Authors & Affiliations
Levchenko V.A., Kascheev M.V., Dorokhovich S.L., Zaytsev A.A.
The Limited Liability Company “Simulation Systems Ltd.”, Obninsk, Russia
Levchenko V.A. – Director, Cand. Sci. (Tech.).
Kascheev M.V. – Chief Researcher, Dr. Sci. (Tech.). Contacts: 133, Lenin avenue, Obninsk, Kaluga region, Russia, 249035. Tel.: +7 (484) 396-03-61; e-mail:
Dorokhovich S.L. – Chief Engineer, Cand. Sci. (Tech.), Associate Professor.
Zaytsev A.A. – Head of the Laboratory, Cand. Sci. (Tech.), The Limited Liability Company “Simulation Systems Ltd.”.
Abstract
The problem of determining a non-stationary two-dimensional temperature field in an annular fuel element consisting of five layers: a fuel core, two fuel claddings and two gaps is solved. In the fuel core, there are heat sources that depend on the coordinates and time. The initial temperatures in the layers are functions of coordinates. The symmetry condition is fulfilled in the center of the fuel element. At the boundary of the contact of the layers, there is an ideal thermal contact: the continuity of temperatures and heat flows. On the inner and outer side surfaces and ends, heat exchange occurs according to the Newton – Richmann law with environments whose temperatures change over time according to an arbitrary law. The thermophysical properties in each layer are constant. The problem is solved taking into account simplifying assumptions: the presence of gaps is taken into account by thermal resistance, and the fuel claddings are considered as plates. For the solution of the problem the following approach is used: by means of the method of finite integral transformations differential operations on longitudinal and transverse coordinates are sequentially excluded, and the determination of time dependence of temperature is reduced to the solution of the ordinary differential equation of the first order. Solutions of the two-dimensional problem of non-stationary thermal conductivity for a fuel element with a central axial hole in fuel pellets, a fuel element without a central hole and a single-zone fuel element (a fuel rod without a fuel cladding) are obtained from the solution for an annular fuel element by simplifications.
Keywords
two-dimensional problem of non-stationary thermal conductivity, annular fuel element, heat sources, thermal resistance, method of finite integral transformations,
characteristic numbers, the transcendental equation, environment
Article Text (PDF, in Russian)
UDC 536.21