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We investigate analytically the effect of thermal conduction on the Kelvin-Helmholtz instability (KHI) in a straight pipe with different cross-sections. The results show that the relative tangential velocity of the interface between the upper and lower fluid in the pipe first increases and then decreases with the increase of the wave number. Furthermore, the smaller coefficient of interfacial heat conduction causes the relative tangential velocity to decrease considerably with the increase of the wave number, which is different from the behavior of the straight pipeline with the same cross-section. In addition, the heat conduction increases the growth rate of KHI, which is in accordance with the scenario of straight pipeline with the same cross-section.
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Keywords:
- Kelvin-Helmholtz instability /
- thermal conduction /
- coefficient of interfacial heat conduction
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图 1 两种不同横截面的直管道示意图
Figure 1. Schematic diagram of a straight pipe with two different cross sections.
图 2 上下流体的界面相对切向速度与波数的关系
Figure 2. Wavenumber dependence of the relative tangential velocity at the interface between upper and lower fluids.
图 3 KHI的增长率与波数的关系
Figure 3. Wavenumber dependence of the growth rate of KHI.
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[1] Rayleigh L 1883 Proc. London Math. Soc. 14 170
Google Scholar
[2] Taylor G I 1950 Proc. R. Soc. London, Ser. A 201 192
Google Scholar
[3] Richtmyer R D 1960 Commun. Pure Appl. Math. 13 297
Google Scholar
[4] Meshkow E E 1969 Fluid Dyn. 4 101
Google Scholar
[5] [6] Helmholtz H 1868 Philos. Mag. Ser. 4 36 337
Google Scholar
[7] Poujade O, Peybernes M 2010 Phys. Rev. E 81 016316
Google Scholar
[8] Horton W, Tajima T, Kamimura T 1987 Phys. Fluids 30 3485
Google Scholar
[9] Volovik G E 2002 JETP Lett. 75 418
Google Scholar
[10] Blaauwgeers R, Eltsov V B, Eska G, Finne A P, Haley R P, Krusius M, Ruohio J J, Skrbek L, Volovik G E 2002 Phys. Rev. Lett. 89 155301
Google Scholar
[11] Cao Y G, Guo H Z, Zhang Z F, Sun Z H, Chow W K 2011 J. Phys. A:Math. Theor. 44 275501
Google Scholar
[12] Zhao Y B, Xia M J, Cao Y G 2020 AIP Adv. 10 015056
Google Scholar
[13] 夏同军, 董永强, 曹义刚 2013 62 114702
Google Scholar
Xia T J, Dong Y Q, Cao Y G 2013 Acta Phys. Sin. 62 114702
Google Scholar
[14] 王立锋, 叶文华, 李英骏 2008 57 3038
Google Scholar
Wang L F, Ye W H, Li Y J 2008 Acta Phys. Sin 57 3038
Google Scholar
[15] Chen F, Xu A G, Zhang Y D, Zeng Q K 2020 Phys. Fluids 32 104111
Google Scholar
[16] 王立锋, 叶文华, 范征锋, 孙彦乾, 郑炳松, 李英骏 2009 58 6381
Google Scholar
Wang L F, Ye W H, Fan Z F, Sun Y Q, Zheng B S, Li Y J 2009 Acta Phys. Sin. 58 6381
Google Scholar
[17] Gan Y B, Xu A G, Zhang G C, Lin C D, Lai H L, Liu Z P 2019 Front. Phys. 14 43602
Google Scholar
[18] Chen J Y, Wang Y C, Zhang W, Qiu L M, Zhang X B 2016 Chem. Eng. Sci. 144 395
Google Scholar
[19] Asthana R, Agrawal G S 2007 Physica A 382 389
Google Scholar
[20] Awasthi M K, Asthana R, Agrawal G S 2014 Int. J. Heat Mass Transfer 78 251
Google Scholar
[21] Barnea D, Taitel Y 1993 Int. J. Multiphase Flow 19 639
Google Scholar
[22] Yang X C, Cao Y G 2021 Physica D 424 132950
Google Scholar
[23] Kwon H J 2008 KSCE J. Civil Eng. 12 205
Google Scholar
[24] Xia T J, Wang H L, Dong Y Q, Guo H Z, Cao Y G 2015 Int. J. Heat Mass Transfer 84 158
Google Scholar
[25] Funada T, Joseph D D 2001 J. Fluid Mech. 445 263
Google Scholar
[26] Awasthi M K, Asthana R, Agrawal G S 2015 Appl. Mech. Mater. 110 4628
Google Scholar
[27] 谢海英 2013 水资源与水工程学报 24 152
Google Scholar
Xie H Y 2013 J. Water Resour. Water Eng. 24 152
Google Scholar
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