The design of a fuel channel for SCWRs is an arduous undertaking due to high operating temperatures, which require materials that withstand temperatures as high as 625°C under normal operating conditions. In contrast, current materials, which withstand such design temperatures, have high absorption cross-sections for thermal neutrons. Consequently, a fuel-channel design must address the limitations due to material options to allow for maximum performance using available materials. AECL has proposed several fuel-channel designs for SCWRs. These fuel-channel designs can be classified into two categories: direct — flow and re-entrant channel concepts, which will be described in Sections 4.1 and 4.2. It should be noted that a re-entrant fuel-channel concept was developed by Russian scientists and was utilized at Unit 1 of the Beloyarskaya NPP in the 1960s (Saltanov et al., 2009).

The work processes have been simulated by the SIMULINK of MATLAB software and all responses such as oscillation and transient responses have been analyzed by it as well. The main function (F) is Fcn. It includes two other functions that are: u[1] and u[2] which are defined for SIMULINK. u[1] is one of two input functions of Mux that has been shown by the input block that is: H. This block is presenting amount of the Keff. u[2] equals with amount of the feedback which has been sampled as follows: x(t).

Thus:

Because of the control rod movement is steady, in order to calculate the total amount of the discrete movements of control rod, the Discrete-time Integrator block has been used. The Fcn produced function has been transferred to Zero-Order Hold block which plays logic converter role. In addition the Transport Delay block is related to the inherent delay time that is: tD. The parameters which must be adjusted are: Set Point that is: the default amount of Keff as reference K, ff and the meaning of the Set Point=100 is: K, ff=1, the velocity of control rod (v), recent Kgff (block H) and the stop time that is: the innate delay time or tD. The graphs can be observed by the oscilloscope.

While atomistic methods can probe the primary damage state with great detail, they can also be used to probe the interactions of the defects formed with the underlying microstructure. An example is the case of creep due to irradiation in materials. Creep of metals and alloys under irradiation has been the subject of many experimental and theoretical studies for more than 30 years. Although a vast amount of knowledge of irradiation creep has accumulated, the database on irradiation creep comes from many relatively small experiments, and there were often differences in experimental conditions from one study to the next. Theoretical models are based on linear elasticity. Among the many theories that exist to describe the driving force for irradiation creep, the most important are the SIPN, SIPA, and SIPA-AD effects.

Stress Induced Preferential Nucleation of loops (SIPN) is based on the idea that the application of external stress will result in an increased number of dislocation loops nucleating on planes of preferred orientations. Interstitial loops will tend to be oriented perpendicular to the applied tensile stress, while vacancy loops will prefer to be oriented parallel to the stress. The net result is elongation of the solid in the direction of applied stress. While there is some experimental support of this theory, it is thought that it cannot account fully for creep seen in materials.

An alternative theory is Stress Induced Preferential Absorption/Attraction (SIPA). The essential idea behind SIPA is that interstitials are preferentially absorbed by dislocations of particular orientations, resulting in climb; this is described by an elastic interaction between the stress fields of the defect and dislocation. A variant on SIPA that accounts for anistropic diffusion is SIPA-AD. This theory uses the full diffusion equations, derived by Dederichs and Schroeder (1978), to take into account anisotropic stress fields. Savino and Tome developed this theory and found that it generally gives a larger contribution to dislocation climb than the original SIPA (Tome, Cecatto et al.). A thorough review of many dislocation creep models was prepared by Matthews and Finnis (1988).

These models go a long way towards explaining irradiation creep due to dislocations. However, all models based on linear elasticity break down near a dislocation core due to the 1/r terms in the stress and strain field expressions. Atomistic calculations do not suffer from this problem, so they can be used to verify the range of validity of theoretical expressions and successfully predict true behavior at the core.

Molecular statics calculations can be performed in order to understand the interactions between vacancies and interstitials and line dislocations in bcc iron. These can be compared to similar results given by dipole tensor calculations based in linear elasticity theory. Results from two methods are used to calculate the interaction energy between a dislocation and a point defects in bcc iron are compared. For vacancies and a variety of self-interstitial dumbbell configurations near both edge and screw dislocation cores, there are significant differences between direct calculations and atomistics. For vacancies some interaction is seen with both edge and screw dislocations where none is predicted. Results for interstitials tended to have a strong dependence on orientation and position about the core. Particularly for the screw, continuum theory misses the tri-fold splitting of the dislocation core which has a large influence on atomistic results.

Fig. 4d. Final position of the dislocation with the interstitial absorbed in the core

Figures 4a-d shows the evolution of a defect in the vicinity of the dislocation. In this example an interstitial is positioned near a dislocation core and the energy of the system is minimized. The interstitial moves into the dislocation core and forms an extended jog in the dislocation core structure. Such a process is not captured by linear elasticity calculations which fail to capture the core structure and the core-defect interactions.

The relationship between crystal plasticity and dislocation behavior in materials has motivated a wide range of experimental and computational studies of dislocation behavior (Vitek 1976; Osetsky, Bacon et al. 1999). Computational studies of dislocation activity can be performed at several different length and time scales. In some cases, a multi-scale modeling approach is adopted(Ghoniem et al. 2003). Core properties and atomic mechanisms are simulated using first principles calculations and molecular dynamics simulations. These results can be used to form the rules that govern large-scale Dislocation Dynamics (DD) simulations (Wen et al. 2005) that account for the activity of a large number of dislocation segments. Polycrystalline plasticity models are then developed that utilize the information at the atomistic scale to parameterize partial differential equations of rate dependent viscoplasticity(Deo, Tom et al. 2008). While understanding dislocation creep processes, dislocation climb rates and hence, the interaction of dislocations with point defects is an important quantity to be calculated. Here, we show how the dislocation core affects the interaction energy between the dislocation and the point defect using both linear elasticity as well as atomistic calculations.

The relationship between the irradiation time and the calculated specific 99Mo generation (generated 99Mo activity per 1 g of molybdenum) is shown in Fig. 3. When the irradiation time is 6 days (144 h), the specific 99Mo generation is 0.286 TBq/g-Mo as shown in Fig. 3.

Irradiation time (h)

Fig. 3. Relationship between irradiation time and specific 99Mo generation

Using the specific 99Mo generation of 0.286 TBq/g-Mo, 99Mo production rates are estimated. In the case using the aqueous (NH4)6Mo7O24-4H2O solution as the irradiation target,

(99Mo production in the case using the aqueous (NH4)6Mo7O24-4H2O solution)

= 372.8 g x 0.286 TBq/g-Mo = 106.6 TBq = 2,881.9 Ci

In the case using the aqueous K2MoO4 solution as the irradiation target,

(99Mo production in the case using the aqueous K2MoO4 solution)

= 702.7 g x 0.286 TBq/g-Mo = 201.0 TBq = 5,431.7 Ci

Here, the dilution effect by the unirradiated aqueous molybdate solution and the decay time of 99Mo from the generation to the shipment are considered. It is assumed that the volume of the aqueous molybdate solution in the capsule and the pipes in the irradiation system and the supply and circulation system of the 99Mo production system is about 2,500 cm3 and that the time from the post-irradiation to the shipment is one day. After one day, 99Mo decays to 0.78 times. Time from the irradiation to the shipment is one week. The 99Mo production rates at the shipment are estimated as follows:

(99Mo shipping activity in the case using the aqueous (NH4)6Mo7O24-4H2O solution)

= 2,881.9 Ci x 1,663/2,500 x 0.78 = 1,495.3 Ci/w

(99Mo shipping activity in the case using the aqueous K2MoO4 solution)

= 5,431.7 Ci x 1,663/2,500 x 0.78 = 2818.3 Ci/w

The 99Mo production rate in the case using the aqueous K2MoO4 solution is about twice compared with that in the case using the aqueous (NH4)6Mo7O24-4H2O solution. It is a distinct advantage of the aqueous K2MoO4 solution. However, in order to aim to provide 100% of the 99Mo (5,000 Ci/w) imported into Japan and to increase the production rate, some ideas such as the concentration of 98Mo are needed.

In order to calculate the fuel centerline temperature, steady-state one-dimensional heat- transfer analysis was conducted. The MATLAB and NIST REFPROP software were used for programming and retrieving thermophysical properties of a light-water coolant, respectively. First, the heated length of the fuel channel was divided into small segments of one-millimeter lengths. Second, the temperature profile of the coolant was calculated. Third, sheath-outer and inner surface temperatures were calculated. Fourth, the heat transfer through the gap between the sheath and the fuel was determined and used to calculate the outer surface temperature of the fuel. Finally, the temperature of the fuel in the radial and axial directions was calculated. It should be noted that the radius of the fuel pellet was divided into 20 segments. The results will be presented for fuel-sheath gap widths of zero, 20 ^m and 36 ^m. Moreover, the fuel centerline temperature profiles have been calculated based on a no-gap condition in order to determine the effect of gap conductance on the fuel centerline temperature. Figure 12 illustrates the methodology based on which fuel centerline temperature was calculated. The following section provides more information about each step shown in Fig. 12.

As shown in Fig. 12, the convective heat transfer between the sheath and the coolant is the only heat transfer mode which has been taken directly into consideration. In radiative heat transfer, energy is transferred in the form of electromagnetic waves. Unlike convection and conduction heat transfer modes in which the rate of heat transfer is linearly proportional to temperature differences, a radiative heat transfer depends on the difference between absolute temperatures to the fourth power. The sheath temperature is high[12] at SCWR conditions; therefore, it is necessary to take into account the radiative heat transfer.

In the case of the sheath and the coolant, the radiative heat transfer has been taken into consideration in the Nusselt number correlation, which has been used to calculate the HTC. In general, the Nusselt number correlations are empirical equations, which are developed based on experiments conducted in water using either bare tubes or tubes containing electrically heated elements simulating the fuel bundles. To develop a correlation, surface temperatures of the bare tube and/or simulating rods are measured along the heated length of the test section by the use of thermocouples or Resistance Temperature Detectors (RTDs). These measured surface temperatures already include the effect of the radiative heat transfer; therefore, the developed Nusselt number correlations represent both radiative and convection heat transfer modes. Consequently, the radiative heat transfer has been taken indirectly into consideration in the calculations.

A unique type of neutron detector that is widely applied for in-core use is the self-powered detector (SPD). These devices incorporate a material chosen for its relatively high cross section for neutron capture leading to subsequent beta or gamma decay. In its simplest form, the detector operates on the basis of directly measuring the beta decay current following capture of the neutrons. This current should then be proportional to the rate at which neutrons are captured in the detector. Because the beta decay current is measured directly, no external bias voltage need be applied to the detector, hence the name self­powered. Another form of the self-powered detector makes use of the gamma rays emitted following neutron capture. Some fraction of these gamma rays will interact to form secondary electrons through the Compton, photoelectric, and pair production mechanisms. The current of the secondary electrons can then be used as the basic detector signal. Nonetheless, the self powered neutron detector (SPND) remains the most common term

applied to this family of devices. Compared with other neutron sensors, self-powered detectors have the advantages of small size, low cost, and the relatively simple electronics required in conjunction with their use. Disadvantages stem from the low level of output current produced by the devices, a relatively severe sensitivity of the output current to changes in the neutron energy spectrum, and, for many types, a rather slow response time. Because the signal from a single neutron interaction is at best a single electron, pulse mode operation is impractical and self-powered detectors are always operated in current mode.

Figure 2 shows a sketch of a typical SPD based on beta decay.

The heart of the device is the emitter, which is made from a material chosen for its relatively high cross section for neutron capture leading to a beta-active radioisotope. Ideally, the remainder of the detector does not interact strongly with the neutrons, and construction materials are chosen from those with relatively low neutron cross sections.

Let us consider the following boundary value problem:

Аф(г) = 0 r Є V (3.1)

Вф(г) = f (r) r Є dV, (3.2)

where A and В are linear operators. Group theory is not a panacea to the solution of boundary value problems; its application is limited. The main condition that must be met in nuclear engineering problems is that material distributions have symmetry. This is generally true in reactor cores, core cells and cell nodes.

In the following we give a heuristic outline of how the machinery presented above enters into the solution algorithm of a boundary value problem, and what benefits can be expected.

Symmetry is the key. If we have determined that the physical problem has symmetries these symmetries must form a group G. The symmetry operator Og must commute for all g Є G with the linear operators A and В for group theory to be applicable. That is

Og A = AOg and Og В = BOg (3.3)

must hold for all g Є G. If this condition is met, the boundary value problem can be written

as

AOgf(r) = 0 r Є V (3.4)

BOgf(r) = Ogf(r) r Є dV. (3.5)

We can now use the projection operator (2.20) to form a set of boundary value problems

APxf(r) = 0 r Є V (3.6)

BP>(r) = Paf (r) r Є dV. (3.7)

Since the projection operator creates linearly independent components, we have decomposed the boundary value problem into a number (equal to the number of irreducible components) of independent boundary value problems. These are

Atfx (r) = 0 r Є V (3.8)

Вфа (r) = fa (r) r Є dV, (3.9)

whose solution (r) belongs to the a-th irreducible representation. From this complete set of

linearly independent orthogonal functions we reconstruct the solution to the original problem as

nc

Hr) = E (r), (3.10)

a=1

where nc is the number of classes in G.

Why is this better? Recall that we are applying harmonic analysis. The usual approach is to use some series that forms an incomplete set of expansion functions and results a coupled set of equations; one "large" matrix problem. With group theory, we find a relatively small set of complete basis functions that form the solution from symmetry considerations. These are found by solving a set of "small" boundary value problems. It is clear that the effectiveness of group theory is problem dependent. However, experience over the past half century has proven group theory’s effectiveness in both nuclear engineering and other fields.

We present an especially simple example (Allgover et al., 1992) that demonstrates the advantages of symmetry considerations. The example is the solution of a linear system of equations with six unknowns:

The example has been constructed so that the basis of the reduction is the observation that the matrix is invariant under the following permutations: pi = (1,6)(2,5)(3,4) and p2 = (1,5,3) (2,6,4). As pi and p2 generate a group Об of six element, the matrix commutes with the representation of group Об by matrices of order six. This suggests the application of group theory: decompose the matrix and the vector on the right hand side of the equation into irreducible components, and solve the resulting equations in the irreducible subspaces. The Об group is isomorphic to the symmetry group of the regular triangle discussed in Section 2.2.

The character table of the group Об can be found in tables (Atkins, 1970; Conway, 2003; Landau & Lifshitz, 1980), or, can be looked up in computer programs, or libraries (GAP, 2008).

Using the character table, and projector (2.17), one can carry out the following calculations. The observation that Об is isomorphic to the symmetry group of the equilateral triangle makes the problem easier. (Mackey, 1980) has made the observation: There is an analogy of the group characters and the Fourier transform. This allows the construction of irreducible vectors by the following ad hoc method. Form the following N-tuples (N = |G|):

Є2Ц = (cos(2n/N * (2k — 1) * 1),…, cos(2n/N * (2k — 1) * N),

e2k = (sin(2n/N * (2k) * 1),… ,sin(2n/N * (2k) * N),k = 1,2,… N. (3.12)

These vectors are orthonormal and can serve as an irreducible basis. After normalization, one gets a set of irreducible vectors in the N copies of the fundamental domain. Here one may exploit the isomorphism with the symmetry group of an equilateral triangle with the points positioned as shown in Fig. 1. Applying the above recipe to the points in the triangle, we get the following irreducible basis:

e1 = (1,1,1,1,1,1) e2 = (2, —1, —1,2, —1, —1) e3 = (0,1, —1,0,1, —1) (3.13)

e4 = (2,1, —1, —2, —1,1) e5 = (0,1,1,0, —1, —1)) еб = (1, —1,1, —1,1, —1). (3.14)

We note that the points in the vectors e; do not follow the order shown in Fig. 1. Thus we need to renumber the points, and normalize the vectors. For ease of interpolation we also renumber the vectors given above. It is clear that the vectors formed from cos and sin transform together. Thus they form a two-dimensional representation. We bring forward the one-dimensional representations. The projection to the irreducible basis is through a б x б matrix that contains

Fig. 1. Labeling Positions of Points on an Orbit the orthonormal e’; vectors:

where the prime indicates rearranging in accordance with Fig. 1. Using the rearranging

Ax = b, OAO-1 (Ox) = Ob,

21 0 0 0 0 0

0 -10 0 0 0

0 0 -6 2a 0 0

0 0 — a -10 0 ,

0 0 0 0 -6 2a

0 0 0 0 — a -1

where a = /3. Compare the structure of the above matrix with that given in Section 3, where the similar form is achieved by geometrical similarity. In the present example there is no geometry, just a matrix invariant under a group of transformations.

In order to solve the resulting equations, we need the transformed right hand side of the equation:

Ob = (l4C6,q/|,o,-8,4,

Finally, note that instead of solving one equation with six unknowns, we have four equations, two of them are solved by one division for each, and we have to solve two pairs of equations with two unknowns for each. At the end, we have to transform back from Ox to x.

The Reader may ask: What is the benefit of the reduction? In a problem which is at the verge of solvability, that kind of reduction may become important. [15]

A more favorable situation is when there are geometric transformations leaving the equation and the volume under consideration, invariant. But before immersing into the symmetry hunting, we investigate the diffusion equation.

Boiling two-phase flow in a simulated fuel assembly excited by oscillation acceleration was performed by the improved ACE-3D in order to investigate how the three-dimensional behavior of boiling two-phase flow in a fuel assembly under oscillation conditions is evaluated by the improved ACE-3D.

1.3 Computational condition

In this analysis, a 7 x 7 fuel assembly in a current BWR core is simulated, as shown in Fig. 9. Fuel rod diameter is 10.8 mm; the narrowest gap between fuel rods is 4.4 mm, and the axial heat length is 3.66 m.

Four subchannels surrounded by nine fuel rods without channel boxes are adopted as the computational domain shown in Fig. 9; this is the smallest domain that can describe the
three-dimensional behavior of boiling two-phase flow. This computational domain was determined to reflect the basic thermal-hydraulic characteristics in fuel assemblies under earthquake conditions.

In this domain, single-phase water flows in from the bottom of the channel with a mass velocity of 1673 kg/m2s and inlet temperature of 549.15 K. At the exit of the computational domain, pressure was fixed at 7.1 MPa. The mass velocity, inlet temperature, and exit pressure reflect the operating conditions in a current BWR core. The core thermal power is 351.9 W. The axial power distribution of the fuel-rod surfaces is shown in Fig. 9 and it simulates the power distribution in a current BWR core.

Figure 10 shows the boundary conditions and the computational block divisions. Here, the non-slip condition is set for each fuel-rod surface, and the slip condition is set for each symmetric boundary. In this analysis, the computational domain was divided into 9 blocks. The computational grids in each block have 10 and 256 grids in the radial and axial directions, respectively. The number of grids in the peripheral direction is as follows: 30 in block 1, block 3, block 7, and block 9; 60 in block 2, block 4, block 6, and block 8; and 120 in block 5.

In this study, the boiling two-phase flow analysis was performed under steady-state conditions to obtain a steady boiling two-phase flow. Subsequently, oscillation acceleration was applied. The time when the oscillation acceleration was applied is regarded as t = 0 s.

Fuel rod

OObOOQfO

004)0000

ООМЛ06Г

ooioaoo

OOSe-QOO

OOOOOOO

OQOOQpO

10.8 mm 4.4 mm

7×7 fuel assembly

ratio [-]

Fig. 9. Computational domain and axial power ratio

Fig. 11. Time variation in oscillation acceleration

In this analysis, in-phase sine wave acceleration was applied in the X and Y directions as shown by the black arrow in Fig. 10. The magnitude and oscillation period of the oscillation acceleration in the X and Y directions were 400 Gal and 0.2 s, respectively, as shown in Fig. 11; these values are based on actual earthquake data measured in the Kashiwazaki-Kariwa nuclear power plant. The computable physical time in this analysis after applying the oscillation acceleration was 1 s based on the results described in section 2.

Reactivity is a physical characteristic of the core (based on composition, geometry, temperature, pressure, and the ability of the core to produce fission neutrons) and may be either constant or changing with time. In reactor operation or experiments, signals indicating reactor power (or neutron flux) and reactor period are generally used for direct information on the state of the reactor. However, the most important time dependent parameter is reactivity and continuous information on its value from instant to instant should be highly useful. Since reactivity measurement is one of the challenges of monitoring, control and investigation of a nuclear reactor and is in relation with reactor power measuring. Thus, design and construction of a digital reactivity meter as a continuous monitoring of the reactivity will be reviewed in a research reactor. The device receives amplified output of the fission chamber, which is in mA range, as the input. Using amplifier circuits, this current is converted to voltage and then digitalized with a microcontroller to be sent to serial port of computer. The device itself consists of software, which is a MATLAB real time programming for the computation of reactivity by the solution of neutron kinetic equations. After data processing the reactivity is calculated and presented using LCD. Tehran research reactor is selected to test the reactivity meter device. The results of applying this reactivity meter in TRR are compared with the experimental data of control rod worth, void coefficient of reactivity and reactivity changes during approach to full power. Three experiments for system verification for TRR are; determination of control rod worth, void coefficient experiment, and measuring of reactivity during approach to full power (Khalafi and Mosavi, 2011). For investigating the results of reactivity meter, the reactor power and reactivity plots during the step-wise approach to full power of a particular run of TRR reactor are shown in Figure 13. In this experiment the reactor power was initially stable and critical at 100 kW and a positive reactivity insertion was introduced in the core by changes in control rods positions.

The maximum relative error in three experiments is 13.3%. This error is caused by discrete signal that is transferred to the reactivity meter device. A great portion of the data is lost in the discrete signal and some others in the sampling process. As described in this section, the system of a digital reactivity meter developed on a PIC microcontroller and the personal computer is proved to function satisfactorily in the nuclear research reactor and the utilization of the plant instrument signals makes the system simple and economical. Besides, this device can be used to determine the positive reactivity worth of the fresh fuel and the reflector elements added to the core, effectively. According to the above experiments, the relative error of the digital reactivity meter can be reduced by increasing the sampling frequency of the device. Also by using digital signal processing (DSP) utilities, the rate and accuracy of the reactivity meter can be improved. Because derivative circuits are not used in this device, the error due to the noise that is observed in analog circuits decreases extremely.

Yoshitomo Inaba

Japan Atomic Energy Agency Japan

1. Introduction

Technetium-99m (99mTc, half-life: 6.01 hours) is the world’s most widely used

radiopharmaceutical for exams of cancer, bowel disease, brain faculty and so on, and it is used for more than twenty million exams per year in the world and more than one million exams per year in Japan. The demand for 99mTc is continuously growing up year by year. The features of 99mTc as the radiopharmaceutical are as follows:

1. It is easy to add 99mTc to diagnostic medicines.

2. It is easy to measure the y-ray energy with 0.14 MeV generated by isomeric transition from outside the body.

3. P rays are not emitted.

4. The patients’ exposure associated with the exams is kept to the minimum because of the short half-life.

The production of the short-lived 99mTc is conducted by extracting from molybdenum-99 (99Mo, half-life: 65.94 hours), which is the parent nuclide of 99mTc. Therefore, the stable production and supply of 99Mo is very important in every country. All of 99Mo used in Japan is imported from foreign countries. However, a problem has emerged that the supply of 99Mo is unstable due to troubles in the import and the aging production facility (Atomic Energy of Canada Limited [AECL], 2007, 2008). In order to solve the problem, the establishment of an efficient and low-cost 99Mo production method and the domestic production of 99Mo are needed in Japan.

As a major 99Mo production method, the fission method ((n, f) method) exists, and as a minor 99Mo production method, the neutron capture method ((n, y) method) exists. In order to apply to the Japan Materials Testing Reactor (JMTR) of the Japan Atomic Energy Agency (JAEA), two types of 99Mo production methods based on the (n, y) method have been developed in JAEA (Inaba et al., 2011): one is a solid irradiation method, and the other is a solution irradiation method, which was proposed as a new 99Mo production technique (Ishitsuka & Tatenuma, 2008).

The solution irradiation method aims to realize the efficient and low-cost production and the stable production and supply of 99Mo, and the fundamental research and development for the practical application of the method has been started (Inaba et al., 2009).

In this paper, a comparison between [22]Mo production methods, an overview of the solution irradiation method containing the structure of 99Mo production system with the method and the progress of the development made thus far, estimates of 99Mo production with the method, and the results of a newly conducted test are described.

99