For the tests of control rod drive mechanism (CRDM) in nuclear power station, the schematic diagram of the experimental apparatus is given in Fig.8. And the photos of the test system are shown in Figs 9~11.

Fig. 9. Photograph 1 of the test system (CRDM)

There are four floors in the test bench, whose site area is 5m*5m and height is 25m. The photo of the test bench is shown in Fig. 9. The first floor is used to provide ground support for the test section and to settle the pump and pipeline. The second floor is adopted to upper support for
the test section. The test section is joined with CRDM by J seal weld on the second floor. The photo of partial test section is shown in Fig. 10 and Fig. 11. CRDM is settled on the third floor. And the fourth floor is used to settle the crane and provide moving space for the driving rod.

Fig. 10. Photograph 2 of the test system (CRDM)

Fig. 11. Photograph 3 of the test system (CRDM)

The fatigue check takes a central position within the ageing management. The successful fatigue check shows the design-conforming state of cyclic operational loads. During operation of NPPs, particularly the thermal cyclic loadings are fatigue relevant. They are due to transient states of operation. E. g., respective cold or hot feed conditions occur during start-up and shut­down as well as testing conditions of the safety equipment. Furthermore, permanently occurring mixing events of hot and cold flows at junction locations (t-sections) may induce high cycle fatigue loads. Certain plant conditions may induce temperature stratification events within larger pipes at lower flow rates and an existing temperature difference. These phenomena may equally induce cyclic loads in the pipeline and the attached components. Of course, cyclic mechanical loads such as internal pressure or piping loads have to be considered for the fatigue check as well. Until now, the design and operation of NPPs was concentrated on the purpose of base load generation for the respective electrical network. In the future, NPPs will have to take increasing parts of the average and peak load generation due to the growing utilization of renewable energy sources such as wind and solar energy. This generates permanently changing states of the plant which have to be considered within the fatigue check. All these expected loads are examined in the design phase of a power plant as well as
recorded and described in a design transient catalogue. These so called design transients are characterized by the expected temperature ranges, temperature change rates and the expected frequencies of occurrence. Furthermore, the expected internal pressure and — if applicable — stratification states are considered. This transient catalogue constitutes the basis of the design fatigue checks. This first fatigue check is part of the licensing documents and should also indicate fatigue relevant positions and plant processes. If necessary, modifications of the plant processes and/or components are carried out in the design phase with the aim of eliminating potentially critical positions. The task of the fatigue check changes somewhat during the operation of the NPP. In this phase, the fatigue check is primarily used to show that the operation of the plant is within the specified limits. That is to say, the fatigue usage factor for the relevant components has to be reported in a regulated cyclic sequence. As the operational processes differ even for identical technological procedures a simple counting of technological procedures (events) will not necessarily deliver a covering fatigue usage factor. It is also possible to overestimate fatigue usage in case of conservatively specified design transients.

The preliminary qualitative analysis and screening of external events considered for the IRIS PRA was, in general, based on the external events PRA methodology developed by the American Nuclear Society (ANSI/ ANS-58.21, 2003) and on the PRA’s of other NPPs (CESSAR-DC, 1997).

For the quantitative analyses, bounding site characteristics were used in order to minimize potential future restrictions on plant siting. The following four separate steps were performed in order to identify external events to be considered:

1. Initial identification of external events to be analysed in detail.

2. Grouping of events with similar plant effects and consequences.

3. Screening criteria establishment to determine which events are risk insignificant and can therefore be excluded from detailed quantitative analysis.

4. Each event evaluation against the screening criteria to determine if the event is risk — significant and thus requires further quantitative analysis.

PRA Guides and PRAs of existing plants were used as the sources for list of external events development in order to ensure that all external events already recognized as possible threats for IRIS were taken into consideration. The resultant set of external events represented a consensus listing of external events. Then, the list was reviewed in order to group all the external events that are likely to have the same impact on the plant. During this grouping the specific screening criteria were also applied to determine, which events are risk-insignificant and could be excluded from quantitative analysis.

The criteria used for excluding external events from detailed quantitative analysis are:

1. The plant design encompasses events of greater severity than the event under consideration. Therefore, the potential for significant plant damage from the event is negligible.

2. The event cannot occur close enough to the plant to have an effect on the plant’s operation.

3. The event has a significantly lower mean frequency of occurrence than other events with similar uncertainties and could not result in worse consequences than those events.

4. The event is included, explicitly or implicitly, in the occurrence frequency data for another event (internal or external).

5. The event is slow in developing, and it can be demonstrated that there is sufficient time to eliminate the source of the threat or to provide an adequate response.

As it is evident form screening criteria, some external events may not pose a significant threat of a severe accident, if they have a sufficiently low contribution to core damage frequency or plant risk. So, the final step in the qualitative analysis process was the evaluation of each external event against the screening criteria to determine if the event was risk-insignificant and could be excluded from further analysis. Thus, the external events identified as described above were screened out in order to select only the significant events for detailed risk quantification.

As a result of the qualitative analysis or screening criteria application, the identified external events that had beed needed further quantitative scoping evaluation to determine their impact on the core damage were as follows: aircraft crash, high winds or tornadoes and seismic activity.

This list of external events that require an additional analysis was consistent with previous PRAs and with what had been suggested for analysis and the individual plant examination of external events (NUREG-1407, 1991). In addition, a few so called area events such as internal flooding and internal fires were also considered for IRIS. Also an impact of aircraft crash, that had been modelled and quantitatively analysed previously (Alzbutas et al., 2003) was included in the IRIS PRA and presented as an example related to risk zoning (Alzbutas & Maioli, 2008).

1.1.1 Jet switch model

(Roberts, 1962, 1966) considered both a single and a double row of cylinders normal to flow. His analysis was limited to in-flow motion (experiments indicated that instability was purely in the in-flow direction). Roberts assumed that the flow downstream of two-adjacent cylinders could be represented by two wake regions, one large and one small, and a jet between them as shown in Figure 1.

Downstream

Considering a downstream cylinder moving upstream; as the two cylinders cross, insufficient fluid flows in to the large wake region to maintain the entrainment, causing the wake to shrink and the jet to switch directions. Roberts has given the flow equation of motion for a cylinder or tube in a row.

where Cpb is the base pressure coefficient, т is non-dimensional time (trnn), D is the tube diameter, mn is the natural frequency, x is the in-flow cylinder displacement, £ is the damping factor or ratio, S is the logarithmic decrement, and m is mass of the tube. Equation 1 was solved using the method of Krylov and Bogoliubov (Minorsky, 1947) giving Vc, the velocity just sufficient to initiate limit cycle motion for any mS / pD2 . Neglecting unsteady terms and fluid damping, the solution reduces to

C = K 2 I (2)

®nsD PD2)

where є is the ratio of fluid-elastic frequency to structural frequency, which is approximately 1.0 and p is the fluid density. This has the same form as the classical Connors equation (Blevins, 1979). Figure 2 presents Robert’s experimental data for pitch-to — dia. ratio (P / D = 1.5 ), showing a good agreement with this theoretical model.

Fig. 2. Theoretical stability boundary for fluid-elastic instability obtained by Roberts for a single flexible cylinder in a row of cylinders (Roberts, 1966).

1.5 Development of an improved installation procedure for RVI modularization

Under the existing installation procedure, six snubber shims were assembled between the RV core-stabilizing lugs and the CSB snubber lugs after alignment of the CSB and the RV. Subsequently, assembly and flexure welding of the LSS and the CS were conducted. The new and improved installation procedure for RVI modularization was developed allowing assembly and flexure welding of the LSS and the CS to be performed before the main installation process. Alignment of the CSB assembly and the RV and assembly of the snubber shims were undertaken during the main installation process.

The improved installation procedure for RVI modularization (Ko, 2011) appears in Table 4 as order 1 and order 3. A detailed explanation is given below of the flexure welding of the LSS and the CS in the CSB as well as of the alignment and installation of the snubber shims of the CSB assembly and the RV.

1.5.1 Alignment of the CSB and RV and calculation of the dimensions of the snubber

shim

1. The dimensions between the RV outlet nozzle and the reactor coolant loop (RCL) were measured after the welding of the RCL. They were recorded along with the measured dimensions before the welding. The widths of the RV core-stabilizing lugs were also measured.

2. The measured positions were marked on RV keyways and the relative positions of the keyways on the RV centerline were measured using the widths and vertical degrees.

3. The target-hole positions of the RV flange on the RV centerline and the dimensions of the gauge blocks of the RV core stabilizing lug were also measured. Here, the dimensions of the required measurements were the heights and widths of the gauge blocks.

4. Before installation of the gauge blocks, the integrity of the RV core-stabilizing lugs and the cap screws was checked. Neolube was applied twice on both the threaded surfaces on the cap screws and the surfaces of the bearings.

5.1 TRACE code

TRACE (TRACE V5.0, 2010) is a component-oriented code designed to perform best estimate analyses for LWR. In particular this code is developed to simulate operational transients, LOCA, other transients typical of the LWR and to model the thermal hydraulic phenomena taking place in the experimental facilities used to study the steady state and transient behavior of reactor systems (Mascari et al., 2011a).

TRACE is a finite volume, two fluid, code with 3D capability. The code is based on two fluid, two-phase field equations. This set of equations consists of the conservation laws of mass, momentum and energy for liquid and gas fields (Reyes, 2005a):

• Mixture mass conservation equation:

0

—pva +(1 — a)pl ] + V • [pvvva + plvl (1 — a)] = 0 ot

Vapor mass conservation equation:

o

—(Pva) + V-(PvVva) = Tv ot

Liquid momentum conservation equation:

Gas momentum conservation equation:

• Mixture energy conservation equation:

3

T-[(Pvaev + Pi (1 ~ah ] + v • [PvaevVv +Pt (1 — a)eivi ] = — pV — [avv + (1 — a)v1 ] + qwl + qdlv 3t

• Vapor energy conservation equation:

3 3&

—(Pvaev)+^ (Pvaevvv) = — p^r — pv^ (avv)+qwv+qdv + qiv + rvh v 3t 3t

The resulting equation set is coupled to additional equations for non-condensable gas, dissolved boron, control systems and reactor power. Relations for wall drag, interfacial drag, wall heat transfer, interfacial heat transfer, equation of state and static flow regime maps are used for the closure of the field equations. The interaction between the steam — liquid phases and the heat flow from solid structures is also considered. These interactions are in general dependent on flow topology and for this purpose a special flow regime dependent constitutive-equation package has been incorporated into the code.

TRACE uses a pre-CHF flow regime, a stratified flow regime and a post-CHF flow regime. In order to study the thermal history of the structures the heat conduction equation is applied to different geometries. A 2D (r and z) treatment of conduction heat transfer is taken into account as well.

A finite volume numerical method is used to solve the partial differential equations governing the two-phase flow and heat transfer. By default, a multi-step time-differencing procedure that allows the material Courant-limit condition to be exceeded is used to solve the fluid-dynamics equations.

TRACE can be used together with a user-friendly front end, Symbolic Nuclear Analysis Package (SNAP), able to support the user in the development and visualization of the nodalization, to show a direct visualization of selected calculated data, and accepts existing RELAP5 and TRAC-P input. The TRACE/SNAP architecture is shown in figure 11.

SNAP (SNAP users manual, 2007) is a suite of integrated applications including a "Model Editor", "Job Status", the "Configuration Tool" client applications and a "Calculation Server". In particular, the "Model Editor" is used for the nodalization development and visualization and for the visualization of the selected calculated data by using its graphical and animation model capability. The codes currently supported in SNAP are CONTAIN, COBRA, FRAPCON-3, MELCOR, PARCS, RELAP5 and TRACE.

As an application example, the spray line of a PWR system is subject of a detailed code­based fatigue analysis. The load input covers the temperature transients measured during operation. Figure 13 gives an example of a specified temperature transient. This specification of the plant-specific thermo-hydraulic loads in official reports and transient handbooks is realistic, but still conservative. It is obvious that the load specification takes a decisive influence on the fatigue usage calculation and is a source of conservatism.

In the subsequent calculation process all relevant loads and relevant components have to be considered. Furthermore the interaction between the components and the adjacent piping system (supplementary loads resulting from the deformation of the piping sections) cannot be neglected. Based on this requirement, a decision was taken to model the complete spray line system by means of shell type elements. This model containing the spray line, the aux­iliary spray line, and the pressurizer is shown in Figure 14. It allows for the identification of realistic transient piping loads on the fatigue relevant components which are modeled in detail based on brick type elements.

The spray line nozzle, the spool, and the t-section (see Figure 15) were identified as fatigue­relevant components within the spray line system. In a next step, detailed brick type FE models of these three components were generated and integrated into the overall shell type model of the spray line. It is pointed out that the detailed models were considered subse­quently and not simultaneously due to model and file sizes as well as analysis time. Some model statistics are given in Figure 16 for the example of the t-section.

The connection between the shell type and the brick type part of the complete model is achieved by constraint equations (CE) in the case of the transient temperature field analyses and by means of multiple point constraints (MPC) in the case of the structural mechanical

analyses. Nearly one million nodes yield considerable computing times in the transient nonlinear analyses. The complete workflow of the fatigue analysis is shown in Figure 11. A simplified elasto-plastic fatigue analysis was not applicable in this application example. All transient analyses were based on a nonlinear material law with kinematic hardening.

The transient temperature fields were analyzed for all relevant N model transients accord­ing to Figure 11. These transient temperature fields were the input data for the subsequent transient nonlinear structural mechanical analyses yielding the local strains required for code-conforming fatigue assessment. Note that the code-conforming damage accumulation algorithm is not trivial in the case of elasto-plastic analyses. More details on the implementation can be found in [14]. Cycle counting was done in accordance with the requirements of the ASME code as implemented in the ANSYS® Classic Post 1 Fatigue module.

An example of the temperature distribution in the t-joint is shown in Figure 17. It represents one point of time of one model transient. Note that the temperature distribution remains continuous at the border between the solid type and the shell type part of the model. The resulting von-Mises stress distribution for the same point of time is shown qualitatively in Figure 18. Again, the stress distribution remains continuous at the border between the solid type and the shell type part of the model. The MPC approach works very well. It is clearly shown that the thick walled transition regions and thermal sleeve connections are particularly prone to fatigue damage.

Consequently, the fatigue usage analysis revealed the thick walled transition region to be the most relevant location for the fatigue check. Only the elasto-plastic fatigue analysis assured fatigue usage below the admissible value of 1.0.

For more details on the code-conforming fatigue check and associated further developed methods see e. g [15].

Detail model of spool (brick type elements)

Detail model of t-section
(brick type elements)

Detail model of spray line nozzle (brick type elements)

Transient temperature field analyses:

• SHELL131 + SOLID90

• Constraint equations (CE)

Structural mechanical analyses:

• SHELL181 + SOLID95

• „Multiple Point Constraints“ (MPC)

Model statistics:

• 912281 nodes, 243120 elements

• 9 supports

• Pipeline (SHELL):

35700 nodes, 35568 elements

• T-joint (SOLID):

877331 nodes, 207552 elements

Pipeline connection
(shell model)

Fig. 18. Exemplary von-Mises stress distribution in t-section due to thermal loading

7. Conclusions

The AREVA integrated and sustainable concept of fatigue design expresses the importance of design against fatigue in NPPs. Actually, new plants with scheduled operating periods of 60 years, lifetime extension, the modification of the code based approaches and the improvement of operational availability are driving forces in this process. Therefore, applying the AFC is an expression of responsibility sense, as well as an economic requirement. Moreover, the fatigue concept is widely supported by measured data. Indeed, the results of the fatigue monitoring can be the basis for decisions of optimized operating modes and thus influence the fatigue usage factors.

The main modules are FAMOS, the first design analysis before operation, and the three stages of fatigue data evaluation. As all modules are closely connected, it is reasonable to apply the approach as a whole, with an additional cost reduction effect, compared to separate solutions. An integrated software ensures the effective data processing from
measurement to fatigue data calculation and offers the user an easy to use interface to NPP’s loading data. Thus, the integrated fatigue approach makes a significant contribution to the safety margins monitoring, the operational availability and the protection of investment.

8. Acknowledgment

The authors wish to express special thanks to all contributors to the AFC within AREVA.

1.1 Problem formulation

The goal in this chapter is to study the use of the feed-water flow-rate as a manipulated variable to maintain the SG water level within allowable limits, in the face of the changing steam demand resulting from a change in the electrical power demand. The design goal of an FMPC is to minimize the predictive error between an output and a given reference trajectory in the next Ny steps through the selection of Nu step optimal control policies.

The optimization problem can be formulated as

min J(n) (6)

Au(n),Au(n+1,…,Au(n+Nu))

Ny Nu

J(n) = (y(n + i) — yr (n + i ))2 + ‘^uiAu(n + i )2

І=1 І=1

The weighted sum of the local control policies gives the overall control policy:

P

Au(n + i) = ^®;AMj (n + i) (8)

j=1

Substituting (2) and (8) into (7) yields (9)

‘ p у

^ffljAuj (n + i)

U1 )

To simplify the computation, an alternative objective function is proposed as a satisfactory approximation of (9) (Huang et al., 2000).

min J(n) =

Au(n),Au(n+1),…,Au(n+Nu-1)

P 2

min L(yi) +J (n)

Au(n),Au(n+1),…,Au(n+Nu-1) і=1 V ‘

~ У / ‘ 2

V (n) = Ltt (y і (n+г)- у (n+г))

i=1

Nu-1 2

+ L yi (Aui (n+г))

Using the alternative objective function (12), we can derive a controller by a hierarchical control design approach.

1.2 Controller design

1. Lower Layer Design: For the jth subsystem, the optimization problem is defined as follows:

min Ji (n) (13)

Au(n),Au(n+1),…/Au(n+Nu-1)

IF у(n + k -1) is A0/•••, у(n + k- m) is A, m_1 Rj: . . t (14)

THEN у. (n + k) = у. (n + k -1) +L h. Au (n + k — i) +6і (n + k -1)

i=1

where є1 (n + k -1) serves for system coordination and it is determined at the upper layer.

2. Upper Layer Design: The upper layer coordination targets the identification of globally optimal control policies through coordinating 6і (n + k -1) for each local subsystem.

3. System Coordination: The controller is designed through a hierarchical control design (Figure 1). From the lower layer, the local information of output and control is transmitted to the upper layer. The whole design is decomposed into the derivation of p local controllers. The subsystems regulated by those local controllers will be coordinated to derive a globally optimal control policy.

The objective function defined in (11) can be rewritten in a matrix form:

J. (n) = (Y+ (n) — Yr (n))T W. (Y+ (n) — Yr (n)) +

+ (A U + (n))T W2 (A U + (n))

(21) (22) (23) (24) (25) (26) (27) (28) (29) (30)
a[ 0 0 — 0 4 a1 0 0 a3 a2 a1 0 aN У a UNy-1 a1 — UNy — 2 a uNy — Nu+1 al J? —W2 II
Y(n) = (УпаІ (n) УпаІ (n) — У (n)Dd)
P1 (n )=( Pi (n) P’ (n) — Pjy (n))
yT
E+ (n ) =
i T РІ (n) = ^ ^ hlAu(n + k -1) k=1 l=k+1
The resulting control policy for the fh subsystem can be derived as
J1 (n) = (a U+ (n) ) T (a 1 W1A + W2′) A U+ (n) + + (a U+ (n)) T A1 W/Z1 (n) + + ((n)) T W1A1AU+ (n) + ((n)) T WjZ1 (n) where:
Z1 (n) = Y(n) — Yr (n) + P1 (n) + E+ (n) Minimizing (26) yields
S~J (n) = 2(A1T W11A1+ W2) AU+ (n) SAU+ (n) 1 2) +У ’ + 2A1 W1Z1 (n) = 0

The control law by the jth FI can be identified as

(A U + (и ))=- Kj Zj (n) (31)

Kj = (a ’T W1Aj + W2) 1A’T W/ (32)

The optimal global control policies can be derived at the upper layer.

AU+ (n) = (u(и) Am(n +1) ••• Au(n + Nu -1)T (33)

Two types of vibration damage are prevalent in cross-flow regions of steam generators (Shin & Wambsganss, 1975).

• Tube-to-baffle impact.

• Tube-to-tube collision.

(Thorngren, 1970) deduced "damage numbers" for the two types of damage, based on the assumption that tube is supported by baffles and deflected by a uniformly distributed lift force. These damage numbers are given by following equations:

where

NBD < 1 for safe design. NcD < 1 for safe design.

CT = Maximum gap between tubes. d = Tube outer diameter.

dt = Tube inner diameter. /B1 = Tube-to-baffle-hole clearance factor.

E = Modulus of elasticity. gc = Gravitational constant.

Bt = Baffle thickness. p = Mass density of shell side fluid.

l = Length of tube between supports. V = Free stream velocity.

Sm = Maximum allowable fatigue stress [ASME Pressure Vessel code Sec. III].

Collision damage is usually predicted together with baffle damage, whereas the latter can be predicted without collision damage being indicated, i. e., baffle damage is important factor when appraising design (Erskine et al., 1973). (Burgreen et al., 1958) were the first to conduct an experiment to investigate vibration of tube for fluid flowing parallel to tube axis. (Quinn, 1962) and (Paidoussis, 1965) have developed analytical and empirical expressions respectively for peak amplitude. Paidoussis give the following expression:

A = a_4 U 1-6s1srQ-25 f dh_’I0’4 P2/3(5 x1Q-4 x Kp) d ~ai I + U2 I d ) I + 4p

Later on a number of expressions for peak and RMS amplitudes have been developed (Shin et al., 1975, Blevins, 1977).

SEA is a systematic process for evaluating the environmental consequences and for identifying the adverse effects of emerging environmental and/or health risks of a proposed policy, plan or programme. This is necessary in order to ensure that they are fully included and appropriately addressed at the earliest appropriate stage of decision making, on a par with economic and social considerations. As such, SEA may also include social and economic considerations. Due to these features SEA is often interchanged with SA, however, some countries and practitioners make SEA more narrow in its scope and almost purely environment oriented. Figure 2 schematically shows different combinations of depth and scope of the assessment.

SEA deals with impacts that are difficult to consider at the project level. It deals with cumulative and synergistic impacts of technologies or multiple projects. This is very difficult to address by individual project oriented EIAs.

SEA promotes a better consideration of alternatives and affects the decision-making process at a stage where more alternatives are available for consideration. The following characteristics of SEA should be recognised (Therivel, 2005):

1. SEA is a tool for improving the strategic action, not a post-hoc snapshot;

2. In order to fit into the timescale and resources of the decision-making process, SEA should focus on key environmental/sustainability constraints, thresholds and limits at the appropriate plan-making level. It should not aim to be as detailed as a project oriented environmental impact assessment;

3. SEA aims to identify the best alternative for the development and implementation of policies, plans and programmes;

4. SEA aims to minimize negative impacts, optimize positive ones, and to compensate for the loss of valuable (environmental and other) features and benefits.