**3. Factors influencing durability of WWER FE cladding under normal conditions**

Using the CET cladding durability estimation method, an analysis of the cladding (stress relieved zircaloy) durability estimation sensitivity to the WWER–1000 main regime and design initial data uncertainty, under variable loading conditions, has been done. The WWER–1000 main regime and design parameters have been devided into two groups: the parameters that influence the cladding failure conditions slightly and the parameters that determine the cladding failure conditions. The second group includes such initial parameters that any one of them gives a change of τ0 estimation near 2 % (or greater) if the initial parameter has been specified at the value assignment interval of 3 %. This group consists of outer cladding diameter, pellet diameter, pellet hole diameter, cladding thickness, pellet

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

> Amplitude of АО change during the maneuver

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

Using this approach, the сomplex 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

Using the CET cladding durability estimation method, an analysis of the cladding (stress relieved zircaloy) durability estimation sensitivity to the WWER–1000 main regime and design initial data uncertainty, under variable loading conditions, has been done. The WWER–1000 main regime and design parameters have been devided into two groups: the parameters that influence the cladding failure conditions slightly and the parameters that determine the cladding failure conditions. The second group includes such initial parameters that any one of them gives a change of τ0 estimation near 2 % (or greater) if the initial parameter has been specified at the value assignment interval of 3 %. This group consists of outer cladding diameter, pellet diameter, pellet hole diameter, cladding thickness, pellet

CF

amplitude 0.929 <sup>705</sup>

than 10 times less 0.942 <sup>706</sup>

The number of daily cycles *Ne,*<sup>0</sup>that cladding can withstand prior to the rapid creep beginning, eff. days

Easy of NR power field stabilization

divergency considerable

divergency amplitude is more

Тable 3. Efficiency comparison for two daily maneuvering algorithms.

efficiency, has been proposed and grounded (Maksimov and Pelykh, 2010).

**3. Factors influencing durability of WWER FE cladding under normal** 

fulfilled – see Table 3.

Divergency of instantaneous and equilibrium АО diagrams

considerable

slight

Аlgorithm

"Tested"

"Proposed"

al., 2009).

**conditions** 

effective density, maximum FE linear heat rate, coolant inlet temperature, coolant inlet pressure, coolant velocity, initial He pressure, FE grid spacing, etc. (Maksimov and Pelykh, 2009). For example, dependence of cladding SDE on the number of effective days *N*, for pellet centre hole diameter *hole d* = 0.140 сm, 0.112 сm and 0.168 сm, is shown in Fig. 4.

Fig. 4. Dependence of SDE on *N* for *hole d* : 0.140 сm (1); 0.112 сm (2); 0.168 сm (3).

Dependence of cladding equivalent stress max( ) σ τ *<sup>e</sup>* and yield stress max 0 σ τ( ) , for the cladding point having the maximum temperature, on the number of effective days *N*, for *hole d* = 0.112 сm and 0.168 сm, is shown in Fig. 5.

Fig. 5. Dependence of cladding yield stress (1) and equivalent stress (2; 3) on *N* for *dhole*: 0.112 сm (2); 0.168 сm (3). Determination of τ0 for *dhole* = 0.112 сm.

Theory of Fuel Life Control Methods at Nuclear

estimation of cladding material failure parameter

fuel operating period (Maksimov and Pelykh, 2009).

operation at 100 % power level when *ql,*max *≤* 273 W/cm – see Table 4.

2010).

Parameter

0 τ

ω

0 τ

ω

loading of WWER-1000.

cladding corrosion rate on its durability.

Power Plants (NPP) with Water-Water Energetic Reactor (WWER) 211

For the combined cycle, the maximum SDE value was obtained for a medium-loading FE of the FA produced by WESTINGHOUSE, which has no pellet centre hole (see Table 1). The same result was obtained for the stationary regime of WWER-1000 (Maksimov and Pelykh,

It has been found that cladding running time, expressed in cycles, for the WWER-1000 combined load cycle decreases from 1925 to 1351 cycles, when FE maximum LHR *ql,*max increases from 248 W/cm tо 298 W/cm (Maksimov and Pelykh, 2010). Having done

the WWER-1000 combined load cycle has an advantage in comparison with stationary

According to FEM, a FE length is divided into *n* equal length AS. In the first publications devoted to the CET-method it was supposed that the central AS is most strained and shortest-lived. However, this assumption does not consider that segments differ in LHR jump value. In addition, it was assumed that a FA stays in the same place over the whole

 , ef. d. 2211 2078 2016 1904 1631 *A*<sup>0</sup> , МJ/m3 33.37 35.66 36.87 39.74 47.64

, % 60 65 68 74 94

 , ef. d. 2246 2102 2032 1903 1576 *A*<sup>0</sup> , МJ/m3 27.36 29.14 30.05 32.10 37.69

, % 57 64 67 74 100

At last, influence of cladding corrosion rate on cladding durability at variable loading was not taken into account. Thus it is necessary to estimate influence of varying duty on all AS, to take account of a real FA transposition algorithm as well as to consider influence of

The amplitude of LHR jumps in AS occurring when the NR thermal power capacity *N* increases from 80% to 100% level, was estimated by the instrumentality of the RS code, which is a verified tool of the WWER-1000 calculation modelling (Philimonov and Мамichev, 1998). Using the RS code, the WWER-1000 core neutron-physical calculation numerical algorithms are based on consideration of simultaneous two-group diffusion equations, which are solved for a three-dimensional object (the reactor core) composed of a limited number of meshes.

Таble 4. Cladding damage parameter for stationary loading and the combined variable

**4. Method to determine the most strained cladding axial segment** 

ω

FE mаximum LHR, W/сm 248 258 263 273 298 Average fast neutron flux density, сm-2s-1 11014 1.041014 1.061014 1.11014 1.21014 Stationary loading

Combined variable loading

after 1576 еf. days, it was found that

Using the value of 0 τ and the calculated dependence of SDE on *N*, the value of *A*0 is found – see Fig. 6.

Fig. 6. Calculation of *A0*.

For the combined variable load cycle, dependence of cladding SDE on the number of effective days *N* for a medium-loading FE of UTVS , ТVS-А and ТVS-W, is shown in Fig. 7.

Fig. 7. Dependence of SDE on *N* for UTVS, TVS-A and TVS-W.

For the combined variable load cycle, dependence of cladding SDE on the number of effective days *N* for a medium-loading FE of UTVS , ТVS-А and ТVS-W, is shown in Fig. 7.

Fig. 7. Dependence of SDE on *N* for UTVS, TVS-A and TVS-W.

and the calculated dependence of SDE on *N*, the value of *A*0 is found

Using the value of 0

Fig. 6. Calculation of *A0*.

– see Fig. 6.

τ

For the combined cycle, the maximum SDE value was obtained for a medium-loading FE of the FA produced by WESTINGHOUSE, which has no pellet centre hole (see Table 1). The same result was obtained for the stationary regime of WWER-1000 (Maksimov and Pelykh, 2010).

It has been found that cladding running time, expressed in cycles, for the WWER-1000 combined load cycle decreases from 1925 to 1351 cycles, when FE maximum LHR *ql,*max increases from 248 W/cm tо 298 W/cm (Maksimov and Pelykh, 2010). Having done estimation of cladding material failure parameter ω after 1576 еf. days, it was found that the WWER-1000 combined load cycle has an advantage in comparison with stationary operation at 100 % power level when *ql,*max *≤* 273 W/cm – see Table 4.

According to FEM, a FE length is divided into *n* equal length AS. In the first publications devoted to the CET-method it was supposed that the central AS is most strained and shortest-lived. However, this assumption does not consider that segments differ in LHR jump value. In addition, it was assumed that a FA stays in the same place over the whole fuel operating period (Maksimov and Pelykh, 2009).


Таble 4. Cladding damage parameter for stationary loading and the combined variable loading of WWER-1000.

At last, influence of cladding corrosion rate on cladding durability at variable loading was not taken into account. Thus it is necessary to estimate influence of varying duty on all AS, to take account of a real FA transposition algorithm as well as to consider influence of cladding corrosion rate on its durability.
