Viscosity, heat conductivity, and Prandtl number effects in the Rayleigh–Taylor Instability

doi:10.1007/s11467-016-0603-4

Frontiers of Physics

2016, Vol. 11

Issue (6): 114703 https://doi.org/10.1007/s11467-016-0603-4

本期目录

Viscosity, heat conductivity, and Prandtl number effects in the Rayleigh–Taylor Instability

Feng Chen^1,^*(

),Ai-Guo Xu^2,^3,^*(

),Guang-Cai Zhang²

¹. School of Aeronautics, Shan Dong Jiaotong University, Jinan 250357, China
². National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009-26, Beijing 100088, China
³. Center for Applied Physics and Technology, MOE Key Center for High Energy Density Physics Simulations, College of Engineering, Peking University, Beijing 100871, China

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Abstract：

The two-dimensional Rayleigh–Taylor instability problem is simulated with a multiple-relaxation-time discrete Boltzmann model with a gravity term. Viscosity, heat conductivity, and Prandtl number effects are probed from macroscopic and nonequilibrium viewpoints. In the macro sense, both viscosity and heat conduction show a significant inhibitory effect in the reacceleration stage, which is mainly achieved by inhibiting the development of the Kelvin–Helmholtz instability. Before this, the Prandtl number effect is not sensitive. Viscosity, heat conductivity, and Prandtl number effects on nonequilibrium manifestations and the degree of correlation between the nonuniformity and the nonequilibrium strength in the complex flow are systematically investigated.

Key words： discrete Boltzmann model/method multiple-relaxation-time Rayleigh–Taylor instability nonequilibrium

收稿日期: 2016-05-08 出版日期: 2016-08-16

Corresponding Author(s): Feng Chen,Ai-Guo Xu

引用本文:

. [J]. Frontiers of Physics, 2016, 11(6): 114703.
Feng Chen,Ai-Guo Xu,Guang-Cai Zhang. Viscosity, heat conductivity, and Prandtl number effects in the Rayleigh–Taylor Instability. Front. Phys. , 2016, 11(6): 114703.

链接本文:

https://academic.hep.com.cn/fop/CN/10.1007/s11467-016-0603-4
https://academic.hep.com.cn/fop/CN/Y2016/V11/I6/114703

1	L. Rayleigh, Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density, Proc. London Math. Soc. s1–14(1), 170 (1882)
2	G. Taylor, The instability of liquid surfaces when accelerated in a direction perpendicular to their planes (I), P. Roy. Soc. A 201(1065), 192 (1950) https://doi.org/10.1098/rspa.1950.0052
3	W. H. Ye, W. Y. Zhang, G. N. Chen, C. Q. Jin, and J. Zhang, Numerical simulations of the FCT method on Rayleigh–Taylor and Richtmyer–Meshkov instabilities, Chin. J. Comput. Phys. 15(3), 277 (1998)
4	X. L. Li, B. X. Jin, and J. Glimm, Numerical study for the three dimensional Rayleigh–Taylor instability through the TVD/AC scheme and parallel computation, J. Comput. Phys. 126(2), 343 (1996) https://doi.org/10.1006/jcph.1996.0142
5	G. Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi, W. Tauber, J. Han, S. Nas, and Y. J. Jan, A front-tracking method for the computations of multiphase flow, J. Comput. Phys. 169(2), 708 (2001) https://doi.org/10.1006/jcph.2001.6726
6	Y. K. Li and A. Umemura, Mechanism of the large surface deformation caused by Rayleigh–Taylor instability at large Atwood number, J. Appl. Math. Phys. 2(10), 971 (2014) https://doi.org/10.4236/jamp.2014.210110
7	M. S. Shadloo, A. Zainali, and M. Yildiz, Simulation of single mode Rayleigh–Taylor instability by SPH method, Comput. Mech. 51(5), 699 (2013) https://doi.org/10.1007/s00466-012-0746-2
8	L. Duchemin, C. Josserand, and P. Clavin, Asymptotic behavior of the Rayleigh–Taylor instability, Phys. Rev. Lett. 94(22), 224501 (2005) https://doi.org/10.1103/PhysRevLett.94.224501
9	A. W. Cook and P. E. Dimotakis, Transition stages of Rayleigh–Taylor instability between miscible fluids, J. Fluid Mech. 443, 69 (2001) https://doi.org/10.1017/S0022112001005377
10	A. Celani, A. Mazzino, and L. Vozella, Rayleigh–Taylor turbulence in two dimensions, Phys. Rev. Lett. 96(13), 134504 (2006) https://doi.org/10.1103/PhysRevLett.96.134504
11	W. Cabot, Comparison of two- and three-dimensional simulations of miscible Rayleigh–Taylor instability, Phys. Fluids 18(4), 045101 (2006) https://doi.org/10.1063/1.2191856
12	A. Celani, A. Mazzino, P. Muratore-Ginanneschi, and L. Vozella, Phase-field model for the Rayleigh–Taylor instability of immiscible fluids, J. Fluid Mech. 622, 115 (2009) https://doi.org/10.1017/S0022112008005120
13	R. Betti and J. Sanz, Bubble acceleration in the ablative Rayleigh–Taylor instability, Phys. Rev. Lett. 97(20), 205002 (2006) https://doi.org/10.1103/PhysRevLett.97.205002
14	M. R. Gupta, L. Mandal, S. Roy, and M. Khan, Effect of magnetic field on temporal development of Rayleigh– Taylor instability induced interfacial nonlinear structure, Phys. Plasmas 17(1), 012306 (2010) https://doi.org/10.1063/1.3293120
15	P. K. Sharma, R. P. Prajapati, and R. K. Chhajlani, Effect of surface tension and rotation on Rayleigh–Taylor instability of two superposed fluids with suspended particles, Acta Phys. Pol. A 118(4), 576 (2010) https://doi.org/10.12693/APhysPolA.118.576
16	R. Banerjee, L. K. Mandal, S. Roy, M. Khan, and M. R. Gupta, Combined effect of viscosity and vorticity on single mode Rayleigh–Taylor instability bubble growth, Phys. Plasmas 18(2), 022109 (2011) https://doi.org/10.1063/1.3555523
17	H. Liu, W. Kang, Q. Zhang, Y. Zhang, H. Duan, and X. T. He, Molecular dynamics simulations of microscopic structure of ultra strong shock waves in dense helium, Front. Phys. 11(6), 115206 (2016) https://doi.org/10.1007/s11467-016-0590-5
18	S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford: Oxford University Press, 2001
19	R. Benzi, S. Succi, and M. Vergassola, The lattice Boltzmann equation: Theory and applications, Phys. Rep. 222(3), 145 (1992) https://doi.org/10.1016/0370-1573(92)90090-M
20	A. Xu, G. Gonnella, and A. Lamura, Phase-separating binary fluids under oscillatory shear, Phys. Rev. E 67(5), 056105 (2003) https://doi.org/10.1103/PhysRevE.67.056105
21	A. G. Xu, G. Gonnella, and A. Lamura, Morphologies and flow patterns in quenching of lamellar systems with shear, Phys. Rev. E 74(1), 011505 (2006) https://doi.org/10.1103/PhysRevE.74.011505
22	A. G. Xu, G. Gonnella, and A. Lamura, Simulations of complex fluids by mixed lattice Boltzmann-finite difference methods, Physica A 362(1), 42 (2006) https://doi.org/10.1016/j.physa.2005.09.015
23	X. Shan and H. Chen, Lattice Boltzmann model for simulating flows with multiple phases and components, Phys. Rev. E 47(3), 1815 (1993) https://doi.org/10.1103/PhysRevE.47.1815
24	X. Shan and H. Chen, Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation, Phys. Rev. E 49(4), 2941 (1994) https://doi.org/10.1103/PhysRevE.49.2941
25	G. Gonnella, E. Orlandini, and J. M. Yeomans, Spinodal decomposition to a lamellar phase: Effects of hydrodynamic flow, Phys. Rev. Lett. 78(9), 1695 (1997) https://doi.org/10.1103/PhysRevLett.78.1695
26	H. Fang, Z. Wang, Z. Lin, and M. Liu, Lattice Boltzmann method for simulating the viscous flow in large distensible blood vessels, Phys. Rev. E 65(5), 051925 (2002) https://doi.org/10.1103/PhysRevE.65.051925
27	Z. Guo and C. Shu, Lattice Boltzmann Method and Its Applications in Engineering (advances in computational fluid dynamics), World Scientific Publishing Company, 2013 https://doi.org/10.1142/8806
28	A. Xu, G. Zhang, Y. Li, and H. Li, Modeling and simulation of nonequilibrium and multiphase complex systemslattice Boltzmann kinetic theory and application, Prog. Phys. 34(3), 136 (2014)
29	R. Zhang, Y. Xu, B. Wen, N. Sheng, and H. Fang, Enhanced permeation of a hydrophobic fluid through particles with hydrophobic and hydrophilic patterned surfaces, Sci. Rep. 4, 5738 (2014) https://doi.org/10.1038/srep05738
30	X. B. Nie, Y. H. Qian, G. D. Doolen, and S. Y. Chen, Lattice Boltzmann simulation of the two-dimensional Rayleigh–Taylor instability, Phys. Rev. E 58(5), 6861 (1998) https://doi.org/10.1103/PhysRevE.58.6861
31	X. Y. He, S. Y. Chen, and R. Y. Zhang, A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh–Taylor instability, J. Comput. Phys. 152(2), 642 (1999) https://doi.org/10.1006/jcph.1999.6257
32	X. Y. He, R. Y. Zhang, S. Y. Chen, and G. D. Doolen, On the three-dimensional Rayleigh–Taylor instability, Phys. Fluids 11(5), 1143 (1999) https://doi.org/10.1063/1.869984
33	R. Y. Zhang, X. Y. He, and S. Y. Chen, Interface and surface tension in incompressible lattice Boltzmann multiphase model, Comput. Phys. Commun. 129(1-3), 121 (2000) https://doi.org/10.1016/S0010-4655(00)00099-0
34	Q. Li, K. H. Luo, Y. J. Gao, and Y. L. He, Additional interfacial force in lattice Boltzmann models for incompressible multiphase flows, Phys. Rev. E 85(2), 026704 (2012) https://doi.org/10.1103/PhysRevE.85.026704
35	G. J. Liu and Z. L. Guo, Effects of Prandtl number on mixing process in miscible Rayleigh–Taylor instability: A lattice Boltzmann study, Int. J. Numer. Method. H. 23(1), 176 (2013) https://doi.org/10.1108/09615531311289178
36	H. Liang, B. C. Shi, Z. L. Guo, and Z. H. Chai, Phasefield- based multiple-relaxation-time lattice Boltzmann model for incompressible multiphase flows, Phys. Rev. E 89(5), 053320 (2014) https://doi.org/10.1103/PhysRevE.89.053320
37	M. Sbragaglia, R. Benzi, L. Biferale, H. Chen, X. Shan, and S. Succi, Lattice Boltzmann method with self-consistent thermo-hydrodynamic equilibria, J. Fluid Mech. 628, 299 (2009) https://doi.org/10.1017/S002211200900665X
38	A. Scagliarini, L. Biferale, M. Sbragaglia, K. Sugiyama, and F. Toschi, Lattice Boltzmann methods for thermal flows: Continuum limit and applications to compressible Rayleigh–Taylor systems, Phys. Fluids 22(5), 055101 (2010) https://doi.org/10.1063/1.3392774
39	L. Biferale, F. Mantovani, M. Sbragaglia, A. Scagliarini, F. Toschi, and R. Tripiccione, Reactive Rayleigh–Taylor systems: Front propagation and non-stationarity, Europhys. Lett. 94(5), 54004 (2011) https://doi.org/10.1209/0295-5075/94/54004
40	A. Xu, G. Zhang, Y. Gan, F. Chen, and X. Yu, Lattice Boltzmann modeling and simulation of compressible flows, Front. Phys. 7(5), 582 (2012) https://doi.org/10.1007/s11467-012-0269-5
41	B. Yan, A. Xu, G. Zhang, Y. Ying, and H. Li, Lattice Boltzmann model for combustion and detonation, Front. Phys. 8(1), 94 (2013) https://doi.org/10.1007/s11467-013-0286-z
42	C. Lin, A. Xu, G. Zhang, and Y. Li, Polar coordinate lattice Boltzmann kinetic modeling of detonation phenomena, Commum. Theor. Phys. 62(5), 737 (2014) https://doi.org/10.1088/0253-6102/62/5/18
43	A. Xu, C. Lin, G. Zhang, and Y. Li, Multiple-relaxationtime lattice Boltzmann kinetic model for combustion, Phys. Rev. E 91(4), 043306 (2015) https://doi.org/10.1103/PhysRevE.91.043306
44	A. Xu, G. Zhang, and Y. Ying, Progess of discrete Boltzmann modeling and simulation of combustion system, Acta Phys. Sin. 64(18), 184701 (2015)
45	C. Lin, A. Xu, G. Zhang, and Y. Li, Doubledistribution- function discrete Boltzmann model for combustion, Combust. Flame 164, 137 (2016) https://doi.org/10.1016/j.combustflame.2015.11.010
46	Y. Zhang, A. Xu, G. Zhang, C. Zhu, and C. Lin, Kinetic modeling of detonation and effects of negative temperature coefficient, Combust. Flame (2016) (in press) https://doi.org/10.1016/j.combustflame.2016.04.003
47	Y. Gan, A. Xu, G. Zhang, and S. Succi, Discrete Boltzmann modeling of multiphase flows: Hydrodynamic and thermodynamic non-equilibrium effects, Soft Matter 11 11(26), 5336 (2015)
48	C. Lin, A. Xu, G. Zhang, Y. Li, and S. Succi, Polarcoordinate lattice Boltzmann modeling of compressible flows, Phys. Rev. E 89(1), 013307 (2014) https://doi.org/10.1103/PhysRevE.89.013307
49	F. Chen, A. Xu, G. Zhang, Y. Wang, Two-dimensional MRT LB model for compressible and incompressible flows, Front. Phys. 9(2), 246 (2014) https://doi.org/10.1007/s11467-013-0368-y
50	H. Lai, A. Xu, G. Zhang, Y. Gan, Y. Ying, and S. Succi, Thermo-hydrodynamic non-equilibrium effects on compressible Rayleigh–Taylor instability, arXiv: 1507.01107
51	D. Layzer, On the instability of superposed fluids in a gravitational field, Astrophys. J. 122, 1 (1955) https://doi.org/10.1086/146048
52	S. F. Li, W. H. Ye, Y. Zhang, S. Shu, and A. G. Xiao, High order FD-WENO schemes for Rayleigh–Taylor instability problems, Chin. J. Comput. Phys. 25(4), 379 (2008)
53	D. Youngs, Numerical simulation of turbulent mixing by Rayleigh–Taylor instability, Physica D 12(1–3), 32 (1984)
54	Y. D. Zhang, Modeling and research of detonation based on discrete Boltzmann method, A Dissertation Submitted for the Degree of Master, Beihang University, 2015

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