ISSN 10637788, Physics of Atomic Nuclei, 2014, Vol. 77, No. 14, pp. 1664–1670. © Pleiades Publishing, Ltd., 2014. Original Russian Text © A.V. Varivtsev, I.Yu. Zhemkov, 2012, published in VANT. Fizika yadernykh reaktorov, 2012, No. 4, pp. 31–38.

Improved Method for Calculating the Radiation Heat Generation in the BOR60 Reactor A. V. Varivtsev* and I. Yu. Zhemkov JSC “SSC RIAR,” Dimitrovgrad10, Ul’yanovsk oblast, 433510 Russia *email: [email protected] Received May 30, 2012

Abstract—The results of theoretical and experimental studies aimed at determining the radiation heat gen eration in the BOR60 reactor reveal the drawbacks of the computational methods used at present. An algo rithm that is free from these drawbacks and allows one to determine the radiation heat generation computa tionally is proposed. Keywords: irradiation device, radiation heat generation, calorimeter, gamma quantum, gamma radiation, fis sion products. DOI: 10.1134/S1063778814140087

INTRODUCTION The research and development activities in support of the projects of advanced fastneutron nuclear reac tors have intensified greatly in recent years. Reactor tests of novel construction materials designed to with stand severe operating conditions constitute a consid erable part of these activities. The validation of the guaranteed service life of assembly components and devices made from these materials requires reliable data on the changes in their initial structure, mechanical properties, and chemical composition induced by the reactor radiation, tem perature, and environment. Such data may be obtained only in the process of reactor tests of samples of these materials under specific conditions with con trolled parameters. Of all the Russian research reactors, the one that provides neutronphysics characteristics (NPCs) and temperature regimes that are the most suitable for test ing the fast reactor materials is the BOR60 fastneu tron research reactor. At the same time, the capabili ties of the BOR60 in terms of monitoring the irradia tion conditions are, for a number of reasons, limited. Hence, the computational methods for determining the parameters of tests of material samples (in partic ular, such an important parameter as the temperature of irradiated samples) require constant improvement. The temperature of irradiated samples depends on the design of the irradiation device (ID) used and the radiation heat generation both in the samples them selves and in the device materials. Therefore, the prob lem of improving the accuracy of calculation of the irradiated sample temperature is related to the prob

lem of reducing the uncertainty in computational esti mates of the radiation heat generation in IDs. The present paper details the results of studies aimed at refining the method for calculating the radi ation heat generation in the BOR60 reactor with the use of modern software packages and experimental data. 1. EXPERIMENTAL The calculation methods may be refined only with the use of experimental data obtained as a result of direct incore measurements. However, reactor exper iments require extensive planning, the development and construction of a specialized experimental device (ED), and considerable material resources and reactor time. In addition, the irradiation time in cell E23 of the BOR60 reactor (the only cell that allows one to perform an experiment with data output) is presently in high demand and may not be available for years to come. Taken together, all these factors render it difficult to perform a dedicated experiment aimed at determining the radiation heat generation. Therefore, we used the data obtained in a unique experiment for the determi nation of the radiation heat generation in the BOR60 reactor core (Fig. 1). This experiment was conducted in 1977 [1]. Since the atomic numbers of components of the majority of the tested construction materials typically fall within the range from 20 to 40, the radiation heat generation in BOR60 was determined in copper sam ples (Z = 29) with the use of the radiation calorimetry techniques [1].

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Fig. 1. The BOR60 reactor core map at the time of measurements. FA is a fuel assembly; EFA is an experimental fuel assembly, MP is a materials research package, SASH is a steel assembly of the side shield, BASH is a breeder assembly of the side shield, and AC, MC, and EP are the CPS rods of automatic and manual control and emergency protection.

An experimental device that incorporated 11 calo rimeters, nine of which were positioned in the median plane (MP) of the core and provided the data on the radial distribution of heat generation within the cell (see Fig. 2), was used in the measurements. The remaining two calorimeters (nos. 1 and 11) were posi tioned at the ED central axis similarly to calorimeter no. 4 at the boundary between the core and the axial blankets (ABs) and provided the data on the axial dis tribution of heat generation. Calorimeter no. 1 was located in the upper part of the ED, and calorimeter no. 11 was positioned in the lower part of the device. The device was installed in cell E23. The BOR60 reactor core map at the time of measurements is shown in Fig. 1. The measurements were conducted at reactor thermal output levels below the nominal one (specifically, at 10, 15, and 20 MW). However, the measurement results were then normalized to the nominal reactor thermal output of the time (40 MW). PHYSICS OF ATOMIC NUCLEI

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The error in the radiation heat generation measure ments was evaluated at ±(6–7)%. 2. SOFTWARE PACKAGES AND CALCULATION MODELS The MCURR software package [2] is designed for calculating the NPCs of nuclear reactors and subcriti cal systems with the use of the Monte Carlo method in arbitrary threedimensional geometry with thorough consideration of the energy dependence of cross sec tions of the interaction of neutrons and gamma quanta with matter. The MCURR calculation results agreed well with the data from various experimental studies in the BOR60 core and outside it (in the side shield, the smaller rotating plug, horizontal channels, and the biological shield). The MCURR heat generation cal culations were performed with the use of the PNDOUS submodule [3].

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(b) 1

+20 cm

2 ... 10

8

Core MP 7

6 5 4 3

2

9 11

To the core center

10

−20 cm

Fig. 2. Arrangement of calorimeters in the ED: (a) the ED transverse section at the core MP level and (b) the ED longitudinal section.

We used the AFPA code [4] and the publicly avail able TORI database [5] to calculate the changes in the nuclide composition of the fuel. The database con tains the data on decay constants of various nuclides, energies and intensities of the emitted gamma quanta, etc. The AFPA code implements analytical treatment of the equations describing the isotope kinetics and allows one to calculate the afterheat, radiation charac teristics (the integral activity and its components and the radiation spectrum and intensity), the burnup, the changes in the isotopic composition of fuel assemblies in the process of irradiation in the reactor, the number of fissions, and the released energy. The afterheat is calculated on the basis of the decay functions from a fission event for fissile isotopes. The results of preliminary theoretical studies of the radiation heat generation obtained in the process of modeling the abovedescribed experiment are detailed in [6]. The present paper gives the calculation data obtained using the BOR60 calculation model with a refined material composition of fuel assemblies, side shield assemblies, working elements of the control and protection system (CPS), and materials research packages. A threedimensional homogenous model of the BOR60 that corresponded to the reactor state at the time of measurements was constructed for the theoret ical study (Fig. 1). The model consists of a set of hex agonal prisms with a size of 45 mm on a turnkey basis with different sections varying in height: the core, the blanket region, etc. Each such section is filled with a homogeneous mixture of fuel (for fuel assemblies), absorber (for CPS rods), steel, coolant, and/or other

materials with their densities being equal to the densi ties of the mentioned materials in actual assemblies. The ED was located in cell E23. The geometry and composition of the ED were described in detail: copper detectors and shells of cal orimeters, the ED cover, and other elements were con sidered separately. The arrangement of calorimeters within the ED in the calculation model corresponded to the actual one. The material of thermocouple wires was mixed homogeneously in the section modeling the coolant. The error in calculated values attributed to the error in nuclear constants and the calculation model inaccuracies (the homogeneous approximation, errors in the isotopic composition of burnup fuel in fuel assemblies and coolant in CPS elements) was evalu ated at ±(3–5)%. 3. COMPARISON BETWEEN THE CALCULATED AND THE EXPERIMENTAL DATA Table 1 gives a comparison of the calculated (Qcalc) and experimental (Qexp) values of the radiation heat generation in calorimeters. For reasons detailed in [1], the results obtained using calorimeters nos. 3, 9, 10, and 11 were deemed unreliable and are not presented in the table. It follows from Table 1 that the calculated radiation heat generation values obtained using the MCURR code differ considerably from the experimental ones. The discrepancies fall within a range of 26–40%, and the mean deviation is 35%. Since this value is well above the errors of experimental studies, it is safe to say

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that the results of calculations of the radiation heat generation in copper samples are systematically understated. Precisionclass codes such as MCURR are rightly considered to be the most reliable codes for modeling the radiation transport and are widely used for the cal culation of reactor NPCs. However, it is known that the codes such as, but not limited to, MCURR and MCNP do not take into account the delayed gamma radiation from fission fragments in calculations per taining to steady states. It is also known [7] that 7– 8 MeV of energy is released in the form of prompt gamma radiation, and another 6–7 MeV is released in the form of delayed gamma radiation in the process of fission of uranium and plutonium nuclei. Thus, the gamma quanta emitted by fission fragments should produce a significant contribution to the radiation heat generation. The share of gamma component Qγ in the total radia tion heat generation is a dominant one (in excess of 90%) for the majority of construction materials. Thus, one should estimate the contribution from the delayed gamma quanta to the gamma component of the radiation heat generation. The component associated with gamma quanta produced in the activation of construction materials with neutrons was not taken into account in the present study. This component is insignificant com pared to the gamma radiation emitted by products of fission of nuclei of the fuel composition in the reactor core.

Table 1. Comparison of the calculated and the experimen tal data Calorimeter no.

Qcalc, W/g

Qexp, W/g

Q calc − Q exp , % exp Q

1 2 4 5 6 7 8

1.65 3.75 3.58 3.54 3.50 3.64 3.51

2.23 6.22 5.61 5.42 5.35 5.92 5.32

–26 –40 –36 –35 –35 –38 –34

4. ESTIMATION OF THE CONTRIBUTION FROM THE DELAYED GAMMA QUANTA TO THE RADIATION HEAT GENERATION Additional theoretical studies were conducted in order to estimate the contribution from the delayed gamma quanta emitted by fission products to Qγ. The NPCs in reactor fuel assemblies under opera tion at an output of 20 MW were first determined. The neutron flux density values and 26group neutron spectra (BNAB groups) were obtained for each fuel assembly. The following values were determined for subsequent calculations: the neutron spectrum averaged over the core (Fig. 3); the neutron flux density averaged over the core: 9.5 × 1014 cm–2 s–1. The obtained results were used as the initial data at the next calculation stage where the nuclide composi tion of the irradiated fuel in the reactor core and spec tral and integral characteristics of the delayed gamma

Neutron fraction, rel. units 1.0E+00 1.0E–01 1.0E–02 1.0E–03 1.0E–04 1.0E–05 1.0E–06 1.0E–07 1.0E–08 1.0E–01

1.0E+01

1.0E+03

1.0E+05 1.0E+07 Neutron energy, eV

Fig. 3. Neutron spectrum averaged over the BOR60 core. PHYSICS OF ATOMIC NUCLEI

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Table 2. Comparison of the experimental and the refined calculated data Calorimeter no.

Qcalc, W/g

Qexp, W/g

Q calc − Q exp , % exp Q

1 2 4 5 6 7 8

2.28 5.42 5.16 5.09 5.06 5.27 5.09

2.23 6.22 5.61 5.42 5.35 5.92 5.32

2 –13 –8 –6 –5 –11 –4

radiation from products of fission of nuclei of the fuel composition under power operation were determined. The calculation was performed using the AFPA code. The fuel composition averaged over the core (with allowance for burnup) was used in the evaluation cal culation. The changes in the nuclide composition of raw materials in breeder shields of the BOR60 reactor were not taken into account. This calculation allowed us to determine the following: activity values of various fission products; intensity values of the gamma radiation from fis sion products for various periods of reactor power operation; the energy spectrum (15 groups) of gamma quanta emitted by fission fragments averaged over the core. The authors of [6] used the intensity value of the delayed gamma quanta corresponding to an estab lished (steady) state to calculate the delayed radiation heat generation component. However, bringing the reactor to power (20 MW) and the measurements themselves took about 5–6 h. In the present study, the intensity value of the delayed gamma radiation in the core is taken to be 4.2 × 1018 s–1, which corresponds to 0.2 days of reactor operation at a power of 20 MW. The radiation heat generation from the delayed gamma radiation in copper detectors was then calcu lated using the MCURR code. We modeled a fixed source of gamma quanta with an energy spectrum obtained using the AFPA code and distributed over the reactor core proportionally to the neutron flux density. In a fashion similar to the experimental values, the obtained calculated heat generation values were nor malized to a reactor thermal output of 40 MW. The calculated radiation heat generation value that includes the delayed gamma radiation is defined by the following sum: Qcalc = Qn + Qγpr + Q γdel , (1) where Qn is the heat generation component associated with neutrons and Qγpr and Qγdel are the components associated with prompt and delayed gamma quanta, respectively.

Table 2 lists the values of the radiation heat genera tion in the detectors obtained experimentally (Qexp) and through calculation (Qcalc) with allowance for the delayed gamma quanta (1). It can be seen from the table that the refined calculated radiation heat gener ation values agree well with the experimental ones. The mean deviation of the calculated values from the experimental data is 7%. This value stays well within the overall uncertainty (9–12%) of the calculation and the experiment. Thus, it may be concluded that the abovedescribed significant discrepancies between the experimental data and the calculated values obtained with the use of the MCURR precision code result primarily from neglecting the delayed gamma radiation from fission products. It follows from the above that a refined method for the calculation determination of the radiation heat generation should be used for planning the irradiation of materials. The algorithm underlying this method is as follows: (i) determine the values of Qn and Qγpr in the studied ID (the calculation is performed using the MCURR code in the criticality calculation regime); (ii) determine the flux density and spectrum of neutrons in each fuel assembly in the reactor core; (iii) calculate (using the AFPA code) the intensity and spectrum of gamma radiation of spent fuel from the reactor fuel assemblies for the specified point in time; (iv) calculate (using the MCURR code) the Q γdel value for a fixed gamma radiation source with given intensity and spectrum; (v) determine the Qcalc value using formula (1). A correction factor for Qγ may be determined using the MCURR code for operational planning and cal culation support of reactor test programs. This factor is calculated according to the following formula: K = Qγ Qγpr ,

(2)

where Qγ may be calculated in two ways: (i) Qγ = Qexp – Qncalc and (ii) Qγ = Q γdel + Qγpr . The averaged value of the correction factor deter mined using Eq. (2) for the Qγ value calculated with MCURR is K = 1.56. For the purposes of operational planning of reactor test programs, one should define the K factor for a typ ical present reactor operating period using formula (2) and use the corrected radiation heat generation values to calculate the temperatures in the ID: Q corr = Qn + Qγpr K .

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1.6

5

1.5

4

1.4

3

1.3

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1 0 4.5

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13.5

18.0 22.5 Core radius, cm

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Specific radiation heat generation, W/g

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1.0 36.0

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1.2 Prompt gamma quanta Prompt + delayed gamma quanta Factor K

1

0 −35 −30 −25 −20 −15 −10 −5 0 5 Core radius, cm

10

15

20

Factor K, rel. units

Specific radiation heat generation, W/g

Fig. 4. Radial distribution of the radiation heat generation in iron.

1.1

25

1.0 30

Fig. 5. Axial distribution of the radiation heat generation in iron.

5. ESTIMATION OF THE CONTRIBUTION FROM THE DELAYED GAMMA QUANTA TO HEAT GENERATION FOR THE CURRENT REACTOR STATE It should be noted that the K factor value for cur rent reactor states may differ from the value obtained for the reactor state in 1977. In the absence of experi mental data, the K factor for current reactor states may be determined only from the calculated values (the second method). The theoretical studies of the radia tion heat generation field from the delayed gamma PHYSICS OF ATOMIC NUCLEI

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quanta for the current reactor state were carried out this way. Figure 4 shows the radial distributions of the gamma component of the radiation heat generation in iron (the most widespread element of construction materials of fast reactors), and Fig. 5 shows the corre sponding axial distributions. The figures also present the K factor dependences on coordinates. It can be seen from these dependences that the K factor may be considered to be constant (~1.53) within the core. The value of 1.53 may be used for operational planning of current reactor test programs. The delayed

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gamma radiation from fission products decays fairly rapidly outside the core (in axial blankets and the side shield). However, a more detailed analysis requires the esti mation of the contribution from the delayed radiation of fission products accumulated in the axial blanket and from the products of activation of construction materials and coolant with neutrons. The contribution from these components was not taken into account in the present study. It should be noted that the delayed gamma radia tion produces a significant contribution to heat gener ation not only in construction materials and coolant but also in fuel materials differing significantly from the standard BOR60 fuel. For example, the contribu tion from the delayed gamma quanta to the overall heat generation for uranium oxide fuel with an enrich ment of 26% (BN600 fuel) is ~5–6%, and the corre sponding contribution for uranium oxide fuel with an enrichment of 10% (fuel of a leadbismuth fast reac tor) is ~6–8%. The improved method for calculating the radiation heat generation described in the present study was tested in a methodological experiment aimed at pro viding the required temperature conditions of irradia tion of materials (steel and hafnium hydride) in vari ous filling media (sodium and lead) in the BOR60 core. The calculation results agreed with the experi mental data within the calculated experimental accu racy. The described method is presently applied in plan ning and calculation support of irradiation programs at the BOR60 reactor. CONCLUSIONS Our studies revealed the drawbacks (specifically, the discrepancy between the calculated and the exper imental radiation heat generation values resulting from the underestimation of the gamma component of the radiation heat generation) of the currently used calculation methods for determining the conditions of irradiation of materials in the BOR60 core. An algorithm for determining the radiation heat generation computationally was proposed. This algo rithm takes into account the delayed gamma quanta emitted by fission products and was implemented on the basis of the MCURR and AFPA software pack ages.

It is sufficient to use the radiation heat generation values corrected according to formula (3) with the fac tor K being determined using Eq. (2) for operational calculation support of irradiation of construction materials in the BOR60 core. The proposed method for computational determi nation of the radiation heat generation made it possi ble to reduce the earlier observed discrepancies between the results of calculations of temperatures and the data from various experiments conducted at the BOR60. The described method may be used most efficiently in the studies conducted at research reactors with a large number of materials research packages (prima rily nonfuel ones) in their cores. The method may also be applied in calculations of the radiation heat gener ation in such components of nuclear reactor cores as the CPS working elements and fuel element claddings. These calculations may cover the operation of power reactors. REFERENCES 1. V. A. Neverov, N. A. Aseev, V. M. Gryazev, and N. V. Krasnoyarov, Preprint NIIAR6(414) (Dimitro vgrad, 1980). 2. E. Gomin and L. Maiorov, in Proceedings of the Inter national Conference on on Mathematics and Computa tion, Reactor Physics, and Environmental Analyses in Nuclear Applications, September 27–30, 1999 (Madrid, Spain, 1999), Vol. 2, p. 997. 3. Yu. E. Vaneev and N. Yu. Marikhin, in Collection of Sci entific Works of State Scientific Center Research Institute of Atomic Reactors (GNTs NIIAR, Dimitrovgrad, 2009), No. 1, p. 27 [in Russian]. 4. G. A. Arkhangel’skaya, Report GNTs RFFEI No. X 33100 (1980). 5. S. Y. F. Chu, L. P. Ekström, and R. B. Firestone, WWW Table of Radioactive Isotopes, Database Version 2/28/99. http://nucleardata.nuclear.lu.se/nucleardata/ toi/. Cited February 6, 2012. 6. A. V. Varivtsev, I. Yu. Zhemkov, O. V. Ishunina, Yu. V. Naboishchikov, V. A. Neverov, Izv. Vyssh. Uchebn. Zaved., Yad. Energet., No. 1, 91 (2012). 7. I. N. Nigmatulin and B. I. Nigmatulin, Nuclear Power Plants (Energoatomizdat, Moscow, 1986) [in Russian].

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