In order to ensure predictable temperatures and uniform depletion of the fuel installed in a reactor, numerous measures are taken to provide an even distribution of flux throughout the power producing section of the reactor. This shaping, or flattening, of the neutron flux is normally achieved through the use of reflectors that affect the flux profile across the core, or by the installation of poisons to suppress the neutron flux where desired. The last method, although effective at shaping the flux, is the least desirable since it reduces the neutron economy by absorbing the neutrons (DOE, 1993).

In recent years, power monitoring systems are under developing in research centers. Sakai et al. (Sakai et al., 2010) invented a power monitoring system for boiling water reactors (BWRs). In the BWR, the output power alternately falls and rises due to the generation and disappearance of voids, respectively, which may possibly generate power oscillation whereby the output power of the nuclear reactor oscillates and is amplified. The power monitoring system has a local power range monitor (LPRM) unit that has a plurality of local power channels to obtain local neutron distribution in a nuclear reactor core; an averaged power range monitor (APRM) unit that receives power output signals from the LPRM unit and obtains averaged output power signal of the reactor core as a whole; and an oscillation power range monitor (OPRM) unit that receives the power output signals from the LPRM unit and monitors power oscillation of the reactor core. The output signals from the LPRM unit to the APRM unit and the output signals from the LPRM unit to the OPRM unit are independent. A new flux mapping system (FMS) in Korea Electric Power Research Institute (KEPRI) was installed in Kori’s unit 1 nuclear power plant. An in-core neutron FMS in a pressurized water reactor (PWR) yields information on the neutron flux distribution in the reactor core at selected core locations by means of movable detectors. The FMS having movable neutron detectors is equipped with detector cable drive units and path selectors located inside the reactor containment vessel. The drive units push and pull their detector cables, which run through guide tubes, and the path selectors route the detector cables into the predetermined guide tubes. Typically, 36-58 guide tubes (thimbles) are allocated in the reactor depending on the number of fuel assemblies. A control system of FMS is located at the main control room to control the detector drive system and measure the flux signal sensed by the detectors. The flux mapping data are used to verify the reactor core design parameters, and to determine the fission power distribution in the core. The new designed path selector for a guide the neutron detectors through the reactor core are shown in Figure 1.

The path selector system is composed of four inner path selectors and an outer path selector. With the benefit of the double indexing path selector mechanism, the reliability of the detector drive system has been improved five times higher than that of a conventional system. Currently, the developed in-core flux mapping systems have been deployed at the Kori nuclear units 1-4.

The application of the information in an abstract group to a physical problem, especially to the calculation of the solution of the boundary value problem that models the physical setting, requires a mathematical "connection" between the two. This connection originates with the transformations of coordinates that define the symmetry operations reflected in the actions of a point group.

As a simple illustration, let us again consider the abstract group G = {E, A, B, a’, b’, c’} in the form of its realization in forms of rotations and reflections of an equilateral triangle, namely the point group C3v = {E, C3, C^, dv, d’v, d"v}. Let this group be consistent with a physical problem in terms of, for example, material distribution and the geometry of the boundary. Furthermore, let us consider a two-dimensional vector space with an orthonormal basis {ei, Є2} relative to which the physical model is defined. Each operation by an element g of the group C3v can be represented by its action on an arbitrary vector r in a two-dimensional vector space. In the usual symbolic form we have

r’ = D(g)r for all g Є C3v

and where r’ = Г1Є1 + Г2Є2 is the transformed vector, and D(g) is the matrix operator associated with the action of group element g Є C3v. It is well known from linear algebra that the matrix representation of operator D (g) for each g Є C3v is obtained by its action on

j=1

and that the transpose of matrix Dji(g) gives the action of the group element g on the coordinates of the vector r as

2

r = E D-j 1(g)Tj, i = 1,2. (2.1)

j=1

For the point group C3v we obtain the following six matrix representations. To spare room we replace the matrices by permutations:

E = (1,2,3); D(C3) = (3,1,2); D(C2) = (2,3,1); (2.2)

D(^1) = (1,3,2); D(^2) = (3,2,1); Dfo) = (2,1,3). (2.3)

These matrices satisfy the group multiplication table of C3v, and therefore also the multiplication table of the abstract group G that is isomorphic to C3v. We note that this is not the only matrix representation of C3v. There are two one-dimensional representations, in particular that also satisfy the multiplication table of C3v, and will be of interest later. These are

D(E) = D(C3) = D(C32) = D(av) = D(^) = D(a"v) = E2, (2.4)

where E2 is the 2 x 2 identity matrix; and

D(E) = D(C3) = D(C2) = E2 D(av) = D(^) = D(a"v) = — E2. (2.5)

The role played by these representations will become clear in later discussions of irreducible representations of groups, and their actions on function spaces.

Takeharu Misawa, Hiroyuki Yoshida and Kazuyuki Takase

Japan Atomic Energy Agency Japan

1. Introduction

Safe operation of nuclear reactors under earthquake conditions cannot be guaranteed because the behavior of thermal fluids under such conditions is not yet known. For instance, the behavior of gas-liquid two-phase flow during earthquakes is unknown. In particular, fluctuation in the void fraction is an important consideration for the safe operation of a nuclear reactor, especially for a boiling water reactor (BWR). The void fraction in the coolant is one of the physical parameters important in determining the thermal power of the reactor core, and fluctuations in the void fraction are expected to affect the power of the plant.

To evaluate fluctuation in the void fraction, numerical simulation is the most effective and realistic approach. In this study, we have developed a numerical simulation technique to predict boiling two-phase flow behavior, including fluctuation in the void fraction, in a fuel assembly under earthquake conditions.

In developing this simulation technique, we selected a three-dimensional two-fluid model as an analytical method to simulate boiling two-phase flow in a fuel assembly because this model can calculate the three-dimensional time variation in boiling two-phase flow in a large-scale channel such as a fuel assembly while incurring only a realistic computational cost. In addition, this model has been used to successfully predict the void fraction for a steady-state boiling two-phase flow simulation (Misawa, et al., 2008). We expect that the development of the boiling two-phase flow analysis method for a fuel assembly under earthquake conditions can be achieved by improving the three-dimensional two-fluid model analysis code ACE-3D (Ohnuki, et al., 2001; Misawa, et al., 2008), which has been developed by the Japan Atomic Energy Agency.

This paper describes an analytical method for boiling two-phase flow in a fuel assembly under earthquake conditions by improving ACE-3D and shows how the three-dimensional behavior of boiling two-phase flow under these conditions is evaluated by the improved ACE-3D.

Silicon carbide (SiC) is an interesting material for nuclear-reactor power monitor detectors. It has a wide band-gap, small volume and high break down electric field. In addition, SiC is chemically and neutronically inactive. Using SiC power monitors as in-core detectors provides the ability for high counting rate that may help to increase the safety margins of nuclear reactors. To observe the triton response in the SiC p-n diode, a detector with a 1.56 pm LiF converter (with 95% enriched 6LiF) was used. 6Li atoms in the LiF converter may absorb thermal neutrons and generate 2.05 MeV alpha and 2.73 MeV triton particles (6Li(n,3H)a reaction). An 8 pm Al layer was used to minimize damage in the SiC by blocking all alpha particles. However, most tritons have enough energy to pass through this layer and reach the 4.8 pm SiC active layer. The diameter of the LiF converter is 0.508 cm and the SiC diode area is 1.1 mm x 1.1 mm (diode is a square). The active area of the diode is approximately 0.965 mm2. Upon irradiation in the thermal column (TC) facility, one can observe the triton peak in the recorded detector pulse-height spectra and the concomitant triton induced radiation damage on the detector. A schematic of the detector is shown in Figure 8.

The SiC detector package was connected to a pulse processing system consisting of a preamplifier (ORTEK 142 B) and a digital spectrum analyzer (Canberra DSA 2000). An oscilloscope (Hewlett Packard 54601B, 100 MHz) was used to study the shape of the signal from the amplifier. Bias voltage was provided by the DSA to the detector through the preamplifier. A power monitoring program was used to verify the reactor power that was displayed in the control room. In addition, the degradation of the SiC detectors in the TC’s thermal neutron environment was evaluated in terms of dose and dose rate effects. After irradiating the detector at 455 kW, the count rate per kW decreased by a factor of 2 after 11 hr. The I-V characteristics recorded during pre-irradiation and post-irradiation, confirm degradation of the detectors. A theoretical model of the SiC schottky diode detectors was constructed based on MCNP and TRIM computer codes to study the damage induced by tritons for a given diode detector package configuration in the TC’s thermal neutron environment. The predicted count rate was compared with the experimental results that were obtained in the TC irradiation field using a charge sensitive preamplifier. The
experimental results are in agreement with the predicted response to within a factor of three. I-V measurements show some annealing effects occurring at room temperature. Maintaining the detectors at a higher temperature during irradiation may cause more annealing to occur, thus reducing degradation of the detector. Experiments are necessary to test the degradation of the detector at elevated temperatures, to determine if the effects of annealing are sufficiently great so that the detectors may be useful for neutron power monitoring at high count rates.

Turgay Korkut1, Fuat Koksal2 and Osman Gencel3 1Faculty of Science and Art, Department of Physics, Ibrahim Cecen University, Agri 2Department of Civil Engineering, Faculty of Engineering and Architecture, Bozok

University, Yozgat

3Department of Civil Engineering, Faculty of Engineering, Bartin University, Bartin

Turkey

1. Introduction

Nuclear reactor technology is known as an emerging area of study from past to present. It is an implementation of the nuclear sciences including reactions about atomic nucleus and productions. During the construction of a nuclear reactor, the most important issue is nuclear safety. The term of security can be attributed radiation shielding processes. For nuclear reactors, there are several different materials used to radiation shielding. While determining the most appropriate material to shield, the type and energy of radiation is extremely important.

There are two types of nuclear reactions reveals very large energies. These are the disintegration of atomic nuclei (fission) and merging small atomic nuclei (fusion) reactions. Therefore, nuclear reactors can be divided into two groups according to the type of reaction occurred during as fission reactors and fusion reactors. Currently a nuclear reactor working with fusion reactions is not available. Today, there are the hundreds of nuclear reactors based on the fission reactions. For the realization of nuclear fission, a large fissile atomic nucleus such as 235U can absorb a neutron particle. At the end of nuclear fission event, fission products (two or more light nucleus, kinetic energy, gamma radiation and free neutrons) arise. Fission reactions are controls by using neutron attenuators such as heavy water, cadmium, graphite, beryllium and several hydrocarbons. While designing a reactor shield materials against gamma and neutron radiations should be used.

Vermiculite is a monoclinic-prismatic crystal mineral including Al2O3, H2O, MgO, FeO and SiO2. It is used in heat applications, as soil conditioner, as loose-fill insulation, as absorber package material and lightweight aggregate for plaster etc. Its chemical formula is known as (MgFe, Al)3(Al, Si)4Oio(OH)2 4H2O and physical density of it about 2.5 g. cm-3. Melting point of vermiculite is above 13500C. This mineral can be used as additive building material in terms of mineral properties.

Vermiculite is a component of the phyllosilicate or sheet silicate group of minerals. It has high-level exfoliation property. So if vermiculite is heated, it expands to many times its

original volume. This feature is a striking ability for a mineral. Because it looks like vermicularis, its name is vermiculite. They molecular structure consists of two tetrahedral layers as silica and alumina and an octahedral layer including O, Mg, Fe and hydroxyl molecules. Water located between layers is an important member in the vermiculite. If mineral heats suddenly, inter-layer water transforms to steam and exfoliation feature occurs.

Vermiculite is clean to handle, odorless and mould durable. It has a wide range of uses as thermal insulation, fire durability, liquid absorption capability, low density and usefulness etc… The main uses of minerals are listed as follows;

i. Construction Industry (lightweight concretes, vermiculite-loaded plasters, loosefill insulation)

ii. Animal Feedstuff Industry

iii. Industrial Insulation for High Temperatures (up to 11000C)

iv. Automotive Industry

v. Packaging Materials

vi. Horticulture

In literature, there are several studies about vermiculite and its usage. A comparative study about the effects of grinding and ultrasonic treatment on vermiculite was done. The effect of mechanical treatment and cation type on the clay micro porosity of the Santa Olalla vermiculite untreated and mechanically treated (sonicated and ground) and saturated with different captions was investigated. An experimental study was performed about thermal conductivity of expanded vermiculite based samples. In this paper, measurements were carried out on samples in the temperature range of 300-1100 K. Because of the high heat insulation properties of vermiculite mineral, we frequently encounter studies on thermal properties of it. In another study, researchers produced new materials including vermiculite that can withstand up to 11500C. The cement-vermiculite composition was used to produce new materials to leach 54Mn and 89Sr radionuclide. Researchers have received the best results when using 95% Portland cement and 5% vermiculite composition. The effect on ultrasounds on natural macroscopic vermiculite flakes has been studied and effects of ultrasound treatment on the several parameters (particle sizes, crystal structure, surface area, etc…) were investigated. Finally, micron and submicron-sized vermiculites were prepared. High surface area silica was obtained by selectively leaching vermiculite. In this study, also the characteristics of the porous silica obtained from vermiculite are compared with those from other clay minerals. Studies are performed on the material composition and typical characteristics of micaceous minerals of the vermiculite series in the Tebinbulak deposit. Thermal treatments of nano-layered vermiculite samples were studied up to 9000C. In another thermal effect study was achieved for 15-8000C temperature range vermiculite originated by Tanzania region. Thermal properties of polypropylene-vermiculite composites were investigated using differential scanning calorimetry (DSC) and thermogravimetry (TG) techniques. At the end of this study, new composites with high thermal stability were produced. The effect of sodium ion exchange on the properties of vermiculite was studied by several methodology (scanning electron microscopy, X-ray fluorescence spectroscopy, inductively coupled plasma mass spectroscopy, X-ray diffraction and thermo mechanical analysis) and sodium exchange lowered the exfoliation onset temperature to below 300 °C. A comparative study about oil affinity of expanded and hydrophobized vermiculite was done. According to the results of this study, the expanded vermiculite had a greater affinity for oil than hydrophobized vermiculite. XRD characteristics of Poland vermiculites were studied and crystal structure of it was determined. A general study about typical properties and some parameters of different vermiculites was performed. In this study, especially heat conduction coefficients were commented and an evaluation was done about vermiculite based building materials. In another study, flyash-based fibre-reinforced hybrid phenolic composites filled with vermiculite were fabricated and characterized for their physical, thermal, mechanical and tribological performance.

Neutron shielding studies have a wide range of literature. For example, colemanite and epoxy resin mixtures have been prepared for neutron shielding applications by Okuno, 2005. Agosteo et al. have investigated double differential neutron distribution and neutron attenuation in concrete using 100-250 MeV proton accelerator. In another study, neutron transmission measurements were studied through pyrolytic graphite crystals by Adib et al. Neutron attenuation properties of zirconium borohydrite and zirconium hydride were determined by Hayashi et al., 2009. Sato et al. designed a new material evaluation method by using a pulsed neutron transmission with pixel type detectors.

In this paper; we investigated usability of vermiculite loaded samples for nuclear reactor shielding processes, because of excellent thermal insulation properties of it. This mineral was doped in cement and new samples including different vermiculite percents were produced. 4.5 MeV neutron dose transmission values were determined. Also 4.5 MeV neutron attenuation lengths were calculated for each sample.

The treatment of the neutron transport as a diffusion process has only been validated. For example, in a Light Water Reactor (LWR) the mean free path of thermal neutrons is typically around 1 cm.

The fractional model has been derived for the NPK equations with n groups of delayed neutrons, is given by:

Where:

t is the relaxation time, k is the anomalous diffusion order (for sub-diffusion process: 0 < k < 1; while that for super-diffusion process: 1 < k < 2), n is the neutron density, Ci is the concentration of delayed neutron precursor, l is the prompt-neutron lifetime for finite media, K is the neutron generation time, в is the fraction of delayed neutrons, and p is the reactivity. When Tk ^ 0, the classic NPK equation is recovered.

The fractional model includes three additional terms relating to the classic equations which are contained of fractional derivatives (Gilberto and Espinosa, 2011):

dk+1n dtk+1 ‘

dkn

and:

dkCj dtk

The physical meaning of above terms suggests that for sub-diffusion processes, the first term has an important contribution for rapid changes in the neutron density (for example in the turbine trip in a BWR nuclear power plant (NPP)), while the second term represents an important contribution when the changes in the neutron density is almost slow, for example during startup in a NPP that involves operational maneuvers due to movement of control rod mechanism. The importance of third term is when the reactor sets in shutdown state, it
could also be important to understand the processes in the accelerator driven system (ADS), which is a subcritical system characterized by a low fraction of delayed neutrons and by a small Doppler reactivity coefficient and totally there are many interesting problems to consider under the view point of fractional differential equations (FDEs) (Gilberto and Espinosa, 2011).

The neutron point kinetics (NPK) equations are one of the most important reduced models of nuclear engineering, and they have been the subject of countless studies and applications to understand the neutron dynamics and its effects. These equations are shown below:

If these both Sn(t) and SC(t) equations to matrix format are written, then the matrix format of them is shown as below:

In the linear state can write last equation as the following:

In case the point kinetic equations of reactor from both neutron density and fission fragments aspects are considered, it can be written:

s + в — Я

Л

-в,

— s + Я Л

(43)

Where:

(44)

Therefore the transfer function will be as shown:

(45)

Where:

Pe(s) — P0 — Pf (s)

Also the equation of zero power transfer function is as following:

_ n0(s + Я)

s(s + Я + в) s(s + в) ^Л + й

Л Л

and for variation of fission fragment density as per error reactivity variation, it can write:

(48)

In case the point kinetic equations of reactor from neutron density and fission fragments aspects and also temperature aspect (according to Newton’s low of cooling) are considered, it can be expressed:

Where:

In this stage according to the main transfer function that has mentioned in the last stage, G(p) is defined:

Therefore through G(p), the parts of G(p) will be defined and the stability condition through V function is applied.

So can write:

G(s) — cT 0(s)h

In large twin reactor’s cores, it can be written:

n(t) = p-en(t) + f^Q (t) + q{ (t)

л u

It is also supposed:

and:

a 12 — a21

q2 , q2 and pi are respectively as following:

qi(t) = a n2(t — T12), Л1

q2(t)=a2L n1(t — t21) Л2

and:

So qi (t) divided by pi equals:

According to Newton’s low of cooling can write:

T (t) — — n(t) — aT(t) (61)

mcp

If the variations of neutron density than initial neutron numbers, fission fragment density than initial fission fragment density and temperature than initial temperature as system variables are considered respectively as below:
and:

z; (t) = ax; (t) — az; (t) (67)

If these system variables differentials are to matrix format are written, then can write:

(68)

At the smallest scales, radiation damage is continually initiated with the formation of energetic primary knock-on atoms (PKA) primarily through elastic collisions with high —

energy neutrons. Concurrently, high concentrations of fission products (in fuels) and transmutants (in cladding and structural materials) are generated, which can cause pronounced effects in the overall chemistry of the material, especially at high burnup. The primary knock-on atoms, as well as recoiling fission products and transmutant nuclei quickly lose kinetic energy through electronic excitations (that are not generally believed to produce atomic defects) and a chain of atomic collision displacements, generating cascade of vacancy and self-interstitial defects. High-energy displacement cascades evolve over very short times, 100 picoseconds or less, and small volumes, with characteristic length scales of 50 nm or less, and are directly amenable to molecular dynamics (MD) simulations if accurate potential functions are available and chemical reactions are not occurring. If change in electronic structure need to be included, then ab initio MD is needed and this is beyond current capabilities.

In order to simulate the appropriate reactor conditions for all models, it is important to connect the parameters of the atomistic models with reactor conditions and the type of irradiation encountered. The radiation damage event is composed of several distinct processes concluded by a displacement cascade (collection of point defect due to the PKA) and by the formation of an interstitial — which occurs when the PKA comes to rest-. In order to simulate the radiation effects, it is important to determine the type of energetic particle interaction we wish to model. In nuclear reactors, neutrons and charged fission product particles are the dominant energetic species produced (Beta and Gamma rays are also produced, but these create less damage than the neutrons and charged particles). The type of reactor determines the nature of the dominant energetic particle interaction. The proposed study will focus on neutrons and He ions. The additional aspect to consider concerns the energy of the PKA, which in the case of D-T fusion reaction can reach the order of ~1MeV. These energies are out of reach of atomistic simulations. Nonetheless cascade event simulations at lower energies — ranging from 5to 45 KeV — can yield significant insight on the evolution of defect type and number as a function of PKA energy. Was (2007) and Olander (1981) have extensively documented how it is possible to determine the primary damage state due to irradiation by energetic particles. The simplest model is one that approximates the event as colliding hard spheres with displacement occurring when the transferred energy is high enough to knock the struck atom off its lattice site.

The physics of primary damage production in high-energy displacement cascades has been extensively studied with MD simulations(Was 2007). The key conclusions from those MD studies of cascade evolution have been that i) intra-cascade recombination of vacancies and self-interstitial atoms (SIAs) results in ~30% of the defect production expected from displacement theory, ii) many-body collision effects produce a spatial correlation (separation) of the vacancy and SIA defects, iii) substantial clustering of the SIAs and to a lesser extent, the vacancies occurs within the cascade volume, and iv) high-energy displacement cascades tend to break up into lobes, or sub-cascades which may also enhance recombination(Calder and Bacon 1993; Calder and Bacon 1994; Bacon, Calder et al. 1995; Phythian, Stoller et al. 1995).

It is the subsequent transport and evolution of the defects produced during displacement cascades, in addition to solutes and transmutant impurities, that ultimately dictate radiation effects in materials, and changes in material microstructure(Odette et al. 2001; Wirth et al. 2004). Spatial correlations associated with the displacement cascades continue to play an important role over much larger scales, as do processes including defect recombination, clustering, migration and gas and solute diffusion and trapping. Evolution of the underlying materials structure is thus governed by the time and temperature kinetics of diffusive and reactive processes, albeit strongly influenced by spatial correlations associated with the sink structure of the microstructure and the continual production of new radiation damage. Extended defects including dislocations, precipitate interfaces and grain boundaries, which exist in the original microstructure and evolve during irradiation, serve as sinks for point defect absorption and for vacancy — self-interstitial recombination and/or point defect — impurity clustering.

The inherently wide range of time scales and the "rare-event" nature of the controlling mechanisms make modeling radiation effects in materials extremely challenging and experimental characterization is often unattainable. Indeed, accurate models of microstructure (point defects, dislocations, and grain boundaries) evolution during service are still lacking. To understand the irradiation effects and microstructure evolution to the extent required for a high fidelity nuclear materials performance model will require a combination of experimental, theoretical, and computational tools.

Furthermore, the kinetic processes controlling defect cluster and microstructure evolution, as well as the materials degradation and failure modes may not entirely be known. Thus, a substantial challenge is to develop knowledge of, and methodologies to determine, the controlling processes so that they can be included within the models. Essentially, this is to avoid the detrimental consequences of in-service surprises. A critical issue that needs to be addressed is not only the reliability of the simulation but also the accuracy of the model for representing the critical physical phenomena.

Unirradiation and y-ray irradiation tests were carried out by using the selected two aqueous molybdate solutions (aqueous (NH4)6Mo7O24^4H2O and K2MoO4 solutions), and compatibility between the two solutions and the structural materials of stainless steel and aluminum, the chemical stability, the circulation characteristics, the radiolysis and the у heating of the two solutions were investigated. In addition, the integrity of PZC was investigated under y-ray irradiation. As a result, the following were found:

1. The compatibility between the two static aqueous molybdate solutions and stainless steel is very well under unirradiation and y-ray irradiation.

2. The two solutions are chemically stable and have smooth circulation under unirradiation and y-ray irradiation.

3. The ratios of hydrogen in the gases generated by the radiolysis of the two solutions are higher than that of pure water.

4. The effect of у heating on the two solutions is the same level as that on pure water.

5. The integrity of PZC is maintained under y-ray irradiation.

However, the pH of the aqueous (NH4)6Mo7O24 4H2O solution needs to be adjusted from weak alkaline to weak acid for the prevention of precipitation. This is a disadvantage as one of the candidates for the irradiation target.

At present, the aqueous K2MoO4 solution, which has no pH adjustment and has higher molybdenum content than that of the aqueous (NH4)6Mo7O24^ 4H2O solution, is investigated as the first candidate of the irradiation target.

Currently, there is a high interest in developing high thermal-conductivity fuels, and improving the thermal conductivity of low thermal-conductivity fuels such as UO2. High thermal conductivities result in lower fuel centerline temperatures and limit the release of gaseous fission products (Hollenbach and Ott, 2010). As shown previously, UO2 has a very low thermal conductivity at high temperatures compared to other fuels such as UC and UN. However, there is a possibility to increase the thermal conductivity of UO2. This increase in the thermal conductivity of UO2 can be performed either by adding a continuous solid phase or long, thin fibbers of a high thermal-conductivity material (Hollenbach and Ott, 2010; Solomon et al., 2005).

A high thermal-conductivity material must have a low thermal-neutron absorption cross­section, assuming that the fuel will be used in a thermal-spectrum nuclear reactor (Hollenbach and Ott, 2010). In addition, it must have a high melting point and be chemically compatible with the fuel, the cladding, and the coolant. The need to meet these requirements narrows the potential materials to silicon carbide (SiC), beryllium oxide (BeO), and graphite (C). The following sections provide some information about UO2 fuel composed of the aforementioned high thermal-conductivity materials.

5.3.1 UO2 — SiC

The thermal conductivity of UO2 fuel can be improved by incorporating silicon carbide (SiC) into the matrix of the fuel. SiC has a high melting point approximately at 2800°C, high thermal conductivity (78 W/m K at 727°C), high corrosion resistance even at high temperatures, low
thermal neutron absorption, and dimensional stability (Khan et al., 2010). Therefore, when used with UO2, SiC can address the problem of low thermal conductivity of UO2 fuel.

Calculation of the thermal conductivity of UO2 plus SiC the fuel falls under the theories of composites. Generally, theories contemplating the thermal conductivity of composites are classified into two categories. One category assumes that inclusions are randomly distributed in a homogeneous mixture. The effective thermal conductivities of the composites, based on the aforementioned principle, are formulated by Maxwell. The other category, which is based on the work performed by Rayleigh, assumes that particles are distributed in a regular manner within the matrix.

Khan et al. (2010) provided the thermal conductivity of UO2-SiC fuel as a function of temperature and weight percent of SiC. Khan et al. (2010) assumed that the thin coat of SiC covered UO2 particles and determined the thermal conductivity of the composite fuel for three cases. The results of the study conducted by Khan et al. (2010) indicate that the continuity of SiC layer leads to a relatively significant increase in thermal conductivity. However, the discontinuity of SiC resulted in little improvement in the ETC of the fuel. Thus, the addition of a continuous solid phase of SiC to UO2 fuel increases the effective thermal conductivity of the fuel. In the present study, UO2-SiC fuel with 12wt% SiC with an overall 97 percent TD has been examined and its thermal conductivity has been calculated using Eq. (15).

keff= -9.59 • 10-9 T3+ 4.29• 10-5 T2 — 6.87 • 10-2 T+ 4.68• 10 (15)

In thermal nuclear reactors, most of the power is generated through fission induced by slow neutrons. Therefore, nuclear sensors those are to be part of reactor control or safety systems are generally based on detectors that respond primarily to slow neutrons. In principle, many of detector types can be adapted for application to reactor measurements. However, the extreme conditions associated with reactor operation often lead to substantial design changes, and a category of slow neutron detectors designed specifically for this application has gradually evolved.