Influence of the tangential velocity on the compressible Kelvin−Helmholtz instability with nonequilibrium effects

doi:10.1007/s11467-022-1200-3

Frontiers of Physics

2022, Vol. 17

Issue (6): 63500 https://doi.org/10.1007/s11467-022-1200-3

本期目录

Influence of the tangential velocity on the compressible Kelvin−Helmholtz instability with nonequilibrium effects

Yaofeng Li¹, Huilin Lai¹(

), Chuandong Lin²(

), Demei Li¹

¹. College of Mathematics and Statistics, FJKLMAA, Center for Applied Mathematics of Fujian Province (FJNU), Fujian Normal University, Fuzhou 350117, China
². Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Zhuhai 519082, China

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Abstract：

Kelvin−Helmholtz (KH) instability is a fundamental fluid instability that widely exists in nature and engineering. To better understand the dynamic process of the KH instability, the influence of the tangential velocity on the compressible KH instability is investigated by using the discrete Boltzmann method based on the nonequilibrium statistical physics. Both hydrodynamic and thermodynamic nonequilibrium (TNE) effects are probed and analyzed. It is found that, on the whole, the global density gradients, the TNE strength and area firstly increase and decrease afterwards. Both the global density gradient and heat flux intensity in the vertical direction are almost constant in the initial stage before a vortex forms. Moreover, with the increase of the tangential velocity, the KH instability evolves faster, hence the global density gradients, the TNE strength and area increase in the initial stage and achieve their peak earlier, and their maxima are higher for a larger tangential velocity. Physically, there are several competitive mechanisms in the evolution of the KH instability. (i) The physical gradients increase and the TNE effects are strengthened as the interface is elongated. The local physical gradients decrease and the local TNE intensity is weakened on account of the dissipation and/or diffusion. (ii) The global heat flux intensity is promoted when the physical gradients increase. As the contact area expands, the heat exchange is enhanced and the global heat flux intensity increases. (iii) The global TNE intensity reduces with the decreasing of physical gradients and increase with the increasing of TNE area. (iv) The nonequilibrium area increases as the fluid interface is elongated and is widened because of the dissipation and/or diffusion.

Key words： Kelvin−Helmholtz instability thermodynamic nonequilibrium effect viscous stress discrete Boltzmann method

收稿日期: 2022-04-26 出版日期: 2022-09-06

Corresponding Author(s): Huilin Lai,Chuandong Lin

引用本文:

. [J]. Frontiers of Physics, 2022, 17(6): 63500.
Yaofeng Li, Huilin Lai, Chuandong Lin, Demei Li. Influence of the tangential velocity on the compressible Kelvin−Helmholtz instability with nonequilibrium effects. Front. Phys. , 2022, 17(6): 63500.

链接本文:

https://academic.hep.com.cn/fop/CN/10.1007/s11467-022-1200-3
https://academic.hep.com.cn/fop/CN/Y2022/V17/I6/63500

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1	Chandrasekhar S., Hydrodynamic and Hydromagnetic Stability, Oxford University Press, London, 1961
2	K. Batchelor C., An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, 2000
3	Luce H., Kantha L., Yabuki M., Hashiguchi H.. Atmospheric Kelvin−Helmholtz billows captured by the MU radar, lidars and a fish-eye camera. Earth Planets Space , 2018, 70( 1): 162 https://doi.org/10.1186/s40623-018-0935-0
4	F. Wang L., H. Ye W., T. He X., F. Wu J., F. Fan Z., Xue C., Y. Guo H., Y. Miao W., T. Yuan Y., Q. Dong J., Jia G., Zhang J., J. Li Y., Liu J., Wang M., K. Ding Y., Y. Zhang W.. Theoretical and simulation research of hydrodynamic instabilities in inertial-confinement fusion implosions. Sci. China: Phys. Mech. Astron. , 2017, 60( 5): 055201 https://doi.org/10.1007/s11433-017-9016-x
5	V. Coelho R., Mendoza M., M. Doria M., J. Herrmann H.. Kelvin−Helmholtz instability of the Dirac fluid of charge carriers on graphene. Phys. Rev. B , 2017, 96( 18): 184307 https://doi.org/10.1103/PhysRevB.96.184307
6	V. Mishin V., M. Tomozov V.. Kelvin−Helmholtz instability in the solar atmosphere, solar wind and geomagnetosphere. Sol. Phys. , 2016, 291( 11): 3165 https://doi.org/10.1007/s11207-016-0891-4
7	Petrarolo A., Kobald M., Schlechtriem S.. Understanding Kelvin−Helmholtz instability in paraffin-based hybrid rocket fuels. Exp. Fluids , 2018, 59( 4): 62 https://doi.org/10.1007/s00348-018-2516-1
8	K. Azadboni R., Heidari A., X. Wen J.. Numerical studies of flame acceleration and onset of detonation in homogenous and inhomogeneous mixture. J. Loss Prev. Process Ind. , 2020, 64 : 104063 https://doi.org/10.1016/j.jlp.2020.104063
9	Y. Zhang X., P. Li S., Y. Yang B., F. Wang N.. Flow structures of over-expanded supersonic gaseous jets for deep-water propulsion. Ocean Eng. , 2020, 213 : 107611 https://doi.org/10.1016/j.oceaneng.2020.107611
10	F. Xiao X., B. Zhao G., X. Zhou W., Martynenko S.. Large-eddy simulation of transpiration cooling in turbulent channel with porous wall. Appl. Therm. Eng. , 2018, 145 : 618 https://doi.org/10.1016/j.applthermaleng.2018.09.056
11	Huang W., Du Z., Yan L., Xia Z.. Supersonic mixing in airbreathing propulsion systems for hypersonic flights. Prog. Aerosp. Sci. , 2019, 109 : 100545 https://doi.org/10.1016/j.paerosci.2019.05.005
12	C. Harding E., F. Hansen J., A. Hurricane O., P. Drake R., F. Robey H., C. Kuranz C., A. Remington B., J. Bono M., J. Grosskopf M., S. Gillespie R.. Observation of a Kelvin−Helmholtz instability in a high-energydensity plasma on the omega laser. Phys. Rev. Lett. , 2009, 103( 4): 045005 https://doi.org/10.1103/PhysRevLett.103.045005
13	K. Awasthi M., Asthana R., Agrawal G.. Viscous correction for the viscous potential flow analysis of Kelvin−Helmholtz instability of cylindrical flow with heat and mass transfer. Int. J. Heat Mass Transf. , 2014, 78 : 251 https://doi.org/10.1016/j.ijheatmasstransfer.2014.06.082
14	Akula B., Suchandra P., Mikhaeil M., Ranjan D.. Dynamics of unstably stratified free shear flows: An experimental investigation of coupled Kelvin−Helmholtz and Rayleigh−Taylor instability. J. Fluid Mech. , 2017, 816 : 619 https://doi.org/10.1017/jfm.2017.95
15	D. Lin C., G. Xu A., C. Zhang G., J. Li Y., Succi S.. Polarcoordinate lattice Boltzmann modeling of compressible flows. Phys. Rev. E , 2014, 89( 1): 013307 https://doi.org/10.1103/PhysRevE.89.013307
16	G. Xu A., C. Zhang G., B. Gan Y., Chen F., J. Yu X.. Lattice Boltzmann modeling and simulation of compressible flows. Front. Phys. , 2012, 7( 5): 582 https://doi.org/10.1007/s11467-012-0269-5
17	P. Parker J., P. Caulfield C., R. Kerswell R.. The effects of Prandtl number on the nonlinear dynamics of Kelvin−Helmholtz instability in two dimensions. J. Fluid Mech. , 2021, 915 : A37 https://doi.org/10.1017/jfm.2021.125
18	Mohan V., Sameen A., Srinivasan B., S. Girimaji S.. Influence of Knudsen and Mach numbers on Kelvin−Helmholtz instability. Phys. Rev. E , 2021, 103( 5): 053104 https://doi.org/10.1103/PhysRevE.103.053104
19	B. Gan Y., G. Xu A., C. Zhang G., D. Lin C., L. Lai H., P. Liu Z.. Nonequilibrium and morphological characterizations of Kelvin−Helmholtz instability in compressible flows. Front. Phys. , 2019, 14( 4): 43602 https://doi.org/10.1007/s11467-019-0885-4
20	G. Lee H., Kim J.. Two-dimensional Kelvin− Helmholtz instabilities of multi-component fluids. Eur. J. Mech. BFluids , 2015, 49 : 77 https://doi.org/10.1016/j.euromechflu.2014.08.001
21	S. Kim K., H. Kim M.. Simulation of the Kelvin−Helmholtz instability using a multi-liquid moving particle semi-implicit method. Ocean Eng. , 2017, 130 : 531 https://doi.org/10.1016/j.oceaneng.2016.11.071
22	J. Yao M., Q. Shang W., Zhang Y., Gao H., X. Zhang D., Y. Liu P.. Numerical analysis of Kelvin−Helmholtz instability in inclined walls. Chin. J. Comput. Phys. , 2019, 36 : 403
23	I. Ebihara K., Watanabe T.. Lattice Boltzmann simulation of the interfacial growth of the horizontal stratified two-phase flow. Int. J. Mod. Phys. B , 2003, 17( 01n02): 113 https://doi.org/10.1142/S0217979203017175
24	B. Gan Y., G. Xu A., C. Zhang G., J. Li Y.. Lattice Boltzmann study on Kelvin−Helmholtz instability: Roles of velocity and density gradients. Phys. Rev. E , 2011, 83( 5): 056704 https://doi.org/10.1103/PhysRevE.83.056704
25	G. Li Y., G. Geng X., J. Liu Z., P. Wang H., Y. Zang D.. Simulating Kelvin−Helmholtz instability using dissipative particle dynamics. Fluid Dyn. Res. , 2018, 50( 4): 045512 https://doi.org/10.1088/1873-7005/aac769
26	Q. Shang W., Zhang Y., Q. Chen Z., P. Yuan Z., H. Dong B.. Numerical simulation of two-dimensional Kelvin−Helmholtz instabilities using a front tracking method. Chin. J. Comput. Mech. , 2018, 35 : 424
27	A. Hoshoudy G., K. Awasthi M.. Compressibility effects on the Kelvin−Helmholtz and Rayleigh−Taylor instabilities between two immiscible fluids flowing through a porous medium. Eur. Phys. J. Plus , 2020, 135( 2): 169 https://doi.org/10.1140/epjp/s13360-020-00160-x
28	P. Budiana E.. The meshless numerical simulation of Kelvin−Helmholtz instability during the wave growth of liquid−liquid slug flow. Comput. Math. Appl. , 2020, 80( 7): 1810 https://doi.org/10.1016/j.camwa.2020.08.006
29	M. McMullen R., C. Krygier M., R. Torczynski J., A. Gallis M.. Navier−Stokes equations do not describe the smallest scales of turbulence in gases. Phys. Rev. Lett. , 2022, 128( 11): 114501 https://doi.org/10.1103/PhysRevLett.128.114501
30	G. Xu A., D. Lin C., C. Zhang G., J. Li Y.. Multiple-relaxation-time lattice Boltzmann kinetic model for combustion. Phys. Rev. E , 2015, 91( 4): 043306 https://doi.org/10.1103/PhysRevE.91.043306
31	D. Lin C., H. Luo K.. Discrete Boltzmann modeling of unsteady reactive flows with nonequilibrium effects. Phys. Rev. E , 2019, 99( 1): 012142 https://doi.org/10.1103/PhysRevE.99.012142
32	L. Su X., D. Lin C.. Nonequilibrium effects of reactive flow based on gas kinetic theory. Commum. Theor. Phys. , 2022, 74( 3): 035604 https://doi.org/10.1088/1572-9494/ac53a0
33	B. Gan Y., G. Xu A., C. Zhang G., Succi S.. Discrete Boltzmann modeling of multiphase flows: Hydrodynamic and thermodynamic nonequilibrium effects. Soft Matter , 2015, 11( 26): 5336 https://doi.org/10.1039/C5SM01125F
34	B. Gan Y., G. Xu A., C. Zhang G., D. Zhang Y., Succi S.. Discrete Boltzmann trans-scale modeling of high-speed compressible flows. Phys. Rev. E , 2018, 97( 5): 053312 https://doi.org/10.1103/PhysRevE.97.053312
35	L. Lai H., G. Xu A., C. Zhang G., B. Gan Y., J. Li Y., Succi S.. Nonequilibrium thermohydrodynamic effects on the Rayleigh−Taylor instability in compressible flows. Phys. Rev. E , 2016, 94( 2): 023106 https://doi.org/10.1103/PhysRevE.94.023106
36	M. Li D., L. Lai H., G. Xu A., C. Zhang G., D. Lin C., B. Gan Y.. Discrete Boltzmann simulation of Rayleigh−Taylor instability in compressible flows. Acta Physica Sinica , 2018, 67( 8): 080501 https://doi.org/10.7498/aps.67.20171952
37	Y. Ye H., L. Lai H., M. Li D., B. Gan Y., D. Lin C., Chen L., G. Xu A.. Knudsen number effects on two-dimensional Rayleigh−Taylor instability in compressible fluid: Based on a discrete Boltzmann method. Entropy (Basel) , 2020, 22( 5): 500 https://doi.org/10.3390/e22050500
38	Chen L., L. Lai H., D. Lin C., M. Li D.. Specific heat ratio effects of compressible Rayleigh−Taylor instability studied by discrete Boltzmann method. Front. Phys. , 2021, 16( 5): 52500 https://doi.org/10.1007/s11467-021-1096-3
39	Chen L., L. Lai H., D. Lin C., M. Li D.. Numerical study of multimode Rayleigh−Taylor instability by using the discrete Boltzmann method. Acta Aerodyn. Sin. , 2022, 40 : 1
40	D. Lin C., G. Xu A., C. Zhang G., J. Li Y.. An efficient two-dimensional discrete Boltzmann model of detonation. Adv. Condens. Matter Phys. , 2015, 4( 3): 102 https://doi.org/10.12677/CMP.2015.43012
41	Chen F., G. Xu A., C. Zhang G.. Collaboration and competition between Richtmyer−Meshkov instability and Rayleigh-Taylor instability. Phys. Fluids , 2018, 30( 10): 102105 https://doi.org/10.1063/1.5049869
42	D. Zhang Y., G. Xu A., C. Zhang G., H. Chen Z., Wang P.. Discrete Boltzmann method for non-equilibrium flows: Based on Shakhov model. Comput. Phys. Commun. , 2019, 238 : 50 https://doi.org/10.1016/j.cpc.2018.12.018
43	D. Lin C., H. Luo K., B. Gan Y., P. Liu Z.. Kinetic simulation of nonequilibrium Kelvin−Helmholtz instability. Commum. Theor. Phys. , 2019, 71( 1): 132 https://doi.org/10.1088/0253-6102/71/1/132
44	J. Zhang D., G. Xu A., D. Zhang Y., J. Li Y.. Two-fluid discrete Boltzmann model for compressible flows: Based on ellipsoidal statistical Bhatnagar−Gross−Krook. Phys. Fluids , 2020, 32( 12): 126110 https://doi.org/10.1063/5.0017673
45	Chen F., G. Xu A., D. Zhang Y., K. Zeng Q.. Morphological and nonequilibrium analysis of coupled Rayleigh−Taylor−Kelvin−Helmholtz instability. Phys. Fluids , 2020, 32( 10): 104111 https://doi.org/10.1063/5.0023364
46	D. Lin C., H. Luo K., G. Xu A., B. Gan Y., L. Lai H.. Multiple-relaxation-time discrete Boltzmann modeling of multicomponent mixture with nonequilibrium effects. Phys. Rev. E , 2021, 103( 1): 013305 https://doi.org/10.1103/PhysRevE.103.013305
47	Chen F., G. Xu A., D. Zhang Y., B. Gan Y., B. Liu B., Wang S.. Effects of the initial perturbations on the Rayleigh−Taylor−Kelvin−Helmholtz instability system. Front. Phys. , 2022, 17( 3): 33505 https://doi.org/10.1007/s11467-021-1145-y
48	Benzi R., Succi S., Vergassola M.. The lattice Boltzmann equation: Theory and applications. Phys. Rep. , 1992, 222( 3): 145 https://doi.org/10.1016/0370-1573(92)90090-M
49	Y. He X. Y. Chen S. D. Doolen G., A novel thermal model for the lattice Boltzmann method in incompressible limit, J. Comput. Phys . 146(1), 282 ( 1998)
50	H. Chai Z., C. Shi B.. Multiple-relaxation-time lattice Boltzmann method for the Navier−Stokes and nonlinear convection-diffusion equations: Modeling, analysis, and elements. Phys. Rev. E , 2020, 102( 2): 023306 https://doi.org/10.1103/PhysRevE.102.023306
51	Li Q., Yang H., Z. Huang R.. Lattice Boltzmann simulation of solidliquid phase change with nonlinear density variation. Phys. Fluids , 2021, 33( 12): 123302 https://doi.org/10.1063/5.0070407
52	D. Wang Z. K. Wen Y. H. Qian Y., A novel thermal lattice Boltzmann model with heat source and its application in incompressible flow, Appl. Math. Comput . 427, 127167 ( 2022)
53	G. Xu A., Chen J., H. Song J., W. Chen D., H. Chen Z.. Progress of discrete Boltzmann study on multiphase complex flows. Acta Aerodyn. Sin. , 2021, 39 : 138
54	G. Xu A., H. Song J., Chen F., Xie K., J. Ying Y.. Modeling and analysis methods for complex fields based on phase space. Chin. J. Comput. Phys. , 2021, 38 : 631
55	G. Xu A., M. Shan Y., Chen F., B. Gan Y., D. Lin C.. Progress of mesoscale modeling and investigation of combustion multiphase flow. Acta Aero. Astro. Sin. , 2021, 42 : 625842
56	P. Klaassen G., R. Peltier W.. Evolution of finite amplitude Kelvin−Helmholtz billows in two spatial dimensions. J. Atmos. Sci. , 1985, 42( 12): 1321 https://doi.org/10.1175/1520-0469(1985)042<1321:EOFAKB>2.0.CO;2
57	P. Klaassen G., R. Peltier W.. The effect of prandtl number on the evolution and stability of Kelvin−Helmholtz billows. Geophys. Astrophys. Fluid Dyn. , 1985, 32( 1): 23 https://doi.org/10.1080/03091928508210082
58	Fatehi R., S. Shadloo M., T. Manzari M.. Numerical investigation of two-phase secondary Kelvin−Helmholtz instability. Proc. Instit. Mech. Eng. C:J. Mech. Eng. Sci. , 2014, 228( 11): 1913 https://doi.org/10.1177/0954406213512630
59	Kiuchi K., Cerdá-Durán P., Kyutoku K., Sekiguchi Y., Shibata M.. Efficient magnetic-field amplification due to the Kelvin−Helmholtz instability in binary neutron star mergers. Phys. Rev. D , 2015, 92( 12): 124034 https://doi.org/10.1103/PhysRevD.92.124034
60	D. Zhang Y., G. Xu A., C. Zhang G., M. Zhu C., D. Lin C.. Kinetic modeling of detonation and effects of negative temperature coefficient. Combust. Flame , 2016, 173 : 483 https://doi.org/10.1016/j.combustflame.2016.04.003
61	D. Lin C. H. Luo K. L. Fei L. Succi S., A multi-component discrete Boltzmann model for nonequilibrium reactive flows, Sci. Rep . 7(1), 14580 ( 2017)

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