此一論文主要目的，在於以頻域程式—LAPUR為主體並結合相關程式，發展一套以此程式處理沸水式核反應器穩定性的控制機制、理論模式與分析方法。首先，本研究進行國內外文獻之蒐集，而後對現有的研究方法、法規與爐心裝填分析做歸納、探討與驗證，並參考國外對於異常事件的研究與討論，確立穩定性分析之特質。此外，透過對LAPUR模分析程式中，中子理論及熱流理論的瞭解，架構出頻域分析的基礎模式，並歸納建立LAPUR5.2程式之方法論。此一方法論之建立，乃是利用LAPUR5.2程式並結合其他相關程式的分析模式，經過核一廠、核二廠爐心核燃料重新裝填之平行驗證已確認其準確性。因而建立標準的分析工作流程，並確認此方法論的可行性，推廣至核四廠的爐心核燃料裝填分析。此外沸水式反應器需建立穩定運轉邊界，以避免不穩定事件發生﹔經由研究發現針對在穩定邊界上的功率/流量點所做的參數靈敏度分析，以熱流相關參數而言，壓力與流量在高功率/流量點會具有較大的變異性，而中子相關參數則是以密度反應度係數與遲延中子分數高功率/流量點會具有較大的變異性。此外這些重要參數，也會因軸向功率形狀與爐心功率震盪形式之不同而有截然不同的結果，這些分析經驗與心得可供核電廠之管制單位與相關研究機構參考。

The purpose of this research which uses a frequency domain code- LAPUR to investigate the controlling mechanisms is to develop analysis methodology for operational instabilities in nuclear boiling water reactor (BWR). This research initially collected the relevant literatures, and then summarized their approaches and regulations. By referring to the studies and discussions on abnormal events, the characteristics of stability analysis have been constructed. We have established LAPUR5.2 methodologies based on the frequency domain code LAPUR5.2 where coupling between neutronic and thermal-hydraulic behaviors are considered. Meanwhile, we have also completed the parallel verifications against vendor’s results for Chinshan (BWR4) and Kuosheng (BWR6) reload design and extended to check Lungmen (ABWR) load design. Sensitivity analyses on various important parameters have been conducted for comparisons. To quantify the effects of various conditions on the global mode and the regional mode, this study employs the reduced-order model and conducts a study of the fractional change in the decay ratio to evaluate the parametric effect of instability on the stability boundary. With respect to global and regional mode parametric sensitivity, density reactivity coefficient, system pressure, delayed-neutron fraction and total core flow and recirculation loop gain were associated with larger fractional changes of decay ratios at points of higher power/flow operation.

1. March-Leuba, J., and Otaduy, P. J., “A Comparison of BWR Stability measurements with calculations using the code LAPUR-ΙV”, ORNL/TM-8546, Oak Ridge National Laboratory, January 1983.
2. March-Leuba Jose and Blakeman E. D., “A Mechanism for
Out-Of-Phase Power Instabilities in Boiling Water Reactors,” Nuclear
Science and Engineer, 107, pp.173-179, 1991.
3. Boure, J.A., Bergles, A.E. and Tong, L.S., 1973, Review of two phase flow instability, Nucl. Eng. Des., Vol.25, pp. 165-192
4. Park, G. C., Podowski, M. Z. Becker, M. and R. T. Lahey, Jr., 1986, The Development of a Closed-Form Analytical Model for the Stability Analysis of Nuclear-Coupled Density Wave Oscillations in BWR, Nucl. Eng. Des., Vol. 92, pp. 253-281.
5. Fukuda, M., and Kobori T. (1979) J. Nucl. Sci. Technol., 16, 95.
6. Van Der Hagen, T.H.J.J., D.D.B. Van Bragt, F.J. Van Der Kaa, 1997, Exploring the Dodewaard Type-I and Type-II Stability; From Start-Up to Shut-down, From Stable to Unstable, Ann. Nucl. Energy, Vol. 24 No. pp.659-669.
7. Nayak, A.K., Vijayan, P.K., Saha, D., Venkat Raj, V., Aritomi, M., 2002, Study on the Stability Behavior of a Natural Circulation Pressure Tube Type Boiling Water Reactor, Nuclear Engineering and Design 215 pp.127-137.
8. Cheristofer M. Mowry, 1994. Operational control of boiling water reactor stability. Nuclear Technology Vol. 109, pp. 412-428.
9. Anderson, T.T., 1970, Hydraulic impedance: A tool for predicting boiling loop stability, Nucl. Appl. & Tech., vol.9, pp.422-433.
10. Carmichael, L. A., Neimi, R. O., 1978, Transient and Stability test at
Peach Bottom Atomic Power Station Unit 2 at end of cycle 2, EPRI
NP-564.
11. Woffinden, F. B. and Niemi, R. O., 1981, Low-flow stability tests at
Peach Bottom Atomic Power Station Unit 2 at end of cycle 3, EPRI
NP- 972.
12. Enomoto, T., Muto, S., Ishizuka, T., Tanabe, A., Mitsutake, T. and Sakurai, M., 1985, Thermal Hydraulic Stability Experiments in Rod Bundle, Proceedings of the Third Int. Topical Meeting on Reactor Thermal Hydraulics, Newport, R. I., USA, Vol. 1, Paper 9.B.
13. Kruijf, W.J.M., Sengstag, T., Haas, D.W., Van der Hagen, T.H.J.J., 2004, Experimental Theermohydraulic Stability Map of a Frenon-12 Boilig Water Reactor Facility with High Exit Friction, Nuclear Engineer and Design 229 75-80.
14. Meyer, J. E. and Rose, R. P., 1963, Application of a Momentum
Integral Model to the Study of Parallel Channel Boiling Flow
Oscillation, J, Heat Trans. ASME.
15. Yokomizo, O., 1983, Time-Domain Analysis of BWR Core Stability J. Nucl. Sci, and Tech., Vol. 20, pp. 63-76.
16. March-Leuba, J., Pere, R. B. and Cacuci, D. G., 1984, Calculation of Limit Cycle Amplitudes in Commercial Boiling Water Reactors, Trans. Am. Nucl. Soc., Vol. 46.
17. Takigawa, Y., Takeuchi, Y., Tsunoyama, S., Ebata, S., Chan. K.C., Tricoli, C., 1987. Coarso limit cycle analysis with three-dimensional transient code TOSDYN-2 Nucl. Tech., vol. 79, 210-218.
18. Wallis, G. B. and Heasly, J. H., 1961, Oscillation in Two-Phase Flow Systems, J. Heat Transfer, ASME, pp. 363-369.
19. Lahey, R. T. and Moody, F. J., 1977, The Thermal Hydraulics of a Boiling Water Nuclear Reactor, American Nuclear Society, Hinsdale, I11.
20. Saha, P. and Zuber, N., 1978, An Analytical Study of the Thermally
Induced Two-Phase Flow Instabilities Including the Effect of
Thermal Nonequilibrium, Int. J. Heat Mass Transfer, Vol. 21, pp.
415-216.
21. March-Leuba, J., Cacuci, D.G., Perez, R.B., 1986, Nonlinear dynamics and stability of boiling water reactors: Part 1- qualitative analysis. Nuclear Science and Engineering 93, 111-123.
22. 曾文煌，“LASALLE-2沸水式反應爐熱流不穩定性事件”，台電
核能月刊，6/1990，pp. 50-57。
23. March-Leuba, José and Rey, José M., “Coupled Thermohydraulic-
Neutronic Instabilities in Boiling Water Nuclear Reactors：a Review
of the State of the Art,” Nuclear Engineering and Design, Vol. 145,
pp. 97-111, 1993.
24. D’Auria, F. et al, “State of the Art Report (SOAR) on BWR Stability,” OECD-NEA, 5/1996.
25. March-Leuba, J., LAPUR benchmark against in-phase and out-phase
stability tests, NUREG/CR-5605, ORNL/TM-1162, 1990.
26. Muto, S., Yokomizo, Y., Fukahori, T., Ebata, S., 1990. Space
dependent analysis of BWR core nuclear thermal hydraulic instability
and thermal margin. Nuclear Engineer Design 120, 227-239.
27. Araya, F., Yoshida, K., Hirano, M., Yabushita, Y., 1991. Analysis of
neutron flux oscillation event at LaSalle 2. Nucl. Technol. 93, 82-90.
28. 王仲容，”雙相流穩定性時域分析模式之建立與應用”博士論文，清華大學，1993
29. Rao Y.F., Fukuda K. and Kaneshima R. 1995. Analytical study of coupled neutronic and thermohydraulic instabilities in a boiling channel. Nuclear Engineer Design, 154, 133-144.
30. Akitoshi Hotta, Hisahi Ninokata, Hiroyuki Takeuchi, 1997, Development of BWR Regional Instability Model and Verification Based on RIGHALS 1 Test. Ann. Nucl. Energy, Vol. 24 No. 17 pp. 1403-1427.
31. Akitoshi Hotta, Hisahi Ninokata, Hiroyuki Takeuchi, 2000 “Regional instability evaluation of Ringhals unit 1 based on extended frequency domain model” Nuclear Engineer and Design 200 pp.201-220.
32. GN11KI-IN-02.000472.00005, Rev.0, INBERINCO, “Methodology
and procedure for calculation of core and channel decay ratios with
LAPUR”, 2002.
33. Otaduy, P. J., 1979. Modeling of the dynamic behavior of large
boiling water reactor cores” PhD dissertation of The University of Florida.
34. NUREG/CR-6696. ORNL/TM-2000/340, “LAPUR5.2 Verification and User’s Manual”.
35. Munoz-Cobo J. L., Verdu G.,Pereira C., Escriva A., Rodenas J., “Generacion de Parametros Cineticos 1D y Puntuales, a Partir de
SIMULATE-3, para su utilizacion en TRAC/BF1”, Dpto. Ingenieria
Quimica y Nuclear. UPV., 1994.
36. Umbager J. A., Digiovine A. S., “SIMULATE-3, Advanced Three Dimensional Two-Group Reactor Analysis Code. User’s Manual”, Studsvik/SOA-92/01, 1992.
37. GN11KI-IN-02.000472.00005, INBERINCO, “Methodology and procedure for calculation of core and channel decay ratios with LAPUR”, Rev.0, 2002.
38. Escriva, A. and Munoz-Cobo, J. L., “PAPU Models, Correlations,
and User’s Mannul,” ThermalHydraulic and Nuclear Engineering
Group, GTIN-02/001, March 2002.
39. Munoz-Cobo J. L., Verdu G.,Pereira C., Escriva A., Rodenas J.,
Castrillo F., Serra J., “Consistent Generation and Functionalization of One dimensional Cross Sections for TRAC/BF1”, Nuclear Technology, Vol. 107, 1994.
40. Borkowski J. A., Wade N. L., Rouhani S. Z., Shumway R. W.,
Weaver W. L., Retting W. H., Kullberg C. L., “TRAC-BF1/MOD1 Models and Correlations”, NUREGCR4391, EGG-2680, August 1992.
41. 林浩慈、王仲容、施純寬、謝昌倫、邱茗秀, “EXAVERA程式建立與驗證”，, INER-OM-0762R, 中華民國九十四年九月。
42. “STAIF-a computer program for BWR stability analysis in the
frequency domain”, EMF-CC-074(P)(A), 1994.
43. NEDC-32992P-A, DRF A13-00426-00 “ODYSY Application for
Stability Licensing Caculation”, July 2001.
44. 核四龍門電廠（ABWR）訓練教材
45. Masahiro Furuya et al., “Development of BWR Regional Stability Experimental Facility SIRIUS-F, Which Simulates Thermohydraulic-Neutronics Coupling in Reactor Core, and Stability Evaluation of ABWR”, NURETH-11 paper-233, Avignon, France, October 2-6, 2005.
46. Jin Der Lee & Chin Pan “Nonlinear Analysis for a Nuclear-Coupled
Two-Phase Natural Circulation Loop”, Nuclear Engineering and
Design, 235, pp.613-626, 2005.
47. 李進德，”雙相流非線性模式的發展及其應用”， 博士論文，清華大學，2000。
48. J.R. Wang, Chunkuan Shih, B.S. Pei, C. Pan, H.P. Chou, & M.L. Hou, 1991, "Kuosheng BWR/6 Channel Flow Stability Analysis," AIChE Symp. Series, No. 283, 87, 352.
49. J.R. Wang & Chunkuan Shih, 1992, "Kuosheng BWR/6 Recirculation Pump Trip Transient Analysis with RETRAN02/MOD5 Code," Eighth Proc. of Nuclear Thermal/Hydraulics, 95-101, Chicago, USA.
50. Hsieh Chang-Lung., et al., “LAPUR5 BWR stability analysis in Kuosheng nuclear power plant”, The 11th International Topic Meeting on Nuclear Reactor Thermal-Hydraulic, Avignon, France, No.258, October 2-6, 2005.
51. Hao-Tzu Lin, Jong-Rong Wang and Chang-Lung Hsieh et al.,
“Kuosheng BWR/6 stability analysis with LAPUR5 code” Annals of
Nuclear Energy, 33, 289-299, 2006.
52. Hsieh Chang-Lung., et al., “LAPUR5.2 BWR STABILITY ANALYSIS IN CHINSHAN NUCLEAR POWER PLANT”, The 14th International Conference on Nuclear Engineering, Miami, Florida, USA, No.89587, July 17-20, 2006.
53. Hsieh Chang-Lung., et al., “BWR PARAMETRIC SENSITIVITY
EFFECT OF REGIONAL MODE INSTABILITY ON STABILITY BOUNDARY”, The 15th International Conference on Nuclear Engineering, Nagaya, Japan, No.10254, April 22-26, 2007.
54. Hsieh Chang-Lung., et al., “BWR Parametric Sensitivity Effect of Regional Mode Instability on Stability Boundary” Journal of Power and Energy System, Vol.2, NO1, 2008.
55. Hsieh Chang-Lung., et al., “LAPUR5.2 Analysis on Regional Mode Stability” The 12th International Topic Meeting on Nuclear Reactor Thermal-Hydraulic, Pittsburgh, Pennsylvania, USA., No.161, September 30-October 4, 2007.
56. Hsieh Chang-Lung., et al., “A Sensitivity Study of BWR Instability
over Global and Regional Modes at Different Exposures” Nuclear
Engineering and Design, formally accepts in August 2008.
57. Gialdi, E., Grifoni, S., Parmeggiani, C., Tricoli, C., 1985. Core
stability in operating BWR: operational experience. Prog. Nucl.
Energy 15, 447-459.
58. Hänggi Philipp, “Investigating BWR Stability with a New Linear
Frequency-Domain Method and Detailed 3D Neutronics” PhD Dissertation of Swiss Federal Institute of Technology Zurich, (2001).
59. 林浩慈、王仲容、施純寬、謝昌倫,”沸水式反應器穩定性分析
方法之介紹與LAPUR穩定性分析模式之建立”, INER-A0712R,
中華民國九十四年九月。
60. Ping Wu, “Lungmen ODYSY Stability Analysis, Rev. 1”, Ge Nuclear Energy, No.:0000-0026-4971, 4/6/2004