There are several Re-Entrant fuel Channel (REC) designs. As shown in Fig. 6, the first design consists of a pressure tube and a flow tube which are separated by a gap. The coolant flows along the gap between the pressure tube and the flow tube. Then, at the end of the fuel channel, the coolant flows inside the flow tube where a bundle string is placed. The outer surface of the pressure tube is in contact with the moderator. The use of this fuel-channel design is possible only if the liquid moderator is pressurized to reduce heat loss.

Since the heat loss from the aforementioned fuel channel is significantly high, this design has been modified in the form of the fuel channels shown in Figs. 7 and 8. The second design (see Fig. 7) consists of a calandria tube, a pressure tube, and a flow tube. The gap between the pressure tube and the calandria tube is filled with an inert gas, which provides thermal insulation, reducing the heat losses from the ‘hot’ pressure tube to the moderator. As shown in Fig. 7, the outer surface of the calandria tube is exposed to a liquid moderator.

Unlike the HEC design, forces due to fuelling/ refuelling are not exerted directly on the ceramic in the third design shown in Fig. 8, ensuring that the mechanical integrity of the ceramic insulator is maintained. In addition, the ceramic insulator acts as a thermal barrier, which in turn results in relatively lower operating temperatures of the pressure tube while reducing the heat loss from the coolant to the moderator. Such low operating temperatures allow for the use of Zr-2.5%Nb, which has low absorption cross-sections for thermal neutrons, as the material of the pressure tube. Therefore, lower heat losses, a better protection of the ceramic insulator, and the possibility of using Zr-2.5%Nb as the material of the pressure tube are several advantages of this fuel channel.

Sergey Pelykh and Maksim Maksimov

Odessa National Polytechnic University, Odessa

Ukraine

1. Introduction

The problem of fuel life control at nuclear power plants (NPP) with WWER-type light-water reactors (PWR) will be discussed for design (normal) loading conditions only. That is, emergency nuclear reactor (NR) operation leading to cladding material plastic deformation is not studied here, therefore the hot plasticity (stress softening) arising at the expense of yield stress decrease under emergency cladding temperature rise, will not be considered here.

Analysing the current Ukrainian energetics status it is necessary to state that on-peak regulating powers constitute 8 % of the total consolidated power system (CPS), while a stable CPS must have 15 % of on-peak regulating powers at least. More than 95 % of all thermal plants have passed their design life and the Ukrainian thermal power engineering averaged remaining life equals to about 5 years. As known, the nuclear energetics part in Ukraine is near 50 %. Hence, operation of nuclear power units of Ukraine in the variable part of electric loading schedule (variable loading mode) has become actual recently, that means there are repeated cyclic NR capacity changes during NR normal operation.

Control of fuel resource at WWER nuclear units is a complex problem consisting of a few subproblems. First of all, a physically based fuel cladding failure model, fit for all possible regimes of normal NR operation including variable loading and burnups above 50 MW-d/kg, must be worked out. This model must use a certified code developed for fuel element (FE) behaviour analysis, which was verified on available experimental data on cladding destruction.

The next condition for implementation of nuclear fuel resource control is availability of a verified code estimating distribution of power flux in the active core for any reactor normal operation mode including variable loading.

It should be noticed that calculation of nuclear fuel remaining life requires estimating change of the state of a fuel assembly (FA) rack. For instance, the state of a rack can change considerably at core disassembling (after a design accident) or at spent fuel handling. Generally speaking, the total fuel handling time period must be considered including the duration of dry/wet storage. Before designing a nuclear fuel resource control system, using

probability theory and physically based FA failure criteria, the failure probability for all FA must be estimated. Having satisfied the listed conditions, a computer-based system for control of nuclear fuel remaining life can be worked out.

The FEMAXI code has been used to calculate the cladding stress/strain development for such its quality as simultaneous solution of the FE heat conduction and mechanical deformation equations using the finite element method (FEM) allowing consideration of variable loading (Suzuki, 2000). Sintered uranium dioxide was assumed to be the material of pellets while stress relieved Zircaloy-4 was assumed to be the material of cladding (Suzuki, 2010). Cladding material properties in the FEMAXI code are designated in compliance with (MATPRO-09, 1976). But the manufacturing process and the zircaloy alloy used are not specified here.

FE behaviour for UTVS (the serial FA of WWER-1000, V-320 project), TVS-А (the serial FA of WWER-1000 produced by OKBM named after I. I. Aphrikantov) and TVS-W (the serial FA produced by WESTINGHOUSE) has been analysed.

The full list of input parameters used when analyzing the PWR fuel cladding durability can be seen in (Suzuki, 2000). The NR regime and FA constructional parameters were set in compliance with Shmelev’s method (Shmelev et al., 2004). The main input parameters of FE and FA used when analyzing the WWER-1000 fuel cladding durability are listed in Table 1.

FE cladding rupture life control for a power-cycling nuclear unit having the WWER-1000 NR is a key task in terms of rod design and reliability. Operation of a FE is characterized by
long influence of high-level temperature-power stressing leading to uncontrollable cladding material creep processes causing, after a while, its destruction, and fission products enter the circuit in the quantities exceeding both operational limits and limits of safe operation. In this connection, estimation of cladding integrity time for a NR variable loading mode, taking into account some appointed criteria, becomes one of key problems of FE designing and active core operational reliability analysis.

In accordance with the experience, there are following main characteristic cladding destruction mechanisms for the WWER-1000 varying loading mode (Suzuki, 2010): pellet­cladding mechanical interaction (PCMI), especially at low burnups and stress corrosion cracking (SCC); corrosion at high burnups (>50 MWd/kg-U); cladding failure caused by multiple cyclic and long-term static loads.

It is supposed that influence of low-burnup PCMI is eliminated by implementation of the WWER-1000 maximum linear heat rate (LHR) regulation conditions. Non-admission of cladding mechanical damage caused by SCC is ensured by control of linear heat power permissible values and jumps also. The high-burnup corrosion influence is eliminated by optimization of the alloy fabrication technique.

As all power history affects fuel cladding, it is incorrect to transfer experimental stationary and emergency operation cladding material creep data onto the FE cladding working at variable loading. Emergency NR operation leading to cladding material plastic deformation is not studied here, therefore hot plasticity (stress softening) arising at the expense of yield stress decrease under emergency cladding temperature rise, is not considered.

To solve this problem, we are to define main operating conditions affecting FE cladding durability and to study this influence mechanism. The normative safety factor Knorm for cladding strength criteria is defined as

where Rmax is the limit value of a parameter; R is the estimated value of a parameter.

The groupe of WWER-1000 cladding strength criteria includes the criteria SC1…SC5 — see Table 2 (Novikov et al., 2005). According to SC4, the WWER-1000 FE cladding total damage parameter is usually estimated by the relative service life of cladding, when steady-state operation and varying duty are considered separately:

, . NC: T dt „

o(t) = V—— — + I—— < 1

i NCi 0 t

where (Or) is the cladding material damage parameter; NCi and NCtmax are the number of i-type power-cycles and the allowable number of i-type power-cycles, respectively; t is time; tmax is the creep-rupture life under steady-state operation conditions.

The cladding material damage parameter can be considered as a structure parameter describing the material state ((O = 0, for the intact material and (O = 1, for the damaged
material). The second possible approach is considering o(t) as a characteristic of discontinuity flaw. That is when O =0, there are no submicrocracks in the cladding material. But if O =1, it is supposed that the submicrocracks have integrated into a macrocrack situated in some cross-section of the cladding

An experimental study of Zircaloy-4 cladding deformation behavior under cyclic pressurization (at 350 °С) was carried out in (Kim et al., 2007). The investigated cladding had an outer diameter and thickness of 9.5 mm and 0.57 mm, respectively. The microstructure of Zircaloy-4 was a stress-relieved state. A sawtooth pressure waveform was applied at different rates of pressurization and depressurization, where the maximum hoop stress was varied from 310 MPa to 470 MPa, while the minimum hoop stress was held constant at 78 MPa. Using the cladding stress-life diagram and analyzing the metal structure and fatigue striation appearance, it was found that when loading frequency v < 1 Hz, creep was the main mechanism of thin cladding deformation, while the fatigue component of strain was negligibly small.

Taking into account the experimental results (Kim et al., 2007), it can be concluded that estimation of o(t) by separate consideration of NR steady-state operation and varying duty (2) has the following disadvantages: the physical mechanism (creep) of cladding damage accumulation and real stress history are not taken into account; uncertainty of the cladding durability estimate forces us into unreasonably assumption Knorm = 10; there is no public data on Ntmax and fmax for all possible loading conditions.

Now the WWER-1000 fuel cladding safety and durability requirements have not been clearly defined (Semishkin et al., 2009). As strength of fuel elements under multiple cyclic power changes is of great importance when performing validation of a NR project, a tendency to in­depth studies of this problem is observed. The well-known cladding fatigue failure criterion based on the relationship between the maximum circumferential stress amplitude O^^ and the allowable number of power-cycles NCmax is most popular at present (Kim et al., 2007). Nevertheless, in case of satisfactory fit between the experimental and calculated data
describing the maximum number of cycles prior to the cladding failure, still there stays the problem of disagreement between experimental conditions and real operating environment (e. g. fluence; neutron spectrum; rod internal pressure; coolant temperature conditions; cladding water-side corrosion rate; radiation growth; cladding defect distribution; algorithm of fuel pick-and-place operations; reactor control system regulating unit movement amplitude and end effects; loading cycle parameters, etc.). In connection with this problem, to ensure a satisfactory accuracy of the cladding state estimation at variable loading conditions, it is necessary to develop physically based FE cladding durability analysis methods, on the basis of verified codes available through an international data bank.

As is known, when repair time is not considered, reactor capacity factor CF is obtained as

where At — NR operating time at the capacity of Pi ; T — total NR operating time; P — maximum NR capacity (100 %).

Using (3), the number of daily cycles Ne,0 that the cladding can withstand prior to the beginning of the rapid creep stage, expressed in effective days, is defined from the following equation:

Ne, o = No ■ CF,

where No — the number of calendar daily cycles prior to the beginning of the rapid creep

stage.

It should be stressed that CF is a summary number taking into account only the real NR

loading history. For instance, the following NR loading modes can be considered:

1. Stationary operation at 100 % NR capacity level, CF = 1.

2. The NR works at 100 % capacity level within 5 days, then the reactor is transferred to 50 % capacity level within 1 hour. Further the NR works at the capacity level of 50 % within 46 hours, then comes back to 100 % capacity level within 1 hour. Such NR operating mode will be designated as the (5 d — 100 %, 46 h — 50 %) weekly load cycle, CF = 0.860.

3. The NR works at 100 % capacity level within 16 hours, then the reactor is transferred to 75 % capacity level within 1 hour. Further the NR works at 75 % capacity level within 6 hours, then comes back to 100 % capacity level within 1 hour. Such NR operating mode will be designated as the (16 h — 100 %, 6 h — 75 %) daily load cycle, CF = 0.927.

4. The NR works at 100 % capacity level within 16 hours, then the reactor is transferred to 75 % capacity level within 1 hour. Further the NR works at 75 % capacity level within 6 hours, then comes back to 100 % capacity level within 1 hour. But the NR capacity decreases to 50 % level within last hour of every fifth day of a week. Further the reactor works during 47 hours at 50 % capacity level and, at last, within last hour of every seventh day the NR capacity rises to the level of 100 %. Such NR operating mode will be designated as the (5 d — 100 % + 75 %, 2 d — 50 %) combined load cycle, CF = 0.805.

2. The CET-method of fuel cladding durability estimation at variable loading

The new cladding durability analysis method, which is based on the creep energy theory (CET) and permits us to integrate all known cladding strength criteria within a single calculation model, is fit for any normal WWER/PWR operating conditions (Pelykh et al.,

2008) . The CET-model of cladding behaviour makes it possible to work out cladding rupture life control methods for a power-cycling WWER-1000 nuclear unit. As the WWER-1000 Khmelnitskiy nuclear power plant (KhNPP) is a base station for study of varying duty cycles in the National Nuclear Energy Generating Company ENERGOATOM (Ukraine), the second power unit of KhNPP will be considered.

According to CET, to estimate FE cladding running time under multiple cyclic NR power changes, it is enough to calculate the energy A0 accumulated during the creep process, by the moment of cladding failure and spent for cladding material destruction (Sosnin and Gorev, 1986). The energy spent for FE cladding material destruction is called as specific dispersion energy (SDE) A(t). The proposed method of FE cladding running time analysis is based on the following assumptions of CET: creep and destruction processes proceed in common and influence against each other; at any moment т creep process intensity is estimated by specific dispersion power (SDP) W (t), while intensity of failure is estimated by A(t) accumulated during the creep process by the moment т

T

A(T) = J W(T) ■ dT, (4)

0

where SDP standing in (4) is defined by the following equation (Nemirovsky, 2001):

W T) = Oe ■ pe, (5)

where ae is equivalent stress, Pa; pe is rate of equivalent creep strain, s-1.

Equivalent stress <Je is expressed as

(6)

where ae and az are circumferential stress and axial stress, respectively.

The cladding material failure parameter о(т) is entered into the analysis:

aij) = A(T) / A0, (7)

where Ao is SDE at the moment of cladding material failure beginning, known for the given material either from experiment, or from calculation, J/ m3 (Sosnin and Gorev, 1986); о = 0 — for intact material, со = 1 — for damaged material.

The proposed method enables us to carry out quantitative assessment of accumulated о(т) for different NR loading modes, taking into account a real NR load history (Pelykh et al., 2008). The condition of cladding material failure is derived from (4), (5) and (7):

T /Т

га(г) = Ї e Ve ■ dr = 1 (8)

о A0

The CET-method of light-water reactor (LWR) FE cladding operation life estimation can be considered as advancement of the method developed for FE cladding failure moment estimation at loss-of-coolant severe accidents (LOCA) (Semishkin, 2007). The equations of creep and cladding damage accumulation for zirconium alloys are given in (Semishkin, 2007) as

Ve = f(ki, T, Oe, ю(г)), (9)

o{t) = °e Ve, (10)

A,

where ki are material parameters defined from experiments with micromodels cut out along the FE cladding orthotropy directions; T is absolute temperature, К.

According to (Semishkin, 2007), for LOCA-accidents only, using the failure condition (o(t) = 1, the SDE value A0 accumulated by the moment of cladding failure and supposed to be temperature-dependent only, is determined from the equations (9)-(10). At the same time, the assumption that the value of A0 at high-temperature creep and cladding failure analysis is loading history independent, is accepted for LOCA-accidents as an experimentally proved matter.

In contrast to the experimental technique for determining A0 developed in (Semishkin, 2007), the calculation method proposed in (Pelykh et al., 2008) means that A0 can be found by any of two ways:

1. As the SDE value at the moment t0 of cladding stability loss, which is determined by condition oemax (t ) = O^* (t ), when equivalent stress O^3* (г) becomes equal to yield stress o0"ax(r) for the point of the cladding having the maximum temperature (according to the calculation model, a fuel rod is divided into axial and radial segments).

2. As the SDE value at the rapid creep start moment for the cladding point having the maximum temperature. This way is the most conservative approach, and it is not obvious that such level of conservatism is really necessary when estimating A0 .

The equivalent stress ae and the rate of equivalent creep strain pe are calculated by the LWR fuel analysis code FEMAXI (Suzuki, 2000). Though cladding creep test data must have been used to develop and validate the constitutive models used in the finite element code FEMAXI to calculate the equivalent creep strains under cyclic loading, difficulty of this problem is explained by the fact that cladding material creep modeling under the conditions corresponding to real operational variable load modes is inconvenient or impossible as such tests can last for years. As a rule, the real FE operational conditions can be simulated in such tests very approximately only, not taking into account all the variety of possible exploitation situations (Semishkin, 2007).

The code FEMAXI analyzes changes in the thermal, mechanical and chemical state of a single fuel rod and interaction of its components in a given NR power history and coolant conditions. The code analytical scope covers normal operation conditions and transient conditions such as load-following and rapid power increase in a high-burnup region of over 50 MWd/kg-U.

In the creep model used in the code, irradiation creep effects are taken into consideration and rate of equivalent cladding creep strain pe is expressed with a function of cladding stress, temperature and fast neutron flux (MATPRO-09, 1976):

Pe = K-Ф(+ B ■ exp (C-tf^exp (-Q / R ■ T )т~°’5 , (11)

where pe is biaxial creep strain rate, s-1 ; K, B, C are known constants characterizing the cladding material properties; Ф is fast neutron flux (E > 1.0 MeV), 1/m2 s; oe is circumferential stress, Pa; Q = 104 J/mol; R = 1.987 cal/mol K; T is cladding temperature, K; т is time, s.

According to (11), creep strain increases as fast neutron flux, cladding temperature, stress and irradiation time increase.

For creep under uniaxial stress, cladding and pellet creep equations can be represented as (Suzuki, 2010):

Pe = f (e (H’T >ф >F), (12)

where pe is equivalent creep strain rate, c1; de is equivalent stress, Pa; £H is creep

hardening parameter; F is fission rate, 1/m3 s.

When equation (12) is generalized for a multi-axial stress state, the creep strain rate vector { p } is expressed as a vector function { в } of stress and creep hardening parameter:

{p } = {e(M’fH)} , (13)

where T, Ф and F are omitted because they can be dealt with as known parameters.

When a calculation at time tn is finished and a calculation in the next time increment Atn+1 is being performed, the creep strain increment vector is represented as

{APn+a} = Atn+1 {Pn+e}={ P{tfn+e},£]H+e } , (14)

where К+Л = (-e)°n}+^{tfn+a} ; ^+6 =((-0)-єПН + в-£п+і ; 0 ^ 9 ^ 1

In order to stress importance of numerical solution stability, 0 = 1 is set.

Then, when the (r+1)-th iteration by the Newton-Raphson method is being performed after completion of the (r)-th iteration, the creep strain rate vector is expressed (Suzuki, 2010).

As shown in Fig. 1, the analysis model includes a 2-dimensional axisymmetrical system in which the entire length of a fuel rod is divided into AS, and each AS is further divided into concentric ring elements in the radial direction.

Upper plenum

Segment M

Segment M-1

Pellet

Cladding

Segment 2

Segment 1

Lower plenum

Fig. 1. Analysis model.

In this system, stress/strain analysis is performed using FEM with quadrangular elements having four degrees of freedom, as is shown in Fig. 2.

Fig. 3 shows relationship between mesh division and degree of freedom for each node in an AS.

gap

Fig. 3. Mesh division of FEM (for one AS).

In Fig. 3, the number of mesh divisions in the radial direction of pellet and cladding is fixed at 10 and 4, respectively. The inner two meshes of a cladding (11, 12) are metal phase, and the outer two meshes (13, 14) are oxide layer (ZrO2). The model used in the code takes into account that the oxide layer mesh and metal mesh are re-meshed and change their thickness with the progress of corrosion.

The fuel temperature calculation was carried out with the difference between the numerical solution and analytical solution not exceeding 0.1 %. The numerical error arising in the form of residue from iterative creep calculation on each time step, was not estimated as in most cases this error is exceeded by other uncertainties, first of all by thermal conductivity model error (Suzuki, 2010).

Denoting the number of daily load NR power cycles as N, using the CET-model, the dependence A (N), as well as the borders of characteristic creep stages (unsteady, steady and rapid creep) for zircaloy cladding were obtained for the WWER daily load cycle (16 h — 100 %; 6 h — k100 %), where k = 1; 0.75; 0.5; 0.25. Hence the number of daily cycles Ne,0 that the cladding can withstand prior to the rapid creep stage beginning could be calculated. The conclusion was made that the calculated value of Ao is not constant for a given material and depends on the operating mode of multiple cyclic power changes (Pelykh, 2008).

It was found, that the calculated equivalent creep strain pe for zircaloy cladding, for all daily load modes, gradually increases and a hysteresis decrease of pe can be seen at the last creep stage beginning. Then, after the hysteresis decrease, pe starts to grow fast and achieves considerable values from cladding reliability point of view. At the rapid creep beginning, the equivalent stress ae decrease trend changes into the ae increase trend, at the same time pe decreases a little, that is there is a "hysteresis loop", when the pe increase has got a phase delay in comparison with the ae increase. It should be noted, that the cause of the pe hysteresis decrease effect must be additionally studied as pe is expected to continuously increase unless the cladding is subjected to significant compressive creep stresses during the cycle and that this had been properly included in the creep material model.

The following new NR power daily maneuver algorithm was proposed in (Maksimov et al.,

2009) . It is considered that a nuclear unit is working at the nominal power level (100 %),
unwanted xenon oscillations are suppressed by the NR control group movement. At first, boric acid solution is injected so that the NR capacity decreases to 90 %, while the NR inlet coolant temperature is maintained constant at the expense of the Main Steam Line (MSL) pressure rise. To guarantee suppression of xenon oscillations, the optimal instantaneous Axial Offset (АО) is maintained due to the NR control group movement. Further the NR power is lowered at the expense of poisoning. The NR capacity will reach the 80% level in 2-3 h and the capacity will be stabilized by intake of the "pure distillate". The NR capacity will be partly restored at the expense of depoisoning starting after the maximal iodine poisoning. To restore the nominal NR power level, the "pure distillate" is injected into the NR circuit and the MSL pressure is lowered, while the NR coolant inlet temperature is maintained constant. The optimal instantaneous AO to be maintained, the control rod group is extracted from the active core. The automatic controller maintains the capacity and xenon oscillations are suppressed by the control group movement after the NR has reached the nominal power level.

The proposed algorithm advantages: lowering of switching number; lowering of "pure distillate" and boric acid solution rate; lowering of unbalanced water flow; improvement of fuel operation conditions. Also, the proposed NR capacity program meaning the NR inlet coolant temperature stability, while the MSL pressure lies within the limits of 5.8-6.0 MPa and the NR capacity changes within the limits of 100-80 %, has the advantages of the well known capacity program with the first circuit coolant average temperature constancy.

The capacity program with the first circuit coolant average temperature constancy is widely used at Russian nuclear power units with WWER-reactors due to the main advantage of this program consisting of the possibility to change the unit power level when the reactor control rods stay at almost constant position. At the same time, as the MSL pressure lies within the procedural limits, the proposed algorithm is free of the constant first circuit temperature program main disadvantage consisting of the wide range of MSL pressure change. Two WWER-1000 daily maneuver algorithms were compared in the interests of efficiency (Maksimov et al., 2009):

1. The algorithm tested at KhNPP ("Tested") on April 18, 2006: power lowering to 80 % within 1 h — operation at the 80 % power level within 7 h — power rising to 100 % within 2 h.

2. The proposed algorithm ("Proposed"): power lowering to 90 % by boric acid solution injection within 0.5 h — further power lowering to 80 % at the expense of NR poisoning within 2.5 h — operation at the 80 % power level within 4 h — power rising to 100 % within 2 h.

Comparison of the above mentioned daily maneuver algorithms was done with the help of the "Reactor Simulator" (RS) code (Philimonov and Mamichev, 1998). To determine axial power irregularity, AO is calculated as

N — N, N ‘

where Nu, Ni, N are the core upper half power, lower half power and whole power, respectively.

The instantaneous АО corresponds to the current xenon distribution, while the equilibrium АО corresponds to the equilibrium xenon distribution. Having used the proposed method
of cladding failure estimation for zircaloy cladding and WWER-type NR, dependence of the irreversible creep deformation accumulated energy from the number of daily load cycles is calculated for the "Tested" and "Proposed" algorithms, and efficiency comparison is fulfilled — see Table 3.

For the "Proposed" algorithm, taking into account the lower switching number necessary to enter "pure distillate" and boric acid solution during the maneuver, slight divergency of the instantaneous and equilibrium АО diagrams, the lower amplitude of АО change during the maneuver, the higher turbo-generator efficiency corresponding to the higher CF, as well as in consideration of practically equal cladding operation times for both the algorithms, it was concluded that the "Proposed" algorithm was preferable (Maksimov et al., 2009).

Using this approach, the complex criterion of power maneuvering algorithm efficiency for WWER-1000 operating in the mode of variable loading, taking into account FE cladding damage level, active core power stability, NR capacity factor, as well as control system reliability, has been worked out (Pelykh et al., 2009). Also the Compromise-combined WWER-1000 power control method capable of maximum variable loading operation efficiency, has been proposed and grounded (Maksimov and Pelykh, 2010).

The previous examples have looked at the atomistic and mesoscale of radiation damage and defect formation. This information can be used by plasticity models and microstructural mechanics models of the effect of radiation on materials properties. Here an example is presented where the atomistic calculations are used to parameterize a viscoplasticity treatment of hardening in materials due to irradiation.

Hardening and embrittlement are controlled by interactions between dislocations and irradiation induced defect clusters. Radiation hardening and embrittlement that occurs in metals irradiated at low temperatures (below ~0.3 Tm, where Tm is the melting temperature) is a an important technical challenge for advanced nuclear energy systems(Zinkle and Matsukawa 2004). In this example, the Visco Plastic Self Consistent (VPSC) polycrystalline code (Lebensohn and Tome 1993) is employed in order to model the yield stress dependence
in ferritic steels on the irradiation dose. The dispersed barrier hardening model is implemented in the VPSC code by introducing a hardening law, function of the strain, to describe the threshold resolved shear stress required to activate dislocations. The size and number density of the defect clusters varies with the irradiation dose in the model. Such modeling efforts can both reproduce experimental data and also guide future experiments of irradiation hardening.

In order to describe the nature of the yield stress dependence on the irradiation dose, we implemented a new microstructural model at the grain level in the VPSC code. The model assumes that hardening is affected by the presence of the defects and defect clusters produced by irradiation. These defects interact with the pre-existing dislocations in the microstructure leading to an increase in the critical stress necessary to move the dislocations. This leads to an increase in the overall yield stress of the material.

Defects are treated as barriers to the motion of dislocations. Two approximate dislocation barrier models have historically been used to describe radiation hardening in metals (Zinkle and Matsukawa 2004) and are reviewed in (Koppenaal and Arsenault 1971; Kocks 1977). The dispersed barrier model (Seeger, Diehl et al. 1957) is based on straightforward geometrical considerations for obstacles intersecting the dislocation glide plane and it is most appropriate for strong obstacles. An alternative hardening relationship was developed by Friedel-Kroupa-Hirsch (FKH) for weak obstacles (Friedel 1955; Kroupa and Hirsch 1964), where the effective interparticle spacing is increased compared to the planar geometric spacing due to less extensive dislocation bowing prior to obstacle breakaway. Using the simple approximation for dislocation line tension, the functional dependence of polycrystalline yield strength increase on defect cluster size and density for these two limiting cases is given by the following equations:

Aa = Ma/jbJNd, (8)

2

Aa = 8 MjubN 3 d

Equation 8 corresponds to the dispersed barrier hardening model and Equation 9 to the FKH model. In the two equations, Aais the change in the yield stress, M is the Taylor factor (3.06 for non-textured BCC and FCC metals), a is the defect cluster barrier strength, u is the shear modulus, b is the Burgers vector of the primary glide dislocations, and N and d are the defect cluster density and diameter.

Most radiation hardening studies have used the dispersed barrier model (Equation 8) for data interpretation, and in this work we find that it provides a better representation of our experimental results. However, the FKH model (Equation 9) may be more appropriate for many radiation-induced small defect clusters which are weak obstacles to dislocation motion. According to some early analyses (Kocks_ 1977), the FKH model is adequate for barrier strengths up to 1/4 of the Orowan (impenetrable obstacle) limit, i. e., a < 0:25, and the dispersed barrier model is more appropriate for barrier strengths of 0.25<a <1. Typical experimental values of the defect cluster barrier strength for copper and austenitic stainless steel neutron-irradiated and tested near room temperature are a = 0.15-0.2 (Zinkle 1987). The reported barrier strengths for the visible defect clusters in BCC metals (Rice and Zinkle

1998) are a = 0.4 or higher. It is possible that hardening from atomic scale voids in the BCC metals might cause one to overestimate the reported barrier strength for the visible defect clusters.

It is possible to introduce a hardening law that is a function of the strain to describe the threshold resolved shear stress required to activate dislocations. In the present application, however, evolution is not simulated and only the initial threshold is required. We assume that the initial critical resolved shear stress (CRSS) in each grain is affected by irradiation according to the dispersed barrier hardening law and follows the Orowan expression,

t = t0 + aubyfNd, (10)

where t is the initial CRSS, t0 is the unirradiated initial CRSS and the other parameters have the same meaning as in Equations 8 and 9. Observe that the Taylor factor is not included in Eq. 10, since the geometric crystal orientation effects are accounted for by the polycrystal model. The critical stress t is assigned to the 12 (110)[111] and the 12 (110)[112] slip systems of the BCC structure. The initial texture of the rolled ferritic steel is represented using 1000 crystallographic orientations. Each orientation is treated as an ellipsoidal inclusion embedded in and interacting with the effective medium that represents the aggregate. An incremental strain is enforced along the rolling direction, while leaving the lateral strains unconstrained. The stress and the strain is different from grain to grain, and the macroscopic (yield) stress is given by the average over all orientations.

Through Eq. 10 the model includes a dependence of the yield stress on the damage created due to radiation. Radiation damage is usually expressed as a statistical quantity describing the average number of displacements for each atom (dpa). The dpa influences the yield stress by determining the number density and the size of the defect clusters (obstacles) that impede the path of the dislocations and increase the critical stress required to move the dislocation.

It has commonly been assumed that the defect cluster density in irradiated metals increases linearly with increasing dose, up to the onset of cascade overlap which causes a saturation in the cluster density (Makin, Whapman et al. 1962; Koppenaal and Arsenault 1971; Trinkaus, Singh et al. 1996). However, in several pure FCC metals the defect accumulation as measured by electrical resistivity (Makin et al. 1962; Zinkle 1987) or transmission electron microscopy (Zinkle 1987; Muroga, Heinisch et al. 1992) often appears to exhibit an intermediate dose regime where the defect cluster density is proportional to the square root of dose. The defect accumulation behavior was found to be linear at very low doses (<0.0001 dpa, where the probability of uncorrelated point defect recombination is negligible), and proportional to the square root of dose at higher doses. According to simple kinetic models such as the unsaturable trap model (Thompson, Youngblood et al. 1973; Theis and Wollenberger 1980), the critical dose for transition from linear to square root behavior depends on specimen purity. In this model, the transition to square-root accumulation behavior can be delayed up to high doses if impurity trapping of migrating interstitial — type defects is dominant compared to interstitial — interstitial or interstitial-vacancy reactions.

The dependence on irradiation dose (expressed as dpa) of the defect cluster density (N) and the defect diameter (d) are taken from atomic level kinetic Monte Carlo (kMC) simulations and experimental observations (Deo et al. 2006; Deo, Baskes et al. 2007) The kMC model takes atomic level information of the migration energies and jump attempt frequencies of irradiation induced defects (interstitials, vacancies) and transmutation products (e. g., helium under high energy proton irradiation), and evolves the microstructure according to the rates of migration of these defects. The defects are allowed to cluster, and new irradiation damage is introduced during the simulation according to the irradiation dose rate. Our kMC simulations predict that the number density varies as the square root of the displacements per atom for the case of bcc iron irradiated up to 1 dpa by high energy proton irradiation.

The size dependence on irradiation dose is more complicated as the kMC simulations provide an entire distribution of defect cluster sizes. A single value of d as a function of dose is still a simplification of the kMC results. . The defect size usually increases with increasing dose (dpa) and can be fit by a power law; however the exponent of the power law expression can vary from 0 to 0.5 depending on initial simulation conditions (dose rate, temperature) and the defect cluster size considered. At low dpa, the exponent of the power law dependence is small for all defect sizes and increases at higher dpa.

The density of defects N is assumed to vary as the square root of the dpa while two cases of size dependence are considered, one in which the size is invariant with the dose (dpa) while the other in which the defect size varies as the square root of the dose. Additional systematic work is needed to confirm the presence and to understand the physical mechanisms responsible for this square root fluence-dependent defect cluster accumulation regime.

The link between the atomic level simulations and the VPSC calculations was established using the dispersed barrier hardening model. In this model, the vacancy /interstitial clusters produced in radiation cascades are assumed to act as barriers to the gliding dislocation in the slip plane and are therefore taken to be the main source of radiation hardening. A different model of radiation hardening postulates the formation of defect clouds along the length of the grown-in dislocation( see [4,5] for review). These clouds prevent the dislocation from acting as Frank Read dislocation sources and emitting more dislocations. Singh, Golubov et al. (1997) proposed the cascade induced source hardening model which accounted for interstitial cluster formation during radiation cascade formation. Such cluster formation has been observed in molecular dynamics simulations. In the CISH model, glissile loops produced directly in cascades are assumed to decorate grown-in dislocations so they cannot act as dislocation sources. The yield stress is related to the breakaway stress which is necessary to pull the dislocation away from the clusters/loops decorating it. Various aspects of the model (main assumptions and predictions) have been investigated by these researchers using analytical calculations, 3-D dislocation dynamics and molecular dynamics simulations It is possible to investigate such recent radiation hardening mechanisms by including them to develop the links between the atomic level understanding of defect sizes and concentrations and the VPSC model of polycrystalline hardening. Such mechanisms may also be investigated by atomic level simulations of single dislocation motion in the presence of defect impurities.

In a manner similar to the approach of Arsenelis and co-workers (Arsenlis, Wirth et al. 2004), the VPSC model can be used to combine microstructural input from both experimental observations and model predictions to evaluate the contributions from multiple defect cluster types. Although not all of the relevant parameters are currently known, such parameter — studies that can inform future atomic-scale studies of dislocation — obstacle interactions. The VPSC model could also incorporate experimentally observed defect cluster distributions, number densities to assess the effect of multiple defect types and distributions. A detailed multiscale study, wherein the dislocation-obstacle strength and the number density and size of defects are correlated to the increasing strain and each other, would then further explain the effect of irradiation on mechanical properties of ferritic steels.

The VPSC calculations provide a means to link atomistic first principles calculations to macroscopic observables. The formulation of the irradiation hardening law allows for the introduction of parameters such as the defect size and number density that can be calculated from evolution models and simulations such as the kinetic Monte Carlo method. The interaction of the dislocation with defect clusters can be investigated by using atomistic molecular dynamics calculations. In this document we have provided a framework for performing physically based modeling and simulations of hardening behavior observed during irradiation. Such modeling efforts can both reproduce experimental data and also guide future experiments of irradiation hardening. Performing modeling and simulation studies before initiating an expensive neutron or proton beam experiment would prove invaluable and cost-effective.

5. Conclusions

In this chapter, an overview of multiscale materials modeling tools used to simulate structural materials in irradiation conditions is presented. Next generation nuclear reactors will require a new generation of materials that can survive and function in extreme environments. Advanced modeling and simulation tools can study these materials at various length and time scale. Such varied methods are needed as radiation damage affects materials in excess of 10 orders of magnitude in length scale from the sub-atomic nuclear to structural component level, and span 22 orders of magnitude in time from the sub­picosecond of nuclear collisions to the decade-long component service lifetimes. 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. Thus, modeling and simulation of such materials holds great promise if coupled with suitably designed experiments in order to develop and sustain materials for advanced nuclear energy.

Fig. 4 shows the schematic diagram of a test apparatus, which was used in order to investigate compatibility between a flowing aqueous K2MoO4 solution and a structural material and the chemical stability of the solution. The test apparatus consists of a immersion container for immersing specimens under flow, a glass storage tank with a volume of about 700 cm3, a thermocouple inside the storage tank for solution temperature measurement, a feed pump to circulate the solution, a flowmeter, Teflon tubes with an inner diameter of 7.5 mm to connect each component, two syringes, which were used for depressurization, solution supply, air purge and solution sampling, a data logger to collect temperature data and to monitor the temperature and so on. Some components such as the immersion container and the storage tank were installed into a heating chamber to heat the solution.

The immersion container consists of a glass outer tube with an outer diameter of 22 mm and a height of 62.5 mm and a Teflon inner holder with an inner diameter of 13 mm and a height of 60 mm, and two specimens (specimen 1 and 2) were fixed in the center of the container by the holder as shown in Fig. 5 and they were arranged one above the other in the container. The storage tank was located upstream of the immersion container to keep the solution temperature constant and to prevent the solution from pulsating by the feed pump. In addition to the storage tank, a looped long Teflon tube connected between the pump and the storage tank was used to keep the solution temperature in the heating chamber. The total length of the circulation route of the solution was about 6.8 m, and the total quantity of circulating solution was about 300 cm3 except the volume of the storage tank.

, ’ (a) Side view

‘ ’. ‘ To watch the specimens,

‘ one part of the Teflon inner tube was removed j ‘ in this picture.

Fig. 5. Structure of immersion container

The calculation of the sheath temperature requires HTC values along the heated length of the fuel channel. In this study, the Mokry et al. correlation, shown as Eq. (17), has been used to determine HTC. The average Prandtl number in the Mokry correlation is calculated based on the average specific heat using Eq. (18). In Eq. (18) ц and k are the dynamic viscosity and thermal conductivity of the coolant at bulk temperature. The experimental data, based on which this correlation was developed, was obtained within conditions similar to those of proposed SCWR concepts. The experimental dataset was obtained for supercritical water flowing upward in a 4-m-long vertical bare tube. The data was collected at a pressure of approximately 24 MPa for several combinations of wall and bulk fluid temperatures. The temperatures were below, at, or above the pseudocritical temperature. The mass flux ranged from 200-1500 kg/ m2s; coolant inlet temperature varied from 320 to 350°C, for heat flux up to 1250 kW/m2 (Mokry et al., 2009). The Mokry correlation requires iterations to be solved, because it contains two unknowns, which are HTC and sheath wall temperature. To solve this problem through iterations, Newton’s law of cooling should be used.

From a safety point of view, it is necessary to know the uncertainty of a correlation in calculating the HTC and sheath wall temperature. As shown in Fig. 14, the uncertainty associated in the prediction of the HTC using the Mokry et al. correlation is ±25%. In other

words, the HTC values calculated by the Mokry correlation are within ±25% deviation from the corresponding experimental values. However, the uncertainty associated with wall temperature is smaller and lies within ±15%. Figure 15 shows the uncertainty in the prediction of the wall temperature associated with the Mokry et al. correlation.

700 600

500 400

300

exp

Fig. 15. Uncertainty in predicting wall temperature using the Mokry et al. correlation (Mokry et al., 2011).

The BWR NI system, like the PWR system, has three overlapping ranges as illustrated in Figure 4.

J________ T — ————

Source start-up range

1 I I—

10′ 10" 10′ 10“ 10" 10”

Fig. 4. Typical ranges covered by in-core neutron detectors in a BWR (Knoll, 2000)

The three systems are called source, intermediate, and power range monitors. Unlike the PWR, which uses out-of-core neutron detectors, the neutron detectors are all located in-core. There are also many more detectors used in the BWR NI system than in the PWR system.

The source range monitoring system typically consists of four in-core fission chambers operating in pulse mode. Pulse mode operation provides good discrimination against gamma rays, which is necessary when measuring a relatively low neutron flux in the presence of a high gamma flux. A typical intermediate range monitoring system has eight in-core fission chambers operating in the mean square voltage (MSV) mode. The MSV mode promotes the enhanced neutron to gamma response required to provide a proper measure of neutron flux in the presence of gamma rays for both control and safety requirements. The power range monitoring system typically consists of 144-164 fission ion chambers distributed throughout the core. The fission chambers operate in current mode and are called local power range monitors (LPRM). Current mode operation provides satisfactory neutron response at the high flux levels encountered between 2 and 150% full power. In a typical system, approximately 20 LPRMs are summed to provide input to one of the seven or eight average power range monitoring (APRM) systems. The APRM system provides input for both control and reactor protection systems. In-core flux detectors are used at high power levels (above 10% of full power) because they provide spatial information needed, at high power, to control xenon-induced flux tilts and to achieve the optimum flux distribution for maximum power output. The control system flux detectors are of two types. One type has an inconel emitter and is used for the zone control system. The other type has a vanadium emitter, and is used for the flux mapping system. For power mapping validation, channel temperature differentials are used with measured flows (instrumented channels) or predicted flows (other channels) to determine the estimated channel powers, which are then compared with the powers calculated from the flux mapping readings; this provides an ongoing validation of the accuracy of the flux mapping channel powers.

First, the symmetry properties of the solution do not change in time because (4.1) is linear. This is not true for nonlinear equations. Secondly, the equations in (3.3) need to be satisfied. That is, the operations of the equation (4.4) and the boundary conditions must commute with the symmetry group elements. The symmetries of equation (4.4) are determined by the operators, the material parameters (cross-sections) and the geometry of V. The first term involves derivatives:

V(Dk (r)VYk (r, t)) = VDk (r)VYk (r) + Dk (r)V2 Y (r).

Here the first term contains a dot product which is invariant under rotations and reflections. The second term involves the laplace operator, which is also invariant under rotations and reflections. Thus, the major limiting symmetry factors are the material distributions, or the associated cross-sections as functions of space, and the shape of V. We assume the material distribution to be completely symmetric, thus for any cross-section E(r) we assume the transformation property

Og 4r) = Z(D(g)r) = £(r’) = E(r). (4.7)

Here Og is an operator applicable to the possible solutions. D(g) is a matrix representation of the symmetry group of the diffusion equation applicable to r. The following operators are encountered in diffusion theory. The general form of a reaction rate at point r Є V can be expressed as

R(r) = Еададад. (4.8)

k1

Here subscript 1 refers to the symmetric component. Since

OgR(r) = Og £Еи (г)Ти (r) = £ Og (Еи(г)Ти(г)) = £Еи(г^Ти(г) k1 k1 k1

because the material distribution is assumed symmetric hence Og E(r) = Е(г) for every symmetry g, the transformation properties of a reaction rate are completely determined by the transformation properties of the flux Yj-1 (г) . The normal component of the net current at r Є 9V is

Jnk (г) = — Dk (r)(nV)Y (г), (4.9)

where n is the normal vector at r. We apply Og to Jnk (г) to obtain:

OgJnk(г) = — Og (Dk(r)(nV)Y(г)) = — Dk(r)(nV)OgYk(г). (4.10)

Thus, the transformation properties of the normal component of the net current agree with the transformation properties of the flux. In diffusion theory, the partial currents are defined as

11

Ik (г) = 4 (Y (г) — 2Jnk (г)) ; Jk (г) = 4 (Y (г) + 2 Jnt (г)) . (4.11)

From (4.9) it follows that the transformation properties of the partial currents correspond to the transformation properties of the flux.

The boundary condition (4.3) commutes with rotations and reflections provided the material properties do. The same is true for the diffusion equation (4.1). Our first conclusion is that the material distribution may set a limit to the symmetry properties. As to the symmetries, the volume V under consideration may also be a limiting factor. Let Og be an operator that commutes with the operations of the diffusion equation (4.1) and (4.3). Furthermore, the representation D(g) maps V into itself. The set of operators form a group; the group operation is the repeated application. That group is called the symmetry group of the diffusion equation.

Example 4.1 (Symmetries in a homogeneous square). This symmetry group has eight elements, four rotations: E, C4, C|, C| and four reflections ax, ay, called of type av and a^, a^2 called of type а^. Characters of a given class have identical values. This group is known as the symmetry group of the square and denoted as C4v. The first column of a character table gives a mnemonic name to each representation, and a typical expression transforming according to the given representation. The first line is reserved for the most symmetric representation called unit representation. From the character table of the group C4v, we learn that there are groups with the same character tables, there are five irreducible representations labeled A, A2, B1, B2, E where As and Bs are one. dimensional and E is two-dimensional, it has two linearly independent components transforming as the x and y coordinates. □

Example 4.2 (Symmetries in a homogeneous equilateral triangle). The group has six elements, three rotations: E, C3, C2, and three reflections through axis passing one edge: aa, аь, ac called type av. The symmetry group is isomorphic to the C3v group and its character table is the same as that of the group D3. The C3v group is the symmetry group of the equilateral triangle, it has two one-dimensional and one two-dimensional representations. □

The key observation concerning the applications of symmetry considerations in boundary value problems is as follows. For a homogeneous problem (4.4) where there is no external source, the boundary condition is homogeneous, and every macroscopic cross-section Е(г), г Є V is such that

for all Og mapping V into itself. When the boundary conditions kg(r) in the expressions (4.3) transform according to an irreducible subspace fa (r) then the neutron flux Ф(г), the partial currents I(r), J(r), the reaction rate

G

R(r) = £Eg (r)Yg (r) k=1

all transform under the automorphism group of V as do the boundary conditions kg (r).

The symmetry group of the volume V makes it possible to reduce the domain on which we have to determine the solution of the diffusion theory problem. Once we know the transformation rule of the flux, for example, it suffices to calculate the flux in a part of V and exploit the transformation rules. That observation is formulated in the following concise way. Let r Є V a point in V and let g ■ r be the image of r under g Є G. Then the set of points g ■ r, g Є G is called the orbit of r under the group G. If there is a set V0 Є V such that the orbits of r0 Є V) give every point[16] of V we call V0 the fundamental domain of V. It is thus sufficient to solve the problem on the fundamental domain V), and "continue" the solution to the whole volume V.

When the boundary condition is not homogeneous or there is an external source, we exploit the linearity of the diffusion equation. The general solution is the sum of two terms: one with external source but homogeneous boundary condition and one with no external source but with non-homogeneous boundary condition. In either case, it is the external term that determines the transformation properties of the respective solution component.

Seyed Alireza Mousavi Shirazi

Department of Physics, Islamic Azad University, South Tehran Branch, Tehran

Iran

1. Introduction

According to complexity of nuclear reactor technology, applying a highly developed simulation is necessary for controlling the nuclear reactor control rods, so in this proposal the processes of a controlling model for nuclear reactors have been developed and simulated by the SIMULINK tool kit of MATLAB software and all responses, including oscillation and transient responses, have been analyzed.

In this work an arbitrary value of Keff as a comparable value is purposed and attributed to input block (H) of diagram and then this value with the received feedback value from block diagram is compared. Since the stability of the cited simulation depends on either velocity or delay time values, therefore according to this simulation the best response and operation which a reactor can have from stability aspect, have been derived. Meantime by viewing the results, the best ranges of velocity and delay time of control rod movement (in unit per second and millisecond respectively) for stability a nuclear reactor has been deduced.

Though the highlights of this proposal are respectively the following:

• Defining a mathematical model for control rod movement

• Simulation of a mathematical model by SIMULINK of MATLAB

• Determination of the best ranges for both velocity and delay time of control rod movement (in unit per second and millisecond respectively) based on the obtained results for stability an LWR nuclear reactor

In view of the great advancing the nuclear reactors technology, the phenomenal and significant changes in evolution of made nuclear reactors is observed. Since the make of the first nuclear reactor on 1948 until modern reactors, too changes are obvious. The major of these changes to: the kind of reactor design, the percent of fuel enrichment, the kind of coolant and neutron moderator, more safety and the dimensions of core are referred.

The power control system is a key control system for a nuclear reactor, which directly affects the safe operation of a nuclear reactor. Much attention has been spent to the power control system performance of nuclear reactor in engineering (Zhao et al., 2003).

High reliability is one of the main objectives of the design and operation of control systems in nuclear power plants (Basu and Zemdegs, 1978; Stark, 1976).

Prototyping a control-rod driving mechanism (CRDM), which is a crucial safety system in the Taiwan Research Reactor (TRR-II) has been implemented, by iterative parallel procedures. Hence to ensure the mechanical integrity and substance of the prototype, a series of performance testing and design improvement have been interactively executed. Functional testing results show that the overall performance of the CRDM meets the specification requirements (Chyou and Cheng, 2004).

Also the SCK. CEN/ININ joint project, which deals with the design and application of modern/expert control and real-time simulation techniques for the secure operation of a TRIGA Mark III research nuclear reactor, has been undertaken (Dong et al., 2009).

This project has been proposed as the first of its kind under a general collaboration agreement between the Belgian Nuclear Research Centre (SCKCEN) and the National Nuclear Research Institute (ININ) of Mexico (Benitez et al., 2005). In addition to the fuzzy proportional-integral-derivative (fuzzy-PID) control strategy has been applied recently as a nuclear reactor power control system. In the fuzzy-PID control strategy, the fuzzy logic controller (FLC) is exploited to extend the finite sets of PID gains to the possible combinations of PID gains in stable region and the genetic algorithm (Cheng et al., 2009; Park and Cho, 1992).

Until now, manual controlling systems have been used for controlling and tuning the control rods in the core of Gen II and some Gen III reactors (Tachibana et al., 2004).

But by application of this simulation that is the subject of this proposal the best response for operating and the best velocity and delay time of control rod movement in which can be caused to stability and critical state of a nuclear reactor, have been derived.

The safe situation is state in which the reactor stabilizes in the critical situation, meaning that the period is infinite and the Keff is 1 (Lamarsh, 1975).

A fission chamber was utilized for neutron detection in TRR. It was a valuable instrument for in-core/out-core information and the core status monitoring during normal and transient operations. A general theoretical model is presented to calculate the current- voltage characteristics and associated sensitivity for a fission chamber. The chamber was used in the research nuclear reactor, TRR, and a flux-mapping experiment was performed. The experimental current measurement in certain locations of the reactor was compared with the theoretical model results. The characteristic curves were obtained as a function of fission rate, chamber geometry, and chamber gas pressure. An important part of the calculation was related to the operation of the fission chamber in the ionization zone and the applied voltages affecting two phenomena, recombination and avalanche. In developing the theoretical model, the MCNP code was used to compute the fission rate and the SRIM program for ion-pairs computations. In modeling the source for MCNP, the chamber was placed in a volume surrounded by standard air. Figure 16 illustrates the geometrical details of the MCNP simulation (Hashemi-Tilehnoee and Hadad, 2009).

The theoretical model together with the mentioned codes was used to evaluate the effects of different applicable variations on the chamber’s parameters. An effective approach in decreasing the minimum voltage in the plateau zone, and retaining the chamber in the ionization zone, is to reduce the chamber gas pressure. However, by reducing the pressure, we decrease the gas density. This leads to the reduction of ion-pairs generation rate. Reduction of ion-pairs would affect the sensitivity. At high pressures, the plateau zone width would be extended. This extension needs a stronger electric field, which in turn causes the distortion of the electric field due to space charge effect. Thus, pressure is an important parameter in design considerations. Variations in the enrichment of the fissile element resulted in the enhancement of the fission rate and hence the sensitivity while retaining the applied voltage and plateau zone width. However, surface mass increase would require more applied voltage. Sensitivity of detection of the neutron flux would increase by decreasing the inter-electrode gap. In addition, it increases the width of the plateau zone. This extension optimizes the chamber performance and decreases the detection errors. Furthermore, by decreasing the inter-electrode gap, the fission chamber can be used in a low flux neutron surrounding for detection with high resolution. In contrast, by increasing the inter-electrode gap, the fission chamber can be used in a high flux nuclear reactor. Since the pressure variations have significant effects on the sensitivity, the detector components should be designed in accordance with the location, temperature, and neutron flux of the nuclear reactor core. Finally, applying the proper voltage not only enhances the sensitivity and readout, but also increases the longevity of the chamber.

In addition, the chamber is modeled by GEANT4 to evaluate its sensitivity to gamma ray, which exists as background. Figure 17 illustrates geometry of the modeled chamber in GEANT4. The unwanted noises from gamma ray in the core are dispensable, but in laboratory, this sensitivity must be accounted for the experiments as a disturbance signal.

1.1.1 Solid irradiation method

In the conventional solid irradiation method, solid targets including natural molybdenum such as MoO3 pellets are irradiated with neutrons in a testing reactor, and 99Mo is produced by the 98Mo (n, у) 99Mo reaction. The post-irradiation process is only dissolution of the irradiated solid targets with an alkaline solution, and only a small amount of radioactive waste is generated in the process compared with the (n, f) method. The 99Mo production cost of this method or the (n, y) method is only 0.83 US$/37 GBq (Boyd, 1997).

However, the (n, у) method has the disadvantage of producing 99Mo with a low-level specific activity of 37-74 GBq/ g-Mo and therefore the method has not had practical application in earnest. In order to utilize 99Mo with the low-level specific activity, a high — performance adsorbent for (n, y) 99Mo is needed. The Japan Atomic Energy Research Institute (the present organization: JAEA) and KAKEN Inc. had developed the high — performance molybdenum adsorbent of Poly-Zirconium Compound (PZC) in 1995 (Hasegawa et al., 1996) and improved PZC (Hasegawa et al., 1999), and then the practical application of the (n, y) method is just in sight. The molybdenum adsorbent performance of PZC is over 100 times compared with the conventional molybdenum adsorbent of alumina.