Please wait a minute...
Frontiers of Physics

ISSN 2095-0462

ISSN 2095-0470(Online)

CN 11-5994/O4

Postal Subscription Code 80-965

2018 Impact Factor: 2.483

Front. Phys.    2021, Vol. 16 Issue (5) : 52500    https://doi.org/10.1007/s11467-021-1096-3
RESEARCH ARTICLE
Specific heat ratio effects of compressible Rayleigh–Taylor instability studied by discrete Boltzmann method
Lu Chen (陈璐)1, Huilin Lai (赖惠林)1(), Chuandong Lin (林传栋)2(), Demei Li (李德梅)1
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.
 Download: PDF(3287 KB)  
 Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract

Rayleigh–Taylor (RT) instability widely exists in nature and engineering fields. How to better understand the physical mechanism of RT instability is of great theoretical significance and practical value. At present, abundant results of RT instability have been obtained by traditional macroscopic methods. However, research on the thermodynamic non-equilibrium (TNE) effects in the process of system evolution is relatively scarce. In this paper, the discrete Boltzmann method based on non-equilibrium statistical physics is utilized to study the effects of the specific heat ratio on compressible RT instability. The evolution process of the compressible RT system with different specific heat ratios can be analyzed by the temperature gradient and the proportion of the non-equilibrium region. Firstly, as a result of the competition between the macroscopic magnitude gradient and the non-equilibrium region, the average TNE intensity first increases and then reduces, and it increases with the specific heat ratio decreasing; the specific heat ratio has the same effect on the global strength of the viscous stress tensor. Secondly, the moment when the total temperature gradient in y direction deviates from the fixed value can be regarded as a physical criterion for judging the formation of the vortex structure. Thirdly, under the competition between the temperature gradients and the contact area of the two fluids, the average intensity of the non-equilibrium quantity related to the heat flux shows diversity, and the influence of the specific heat ratio is also quite remarkable.

Keywords discrete Boltzmann method      Rayleigh–Taylor instability      non-equilibrium effects      specific heat ratio effects      compressible fluid     
Corresponding Author(s): Huilin Lai (赖惠林),Chuandong Lin (林传栋)   
Issue Date: 23 August 2021
 Cite this article:   
Lu Chen (陈璐),Huilin Lai (赖惠林),Chuandong Lin (林传栋), et al. Specific heat ratio effects of compressible Rayleigh–Taylor instability studied by discrete Boltzmann method[J]. Front. Phys. , 2021, 16(5): 52500.
 URL:  
https://academic.hep.com.cn/fop/EN/10.1007/s11467-021-1096-3
https://academic.hep.com.cn/fop/EN/Y2021/V16/I5/52500
1 G. Dimonte, D. L. Youngs, A. Dimits, S. Weber, M. Marinak, S. Wunsch, C. Garasi, A. Robinson, M. J. Andrews, P. Ramaprabhu, A. C. Calder, B. Fryxell, J. Biello, L. Dursi, P. MacNeice, K. Olson, P. Ricker, R. Rosner, F. Timmes, H. Tufo, Y. N. Young, and M. Zingale, A comparative study of the turbulent Rayleigh–Taylor instability using high-resolution three-dimensional numerical simulations: The Alpha–Group Collaboration, Phys. Fluids 16(5), 1668 (2004)
https://doi.org/10.1063/1.1688328
2 Y. Ping, V. A. Smalyuk, P. Amendt, R. Tommasini, J. E. Field, S. Khan, D. Bennett, E. Dewald, F. Graziani, S. Johnson, O. L. Landen, A. G. MacPhee, A. Nikroo, J. Pino, S. Prisbrey, J. Ralph, R. Seugling, D. Strozzi, R. E. Tipton, Y. M. Wang, E. Loomis, E. Merritt, and D. Montgomery, Enhanced energy coupling for indirectly driven inertial confinement fusion, Nat. Phys. 15(2), 138 (2019)
https://doi.org/10.1038/s41567-018-0331-5
3 J. D. Lindl, P. Amendt, R. L. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Haan, R. L. Kauffman, O. L. Landen, and L. J. Suter, The physics basis for ignition using indirect-drive targets on the national ignition facility, Sci. China Phys. Mech. Astron. 11, 339 (2004)
https://doi.org/10.1063/1.1578638
4 S. Jacquemot, Inertial confinement fusion for energy: overview of the ongoing experimental, theoretical and numerical studies, Nucl. Fusion 57, 102024 (2017)
https://doi.org/10.1088/1741-4326/aa6d2d
5 X. Ribeyre, V. T. Tikhonchuk, and S. Bouquet, Compressible Rayleigh–Taylor instabilities in supernova remnants, Phys. Fluids 16(12), 4661 (2004)
https://doi.org/10.1063/1.1810182
6 F. Fraschetti, R. Teyssier, J. Ballet, and A. Decourchelle, Simulation of the growth of the 3D Rayleigh–Taylor instability in supernova remnants using an expanding reference frame, Astron. Astrophys. 515, A104 (2010)
https://doi.org/10.1051/0004-6361/200912692
7 W. Hillebrandt, M. Kromer, F. K. Röpke, and A. J. Ruiter, Towards an understanding of type Ia supernovae from a synthesis of theory and observations, Front. Phys. 8(2), 116 (2013)
https://doi.org/10.1007/s11467-013-0303-2
8 E. M. Agee, Some inferences of eddy viscosity associated with instabilities in the atmosphere, J. Atmos. Sci. 32(3), 642 (1974)
https://doi.org/10.1175/1520-0469(1975)032<0642:SIOEVA>2.0.CO;2
9 Y. F. Jiang, S. W. Davis, and J. M. Stone, Nonlinear evolution of Rayleigh–Taylor instability in a radiationsupported atmosphere, Astrophys. J. 763(2), 102 (2013)
https://doi.org/10.1088/0004-637X/763/2/102
10 G. A. Houseman and P. Molnar, Gravitational (Rayleigh–Taylor) instability of a layer with non-linear viscosity and convective thinning of continental lithosphere, Geophys. J. Int. 128(1), 125 (1997)
https://doi.org/10.1111/j.1365-246X.1997.tb04075.x
11 B. J. P. Kaus and T. W. Becker, Effects of elasticity on the Rayleigh–Taylor instability: Implications for large-scale geodynamics, Geophys. J. Int. 168(2), 843 (2007)
https://doi.org/10.1111/j.1365-246X.2006.03201.x
12 D. Ghosh, G. Maiti, and N. Mandal, Slab-parallel advection versus Rayleigh–Taylor instabilities in melt-rich layers in subduction zones: A criticality analysis, Phys. Earth Planet. Inter. 307, 106560 (2020)
https://doi.org/10.1016/j.pepi.2020.106560
13 L. Rayleigh, Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density, Proc. Lond. Math. Soc. 14(1), 170 (1882)
https://doi.org/10.1112/plms/s1-14.1.170
14 G. I. Taylor, The instability of liquid surfaces when accelerated in a direction perpendicular to their plane, Proc. R. Soc. Lond. A 201(1065), 192 (1950)
https://doi.org/10.1098/rspa.1950.0052
15 J. L. Barber, K. Kadau, T. C. Germann, P. S. Lomdahl, B. L. Holian, and B. J. Alder, Atomistic simulation of the Rayleigh–Taylor instability, J. Phys. Conf. Ser. 46, 58 (2006)
https://doi.org/10.1088/1742-6596/46/1/008
16 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
17 H. Liang, X. Hu, X. Huang, and J. Xu, Direct numerical simulations of multi-mode immiscible Rayleigh–Taylor instability with high Reynolds numbers, Phys. Fluids 31(11), 112104 (2019)
https://doi.org/10.1063/1.5127888
18 D. L. Youngs, Application of monotone integrated large eddy simulation to Rayleigh–Taylor mixing, Philos. Trans. A Math., Phys. Eng. 367, 2971 (2009)
https://doi.org/10.1098/rsta.2008.0303
19 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
20 O. V. V. S. J. Reckinger, D. Livescu, and O. V. Vasilyev, Comprehensive numerical methodology for direct numerical simulations of compressible Rayleigh–Taylor instability, J. Comput. Phys. 313, 181 (2015)
https://doi.org/10.1016/j.jcp.2015.11.002
21 J. Yang, J. K. H. G. Lee, and J. Kim, Side wall boundary effect on the Rayleigh–Taylor instability, Eur. J. Mech. BFluids 85, 361 (2021)
https://doi.org/10.1016/j.euromechflu.2020.10.001
22 L. F. Wang, W. H. Ye, and Y. J. Li, Interface width effect on the classical Rayleigh–Taylor instability in the weakly nonlinear regime, Phys. Plasmas 17(5), 052305 (2010)
https://doi.org/10.1063/1.3396369
23 T. Wei and D. Livescu, Late-time quadratic growth in single-mode Rayleigh–Taylor instability, Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 86(4), 046405 (2012)
https://doi.org/10.1103/PhysRevE.86.046405
24 X. Bian, H. Aluie, D. Zhao, H. Zhang, and D. Livescu, Revisiting the late-time growth of single-mode Rayleigh–Taylor instability and the role of vorticity, Physica D 403, 132250 (2020)
https://doi.org/10.1016/j.physd.2019.132250
25 A. G. Xu, G. Zhang, Y. B. 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
26 A. G. Xu, G. Zhang, and Y. J. Ying, Discrete Boltzmann modeling of compressible flows, in: Kinetic Theory, edited by G. Kyzas and A. Mitropoulos, InTech, Rijeka, Croatia, Ch. 02, 2018
27 A. G. Xu, J. Chen, J. H. Song, D. W. Chen, and Z. H. Chen, Progress of discrete Boltzmann study on multiphase complex flows, Acta Aerodyn. Sin. 39, 138 (2021) (in Chinese)
28 A. G. Xu, J. H. Song, F. Chen, K. Xie, and Y. J. Ying, Modeling and analysis methods for complex fields based on phase space, Chin. J. Comput. Phys. 38, available at (published online 2021) (in Chinese)
29 Y. B. Gan, A. G. Xu, G. Zhang, and S. Succi, Discrete Boltzmann modeling of multiphase flows: Hydrodynamic and thermodynamic nonequilibrium effects, Soft Matter 11(26), 5336 (2015)
https://doi.org/10.1039/C5SM01125F
30 A. G. Xu, G. Zhang, and Y. J. Ying, Progress of discrete Boltzmann modeling and simulation of combustion system, Acta Physica Sinica 64(18), 184701 (2015)
https://doi.org/10.7498/aps.64.184701
31 H. L. Lai, A. G. Xu, G. Zhang, Y. B. Gan, Y. Ying, and S. Succi, Nonequilibrium thermo-hydrodynamic effects on the Rayleigh–Taylor instability in compressible flows, Phys. Rev. E 94(2), 023106 (2016)
https://doi.org/10.1103/PhysRevE.94.023106
32 C. D. Lin, A. G. 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
33 F. Chen, A. G. Xu, and G. Zhang, Viscosity, heat conductivity, and Prandtl number effects in the Rayleigh–Taylor instability, Front. Phys. 11(6), 114703 (2016)
https://doi.org/10.1007/s11467-016-0603-4
34 C. D. Lin, A. G. Xu, G. C. Zhang, K. H. Luo, and Y. Li, Discrete Boltzmann modeling of Rayleigh–Taylor instability in two-component compressible flows, Phys. Rev. E 96(5), 053305 (2017)
https://doi.org/10.1103/PhysRevE.96.053305
35 A. G. Xu, G. C. Zhang, Y. D. Zhang, P. Wang, and Y. J. Ying, Discrete Boltzmann model for implosion and explosion related compressible flow with spherical symmetry, Front. Phys. 13(5), 135102 (2018)
https://doi.org/10.1007/s11467-018-0777-z
36 F. Chen, A. G. Xu, and G. Zhang, Collaboration and competition between Richtmyer–Meshkov instability and Rayleigh–Taylor instability, Phys. Fluids 30(10), 102105 (2018)
https://doi.org/10.1063/1.5049869
37 Y. D. Zhang, A. G. Xu, G. C. Zhang, and Z. H. Chen, Discrete Boltzmann method with Maxwell-type boundary condition for slip flow, Commum. Theor. Phys. 69(1), 77 (2018)
https://doi.org/10.1088/0253-6102/69/1/77
38 Y. B. Gan, A. G. Xu, G. Zhang, Y. Zhang, and S. Succi, Discrete Boltzmann trans-scale modeling of high-speed compressible flows, Phys. Rev. E 97(5), 053312 (2018)
https://doi.org/10.1103/PhysRevE.97.053312
39 D. M. Li, H. L. Lai, A. G. Xu, G. C. Zhang, C. D. Lin, and Y. B. Gan, Discrete Boltzmann simulation of Rayleigh–Taylor instability in compressible flows, Acta Physica Sinica 67(8), 080501 (2018)
https://doi.org/10.7498/aps.67.20171952
40 Y. B. Gan, A. G. Xu, G. C. Zhang, C. D. Lin, H. L. Lai, and Z. P. Liu, Nonequilibrium and morphological characterizations of Kelvin–Helmholtz instability in compressible flows, Front. Phys. 14(4), 43602 (2019)
https://doi.org/10.1007/s11467-019-0885-4
41 Y. D. Zhang, A. G. Xu, G. Zhang, Z. Chen, and Y. Ying, A one-dimensional discrete Boltzmann model for detonation and an abnormal detonation phenomenon, Commum. Theor. Phys. 71(1), 117 (2019)
https://doi.org/10.1088/0253-6102/71/1/117
42 H. Y. Ye, H. L. Lai, D. M. Li, Y. B. Gan, C. D. Lin, L. Chen, and A. G. Xu, Knudsen number effects on twodimensional Rayleigh–Taylor instability in compressible fluid: Based on a discrete Boltzmann method, Entropy (Basel) 22(5), 500 (2020)
https://doi.org/10.3390/e22050500
43 F. Chen, A. G. Xu, Y. D. Zhang, and Q. Zeng, Morphological and nonequilibrium analysis of coupled Rayleigh-Taylor-Kelvin-Helmholtz instability, Phys. Fluids 32(10), 104111 (2020)
https://doi.org/10.1063/5.0023364
44 C. D. Lin, K. H. Luo, A. G. Xu, Y. B. Gan, and H. L. Lai, Multiple relaxation-time discrete Boltzmann modeling of multicomponent mixture with nonequilibrium effects, Phys. Rev. E 103(1), 013305 (2021)
https://doi.org/10.1103/PhysRevE.103.013305
45 I. B. Bernstein and D. L. Book, Effect of compressibility on the Rayleigh–Taylor instability, Phys. Fluids 26(2), 453 (1982)
https://doi.org/10.1063/1.864158
46 G. Fraley, Rayleigh–Taylor stability for a normal shock wave-density discontinuity interaction, Phys. Fluids 29(2), 376 (1986)
https://doi.org/10.1063/1.865722
47 D. Livescu, Compressibility effects on the Rayleigh–Taylor instability growth between immiscible fluids, Phys. Fluids 16(1), 118 (2004)
https://doi.org/10.1063/1.1630800
48 M. A. Lafay, B. L. Creurer, and S. Gauthier, Compressibility effects on the Rayleigh–Taylor instability between miscible fluids, Europhys. Lett. 79(6), 64002 (2007)
https://doi.org/10.1209/0295-5075/79/64002
49 Y. He, X. W. Hu, and Z. H. Jiang, Compressibility effects on the Rayleigh–Taylor instability growth rates, Chin. Phys. Lett. 25(3), 1015 (2008)
https://doi.org/10.1088/0256-307X/25/3/057
50 C. Xue and W. Ye, Destabilizing effect of compressibility on Rayleigh–Taylor instability for fluids with fixed density profile, Phys. Plasmas 17(4), 042705 (2010)
https://doi.org/10.1063/1.3360295
51 C. Y. Wang, Rayleigh–Taylor instabilities in type Ia supernova remnants undergoing cosmic ray particle acceleration-low adiabatic index solutions, Mon. Not. R. Astron. Soc. 415(1), 83 (2011)
https://doi.org/10.1111/j.1365-2966.2011.18651.x
52 Z. C. Hu and X. R. Zhang, Numerical simulations of the piston effect for near-critical fluids in spherical cells under small thermal disturbance, Int. J. Therm. Sci. 107, 131 (2016)
https://doi.org/10.1016/j.ijthermalsci.2016.03.019
53 Y. Zhao, M. Xia, and Y. Cao, A study of bubble growth in the compressible Rayleigh–Taylor and Richtmyer-Meshkov instabilities, AIP Adv. 10(1), 015056 (2020)
https://doi.org/10.1063/1.5139453
54 Y. D. Zhang, A. G. Xu, G. C. Zhang, Z. H. Chen, and P. Wang, Discrete ellipsoidal statistical BGK model and Burnett equations, Front. Phys. 13(3), 135101 (2018)
https://doi.org/10.1007/s11467-018-0749-3
55 A. Tamura, K. Okuyama, S. Takahashi, and M. Ohtsuka, Three-dimensional discrete-velocity BGK model for the incompressible Navier–Stokes equations, Comput. Fluids 40(1), 149 (2011)
https://doi.org/10.1016/j.compfluid.2010.08.019
56 Y. B. Gan, A. G. Xu, G. Zhang, and Y. Yang, Lattice BGK kinetic model for high-speed compressible flows: Hydrodynamic and nonequilibrium behaviors, Europhys. Lett. 103(2), 24003 (2013)
https://doi.org/10.1209/0295-5075/103/24003
57 B. Yan, A. G. 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
[1] Yang-Ting Fu, Wei-Lun Gu, Zong-Yu Hou, Sher Afgan Muhammed, Tian-Qi Li, Yun Wang, Zhe Wang. Mechanism of signal uncertainty generation for laser-induced breakdown spectroscopy[J]. Front. Phys. , 2021, 16(2): 22502-.
[2] Yu-Dong Zhang, Ai-Guo Xu, Jing-Jiang Qiu, Hong-Tao Wei, Zung-Hang Wei. Kinetic modeling of multiphase flow based on simplified Enskog equation[J]. Front. Phys. , 2020, 15(6): 62503-.
[3] Yan-Biao Gan, Ai-Guo Xu, Guang-Cai Zhang, Chuan-Dong Lin, Hui-Lin Lai, Zhi-Peng Liu. Nonequilibrium and morphological characterizations of Kelvin–Helmholtz instability in compressible flows[J]. Front. Phys. , 2019, 14(4): 43602-.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed