穿臨界(transcritical)有機朗肯循環(organic Rankine cycle，ORC)系統由於在加熱過程中有較高的溫度與較好的熱吻合(thermal match)，可以降低加熱過程中產生的不可逆性，進而增加整體系統熱效率。穿臨界ORC系統的最高操作壓力高於工作流體的臨界壓力，且在升溫的過程中，流體的溫度將會超越臨界溫度，最後工作流體在離開熱交換器之前，會到達超臨界狀態。然而，目前文獻上對有機工作流體在超臨界狀態下的熱傳與壓降特性瞭解相當有限，進而使得穿臨界ORC系統的設計與開發相當困難。本研究的目的在探討穿臨界ORC系統之工作流體在超臨界狀態下的熱傳與壓降特性，包含超臨界熱傳實驗系統的架設與測試標準流成的建立、進行超臨界熱傳不同實驗參數的實驗(如:質量流率、系統壓力、流道管徑)、實驗數據與文獻上經驗式的比較並發展熱傳分析經驗式。
超臨界熱傳實驗參數分別有熱通率、質量流率、系統壓力、與流道管徑等，熱傳遞係數之量測需要壁溫，其可使用埋置於管壁中的T-Type熱電偶直接測量，為了不干擾管內流體流場形態，本研究將用進出口溫度以及能量平衡關係式來內差即可得知管內流體溫度，而實驗所量測溫度對應之熱物理性質均可由NIST 9.1 數據資料庫查詢得知。實驗結果顯示，質量流率的增加對於熱傳能力的提升有著顯著的效果，此與文獻上所呈現的趨勢相符合；管徑尺寸的提升會導致熱傳能力的明顯下降；系統壓力效應對於熱傳能力的影響並不顯著，唯在本研究的最小管徑(2 mm)靠近臨界溫度及假臨界溫度區間時對應的熱傳系數峰值有著隨著壓力增加而上升的趨勢。但是，當管徑增加為4 mm與6 mm，則峰值不再出現。本研究也有發現超臨界熱傳實驗中特有的熱傳惡化的現象。此一現象推測與進入超臨界區域時熱物理性質的劇烈變化有著極大的關係。更進一步分析之後，發現浮力效應在本實驗中也有著顯著的影響，因此在發展經驗式的過程中，也將浮力效應的參數加入迴歸分析，成功發展出合適的經驗式且數據預測的誤差在20%以內，有90%以上的數據在預測範圍之內。

A transcritical organic Rankine cycle (ORC) system has a higher operating temperature and better thermal match during the heating process that can reduce the irreversibility and, therefore, yields a higher thermal efficiency. In a transcritical ORC system, the maximum operation pressure of the working fluid is higher than its critical pressure and the temperature also exceeds the critical temperature during the heating process. Consequently, the fluid reaches its supercritical state during the heating process. However, the knowledge of the heat transfer and pressure drop of the organic fluid at its supercritical states is quite limited, resulting in the difficulty of the design and development of a transcritical ORC system. This study investigates the heat transfer characteristics of the transcritical organic Rankine cycle, including the establishment of the supercritical heat transfer system loop and operating procedures, the conducting experiments at various mass flow rates, system pressures, and tube diameters, the comparison between data and correlations published in literatures, and the development of an empirical correlation to predict the present set of supercritical heat transfer data.
Three different experimental parameters including mass flow rate, system pressure, and tube diameter are varied and their effects on heat transfer are investigated in this study. The wall temperatures along the flow channel are measured using T-type thermocouples embedded within the tube wall, and surface temperatures could then be extrapolated. However, in order to avoid disturbing the flow pattern, local fluid enthalpy can be evaluated based on the energy balance and the corresponding fluid temperature can then be acquired from NIST 9.1 database with other thermophysical properties. The results demonstrate the heat transfer ability increases with increasing mass flow rate. This trend is found to be in good agreement with previous experimental results. The tube diameter has a negative effect on heat transfer ability. Nevertheless, effects of system pressure present insignificant tendency except for the region that the peak of heat transfer coefficient, increasing with the increasing system pressure for the case with the smallest tube diameter. The heat transfer deterioration, which are distinct phenomena to supercritical heat transfer research, are clearly observed. The results also reveal that the heat transfer coefficient is strongly affected by the steep change in thermo-physical properties induced by operation under supercritical conditions. Additionally, it is discovered that buoyancy presents a significant impact on heat transfer ability. Hence, a buoyancy factor, defined as , is chosen to one of the parameters in the development the empirical correlation. Significantly, this study successfully develops an empirical correlation that can predict 90% of present experimental data within 20% error range.

[1] Z. He, Y. Zhang, S. Dong, H. Ma, X. Yu, Y. Zhang, X. Ma, N. Deng, Y. Sheng, Thermodynamic analysis of a low-temperature organic Rankine cycle power plant operating at off-design conditions, Applied Thermal Engineering 113 (2017) 937–951.
[2] B.R. Fu, S.W. Hsu, Y.R. Lee, J.C. Hsieh, C.M. Chang, C.H. Liu, Effect of off-design heat source temperature on heat transfer characteristics and system performance of a 250-kW organic Rankine cycle system, Applied Thermal Engineering 70 (2014) 7–12.
[3] S. Karellas, A. Schuster, Supercritical fluid parameters in Organic Rankine Cycle applications, International Journal of Thermodynamics 11 (2008) 101–108.
[4] I. L. Pioro, and R. B. Duffey, “Experimental heat transfer in supercritical water flowing inside channels”, Nuclear Engineering and Design 235(22) (2005) 2407–2430.
[5] J. W. Ackerman, “Pseudo-boiling heat transfer to supercritical pressure water in smooth and ribbed tubes”, Journal of Heat Transfer 92(3) (1970) 490-497.
[6] A. Rovira, M. Valdes, M.D. Duran, A model to predict the behaviour at part load operation of once-through heat recovery steam generators working with water at supercritical pressure, Applied Thermal Engineering 30 (2010) 1652-1658
[7] M. Ruzickova, T. Schulenberg, D.C. Visser, R. Novotony, A. Kiss, C. Maraczy, A. Toivonen, Overview and progress in European project: ”Supercritical Water Reactor-Fuel Qualification Test”, Progress in Nuclear Energy 77 (2014) 381-389
[8] I. Okajima, M. Hiramatsu, Y. Shimamura, T. Awaya, T. Sako, Chemical recycling of carbon fiber reinforced plastic using supercritical methanol, The Journal of Supercritical Fluids 91 (2014) 68-76
[9] P. Tischer, T. Dresden, Supercritical Carbon Dioxide as Refrigerant, Report on Practice Work in Industry 05/2004
[10] 3M公司網站(http://solution.3m.com.tw/wps/portal/3M/zh_TW/3MNOVEC_A
PAC/Home/)
[11] R. Gabbrielli, A novel design approach for small scale low enthalpy binary geothermal power plants, Energy Conversion and Management 64 (2012) 263–272.
[12] D. Mikielewicz, J. Mikielewicz, A thermodynamic criterion for selection of working fluid for subcritical and supercritical domestic micro CHP, Applied Thermal Engineering 30 (2010) 2357–2362.
[13] J.C. Hsieh, B.R. Fu, T W. Wang, Y. Cheng, Y.R. Lee, J.C. Chang, Design and preliminary results of a 20-kW transcritical organic Rankine cycle with a screw expander for low-grade waste heat recovery, Applied Thermal Engineering 110 (2017) 1120–1127.
[14] G. Kosmadakis, D. Manolakos, G. Papadakis, Experimental investigation of a low-temperature organic Rankine cycle (ORC) engine under variable heat input operating at both subcritical and supercritical conditions, Applied Thermal Engineering 92 (2016) 1–7.
[15] I.H. Aljundi, Effect of dry hydrocarbons and critical point temperature on the efficiencies of organic Rankine cycle, Renewable Energy 36 (2011) 1196–1202.
[16] J.D. Jackson, Fluid flow and convective heat transfer to fluids at supercritical pressure, Nuclear Engineering and Design 264 (2013) 24–40.
[17] S. Pandey, E. Laurien, Heat transfer analysis at supercritical pressure using two layer theory, The Journal of Supercritical Fluids 109 (2016) 80–86.
[18] D. Huang, W. Li, Heat transfer deterioration of aviation kerosene flowing in mini tubes at supercritical pressures, International Journal of Heat and Mass Transfer 111 (2017) 266-278
[19] C.R. Zhao, P.X. Jiang, Experimental study of in-tube cooling heat transfer and pressure drop characteristics of R134a at supercritical pressures, Experimental Thermal and Fluid Science 35 (2011) 1293–1303.
[20] Y.L. Cui, H.X. Wang, Experimental study on convection heat transfer of R134a at supercritical pressures in a vertical tube for upward and downward flows, Applied Thermal Engineering 129 (2018) 1414-1425
[21] P. Forooghi and K. Hooman, Experimental analysis of heat transfer of supercritical fluids in plate heat exchangers. International Journal of Heat and Mass Transfer 74 (2014) 448–59.
[22] S. Garimella, B. Mitra, U.C. Andresen, Y. Jiang, B.M. Fronk, Heat transfer and pressure drop during supercritical cooling of HFC refrigerant blends. International Journal of Heat and Mass Transfer 91 (2015) 477–93.
[23] S.M. Liao, T.S. Zhao, Measurements of heat transfer coefficients from supercritical carbon dioxide flowing in horizontal mini/micro channels, Journal of Heat Transfer–Transactions of the ASME 124 (2002) 413–420.
[24] S.H. Yoon, J.H. Kim, Y.W. Hwang, M.S. Kim, K. Min, Y. Kim, Heat transfer and pressure drop characteristics during the in-tube cooling process of carbon dioxide in the supercritical region, International Journal of Refrigeration 26 (2003) 857–864.
[25] K. Tanimizu, R. Sadr, Experimental investigation of heat transfer characteristics of pseudocritical carbon dioxide in a circular horizontal tube, ASME Summer Heat Transfer Conference, Paper No. HT2012-58331, 2012, July 8–12, Puerto Rico.
[26] K. Tanimizu, R. Sadr, Experimental investigation of buoyancy effects on convection heat transfer of supercritical CO2 flow in a horizontal tube, Heat and Mass Transfer 52 (2016) 713–726.
[27] W.J. Bai, X.X. Xu, Y.Y. Wu, Heat transfer characteristics of supercritical CO2 at low mass flux in tube, Journal of Chemical Industry and Engineering 67 (2016) 1244–1250.
[28] J. G. Wang, H. X. Li, B. Guo, S. Q. Yu, Y. Q. Zhang, and T. K Chen,“Investgation of forced convection heat transfer of supercritical pressure water in a vertically upward internally ribbed tube”, Nuclear Engineering and Design, 239 (2009) 1956-1964.
[29] Z.H. Li, P.X. Jiang, C.R. Zhao, Y.S. Lin, Experimental investigation of convection heat transfer of CO2 at supercritical pressures in vertical circular Tube, Engineering Thermophysics 29 (2008) 461–464.
[30] Y.Y. Bae, Mixed convection heat transfer to carbon dioxide flowing upward and downward in a vertical tube and an annular channel, Nuclear Engineering and Design 241 (2011) 3164–3177.
[31] Z.H. Li, P.X. Jiang, Correlations of CO2 at supercritical pressures in a vertical circular tube, Nuclear Power Engineering 31 (2010) 72–75.
[32] S.H. Liu, Y.P. Huang, G.X. Liu, Improvement of buoyancy and acceleration parameters for forced and mixed convective heat transfer to supercritical fluids flowing in vertical tubes, International Journal of Heat and Mass Transfer 106 (2017) 1144–1156.
[33] G. Liu, Y. Huang, J. Wang, L.H.K. Leung, Heat transfer of supercritical carbon dioxide flowing in a rectangular circulation loop, Applied Thermal Engineering 98 (2016) 39–48.
[34] T. Ma, W.X. Chu, X.Y. Xu, Y.T. Chen, Q.W. Wang, An experimental study on heat transfer between supercritical carbon dioxide and water near pseudo-critical temperature in a double pipe heat exchanger, International Journal of Heat and Mass Transfer 93 (2016) 379-387
[35] W. Li, D. Huang, G.Q. Xu, Z. Tao, Z. Wu, H.T. Zhu, Heat transfer to aviation kerosene flowing upward in smooth tubes at supercritical pressures, International Journal of Heat and Mass Transfer 85 (2015) 1084-1094
[36] G. Liu, Y. Huang, J. Wang, F. Lv, Effect of buoyancy and flow acceleration on heat transfer of supercritical CO2 in natural circulation loop, International Journal of Heat and Mass Transfer 91 (2015) 640-646
[37] Z.X. Hu, H.Y. Gu, Heat transfer of supercritical water in annuli with spacers, International Journal of Heat and Mass Transfer 120 (2018) 411-421
[38] Z.B. Liu, Y.L. He, Z.G. Qu, W.Q. Tao, Experimental study of heat transfer and pressure drop of supercritical CO2 cooled in metal foam tubes, International Journal of Heat and Mass Transfer 85 (2015) 679-693
[39] W. Zhang, S.X. Wang, C.D. Li, J.L. Xu, Mixed convective heat transfer of CO2 at supercritical pressures flowing upward through a vertical helically coiled tube, Applied Thermal Engineering 88 (2015) 61–70
[40] C.Y. Yang, K.C. Liao, Effect of Experimental Method on the Heat Transfer Performance of Supercritical Carbon Dioxide in Microchannel, Journal of Heat Transfer–Transactions of the ASME 139 (2017) 112404.
[41] T.L. Bergman, F.P. Incropera, Fundamentals of heat and mass transfer.(7th ed.) Wiley. ISBN:9780470501979. OCLC 713621645. (2011-01-01).
[42] M. Jaromin, H. Anglart, A numerical study of heat transfer to supercritical water flowing upward in vertical tubes under normal and deteriorated conditions, Nuclear Engineering and Design 264 (2013) 61–70
[43] M.H. Kim, J. Pettersen, C.W. Bullard, Fundamental process and system design issues CO2 vapor compression systems, Progress in Energy and Combustion Science 30 (2004) 119–174
[44] Y. Chen, C. Yang, M. Zhao, K. Bi, K. Du, Forced convective heat transfer experiment of supercritical water in different diameter of tubes, Journal of Energy and Power Engineering 8 (2014) 1495-1504
[45] A. Eter, D. Groeneveld, S. Yavoularis, Convective heat transfer in supercritical flows of CO2 in tubes with and without flow obstacles, Nuclear Engineering and Design 313 (2017) 162-176
[46] Y. Fu, H. Huang, J. Wen, G. Xu, W. Zhao, Experimental investigation on convective heat transfer of supercritical RP-3 in vertical miniature tubes with various diameters, International Journal of Heat and Mass Transfer 112 (2017) 814-824
[47] T. Ding, Z. Li, Research on convection heat transfer character of super critical carbon dioxide flows inside horizontal tube, International Journal of Heat and Mass Transfer 92 (2016) 665-674
[48] D. Huang, Z. Wu, B. Sunden, W. Li, A brief review on convective heat transfer of fluids at supercritical pressures in tubes and recent progress, Applied Energy, 162 (2016) 494-505
[49] Z. Liu, Q. Bi, Y. Guo, J. Yan, Z. Yang, Convective heat transfer and pressure drop characteristics of near critical pressure hydrocarbon fuel in a minichannel, Applied Thermal Engineering 51 (2013) 1047-1054
[50] Gnielinski, Volker, Neue Gleichungen für den Wärme- und den Stoffübergang in turbulent durchströmten Rohren und Kanälen". Forsch. Ing.-Wes. 41 (1975) 8–16.
[51] J. D. Jackson, Consideration of the heat transfer properties of supercritical pressure water in connection with the cooling of advanced nuclear reactors, Proceedings of the 13th Pacific Basin Nuclear Conference, Shenzhen City, China, October 21–25 (2002)
[52] J.D. Jackson, W.B. Hall, J. Fewster, A. Watson, M.J. Watts, Heat Transfer to Supercritical Pressure Fluids, U.K.A.E.A. A.E.R.E.-R 8158, Design Report 34. (1975)
[53] M. Bazargan, D. Fraser, V. Chatoorgan, Effect of buoyancy on heat transfer in supercritical water flow in a horizontal round tube, Journal of Heat Transfer 127 (2005) 897-902
[54] B. Zhang, JQ. Shan, J. Jiang, Numerical analysis of supercritical water heat transfer in horizontal circular tube, Progress of Nuclear Energy 52 (2010) 678-684
[55] J. Wen, H. Huang, Z. Jia, Y. Fu, G. Xu, Buoyancy effects on heat transfer to supercritical pressure hydrocarbon fuel in a horizontal miniature tube, International Journal of Heat Mass Transfer 115 (2017) 1173-1181