Skip to main content
SpringerLink
Log in

An Alternative Formalism for the Single-Heated Channel Numerical Analysis

  • Published:
Mathematical Models and Computer Simulations Aims and scope

Abstract—

Development of quick and versatile simulation packages to investigate time dependent heat transfer phenomena in nuclear reactors or steam generators is an ongoing research interest. The work presented herein is an alternative attempt to address this issue employing a single heated channel framework. A homogenous equivalent mixture is assumed for the two phase flow inside the channel. The sectionalized compressible formalism is further refined and the resultant PDEs are cast into a nodalized layout employing the method of lines as a reduction scheme. Simulation results are presented for the transient heat transfer inside a coolant channel of a nuclear reactor core wherein the incumbent heat flux is affected through an inherent thermo-neutronic feedback mechanism. The overall model reduction strategy likewise provides a suitable platform for the purpose of stability analysis or control synthesis practices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.

Similar content being viewed by others

REFERENCES

  1. S. Bendedk, “A computer code for nuclear reactor core thermal transients,” Kernenergie 21, 29–34 (1978).

    Google Scholar 

  2. W. L. Woodruff, “A kinetics and thermal hydraulics capability for the thermal analysis of research reactors,” Nucl. Technol. 64 (2), 196–206 (1984). https://doi.org/10.13182/NT84-A33342

    Article  Google Scholar 

  3. N. Khola and M. Pandey, “Numerical computation of one-dimensional unsteady two-phase flow using HEM model and IAPWS IF-97 equations of state,” in Proc. 21st Int. Conf. on Nuclear Engineering (Chengdu, China, July 29– August 2, 2013), Vol. 4: Thermal Hydraulics, p. ICONE21-16611 (ASME, 2013). https://doi.org/10.1115/ICONE21-16611

  4. S. H. Sangestani, M. Rahgoshay, N. Vosoughi, and M. A. Allaf, “Study of fast transient pressure drop in VVER‑1000 nuclear reactor using acoustic phenomenon,” Sci. Technol. Nucl. Install. 2018,  7862847 (2018). https://doi.org/10.1155/2018/7862847

    Article  Google Scholar 

  5. J. Al Zain, O. El Hajjaji, T. El Bardouni, and Y. Boulaich, “Coupling of neutronics and thermal-hydraulic codes for simulation of the MNSR reactor,” Nucl. Sci. Eng. 193 (11), 1276–1289 (2019). https://doi.org/10.1080/00295639.2019.1622927

    Article  Google Scholar 

  6. J. E. Meyer, “Hydrodynamic models for the treatment of reactor thermal transients,” Nucl. Sci. Eng. 10 (3), 269–277 (1961). https://doi.org/10.13182/NSE61-A25970

    Article  Google Scholar 

  7. M. Lee and M. S. Kazimi, Transient Response of a Single Heated Channel (MIT, Cambridge, MA, 1984).

    Google Scholar 

  8. J. H. Mahaffy, “Numerics of codes: stability, diffusion and convergence,” Nucl. Eng. Des. 145 (1–2), 131–145 (1993). https://doi.org/10.1016/0029-5493(93)90063-F

    Article  Google Scholar 

  9. H.-X. Li and C. Qi, “Modeling of distributed parameter systems for applications—A synthesized review from time-space separation,” J. Process Control 20 (8), 891–901 (2010). https://doi.org/10.1016/j.jprocont.2010.06.016

    Article  Google Scholar 

  10. F. Shakeri and M. Dehghan, “The method of lines for solution of the one-dimensional wave equation subject to an integral conservation condition,” Comput. Math. Appl. 56 (9), 2175–2188 (2008). https://doi.org/10.1016/j.camwa.2008.03.055

    Article  MathSciNet  MATH  Google Scholar 

  11. M. N. Mikhail, “On the validity and stability of the method of lines for the solution of partial differential equations,” Appl. Math. Comput. 22 (2–3), 89–98 (1987). https://doi.org/10.1016/0096-3003(87)90038-5

    Article  MathSciNet  MATH  Google Scholar 

  12. M. Zarei, “On a reduced order modeling of the nuclear reactor dynamics,” Appl. Math. Comput. 393, 125819 (2021). https://doi.org/10.1016/j.amc.2020.125819

    Article  MathSciNet  MATH  Google Scholar 

  13. S. Paul and S. Singh, “Linear stability analysis of flow instabilities with a nodalized reduced order model in heated channel,” Int. J. Therm. Sci. 98, 312–331 (2015). https://doi.org/10.1016/j.ijthermalsci.2015.07.027

    Article  Google Scholar 

  14. W. J. Garland and B. J. Hand, “Simple functions for the fast approximation of light water thermodynamic properties,” Nucl. Eng. Des. 113 (1), 21–34 (1989). https://doi.org/10.1016/0029-5493(89)90293-8

    Article  Google Scholar 

  15. R. Ashino, M. Nagase, and R. Vaillancourt, “Behind and beyond the MATLAB ODE suite,” Comput. Math. Appl. 40 (4–5), 491–512 (2000). https://doi.org/10.1016/S0898-1221(00)00175-9

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Engineering Department, Shahid Beheshti University, P.O. Box. 1983969411, Tehran, Iran

    M. Zarei

Authors
  1. M. Zarei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Zarei.

Ethics declarations

The author declares that he has no conflicts of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zarei, M. An Alternative Formalism for the Single-Heated Channel Numerical Analysis. Math Models Comput Simul 14, 1044–1050 (2022). https://doi.org/10.1134/S2070048222060187

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2070048222060187

Keywords:

Search

Navigation