Atomic Energy, Vol. 116, No. 1, May, 2014 (Russian Original Vol. 116, No. 1, January, 2014)

ARTICLES CHANGE IN THE TEMPERATURE COEFFICIENT OF REACTIVITY IN LIGHT-WATER REACTORS DURING FUEL BURNUP

A. D. Klimov,1 V. D. Davidenko,2 V. F. Tsibul’skii,2 and S. V. Tsibul’skii2

UDC 621.039.5

The results of computational studies of the effect of different approximations on the estimation of the temperature coefficient of reactivity are presented. The Doppler effect is evaluated for fuel elements and groups of fuel elements in a light-water reactor (VVER, PWR) fuel assembly using a modified option of the UNC program intended for calculating two-dimensional regions with complex geometry by the first-collision probabilities (FCP) method. It is shown that taking account of the spatial nonuniformity of the resonance absorption and temperature distribution along the radius of a pellet gives a correction to the temperature coefficient of reactivity (toward lower values) by approximately 10% in PWR compared with a calculation by a conventional method, which, as a rule, neglects the factors enumerated. This is characteristic for one fuel element or a group of fuel elements.

An accurate calculation of the temperature coefficient of reactivity is an important problem for formulating the conditions for stable and safe operation of a reactor. A reliable calculation can be performed using computer software that makes it possible to take account of the nonuniformity of the resonance absorption of neutrons along the radius of a fuel pellet, including due to a nonuniform temperature distribution. During burnup, the fuel composition changes and new isotopes appear in the fuel composition, which has an appreciable effect on the temperature coefficient of reactivity. To determine these effects and evaluate their significance, the present investigations were performed using a software system that performs both thermophysical and neutron-physical calculations. As a rule, in most modern software the calculation is performed using an approximate evaluation of the resonance absorption by means of the equivalence theorem. This does not permit analyzing with the required degree of detail the distribution of the resonance absorption along the radius of a fuel pellet or take account of the nonuniformity of the accumulation of new isotopes or accurately determine the effect of the nonuniformity of the temperature distribution on the result. In addition, it is necessary to take detailed account of neutron absorption on individual resonance isotopes taking account of the Doppler broadening of the resonance levels. In the present studies, we used the UNK software which included a module for performing thermophysical calculations making it possible to determine the temperature in all structural elements of a fuel element [1, 2]. A particularity of the UNK software is a detailed calculation of the region of resonance absorption. The energy groups in this computational region

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Dollezhal Research and Development Institute of Power Engineering (NIKIET), Moscow. National Research Center Kurchatov Institute, Moscow.

Translated from Atomnaya Énergiya, Vol. 116, No. 1, pp. 3–5, January, 2014. Original article submitted October 10, 2013.

1063-4258/14/11601-0001 ©2014 Springer Science+Business Media New York

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Fig. 1. Neutron spectrum near a 238U resonance calculated for a fuel pellet (A) and moderator (B) using the UNK and MCU software (——).

Fig. 2. Temperature coefficient of reactivity versus burnup.

were chosen so as to describe in detail the resonance structure of the cross sections of different isotopes. The number of energy groups in the region of allowed resonances is 7000. In addition, a fine nonuniform grid in energy makes it possible to describe well the energy behavior of the neutron cross sections and to perform calculations without blocking resonances beforehand. As an example, the spectra of neutrons in a PWR cell calculated using the MCU and UNK software are presented in Fig. 1. As one can see, good agreement obtains for the energy distribution of the neutrons in a fuel pellet and in the surrounding water. The temperature field in a fuel element is calculated using the heat conduction equation in a cylindrical geometry: 1 ∂ ∂ λ(r )r T (r ) + q v (r ) = 0, r ∂r ∂r

(1)

where λ(r) is the thermal conductivity, T(r) is the temperature, and qv(r) is the energy release. The fuel pellet was divided into 10 concentric zones and the temperature was determined in each zone on the basis of the energy release obtained from a neutron-physical calculation. The BURNUP software was used to calculate the fuel burnup [3]. Two series of computational studies were conducted: at the cell and fuel-assembly levels for a light-water reactor, including with asymmetric boundary conditions [4, 5]. 2

Fig. 3. Fuel temperature distribution at the start (1) and end (2) of a run (burnup 30 GW·days/ton).

Fig. 4. Burnup distribution along the radius of a pellet, average burnup 29 GW·days/ton.

Temperature Coefficient of Reactivity of a PWR Fuel Cell. The calculations were performed for a cell with equivalent radius 0.7108 cm, for a fuel element with outer radius 0.4768 cm, radius of a fuel pellet 0.401 cm with oxide fuel with enrichment 2.6 and 3.8% and water coolant density 0.703 g/cm2. Curve 1 in Fig. 2 corresponds to a conventional calculation of a fuel pellet in the form of one zone with average temperature, curve 2 corresponds to a calculation performed in an approximation of constant temperature along the radius of the fuel element but taking account of the spatial nonuniformity of the resonance absorption, curve 3 corresponds to a calculation with a variable temperature distribution along the radius, and curves 4 and 5 correspond to calculations taking account of the change in the temperature distribution and the increase in the geometric dimensions of a fuel pellet during burnup. On the whole, it can be stated that taking account of the spatial distribution of the resonance absorption over the pellet radius and the nonuniformity of the fuel temperature along the radius leads to an effect where the coefficient of reactivity will be approximately 10% smaller than that obtained in the conventional approximation – a single, constant pellet temperature. During fuel burnup, the temperature changes along the radius of the fuel pellet (Fig. 3). Fuel burnup is also nonuniform along the pellet radius (Fig. 4). Similar conditions also obtain in cells with higher enrichment 3.8% but the nonuniformity of the isotope accumulations and burnup along the radius of a fuel pellet is more pronounced. Fuel Assembly. In the fuel-assembly calculation, all fuel elements were combined into 10 groups with similar burnup conditions. In each group, the fuel elements were represented as multilayer cylinders; a fuel pellet was divided into five cylindrical zones and the temperature in each was calculated along the radius (Fig. 5). The temperature coefficient of reactivity was calculated in an approximation corresponding to the standard representation of a pellet by one zone (Fig. 6, curve 1) and with a fixed temperature distribution along the radius of a pellet (curve 3) 3

Fig. 5. Geometry of PWR fuel assembly: a, A) fuel element; A) absorber.

Fig. 6. Temperature coefficient of reactivity versus the irradiation temperature.

and by five zones assuming the average temperature of a pellet varies (curve 2) and taking account of the temperature change along the radius versus the irradiation time (curve 4). As one can see, taking account of the spatially distributed resonance absorption and temperature nonuniformity underestimates by approximately 10% the temperature coefficient of reactivity compared with a calculation by the standard procedure for a one-zone fuel pellet. Similar calculations were performed for a fuel assembly with asymmetric boundary conditions, which can be interpreted as calculations for a fuel assembly located at the core boundary in a neutron field with a large gradient. The investigations show that for the reactor as a whole the calculation taking account of fuel burnup, spectral changes in different regions, and a nonuniform temperature distribution in the fuel pellet leads to 10–20% deviations in the estimate of the temperature coefficient of reactivity locally in different locations in the core. The total value will depend considerably on how accurately the local values are averaged. It can be supposed that the importance of taking account of the detailed profile of the temperature in a fuel pellet will increase in an analysis of nonstationary processes, when the temperature profile will vary over a much larger range compared with the stationary regime. VVER-1000 Temperature Coefficient of Reactivity. It was calculated using a detailed description of the resonance absorption of neutron in fuel elements. A fuel pellet was divided along the radius into five zones of different volumes and the energy release and fuel temperature based on it were calculated at each burnup step. The temperature coefficient of reactivity was also calculated for a fuel assembly. 4

The computed temperature coefficient of reactivity taking account of and neglecting the spatial distribution of the temperature along the radius of the fuel pellet for the geometry and composition of the fuel characteristic for VVER differs by approximately 5%. The reduction of the effect of the spatial distribution of the temperature along the radius of the pellet on the temperature coefficient of reactivity in VVER compared with PWR is associated with the smaller radius of the fuel pellet.

REFERENCES 1. 2. 3. 4. 5.

N. I. Belousov, V. D. Davidenko, and V. F. Tsibul’skii, UNK Software for Detailed Calculation of the Neutron Spectrum of a Reactor, Preprint IAE-6083/4 (1998). V. D. Davidenko and V. F. Tsibulsky, “Detailed calculation of neutron spectrum in cell of a nuclear reactor,” Int. Conf. Physics of Nuclear Science and Technology, Long Island, New York, Oct. 5–8, 1998, pp. 1755–1760. V. D. Davidenko and V. F. Tsibul’skii, “Burnup calculation in the UNK software,” Neutronics-1999 (2000), pp. 53–55. NEA/NSC/DOC20, Pressurized Water Reactor MOX/UO2 Core Transient Benchmark: Final Report, (2006). IAEA-TECDOC-815, In-Core Fuel Management Code Package Validation for PWRs (1995).

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