Remarks on boiling water reactor stability analysis – part 1: theory and application of bifurcation analysis

References

1 Kirchenmayer, A.: Dynamik des Siedewasserreaktors mit Naturumlauf. Nukleonik, 4 (1962) 122–136Search in Google Scholar

2 Miro, R.;Ginestar, D.;Hennig, D.;Verdu, G.: On the Regional Oscillation Phenomenon in BWR. Progress in Nuclear Energy36 (2000) 189–22910.1016/S0149-1970(00)00005-6Search in Google Scholar

3 Dokhane, A.: BWR Stability and Bifurcation Analysis using a Novel Reduced Order Mode and the System Code RAMONA. Doctoral Thesis, EPFL; Switzerland, 200410.1115/ICONE12-49050Search in Google Scholar

4 Lange, C.: Advanced nonlinear stability analysis of boiling water nuclear reactors. Ph.D. Dissertation; TU Dresden; Germany; 2009Search in Google Scholar

5 Hennig, D.: A Study of Boiling Water Reactor Stability Behaviour. Nuclear Technology125 (1999) 10–31Search in Google Scholar

6 Karve, A. A.;Rizwanuddin, Dorning J. J.: Stability Analysis of BWR Nuclear Coupled Thermal-Hydraulics Using a Simple Model. Nucl. Eng. and Design177 (1997) 155–17710.1016/S0029-5493(97)00192-1Search in Google Scholar

7 Lange, C.;Hennig, D.;Hurtado, A.: An Advanced Reduced Order Model for BWR Stability Analysis. Progress in Nuclear Energy53 (2011) 139–16010.1016/j.pnucene.2010.07.006Search in Google Scholar

8 van Bragt, D. D. B.: Analytical Modelling of BWR Dynamics. PhD Thesis of the Technical University Delft, Delft, The Nederland, 1998Search in Google Scholar

9 Zhou, Q.: Stability and Bifurcation Analyses of Reduced-Order Models of Forced and Natural Circulation BWRs. Ph.D. Dissertation, University of Illinois at Urbana-Champaign, 2006Search in Google Scholar

10 Analytis, M.;Hennig, D.;Karlsson, J. K.-H.: The Physical Mechanism of Core-Wide and Local Instabilities at the Forsmark-1 BWR. Nuclear Engineering and Design205 (2001) 91–9510.1016/S0029-5493(00)00371-XSearch in Google Scholar

11 Lange, C.;Hennig, D.;Hurtado, A.;Dykin, V.;Demazière, C.: Comments on Local Power Oscillation Phenomenon at BWRs. Progress in Nuclear Energy, 60, (2012) 73–8810.1016/j.pnucene.2012.04.008Search in Google Scholar

12 Nayfeh, A. H.;Balachandran, B.: Applied Nonlinear Dynamics. John Wiley & Sons, Inc, New York, Chichester, Brisbane, Toronto, Singapore, 199510.1002/9783527617548Search in Google Scholar

13 Guggenheimer, J.;Holmes, P.: Nonlinear Oscillation, Dynamical Systems, and Bifurcation in Vector Fields. Applied Mathematical Sciences42, Springer Verlag, 198410.1007/978-1-4612-1140-2Search in Google Scholar

14 Karve, A. A.: Nuclear-Coupled Thermal-hydraulic Stability Analysis of Boiling Water Reactors. Ph.D. Dissertation, Virginia University, USA, 1998Search in Google Scholar

15 Hetrick, D. L.: Dynamics of Nuclear Reactors. The University of Chicago Press; Chicago and London, 1971Search in Google Scholar

16 Akcasu, Z.;Lellouche, G. S.;Shotkin, L. M.: Mathematical Methods in the Reactor Dynamics. Academic Press, New York and London, 1971Search in Google Scholar

17 Shotkin, L. M.;Hetrick, D. L.;Schmidt, Th. R.: Effect of delayed Neutrons on Autonomous Nonlinear Power Oscillations. NSE42 (1970) 10–15Search in Google Scholar

18 Hassard, B. D.;Kazarinoff, N. D.;Wan, Y. H.: Theory and Application of Hopf Bifurcation. Cambridge University Press, Cambridge, London, New York, Melbourne, Sydney, 1981Search in Google Scholar

19 Lange, C.;Hennig, D.;Hurtado, A.: A Saddle-Node Bifurcation of Cycles Found in the Parameter Space of a BWR. International Journal of Bifurcation and Chaos22 (2012) 210.1142/S0218127412500411Search in Google Scholar

20 Lange, C.;Hennig, D.;Schulze, M.;Hurtado, A.: Comments on the Application of Bifurcation Analysis in BWR Stability Analysis. Progress in Nuclear Energy, submitted in April 201210.1016/j.pnucene.2013.04.003Search in Google Scholar

21 Dokhane, A.;Hennig, D.;Rizwanuddin, Chawla R.: BWR stability and bifurcation analysis using reduced order models and system codes: Identification of a subcritical Hopf bifurcation using RAMONA. Annals of Nuclear Energy34 (2007) 792–80210.1016/j.anucene.2007.04.003Search in Google Scholar

22 Dokhane, A.;HennigD.;Chawla, R.;Rizwan-Uddin: Semi-analytical bifurcation analysis of two-phase flow in a heated channel. International Journal of Bifurcation and Chaos15 (2005) 2395–240910.1142/S0218127405013381Search in Google Scholar

23 Dokhane, A.;Hennig, D.;Rizwanuddin,ChawlaR.: Nonlinear Stability Analysis with a Novel BWR Reduced Order Model. Physor 2002, Proc. of International Conference on the New Frontiers of Nuclear Technology: Reactor Physics, Safety and High Performance Computing, Seoul, Korea, Oct. 7–10, 2002, CD-ROMSearch in Google Scholar

24 Dokhane, A.;Hennig, D.;Rizwanuddin,Chawla, R.: Nuclear-Coupled Thermal-Hydraulic Nonlinear Stability Analysis Using a Novel BWR Reduced Order Model: Part1 – The Effect of Using Drift Flux Versus Homogeneous Equilibrium Models, Part2: Stability Limits for In-phase and Out-of-phase Oscillations. ICONE11, Tokyo, Japan, April 20–23, 2000Search in Google Scholar

25 Lahey, R. T.Jr.: Wave propagation phenomena in two-phase flow. in: Boiling Heat Transfer, Elsevier Science Publishers B. V., (1992) 123–168Search in Google Scholar

26 Munoz-Cobo, J. L.;Vedu, G.: Application of Hopf Bifurcation and Variational Method to the study of Limit Cycles in Boiling Water Reactors, Ann. of Nucl. Energy15 (1991) 269–30210.1016/0306-4549(91)90012-MSearch in Google Scholar

27 March-Leuba: Dynamical Behaviour of Boiling Water Reactor. Ph.D. Thesis, The University of Tennessee, Knoxville, December 1984Search in Google Scholar

28 Lahey, R. T.Jr. (editor): Boiling Heat Transfer. Elsevier Science Publishers, (1992) 271–315Search in Google Scholar

29 Rizzwan-uddin: Linear and Nonlinear Stability Analyses of Density-Wave Oscillations in Heated Channels. Ph.D. Dissertation of University of Illinois, USA; 1981Search in Google Scholar

30 Achard, J. J.;Drew, L. A.;Lahey, R. T.: The Analysis of Nonlinear Density-Wave Oscillations in Boiling Channels. J. Fluid Mech.155 (1985) 213–23210.1017/S0022112085001781Search in Google Scholar

31 AuriaF. D. (editor): State of the Art Report on BWR Stability. NEA/CSNI/ R(96)21, OECD/GD(97)13, 1997Search in Google Scholar

32 Rizzwan-uddin: Linear and Nonlinear Stability Analyses of Density-Wave Oscillations in Heated Channels. Ph.D. Dissertation of University of Virginia, USA, 1981Search in Google Scholar

33 Yokomizo, O.;Sumida, I.;Anegawa, T.;Yoshimoto, Y.;Fukahori, T.: Examination of Nuclear Thermal Hydraulic Oscillation Modes, in: BWR Core. in: International Workshop on Boiling Water Stability, 17th-19th October 1990, Holtsville, New York, CSNI Report 178, 175–189Search in Google Scholar

34 Tsuji, M.;Nishio, K.;Narita, M.;Ogawa, Y.;Mori, M.: Stability Analysis of BWR Using Bifurcation Theory. Journ. of Nucl. Sciences and Technology30 (1993) 1107–111910.1080/18811248.1993.9734596Search in Google Scholar

35 March-Leuba, Cacuci D. G.;Perez, R. B.: Nonlinear Dynamics and Stability, Part 1. NSE93 (1986) 111–123, Part 2. NSE. 93 (1986) 124–136 (see also: March-Leuba, J.; Blakeman, E. D.: A Mechanism for Out-of-Phase Power Instabilities in Boiling Water Reactors. Nuclear Science and Engineering 107 (1991) 173–179)Search in Google Scholar

36 Akcasu, A. Z.: Mean Square Instability in Boiling Reactors. NSE10 (1961) 337–345Search in Google Scholar

37 Wulff, W.;Cheng, H. S.;Diamond, D. J.;Khatib-Rhabar, M.: A Description and Assessment of RAMONA-3B Mod.0, cycle4: A Computer Code with 3D Neutron Kinetics for BWR System Transients. NUREG/CR-3664, BNL-NUREG-51746, Brookhaven National Laboratory, 1984Search in Google Scholar

38 Rizwan-uddin: Sub- and Supercritical Bifurcations and Turning Points in a Simple BWR Model. PHYSOR 2000, Pittsburgh, USA, May 2000, CD-ROMSearch in Google Scholar

39 Lange, C.;Hennig, D.;Llorens, V. G.;Verdù, G.: Advanced BWR stability analysis with a reduced order model and system code. Proceedings of the 15^th International Conference on Nuclear Engineering, Nagoya, Japan, April 22–26, 2007Search in Google Scholar

40 Lange, C.;Hennig, D.;Hurtado, A.: Remarks to a novel nonlinear BWR stability analysis approach (RAM-ROM methodology). Proceedings of ANFM IV (on CD-ROM, American Nuclear Society, LaGrange Park, IL) April 12–15; Hilton Head Island, South Carolina; USA; 2009Search in Google Scholar

41 van Teefflen: Kernkraftwek Brunsbüttel, Stabilitätsmessungen zum Zyklus 16. KKB Technischer Bericht, 110/01, Dez. 2001Search in Google Scholar

42 Oguma, R.;Bergdahl, B-G.: Investigation of BWR stability at KKW Brunsbüttel. GSE-05-003, Februar 2005Search in Google Scholar

43 Oguma, R.;Bergdahl, B-G.: Investigation of BWR stability during Cycle 18 operation at KKW Brunsbüttel. GSE-05-006, June 2005Search in Google Scholar