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传热恶化是超临界流体(supercutical fluid, SCF)传热研究重要问题之一, 但由于SCF在跨过拟临界点时, 流体存在非平衡过程, 类气和类液之间的转变对传热的影响尚没有统一认识. 本文假设SCF在宏观上存在类似于亚临界流动沸腾现象, 通过类比亚临界沸腾传热, 认为超临界CO2传热恶化原因之一是由于流体膨胀导致热量不能被及时从壁面被带走, 并提出一个类沸腾临界点模型. 结果表明: 类沸腾引起的传热恶化发生在大温度梯度下, 较大的温度梯度使类过热液层覆盖在壁面, 并使类气和类液呈现不同的分布形式, 从而表现出不同的传热特性; 当内壁温高于拟临界温度时, 覆盖在壁面的过热类液焓值超过一定值会发生传热恶化, 提出的理论模型能够较好地解释实验结果, 此外考虑类沸腾的传热关联式, 预测精度大大提高. 本文从理论上建立超临界和亚临界传热之间的联系, 为SCF传热恶化研究提供了新思路, 丰富了超临界压力下的传热理论.Heat transfer deterioration (HTD) is one of the important issues in the study of supercritical fluid (SCF) heat transfer. However, when the SCF crosses the pseudo-critical point, the none-quilibrium process occurs in liquid, so SCF is very complicated. Recently, the existence of SCF pseudo-boiling on a macro scale has sparked controversy. There is still no unified understanding of the mechanism of gas-like and liquid-like transition affecting heat transfer. In this work, it is assumed that SCF has a macroscopic phenomenon similar to subcritical flow boiling. By analogy with subcritical boiling heat transfer, a boiling critical point model is proposed to describe the HTD in supercritical CO2. Our study reveals that the HTD caused by pseudo-boiling only occurs under large temperature gradient, which makes the superheated liquid-like layer cover the wall, and the gas-like and liquid-like may present different distribution forms, thus changing the heat transfer characteristics. When the wall temperature is higher than the pseudo-critical temperature and the enthalpy of the fluid layer covering the wall exceeds a certain value, the HTD may occur. The proposed theoretical model can explain the experimental results well, and the prediction accuracy of heat transfer correlation considering pseudo-boiling is greatly improved. In this work, the connection between supercritical heat transfer and subcritical heat transfer is established theoretically, which provides a new idea for studying the deterioration of SCF heat transfer, thus enriching the theory of supercritical heat transfer.
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Keywords:
- supercritical fluid /
- expansion /
- pseudo-boiling /
- heat transfer deterioration /
- theoretical model
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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图 2 亚临界和超临界CO2热力学特性 (a) 密度; (b) 潜热; (c) 饱和密度
Fig. 2. Thermodynamic characteristics of subcritical and supercritical CO2: (a) Density; (b) latent heat; (c) saturated density.
图 3 (a) 正常传热工况下的R22 (二氟一氯甲烷)壁温分布及流型; (b) 传热恶化工况下的R134a (四氟乙烷)壁温分布及流型
Fig. 3. (a) R22 (CHCLF2) wall temperature distribution and flow pattern under NHT; (b) R134a (CH2FCF3) wall temperature distribution and flow pattern under HTD.
图 4 (a) 亚临界压力下的汽泡层模型; (b) 超临界压力下的膨胀层模型
Fig. 4. (a) Bubble layer model under subcritical pressure; (b) expansion layer model under supercritical pressure.
图 6 SBO的微小变化决定两种传热特性的突变 (a)正常传热; (b)传热恶化
Fig. 6. Sudden changes of two heat transfer characteristics with small deviation from the critical SBO: (a) Normal heat transfer; (b) heat transfer deterioration.
图 7 不同超临界压力流体在正常传热和恶化传热过程中的Twi/TPB和Tb/TPB随焓值变化分布
Fig. 7. Distribution of Twi/TPB and Tb/TPB with enthalpy during normal heat transfer and heat transfer deterioration of different supercritical fluids.
图 8 上升流和下降流大温度梯度下的sCO2传热恶化 (a) 传热恶化工况下的壁温分布; (b) 温度梯度分布
Fig. 8. The HTD under large temperature gradient in upflow and downflow operation: (a) Wall temperature distribution at heat transfer deterioration; (b) temperature gradient distribution.
图 9 K数关联预测超临界H2O、超临界R134a和sCO2壁温的能力 (a) 超临界H2O; (b) 超临界R134a; (c) 超临界CO2
Fig. 9. Capability of the K number correlation to predict the H2O, R134a and CO2 data at supercritical: (a) Supercritical water; (b) supercritical R134a; (c) supercritical CO2.
图 10 K数关联式和其他传热关联式预测结果与实验数据比较
Fig. 10. Comparison of the K number correlation and other heat transfer correlations with experimental database.
表 1 超临界流体传热关联式回顾
Table 1. Review of supercutical fluids heat transfer correlations.
Ref. Correlation Operatings parameters [25] $N{u_{\text{b}}} = 0.023 Re_{\text{b}}^{1.03}Pr_{\text{b}}^{0.5}{F_1}{F_2} \qquad\qquad \qquad \qquad \qquad \qquad \qquad \qquad $ CO2/H2O/R134a ${F_1} = \left\{ {\begin{aligned} &0.98, & &{\text{ for }}{{\textit{π}} _{\text{A}}} < 1.75 \times {{10}^{ - 4}}, \\ &0.85 + 0.056{{\left( {{{10}^4}{{\textit{π}} _{\text{A}}}} \right)}^{1.5}}, & &{\text{ for }}1.75 \times {{10}^{ - 4}} \leqslant {{\textit{π}} _{\text{A}}} < 3.75 \times {{10}^{ - 4}}, \\ &13.1/4.5 + {{\left( {104{{\textit{π}} _{\text{A}}}} \right)}^{1.35}}, & &{\text{ for }}3.75 \times {{10}^{ - 4}} < {{\textit{π}} _{\text{A}}} ,\end{aligned}} \right.$ $ {F_2} = \left\{ {\begin{aligned} & 0.93 Pr_{\text{b}}^{0.265}, & &{\text{ for }}P{r_{\text{b}}} \leqslant 2.5, \\ &1.61 Pr_{\text{b}}^{ - 0.333}, & &{\text{ for }}P{r_{\text{b}}} > 2.5, \end{aligned}} \right. \qquad {{\textit{π}} _{\text{A}}} = \dfrac{{{q_{\text{w}}}{\beta _{\text{b}}}}}{{G{c_{{\text{p}}, {\text{b}}}}}} \qquad\qquad \qquad\qquad $ [26] $N u_{\mathrm{w}}=0.0033 R e_{\mathrm{w}}^{0.94} \overline{Pr}_{\mathrm{w}}^{0.76}\left( {\rho_{\mathrm{w}}}/{\rho_{\mathrm{b}}}\right)^{0.16}\left( {\mu_{\mathrm{w}}}/{\mu_{\mathrm{b}}}\right)^{0.4} $ — [27] $N u_{\mathrm{b}}=0.0061 R e_{\mathrm{b}}^{0.904} P r_{\mathrm{b}, \mathrm{ave}}^{0.684}\left({\rho_{\mathrm{w}}}/{\rho_{\mathrm{b}}}\right)^{0.564}$ H2O
P = 24 MPa; di = 10.0 mm
G = 200—1500 kg/(m2·s)
qw = 0—1250 kW/m2$P{r_{{\mathrm{b, ave}}}} = \dfrac{{{\mu _{\text{b}}}}}{{{\lambda _{{\mathrm{b}}} }}}\dfrac{{{i_{{\mathrm{w}}} } - {i_{{\mathrm{b}}} }}}{{{T_{{\mathrm{w}}} } - {T_{{\mathrm{b}}} }}}$ [28] $ N{u_{\mathrm{b}}} = 0.226 Re_{\mathrm{b}}^{1.174}Pr_{{{\mathrm{b}}} , {\mathrm{ave}}}^{1.057}{\left( {\dfrac{{{\rho _{\mathrm{w}}}}}{{{\rho _{{\mathrm{b}}} }}}} \right)^{0.571}}{\left( {\dfrac{{{{\overline c }_{{{\mathrm{p, b}}}}}}}{{{c_{{{\mathrm{p} , b}}}}}}} \right)^{1.023}}A{c^{0.489}}B{u^{0.0021}} $ CO2
P = 7.46—10.26 MPa
di = 4.5 mm
G = 208–847 kg/(m2·s)
qw = 38—234 kW/m2$Ac = \dfrac{{{q_{{\mathrm{w}}} }{\beta _{{\mathrm{b}}} }}}{{G{c_{{{\mathrm{p}}} , {\mathrm{b}}}}Re_{{\mathrm{b}}} ^{0.625}}}\left( {\dfrac{{{\mu _{{\mathrm{w}}} }}}{{{\mu _{{\mathrm{b}}} }}}} \right){\left( {\dfrac{{{\rho _{{\mathrm{b}}} }}}{{{\rho _{{\mathrm{w}}} }}}} \right)^{0.5}}$, $Gr{=}\dfrac{{{g} {\beta _{{\mathrm{b}}} }d_{\mathrm{i}}^4{q_{{\mathrm{w}}} }}}{{v_{\mathrm{b}}^2{\lambda _{{\mathrm{b}}} }}}$ $ Bu = \dfrac{{Gr}}{{Re_{{\mathrm{b}}} ^{3.425}P{r^{0.8}}}}\left( {\dfrac{{{\mu _{{\mathrm{w}}} }}}{{{\mu _{{\mathrm{b}}} }}}} \right){\left( {\dfrac{{{\rho _{{\mathrm{b}}} }}}{{{\rho _{{\mathrm{w}}} }}}} \right)^{0.5}}$, ${\overline c _{{{\mathrm{p, b}}}}} = \dfrac{{{i_{{\mathrm{w}}} } - {i_{{\mathrm{b}}} }}}{{{T_{{\mathrm{w}}} } - {T_{{\mathrm{b}}} }}}$ [29] $ N u_{\mathrm{b}}=\dfrac{(\xi / 8) R e_{\mathrm{b}} \overline{{Pr}}_{\mathrm{b}}}{1+900 / R e_{\mathrm{b}}+12.7 \sqrt{\xi / 8}\left(\overline{P r}_{\mathrm{b}}^{2 / 3}-1\right)}$ — $\xi=\left[1.82 \log _{10}\left(R e_{\mathrm{b}}\right)-1.64\right]^{-2}\left( {\rho_{\mathrm{w}}}/{\rho_{\mathrm{b}}}\right)^{0.4}\left({\mu_{\mathrm{w}}}/{\mu_{\mathrm{b}}}\right)^{0.2}$ 
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[1] Jackson J D 2017 Appl. Therm. Eng. 124 1481
Google Scholar
[2] Huang D, Wu Z, Sunden B, Li W 2016 Appl. Energ. 162 494
Google Scholar
[3] Xie J Z, Liu D C, Yan H B, Xie G N, Boetcher S K S 2020 Int. J. Heat Mass Tran. 149 119233
Google Scholar
[4] Cabeza L, Gracia A, Fernández A, Farid M 2017 Appl. Therm. Eng. 125 799
Google Scholar
[5] Chen W W, Fang X D, Yu X, Su X H 2015 Ann. Nucl. Energy 76 451
Google Scholar
[6] Cheng X, Liu X J 2018 J. Nucl. Eng. Radiat Sc. 4 011003
Google Scholar
[7] Maxim F, Contescu C, Boillat P, Niceno B, Karalis K, Testino A, Ludwig C 2019 Nat. Commun. 10 4114
Google Scholar
[8] Maxim F, Karalis K, Boillat P, Banuti D, Marquez J, Damian B, Niceno P, Ludwig C 2021 Adv. Sci. 8 2002312
Google Scholar
[9] Liu M Y, Tang J, Liu S H 2022 J. Supercrit. Fluids 183 105554
Google Scholar
[10] Ackerman J W 1970 J. Heat Tran. 92 490
Google Scholar
[11] Zhu B G, Xu J L, Wu X M, Xie J, Li M J 2019 J Int. J. Therm. Sci. 136 254
Google Scholar
[12] Zhang H S, Xu J L, Zhu X J, Xie J, Li M J, Zhu B G 2021 Appl. Therm. Eng. 182 116078
Google Scholar
[13] Wang Q Y, Ma X J, Xu J L, Li M J, Wang Y 2021 Int. J. Heat Mass Tran. 181 121875
Google Scholar
[14] Tripathi P, Basu S 2021 Phys. Fluids 33 043304
Google Scholar
[15] Wang J T, Li Z H, Zhai Y L, Wang H 2023 Int. J. Heat Mass Tran. 201 123571
Google Scholar
[16] Peeters J 2022 Int. J. Heat Mass Tran. 186 122441
Google Scholar
[17] Fan Y H, Tang G H, Sheng Q, Li X 2023 Energy 262 125470
Google Scholar
[18] Banuti D T 2015 J. Supercrit. Fluids 98 12
Google Scholar
[19] 何孝天, 徐进良, 程怡玮 2023 物理学报 72 057801
Google Scholar
He X T, Xu J L, Cheng Y W 2023 Acta Phys. Sin. 72 057801
Google Scholar
[20] 林瑞泰 1988 沸腾换热 (北京: 科学出版社) 第278页
Lin R T 1988 Boiling Heat Transfer (Beijing: Science Press) p278
[21] Xu J L, Zhang H S, Zhu B G, Xie J 2020 Solar Eng. 195 27
Google Scholar
[22] 张海松, 徐进良, 朱鑫杰 2021 物理学报 70 044401
Google Scholar
Zhang H S, Xu J L, Zhu X J 2021 Acta Phys. Sin. 70 044401
Google Scholar
[23] Zhang H S, Xu J L, Wang Q Y 2023 Int. J. Therm. Sci. 188 108242
Google Scholar
[24] Zhu B G, Xu J L, Yan C S, Xie J 2020 Int. J. Heat Mass Tran. 148 119080
Google Scholar
[25] Cheng X, Zhao M, Feuerstein F, Liu X J 2019 Int. J. Heat Mass Tran. 131 527
Google Scholar
[26] Gupta S, Mokry S, Pioro I 2011 Proc. ICONE-19 43503 11
Google Scholar
[27] Mokry S, Pioro I, Farah A, King K, Gupta S, Peiman W, Kirillov P 2011 Nucl. Eng. Des. 241 1126
Google Scholar
[28] Kim D, Kim M 2010 Nucl. Eng. Des. 240 3336
Google Scholar
[29] Petukhov B, Kirillov S 1958 Thermal Eng. 4 63
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