5.1.1 UO2 and MOX

As a ceramic fuel, Uranium Dioxide (UO2) is a hard and brittle material due to its ionic or covalent interatomic bonding. In spite of that, the uranium dioxide fuel is currently used in PWRs, BWRs, and CANDU reactors because of its properties. Firstly, oxygen has a very low thermal-neutron absorption cross-section, which does not result in a serious loss of neutrons. Secondly, UO2 is chemically stable and does not react with water within the operating temperatures of these reactors. Thirdly, UO2 is structurally very stable. Additionally, the crystal structure of the UO2 fuel retains most of fission products even at high burn-up (Cochran and Tsoulfanidis, 1999). Moreover, UO2 has a high melting point; however, its thermal conductivity is very low, minimizing the possibility of using UO2 as a fuel of choice for SCWRs. The thermal conductivity of 95% Theoretical Density (TD) UO2 can be calculated using the Frank correlation, shown as Eq. (1) (Carbajo et al., 2001). This correlation is valid for temperatures in the range of 25 to 2847°C.

kuo (T) =————————————- 10°————————— + ^°°5/2exp-16-35/(10-3T) (1)

2 7.5408 + 17.692 (10-3 T) + 3.6142 (10-3 T )2 (10-3 T )5/2

Mixed Oxide (MOX) fuel refers to nuclear fuels consisting of UO2 and plutonium dioxide (PuO2). MOX fuel was initially designed for use in Liquid-Metal Fast Breeder Reactors (LMFBRs) and in LWRs when reprocessing and recycling of the used fuel is adopted (Cochran and Tsoulfanidis, 1999). The uranium dioxide content of MOX may be natural, enriched, or depleted uranium, depending on the application of MOX fuel. In general, MOX fuel contains between 3 and 5% PuO2 blended with 95 — 97 % natural or depleted uranium dioxide (Carbajo et al., 2001). The small fraction of PuO2 slightly changes the thermophysical
properties of MOX fuel compared with those of UO2 fuel. Nonetheless, the thermophysical properties of MOX fuel should be selected when a study of the fuel is undertaken.

Most thermophysical properties of UO2 and MOX (3 — 5 % PuO2) have similar trends. For instance, thermal conductivities of UO2 and MOX fuels decrease as the temperature increases up to 1700°C (see Fig. 9). The most significant differences between these two fuels have been summarized in Table 2. Firstly, MOX fuel has a lower melting temperature, lower heat of fusion, and lower thermal conductivity than UO2 fuel. For the same power, MOX fuel has a higher stored energy which results in a higher fuel centerline temperature compared with UO2 fuel. Secondly, the density of MOX fuel is slightly higher than that of UO2 fuel.

The thermal conductivity of the fuel is of importance in the calculation of the fuel centerline temperature. The thermal conductivities of MOX and UO2 decrease as functions of temperature up to temperatures around 1527 — 1727°C, and then it increases as the temperature increases (see Fig. 9). In general, the thermal conductivity of MOX fuel is slightly lower than that of UO2. In other words, addition of small amounts of PuO2 decreases the thermal conductivity of the mixed oxide fuel. However, the thermal conductivity of MOX does not decrease significantly when the PuO2 content of the fuel is between 3 and 15%. But, the thermal conductivity of MOX fuel decreases as the concentration of PuO2 increases beyond 15%. As a result, the concentration of PuO2 in commercial MOX fuels is kept below 5% (Carbajo et al., 2001). Carbajo et al. (2001) recommended the following correlation shown as Eq. (2) for the calculation of the thermal conductivity of 95% TD MOX fuel. This correlation is valid for temperatures between 427 and 2827°C, x less than 0.05, and PuO2 concentrations between 3 and 15%. In Eq. (2), T indicates temperature in Kelvin.

Where x is a function of oxygen to heavy metal ration and

A(x) = 2.58x + 0.035 (mK/W), C (x) = -0.715 x + 0.286 (m/K)

As is shown, the operating reactor power history as well as the WWER-1000 main regime and design parameters included into the second conditional group (pellet hole diameter, cladding thickness, pellet effective density, maximum FE linear heat rate, etc.) influence significantly on fuel cladding durability. At normal operation conditions, the WWER-1000 cladding corrosion rate is determined by design constraints for cladding and coolant, and depends slightly on the regime of variable loading. Also the WWER-1000 FE cladding rupture life, at normal variable loading operation conditions, depends greatly on the coolant temperature regime and the FA transposition algorithm. In addition, choice of the group of regulating units being used at NR power maneuvering influences greatly on the offset stabilization efficiency (Philimonov and MaMichev, 1998).

Hence, under normal operation conditions, the following methods of fuel cladding durability control at NPP with WWER can be considered as main ones:

— choice of the group of regulating units being used at power maneuvering.

— balance of stationary and variable loading regimes;

— choice of FE consrtuction and fuel physical properties, e. g., for the most strained AS, making the fuel pellets with centre holes;

— assignment of the coolant temperature regime;

— assignment of the FA transposition algorithm;

To create a computer-based fuel life control system at NPP with WWER, it is necessary to calculate the nominal and maximum permissible values of pick-off signals on the basis of calculated FA normal operation probability (Philipchuk et al., 1981). Though a computer — based control system SAKOR-M has already been developed for NPP with WWER at the OKB "Gidropress" (Bogachev et al., 2007), this system does not control the remaining life of fuel assemblies.

As the described CET-method can be applied to any type of LWR including prospective thorium reactors, the future fuel life control system for NPP with LWR can be created using this physically based method.

5. Conclusions

Taking into account the WWER-1000 fuel assembly four-year operating period transposition algorithm, as well as considering the disposition of control rods, it has been obtained that the axial segment, located between z = 2.19 m and z = 2.63 m, is most strained and limits the fuel cladding operation time at day cycle power maneuvering.

For the WWER-1000 conditions, the rapid creep stage is degenerated when using the Zircaloy-4 cladding corrosion models MATPRO-A and EPRI, at the correcting factor COR = — 0.431. This phenomenon proves that it is possible, for four years at least, to stay at the steady creep stage, where the cladding equivalent creep strain and radial total strain do not exceed 1-2%, on condition that the corrosion rate is sufficiently small.

The WWER-1000 thermal neutron flux axial distribution can be significantly stabilized, at power maneuvering, by means of a proper coolant temperature regime assignment. Assuming the maximum divergence between the instant and equilibrium axial offsets equal to 2%, the regulating unit movement amplitude at constant average coolant temperature is 6%, while the same at constant inlet coolant temperature is 4%. Therefore, when using the method with < T > =const, a greater regulating unit movement amplitude is needed to guarantee the linear heat rate axial stability, than when using the method with Tin = const, on the assumption that all other conditions for both the methods are identical.

The WWER-1000 average cladding failure parameter after 500 day cycles, for the most strained sixth axial segment, at power maneuvering according to the method with < T > =const, is 8.7% greater than the same for the method with Tin = const, on the assumption that the thermal neutron flux axial distribution stability is identical for both the methods.

The physically based methods of WWER-1000 fuel cladding durability control include: optimal choice of the group of regulating units being used at reactor power maneuvering, balance of stationary and variable loading regimes, choice of fuel element consrtuction and fuel physical properties considering the most strained fuel element axial segment, assignment of the coolant temperature regime and the fuel assembly transposition algorithm.

Although the basic mathematical definition of a group and much of the abstract algebraic machinery applies to finite, infinite, and continuous groups, our interest for applications in nuclear engineering is limited to finite point groups. Furthermore, it should be kept in mind that most of the necessary properties of the crystallographic point groups for applications, such as the group multiplication tables, the class structures, irreducible representations, and characters are tabulated in reference books or can be obtained with modern software such as MAPLE or MATHEMATICA for example.

The surface states of the two SUS304 specimens before and after the immersion in the flowing aqueous K2MoO4 solution for a total of 84.5 days are shown in the Fig. 6, and the relationships between the immersion time and corrosion rates of the specimens are shown in Fig. 7. The corrosion rates were estimated by the following equation:

_ . Weight change

Corrosion rate = (6)

Surface area x Immersion time x Density

The equation (6) shows the wastage thickness per unit time. In the visual observation and comparison of the two specimens’ surfaces before and after the compatibility test, whereas streamlined patterns, partly slight tarnish and the partly slight loss of metallic luster were found on the surfaces, obvious corrosion such as corrosion products was not found. The corrosion rate of the specimen 1 increased temporarily to 0.10 mm/y in the initial stage of the test (an immersion time of 21 days) and decreased finally to 0.02 mm/y. On the other hand, the corrosion rate of the specimen 2 was 0 mm/y at the beginning and end of the test. There was no change in the state of the specimen 1 surface in the initial stage of the test, and the temporary increase of the specimen 1 corrosion rate might be affected by taking out from the immersion container.

For the confirmation of the detailed surface states, the specimen 2 as the representative of the two specimens were observed and analyzed with an inverted materials microscope and a field emission Electron Probe Micro Analyzer (EPMA). Fig. 8 shows the inverted materials microscope photograph of the specimen 2 surface. The black lines and dots in Fig. 8 are preexistent scratches and hollows. Tarnish is recognized on the surface. Fig. 9 shows the Scanning Electron Microscope (SEM) photograph of the specimen 2 cross-section surface taken with the EPMA, and Fig. 10 shows the color map of the specimen 2 cross-section surface analyzed with the EPMA. The cross-section surface was prepared by cutting the center of the specimen 2, mounting in a resin and polishing. A thin coating layer, which is thought to be the cause of the tarnish, is found on the surface as shown in Fig. 9. To see Fig. 10, K and Mo, which are the main components of K2MoO4, are not detected and a relatively — high level of Si is detected on the surface. After the test, the corrosion of the glass outer tube in the immersion container was found, and then it is considered that the main component of
the coating layer is Si eluted from the tube. This Si coating layer might inhibit the corrosion of the specimens. In any case, the progress of the corrosion was not observed in the SUS304 specimens, and SUS304 has good compatibility with a flowing aqueous K2MoO4 solution.

Coating layer

Base material
(SUS304)

Heat transfer through the fuel-sheath gap is governed by three primary mechanisms (Lee et al., 1995). These mechanisms are 1) conduction through the gas, 2) conduction due to fuel — sheath contacts, and 3) radiation. Furthermore, there are several models for the calculation of heat transfer rate through the fuel-sheath gap. These models include the offset gap conductance model, relocated gap conductance model, Ross and Stoute model, and modified Ross and Stoute model.

In the present study, the modified Ross and Stoute model has been used in order to determine the gap conductance effects on the fuel centerline temperature. In this model, the total heat transfer through the gap is calculated as the sum of the three aforementioned terms as represented in Eq. (21):

htotal — hg + hc + hr (21)

The heat transfer through the gas in the fuel-sheath gap is by conduction because the gap width is very small. This small gap width does not allow for the development of natural convection though the gap. The heat transfer rate through the gas is calculated using Eq. (22).

Where, hg is the conductance through the gas in the gap, kg is the thermal conductivity of the gas, R1 and R2 are the surface roughnesses of the fuel and the sheath, and tg is the circumferentially average fuel-sheath gap width.

The fuel-sheath gap is very small, in the range between 0 and 125 y. m (Lassmann and Hohlefeld, 1987). CANDU reactors use collapsible sheath, which leads to small fuel-sheath gaps approximately 20 ^m (Lewis et al., 2008). Moreover, Hu and Wilson (2010) have reported a fuel-sheath gap width of 36 ^m for a proposed PV SCWR. In the present study, the fuel centerline temperature has been calculated for both 20-um and 36-um gaps. In Eq. (22), g is the temperature jump distance, which is calculated using Eq. (23) (Lee et al., 1995).

(23)

Where, g is the temperature jump distance, yi is the mole fraction of the ith component of gas, go/i is the temperature jump distance of the ith component of gas at standard temperature and pressure, Tg is the gas temperature in the fuel-sheath gap, Pg is the gas pressure in the fuel-sheath gap, and s is an exponent dependent on gas type.

In reality, the fuel pellets become in contact with sheath creating contact points. These contact points are formed due to thermal expansion and volumetric swelling of fuel pellets. As a result, heat is transferred through these contact points. The conductive heat transfer rate at the contact points are calculated using Eq. (24) (Ainscough, 1982). In Eq. (24), A is a constant, Pa is the apparent interfacial pressure, H is the Mayer hardness of the softer material. A and n are equal to 10 and 0.5.

hc = A——————

(kf + ksheath )

The last term in Eq. (21) is the radiative heat transfer coefficient through the gap, which is calculated using Eq. (25) (Ainscough, 1982). It should be noted that the contribution of this heat transfer mode is negligible under normal operating conditions. However, the radiative heat transfer is significant in accident scenarios. Nevertheless, the radiative heat transfer through the fuel-sheath gap has been taken into account in this study. In Eq. (25), ef and £sheath are surface emissivities of the fuel and the sheath respectively; and temperatures are in degrees Kelvin.

/t4 _t4

if/o isheath, ij

ef + esheath _ ef esheath ff _ Tsheath/i /

The power range channels of nuclear reactors are linear, which cover only one decade, so they do not show any response during the startup and intermediate range of the reactor operation. So, there is no prior indication of the channels during startup and intermediate operating ranges in case of failure of the detectors or any other electronic fault in the channel. A new reliable instrument channel for power measurement will be studied in this section. The device could be programmed to work in the logarithmic, linear, and log-linear modes during different operation time of the reactor life cycle. A new reliable nuclear channel has been developed for reactor power measurement, which can be programmed to work in the logarithmic mode during startup and intermediate range of operation, and as the reactor enters into the power range, the channel automatically switches to the linear mode of operation. The log-linear mode operation of the channel provides wide-range monitoring, which improves the self-monitoring capabilities and the availability of the reactor. The channel can be programmed for logarithmic, linear, or log-linear mode of operation. In the log-linear mode, the channel operates partially in log mode and automatically switches to linear mode at any preset point. The channel was tested at Pakistan Research Reactor-1 (PARR-1), and the results were found in very good agreement with the designed specifications. A wide range nuclear channel is designed to measure the reactor power in the full operating range from the startup region to 150% of full power. In the new channel, the status of the channels may be monitored before their actual operating range. The channel provides both logarithmic and linear mode of operation by automatic operating mode selection. The channel can be programmed for operation in any mode, log, linear or log-linear, in any range. In the log-linear mode, the logarithmic mode of operation is used for monitoring the operational status of the channel from reactor startup to little kilowatt reactor power where the mode of operation is automatically changed to linear mode for measurement of the reactor power. At the low power operation, the channel will provide monitoring of the proper functioning of the channel, which includes connection of the electronics with the chamber and functioning of the chamber, amplifier, high-voltage supply of the chamber, and auxiliary power supply of the channel. The channel has been developed using reliable components, and design has been verified under recommended reliability test procedures. The channel consists of different electronic circuits in modular form including programmable log-linear amplifier, isolation amplifier, alarm unit, fault monitor, high-voltage supply, dc-dc converter, and indicator. The channel is tested at PARR-1 from reactor startup to full reactor power. Before testing at the reactor, the channel was calibrated and tested in the lab by using a standard current source. The channel has been designed and developed for use in PARR-1 for reactor power measurement. The response of the channel was continuously compared with 16N channel of PARR-1, and the test channel was calibrated according to the 16N channel at 1 MW. After calibration, it was noticed that the test channel gave the same output as the 16N channel. The channel response with Reactor Power is shown in Figure 5.

The channel shows an excellent linearity. A very important check was the response of the test channel at the operating mode switching level, and it was found that the channel smoothly switched from log to linear operating mode. The designed channel has shown good performance throughout the operation and on applying different tests. The self­monitoring capabilities of the channel will improve the availability of the system.

It is known that the diffusion (as well as the transport) equation has a well defined solution in V provided the entering current is given along the boundary dV. From the Green’s function and from the operators in (4.11) we set up the following iteration scheme. To formalize this, we write the solution as

Yk(r) = E Gkk'(r’ ^ r)4′ (r’)dr’.

V=1J dV

that can be put into the concise form

G

Jk = E Rkk’ Ik’, (4.25)

k’=1

where we have suppressed that the partial currents depend on position along the boundary and the response matrix R includes an integration over variable r’.

When volume V is large, we subdivide it into subvolumes (nodes) and determine the response matrices for each subvolume. At internal boundaries, the exiting current is the
incident current of the adjacent subvolume. Thus in a composite volume the partial currents are connected by response matrices and adjacency. We collect the response matrices and adjacency into two big response matrices:

J_ = RI; I = HJ, (4.26)

and because the adjacency is an invertible relationship, we multiply the first expression by H and get

I = HRI. (4.27)

Since there is a free parameter keff in matrix R, it makes the equation solvable. At external boundaries there is no adjacency, but the boundary condition there provides a rule to determine the entering current from the exiting current. With these supplements, the solution of equation (4.27) proceeds

I(m+1) = HR(m) l(m). (4.28)

The iteration starts with m = 0 with an initial guess for the keff and the entering currents I. Let us assume that the needed matrices are available, their determinations are discussed in the subsequent Subsection. The iteration proceeds as follows. We sweep through the subvolumes in a given sequence and carry out the following actions (in node m):

• collect the actual incoming currents of subvolume m.

• determine the actual response matrix to calculate the new exiting currents and contributions to volume integrals[17].

• determine the new exiting currents (J) from the entering currents and the response matrices using equation (4.26) and the contributions to the volume integrals.

After this, pass on to the next node. When the iteration reaches the last node, the sweep ends and the maximal difference is determined between the entering currents of the last two iterations. At the end of an iteration step, the parameter keff is re-evaluated from the condition that the largest eigenvalue of HR should equal one. If the difference of the last two estimates is greater than the given tolerance limit, a new iteration cycle is started, otherwise the iteration terminates. If we have a large number of nodes, the improvement after the calculations of a given node is small. This shows that the iteration process is rather slow, acceleration methods are required.

It has been proven (Mika, 1972) that the outlined iteration is convergent. The goal of the iteration is to determine the partial current vector. The length of vector I is Nnode x nf x G. From the point of view of mathematics, the iteration is a transformation of the following type:

A(keff )xm = aXm+1, (4.29)

where m is the number of the iteration, matrix A(keff) makes the new entering current vector xm+1 from the old entering current vector xm. In the case of neutron diffusion or transport, operator A(keff) maps positive vectors into positive vectors. In accordance with the Krein-Ruthman theorem, A(keff) has a dominant eigenvalue and the associated eigenfunction[18]. When keff is a given value, the power method is a simple iteration technique to find a good estimate of x = lim,^^, x,. Solution methods have been worked out for practical problems in nuclear reactor theory: for the solution of the diffusion and transport equations in the core of a power reactor. The original numerical method is described elsewhere, see Refs. (Weiss, 1977), (Hegedus, 1991).

Note that the iteration (4.29) is just an example of the maps transforming an element of the solution space into another element. Thus in principle one can observe chaotic behavior, divergence, strange attractors[19] etc. Therefore it is especially important to design carefully the iteration scheme. The iteration includes derived quantities of two types: volume integrated and surface integrated. When you work with an analytical solution, the two are derived from the same analytical solution. But when you are using approximations (such as polynomial approximation), it has to be checked if the polynomials used inside the node and at the surface of the node are consistent. In an eigenvalue problem, parameter keff in equation (4.29)should be determined from the condition that the dominant eigenvalue a in (4.29) should equal one. First we deal with the general features of the iteration.

As has been mentioned, one iteration step (4.29) sweeps through all the subvolumes. The number of subvolumes (Gado et al., 1994) varies between 590 and 7980, the number of unknowns is 9440 and 111680. At the boundary of two adjacent subvolumes, continuity of Ф and DdnФ (the normal current) is prescribed.

In node m in iteration i. In the derivation of the analytical solution we have assumed the node to be invariant under the group Gy. Actually, not the material properties are stored in a program because the material properties depend on:

• actual temperature of the node;

• the initial composition of the fuel (e. g. enrichment);

• the actual composition of the fuel as it may change with burn-up;

• the void content of the moderator;

• the power level;

In the calculations, app. 50-60% of the time is spent on finding the actual response matrix elements, because those depend on a number of local material parameters (e. g. density, temperature, void content). We mention this datum to underline how important it is to reduce the parametrization work in a production code.

There are several methods for investigation of nuclear reactors dynamics.

One of the most important methods to study reactor dynamics and the stability of nuclear reactor is define of transfer’s functions and application of it to analyze the closed loop function.

According to following figure a closed loop system including transfer function, feedback and related applied reactivity are shown:

Where:

Pi (s) is: input reactivity in frequency field, Pf (s) is: reactivity due to feedback in frequency field, pe (s) is: error reactivity in frequency field that is as input reactivity to transfer function, G(s) is: transfer function, H(s) is: feedback function and n(s)is: output of closed loop conversion function that means the density of neutrons.

There is also:

Pe (s) = Pi (s) -Pf (s) (1)

According to Fig.1 for both transfer function and feedback function existing in closed loop can write:

In order to survey the stability of a closed loop system the term of [1 + G(s).H(s)] must be set zero and by solving this equation, all the roots that are as zero and pole for closes loop system, will be defined. The stability condition of a closed loop system is lack of positive real part of poles. It means all the poles must be the left side of real-imagine graph.

Reactivity feedback causes the steady operation of nuclear reactor and equilibrium of its dynamical system.

A transfer function can be either linear or not. Each system variable can be affected as an input reactivity to transfer function as shown in Fig.2 :

To evaluate the thermal hydraulic performance of the IPR-R1 reactor one instrumented fuel element was put in the core for the experiments. The instrumented fuel is identical to standard fuel elements but it is equipped with three chromel-alumel thermocouples, embedded in the zirconium pin centerline. The sensitive tips of the thermocouples are located one at the center of the fuel section and the other two 25.4 mm above, and 25.4 mm below the center. Figure 18 shows the diagram and design of the instrumented fuel element (Zacarias Mesquita and Cesar Rezende, 2010).

The instrumented fuel element which is placed in proper thimble (B6 position) is obvious in Figure 19, a core upper view.

During the experiments it was observed that the temperature difference between fuel element and the pool water below the reactor core (primary loop inlet temperature) do not change for the same power value. Figure 20 compares the reactor power measuring results using the linear neutron channel and the temperature difference channel method (Zacarias Mesquita and Cesar Rezende, 2007).

There is a good agreement between the two results, although the temperature difference method presents a delay in its response, and it is useful for steady-state or very slow transient. It is notable that the thermal balance method presented in this report is now the standard methodology used for the IPR-R1 TRIGA Reactor power calibration. The heat balance and fuel temperature methods are accurate, but impractical methods for monitoring the instantaneous reactor power level, particularly during transients. For transients the power is monitored by the nuclear detectors, which are calibrated by the thermal balance method (Zacarias Mesquita and Cesar Rezende, 2007).

1.2 Structure of 99Mo production system with solution irradiation method

The schematic diagram of the 99Mo production system with the solution irradiation method is shown in Fig. 1. The system consists of an irradiation system, a supply and circulation system, and a collection and subdivision system. In the irradiation system, an aqueous molybdenum solution in a capsule installed in a reactor core is irradiated with neutrons under static or circulation condition, and 99Mo is generated. In the supply and circulation system, the solution is supplied to the capsule through pipes and is circulated by a circulator in irradiation operation. A gas disposal device and a heat exchanger are installed in order to take measures against the radiolysis gas and heat generated from the solution by irradiation. The system is designed so as to minimize unirradiated solution. In the collection and subdivision system, after the solution including the generated 99Mo is collected from the capsule through pipes, it is treated so as to be products such as PZC-99Mo columns or 99Mo transport containers.

The detailed design of the 99Mo production system is carried out based on the results of future investigations and tests.