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

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.

Graphical abstract

Keywords

Kelvin−Helmholtz instability / thermodynamic nonequilibrium effect / viscous stress / discrete Boltzmann method

References

[1] S.Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Oxford University Press, London, 1961

[2] C.K. Batchelor, An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, 2000

[3] H.Luce, L.Kantha, M.Yabuki, H.Hashiguchi. Atmospheric Kelvin−Helmholtz billows captured by the MU radar, lidars and a fish-eye camera. Earth Planets Space , 2018, 70( 1): 162

[4] L.F. Wang, W.H. Ye, X.T. He, J.F. Wu, Z.F. Fan, C.Xue, H.Y. Guo, W.Y. Miao, Y.T. Yuan, J.Q. Dong, G.Jia, J.Zhang, Y.J. Li, J.Liu, M.Wang, Y.K. Ding, W.Y. Zhang. Theoretical and simulation research of hydrodynamic instabilities in inertial-confinement fusion implosions. Sci. China: Phys. Mech. Astron. , 2017, 60( 5): 055201

[5] R.V. Coelho, M.Mendoza, M.M. Doria, H.J. Herrmann. Kelvin−Helmholtz instability of the Dirac fluid of charge carriers on graphene. Phys. Rev. B , 2017, 96( 18): 184307

[6] V.V. Mishin, V.M. Tomozov. Kelvin−Helmholtz instability in the solar atmosphere, solar wind and geomagnetosphere. Sol. Phys. , 2016, 291( 11): 3165

[7] A.Petrarolo, M.Kobald, S.Schlechtriem. Understanding Kelvin−Helmholtz instability in paraffin-based hybrid rocket fuels. Exp. Fluids , 2018, 59( 4): 62

[8] R.K. Azadboni, A.Heidari, J.X. Wen. Numerical studies of flame acceleration and onset of detonation in homogenous and inhomogeneous mixture. J. Loss Prev. Process Ind. , 2020, 64 : 104063

[9] X.Y. Zhang, S.P. Li, B.Y. Yang, N.F. Wang. Flow structures of over-expanded supersonic gaseous jets for deep-water propulsion. Ocean Eng. , 2020, 213 : 107611

[10] X.F. Xiao, G.B. Zhao, W.X. Zhou, S.Martynenko. Large-eddy simulation of transpiration cooling in turbulent channel with porous wall. Appl. Therm. Eng. , 2018, 145 : 618

[11] W.Huang, Z.Du, L.Yan, Z.Xia. Supersonic mixing in airbreathing propulsion systems for hypersonic flights. Prog. Aerosp. Sci. , 2019, 109 : 100545

[12] E.C. Harding, J.F. Hansen, O.A. Hurricane, R.P. Drake, H.F. Robey, C.C. Kuranz, B.A. Remington, M.J. Bono, M.J. Grosskopf, R.S. Gillespie. Observation of a Kelvin−Helmholtz instability in a high-energydensity plasma on the omega laser. Phys. Rev. Lett. , 2009, 103( 4): 045005

[13] M.K. Awasthi, R.Asthana, G.Agrawal. 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

[14] B.Akula, P.Suchandra, M.Mikhaeil, D.Ranjan. Dynamics of unstably stratified free shear flows: An experimental investigation of coupled Kelvin−Helmholtz and Rayleigh−Taylor instability. J. Fluid Mech. , 2017, 816 : 619

[15] C.D. Lin, A.G. Xu, G.C. Zhang, Y.J. Li, S.Succi. Polarcoordinate lattice Boltzmann modeling of compressible flows. Phys. Rev. E , 2014, 89( 1): 013307

[16] A.G. Xu, G.C. Zhang, Y.B. Gan, F.Chen, X.J. Yu. Lattice Boltzmann modeling and simulation of compressible flows. Front. Phys. , 2012, 7( 5): 582

[17] J.P. Parker, C.P. Caulfield, R.R. Kerswell. The effects of Prandtl number on the nonlinear dynamics of Kelvin−Helmholtz instability in two dimensions. J. Fluid Mech. , 2021, 915 : A37

[18] V.Mohan, A.Sameen, B.Srinivasan, S.S. Girimaji. Influence of Knudsen and Mach numbers on Kelvin−Helmholtz instability. Phys. Rev. E , 2021, 103( 5): 053104

[19] Y.B. Gan, A.G. Xu, G.C. Zhang, C.D. Lin, H.L. Lai, Z.P. Liu. Nonequilibrium and morphological characterizations of Kelvin−Helmholtz instability in compressible flows. Front. Phys. , 2019, 14( 4): 43602

[20] H.G. Lee, J.Kim. Two-dimensional Kelvin− Helmholtz instabilities of multi-component fluids. Eur. J. Mech. BFluids , 2015, 49 : 77

[21] K.S. Kim, M.H. Kim. Simulation of the Kelvin−Helmholtz instability using a multi-liquid moving particle semi-implicit method. Ocean Eng. , 2017, 130 : 531

[22] M.J. Yao, W.Q. Shang, Y.Zhang, H.Gao, D.X. Zhang, P.Y. Liu. Numerical analysis of Kelvin−Helmholtz instability in inclined walls. Chin. J. Comput. Phys. , 2019, 36 : 403

[23] K.I. Ebihara, T.Watanabe. Lattice Boltzmann simulation of the interfacial growth of the horizontal stratified two-phase flow. Int. J. Mod. Phys. B , 2003, 17( 01n02): 113

[24] Y.B. Gan, A.G. Xu, G.C. Zhang, Y.J. Li. Lattice Boltzmann study on Kelvin−Helmholtz instability: Roles of velocity and density gradients. Phys. Rev. E , 2011, 83( 5): 056704

[25] Y.G. Li, X.G. Geng, Z.J. Liu, H.P. Wang, D.Y. Zang. Simulating Kelvin−Helmholtz instability using dissipative particle dynamics. Fluid Dyn. Res. , 2018, 50( 4): 045512

[26] W.Q. Shang, Y.Zhang, Z.Q. Chen, Z.P. Yuan, B.H. Dong. Numerical simulation of two-dimensional Kelvin−Helmholtz instabilities using a front tracking method. Chin. J. Comput. Mech. , 2018, 35 : 424

[27] G.A. Hoshoudy, M.K. Awasthi. 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

[28] E.P. Budiana. The meshless numerical simulation of Kelvin−Helmholtz instability during the wave growth of liquid−liquid slug flow. Comput. Math. Appl. , 2020, 80( 7): 1810

[29] R.M. McMullen, M.C. Krygier, J.R. Torczynski, M.A. Gallis. Navier−Stokes equations do not describe the smallest scales of turbulence in gases. Phys. Rev. Lett. , 2022, 128( 11): 114501

[30] A.G. Xu, C.D. Lin, G.C. Zhang, Y.J. Li. Multiple-relaxation-time lattice Boltzmann kinetic model for combustion. Phys. Rev. E , 2015, 91( 4): 043306

[31] C.D. Lin, K.H. Luo. Discrete Boltzmann modeling of unsteady reactive flows with nonequilibrium effects. Phys. Rev. E , 2019, 99( 1): 012142

[32] X.L. Su, C.D. Lin. Nonequilibrium effects of reactive flow based on gas kinetic theory. Commum. Theor. Phys. , 2022, 74( 3): 035604

[33] Y.B. Gan, A.G. Xu, G.C. Zhang, S.Succi. Discrete Boltzmann modeling of multiphase flows: Hydrodynamic and thermodynamic nonequilibrium effects. Soft Matter , 2015, 11( 26): 5336

[34] Y.B. Gan, A.G. Xu, G.C. Zhang, Y.D. Zhang, S.Succi. Discrete Boltzmann trans-scale modeling of high-speed compressible flows. Phys. Rev. E , 2018, 97( 5): 053312

[35] H.L. Lai, A.G. Xu, G.C. Zhang, Y.B. Gan, Y.J. Li, S.Succi. Nonequilibrium thermohydrodynamic effects on the Rayleigh−Taylor instability in compressible flows. Phys. Rev. E , 2016, 94( 2): 023106

[36] D.M. Li, H.L. Lai, A.G. Xu, G.C. Zhang, C.D. Lin, Y.B. Gan. Discrete Boltzmann simulation of Rayleigh−Taylor instability in compressible flows. Acta Physica Sinica , 2018, 67( 8): 080501

[37] H.Y. Ye, H.L. Lai, D.M. Li, Y.B. Gan, C.D. Lin, L.Chen, A.G. Xu. Knudsen number effects on two-dimensional Rayleigh−Taylor instability in compressible fluid: Based on a discrete Boltzmann method. Entropy (Basel) , 2020, 22( 5): 500

[38] L.Chen, H.L. Lai, C.D. Lin, D.M. Li. Specific heat ratio effects of compressible Rayleigh−Taylor instability studied by discrete Boltzmann method. Front. Phys. , 2021, 16( 5): 52500

[39] L.Chen, H.L. Lai, C.D. Lin, D.M. Li. Numerical study of multimode Rayleigh−Taylor instability by using the discrete Boltzmann method. Acta Aerodyn. Sin. , 2022, 40 : 1

[40] C.D. Lin, A.G. Xu, G.C. Zhang, Y.J. Li. An efficient two-dimensional discrete Boltzmann model of detonation. Adv. Condens. Matter Phys. , 2015, 4( 3): 102

[41] F.Chen, A.G. Xu, G.C. Zhang. Collaboration and competition between Richtmyer−Meshkov instability and Rayleigh-Taylor instability. Phys. Fluids , 2018, 30( 10): 102105

[42] Y.D. Zhang, A.G. Xu, G.C. Zhang, Z.H. Chen, P.Wang. Discrete Boltzmann method for non-equilibrium flows: Based on Shakhov model. Comput. Phys. Commun. , 2019, 238 : 50

[43] C.D. Lin, K.H. Luo, Y.B. Gan, Z.P. Liu. Kinetic simulation of nonequilibrium Kelvin−Helmholtz instability. Commum. Theor. Phys. , 2019, 71( 1): 132

[44] D.J. Zhang, A.G. Xu, Y.D. Zhang, Y.J. Li. Two-fluid discrete Boltzmann model for compressible flows: Based on ellipsoidal statistical Bhatnagar−Gross−Krook. Phys. Fluids , 2020, 32( 12): 126110

[45] F.Chen, A.G. Xu, Y.D. Zhang, Q.K. Zeng. Morphological and nonequilibrium analysis of coupled Rayleigh−Taylor−Kelvin−Helmholtz instability. Phys. Fluids , 2020, 32( 10): 104111

[46] C.D. Lin, K.H. Luo, A.G. Xu, Y.B. Gan, H.L. Lai. Multiple-relaxation-time discrete Boltzmann modeling of multicomponent mixture with nonequilibrium effects. Phys. Rev. E , 2021, 103( 1): 013305

[47] F.Chen, A.G. Xu, Y.D. Zhang, Y.B. Gan, B.B. Liu, S.Wang. Effects of the initial perturbations on the Rayleigh−Taylor−Kelvin−Helmholtz instability system. Front. Phys. , 2022, 17( 3): 33505

[48] R.Benzi, S.Succi, M.Vergassola. The lattice Boltzmann equation: Theory and applications. Phys. Rep. , 1992, 222( 3): 145

[49] X.Y. He S. Y. Chen G.D. Doolen, A novel thermal model for the lattice Boltzmann method in incompressible limit, J. Comput. Phys . 146(1), 282 ( 1998)

[50] Z.H. Chai, B.C. Shi. 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

[51] Q.Li, H.Yang, R.Z. Huang. Lattice Boltzmann simulation of solidliquid phase change with nonlinear density variation. Phys. Fluids , 2021, 33( 12): 123302

[52] Z.D. Wang Y.K. Wen Y.H. Qian, A novel thermal lattice Boltzmann model with heat source and its application in incompressible flow, Appl. Math. Comput . 427, 127167 ( 2022)

[53] A.G. Xu, J.Chen, J.H. Song, D.W. Chen, Z.H. Chen. Progress of discrete Boltzmann study on multiphase complex flows. Acta Aerodyn. Sin. , 2021, 39 : 138

[54] A.G. Xu, J.H. Song, F.Chen, K.Xie, Y.J. Ying. Modeling and analysis methods for complex fields based on phase space. Chin. J. Comput. Phys. , 2021, 38 : 631

[55] A.G. Xu, Y.M. Shan, F.Chen, Y.B. Gan, C.D. Lin. Progress of mesoscale modeling and investigation of combustion multiphase flow. Acta Aero. Astro. Sin. , 2021, 42 : 625842

[56] G.P. Klaassen, W.R. Peltier. Evolution of finite amplitude Kelvin−Helmholtz billows in two spatial dimensions. J. Atmos. Sci. , 1985, 42( 12): 1321

[57] G.P. Klaassen, W.R. Peltier. The effect of prandtl number on the evolution and stability of Kelvin−Helmholtz billows. Geophys. Astrophys. Fluid Dyn. , 1985, 32( 1): 23

[58] R.Fatehi, M.S. Shadloo, M.T. Manzari. Numerical investigation of two-phase secondary Kelvin−Helmholtz instability. Proc. Instit. Mech. Eng. C:J. Mech. Eng. Sci. , 2014, 228( 11): 1913

[59] K.Kiuchi, P.Cerdá-Durán, K.Kyutoku, Y.Sekiguchi, M.Shibata. Efficient magnetic-field amplification due to the Kelvin−Helmholtz instability in binary neutron star mergers. Phys. Rev. D , 2015, 92( 12): 124034

[60] Y.D. Zhang, A.G. Xu, G.C. Zhang, C.M. Zhu, C.D. Lin. Kinetic modeling of detonation and effects of negative temperature coefficient. Combust. Flame , 2016, 173 : 483

[61] C.D. Lin K.H. Luo L.L. Fei S.Succi, A multi-component discrete Boltzmann model for nonequilibrium reactive flows, Sci. Rep . 7(1), 14580 ( 2017)

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51806116 and 11875001) and the Natural Science Foundation of Fujian Provinces (Grant Nos. 2021J01652 and 2021J01655).

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