熔鹽式反應系統的特色為使用熔鹽作為工作流體，而可裂變核種溶解於熔鹽中，此一特性有別於傳統固態燃料反應系統，需要另外考量燃料的膨脹與流動。此系統中，中子物理性質會與熱流性質互相影響，因此中子物理與熱流耦合計算為一了解其特性的步驟。本研究建立一個耦合計算方法，以模擬Feynberg提出自然循環熔鹽迴路的起爐暫態，也更進一步的考量反應器動力學以模擬Molten Salt Reactor Experiment （MSRE）的暫態。
本研究使用SCALE-CSAS6作為爐心物理的計算程式，FLUENT作為熱流的計算程式。兩個自行建立的程式，分別為中子物理與熱流耦合程式（Neutronics and Thermal-hydraulic Coupling Code, NTC）與耦合使用者自訂函式（Coupling User Defined Functions, Coupling UDF）被用於自動化計算流程以進行SCALE-CSAS6與FLUENT之間的資料交換。為確認本研究SCALE-CSAS6與FLUENT使用的經驗與技術無誤，本研究分別使用這兩個工具模擬文獻上的案例，並確認結果與文獻符合，也將自行建立的程式用於莊鈞皓論文中的案例，其使用手動的方式進行中子物理以及熱流的資料交換。本研究結果與莊鈞皓論文中的結果具有一致性，說明了自行建立的程式可正確完成其功能。
第一個案例使用此方法進行自然循環熔鹽迴路的耦合計算，為使模擬在物理上較為合理，本研究建立了新模型、考量熱膨脹對於反應度的負回饋以及移動控制棒以補償負反應度回饋。經由起爐暫態分析，本研究得到了此系統起爐以及穩定運轉狀態時的功率、溫度以及速度分佈。第二個案例模擬具有實驗值的MSRE暫態，當系統爐心功率會隨時間變化時就必須考慮反應器動力學，為此本研究另外開發反應器動力學以及延遲中子孕母流動造成反應度損失的計算工具。本案例耦合計算結果與實驗值對照大致符合，證明本研究的方法可行。

Molten salt system is characterized by using molten salt as its working fluid and fissile dissolved in the molten salt. Unlike traditional solid fuel systems, molten salt expansion and circulation should be additionally considered. Since neutronics and thermal-hydraulic influence each other in the system, neutronics and thermal-hydraulic coupling analysis is a step to understand its characteristics. This study developed a coupling methodology to analysis a molten salt natural circulation loop and the Molten Salt Reactor Experiment (MSRE).
This study used SCALE-CSAS6 as neutronics calculation code and FLUENT as thermal-hydraulic calculation code. Two self-developed codes, Neutronics and Thermal-hydraulic Coupling Code (NTC) and Coupling User Defined Functions (Coupling UDF), were used to automatically control the calculation and exchange data between SCALE-CSAS6 and FLUENT. This study has showing that it operated SCALE-CSAS6 and FLUENT correctly by reproducing the results in the references respectively. The self-developed codes were also applied to the case of Chuang's calculation which exchanged neutronics and thermal-hydraulic data manually. The corresponding results imply that NTC and Coupling UDF can operate correctly.
The first case is startup analyses for the simple natural circulation loop. To make the calculation more physically realistic, this study built new models, considered negative reactivity feedback from thermal expansion, and moved the control rods to compensate the negative reactivity feedback. Via the analyses, my research obtained the temperature, velocity, and power distribution at the startup and stable operational state. The second case is MSRE transient simulation. It is necessary to take account of reactor dynamics when reactor power varies with time. Reactor dynamics and delayed neutron precursors movement reactivity loss codes were additionally developed. This study obtained similar results with the experimental data and thus proved that the coupling methodology is feasible.

[1] 莊鈞皓, “三維簡易自然對流熔鹽式反應器中子及熱水流耦合計算分析,” 國立清華大學, 碩士論文, ROC, 2016.
[2] M. W. Rosenthal, P. R. Kasten, and R. B. Briggs, Molten-Salt Reactors – History, Status, and Potential, Oak Ridge National Laboratory, Tennessee, 1969.
[3] R. C. Robertson, MSRE design and operations report part I description of reactor design, ORNL/TM/728, Oak Ridge National Laboratory, 1965.
[4] Historic Molten-Salt Reactor Experiment Brochure, Oak Ridge National Laboratory, 1965-1972.
[5] Neutronics White Paper V1.1, Transatomic Power Corporation, 2016.
[6] R. Bican, Design of a Small Molten Salt Loop, Nuclear Research Institude Rez, Czech, 2011.
[7] O. Feynberg, “Molten Salt Reactors: New Possibilities, Problems and Solutions,” Taiwanese-Russian Scientific Cooperation Meeting on Nuclear Research and Medicine Application, Moscow, 2012.
[8] M. Aghaie, A. Zolfaghari, and A. Minuchehr, “Coupled Neutronic Thermal-Hydraulic Transient Analysis of Accidents in PWRs,” Annals of Nuclear Energy, vol. 50, 2012, pp. 158-166.
[9] H. Wu and Rizwan-uddin, “A Tightly Coupled Scheme for Neutronics and Thermal-hydraulics Using Open-source Software,” Annuals of Nuclear Energy, vol. 87, 2015, pp. 16-22.
[10] J. Kópházi, D. Lathouwers, and J. L. Kloosterman, “Development of a Three-Dimensional Time-Dependent Calculation Scheme for Molten Salt Reactors and Validation of the Measurement Data of the Molten Salt Reactor Experiment,” Nuclear Science and Engineering, vol. 163, 2009, pp. 118-131.
[11] A. Cammi, V. D. Marcello, L. Luzzi, V. Memoli, and M. E. Ricotti, “A Multi-Physics Modelling Approach to the Dynamics of Molten Salt Reactors,” Annals of Nuclear Energy, vol. 38, 2011, pp. 1356-1327.
[12] C. Fiorina, D. Lathouwers, M. Aufiero, A. Cammi, C. Guerrieri, J. L. Kloosterman, L. Luzzi, and M. E. Ricotti, “Modelling and Analysis of the MSFR Transient Behaviour,” Annals of Nuclear Energy, vol. 64, 2013, pp. 485-498.
[13] K. Nagy, D. Lathouwers, C. G. A. T'Joen, J. L. Kloosterman, and T. H. J. J. van der Hagen, “Steady-State and Dynamic Behavior of a Moderated Molten Salt Reactor,” Annals of Nuclear Energy, vol. 64, 2013, pp. 365-379.
[14] J. Zhou, D. Zhang, S. Qiu, G. Su, W. Tian, and Y. Wu, “Three Dimensional Neutronic/Thermal-hydraulic Coupled Simulation of MSR in Transient State Condition,” Nuclear Engineering and Design, vol. 282, 2014, pp. 93-105.
[15] K. Zhung, Y. Zheng, L. Cao, T. Hu, and H. Wu, “Improvements and Validation of the Transient Analysis Code MOREL for Molten Salt Reactors,” Journal of Nuclear Science and Technology, vol. 54, 2017, pp.878-890.
[16] W. Li, X. Wu, D. Zhang, G. Su, W. Tian, and S. Qiu, “Preliminary Study of Coupling CFD code Fluent and System Code RELAP5,” Annals of Nuclear Energy, vol. 73, 2014, pp. 96-107.
[17] S. M. Bowman, KENO-VI Primer: A Primer for Criticality Calculations with SCALE/KENO-VI Using GEEWIZ, Oak Ridge National Laboratory, 2008.
[18] ANSYS FLUENT 12.0 User's Guide, ANSYS, Inc, 2009.
[19] ANSYS Fluent UDF Manual, 12 ed., ANSYS, Inc, 2009.
[20] ANSYS Fluent Theory Guide, 18ed., ANSYS, Inc, 2017.
[21] J. Y. Kudariyawar, A. M. Vaidya, N. K. Maheshwari, and P. Satyamurthy, “Computational Study of Instabilities in a Rectangular Natural Circulation Loop Using 3D CFD Simulation,” International Journal of Thermal Sciences, vol. 101, 2015, pp. 193-206.
[22] K. O. Ott and R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, USA, 1985.
[23] 趙芝震, “熔鹽式反應器爐心物理自動化計算程序開發與應用,” 國立清華大學, 碩士論文, ROC, 2013.
[24] M. A. Jessee and M. D. DeHart , TRITON- A Multipurpose Transport, Depletion, and Sensitivity, and Uncertainty Analysis Module, Oak Ridge National Laboratory, 2011.
[25] J. Y. Kudariyawar, A. K. Srivastava, A. M. Vaidya, N. K. Maheshwari, and P. Satyamurthy, “Computational and Experimental Investigation of Steady State and Transient Characteristics of Molten Salt Natural Circulation Loop,” Applied Thermal Engineering, vol. 99, 2016, pp.560-571.
[26] D. Samuel, “Molten Salt Coolants For High Temperature Reactors A Literature Summary Of Key R&D Activities AND Challenges,” IAEA Internship, 2009.
[27] M. Zanetti, A. Cammi, C. Fiorina, and L. Luzzi, “A Geometric Multiscale Modelling Approach to the Analysis of MSR Plant Dynamics,” Progress in Nuclear Energy, vol. 83, 2015, pp. 82-98.
[28] R. E. Thoma, Chemical Aspects of MSRE Operations, ORNL-4658, Oak Ridge National Laboratory, 1971.
[29] S. E. Beall, P. N. Haubenreich, R. B. Lindauer, and J. R. Tallackson, MSRE Design and Operations Report Part V, ORNL/TM/732, Oak Ridge National Laboratory, 1964.
[30] M. Zanetti, L. Luzzi, A. Cammi, and C. Fiorina, “An Innovative Approach to Dynamics Modeling ans Simulation of the Molten Salt Reactor Experiment,” PHYSOR 2014, 2014.
[31] M.W. Rosenthal, R.B. Briggs, and P.R. Kasten, Molten-Salt Reactor Program Semiannual Progress Report, ORNL-4396, Oak Ridge National Laboratory, 1969.
[32] F. P. Incropera, D. P. Dewitt, T. L. Bergman, and A .S. Lavine, Principles of Heat and Mass Transfer, 7th Edition, John Wiley & Sons, Inc, 2013.
[33] R. B. Briggs, Molten-Salt Reactor Program Semiannual Progress Report, ORNL-3708, Oak Ridge National Laboratory, 1964.
[34] Y. A. Chao and A. Attard, “A Resolution of the Stiffness Problem of Reactor Kinetics,” Nuclear Science and Engineering, vol. 90, 1985, pp. 40-46.
[35] J. Sánchez, “On the Numerical Solution of the Point Reactor Kinetics Equations by Generalized Runge-Kutta Methods,” Nuclear Science and Engineering, vol. 103, 1989, pp. 94-99.
[36] H. Li, W. Chen, L. Luo. and Q. Zhu, “A New Integral Method for Solving the Point Reactor Neutron Kinetics Equations,” Annals of Nuclear Energy, vol. 36, 2011, pp.427-432.
[37] C. Z. Petersen, M. T. M. B.Vilhena, S. Dulla, and P. Ravetto, “An Analytical Solution of the Point Kinetics Equations with Time-Variable Reactivity by the Decomposition Method,” Progress in Nuclear Energy, vol. 53, 2011, pp. 1091-1094.
[38] D. McMahon and A. Pierson, “A Taylor Series Solution of the Reactor Point Kinetics Equations,” Computational Physics, 2010.
[39] B. Quintero-Leyva, “CORE: A Numerical Algorithm to Solve the Point Kinetics Equations,” Annals of Nuclear Energy, vol. 35, 2008, pp. 2136-2138.
[40] M. Kinard and E. J. Allen, “Efficient Numerical Solution of the Point Kinetics Equations in Nuclear Reactor Dynamics,” Annals of Nuclear Energy, vol. 31, 2004, pp. 1038-1051.
[41] R.C. Steffy, Jr., Experimental Dynamic Analysis of the MSRE with 233U Fuel, ORNL/TM/2997, Oak Ridge National Laboratory, 1970.