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The saturated pool boiling heat transfer on a conical structure surface under the action of an electric field is numerically investigated by using the lattice Boltzmann (LB) model coupled with an electric field model. A comparison study of boiling heat transfer phenomenon smooth surface and conical surface without the action of an electric field is first conducted in order to quantitatively analyze the mechanism of the electric field effect on boiling heat transfer on the conical structure surface. It is discovered that the conical structure has more active nucleation sites during the nucleate boiling regime, improving the boiling heat transfer efficiency and enhancing the critical heat flux (CHF). However, in the transition boiling stage and film boiling stage, the conical structure increases the flow resistance of the fluid on the fin surface, hindering heat transfer between the vapor and liquid and producing lower heat transfer performance than smooth surface. Based on the aforementioned findings, the boiling heat transmission on the conical structure surface is enhanced by applying an electric field. Numerical results indicate that the effect of the electric field on the boiling heat transfer performance on the conical structure surface is related to the boiling regime. In the earlier stage of the nucleation boiling regime, when an electric field is present, the onset time of bubble nucleation is slightly delayed, bubble size decreases a little, and boiling is slightly suppressed. However, the combination effect of electric field and conical structure, especially the tip effect, prevents the spread and diffusion of dry areas on the heating surface, thereby enhancing boiling heat transfer in the fully developed nucleate boiling stage. The tip effect grows more evidently in the transition boiling regime and film boiling regime, and increasing electric field intensity causes boiling to continue in the nucleate boiling regime at a higher superheat level. As a result, boiling heat transfer performance is greatly improved, and CHF steadily rises.
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Keywords:
- conical structure /
- electric field /
- lattice Boltzmann method /
- pool boiling
[1] Zaidi S 2015 Chem. Eng. Res. Des. 98 44
Google Scholar
[2] Massih A R, Persson S 1992 J. Nucl. Mater. 188 323
Google Scholar
[3] Mohammed H I, Giddings D, Walker G S 2019 Int. J. Heat Mass Transfer 130 710
Google Scholar
[4] Nikolayev V S, Chatain D, Garrabos Y, Beysens D 2006 Phys. Rev. Lett. 97 184503
Google Scholar
[5] Li W, Dai R K, Zeng M, Wang Q W 2020 Renew. Sust. Energ. Rev. 130 109926
Google Scholar
[6] Tian Z, Etedali S, Afrand M, Abdollahi A, Goodarzi M 2019 Powder Technol. 356 391
Google Scholar
[7] Wei J J, Honda H 2003 Int. J. Heat Mass Transfer 46 4059
Google Scholar
[8] Li Q, Zhao J H, Sun X Z, Liu B 2022 Appl. Therm. Eng. 215 118924
Google Scholar
[9] Kong X, Zhang Y H, Wei J J 2018 Exp. Therm. Fluid Sci. 91 9
Google Scholar
[10] Kim S H, Lee C G, Kang J Y, Moriyama K, Kim M H, Park H S 2015 Int. J. Heat Mass Transfer 91 1140
Google Scholar
[11] Elkholy A, Swift J, Kempers R 2023 Appl. Therm. Eng 219 119665
Google Scholar
[12] Clubb L 1916 UK Patent 100796 [1916-07-09
[13] Dong W, Li R Y, Yu H L, Yan Y Y 2006 Exp. Therm. Fluid Sci. 30 579
Google Scholar
[14] Gao M, Cheng P, Quan X J 2013 Int. J. Heat Mass Transfer 67 984
Google Scholar
[15] Hristov Y, Zhao D, Kenning D B R, Sefiane K, Karayiannis T G 2009 Heat Mass Transfer 45 999
Google Scholar
[16] Garivalis A I, Manfredini G, Saccone G, Di Marco P, Kossolapov A, Bucci M 2021 NPJ Microgravity 7(1) 37
Google Scholar
[17] Quan X J, Gao M, Cheng P, Li J S 2015 Int. J. Heat Mass Transfer 85 595
Google Scholar
[18] Liu B, Garivalis A I, Cao Z, Zhang Y, Wei J 2022 Int. J. Heat Mass Transfer 183 122154
Google Scholar
[19] Liu X, Chai Z H, Shi B C 2019 Phys. Fluids 31 092103
Google Scholar
[20] Liu X, Chai Z H, Shi B C 2021 Commun. Comput. Phys. 30 1346
Google Scholar
[21] Feng Y, Li H, Guo K, Lei X, Zhao J 2019 Int. J. Heat Mass Transfer 135 885
Google Scholar
[22] Li W X, Li Q, Chang H Z, Yu Y, Tang S 2022 Phys. Fluids 34 123327
Google Scholar
[23] Lou Q, Wang H Y, Li L 2023 Phys. Fluids 35 123327
Google Scholar
[24] Ezzatneshan E, Salehi A, Vaseghnia H 2023 Int. J. Therm. Sci 184 107913
Google Scholar
[25] Gong S, Cheng P 2012 Int. J. Heat Mass Transfer 55 4923
Google Scholar
[26] Guo Z L, Zheng C G, Shi B C 2011 Phys. Rev. E 83 036707
Google Scholar
[27] Chai Z H, Zhao T S 2012 Phys. Rev. E 86 016705
Google Scholar
[28] Panofsky W, Phillips M, Jauch J M 1956 Am. J. Phys. 24 416
[29] He X Y, Ning L 2000 Comput. Phys. Commun. 129 158
Google Scholar
[30] Chai Z H, Shi B C 2008 Appl. Math. Model. 32 2050
Google Scholar
[31] Chai Z H, Liang H, Du R, Shi B C 2019 SIAM J. Sci. Comput. 41 B746
Google Scholar
[32] Wang L, Wei Z C, Li T F, Chai Z H, Shi B C 2021 Appl. Math. Model. 95 361
Google Scholar
[33] Wang H Y, Lou Q, Liu G J, Li L 2022 Int. J. Therm. Sci. 178 107554
Google Scholar
[34] Lou Q, Guo Z L, Shi B C 2013 Phys. Rev. E 87 063301
Google Scholar
[35] Ladd A J C 1994 J. Fluid Mech. 271 285
Google Scholar
[36] Li L, Chen C, Mei R, Mei M, Klausner J 2014 Phys. Rev. E 89 043308
Google Scholar
[37] Gong S, Cheng P 2017 Int. Commun. Heat Mass Transfer 87 61
Google Scholar
[38] Li Q, Yu Y, Luo K H 2019 Phys. Rev. E 100 053313
Google Scholar
[39] Sadasivan P, Unal C, Nelson R 1995 J. Heat Transfer 117 558
Google Scholar
[40] 柴立和, 彭晓峰, 王补宣 1999 原子能科学技术 33 533
Chai L H, Peng X F, Wang B X 1999 Atomic Energy Sci. Techno. 33 533
[41] Berghmans J 1976 Int. J. Heat Mass Transfer 19 791
Google Scholar
[42] Johnson R 1968 AIAA J. 6 8
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图 1 物理问题示意图
Figure 1. Schematic diagram of the physical problem.
图 2 平滑表面和锥翅表面的沸腾曲线
Figure 2. Boiling curves for smooth and conical surfaces.
图 3 $ T_{\rm{b}}=0.96 T_{\rm{c}} $时, 平滑表面和锥翅表面的沸腾过程
Figure 3. Snapshots of the boiling processes on smooth and conical surfaces under $ T_{\rm{b}}=0.96 T_{\rm{c}} $.
图 4 $ t^*=33.50 $时刻, 加热温度为$ T_{\rm{b}}=0.96 T_{\rm{c}} $的温度分布
Figure 4. Temperature distribution during the boiling process with $ T_{\rm{b}} = 0.96 T_{\rm{c}} $ and $ t^*=33.50 $.
图 5 $ T_{\rm{b}}=1.04 T_{\rm{c}} $时, 平滑表面 (a)和锥翅表面 (b)的沸腾过程及流场分布
Figure 5. Snapshots of the boiling process and the flow field distributions on smooth (a) and conical (b) surfaces under $ T_{\rm{b}}=1.04 T_{\rm{c}} $.
图 6 加热温度$ T_{\rm{b}}=1.04 T_{\rm{c}} $下, 平滑表面和锥翅表面空间平均热流密度随时间的变化
Figure 6. The time histories of space-averaged heat flux on smooth and conical surfaces under $ T_{\rm{b}}=1.04 T_{\rm{c}} $.
图 7 $ T_{\rm{b}}=1.06 T_{\rm{c}} $, 平滑表面 (a)和锥翅表面 (b)的沸腾过程和对应的流场分布
Figure 7. Snapshots of the boiling process and the flow field distributions on smooth (a) and conical (b) surfaces under $ T_{\rm{b}}=1.06 T_{\rm{c}} $.
图 8 $ T_{\rm{b}}=1.12 T_{\rm{c}} $, 平滑表面 (a)和锥翅表面 (b)的沸腾过程
Figure 8. Snapshots of the boiling processes on smooth (a) and conical (b) surfaces under $ T_{\rm{b}}=1.12 T_{\rm{c}} $.
图 9 加热温度为$ T_{\rm{b}}=1.12 T_{\rm{c}} $, $ t^*=96.03 $时刻平滑表面和锥翅表面的局部热流密度
Figure 9. Local heat flux on smooth and conical surfaces with $ T_{\rm{b}}=1.12 T_{\rm{c}} $ and $ t^*=96.03 $.
图 10 $ T_{\rm{b}}=0.96 T_{\rm{c}} $时, 不同电场强度下锥翅表面的沸腾过程 (a) E0 = 0; (b) E0 = 0.0517; (c) E0 = 0.0862; (d) E0 = 0.1207
Figure 10. Snapshots of boiling processes on the conical surface at $ T_{\rm{b}}=0.96 T_{\rm{c}} $ under different electric field intensities: (a) E0 = 0; (b) E0 = 0.0517; (c) E0 = 0.0862; (d) E0 = 0.1207
图 11 加热温度$ T_{\rm{b}}=0.96 T_{\rm{c}} $, 不同电场强度作用下锥翅表面空间平均热流密度随时间的变化
Figure 11. The time histories of space-averaged heat flux on the conical surface with $ T_{\rm{b}}=0.96 T_{\rm{c}} $ under different electric field intensities.
图 12 $ T_{\rm{b}}=1.04 T_{\rm{c}} $下, 电场强度$ E_0=0 $ (a) 和 $ E_0= $$ 0.0862 $ (b)时锥翅表面的沸腾过程及局部电场力分布
Figure 12. Snapshots of boiling processes and the distribution of localized electric field forces on the conical surface at $ T_{\rm{b}}=1.04 T_{\rm{c}} $ with $ E_0=0 $ (a) and $ E_0=0.0862 $ (b).
图 13 锥翅结构周围电场强度的模$ |\boldsymbol{E}| $的分布(电势差$ V= $$ 50 $, $ t^*=44.66 $)
Figure 13. Distribution of electric field strength $ |\boldsymbol{E}| $ around the conical structure (potential difference $ V=50 $, $ t^*= $$ 44.66 $).
图 14 加热温度$ T_{\rm{b}}=1.04 T_{\rm{c}} $时, 电场强度分别为$ E_0=0 $和$ E_0=0.0862 $的空间平均热流密度随时间的变化
Figure 14. The time histories of space-averaged heat flux with $ T_{\rm{b}}=1.04 T_{\rm{c}} $ under different electric intensities of $ E_0=0 $ and $ E_0=0.0862 $.
图 15 $ E_0=0.1207 $时不同壁面过热度得到的锥翅表面的沸腾过程及局部电场力分布 (a) Tb = 1.06 Tc; (b) Tb = 1.12 Tc
Figure 15. Snapshots of boiling processes and the distribution of localized electric field forces on the conical surface with $ E_0=0.1207 $ under different wall superheat degrees: (a) Tb = 1.06 Tc; (b) Tb = 1.12 Tc.
图 16 电场强度$ E_0=0 $和$ E_0=0.1207 $时(a)$ T_{\rm{b}}=1.06 T_{\rm{c}} $ 和(b)$ T_{\rm{b}}=1.12 T_{\rm{c}} $的空间热流密度随时间的变化
Figure 16. The time histories of space-averaged heat flux with $ E_0=0 $ and $ E_0=0.1207 $ under (a)$ T_{\rm{b}}=1.06 T_{\rm{c}} $ and (b)$ T_{\rm{b}}=1.12 T_{\rm{c}} $.
图 17 锥翅表面不同电场强度下的沸腾曲线
Figure 17. Boiling curves on the conical surface for different electric field intensities.
表 1 格子单位与物理单位转换
Table 1. The unit conversion from lattice unit to physical unit.
符号 格子单位 物理单位 转换因子 $ \rho_{\rm{l}} $ 5.426 570.02 $ {\rm{kg/m^3}} $ 106.16 $ {\rm{kg/m^3}} $ $ \rho_{\rm{v}} $ 0.8113 86.13 $ {\rm{kg/m^3}} $ 106.16 $ {\rm{kg/m^3}} $ $ l_0 $ 16 $ 4.72\times 10^{-6}\;{\rm{m}} $ $ 2.95\times 10^{-7}\;{\rm{m}} $ $ u_0 $ 0.0358 38.56 $ {\rm{m/s}} $ 1077.09 $ {\rm{m/s}} $ $ t_0 $ 447.8 $ 1.224\times 10^{-7}\;{\rm{s}} $ $ 2.734\times 10^{-10}\;{\rm{s}} $ $ \nu $ 0.06 $ 0.19\times 10^{-4}\;{\rm{m^2/s}} $ $ 3.18\times 10^{-4}\;{\rm{m^2/s}} $ $ T_{\rm{c}} $ 0.1961 647.2 $ {\rm{K}} $ 3300.36 $ {\rm{K}} $ $ p_{\rm{c}} $ 0.1784 $ 0.221\times 10^{8}\;{\rm{Pa}} $ $ 1.24\times 10^{8}\;{\rm{Pa}} $ $ c_{\rm{vl}} $ 4.0 1405.9 $ {\rm{J/(kg\cdot K)}} $ 351.48 $ {\rm{J/(kg\cdot K)}} $ $ h_{\rm{fg}} $ 0.624 $ 0.726\times 10^{6}\;{\rm{J/kg}} $ $ 1.16\times 10^{6}\;{\rm{J/kg}} $ $ \lambda_{\rm{s}} $ 32.556 390.67 $ {\rm{W/(m\cdot K)}} $ 12.0 $ {\rm{W/(m\cdot K)}} $ $ q_0 $ 0.01269 $ 1.69\times 10^{9}\;{\rm{J/(m^2\cdot s)}} $ $ 1.33\times 10^{11}\;{\rm{J/(m^2\cdot s)}} $ $ \varepsilon_0\varepsilon_{\rm{l}} $ 2.236 $ 1.98\times 10^{-11}\;{\rm{F/m}} $ $ 8.85\times 10^{-12}\;{\rm{F/m}} $ $ \varepsilon_0\varepsilon_{\rm{v}} $ 1 $ 8.85\times 10^{-12}\;{\rm{F/m}} $ $ 8.85\times 10^{-12}\;{\rm{F/m}} $ $ V $ 1 1096.96 $ {\rm{V}} $ 1096.96 $ {\rm{V}} $ 
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[1] Zaidi S 2015 Chem. Eng. Res. Des. 98 44
Google Scholar
[2] Massih A R, Persson S 1992 J. Nucl. Mater. 188 323
Google Scholar
[3] Mohammed H I, Giddings D, Walker G S 2019 Int. J. Heat Mass Transfer 130 710
Google Scholar
[4] Nikolayev V S, Chatain D, Garrabos Y, Beysens D 2006 Phys. Rev. Lett. 97 184503
Google Scholar
[5] Li W, Dai R K, Zeng M, Wang Q W 2020 Renew. Sust. Energ. Rev. 130 109926
Google Scholar
[6] Tian Z, Etedali S, Afrand M, Abdollahi A, Goodarzi M 2019 Powder Technol. 356 391
Google Scholar
[7] Wei J J, Honda H 2003 Int. J. Heat Mass Transfer 46 4059
Google Scholar
[8] Li Q, Zhao J H, Sun X Z, Liu B 2022 Appl. Therm. Eng. 215 118924
Google Scholar
[9] Kong X, Zhang Y H, Wei J J 2018 Exp. Therm. Fluid Sci. 91 9
Google Scholar
[10] Kim S H, Lee C G, Kang J Y, Moriyama K, Kim M H, Park H S 2015 Int. J. Heat Mass Transfer 91 1140
Google Scholar
[11] Elkholy A, Swift J, Kempers R 2023 Appl. Therm. Eng 219 119665
Google Scholar
[12] Clubb L 1916 UK Patent 100796 [1916-07-09
[13] Dong W, Li R Y, Yu H L, Yan Y Y 2006 Exp. Therm. Fluid Sci. 30 579
Google Scholar
[14] Gao M, Cheng P, Quan X J 2013 Int. J. Heat Mass Transfer 67 984
Google Scholar
[15] Hristov Y, Zhao D, Kenning D B R, Sefiane K, Karayiannis T G 2009 Heat Mass Transfer 45 999
Google Scholar
[16] Garivalis A I, Manfredini G, Saccone G, Di Marco P, Kossolapov A, Bucci M 2021 NPJ Microgravity 7(1) 37
Google Scholar
[17] Quan X J, Gao M, Cheng P, Li J S 2015 Int. J. Heat Mass Transfer 85 595
Google Scholar
[18] Liu B, Garivalis A I, Cao Z, Zhang Y, Wei J 2022 Int. J. Heat Mass Transfer 183 122154
Google Scholar
[19] Liu X, Chai Z H, Shi B C 2019 Phys. Fluids 31 092103
Google Scholar
[20] Liu X, Chai Z H, Shi B C 2021 Commun. Comput. Phys. 30 1346
Google Scholar
[21] Feng Y, Li H, Guo K, Lei X, Zhao J 2019 Int. J. Heat Mass Transfer 135 885
Google Scholar
[22] Li W X, Li Q, Chang H Z, Yu Y, Tang S 2022 Phys. Fluids 34 123327
Google Scholar
[23] Lou Q, Wang H Y, Li L 2023 Phys. Fluids 35 123327
Google Scholar
[24] Ezzatneshan E, Salehi A, Vaseghnia H 2023 Int. J. Therm. Sci 184 107913
Google Scholar
[25] Gong S, Cheng P 2012 Int. J. Heat Mass Transfer 55 4923
Google Scholar
[26] Guo Z L, Zheng C G, Shi B C 2011 Phys. Rev. E 83 036707
Google Scholar
[27] Chai Z H, Zhao T S 2012 Phys. Rev. E 86 016705
Google Scholar
[28] Panofsky W, Phillips M, Jauch J M 1956 Am. J. Phys. 24 416
[29] He X Y, Ning L 2000 Comput. Phys. Commun. 129 158
Google Scholar
[30] Chai Z H, Shi B C 2008 Appl. Math. Model. 32 2050
Google Scholar
[31] Chai Z H, Liang H, Du R, Shi B C 2019 SIAM J. Sci. Comput. 41 B746
Google Scholar
[32] Wang L, Wei Z C, Li T F, Chai Z H, Shi B C 2021 Appl. Math. Model. 95 361
Google Scholar
[33] Wang H Y, Lou Q, Liu G J, Li L 2022 Int. J. Therm. Sci. 178 107554
Google Scholar
[34] Lou Q, Guo Z L, Shi B C 2013 Phys. Rev. E 87 063301
Google Scholar
[35] Ladd A J C 1994 J. Fluid Mech. 271 285
Google Scholar
[36] Li L, Chen C, Mei R, Mei M, Klausner J 2014 Phys. Rev. E 89 043308
Google Scholar
[37] Gong S, Cheng P 2017 Int. Commun. Heat Mass Transfer 87 61
Google Scholar
[38] Li Q, Yu Y, Luo K H 2019 Phys. Rev. E 100 053313
Google Scholar
[39] Sadasivan P, Unal C, Nelson R 1995 J. Heat Transfer 117 558
Google Scholar
[40] 柴立和, 彭晓峰, 王补宣 1999 原子能科学技术 33 533
Chai L H, Peng X F, Wang B X 1999 Atomic Energy Sci. Techno. 33 533
[41] Berghmans J 1976 Int. J. Heat Mass Transfer 19 791
Google Scholar
[42] Johnson R 1968 AIAA J. 6 8
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