Chapter 1

1. The bumup equations of U and Pu can be given by

dN25(t)

dt

=а™фЫ2а-ai9<pNi9 it)

dNi9(t)

dt

For an initial condition of N49(0) = 0, the atomic densities of 235U and 239Pu are obtained as

!V26(O=iV26(0)e-o’”!,<

(Graph skip)

2. The production and destruction equations of 135I and 135Xe after changing neutron flux to ф1 can be solved by using the equilibrium-state solutions at neutron flux ф0 as initial conditions. The atomic densities of 135I and 135Xe can be obtained as

I (0=-^^{фое~ы+ф1(1— е~ыУ

Ai

Х(О=(П + 7-)і:^0 е-^Л^Ф^^Г^ЇХ^фі (1_в-дд+5^^) Лхе + (УаЄфо ЛХе + <УаЄфі

_І_ У/^(0і~0о) (^е-аХе^фі)і_еГхІі^

Ххе ^ <Уа Єфі~^І

where t represents time after the neutron flux change.

(Graph skip)

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

3. Skip

4. Skip

5.

By the one-group first-order perturbation theory

The perturbation parts can be expressed in terms of temperature coefficient as 8Ъг=^гЛТ=Ъг(аад1-^-Ъв^ЛТ

sz—(0+W)AT-{z:ac, i-+z-(-^-si>)}jT

where в is the linear expansion coefficient of the medium, and Tn = aT is assumed (Tn is the neutron temperature and T is the medium temperature). Substituting them into the reactivity expression gives

where the criticality condition

is used.

Chapter 2

1. (a) Express atomic or molecular mass, density, and atomic number density as M, p (g/cm3), N (#/cm3) respectively. 235U enrichment (wt%) can be calculated as

(1.1)

According to Eq. (1.1), N(235U): N(238U) = 1: 29.868, namely, the 235U enrichment is 3.24 atm%.

M(U) = 0.324 x M(235U) + (1 — 0.324) x M(238U) = 237.075 M(UO2) = M(U) + 2 x M(O) = 269.075

N(U) = N(UO2) = p(UO2)/M(UO2) x Na

= 10.4/269.075 x (0.6022 x 1024) = 2.320 x 1022atoms/cm3

N(235U) = N(U) x 3.24/100 = 7.516 x 1020atoms/cm3

N(235U) = N(U) x (1 — 3.24/100) = 2.245 x 1022atoms/cm3 N(O) = N(U) x 2 = 4.640 x 1022atoms/cm3

(b) I (UO2) = N (235 U) (ja (235U) + N(238U)ffa(238U) + N(O)aa (O)

= (7.516 x 1020) x (50 x 10-24) + (2.245 x 1022) x (1.0 x 10-24) + (4.640 x 1022) x (0.0025 x 10-24)

= 6.014 x 10-2 cm-1

If (UO2) = N(235U)o/ (235U) + N(238U)o/ (238U)

= (7.516 x 1020) x (41 x 10-2) + (2.245 x 1022) x (0.1 x 10-24)

= 3.306 x 10-2cm-1

The probability that a neutron absorbed in pellet fissions, Pf, can be given by

Pf = If (UO2)/Ia(UO2) = (3.306 x 10-2)/(6.014 x 10-2)

= 0.55 = 55%

(c) The mass of metal uranium included in a pellet, w(U) can be calculated as

p(U) = N(235U)/NA x M(235U) + N(238U)/Na x M(238U)

= 9.167g/cm3

w(U) = p(U) x VP (pellet volume)

= 9.167 x (3.1416 x (0.81/2)2 x 1.0) = 4.72g = 4.72 x 10-6ton

InitialUraniumMassIncludedinaFuelAssembly = w(U) x 366 x 265 = 0.46ton Uranium Loading Amount in Core (Metal Uranium Mass) = 0.46 x 193 = 88 ton

(d) Since the pellet length is 1 cm, the linear power of fuel rod q’ (W/cm) is equal to energy released from a pellet. Therefore,

q = Klf (UO2 )фУр

= (200 x 1.602 x 10“13) x (3.306 x 10“2) x (3.2 x 1014) x 0.515 = 175 W/pellet = 175 W/cm

Since w(U) = 4.72 x 10 6 ton/pellet,

Specific Power = (175 W/pellet)/(4.72 x 10“6ton/pellet) = 3.70 x 107W/ton = 37MW/ton

(e) Since burnup is a time integral of specific power,

Burnup = (36.0 x 285) А (41.0 x 290) А (38.0 x 280) = 32800MWd/ton

(f) Total heat generation of pellet is,

Burnup 32,800 MWd/ton x w(U) = 32800 x (4.72 x 10“6) ton/pellet = 0.155 MWd = 1.34 x 1010 J.

The heat generation by uranium (235U and 238U) fission is

1.34 x 1010J x 2/3 = 8.92 x 109 J.

Since the heat release per fission is 200 x (1.602 x 10“ 13) J/fission, Total number of uranium fission is 8.92 x 109/(200 x 1.602 x 10“13) = 2.78 x 1020fission.

The number of 235U fission is X If(235U)/<ZK235U)+Z/-(238U)} =(2.78X 102°)x0.932 =2.60 XlO20 fission

235

(Total number of uranium fission)

Since the amount of 235U decreases by other reactions such as the (n, y) reaction, the number of 235U absorption reaction is calculated as

Number of 235U absorption = (Total number of 235U fissions) x Za(235U)/X/-(235U)

=(2.60 X102°)X 1.22 =3.17 XlO20

which can be converted to 235U mass as (3.17 x 1020)/NA x M (235U) = 0.12 g.

Therefore, 235U decreased by about 0.12 g in a pellet of 32,800 MWd/t burnup.

2. For example, for N = 4,

аф0 А Ьф1 А аф2 = S аф1 А Ьф2 А афъ = S аф2 А Ъфъ А аф4 = S ф0 = ф1 (Left boundary condition) ф4 = 0.0 (Right boundary condition)

where

Substitution of d/2 = 200 cm, D = 1.0 cm, = 2.5 x 10 4 cm l, S0 = 1.0 x 10_3 atoms/cm2s gives the following neutron flux distribution.

3. (a) Considering upscattering (£2!1) as zero,

Thermal group : — D2 F202+Xa,202 = ^2^Vl^1^1+V2^2^2^ +ъ1_+2ф1

keff

(b) For infinite medium, leakage is zero. x1 = 1, x2 = 0.0 give

keff

Sa,2 Ф2 = ^1!2 Ф1 which can be rewritten as

10i+v2X/, 2 02 Total Production Rate

Xa, i0i+^a,2 02 Total Absorption Rate

УіХ/-д + У2Х/-;2(Х i-»2/Xa>2)

2o. l + 2l-

4. Assuming the atomic densities of 135I and with burnup time can be given by

dN1

dt

UXeJr(j$e0)NXe

where Л1 and AXe are the decay constants and Ф is one-group collapsed neutron flux.

Assuming Ф > AXe/^Xe = 7 x 1012 n/cm2s, NXe can be expressed as

Assuming ol0 « 0, the equilibrium atomic densities are obtained as

Chapter 3

1. The advanced standardization of LWRs has had the goal of improvements in reliability and availability, and reduction in exposure of radiation workers.

The first stage of advanced standardization in Japan took place from 1975 to 1977. In BWRs, there were improvements in the shape of the containment vessel head, security of maintenance space such as for the main steam isolation valve, and workability. Efforts were also made for reliability improvement by measures against stress corrosion cracking, automation of in-service inspection (ISI), and more efficient inspection (using remote and automatic techniques). In PWRs, high tensile strength steel for the containment vessel and the prestressed con­crete containment vessel (PCCV) were developed. As a measure against fuel rod bowing for reliability improvement, the number of fuel rod grid spacers was increased from 8 to 9. The eddy current technique was developed to measure leakage from steam generator tubes, and improvements in its inspection accu­racy and efficiency were made.

The second stage of advanced standardization was implemented from 1978 to 1980. There were improvements in operation and maintenance, efficient and regular inspections, and reduction in exposure of radiation workers.

The third stage was carried out from 1981 to 1985. The goals dealt with load following, longer cycle length, core performance improvements, more compact plant size, and shorter construction time. ABWRs and APWRs were developed. Internal pump, improved control rod drive mechanism, reinforced concrete containment vessel, high burnup fuel, and large-size turbine were developed and adopted in ABWRs.

The table presents an overview of the advanced standardization plan of LWRs.

Previous plant (800 and 1,100 MW class) First advanced standard plant (800 and 1,100 MW class) Second advanced standard plant (800 and 1,100 MW class) Third advanced standard plant (1,300 and 1,500 MW class) Improvements BWR PWR Availability factor Depends on plant ~75 % ~80 % SSC-resistant material Fuel improvement (against fuel bowing) Capacity factor Depends on plant ~70 % ~75 % ~80 % Core design improvement Steam generator improvement Regular inspection period 90-100 days ~85 days ~75 days ~50 days Automatic replacement of control rod Drive mechanism Improvement of fuel handling machine Development of integrated reactor vessel head material Improvement of fuel inspection system Worker exposure (100 %) ~75 % ~50 % ~40 % Pipes and components Introduction of automatic ISI of pipes Cobalt-free materials Containment improvement Development of steam generator, Manipulator, mounter Improvement of Nozzle cap for steam generator water chamber Source: Department of Nuclear Power Plant (1999) Agency for Natural Resources and Energy: nuclear handbook, 385

2. Calculation examples of 10 x 10 fuel specifications are as follows.

(a) Size Specifications of Water Rod

An approximate fuel rod pitch of 10 x 10 fuel assembly: 134/10 = 13.4 mm. In the case that four rods are replaced with a large- diameter water rod in the same way of Step II fuel, if the water rod outer diameter and thickness are set as 26 mm, which is twice of the fuel rod arrangement, and 1.5 mm respectively, the cross-sectional area in two water rods is 2 x (23)2 x n/4 = 831 mm2. Thus, a non-boiling region larger than that of Step II fuel can be secured within channel box.

(b) Fuel Rod Specifications

The number of fuel rods becomes 92 excluding eight fuel rods which were replaced with two water rods.

The cross-sectional area of pellets in 60 fuel rods at Step II fuel can be obtained as

Spellet = n x (10.4)2/4 x 60 = 5097 mm2

To maintain the same fuel inventory as Step II fuel, the pellet diameter will be

Pellet Diameter = (4Spellet/92/n)1/2 = 8.40mm

The cladding inner diameter will be given by applying the same gap between pellet and cladding as 0.18 mm of Step II fuel as

Cladding Inner Diameter = 8.40 + 0.18 = 8.58mm

Assuming the cladding thickness as 0.65 mm to maintain the same ratio between cladding thickness and cladding inner diameter, the cladding outer diameter will be

Cladding Outer Diameter = 8.58 + 2 x 0.65 = 9.88 mm

(c) Non-Boiling Region Area within Channel Box

Cross-sectional area of fuel rods and water rods within channel box is

= 92 x (9.88)2 x n/4 + 2 x (26)2 x n/4 = 8115 mm2 Cross-sectional area of non-boiling region within channel box is = 179.3 — 81.1 = 98.1cm2 which is almost the same as 99 cm2 of Step II fuel.

3. (a) Cycle Burnup = (Specific Power) x (Cycle Length) x Load Factor

Bc(12) = 26.2 x 365 x 1.0 = 9563MWd/t = 9.563GWd/t

(b) For cycle length = 12 months and discharge burnup = 45 GWd/t, the fuel batch size is given by

n(12) = 45 ^ 9.563 = 4.7056

The core average burnup BEOC can be calculated by the following equation

BEOC = (2n — [n]) x ([n] + 1) x Bc/2n Substituting Bc(12) and the integer part of n(12) gives BEOC = (2 x 4.70 — 4) x 5 x 9.563/(2 x 4.70) = 27.5GWd/t

(c) For cycle length = 15 months, the cycle burnup Bc(15) is given by

Bc(15) = Bc(12) x (15/12) = 11.95GWd/t

In the linear reactivity model, the sum of cycle length and discharge burnup has a constant relation in using the same fuel. Therefore, the dis­charge burnup Bd(15) can be given by

Bd(15) = (Bd(12) + Bc(12)) — Bc(15) = 42.6GWd/t

The fuel batch size n(15) becomes 3.56. Such a prolongation of operation cycle length with the same fuel decreases the discharge burnup.

4. (a) In BWRs, burnup reactivity decline is compensated by burnable poison

(gadolinia) addition, core flow rate control, and control rod operation. Most of the burnup reactivity is controlled by burnable poison (gadolinia) added to pellets. The concentration of gadolinia is designed to be depleted out at EOC for fuel economy. Since BWR cores have negative void reactivity coefficients, the burnup reactivity decline can be compensated by changing the pumping speed of coolant recirculation pumps and increasing the core flow rate, namely, reducing the core void fraction, and by control rod operation as well. From the viewpoint of fuel econ­omy, generally all control rods are designed to be withdrawn at EOC.

(b) In ABWRs, since the core average void fraction is about 40 %, the void reactivity coefficient at the end of equilibrium cycle is about —8 x 10—4 Ak/k/% void fraction. Therefore, change of the void fraction to 5 % gives a reactivity variation of about 4 x 10—3 Ak/k.

(c) At BOC, the excess reactivity is controlled by control rod insertion at a core flow rate slightly lower than the rated one. Since the excess reactivity tends to increase during the first half of the operating cycle, the core flow rate is mainly reduced without moving control rods. When the core flow rate exceeds the range of the flow control, it is recovered by inserting control rods. Since the core reactivity tends to decrease during the latter half of the operating cycle, the core flow rate is increased by adjusting the recirculation flow rate and control rods are withdrawn when the core flow rate exceeds the range of the flow control.

Figure Core flow rate and control rod position adjustment for reactivity control 5. Main challenges for high burnup:

(a) Nuclear characteristics are changed as fuel enrichment increases; these changes include neutron spectrum hardening, more negative void reactivity coefficient, and control rod worth reduction.

(b) At high burnup, the reactivity difference between fuel assemblies loaded in the core becomes large and mismatch of the fuel assembly power increases. As fuel enrichment increases, since the number of gadolinia-added fuel rods increases to control the excess reactivity, the local power peaking of a fuel assembly increases and the fuel linear heat generation rate increases.

(c) The internal pressure of cladding increases.

(d) The corrosion amount of cladding increases with increase in neutron irradi­ation and residence time in the core.

Countermeasures:

(i) Increase in number and size of water rods

As a countermeasure for (a), H/U ratio increase and neutron spectrum softening are general countermeasures. Specially, the number of water rods has been increased to enlarge the non-boiling water region within a channel box and the arrangement of large-diameter water rods and the water channel has been implemented.

(ii) Increase in number of fuel rods

As a countermeasure for (b) and (c), an increase in the number of fuel rods is a general countermeasure. Fuel assemblies of 7 x 7, 8 x 8, and 9 x 9 designs have been implemented and the lattice arrangement has also been changed.

(iii) Improvement in corrosion resistance

As a countermeasure for (d), more easily fabricated high corrosion — resistant claddings with better composition have been developed and put into practical use.

(iv) Reduction in pressure drop of fuel assembly

From the viewpoint of fuel economy, items (i) and (ii) without reduction in fuel inventory cause an increase in pressure drop of a fuel assembly. Such an increased pressure drop leads to an increase in coolant pump capacity and less stability, so countermeasures against pressure drop are important. The designs of spacer and top tie plate of low pressure drop, and the use of a partial-length fuel rod have been implemented.

6. The cycle burnup at equilibrium cycle can be calculated as

2625/(0.46 x 157) x 413 = 15170MWd/t

The fuel assembly average burnup can be given by

1 Cycle Burned Fuel: 60 assemblies, 15,170 MWd/t

2 Cycle Burned Fuel: 60 assemblies, 15,170 x 2 MWd/t

3 Cycle Burned Fuel: 37 assemblies, 15,170 x 3MWd/t

Therefore, the core average burnup at the end of equilibrium cycle is given by

(15170 x 60 + 15170 x 2 x 60 + 15170 x 3 x 37)/(60 + 60 + 37)

= 28100 MWd/t

7. Since the reactivity control by soluble boron in the primary coolant causes waste production, it is desirable that a core design with no use of soluble boron is realized to reduce waste. An idea is that the soluble boron is not to be used during normal operation, and to be used only for backup shutdown. Therefore, the following roles currently taken by soluble boron are needed to be substituted by other means.

(i) Reactivity variation from cold to hot temperature: about 6 %Лк/к

(ii) Reactivity decline during operating cycle: about 10 %Лк/к or more

(iii) Xe reactivity (maximum after shutdown): about 6 %Лк/к

As an alternative way for reactivity control, roles (i) and (iii) can be done by using control rods, and role (ii) can be done with gadolinia or burnable poison.

(a) Reactivity Controllability Enhancement of Control Rods

Reactivity controllability enhancement of control rods by about 12 % Ak/k for (i) and (iii) is necessary which corresponds to three times as much as the current design. Two measures could be applied. One is to enhance the absorption capability of neutron absorbers and the other is to increase the number of rod cluster control assembies. In the former, even enriched 10B — containing B4C does not attain twice the reactivity of the current Ag-In-Cd absorber. In the latter, the number of control rod clusters can be increased by a maximum 50 % due to limitation of the current design of the control rod drive mechanism (to increase more, development of a small control rod drive mechanism is needed). Thus, the reactivity controllability can be enchanced at most to twice as much as the current one even applying both measures. Therfore, it is also necessary to reduce the reactivity required for (i) and (iii). But, to realize the reduction, we have to considerably reduce the moderator — to-fuel volume ratio. However, since such a reduction in moderator-to-fuel volume ratio causes a reduction in control rod worth, it is necessary to get a balance between both.

(b) Excess Reactivity Controllability Enhancement by Gadolinia

The number of gadolinia-added fuel rods and fuel assemblies can be increased to control total reactivity corresponding to (ii). However, this is not practically easy because it gives rise to a deterioration of the power distribution. Numerous gadolinia-added fuel cause a higher power increase in high power fuel at early period of burnup because the reactivity increases further as burnup progresses at early period of burnup. This behavior is remarkable in the axial power distribution. The power variation goes into reverse as the burnup proceeds to some extent and then it leads to an oscillation in the axial power distribution as burnup progresses.

Thus, it is quite hard not to use soluble boron. In other words, it is recognized once again that the reactivity control by soluble boron is power­ful and superior. By the way, the reactor of the nuclear power ship “Mutsu” was designed to use only control rods without soluble boron. Its control rods were not the cluster type but the cruciform type. The excess reactivity was smaller than that of conventional power plants and the power peaking factor was higher.

8. As shown in Fig. 3.38, the reactor can be controlled only by control rods until hot shutdown. Since the hot temperature condition is maintained for a while after shutdown, the reactivity varies mostly by accumulation and decay of Xe and its variation is compensated by adjusting the boron concentration. After the adjust­ment of the boron concentration, the criticality is generally attained by control rod withdrawal.

(i) 8 h later

The accumulation of Xe peaks and the reactivity of Xe increases (i. e. the reactivity of core decreases) by about 3 %Ak/k (= 3,000 pcm) at 8 h after shutdown. The boron concentration is to be reduced by correspondingly

converting this reactivity (dilution). According to Fig. 3.45, the conversion is about 7 pcm/ppm. The boron concentration is diluted as 3,000/ 7«430 ppm. It is noted that the limit of the dilution speed is 10 ppm/min or so, and further the speed becomes slower at low boron concentration. Therefore, it is necessary to start the dilution considerably before the expected criticality time.

20 h later

Accumulation of Xe is over, and it is back to almost the concentration at full power equilibrium (namely, the concentration at shutdown). Therefore, it is not necessary to adjust the boron concentration.

(iii) 90 h later

Xenon is almost gone, having decreased by about 3 % Ak/k since shut­down. In other words, the boron concentration should be increased by about 430 ppm in the opposite direction to (i).

9. (i) As shown in Fig. 3.35, the boron concentration decrease by 120 ppm is required to move the moderator temperature coefficient to a more negative value by 2 pcm/°C. To realize that, the fuel loading pattern should be re-designed by additionally using 240 burnable poison rods. For example, 12 fuel assemblies containing 20 burnable poison rods can be prepared. However, the increase of 120 burnable poison rods leads to an increase in reactivity penalty at EOC by about 20 ppm (converted value to the soluble boron concentration). It is required to achieve the given cycle length con­sidering the reactivity penalty.

(ii) The same as in (i), it is necessary to reduce the boron concentration by 120 ppm which is compensated by control rods insertion. The boron worth at BOC is about 7 pcm/ppm from Fig. 3.45. Therefore, the reactivity of 120 x 7 = 840 pcm should be suppressed by control rod insertion. In Fig. 3.42, it corresponds to the insertion of control bank D to 50 steps (178 steps for control bank C). In other words, the moderator temperature coefficient can be maintained as negative at hot zero power if control bank D is restricted not to be withdrawn above 50 steps.

Chapter 4

1. Calculate the number of fuel assemblies from core thermal power as

TotalLengthofFuelElements (L) = 2 500 x 106 x 0.92 ^ 230 Number of Fuel Elements (Nel) = L ^ 100 Number of Fuel Assemblies (Na) = Nel + 271

Table 1 Number of assemblies of each layer in hexagonal arrangement Layer number Number of assemblies Cumulative number of assemblies 1 1 1 2 6 7 3 12 19 4 18 37 5 24 61 6 30 91 7 36 127 8 42 169 9 48 217 10 54 271 11 60 331 12 66 397 13 72 469 14 78 547 15 84 631 16 90 721

Then, the number of fuel assemblies is 369.

■ Guess the number of control rods (finally determined by evaluating control rod

worth)

Set the number of control rods as a multiple of 6 or 3, considering usual symmetric arrangement of control rods. The number of control rods-to-fuel assemblies ratio of 7-10 % gives 30 or 36 control rods. From the viewpoint of control rods cost, the smaller number of control rods is the first candidate.

■ Guess core arrangement

Take 397 or 403 fuel and control rod assemblies as a multiple of 6 + 1. Divide the core into two almost equal volume regions and arrange the fuel assemblies. Consider a symmetric arrangement of control rods for power distribution flattening and place as many of the control rods in the inner core region as possible to increase their reactivity worth.

Table 1 shows the cumulative number of fuel assemblies per each layer when the fuel assemblies are placed in a hexagonal arrangement. Since the control rods are arranged in the inner core region, construct the inner core region using 217 fuel assemblies until the ninth layer and the outer core region with 180 fuel assemblies until the 12th layer. Figure 1 shows the arrangement of assemblies. Consider a uniform and symmetric distribution of 30 control rods. Figure 2 shows a core layout with control rods.

In the core design, the core characteristics (such as power distribution, control rod worth, and reactivity coefficients) are iteratively evaluated by changing the

Fig. 1 Arrangement of assemblies

Fig. 2 Example of core layout (1,000 MWe)

core layout and finally the core layout for achieving the design targets are determined.

2. Calculate the fuel loading amount (W) as

„„ / Cladding Inner Diameter V „ .

W= к (———————————— I XHcXNeXNaXpsX Heavy Metal Fraction

= 38.78 t

Compute the burnup as

BU = Q x Core Power Fraction x D x Nb/W = 12.99 x 10[8] = 130GWd/t

3. The relation of pellet temperature, linear power, and thermal conductivity can be

given by

where

X: Linear power k: Thermal conductivity T: Temperature

T0: Fuel centerline temperature TS: Fuel surface temperature

Assuming a constant thermal conductivity, then

Therefore, the pellet centerline temperature is calculated as 2,285 0C by 4

[1] Coolant temperature coefficient

Since the moderator also serves as a coolant in LWRs, the coolant temperature coefficient is identical to the moderator temperature coefficient. In thermal reactors with different moderator and coolant materials such as graphite­moderated reactors, the coolant temperature coefficient is separately used. As mentioned before, the moderator temperature coefficient in thermal reactors is determined by the net effect of both the negative and positive temperature coefficients of p and f, respectively. In thermal reactors with a separate moderator material, since coolant expansion does not lead to a sufficient reduction in the neutron moderating power, it should be noted that the positive effect of f may become dominant for the coolant temperature coefficient.

[2]106)

Jvvi:f(.r)<p4r)d3r

The reactivity change in the perturbation theory is expressed with the neutron flux and its adjoint flux operating to cause the change in the macroscopic cross sections. The product of the neutron flux and the change in the macroscopic cross sections represents the change in reactor rate. The adjoint neutron flux is interpreted to be multiplied as an importance. This physical interpretation of the adjoint flux can be clearly made in considering a time-dependent problem. For more details, the references [23—25] should be consulted.

[3] Most practical codes of the finite difference method take neutron fluxes at the center points of divided meshes [13]. A simple and easy to understand method was employed here.

[4] Substitute the solution of Eq. (2.80), 0^, for the second term in the RHS

of Eq. (2.81) and then solve this for 02^.

[6] For simplicity, it is assumed that %dig = xg which is reasonable for the two-group problem.

[7] Shibata K et al (2011) JENDL-4.0: a new library for nuclear science and engineering. J Nucl Sci Tech 48:1

[8] The constituent components of fast reactor cores are characterized by fuel assemblies, blanket assemblies, control rod assemblies, and the radial shieldings, all of which produce quite different heats. For effective heat removal, it is necessary to distribute coolant flow rate adequately for each core component corresponding to each heat generation. The coolant flow allocation with no waste flow leads to a high core outlet temperature and high thermal efficiency and contributes to reduction in power generation cost.

In the thermal limitations of the fast reactor core thermal-hydraulic design, there are limits for fuel and cladding temperatures. While the fuel temperature is influenced by linear power of fuel, the cladding temperature is strongly depen­dent on coolant temperature. For a core flow allocation of fast reactors, therefore, coolant flow rate should be distributed to maintain the maximum cladding temperatures under the design limits for fuel and blanket assemblies at the rated core power. For a design of coolant flow allocation, fuel assemblies requiring nearly equal coolant flow should be classified into same flow allocation group and the number of core flow regions should be minimized in order to avoid complicated coolant flow control mechanism.