The 135Xe buildup occurs when a reactor is brought to a low power level as well as at shutdown and then the 135Xe concentration begins to decrease soon, or vice versa, when the power level is increased. This is called the “Xe transient” which is characterized by times of the order of about 8 h [9] and therefore it should be controlled properly.

In a large power reactor, local changes in the power distribution by such factors as control rod movement can lead to spatial oscillations even though the reactor power is kept constant. In the region of increased power density, 135Xe burns out more rapidly and then its concentration decreases. This decrease leads to a higher reac­tivity in this region, which, in turn, leads to an increased neutron flux. This again leads to a more increased power density in this region. Meanwhile, in the region of decreased power density, the 135Xe concentration increases due to its reduced burnup. This increased concentration decreases the local reactivity, which reduces the neutron flux, in turn, decreasing the local power density again. In a short time, however, the decreased 135Xe concentration begins to increase and contrarily the increased concentration begins to decrease. In this way, the local power continues to oscillate between different regions. Calculations show that these oscillations have a period from about 15-30 h. Actually this type of oscillation is easily controlled in practical reactor operations by negative reactivity feedback (moderator void coeffi­cient and Doppler coefficient) and a procedure of control rod movement.

[1] Purpose of lattice calculation

Even using a high performance computer, a direct core calculation with several tens of thousands of fuel pins is difficult to perform in its heterogeneous geometry model form, using fine-groups (e. g., 107 groups in SRAC) of a prepared reactor constant library. The Monte Carlo method can handle such a core calculation, but it is not easy to obtain enough accuracy for a local calculation or small reactivity because of accompanying statistical errors. Hence, the Monte Carlo method is not employed for nuclear design calculations requiring a fast calculation time. Instead, the nuclear design calculation is performed in two steps: lattice calculation in a two-dimensional (2D) infinite arrangement of fuel rods or assemblies and core calculation in a three­dimensional (3D) whole core. The lattice calculation prepares few-group homogenized cross sections which maintain the important energy dependence (neutron spectrum) of nuclear reactions, as shown in Fig. 2.8, and this reduces the core calculation cost in terms of time and memory. Since final design parameters in the core calculation are not concerned with the energy depen­dence, the spatial dependence such as for the power distribution is important.

Nuclear reactors and their related systems have to be operated stably against various perturbations. Fluctuations in reactor power due to fluid flow characteristics and reactivity feedback, or some factors related to characteristics of reactor control systems can obstruct stable operation of the reactors. Returning to the original stable state is essential against those perturbations. As kinds of stability required in BWR core design, there are channel stability (thermal-hydraulic stability) against flow vibration caused by a pressure drop feedback in the flow path, core and regional stability against power oscillation caused by the nuclear feedback of thermal — hydraulic properties and void reactivity, plant stability for sufficiently stable control of plants, and Xe stability (Xe spatial oscillation stability) against power oscillation caused by the accumulation and destruction of FP Xe. The channel stability, core stability, and regional stability are particularly important for BWRs with a large variation in coolant density in the core.

As an indicator of stability evaluation, the decay ratio, which is defined as the ratio between the initial and the next oscillation amplitudes, charac­terizes the extent of oscillation amplitude of a watched parameter by a perturbation. The fundamental design criterion is decay ratio <1 for chan­nel stability, core stability, regional stability, and plant stability in all reactor operating conditions. A decay ratio less than 1 (e. g., 0.25) is set for core stability and plant stability during normal operation for a margin to the design criterion.

Characteristics such as pressure drop in the core flow path and void reactivity feedback have a large effect on the above stabilities. Overall, the stability against perturbations can be secured by setting these charac­teristics as a fixed range. The Xe spatial oscillation can be suppressed by designing a negative power coefficient less than a fixed value.

In relation to the mechanical design of reactor core elements other than the main criteria of the BWR core design mentioned above, the endurance of core structure materials is necessary against high-level radiation doses and high temperatures and pressures. The reactor pressure vessel should

also be able to withstand high pressures, high temperatures and radiation doses during the reactor operating period (e. g., 30-60 years). Mechanical design criteria are set for the reactor core elements.

The fuel pool cooling cleanup system has a function to remove decay heat from spent fuel in the heat exchanger and the fuel cooling pool, and to desalt/filter pool water and maintain water purity and transparency. The fuel pool cooling cleanup system is designed to keep pool water tempera­ture below 52 °C in the case of the usual maximum heat load which is defined as the sum of two different decay heats: one is from the discharged spent fuel in one refueling when closing the pool gate which separates the reactor well and fuel pool and the other is from the previously discharged spent fuel. Also, the system should have sufficient cooling performance to maintain the pool water temperature below 65 °C, in combination with residual heat removal system, in the case of maximum heat load which is defined as the sum of two different decay heats: one is from the whole core at the end of cycle and the other is from the previously discharged spent fuel.

The spent fuel pit cooling and purification system has a function to remove decay heat from spent fuel stored in the spent fuel pit and to remove solid and ion impurities in the spent fuel pit water, purifying it. Spent fuel pit pump, spent fuel pit cooler, and spent fuel pit demineralizer and filter are installed as well. Two spent fuel pit coolers operate to maintain the average temperature of the spent fuel pit water below 52 °C in the case that all fuel assemblies in the core are discharged and stored in the spent fuel pit in which spent fuel assemblies discharged from the previous cycles are already stored. Even operation with one spent fuel pit pump can maintain the average temperature of spent fuel pit water below 65 °C.

Exercises of Chapter 3

1. Give an overview of improvements for advanced standardization of LWRs from 1975 to 1985 in Japan.

2. Refer to the specifications (Tables 3.7 and 3.8) of high burnup 8 x 8 fuel (Step II). Determine size specifications of the fuel and water rods in the 10 x 10 fuel assembly to meet the conditions below.

• No change in channel box size

• The same fuel loading weight as Step II fuel

• Non-boiling region area inside the water rod is equal to or larger than Step II fuel.

Main specifications of high burnup 8 x 8 fuel (Step II): channel box inner width, 134 mm; number of fuel rods, 60; cladding outer diameter, 12.3 mm; cladding thickness, 0.86 mm; cladding inner diameter, 10.58 mm; pellet diam­eter, 10.4 mm; water rod inner diameter, 32 mm; inner cross-sectional area of channel box, about 179.3 cm2.

3. Calculate the following items for a BWR of 26.2 MWth/tU specific power.

(a) Cycle burnup at a cycle length of 12 months and load factor of 100 %.

(b) Core average burnup at the end of the equilibrium cycle for a discharge burnup of 45 GWd/t under the above fuel conditions.

(c) Achievable discharge burnup within the linear reactivity model for an extended cycle length to 15 months under the above fuel conditions.

4. Answer the following questions on reactivity control of a BWR in normal operation.

(a) Explain burnup reactivity control of the BWR.

(b) Set a typical void reactivity coefficient for the BWR and calculate the amount of reactivity control when the void fraction of the core is changed by5 % using core flow rate control.

(c) Explain the control rod position adjustment and core flow rate control during the cycle operation for the excess reactivity with cycle burnup as given in the figure below.

Explain challenges and measures in core design for high burnup based on the transition of design specifications of BWR fuel assembly.

Calculate the core average burnup at the end of the equilibrium cycle of the standard 3-loop PWR assuming a constant power with burnup under the follow­ing conditions.

Core thermal power: 2,652 MW Number of fuel assemblies in the core: 157 Initial uranium weight per assembly: 460 kg Number of fresh fuel assemblies: 60 Equilibrium cycle length: 413 days (full power)

7. Discuss design feasibility of a PWR core without soluble boron in the primary coolant for reactivity control.

8. Consider a PWR in hot full power normal operation with 700 ppm boron concentration in the primary coolant as shown in Fig. 3.38. The PWR was instantly put into hot shutdown. Calculate the boron concentration necessary for achieving criticality at the following times after shutdown, while maintaining the hot temperature.

(a) 8 h

(b) 20 h

(c) 90 h

9. Discuss measures against positive moderator temperature coefficients for the following two cases.

(a) In the process of reload core design, the moderator temperature coefficient for a fuel loading pattern was +2 pcm/°C at BOC and hot zero power. How many burnable poison rods are necessary to make the moderator temperature coef­ficient negative? Assume that the dependence of moderator temperature coef­ficient on boron concentration is the same as that in Fig. 3.35 and a burnable poison rod can reduce the critical boron concentration by about 0.5 ppm.

(b) For startup after refueling, the moderator temperature coefficient was measured as +2 pcm/°C at hot zero power. What operational limitations are available to make the moderator temperature coefficient negative at hot zero power? Refer to Figs. 3.45 and 3.42 for boron worth and control rod worth, respectively.

In the thermohydraulic design of the HTTR (see Fig. 4.26), the fuel temperature is calculated based on the power distribution from the nuclear design, the primary coolant flow rate, the engineering hot spot factors and the geometry of the fuel block.

The core components such as the fuel blocks, replaceable reflector blocks and control rod guide blocks have different heat generation. The fuel blocks also have different powers according to their uranium enrichment and loading position. Thus, the adequate core coolant flow rate which directly contributes to cooling the fuel is ensured. The coolant is distributed to each fuel block to keep the maximum fuel temperature as low as possible during normal operation.

[1] Thermohydraulic design codes

The thermohydraulic design consists of the flow distribution calculation and the resulting fuel temperature calculation (see Fig. 4.26). Since the HTTR core is formed by piling up the hexagonal graphite blocks, it is necessary in the fuel temperature calculation to consider not only the coolant flow in the cooling hole which directly contributes to cooling the fuel but also the coolant flow not directly contributing to fuel cooling such as the horizontal cross flow between the piled blocks, the gap flow between the columns, etc.

(1) Flow distribution calculation

The FLOWNET code [47] based on the flow network model is used for the flow distribution calculation. The coolant flow paths in the core are modeled as channels having equivalent length, area and hydraulic diameter. The flow channels are connected by equivalent paths of thermal conduc­tivity. The channel data and heat transfer coefficient, etc. which have been measured beforehand by the hydraulic tests with the same scale as the actual core are conservatively corrected and adopted to the calculation.

The 1/6 core is modeled in the flow distribution calculation by consid­ering the symmetry of the core [28]. The radial and axial flow network models are shown in Fig. 4.37. A column is modeled as a single flow channel. The flow channels including the gap flow paths are connected by horizontal flow paths and thermal conduction. The graphite blocks shrink due to neutron irradiation, which is taken into account for the gap size.

(2) Fuel temperature calculation

The fuel temperature is calculated based on the power distribution from the nuclear design and the coolant flow distribution from the flow distribution calculation considering the thermal conductivity of the fuel blocks and the engineering hot spot factors [48, 49]. The fuel temperature analysis code TEMDIM [50] is used. The core is represented by multi cylindrical chan­nels, and the 2D temperature distribution and thermal deformation of each channel are calculated. Finally, the maximum fuel temperature is obtained by considering the engineering hot spot factors.

The calculation model of fuel rod is a cylindrical model which consists of fuel compacts, the gap between the fuel compact and the graphite sleeve,

Fig. 4.37 Calculation model for coolant flow distribution in core

Graphite block

Graphite sleeve

Radiation heat transfer

Fuel compact

Fig. 4.38 Fuel temperature calculation model

the graphite sleeve, the coolant flow paths and the graphite block as shown in Fig. 4.38. The fuel rod is divided by radial and axial meshes. The power distribution from the nuclear design is corrected by considering the local power peaking and used for the fuel temperature calculation.

The nominal maximum fuel temperature is calculated based on the power distribution from the nuclear design and the coolant flow distribu­tion. Based on this nominal temperature, the systematic maximum fuel temperature is evaluated using the engineering hot spot factors i. e. the random factors and the systematic factors [51]. The thermohydraulic design
must be made so that the systematic maximum fuel temperature does not exceed the allowable design limit (1,495 °C) for normal operation as introduced in the list [4] of Sect. 4.2.2.

The fuel temperature at any position is obtained by adding the temper­ature rises of each component to the inlet coolant temperature. Thus, the nominal temperature TN of an arbitrary position is calculated as:

5

(4.27)

i = l

where

Tin : Core inlet coolant temperature (° c)

ATiN : Norminal temperature rise (°C)

1 = 1: Coolant

2 : Flim

3 : Sleeve

4 : Gap

5 : Fuel compact

The evaluated maximum fuel temperature is the maximum value of the systematic fuel temperature. The systematic fuel temperature is obtained based on the nominal temperature rises ATiN, at an arbitrary burnup step and arbitrary region of interest (entire core or each column) considering the engineering hot spot factors, as shown in Eq. (4.28).

(4.28)

where

Tf : Systematic fuel temprature (° C)

ATi: Temperature rise considering engineering hot spot factors (° C) fs : Systematic factors associated with fuel rod n : Number of systematic factors fR : Random factors associated with fuel rod m : Number of random factor

The maximum fuel temperature at an arbitrary burnup step and arbitrary region of interest is evaluated by Eq. (4.29) based on the systematic temperature:

Tmax = Max {Tf)

where

Tmax: Maximum fuel temperature (° C)