated particle fuel Pin type nitride fuel UOo (with Ziocaloy-4 clad) Reactor outlet coolant temperature (°С) 390 665 750 850 320 Power density (W/cm3) 0.8 2.7 6 100 Bumup (GWd/t) 3.6 18 100 150 44

Graphite block Graphite sleeve lAPP’ 60,0m hei8ht)

Coated fuel particle (Multiple coating by ceramics)

Block type HTGR

HTTR. GTMHR

‘uel kerne!

Helium gat as coolant

Pebble ball fuel (App. 60mm diameter)

Fig. 4.15 Fuel of HTGRs gas coolant and development of the coated particle fuel have enabled high reactor outlet coolant temperatures of nearly 1,000 °C to be reached. One characteristic of the HTGRs in terms of reactor physics is that the conversion ratio of fissile nuclei can be high due to the small absorption cross sections of the helium gas coolant and the graphite moderator. The high performance of the coated particle fuel against release of FPs, as well as the high conversion ratio, enables high burnup more than 100GWd/t.

The HTGRs are categorized as the pebble-bed type and the block type according to the fuel configuration. In the pebble bed type HTGRs, coated particle fuels are mixed with graphite powder. The mixture is formed as spherical fuel balls, each with a diameter of 6 cm. The reactor core is formed by disorderly piling up many fuel balls. The unique characteristic of pebble bed type HTGRs is the capability for continuous refueling during operation. The coolant flows in gaps around the fuel balls. The block type HTGRs use hexagonal block type fuel. The reactor core is formed by piling up blocks in the axial direction. Refueling is carried out by the refueling machine during shutdown period. Fuel configurations of those HTGRs are shown in Fig. 4.15. The specifications of constructed HTGRs are summarized in Table 4.6 [22].

The pebble bed type HTGRs, namely, the Arbeitsgemeinschaft Versuchsreaktor (AVR) [23] and Thorium Hochtemperature Reaktor (THTR-300) [24] were constructed in Germany. The THTR-300 was a prototype power reactor. The Hochtemperature Reaktor 10 MW (HTR-10) [25] was constructed in China as an experimental pebble bed type HTGR. In the Republic of South Africa, construction of the Pebble Bed Modular Reactor (PBMR) [26], which is a modular type HTGR with an annular core, was planned.

Table 4.6 Constructed HTGRs Reactor Dragon Peach bottom AVR Fort St. Vrain THTR-300 HTTR HTR-10 Country UK (OECD) USA Germany USA Germany Japan China Operation period 1964-1976 1966-1974 1966-1988 1974-1989 1983-1989 1998- 2000- Reactor power (MWt/MWe) 20/- 144/42 46/15 842/342 750/308 30/- 10/2.5 Core diameter (m) 1.1 2.8 3.0 6.0 5.6 2.3 1.8 Core height (m) 1.6 2.3 2.5 4.8 6.0 2.9 2.0 Average core power density (W/cm3) 14 8.3 2.5 6.3 6 2.5 2 Fuel kernel uo2 (Th, U)C2 (Th, U)C2 (Th, U)C2 (Th, U)C2 uo2 uo2 (Zr, U)C uo2 ThC2 (Th, U)C Fuel type Rod Rod Pebble ball Block (Multi-hole) Pebble ball Block (Pin-in-block) Pebble ball Core inlet coolant temperature (°С) 350 340 270 408 250 395 250 Reactor outlet coolant Temperature (°С) 750 725 950 785 750 850/950 700 Coolant pressure (MPa) 2 2.4 1.1 4.8 4 4 3

The block type HTGRs, namely, Fort St. Vrain (FSV) [27] in the US and the High Temperature Engineering Test Reactor (HTTR) in Japan were constructed. The HTTR has a thermal power of 30 MW and reactor outlet coolant temperature of 950 °C [28—30]. Its fuel type is the so-called pin-in-block type which is composed of fuel rods and a hexagonal graphite block (Fig. 4.15). The fuel rods are composed of fuel compacts loaded in a graphite sleeve. The fuel compacts are formed by mixing coated particle fuel with graphite powder. The major specifica­tions of the HTTR are summarized in Table 4.7.

Since the reactor outlet coolant of LWRs is around 300 °C, their utilization is limited, namely, for electric power generation. On the other hand, helium gas having high chemical stability is used as the coolant for HTGRs and high reactor outlet temperature around 1,000 °C is possible, which enables high generating efficiency and utilization of HTGRs as a heat source particularly in the chemical industry. Thus, one of the HTGR advantages is its multi-purpose utilizations of nuclear energy.

Here, the core design of the HTTR is presented as an example of HTGRs. Also, the annular core design is described since it is noteworthy from the viewpoint of inherent safety.