Using the diffusion approximation for reactor with cavities calculations
The importance of the radiation calculations in the in-reactor cavities is associated with simulating of the emergency modes in fast breeder reactors (FBR), as well as states with different coolant levels in specially designed channels of passive feedback devices in lead-cooled fast reactors (LFR) or sodium cavities in sodium-cooled fast reactors (SFR).
The Last Flight (LF) method [1 – 8], or the method of the unscattered component is widely known and is commonly used in programs based on the method of spherical harmonics to obtain a solution in a gas medium at some distance from the calculated volume domain (DORT , TORT  and others ). The practice of using it  showed that acceptable results are achievable at a considerable distance from the surface between dense and gas media (more than two meters). A qualitative solution is not guaranteed for cavities within the calculation area.
In addition, it is desirable to implement the cavities calculation methodology in the framework of the approximations used in the reactor calculations, in particular, the diffusion approximation, which introduces certain features: the isotropy of the neutron flux density; forced introduction of a “conditional” calculation cell on the surface between dense and gas media.
If the LF method is oriented on the connection of the source point with the detection point, then in calculating the neutron field in the cavities it is necessary to determine the neutron yield from the surface area of the source and their arrival on a certain surface area of the cavity. To solve the problem, the authors suggested using the approximate solution presented in the paper.
Thus, the authors developed and implemented an algorithm for the in-reactor cavities calculations using the diffusion approximatio
- DOORS3.2 – One-, Two- and Three Dimensional Discrete Ordinates Neutron / Photon Transport Code System, RSICC Computer Code Collection, CCC-650, ORNL, 1988.
- Davison B. The theory of neutron transport. Moscow. Atomizdat Publ., 1960, 520 p. (in Russian).
- Bell D., Glesston S. The theory of nuclear reactors. Moscow. Atomizdat Publ., 1974, 494p. (in Russian).
- Rhoades W.A., Sipmson D.B. The Tort Three-Dimensional Discrete Ordinates Neutron / Photon Transport Code (TORT Version 3), ORNL / TM-13221, October 1997.
- Voloschenko A.M., Russkov A.A. Development of documentation for improved precision code. Report TPI n.a. M.V.Keldysh of the Russian Academy of Sciences. No. 6-12-2012, 2012, 39p. (in Russian).
- Rhoades W.A. and Childs R.L. The DORT Two-Dimensional Discrete Ordinates Code. Nucl. Sci. Eng. 1988, v. 99, pp. 88-89.
- Mynatt F.R., Muckenthaler F.J. and Stevens P.N. Development of a Two-Dimensional Discrete Ordinates Transport Theory for Radiation Shielding, CTC-INF-952, Union Carbide Corp., Nucl. Div., Oak Ridge Natl. Lab. (August 1969).
- «SCALE: A Modular Code System for Performing Standardized Computer Analyses for Licensing Evaluation». January 2009, ORNL/TM-2005⁄39, v. 6, v. I-III, RSICC code package CCC-750.
- Dragunov Yu.G., Lemehov V.V., Smirnov V.S., Chernetsov N.G. Technical solutions and stages of development of the BREST-OD-300 reactor facility. Atomnaya energiya, 2012, v. 113, no. 1 (in Russian).
- Saraev O.M., Noskov Yu.V., Zverev D.L., Vasil’ev B.A., Sedakov V.Yu., Poplavsky V.M., Tsibulya A.M., Ershov V.N., Znamensky S.G. BN-800 design validation and construction status. Atomnaya energiya, 2010, v. 108, iss. 4, pp. 197-201 (in Russian).
- Oshkanov N.N., Saraev O.M., Bakanov M.V., Govorov P.P., Potapov O.A., Ashurko Yu.M., Poplavskii V.M., Vasil’ev B.A., Kamanin Yu.L., Ershov V.N. 30 years of experience in the operation of the sodium fast reactor BN-600. Atomnaya energiya. 2010, v. 108, iss. 4, pp. 186-191 (in Russian).
- Alekseev N.I., Kalugin M.A., Kulakov A.S., Oleinik D.S., Shkarovsky D.A. Testing of the MCU-FR program for calculating the criticality of fast reactors. VANT. Ser. Physics of Nuclear Reactors. 2016, iss. 5, pp. 22-26 (in Russian).
- Gurevich M.I., Kalugin M.A., Oleinik D.S., Shkarovsky D.A. Characteristic features of MCU-FR. VANT. Ser. Physics of Nuclear Reactors. 2016, iss. 5, pp. 17-21 (in Russian).
- Poplavskii V.M., Matveev V.I., Eliseev V.A., Kuznetsov I.A., Volkov A.V., Semenov M.Y., Khomyakov Y.S., Tsibulya A.M. Investigation of the influence of the sodium void effect of reactivity on the technical-economic performance and safety of an advanced fast reactor. Atomnaya Energiya. 2010, v. 108, iss. 4, pp. 289-295 (in Russian).