臺灣博碩士論文加值系統

氣冷式超高溫反應器 (VHTR) 的發展一直是下一代核電廠很重要的一個選項，所以持續有許多針對此反應器之流場與溫度場設計的研究，尤其一些事故後爐心熱流現象的分析在現今核安要求高漲的時期更顯得格外重要。然而任何爐心事故後的分析都必須以事故前正常運作的狀況為準，而模擬爐心正常運作狀況的正確性又根據許多反應器關鍵的設計參數。在prismatic型式的VHTR中除了許多標準規格外，燃料塊 (fuel blocks) 間冷卻氣體的旁通流 (bypass flow) 是一很重要的因素。本篇研究即以bypass flow的現象為依據來探討爐心正常運作的狀況並驗證計算的合理性，並進一步對冷卻流喪失補充事故 (LOFA) 進行分析。LOFA是指因故失去冷卻流體的補充而使反應爐內無法保持強制對流冷卻的事故。該事故後爐心內主要的移熱機制為自然對流，這也正是本研究的目標，針對LOFA事故後的自然對流狀態進行分析。
計算流體力學 (CFD)，是以最基本的方程式模擬多重物理現象，故能獲得非常詳細的熱流資訊並可廣泛的運用在各種領域，而我們也藉助商用的CFD軟體來分析各種的熱流現象。不過CFD分析的可信度仍取決於軟體中的許多參數與設定，當然也包括受限於電腦運算容量的模擬範圍。因此本研究從最小的單一通道逐漸擴大至1/12爐心之子域進行計算，除逐步確認各項參數與設定外，也確保1/12爐心的子域已經過許多前期研究（小範圍）的局部驗證，能獲得較可信的計算結果。
在確認合適之紊流模式後，將其應用在包含bypass flow的十二分之一扇型的稜柱區塊內，進行爐心正常運作下的穩態計算以探討bypass flow在不同間隙寬度與管壁粗糙度下對爐心熱傳的影響。明顯發現增加間隙寬度會提高爐心最高溫與高低溫差，而增加管壁粗糙度只會拉高爐心溫度但對高低溫差沒有影響。紊流模式、功率分佈和計算範圍等因素的局部驗證也進一步套用在LOFA事故後的暫態計算上。研究發現爐心自然對流狀態的分析明顯受model中幾何外型與功率分部的影響，需要使用更大更全面的範圍來分析。本研究也同時利用局部與整體的對稱假設，提供一在有限電腦資源下較大的模擬範圍，並獲得爐心較詳細的自然對流強度與熱傳資訊。另外也因此確認bypass flow在LOFA事故後所扮演的角色已不似在正常運作下的重要。最後各項前置研究則一一應用或被核對在十二分之一爐心的計算中，局部驗證過的大型model成功提供了更完整且更符合實際情況之LOFA事故後自然對流的狀態與資訊。而針對事故後狀況的分析，大型的1/12爐心計算則更顯得重要。

A prismatic gas-cooled very high temperature reactor (VHTR) is being developed under the next generation nuclear plant program (NGNP) for the United States Department of Energy. It is of interest to know the flow and temperature distributions in the core during normal operation and, especially for the thermal hydraulic phenomena in the reactor core during particular accident scenarios. The accident analysis is initiated from normal operating conditions. The accuracy of the simulation for the normal operating condition depends on many design considerations for the reactor core. One important design consideration for the reactor core of a prismatic VHTR is coolant bypass flow, which occurs in the interstitial regions between fuel blocks. Present study begins with the investigation of core bypass flow phenomena for normal operating conditions, and then investigates a loss of flow accident (LOFA). The LOFA occurs when the coolant circulators are lost for some reason, causing a loss of forced convection through the core. One of the mechanisms that may occur after a LOFA for the transport of heat out of the core is by the natural convection of the coolant. It is also the objective of the present work to characterize the phenomenon of natural convection after a LOFA.
Computational fluid dynamics (CFD) codes, which have simulation capabilities based on the physics of fluid flow and heat transfer, are widely used in various industrial fields. This study investigates core thermal hydraulic phenomena with the assistance of commercial CFD codes. However, the accuracy of CFD computations is affected by several parameters as well as the calculation domain, which is dependent on the capacity of computer. Present study begins with the smallest model, a 2D single channel, and then expands the CFD model gradually to partially validate and investigate the thermal hydraulic phenomena for the reactor core. Therefore, confidence in the accuracy of the biggest model involving the 1/12 core section is increased by having performed several pilot investigations.
Turbulence models that perform well are then used to make steady bypass flow calculations in a symmetric one-twelfth sector of a prismatic block that includes bypass flow. Increasing surface roughness increases the maximum fuel and helium temperatures as do increases in gap width. However, maximum coolant temperature variation due to increased gap width is not changed by surface roughness. Partial validations and recommendations on turbulence model selection are also conducted in LOFA transient computations. Moreover, the present study has found that it is necessary to employ representative geometries of the core to estimate the heat transfer. By taking advantage of global and local symmetries, a detailed estimate of the strength of the resulting natural circulation and the level of heat transfer is obtained in the two sub-region model for limited capacity of computer. The effects of bypass flow after the LOFA are no longer as significant as for normal operation. Many detailed and accurate results are obtained from the 1/12 core model to characterize the phenomena occurring during the natural convection after a LOFA. These situations suggest that a larger computational domain might need to be employed for a LOFA transient condition.

摘要 i
Abstract iii
致謝 v
Acknowledgement vii
Contents ix
Table Captions xiii
Figure Captions xv
Symbols xxi
Chapter 1 Introduction 1
1.1 Description of the reference VHTR 1
1.2 Literature review 5
Chapter 2 CFD Models 9
2.1 Thermal properties 10
2.2 Boundary conditions and settings 15
2.3 Best practices 16
Chapter 3 Results for normal operation 19
3.1 Turbulence models 19
3.1.1 Wall shear stress 19
3.1.2 Nusselt number 23
3.2 Effects of graphite surface roughness 25
3.2.1 Wall shear stress and Nusselt number for rough graphite surfaces 25
3.2.2 Results and discussion 28
3.2.2.1 Smooth graphite surfaces 29
3.2.2.2 Surface relative roughness 0.001 30
3.2.2.3 Surface relative roughness 0.00157 30
3.3 Summary 34
Chapter 4 Results for LOFA 35
4.1 Turbulence models 35
4.1.1 Governing equations 35
4.1.1.1 Standard k-epsilon model (SKE) 36
4.1.1.2 Realizable k-epsilon model (RKE) 37
4.1.1.3 Spalart-Allmaras Turbulence model (SAT) 37
4.1.1.4 Reynolds stress model (RSM) 38
4.1.1.5 Two-layer formulation 38
4.1.2 Results and discussion 40
4.2 Modeling strategies for CFD analysis 54
4.2.1 The effects of the upper and lower plena heights 57
4.2.2 The effects of the distribution of heat generation 58
4.2.3 The effects of distance between sectors 61
4.2.4 One-twelfth section of active core 63
4.3 Effects of bypass flow on the LOFA transient computations 68
4.3.1 Steady state normal operations and validations 69
4.3.2 LOFA transients 71
4.4 Summary 78
Chapter 5 Results for the 1/12 core model 81
5.1 The LOFA transient computations in a VHTR using A 1/12 core model 81
5.1.1 Steady state normal operations and partial validations 82
5.1.2 LOFA transients 84
5.2 Discussion of results for the computations 90
5.3 Summary 93
Chapter 6 Conclusions 95
6.1 Summary 95
6.2 Suggestions 98
References 101
Appendix A Dat for turbulence model validation 107
A.1 Wall Shear stress 107
A.2 Nusselt number 113
Appendix B Efficiency of parallel computation 117
B.1 Usage of cores in a node 117
B.2 Efficiency test for STAR-CCM+ in ALPS 117

[1] GA Technologies, Inc., “Preliminary safety information document for the standard MHTGR”, doc. HTGR-86-024 RV. 13, 1992.
[2] DOE/HTGR-86-024, “Preliminary Safety Information Document for the Standard MHTGR”, Stone & Webster Engineering Corp, 1986, HTGR-86-024.
[3] N. Tak, M. H. Kim, and W. Lee, “Numerical investigation of a heat transfer within the prismatic fuel assembly of a very high temperature reactor”, Annals of Nuclear Energy, 35, 2008, 1892-1899.
[4] H. Sato, R. W. Johnson, and R. R. S chultz, “Preliminary studies of coolant by-pass flows in a prismatic very high temperature reactor using computational fluid dynamics”, NURETH-13, 2009, N13P1428.
[5] H. Sato, R. W. Johnson, and R. R. S chultz, “Computational Fluid Dynamic Analysis of Core By-pass Flow Phenomena in a Prismatic VHTR”, Annals of Nuclear Energy, 37, 2010, 1172-1185.
[6] R. W. Johnson and H. Sato, “Bypass flow computations using a one-twelfth symmetric sector for normal operation in a 350 MWth prismatic VHTR”, Nuclear Engineering and Design, 251, 2012, 84-91.
[7] H. C. No, H. S. Lim, J. Kim, C. Oh, L. Siefken and C. Davis, “Multi-component diffusion analysis and assessment of GAMMA code and improved RELAP5 code”, Nuclear Engineering and Design, 237, 2007, 997-1008.
[8] C. H. Oh, H. S. Kang and E. S. Kim, “Air-ingress analysis: part 2 - computational fluid dynamics models”, Nuclear Engineering and Design, 241, 2011, 213-225.
[9] H. Haque, W. Feltes and G. Brinkman, “Thermal response of a modular high temperature reactor during passive cooldown under pressurized and depressurized conditions”, Nuclear Engineering and Design, 236, 2006, 475-484.
[10] J. P. Simoneau, J. Champigny, B. Mays and L. Lommers, “Three-dimensional simulation of the coupled convective, conductive and radiative heat transfer during decay heat removal in an HTR”, Nuclear Engineering and Design, 237, 2007, 1923-1937.
[11] S. K. Choi and S. O. Kim, “Turbulence modeling of natural convection in enclosures:a review”, Journal of Mechanical Science and Technology, 26 (1), 2012, 283-297.
[12] A. Keshmiri, M. A. Cotton, Y. Addad and D. Laurence, “Turbulence Models and Large Eddy Simulations Applied to Ascending Mixed Convection Flows”, Flow Turbulence Combust, 89, 2012, 407-434.
[13] B. E. Launder and B. I. Sharma, “Application of the Energy Dissipation Model of Turbulence to the Calculation of Flow Near a Spinning Disc”, Letter in Heat and Mass Transfer, 1 (2), 1974, 131-138.
[14] ANSYS, Inc., GAMBIT, version 2.4.6, 2004, 275 Technology Drive, Canonsburg, PA 15317.
[15] General Atomics, “Safety Analysis Report use of H451 Graphite in Fort St. Vrain Fuel Elements”, 1977, GLP-5588.
[16] P. MacDonald, J. Sterbentz, R. Sant, P. Bayless, R. Schultz, H. Gougar, R. Moore, A. Ougouag and W. Terry, “NGNP Preliminary Point Design Results of the Initial Neutronics and Thermal-Hydraulic Assessments”, Idaho National Engineering & Environmental Laboratory, 2003, Report INEEL/EXT-03e00870.
[17] http://webbook.nist.gov/chemistry/fluid/
[18] CD-adapco, STARCCM+, version 6.04.016, 2011, 60 Broadhollow Road, Melville, NY 11747.
[19] J. A. Roberson and C. T. Crowe, Engineering Fluid Mechanics, 3rd edition, Houghton Mifflin Co., Boston, 1985.
[20] R. W. Fox and A. T. McDonald, Introduction to Fluid Mechanics, 3rd edition, John Wiley & Sons, New York, 1985.
[21] T. B. Drew, E. C. Koo and W. H. McAdams, “The friction factors for clean round pipes”, Trans. American Institute of Chemical Engineers, 28, 1932, 56–72.
[22] D. M. McEligot, P. M. Magee and G. Leppert, “Effect of large temperature gradients on convective heat transfer: the downstream region”, Journal of Heat Transfer, 87, 1965, 67–76.
[23] C. Warburton, “Surface roughness of graphite and its effect on friction factor”. Proceedings of the Institution of Mechanical Engineers, 188, 1974, 457-460.
[24] J. Nikuradse, Laws of flow in rough pipes, Trans. National Advisory Committee for Aeronautics, Technical Memorandum 1292, Washington, 1950.
[25] B. Gebhart, Heat Transfer, 2nd edition, McGraw-Hill Book Co., New York, 1971.
[26] W. Nunner, V DI-Forschungsh, 22B, 455, 1956, 5-39.
[27] W. P. Jones and B. E. Lander, “The Prediction of Laminarization with a Two-Equation Model of Turbulence”, Intternational Journal of Heat and Mass Transfer, 15, 1972, 301-314.
[28] T. H. Shih, W. W. Liou, A. Shabbir, Z. Yang and J. Zhu, A New k-ε Eddy Viscosity Model for High Reynolds Number Turbulent Flows Model Development and Validation, National Aeronautics and Space Administration, Technical Memorandum 106721, Washington, D.C., 1994.
[29] P. R. Spalart and S. R. Allmaras, “A one-equation turbulence model for aerodynamic flows”, American Institute of Aeronautics and Astronautics, 1992, AIAA-92-0439.
[30] M. M. Gibson and B. E. Launder, “Ground effects on pressure fluctuations in the atmospheric boundary layer”, Journal of Fluid Mechanics, 86(3), 1978, 491-511.
[31] F. S. Lien and M. A. Leschziner, “Assessment of turbulence-transport models including non-linear RNG eddy-viscosity formulation and second-moment closure for flow over a backward-facing step”, Computers Fluids, 23(8), 1994, 983-1004.
[32] M. Wolfstein, “The velocity and temperature distribution in one-dimensional flow with turbulence augmentation and pressure gradient”, Intternational Journal of Heat and Mass Transfer, 12, 1969, 301-318.
[33] W. Xu, Q. Chen and F. T. M. Nieuwstadt, “A new turbulence model for near-wall natural convection”, Intternational Journal of Heat and Mass Transfer, 41, 1998, 3161-3176.
[34] H. D. Baehr and K. Stephan, Heat Transfer, 2nd edition, Springer, Berlin. 2006,
[35] J. R. Lloyd and W. R. Moran, “Natural Convection Adjacent to Horizontal Surfaces of Various Planforms”, Journal of Heat Transfer, 96 (4), 1974, 443-447.
[36] A. Bejan, “Note on Gill’s solution for free convection in a vertical enclosure”, Journal of Fluid Mechanics, 90, 1979, 561-568.
[37] D. R. Chenoweth and S. Paolucci, “Natural-convection in an enclosed vertical air layer with large horizontal temperature differences”, Journal of Fluid Mechanics, 169, 1986, 173-210.
[38] P. MacDonald, J. Sterbentz, R. Sant, P. Bayless, R. Schultz, H. Gougar, R. Moore, A. Ougouag and W. Terry, “GNP Preliminary Point Design Results of the Initial Neutronics and Thermal-Hydraulic Assessments”, 2003, INEEL/EXT-03-00870, Idaho National Engineering & Environmental Laboratory.
[39] R. W. Johnson and R. R. Schultz, “Bounding Estimate for the ‘Hot’ Channel Coolant Temperature and Preliminary Calculation of Mixing in the Lower Plenum for the NGNP Point Design Using CFD”, 2004, Report INEEL/EXT-04-02570 Rev. 1, Idaho National Engineering & Environmental Laboratory.
[40] P. W. Dittus and L. M. K. Boelter, “Heat transfer in automobile radiators of the tubular type”, University of California publications in engineering, 2, No. 13, 1930, 443-461.
[41] V. Gnielinski, “New equations for heat and mass transfer in turbulent pipe and channel flow”, International Chemical Engineering, 16, 1976, 359-368.
[42] Yu-Hsin Tung, Richard W. Johnson and Hiroyuki Sato, “Effects of graphite surface roughness on bypass flow computations for an HTGR”, Nuclear Engineering and Design, 252, 2012, 78-87.
[43] Yu-Hsin Tung, Yuh-Ming Ferng, Richard W. Johnson and Ching-Chang Chieng, “Study of natural circulation in a VHTR after a LOFA using different turbulence models”, Nuclear Engineering and Design, 263, 2013, 206-217.
[44] Yu-Hsin Tung and Richard W. Johnson, “CFD calculations of natural circulation in a high temperature gas reactor following pressurized circulator shutdown”, ASME 2011 International Mechanical Engineering Congress & Exposition, Denver, Colorado, 2011, November 11-17, IMECE2011-64259.
[45] Yu-Hsin Tung, Richard W. Johnson, Ching-Chang Chieng and Yuh-Ming Ferng, “Modeling Strategies to Compute Natural Circulation Using CFD in A VHTR after A LOFA”, ASME 2012 International Mechanical Engineering Congress & Exposition, Houston, Texas, 2012, Nonember 9-15, 2012, IMECE2012-93007.
[46] Yu-Hsin Tung, Richard W. Johnson, Yuh-Ming Ferng, and Ching-Chang Chieng, “Bypass flow computations on the LOFA transient in a VHTR”, Applied Thermal Engineering, 62, 2014, 415-423.
[47] Philip E. MacDonald, James W. Sterbentz, Robert L. Sant, Paul D. Bayless, Richard R. Schultz, Hans D. Gougar, Richard L. Moore, Abderrafi M. Ougouag and William K. Terry, “NGNP Preliminary Point Design – Results of the Initial Neutronics and Thermal-Hydraulic Assessments”, 2003, INEEL/EXT-03-00870 Rev. 1, Idaho National Engineering & Environmental Laboratory.