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Subcritical boiling includes interfacial evaporation and heat transfer induced by bubble dynamics. However, for supercritical heat transfer, direct experimental evidence of the existence of pseudo-evaporation and pseudo-boiling heat transfer, as well as the conversion between them is lacking. In this work, the experimental study of supercritical carbon dioxide pool heat transfer is conducted. The pressure and temperature of the cell are 8–10 MPa and 15 ℃, respectively. As heating element and temperature sensing element, a nickel-chromium alloy wire with a length of 22 mm and diameter of 70 μm is placed horizontally in the high-pressure cell. The fiber optic probe is placed vertically, with its tip 200 μm above the wire. Four heat transfer modes, i.e. natural convection, pseudo-evaporation, transition of evaporation and boiling, and pseudo-boiling, are found to occur sequentially with the increase of heat flux density or wall superheat. Natural convection occurs when the wall temperature is below the pseudo-critical temperature. This work focuses on pseudo-evaporation and pseudo-boiling heat transfer and the transition between them. In the pseudo-evaporation mode, the heat transfer coefficient decreases slightly with wall superheat increasing. The fiber outputs a high frequency signal with small amplitude, and there is no dominant frequency. The multiscale entropy is large, characterizing random signal fluctuations. In the transition of evaporation and boiling mode, the fiber outputs a large-amplitude/low-frequency periodic signal with a significant dominant frequency and small multiscale entropy, representing an ordered periodic pulsating heat transfer. In the pseudo-boiling mode characterized by bubble-like structure, the fiber signal fluctuation amplitude and multiscale entropy are between the counterparts of the first two modes i.e. natural convection mode and pseudo-evaporation mode. The dominant frequency is not obvious. The multiscale entropies in the specific case are calculated under different key parameters, such as dimensionality, time scale factor, and length of origin data. Optimal parameters are selected based on the best separation of heat transfer modes. Finally, pseudo-boiling can be distinguished from pseudo-evaporation by multiscale entropy of 0.9, and from transition of evaporation and boiling by multiscale entropy of 0.5. In this work, direct experimental evidence of supercritical-like boiling is obtained, which deepens the understanding of the supercritical heat transfer mechanism and provides a basis for theoretical studies and engineering applications in future.
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Keywords:
- supercritical fluid /
- pseudo boiling /
- fiber optic /
- multiscale entropy
[1] Saeed M, Kim M H 2022 Energy 239 121868
Google Scholar
[2] Zhang Z, Zhou R, Ge X, Zhang J, Wu X 2020 Energy 190 116411
Google Scholar
[3] Bian X Y, Xuan W, Rui W, Cai J W, Hua T, Shu G Q 2022 Energy 256 124691
Google Scholar
[4] Cengel Y, Boles M 2005 Thermodynamics: An Engineering Approach (5th Ed.) (SI Units) (New York: McGraw-Hill) p119
[5] Huang D, Wu Z, Sunden B, Li W 2016 Appl. Energ. 162 494
Google Scholar
[6] Simeoni G, Bryk T, Gorelli F, Krisch M, Ruocco G, Santoro M, Scopigno T 2010 Nat. Phys. 6 503
Google Scholar
[7] Gorelli F A, Bryk T, Krisch M, Ruocco G, Santoro M, Scopigno T 2013 Sci. Rep. 3 1203
Google Scholar
[8] Ha M Y, Yoon T J, Tlusty T, Jho Y, Lee W B 2018 J. Phys. Chem. Lett. 9 1734
Google Scholar
[9] Kandlikar S G 1999 Handbook of Phase Change: Boiling and Condensation (1st Ed. ) (Routledge) p63
[10] Nasuti F, Pizzarelli M 2021 J. Supercrit. Fluid 168 105066
Google Scholar
[11] Knapp K K, Sabersky R H 1966 Int. J. Heat Mass Transf. 9 41
Google Scholar
[12] Knapp K K 1965 Ph. D. Dissertation (California: California Institute of Technology)
[13] Hahne E, Neumann R 1981 Wärme-und Stoffübertragung 15 171
[14] Rousselet Y, Warrier G R, Dhir V K 2013 J. Heat Trans. 135 022501
Google Scholar
[15] Holman J, Rea S, Howard C 1965 Int. J. Heat Mass Transf. 8 1095
Google Scholar
[16] Sakurai K, Ko H S, Okamoto K, Madarame H 2001 International Conference on Nuclear Engineering, France, April 8–12, 2001 INIS-FR-759
[17] Du X, Zhu X J, Yu X, Wu F Y, Qiu Q G 2022 Nucl. Eng. Des. 386 111574
Google Scholar
[18] Zhu B G, Xu J L, Yan C S, Xie J 2020 Int. J. Heat Mass Transf. 148 119080
Google Scholar
[19] 张海松, 朱鑫杰, 朱兵国, 徐进良, 刘欢 2020 物理学报 69 064401
Google Scholar
Zhang H S, Zhu X J, Zhu B G, Xu J L, Liu H 2020 Acta Phys. Sin. 69 064401
Google Scholar
[20] Maxim F, Contescu C, Boillat P, Niceno B, Karalis K, Testino A, Ludwig C 2019 Nat. Commun. 10 1
Google Scholar
[21] 程洁, 郭亚军, 王腾, 桂淼, 刘朝辉, 随志强 2019 化工学报 70 1375
Cheng J, Guo Y J, Wang T, Gui M, Liu C H, Sui Z Q 2019 Ciesc Journal 70 1375
[22] 潘艳芝, 郑永建, 王栋, 安维峥, 牛棚满 2020 工程热物理学报 41 2756
Pan Y Z, Zheng Y J, Wang D, An W Z, Niu P M 2020 J. Engineering Thermophysics 41 2756
[23] 冷洁, 胡雪音, 田瑞峰 2020 核动力工程 41 74
Leng J, Hu X Y, Tian R F 2020 Nuclear Power Engineering 41 74
[24] 翟路生, 金宁德 2016 物理学报 65 010501
Google Scholar
Zhai L S, Jin N D 2016 Acta Phys. Sin. 65 010501
Google Scholar
[25] 马敏, 郭鑫, 于洁 2022 仪器仪表学报 43 110
Ma M, Guo X, Yu J 2022 Chin. J. Sci. Instrum. 43 110
[26] 刘若琳, 孔明, 曹鸣, 王道档, 单良 2022 光电子·激光 33 840
Liu R L, Kong M, Cao M, Wang D D, Shan L 2022 J. Optoelectro. Laser 33 840
[27] 谭万尧, 刘晓晶, 吴德操, 罗彬彬, 赵明富, 郭裕丰, 龙俊宇, 张颖 2022 光学学报 42 52
Tan W Y, Liu X J, Wu D C, Luo B B, Zhao M F, Guo Y F, Long J Y, Zhang Y 2022 Acta Opt. Sin. 42 52
[28] Avdeev M V, Konovalov A N, Bagratashvili V N, Popov V K, Tsypina S I, Sokolova M, Ke J, Poliakoff M 2004 Phys. Chem. Chem. Phys. 6 1258
Google Scholar
[29] Holman J P 2012 Experimental Methods for Engineers (New York: McGraw Hill) pp64–65
[30] Barney R, Nourgaliev R, McCallen R, Delplanque J P 2021 Int. J. Heat Mass Transf. 178 121572
Google Scholar
[31] Liu H D, Liu W, Yan P G, Chen D Q, Dong K J, Qin J, Liu H Z 2022 Int. J. Heat Mass Transf. 196 123248
Google Scholar
[32] Xu J L, Shen S, Gan Y H, Li Y X, Zhang W, Su Q C 2005 J. Micromech Microeng 15 1344
Google Scholar
[33] Taylor G I 1950 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 201 192
[34] Shannon C E 1948 Bell Sys. Tec. J. 27 379
Google Scholar
[35] Pincus S M 1991 Pro. Nat. Academy Sci. 88 2297
Google Scholar
[36] Richman J S, Moorman J R 2000 Am. J. Physiol-Heart C 278 H2039
Google Scholar
[37] 杨大为, 赵永东, 冯辅周, 江鹏程, 丁闯 2018 兵工学报 39 1683
Google Scholar
Yang D W, Zhao Y D, Feng F Z, Jiang P C, Ding C 2018 Acta Armamentarii 39 1683
Google Scholar
[38] Haryadi B, Liou J J, Wei H C, Xiao M X, Wu H T, Sun C K 2018 Comput. Meth. Prog. Bio. 166 115
Google Scholar
[39] Silva L E V, Duque J J, Felipe J C, Murta L O, Humeau-Heurtier A 2018 Signal Process. 147 224
Google Scholar
[40] Li Y B, Wang X Z, Liu Z B, Liang X H, Si S B 2018 IEEE Access 6 66723
Google Scholar
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图 1 SCF池式传热实验系统 (a) 实验台照片; (b) 实验台原理图 (1-真空泵, 2-阀门, 3-CO2气瓶, 4-增压泵, 5-减压阀, 6-压力变送器, 7-光环行器, 8-分光器, 9-激光光源, 10-光电转换电路, 11-光纤探针, 12-高压釜, 13-LED光源, 14-冷却铜管, 15-加热丝, 16-可视窗, 17-高速相机, 18-热电偶, 19-恒温槽, 20-PID控制器, 21-直流电源, 22-标准电阻, 23-同步器, 24-高速数采仪); (c) 光纤探针封装结构
Figure 1. Experiment system of SCF pool heat transfer: (a) The photo of experiment system; (b) schematic diagram of the experimental system (1-vacuum pump, 2-valve, 3-CO2 cylinder, 4-piston pump, 5-reducing valve, 6-pressure transmitter, 7-optical circulator, 8-splitter, 9-laser light source, 10-optical conversion circuit, 11-fiber optic probe, 12-high pressure vessel, 13-LED light source, 14-circulating pipe, 15-heating wire, 16-viewable window, 17-high-speed camera, 18-thermocouple, 19-thermostat, 20-PID controller, 21-DC power source, 22-standard resistor, 23-synchronizer, 24-high-speed data acquisition); (c) fiber optic probe package structure.
图 2 探针定位和标定 (a) 光纤探针和加热丝安装; (b) 探针对齐; (c) 光纤探针标定
Figure 2. Positioning and calibration of fiber optic probe: (a) Installation of fiber optic probe and heating wire; (b) probe alignment; (c) fiber optic probe calibration.
图 3 不同压力下的传热曲线和传热模式分区 (a), (b) P分别为7.955—8.048 MPa和9.928—10.035 MPa时热流密度与过热度关系; (c), (d) P分别为7.955—8.048 MPa和9.928—10.035 MPa时传热系数与过热度关系
Figure 3. Q-ΔTw and h-ΔTw curves and heat transfer modes under different pressure: (a), (b) Heat flux density versus superheat for P = 7.955–8.048 MPa and 9.928–10.035 MPa, respectively; (c), (d) heat transfer coefficient versus superheat for P = 7.955– 8.048 MPa and 9.928–10.035 MPa, respectively.
图 4 不同传热模式的图像 (a) NC模式; (b) PE模式; (c) TEB模式; (d) PB模式
Figure 4. Images of different heat transfer modes: (a) NC mode; (b) PE mode; (c) TEB mode; (d) PB mode.
图 5 探针温度信号和频谱 (a) PE模式, q = 174.1 kW/m2; (b) TEB模式, q = 359.8 kW/m2; (c) PB模式, q = 409.2 kW/m2
Figure 5. Temperature signal and spectrum of probe: (a) PE mode, q = 174.1 kW/m2; (b) TEB mode, q = 359.8 kW/m2; (c) PB mode, q = 409.2 kW/m2.
图 6 基于主频比α 的传热模式识别 (a) P = 7.955—8.048 MPa; (b) P = 9.928—10.035 MPa
Figure 6. Heat transfer mode identification based on the main frequency ratio α: (a) P = 7.955–8.048 MPa; (b) P = 9.928–10.035 MPa
图 7 多尺度熵关键参数最优选取 (a) p = 0.2; (b) N = 2000; (c) τ = 10
Figure 7. Optimal selection of key parameters of multiscale entropy: (a) p = 0.2; (b) N = 2000; (c) τ = 10.
图 8 基于多尺度熵的传热模式识别 (a) P = 7.955—8.048 MPa; (b) P = 9.928—10.035 MPa
Figure 8. Heat transfer modes identification based on multiscale entropy: (a) P = 7.955–8.048 MPa; (b) P = 9.928–10.035 MPa.
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[1] Saeed M, Kim M H 2022 Energy 239 121868
Google Scholar
[2] Zhang Z, Zhou R, Ge X, Zhang J, Wu X 2020 Energy 190 116411
Google Scholar
[3] Bian X Y, Xuan W, Rui W, Cai J W, Hua T, Shu G Q 2022 Energy 256 124691
Google Scholar
[4] Cengel Y, Boles M 2005 Thermodynamics: An Engineering Approach (5th Ed.) (SI Units) (New York: McGraw-Hill) p119
[5] Huang D, Wu Z, Sunden B, Li W 2016 Appl. Energ. 162 494
Google Scholar
[6] Simeoni G, Bryk T, Gorelli F, Krisch M, Ruocco G, Santoro M, Scopigno T 2010 Nat. Phys. 6 503
Google Scholar
[7] Gorelli F A, Bryk T, Krisch M, Ruocco G, Santoro M, Scopigno T 2013 Sci. Rep. 3 1203
Google Scholar
[8] Ha M Y, Yoon T J, Tlusty T, Jho Y, Lee W B 2018 J. Phys. Chem. Lett. 9 1734
Google Scholar
[9] Kandlikar S G 1999 Handbook of Phase Change: Boiling and Condensation (1st Ed. ) (Routledge) p63
[10] Nasuti F, Pizzarelli M 2021 J. Supercrit. Fluid 168 105066
Google Scholar
[11] Knapp K K, Sabersky R H 1966 Int. J. Heat Mass Transf. 9 41
Google Scholar
[12] Knapp K K 1965 Ph. D. Dissertation (California: California Institute of Technology)
[13] Hahne E, Neumann R 1981 Wärme-und Stoffübertragung 15 171
[14] Rousselet Y, Warrier G R, Dhir V K 2013 J. Heat Trans. 135 022501
Google Scholar
[15] Holman J, Rea S, Howard C 1965 Int. J. Heat Mass Transf. 8 1095
Google Scholar
[16] Sakurai K, Ko H S, Okamoto K, Madarame H 2001 International Conference on Nuclear Engineering, France, April 8–12, 2001 INIS-FR-759
[17] Du X, Zhu X J, Yu X, Wu F Y, Qiu Q G 2022 Nucl. Eng. Des. 386 111574
Google Scholar
[18] Zhu B G, Xu J L, Yan C S, Xie J 2020 Int. J. Heat Mass Transf. 148 119080
Google Scholar
[19] 张海松, 朱鑫杰, 朱兵国, 徐进良, 刘欢 2020 物理学报 69 064401
Google Scholar
Zhang H S, Zhu X J, Zhu B G, Xu J L, Liu H 2020 Acta Phys. Sin. 69 064401
Google Scholar
[20] Maxim F, Contescu C, Boillat P, Niceno B, Karalis K, Testino A, Ludwig C 2019 Nat. Commun. 10 1
Google Scholar
[21] 程洁, 郭亚军, 王腾, 桂淼, 刘朝辉, 随志强 2019 化工学报 70 1375
Cheng J, Guo Y J, Wang T, Gui M, Liu C H, Sui Z Q 2019 Ciesc Journal 70 1375
[22] 潘艳芝, 郑永建, 王栋, 安维峥, 牛棚满 2020 工程热物理学报 41 2756
Pan Y Z, Zheng Y J, Wang D, An W Z, Niu P M 2020 J. Engineering Thermophysics 41 2756
[23] 冷洁, 胡雪音, 田瑞峰 2020 核动力工程 41 74
Leng J, Hu X Y, Tian R F 2020 Nuclear Power Engineering 41 74
[24] 翟路生, 金宁德 2016 物理学报 65 010501
Google Scholar
Zhai L S, Jin N D 2016 Acta Phys. Sin. 65 010501
Google Scholar
[25] 马敏, 郭鑫, 于洁 2022 仪器仪表学报 43 110
Ma M, Guo X, Yu J 2022 Chin. J. Sci. Instrum. 43 110
[26] 刘若琳, 孔明, 曹鸣, 王道档, 单良 2022 光电子·激光 33 840
Liu R L, Kong M, Cao M, Wang D D, Shan L 2022 J. Optoelectro. Laser 33 840
[27] 谭万尧, 刘晓晶, 吴德操, 罗彬彬, 赵明富, 郭裕丰, 龙俊宇, 张颖 2022 光学学报 42 52
Tan W Y, Liu X J, Wu D C, Luo B B, Zhao M F, Guo Y F, Long J Y, Zhang Y 2022 Acta Opt. Sin. 42 52
[28] Avdeev M V, Konovalov A N, Bagratashvili V N, Popov V K, Tsypina S I, Sokolova M, Ke J, Poliakoff M 2004 Phys. Chem. Chem. Phys. 6 1258
Google Scholar
[29] Holman J P 2012 Experimental Methods for Engineers (New York: McGraw Hill) pp64–65
[30] Barney R, Nourgaliev R, McCallen R, Delplanque J P 2021 Int. J. Heat Mass Transf. 178 121572
Google Scholar
[31] Liu H D, Liu W, Yan P G, Chen D Q, Dong K J, Qin J, Liu H Z 2022 Int. J. Heat Mass Transf. 196 123248
Google Scholar
[32] Xu J L, Shen S, Gan Y H, Li Y X, Zhang W, Su Q C 2005 J. Micromech Microeng 15 1344
Google Scholar
[33] Taylor G I 1950 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 201 192
[34] Shannon C E 1948 Bell Sys. Tec. J. 27 379
Google Scholar
[35] Pincus S M 1991 Pro. Nat. Academy Sci. 88 2297
Google Scholar
[36] Richman J S, Moorman J R 2000 Am. J. Physiol-Heart C 278 H2039
Google Scholar
[37] 杨大为, 赵永东, 冯辅周, 江鹏程, 丁闯 2018 兵工学报 39 1683
Google Scholar
Yang D W, Zhao Y D, Feng F Z, Jiang P C, Ding C 2018 Acta Armamentarii 39 1683
Google Scholar
[38] Haryadi B, Liou J J, Wei H C, Xiao M X, Wu H T, Sun C K 2018 Comput. Meth. Prog. Bio. 166 115
Google Scholar
[39] Silva L E V, Duque J J, Felipe J C, Murta L O, Humeau-Heurtier A 2018 Signal Process. 147 224
Google Scholar
[40] Li Y B, Wang X Z, Liu Z B, Liang X H, Si S B 2018 IEEE Access 6 66723
Google Scholar
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