Corresponding author: Sergey B. Vygovskiy (vigovskii@mail.ru)

Academic editor: Boris Balakin

This paper presents the results of the research to study the dependence of the VVER-1000 (1200) cores neutronic characteristics on the cladding – fuel pellet gap conductance coefficient in the process of the fuel burn-up. The purpose of the study was to determine more accurately the dependence of the cladding – fuel pellet gap conductance coefficient on the fuel burn-up as shown in the Final Safety Report for the Bushehr NPP and to determine the extent of the effects this dependence had on the spatial distribution of the neutron field, on the xenon accumulation rate, and on the kinetic and dynamic behavior of the reactor facility. The paper presents the results of calculating the parameters using which the heat engineering safety of the reactor core is monitored in the process of the fuel burn- up (for a generalized fuel load of a VVER-1000) during the transition to an 18-month nuclear fuel cycle. This paper also includes the results of a numerical research to determine the cladding – fuel gap conductance coefficient depending on the fuel burn-up. These results have shown that, in reality, the gap conductance coefficient dependence on the burn-up does not affect greatly the steady-state characteristics. At the same time, it affects to rather a great extent the xenon accumulation rate, specifically in the event of an extended fuel life. In conditions of maneuvering (load following) modes accompanied by the xenon processes in the reactor core. These facts should be into consideration in design of engineering codes, that used to support the operation of the VVER-1000 (1200) and full-scale simulators.

The paper presents the results of the studies into the conductance of the gas gap between the cladding and the fuel pellet (the

The purpose of the study was to investigate the dependence of the VVER-1000 (1200) cores neutronic performance on the gap conductance behavior in a fuel element in the process of burn-up. The study deals with a problem of determining the extent of influence the so-called small effects in reactor physics have on the neutronic performance of thermal neutron reactors. A small effect has nothing to do with manufacturing tolerances or design errors. It is the authors’ opinion that the effect in question is the result of the failure to take into account the thermal resistance of the gap between the fuel cladding and the fuel matrix (Thermal Contact Resistance or the

With only the dependence of the gap conductance relied on for fresh fuel with no burn-up effects taken into account, the magnitude of the temperature reactivity effect at different moments of the fuel cycle can be misjudged severely. The physics of the phenomena taking place in fuel during burn-up is as follows (

The fuel matrix swells and the fuel cracks in the radial direction at the initial burn-up point as gaseous fission products are formed. This leads to a reduction of the fuel element gap between the fuel and the cladding and to an increase in the gap conductance.

The intensity of these processes depends to a large extent on the fuel pellet diameter, the availability of a central hole, and the specific heat load. The larger the diameter of the pellet and the smaller the pellet’s central hole are, and the greater the fuel’s specific heat load is, the more pronounced the process described is. For example, there is a more marked

Based on the calculated Gösgen

Variation in the cladding – fuel pellet gap width at high specific power _{L}

Data from the Bushehr NPP final safety analysis report was analyzed (

The conductance processes in a fuel element were simulated using the procedures to calculate Thermal conductivity coefficient for uranium fuel (UO_{2}) without taking into account the dependence on fuel burn-up and temperature (see Fig.

The gap TCRs were calculated as a function of burn-up at different specific power values based on the developed approximation and compared against the TCRs for the PWR-1000 KONVOI-series fuel dependence (

Fuel gap

Thermal conductivity coefficient of UO2 as a function of temperature at different burn-up values: 1 – 20 MW·day/kg U; 2 – 40 MW·day/kg U; 3 – 60 MW·day/kg U

Gap TCRs as a function of fuel burn-up at different levels of linear power on fuel elements in VVER-1000 (semi-empiric dependences

With regard for the dependences of the

Fig. _{max} = max (_{L}_{L}_{lim}(

Fig.

The maximum difference between the calculated and the maximum allowable linear power on the fuel element of the VVER-1000 at the end of the cycle for stationary fuel loading.: 1 – Gap Conductance Coefficient without taking into account the dependence on burn-up; 2 – Gap Conductance Coefficient taking into account the dependence on burn-up

Dependence of boric acid concentration on the operating time of stationary fuel loading of the VVER-1000 at the end of the cycle: 1 – Gap Conductance Coefficient without taking into account the dependence on burn-up; 2 – Gap Conductance Coefficient taking into account the dependence on burn-up

It can be concluded from the calculation results that there is a small increase in the duration of the reactor cycle for stationary fuel load, with regard for the dependence of conductance on fuel burn-up, which is explained, on the one hand, by a decrease in the effective fuel temperature which improves the neutron multiplying properties of the VVER fuel lattice (

Despite of a small decrease in the linear power margin, it needs to be noted that this leads to somewhat worsened conditions of the reactor core safe operation. Though the extent of the variations obtained is small, the effects the gap conductance dependence on burn-up has on the local power axial distribution across the reactor core shall not be neglected.

The effects the dependence of the gap conductance on burn-up has both on the characteristics and the dynamics of in-core xenon processes has been investigated. Calculations were performed for stationary fuel load with a base power of 3120 MW for an 18-month fuel cycle in different moments of the cycle. The configuration of the in-core axial neutron field was changed by the 20% insertion of the group of regulating control rods and retained in the resultant position for three hours. The reactor power was set as equal to and kept at 75 % of the nominal value by changing the critical concentration of boric acid. Calculations were performed for the moment of cycle: 150, 350 and 485 effective days. The dependences of axial offset on time for 485 effective days are presented in Fig.

Axial offset as a function of time for stationary fuel loading of the VVER-1000 at 75 % of nominal power: 1 – Gap Conductance Coefficient without taking into account the dependence on burn-up; 2 – Gap Conductance Coefficient taking into account the dependence on burn-up

The need for taking into account the dependence of the gap conductance on fuel burn-up is explained by the fact that a high burn-up leads to the greatest possible change in the gap conductance values with, accordingly, the maximum influence on the radial temperature distribution in the fuel pellet. The effect of the thermal contact resistance reduction is comparable with that from the decrease in the fuel conductance. Therefore, it is critical to take into account the dependence of the gap conductance on fuel burn-up leading to a change in the radial temperature distribution in fuel such that the average temperature and, accordingly, the effective fuel temperature decrease as compared to the calculation of the temperature fields in fuel without this effect taken into account. The Doppler effect improves to a certain extent the reactor core’s neutron multiplying properties and leads to increase in the duration of the reactor cycle and a local power growth in the core’s upper and lower parts. The presence of this effect reduces the reactor stability to the local power xenon oscillations in the core at the end of cycle.

Calculations to justify safe operation of the NPP equipment involve the so-called principle of conservatism that can be briefly described as follows. When employed, any approximations and simplifications in the calculation procedures for the nuclear plant safety justification can reduce the nuclear safety level. A valid conclusion on the nuclear safety during calculation of a phenomenon can be made if the calculations really show a safe operation level. And where they provide the results leading indirectly to an increased level of the nuclear safety, approximations and simplifications are better not to be used. It follows from this that there is a need for an increased calculation accuracy of the gap conductance with its dependence on fuel burn-up. These facts should be into consideration in design of engineering codes, that used to support the operation of the VVER-1000 (1200) and full-scale simulators.

_{2}fuel: Review and recommendations.

* Russian text published: Izvestiya vuzov. Yadernaya Energetika (ISSN 0204-3327), 2018, n. 4, pp. 20–30.