Izvestiya vuzov. Yadernaya Energetika

The peer-reviewed scientific and technology journal. ISSN: 0204-3327

Assessment of Neutron Flux Stability in a High Power BN-Type Reactor in Terms of Modal Spatial Kinetic

6/15/2021 2021 - #02 Physics and technology of nuclear reactors

Tormyshev I.V. Gulevich A.V. Eliseev V.A. Stogov V.Yu.

DOI: https://doi.org/10.26583/npe.2021.2.04

UDC: 621.039.51

The article discusses the neutron flux stability in the core of a high-power sodium-cooled fast reactor (of the BN type). The importance of the stability problem for high-power BN-type reactors is associated with the specific features of the layout of their cores, including a large diameter and a ratio of diameter to height about 5. The technique used to substantiate the stability of neutron fields is based on the analysis of the spectrum of the matrix of the system of equations of spatial kinetics describing the core of a high-power BN-type reactor without considering feedback. A computational model of the spatial kinetics of a high-power BN-type reactor has been developed in the modal approximation based on the representation of the unsteady flow as the sum of the eigenfunctions of the conditionally critical problem multiplied by the time-dependent amplitudes. The spectrum of the matrix of the system of ordinary differential equations describing the spatial kinetics of the reactor has been calculated. It is shown that the neutron flux in the core of a high-power BN-type reactor is stable without considering feedback. Test calculations have illustrated the damping of perturbations of the energy release field for a reactor in a critical state. The spatial dependence of unsteady neutron flux is described by the modal approach. The neutron flux is expressed as a sum of the modes of the static diffusion equation, multiplied by the time-dependent expansion coefficients. The ordinary differential equations system for the modal spatial neutron kinetic is developed. The eigenproblem for the ODE system matrix is solved. The stability of the spatial kinetic ODE system without power feedback for BN-type reactor is established. The decay of the neutron field perturbations is demonstrated by the sample spatial kinetic calculations

References

  1. Poplavsky V.M., Matveev V.I., Eliseev V.A., Kuznetsov I.A., Volkov A.V., Shvetsov Yu.E., Khomyakov Yu.S., Tsiboula A.M. Studies on Influence of Sodium Void Reactivity Effect on the Concept of the Core and Safety of Advanced Fast Reactor. Journal of Nuclear Science and Technology. 2011, v. 48, no. 4, pp. 538-546; DOI: https://doi.org/10.1080/18811248.2011.9711731 .
  2. Federal’naya Sluzhba po Ekologicheskomu, Tekhnologicheskomu i Atomnomu Nadzoru. Nuclear Safety Rules for Reactor Facilities of Nuclear Power Plants. NP-082-07. Yadernaya i Radiatsionnaya Bezopasnost’. 2008, no. 1, pp. 52-77 (in Russian).
  3. Akcasu Z. Mathematical Methods in Nuclear Reactor Dynamics. New York. Academic Press, 1971, 460 p.
  4. Coughanowr D.R. Process Systems Analysis and Control. New York. McGraw-Hill, 1991, 566 p.
  5. Bibikov Yu.N. Course in Ordinary Differential Equations. Sankt-Petersburg. Lan’ Publ., 2011, 304 p. (in Russian).
  6. Hashimoto K. Linear Modal Analysis of Out-of-Phase Instability in Boiling Water Reactor Cores. Ann. Nucl. Energy. 1993, v. 20, no. 12, pp. 789-797; DOI: https://doi.org/10.1016/0306-4549(93)90072-W
  7. March-Leuba J. & Blakeman E.D. A Mechanism for Out-of-Phase Power Instabilities in Boiling Water Reactors. Nuclear Science and Engineering. 1991, v. 107, no. 2, pp. 173-179; DOI: https://doi.org/10.13182/NSE91-A15730 .
  8. Miro R., Ginestarb D., Verdu G., Hennigc D. A Nodal Modal Method for the Neutron Diffusion Equation. Application to BWR Instabilities Analysis. Ann. Nuc. Energy. 2002, v. 29, pp. 1171-1194; DOI: https://doi.org/10.1016/S0306-4549(01)00103-7 .
  9. Takeuchi Y., Takigawa Y., Uematsu H. A Study on Boiling Water Reactor Regional Stability from the Viewpoint of Higher Harmonics. Nuclear Technology. 1994, v. 106, no. 3, pp. 300-314; DOI: https://doi.org/10.13182/NT94-A34960 .
  10. Bell J., Glesston S. Nuclear Reactor Theory. Мoscow. Atomizdat Publ., 1974, 494 p. (in Russian).
  11. Gulevich A.V., Dolgikh V.P., Eliseev V.A., Peregudova O.O., Rozhihin E.V., Semenov M.Yu., Stogov V.Yu., Tormyshev I.V. Calculation of the Dominant Ratio for a BN-type Reactor Core. VANT. Ser: Yaderno-Reaktornye Konstanty, 2019, iss. 4, pp. 50-54. (in Russian).
  12. Lehoucq R.B., Sorensen D.C., Yang C. ARPACK Users’ Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1998, 137 p.; DOI: https://doi.org/ 10.1137/1.9780898719628 .
  13. Hindmarsh A.C. «ODEPACK, A Systematized Collection of ODE Solvers», in Scientific Computing, R.S. Stepleman et al. (eds.). North-Holland, Amsterdam, 1983 (Vol. 1 of IMACS Transactions on Scientific Computation), pp. 55-64.
  14. Anderson E., Bai Z., Bischof C., Blackford S., Demmel J., Dongarra J., Du Croz J., Greenbaum A., Hammarling S., McKenney A., Sorensen D. LAPACK Users’ Guide. Philadelphia, PA. Society for Industrial and Applied Mathematics, 1999, 407 p.; DOI: https://doi.org/10.1137/1.9780898719604 .

BN-type reactor neutron field stability spatial kinetic criticality equation eigenfunctions expansion

Link for citing the article: Tormyshev I.V., Gulevich A.V., Eliseev V.A., Stogov V.Yu. Assessment of Neutron Flux Stability in a High Power BN-Type Reactor in Terms of Modal Spatial Kinetic. Izvestiya vuzov. Yadernaya Energetika. 2021, no. 2, pp. 39-48; DOI: https://doi.org/10.26583/npe.2021.2.04 (in Russian).

Open PDF file