The use of supercritical "steam" turbines in NPPs leads to higher thermal efficiencies compared to those of the current NPPs. There are several design options of Rankin cycles in order to convert the thermal energy of the supercritical "steam" into mechanical energy in a supercritical turbine. These design options include direct, indirect, and dual cycles. In a direct cycle, supercritical "steam" from the reactor passes directly through a supercritical turbine eliminating the need for the steam generators. This elimination reduces the costs and leads to higher thermal efficiencies compared to those produced in indirect cycles. In an indirect cycle, the supercritical coolant passes through the heat exchangers or steam generators to transfer heat to a secondary fluid, which passes through the turbine(s). The advantage of an indirect cycle is that potential radioactive particles would be contained inside the steam generators. On the other hand, the temperature of the secondary loop fluid is lower than that of the primary loop (e. g., reactor heat transport system loop). As a result, the thermal efficiency of an indirect cycle is lower than that of a direct cycle (Pioro et al., 2010). Figure 4 shows a single-reheat cycle for SCW NPPs.

With direct cycles, the thermal efficiency can be increased further through a combination of reheat and regeneration options. As shown in Fig. 4, in a single-reheat cycle, supercritical "steam" from the reactor passes through a high pressure turbine where its temperature and pressure drop. Then, the steam from the outlet of the high pressure turbine is sent through the SRH fuel channels inside the reactor core, but at a lower pressure. As the steam passes through the SRH fuel channels its temperature increases to an outlet temperature of 625°C at a pressure between 3 and 7 MPa (Pioro et al., 2010). At the outlet of the SRH channels, SHS passes through the intermediate pressure turbines. When a regenerative option is

considered, steam from high and intermediate turbines are extracted and sent to a series of open and closed feed-water heat exchangers. The steam is used to increase the temperature of the feed-water.

2.1 Analyzing the theory by mathematical model

In this work the value of Keff as a comparable value is supposed and attributed to input parameter block (H) and then this value with the received feedback value is compared.

The unit of the control rod velocity (v) can be mm/ s, the rate is steady, and the control rod movement is only to up and down directions, so: x(0) =0 (Shirazi et al., 2010).

Since the sgn(x) function is nonlinear; so conversion function can not be calculated; thus in this stage arguing the frequency response is not meaningful. Therefore the steady state must be considered for this nonlinear function; though it is rather complicated (Marie and Mokhtari, 2000).

To analyze the controlling system theory these are assumed:

If: Input=H; Output=x(t); in the top of control rod: x=0; in the bottom of the control rod:

x=xmax;

F = kHx(t) + K0

Where:

F : Function, k: constant coefficient, H : input parameter, x(t): the control rod position, K0: initial value of Keff.

Ax = v sgn(F — Ksp ).At

Where Ax is: the amount of control rod movement, At is: time.

Where — is: the velocity of control rod from the movement aspect to up and down, Ksp : the secondary value of Keff in the recent position of control rod.

x(t) = 10 vsgn[kx(t)H(t — tD) + Ko — Ksp ]dt

Supposition: x(0) = 0, So:

x(t) = X0 ± vtsgn(t — tD) (78)

Where x is: absolutely descending, x0 is: the initial value of x and tD is: the innate delay time.

The SIMULINK of MATLAB is an appropriate software to analyze the performance of this simulation (Tewari, 2002).

The simulated model is considered according to Fig.3:

To span length and temporal scales, these methods can be linked into a multi-scale simulation. The objective of the lower length scale modeling is to provide constitutive properties to higher length scale, continuum level simulations, whereas these higher length scale simulations can provide boundary conditions to the lower length scale models, as well as input regarding the verification/validity of the predicted constitutive properties. Here some examples are provided of models and simulations of materials under irradiation. The emphasis is on the development of the model, the assumptions and the underlying physics that goes into model development.

1.1 Atomistic simulations of radiation damage cascades

Damage to materials caused by neutron irradiation is an inherently multiscale phenomenon. Macroscopic properties, such as plasticity, hardness, brittleness, and creep behavior, of structural reactor materials may change due to microstructural effects of radiation. Atomistic models can be a useful tool to generate data about the structure and development of defects, on length and time scales that experiments cannot probe. Data from simulations can be fed into larger scale models that predict the long term behavior of materials subject to irradiation.

The amount of energy that an incident particle can transfer to a lattice atom is a function of their masses and the angle at which the collision occurs. Energy can be lost through inelastic collisions, (n, 2n) or (n, y) reactions, and, most importantly, elastic collisions. Elastic collisions between neutrons and nuclei can be treated within the hard sphere model with the following equations:

T = Y Ei (1 — cos0)

where, T is the total energy transferred, Ei is the energy of the incident neutron, 0 is the angle of collision, and A is the mass of the lattice nucleus. With the assumption that scattering is isotropic in the center of mass system, the average energy transferred over all angles can be shown to be the average of the minimum and maximum possible transfer energies, i. e., .

For iron, the energy required to displace an atom is about 40 eV, depending on the direction from which it is struck. So, a neutron needs a minimum energy of about 581 eV to displace an iron atom. Neutrons produced from fission of uranium carry around 2 MeV of kinetic energy and so have potential to cause damage as they slow down. Additionally, deuterium — tritium fusion reactions produce neutrons with energy of 14.1 MeV.

The first attempt to create a model for defect production based on PKA energy comes from Kinchin and Pease (1955). In this model, above a certain threshold Ed, energy is lost only to electron excitation, while below it, energy is lost only in hard-sphere elastic scattering. Norgett, Robinson et al. (1975) proposed a revised model, taking into account a more realistic energy transfer cross section, based on binary collision model simulations, . Here, ND is the number of Frenkel pairs surviving relaxation and the damage energy ED is the amount of energy available for creating displacements through elastic collisions and is a function of T. Since some of the energy of the cascade is lost to electronic excitation, ED will be less than T; for the energy range considered in this paper ED can be estimated as equal to

T. This model is frequently used as the standard for estimating DP A, but many molecular dynamics simulations have shown that it tends to strongly overestimate the actual damage efficiency. Bacon, Gao et al. (2000)proposed an empirical relationship between ND and T, where A and n are weakly temperature dependent constants fit to particular materials, respectively equal to 5.57 and 0.83 for Fe at 100 K, and T is in keV.

The study of irradiation damage cascades has been a popular topic over the last fifteen or so years. A through literature review of the many different of damage cascade simulations, such as binary collision approximation and kinetic Monte Carlo, that have been performed in a variety of materials is beyond the scope of this paper and readers are referred to (Was 2007). The following brief review will concentrate solely on molecular dynamics simulations in a-Fe. A thorough review of results from many papers was written by Malerba (2006).

Malerba (2006) states that the first published MD study in alpha-iron was performed by Calder and co-workers (Calder and Bacon 1993; Calder and Bacon 1994). Eighty cascades with PKAs of up to 5 keV were analyzed for properties such as percent of defects surviving relaxation, channeling properties, temperature dependence, and clustering. The interatomic potential used was developed by (Finnis and Sinclair 1984) and stiffened by Calder and Bacon to treat small interatomic distance properly. This article established a large base of data for future papers to compare with.

Following this initial study, many papers came out which utilized both the modified FS potential mentioned above and competing multi-body potentials including those from Johnson and Oh (1989), Harrison, Voter et al. (1989), and Simonelli, Pasianot et al. (1994). These papers had three main motivations: to generate data from a new potential, to compare data between two or more potentials, or to compare damage in a-Fe with that in another material such as copper. The main difficulties in comparing results from different authors are defining what makes up a cluster of defects and non-reporting of exactly how cascades were generated.

Many authors contributed to generate databases; some papers of note are described here. Stoller, Odette et al. (1997), using the FS potential modified by Calder and Bacon, ran a number of cascades at energies up to 40 keV. They found evidence for vacancy clustering, a feature not seen in previous works. Bacon et al. (2000) performed a study comparing the cascade characteristics of bcc, hcp, and fcc metals. They found that there were no major differences in interstitial and vacancy production, so concluded that any differences observed experimentally must be due to evolution of the microstructure following the primary damage event. Caturla, Soneda et al. (2000) compared bcc Fe with fcc Cu, finding that clustering in Fe was at least an order of magnitude less than in Cu. Terentyev, Lagerstedt et al. (2006) produced a study looking solely at differences between four available potentials by applying the same defect counting criteria to each. They found that the stiffness of a potential, a somewhat arbitrary feature, was the most important factor in determining cascade properties.

In all primary damage cascade simulations, first, the incident radiation has an interaction with an atom in the crystal lattice, transferring enough energy to remove the atom from its site. This atom, the primary knock-on atom (PKA), goes on to interact with other atoms in the crystal, removing them from their sites and generating a displacement cascade in the thermal spike phase. Atoms that are removed from their perfect lattice sites and come to rest between other atoms are known as interstitials; the empty lattice sites they leave are called vacancies. At some time shortly after the PKA is created, some peak number of Frenkel pairs, Np, will exist in the crystal, where a Frenkel pair is defined as one vacancy plus one interstitial. After this point, the defects will begin to recombine as the energy is dissipated. After a few picoseconds, only a few defects, Nd will remain. This generally results in a core of vacancies surrounded by a shell of interstitials. A profile of the number of defects over time in a typical cascade can be seen in Figure 3.

The atomistic simulations provide information on the number of surviving defects after initial damage and are not able to simulate large time scale or length scales. They provide a good atomistic picture of the unit processes affecting the formation of defects and the evolution of the primary damage state. Experiments cannot yet access this small time and length scale of radiation damage processes, therefore, experimental corroboration is hard to find for such simulations. Results of atomistic simulations of radiation cascades can be used to develop higher length and time scale theories and simulation of radiation effects in materials. Parameters that can be passed to other simulations/theories include the number and spatial distribution of defects created at the conclusion of the radiation cascade phase.

The disintegration rates of 98Mo (isotopic ratio: 24.138%) and 99Mo are shown as following equations:

( + ф—99 ) N99 + ф(Г98^98

The solutions of the equations (1) and (2) are as follows:

N 98 (t) = N 98(0)exp (_—t)

N99 (t) = . ф( 98———— ) N98(0) texp(- Ф-98t) — exp{- ( + —99 )t} ] (4)

Л+Ф (99 — 98 )

where N98 and N99 are the atom number densities of 98Mo and 99Mo (n/cm3), t is time (s), ф is neutron flux (n/(cm2-s)), o98 and o99 are the capture cross section of 98Mo and 99Mo (cm2), and X is the decay constant of 99Mo (1/s). When the neutron flux, the capture cross section, the decay constant and the time are given for the equations (3) and (4), 99Mo generation rate per unit volume can be calculated depending on the time.

The specific activity of the generated 99Mo is calculated from the following equation:

_ dN99 = Wx4.17x 1023 (5)

— dt ~ AT

where W is the mass of 99Mo (g), A is the atomic mass number of 99Mo, and T is the half-life of 99Mo (s).

Beryllium Oxide (BeO) is a metallic oxide with a very high thermal conductivity. BeO is chemically compatible with water, UO2, and most sheath materials including zirconium alloys. In addition to its chemical compatibility, BeO is insoluble with UO2 at temperatures up to 2160°C. As a result, BeO remains as a continuous second solid phase in the UO2 fuel matrix while being in good contact with UO2 molecules at the grain boundaries. BeO has desirable thermochemical and neutronic properties, which have resulted in the use of BeO in aerospace, electrical and nuclear applications. For example, BeO has been used as the moderator and the reflector in some nuclear reactors. However, the major concern with beryllium is its toxicity. But, the requirements for safe handling of BeO are similar to those of UO2. Therefore, the toxicity of BeO is not a limiting factor in the use of this material with UO2 (Solomon et al., 2005).

Similar to other enhanced thermal-conductivity fuels, the thermal conductivity of UO2 can be increased by introducing a continuous phase of BeO at the grain boundaries. The effects of the present of such second solid phase on the thermal conductivity of UO2 is significant such that only 10% by volume of BeO would improve the thermal conductivity of the composite fuel by 50% compared to that of UO2 with 95% TD. For the purpose of this study, UO2-BeO fuel with 13.6 wt% of BeO has been examined.

There is often a need to place neutron sensors within the core of a nuclear reactor to provide information on the spatial variation of the neutron flux. Because of the small size (1-7 cm) of the channel in which these instruments must be located, emphasis is placed on compactness and miniaturization in their design. They may either be left in a fixed position or provided with a motorized drive to allow traverses through the reactor core. Miniaturized fission chambers can be tailored for in-core use over any of the power ranges likely to be encountered in reactor operation. Walls of the chamber are usually lined with highly enriched uranium to enhance the ionization current. These small ion chambers are typically made using stainless steel walls and electrodes, and operating voltage varies from about 50 to 300 V. Argon is a common choice for the chamber fill gas and is used at a pressure of several atmospheres. The elevated pressure ensures that the range of fission fragments within the gas does not exceed the small dimensions of the detector. The gradual burn up of neutron-sensitive material is a serious problem for the long term operation of in-core detectors. Although the change in current-voltage characteristics with increased neutron flux may be greater for in-core detectors than out of core detectors, a similar effect is observed in both the compensated and uncompensated ion chambers used in pressurized water reactors (Knoll, 2000).

As was mentioned at the outset, symmetry as exemplified through group theory brings added information to the solution of physical problems, especially in the application of harmonic analysis. The heart of this information is encapsulated in the so called irreducible representations of the group elements. It should be stated at the outset that the irreducible representations used in most applications are readily available in tabulated form. Yet much of mathematical group theory is devoted to the derivation and properties of irreducible representations. We do not minimize in any way the importance of that material; it is necessary for a clear understanding of the applicability of the mathematical machinery and its physical interpretation. Our objective here is only to touch on a few of the central results used in the applications. Perhaps this may motivate the reader to look further into the subject.

The key property for the application of point groups to physical problems is that for a finite group all representations may be "built up" from a finite number of "distinct" irreducible representations. The number of distinct irreducible representations is equal to the number of classes in the group. Furthermore, the regular representation contains each irregular representation a number of times equal to the number of dimensions of that irreducible representation. Thus, if £a is the dimension of the a-th irreducible representation,

E 4 = |G|, (2.10)

k

where | G| is the order of the group G to be satisfied.

Let us illustrate this with the group C3 that was discussed previously. To identify the classes in C3, as before, we compute a table of TQT, see Table 5. The elements that transform into

Table 5. Classes of Group G3

themselves form a class. There are three classes in C3, denoted as E, C3, and C^ and therefore there are three irreducible representations in the regular representation. The condition

i2+i2 + 4 = з

can only be satisfied by t = £2 = £3 = 1. Therefore, there are three distinct one-dimensional representations. These are the building blocks for decomposing the regular representation to irreducible representations, and can be found in tables:

where ш = exp(2ni/3). The element in each of the three irreducible representation conform to the multiplication of point group C3.

These low dimension irreducible representations are used to build an irreducible representation from the regular representation of the operator Oc3 for example, as follows.

The regular representation has the form of a full matrix,

Ои(Сз) Dii(C3) Оіз(Сз) 010

Оц(Сз) Dii(C3) Оіз(Сз) = 00 1 .

Озі(Сз) D3i(C3) D33C) 100

The irreducible representation has the form of a diagonal (block diagonal in the general case) matrix,

D1^) 0) 0 10 0

0 D2(С3) 0 = 0 ш 0 .

0 0 D3(Q) 0 0 ш*

The mathematical relationship is discussed at length in all texts on the subject, and will not be repeated here. We assume the irreducible representations are known. Of interest is the information for the solution of physical problem, that is associated with irreducible representations.

Recall that starting with an arbitrary function f (r) belonging to a function space L (a Hilbert space for example), we can generate a set of functions fj,…,f|G| that span an invariant subspace Ls C L. This process requires the matrices of coordinate transformations g1,…,g|G| that form the symmetry group G of interest. The diagonal structure of the irreducible representations of G tells us that there exists a set of basis functions {f,f2,…,fn} that split the subspace Ls further into subspaces invariant under the symmetry group G, and are associated with each irreducible representation D(1) (g), D(2) (g),…, D(nc) (g) where nc is the number of classes in G. That is

Ls = Li U L2 U… Lnc (2.14)

and thus an arbitrary function f (r) Є Ls is expressible as a sum of functions that act as basis function in the invariant subspaces associated with each irreducible representation D(a) (g), a = 1,…,nc as

nc

f (r) = E fa (r). (2.15)

a=1

If the decomposition of the regular representation contains irreducible representations of dimension greater than one, we have for each basis function that "belongs to the a-th irreducible representation"

t*

fa (r) = E f»* (r) (2.16)

t=1

where t* is the dimension of the a-th irreducible representation.

The question now remains how do we obtain f * (r), the basis function of each irreducible representation?

To this end we can apply a projection operator that resolves a given function f (r) into basis functions associated with each irreducible representation. This projection operator is defined as

P* = G E Du(8)°g. (2.17)

N geG

The information needed to construct this operator-the coordinate transformations, the irreducible representations-are known in the case of the point groups encountered in practice. So, for example, the i-th basis function of the a irreducible representation that is t* dimensional for a symmetry group with G elements is constructed from an arbitrary function f (r) in invariant space Ls as

fi(r) = G E Dat(g)Ogf (r). (2.18)

|G| geG

This decomposition creates a complete finite set of orthogonal basis functions.

In practice, a more simple projection operator is generally sufficient. This is due to the fact that the Dat (g) ‘s (the diagonal elements of a multidimensional irreducible representation) are quantities that are intrinsic properties of the irreducible representation D* (g). That is they are invariant under the change of coordinates.

Furthermore, the sum of the diagonal elements, or trace, of the irreducible representation Da (g) is also invariant under a change of coordinates. In group theory this trace is denoted by the symbol X* (g) and

X* (g) = E D*t(g), (2.19)

i=l

and referred to as the character of element g e G in the a-th irreducible representation. There are tables of characters for all the point groups of physical interest.

The projection operator in terms of characters is given as

P* = G E X* (g)Og (2.20)

|G| geG

so that the basis functions are

f * (r) = G E X*gOgf (r^

|G| geG

and f (r) is decomposed into a complete finite set of orthogonal functions, with one for each irreducible representation irrespective of its dimension.

The parallel-plate channel, which simulates a single subchannel in a fuel assembly, was adopted as the computational domain, as shown in Fig. 1. Both plates were heated with a uniform heat flux of 270 kW/m2. The single-phase water flows into the parallel-plate channel vertically from the inlet. The hydraulic diameter and heated length of the computational domain are equal to those of the single subchannel in the fuel assembly of a current BWR. The outlet pressure of 7.1 MPa, the inlet velocity of 2.2 m/s, and the inlet temperature of 549.15 K also reflect the operating conditions in the current BWR. The adiabatic wall region is set up on the top of the heated region in order to eliminate the influence of the outlet boundary condition. In this analysis, the maximum bubble diameter in Eq. (8) is set to the channel width of 8.2 mm.

First, an analysis was performed without applying oscillation acceleration. After a steady boiling flow was attained, oscillation acceleration was applied. The time when the oscillation acceleration was applied is regarded as t = 0 s.

Fig. 1. Computational domain

Two cases of oscillation acceleration, in the vertical direction (Z axis) and in the horizontal direction (X axis), were applied. In both cases, the oscillation acceleration was a sine wave with a magnitude of 400 Gal and a period of 0.3 s, as shown in Fig. 2. The magnitude and period of the oscillation accelerations were taken from actual earthquake acceleration data.

Fig. 2. Time variation in oscillation acceleration

Fig. 3. Void fraction distribution at t = 0 s

The case of horizontal oscillation acceleration is shown in Fig. 4, which shows the time variation in the void fraction at Z = 2.0 m and Z = 3.66 m. The void fraction fluctuated in the horizontal direction with the same period as the oscillation acceleration; however, it moved in the direction opposite to the oscillation acceleration at both Z = 2.0 m and Z = 3.66 m.

Figure 5 shows the time variation in the horizontal velocity of liquid and vapor at Z = 2.0 m, where a positive value of velocity corresponds to the positive direction along the X axis, and a negative value of velocity corresponds to a negative direction along the X axis. The liquid velocity fluctuated in the same direction as the oscillation acceleration, while the vapor velocity fluctuated in the opposite direction. These tendencies in liquid and vapor velocities at Z = 2.0 m can also be seen at Z = 3.66 m. If oscillation acceleration is applied in the horizontal direction, a horizontal pressure gradient arises in a direction opposite to that of
the oscillation acceleration in boiling flow. In this case, the liquid phase is driven by the oscillation acceleration because the influence of the oscillation acceleration is relatively large owing to a high liquid density; on the other hand, the vapor phase is driven by the horizontal pressure gradient because the influence of the oscillation acceleration is less than that of the horizontal pressure gradient owing to the low vapor density. This explains why the vapor velocity and the void fraction moved in a direction opposite to that of the oscillation acceleration.

(b) Z=3.66 m

Fig. 4. Time variation in void fraction in the horizontal oscillation acceleration case

Fig. 5. Time variation in liquid and vapor velocities in the horizontal oscillation acceleration case

The case of vertical oscillation acceleration is shown in Fig. 6, which also shows the time variation in the void fraction at Z = 2.0 m and Z = 3.66 m. The distribution of the void fraction at Z = 2.0m and Z = 3.66 m fluctuated with the same period as that of the oscillation
acceleration. The vertical oscillation acceleration caused fluctuations in the pressure in the channel, causing expansion and contraction of the vapor phase. This explains why the void fraction fluctuated with the same period as that of the oscillation acceleration.

A comparison between Fig. 4 and Fig. 6 indicates that the magnitude of the void fraction fluctuation for the horizontal oscillation acceleration case was greater than that for the vertical oscillation acceleration case at any vertical position.

It can therefore be confirmed that the fluctuation of the void fraction with the same period as the oscillation acceleration can be calculated in the case of both horizontal and vertical oscillation acceleration.

t= 1.2s

t = 0.9s t = 0.6s t = 0.3s t = 0.0s

variation in void fraction in the vertical oscillation acceleration case

1.2 Investigation of the effect of oscillation period on boiling two-phase flow behavior

The computational domain and thermal hydraulic conditions are the same as those for boiling two-phase flow in the parallel-plate channel, as described in the preceding section. The oscillation acceleration was applied at t = 0 s, after steady boiling flow was obtained.

Nine cases of oscillation acceleration, as shown in Table 1, were applied in order to investigate the influence of the oscillation period of the oscillation acceleration upon the boiling two-phase flow behavior. As shown in the preceding section, the influence of the horizontal oscillation acceleration upon boiling flow was greater than the influence of the vertical oscillation acceleration. Therefore, only the horizontal oscillation acceleration was investigated in these analyses. The minimum oscillation period of 0.005 s, as listed in Table 1, is equal to half of the minimum time interval of structural analysis in a reactor. The maximum oscillation period of 1.2 s is almost equal to the computable physical time of about 1 s. In all cases, magnitude of the oscillation acceleration was set to 400 Gal. Case G in Table 1 is the same as the horizontal oscillation acceleration case shown in section 2.3.

Table 1. Computational cases

Case I

Figure 8 shows the standard deviation distribution of void fraction fluctuation. In cases where the oscillation period is less than 0.01 s, the influence of the oscillation acceleration is small because the magnitude of the void fraction fluctuation is very small compared to that in the cases where the oscillation period is greater than 0.02 s. When the oscillation period is greater than 0.02 s, although the magnitude of the void fraction fluctuation increases with elevation, it decreases near the top of the heated region.

In cases where the oscillation period is between 0.02 s and 0.30 s, the standard deviation distributions varied significantly with the variation in the oscillation period. In Case F, the magnitude of the void fraction fluctuation was highest locally. Therefore, the distribution of void fraction fluctuation was significantly dependent on the oscillation period in this range.

Case A Case B Case C Case D Case E Case F Case G Case H Fig. 8. Standard deviation distribution of void fraction distribution

On the other hand, in cases where the oscillation period was greater than 0.30 s, the standard deviation distributions hardly varied with the variation in the oscillation period. Therefore, the influence of the oscillation acceleration is small in this range.

From the information above, it can be confirmed that the boiling two-phase flow analysis, which is consistent with the time-series data of oscillation acceleration and has a time period greater than 0.01 s, can be performed. This is because oscillation acceleration with an oscillation period of less than 0.01 s has very little influence on the boiling two-phase flow. In addition, the time variations in the void fraction in cases where the oscillation period is greater than 0.30 s are close to quasi-steady variation. This means that the computable physical time of about 1 s is enough to evaluate the response of the boiling two-phase flow to the oscillation acceleration. Therefore, it can be confirmed that effective analysis can be performed by extracting an earthquake motion of about 1 s at any time during an earthquake.

Cherenkov radiation is a process that could be used as an excess channel for power measurement to enhance redundancy and diversity of a reactor. This is especially easy to establish in a pool type research reactor (the TRR). A simple photo diode array is used in Tehran Research Reactor to measure and display power in parallel with the existing conventional detectors (Arkani and Gharib, 2009). Experimental measurements on this channel showed that a good linearity exists above 100 kW range. The system has been in use for more than a year and has shown reliability and precision. Nevertheless, the system is subject to further modifications, in particular for application to lower power ranges. TRR is originally equipped with four channels, namely, a fission chamber (FC), a compensated ionization chamber (CIC), and two uncompensated ionization chambers (UIC). However, in order to improve the power measuring system, two more channels have also been considered for implementation in recent years. One of these channels is based on 16O (n, p) 16N reaction which is very attractive due to the short half life of 16N (about 7 s). The other channel, at the center of our attention in this work, is based on measurement of Cherenkov radiation produced within and around the core. This channel has a fast response to power change and has been in operation since early 2007. It has been established that the movement of a fast charged particle in a transparent medium results in a characteristic radiation known as Cherenkov radiation. The bulk of radiation seen in and around a nuclear reactor core is mainly due to Beta and Gamma particles either from fission products or directly emanating from the fission process (prompt fission gamma rays). As it will be explained more thoroughly in the following section, Cherenkov radiation is produced through a number of ways when: (a) beta particles emitted by fission products travel with speeds greater than the speed of light in water and (b) indirect ionization by Gamma radiation produces electrons due to photo electric effect, Compton effect and pair production effect. Among these electrons, Compton electrons are the main contributors to Cherenkov radiation. It is established that Cherenkov light is produced by charged particles which pass through a transparent medium faster than the phase velocity of light in that medium. Considering the fact that speed of light in water is 220,000 km/s, the corresponding electron energy that is required to produce Cherenkov light is 0.26 MeV. This is the threshold energy for electrons that are energetic enough to produce Cherenkov light. It is the principal basis of Cherenkov light production in pool type research reactors in which the light is readily visible. For prompt Gamma rays, in general, it makes it possible to assume that Cherenkov light intensity is a linear function of reactor power. It is clear that neutron intensity, fission rate, power density, and total power itself are all inter-related by a linear relationship. In other words, Cherenkov light intensity is also directly proportional to the fission rate. This leads us to the fact that the measured Cherenkov light intensity at any point in a reactor is linearly proportional to the instantaneous power. As long as the measurement point is fixed, the total power could easily be derived from the light intensity with proper calibration. It should be noted here that, as mentioned before, Cherenkov light is also emitted by the electrons produced by the indirect ionization of fission products by Gamma rays, which are confined in fuel elements. For this reason, a linear relationship between reactor power and Cherenkov light intensity would only hold at the higher power range where fission power is dominant in comparison with residual power. Cherenkov light emanating from core is collected by a collimator right above the core and reflected by a mirror onto a sensitive part of the PDA. Figure 11 shows the integrated system at work, overlooking the core.

An important factor to be checked is the system fidelity. This means that the response of the system must be the same when the reactor power is raised or lowered. There is a good fidelity within the linearity range by comparison of the Cherenkov system with the output of CIC power monitoring channel. Moreover, there has been no drift observed in the system in the long run as the system functioned properly for almost 2 years since it was installed. Finally, it is necessary to examine whether the reading from the Cherenkov detector is consistent with other channels. Finally, it is necessary to examine whether the reading from the Cherenkov detector is consistent with other channels. Figure 12 shows its good consistency with other conventional channels (only the fission chamber is shown for the sake of simplicity) within a typical shift operation.

It is observed that the steadiness and stability of the Cherenkov detector is as good as other existing channels. The 16N counts and pool average temperature are also included as further confirmation of the general behavior of the reactor during the operation. Reasonable stability is observed in the hourly readings of all the channels. Based on statistics, the output value of the present PDA system is valid within ±1 % at its nominal power. It is concluded that, at least for the case of research reactors, one can simply increase redundancy and diversity of medium-range reactors by employing the Cherenkov detector as an auxiliary tool for monitoring purposes. It is seen that such a system can provide a stable and reliable tool for the major part of power range, and it can assist in the reactor operation with additional safety interlocks to issue appropriate signals. The advantage of the present detector system over conventional ones is that it is far from the radiation source and thus easily accessible for maintenance and fine tuning. It contains no consumable materials to degrade in long term, and it is relatively inexpensive and simple. Nevertheless, a drawback of the Cherenkov system, which is also true about uncompensated ionization chambers, is its lack of linearity in the low power range.

Nowadays concrete is often used in radiation shielding process. In several studies, some additive materials were added in concrete to increase its radiation shielding capacity. In this study, as an additive material, we have used vermiculite mineral with a good heat insulation material. Produced samples have three different vermiculite and cement ratio values. 4.5 MeV neutron dose transmission values (Fig.5) and attenuation lengths of samples (Table.4) were obtained. Attenuation length is just equal to the average distance a particle travels before being scattered or absorbed. It is a useful parameter for shielding calculations. Also we calculated experimental 4.5 MeV neutron total macroscopic cross sections (p) using by dose transmission values. The various types of interactions of neutrons with matter are combined into a total cross-section value:

у — у + у + у

total scatter capture fission

The attenuation relation in the case of neutrons is thus:

(2)

(3)

where I0 is known as beam intensity value, at a material thickness of x = 0. Equivalent dose rate has been used instead of beam intensity because of our equivalent dose rate measurements. Experimental 4.5 MeV neutron total macroscopic cross sections were shown in Table.5.

2. Conclussions

At the end of this experimental study, we reached the following outcomes;

1. Vermiculite mineral has high-level thermal insulation capacity. Concrete isn’t decomposing with vermiculite addition. This mineral can be used as an additive for radiation shielding process.

2. According to the experimental results, neutron shielding property of concrete increase with increasing fiber steel and silica fume content.

3. To produce good materials which have high radiation shielding capacity and thermal insulation property, vermiculite and fiber steel may be doped in mortar. These materials can be used for neutronic and thermal applications.