安全分析一直是核電廠設計、運轉與安全不可或缺的重要工具。傳統式的核電廠安全分析，端賴系統分析程式，並運用保守度或安全餘裕補足模式之不足以確保核電廠之安全。近年來在電腦運算與儲存能力突飛猛進的助益下，核能安全分析界逐漸地應用計算流體力學(Computational Fluid Dynamics, CFD)程式進行相關之分析。國內既有電廠運轉安全相關改善案或者廠家引進新型燃料之相關安全分析上，也採用CFD程式進行全部或部份分析的案例，並進行分析法制化或申請執照之工作。CFD程式應用於核電廠安全分析，最重要的是理論模式與格點模式的選取以及不準度的評估。然而，核電廠複雜的幾何配置與熱水流現象已超過CFD程式內建一般理論模式的適用範圍。因此，管制單位對於利用泛用型CFD程式進行核電廠安全分析案例之審查，除了如審查相關分析結果與程式驗證報告外，獨立執行CFD分析以做為交叉驗證是必須的。
本研究主要以三維穩態模型為計算基礎，其計算流程包括連續方程式、動量方程式、能量方程式以及紊流方程式。針對不同的燃料管束流進行熱水流分析，並探討不同格點所造成之離散化誤差，量化結果之不準度，作為日後建立CFD分析燃料管束流幾何配置之模式與評估審查導則之先期研究。另外進行紊流模式所造成的不準度進行文獻蒐集及先期分析，作為日後接續計畫之起始研究。

Safety analysis is one of essential tools for the design, operation and safety of nuclear power plants (NPPs). Traditional safety analysis for NPPs depends on system codes with more conservative assumptions or margins to ensure the plant safety, which would scarify the operation flexibility and efficiency. With advantages of dramatic progress in computer power, Computational Fluid Dynamics (CFD) is gradually adopted in the nuclear safety analysis. In addition, Taipower has licensed some safety analysis cases using or partially using the CFD. The most important things for the CFD simulations are the establishment of mesh and models as well as the error estimation. The thermal-hydraulic phenomena related to the reactor safety are so complicated that the models adopted in the commercial CFD may not reasonably capture these characteristics. Independent simulations and cross-check are necessary for the regulator staff to review the CFD issues. Therefore, it is crucial for the regulatory staff to investigate the CFD modeling and assessment. Focusing on modeling the characteristics of fuel bundle flow, this project is to investigate the CFD methodology, influence of different mesh models and its uncertainty. These simulation results can assist the regulator staff in providing the basis of review guidelines for this issue.

摘要 i
ABSTRACT ii
致謝 iii
目錄 iv
表目錄 vi
圖目錄 vii
第一章 緒論 1
1.1 研究背景 1
1.2 研究目的 2
1.3 分析工具 3
第二章 文獻回顧 5
第三章 理論基礎與數值模型 9
3.1 物理模型 9
3.2 統御方程式 (Governing Equation) 12
3.3 紊流模型 (Turbulence Model) 13
3.4 建立格點 15
3.5 數值模式 19
3.6 邊界條件與數值模擬設定 21
第四章 結果與討論 23
4.1 無葉片通道模型分析結果 23
4.2 量化分析 29
4.3 數值格點不準度計算 34
4.4 含葉片通道模型模擬分析結果 40
4.5 量化分析 47
4.6 數值格點不準度計算 51
第五章 模式誤差先期研究 56
5.1 模式誤差介紹 56
5.2 實驗設計 57
5.3 結果討論 60
5.4 未來建議 65
第六章 結論 66
參考文獻 68

1. International Atomic Energy Agency, Use of computational fluid dynamics codes for safety analysis of nuclear reactor systems, IAEA-TECDOC- 1379, 2003.
2. Nuclear Energy Agency, “Assessment of Computational Fluid Dynamics (CFD) for Nuclear Reactor Safety Problems”, NEA/CSNI/R(2007)13, 2008.
3. Nuclear Energy Agency, “Best Practice Guidelines for the use of CFD in nuclear Reactor Safety Applications”, NEA/CSNI/R(2007)5, 2007.
4. M.V. Holloway, H.L. McClusky, D.E. Beasley, “The Effect of Support Grid Features on Local, Single-Phase Heat Transfer Measurements in Rod Bundles”, Journal of Heat Transfer, Volume 126, 2004, pp.43-53.
5. United States Nuclear Regulatory Commission, “Computational Fluid Dynamics Best Practice Guidelines for Dry Cask Applications- Final Report”, NUREG-2152(2013), 2013.
6. L.F. Richardson, “The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, with an Application to the Stresses in a Masonry Dam”, Philosophical Transactions of the Royal Society of London. Series A, Volume 210, 1911, pp.307-357.
7. P.J. Roache, “Quantification of Uncertainty in Computational Fluid Dynamics”, Annual Review of Fluid Mechanics, Volume 29, 1997, pp.123-160.
8. F. Stern, R.V. Wilson, H.W. Coleman, E.G. Paterson, “Comprehensive Approach to Verification and Validation of CFD Simulations—Part 1: Methodology and Procedures”, Journal of Fluids Engineering, Volume 123, 2001, pp.793-802.
9. The American Society of Mechanical Engineers, “Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer”, ASME V&V 20-2009, 2009.
10. P. Spalart, S. Allmaras, “A One-equation Turbulence Model for Aerodynamic Flows”, Technical Report AIAA-92-0439,1992.
11. B. E. Launder, D. B. Spalding, “The Numerical Computation of Turbulent Flows, Computer Methods in Applied Mechanics and Engineering”, Volume 3, Issue 2, 1974, pp.269-289.
12. V. Yakhot, S.A. Orszag, S. Thangam, T.B. Gatski, C.G. Speziale, “Development of Turbulence Models for Shear Flows by a Double Expansion Technique”, Physics of Fluids A, Volume 4, No. 7, 1992, pp.1510-1520.
13. T.H. Shih, W.W. Liou, A. Shabbir, Z. Yang, J. Zhu., “A New k-ε Eddy Viscosity Model for High Reynolds Number Turbulent Flows”, Computers Fluids, Volume 24, No. 3, 1995, pp.227-238.
14. D.C. Wilcox, “Reassessment of the Scale Determining Equation for Advanced Turbulence Models”, AIAA Journal, Volume 26, No. 11, 1988, pp.1299-1310.
15. F.R. Menter, “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications”, AIAA Journal, Volume 32, No. 8, 1994, pp.1598-1605.
16. B. E. Launder, G. J. Reece, W. Rodi, "Progress in the Development of a Reynolds-Stress Turbulent Closure", Journal of Fluid Mechanics, Volume 68, No. 3, 1975, pp.537-566.
17. H. Kato, S. Obayashi, “Approach for uncertainty of turbulence modeling based on data assimilation technique”, Computers & Fluids, Volume 85, 2013, pp.2-7.
18. S.H. Cheung, T.A. Oliver, E.E. Prudencio, S. Prudhomme, R.D. Moser, “Bayesian uncertainty analysis with applications to turbulence modeling”, Reliability Engineering and System Safety, Volume 96, 2011, pp.1137-1149.
19. W. Edeling, P. Cinnella, R. Dwight, H. Bijl, “Bayesian estimates of parameter variability in the k–ε turbulence model”, Journal of Computational Physics, Volume 258, 2014, pp.73-94.
20. Y.S. Tseng, H.H. Fu, T.C. Hung, B.S. Pei, “An optimal parametric design to improve chip cooling”, Applied Thermal Engineering, Volume 27, 2007, pp. 1823-1831.
21. E. Baglietto, H. Ninokata, “A turbulence model study for simulating flow inside tight lattice rod bundles”, Nuclear Engineering and Design, Volume 235, 2005, pp.773–784.