Discrete Boltzmann simulation of Rayleigh-Taylor instability in compressible flows

Li De-Mei; Lai Hui-Lin; Xu Ai-Guo; Zhang Guang-Cai; Lin Chuan-Dong; Gan Yan-Biao

doi:10.7498/aps.67.20171952

Abstract

We use a discrete Boltzmann model (DBM) to simulate the multi-mode Rayleigh-Taylor instability (RTI) in a compressible flow.This DBM is physically equivalent to a Navier-Stokes model supplemented by a coarse-grained model for thermodynamic nonequilibrium behavior.The validity of the model is verified by comparing simulation results of Riemann problems,Sod shock tube,collision between two strong shock waves,and thermal Couette flow with analytical solutions.Grid independence is verified.The DBM is utilized to simulate the nonlinear evolution of the RTI from multi-mode initial perturbation with discontinuous interface.We obtain the basic process of the initial disturbance interface which develops into mushroom graphs.The evolution of the system is relatively slow at the beginning,and the interface moves down on a whole.This is mainly due to the fact that the heat transfer plays a leading role,and the exchange of internal energy occurs near the interface of fluid.The overlying fluid absorbs heat,which causes the volume to expand,and the underlying fluid releases heat,which causes the volume to shrink,consequently the fluid interface moves downward.Meanwhile,due to the effects of viscosity and thermal conduction,the perturbed interface is smoothed.The evolution rate is slow at the initial stage.As the modes couple with each other,the evolution begins to grow faster.As the interface evolves gradually into the gravity dominated stage,the overlying and underlying fluids begin to exchange the gravitational potentials via nonlinear evolution.Lately,the two parts of fluid permeate each other near the interface.The system goes through the nonlinear disturbance and irregular nonlinear stages,then develops into the typical “mushroom” stage.Afterwards,the system evolves into the turbulent mixing stage.Owing to the coupling and development of perturbation modes,and the transformation among the gravitational potential energy,compression energy and kinetic energy,the system first approaches to a transient local thermodynamic equilibrium,then deviates from it and the perturbation grows linearly.After that,at the beginning,the fluid system tends to approach to an equilibrium state,which is caused by the adjustment of the system,and the disturbance of the multi-mode initial interface moves toward a process of the eigenmode stage.Then,the system deviates from the equilibrium state linearly,which is due to the flattening of the system interface and the conversing of the compression energy into internal energy.Moreover, the system tends to approach to the equilibrium state again,and this is because the modes couple and the disturbance interface is further “screened”.The system is in a relatively stable state.Furthermore,the system is farther away from the equilibrium state because of the gravitational potential energy of the fluid system transformation.The compression energy of the system is released further,and the kinetic energy is further increased.After that,the nonequilibrium intensity decreases,and then the system is slowly away from thermodynamic equilibrium.The interface becomes more and more complicated,and the nonequilibrium modes also become more and more abundant.

Keywords:

Authors and contacts

1.
Key Laboratory of Analytical Mathematics and Application in Fujian Province, College of Mathematics and Informatics, Fujian Normal University, Fuzhou 350007, China;
2.
National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
3.
Center for Applied Physics and Technology, Key Center for High Energy Density Physics Simulations of Ministry of Education, College of Engineering, Peking University, Beijing 100871, China;
4.
Center for Combustion Energy, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China;
5.
North China Institute of Aerospace Engineering, Langfang 065000, China

Corresponding author: Lai Hui-Lin, hllai@fjnu.edu.cn;Xu_aiguo@iapcm.ac.cn ; Xu Ai-Guo, hllai@fjnu.edu.cn;Xu_aiguo@iapcm.ac.cn ;

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11301082, 11475028, 11772064), the Natural Science Foundation of Fujian Province, China (Grant No. 2014J05003), the Office of Fujian Province Education Fund, China (Grant Nos. JA13069, JB13020), the Natural Science Foundation of Hebei Province, China (Grant No. A2017409014), the Natural Science Foundation of Hebei Educational Commission, China (Grant No. ZD2017001), and the Training Funds for Talent Engineering in Hebei Province, China (Grant No. A201500111).

References

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[26]	Lin C D, Xu A G, Zhang G C, Li Y J, Succi S 2014 Phys. Rev. E 89 013307
[27]	Lai H L, Xu A G, Zhang G C, Gan Y B, Ying Y J, Succi S 2016 Phys. Rev. E 94 023106
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[29]	Gan Y B, Xu A G, Zhang G C, Yang Y 2013 Europhys. Lett. 103 24003
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[33]	Guo Z L, Zheng C G, Shi B C 2002 Phys. Fluids 14 2007
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[35]	Xu A G, Zhang G C 2016 Special Academic Report of Electromechanical College of Nanjing Forestry University Nanjing, China, Oct. 25, 2016 (in Chinese)[许爱国, 张广财 2016 南京林业大学机电学院专题学术报告, 中国南京, 2016年10月25日]
[36]	Xu A G, Zhang G C 2016 Academic Report on Physics Department of Renmin University of China Beijing, China, Nov. 23, 2016 (in Chinese)[许爱国, 张广财 2016 中国人民大学物理系专题学术报告, 中国北京, 2016 年11 月23日]
[37]	Xu A G, Zhang G C 2016 The 4th Academic Seminar of LBM and Its Applications Beijing, China, Nov. 26, 2016 (in Chinese)[许爱国, 张广财 2016 第四届LBM及其应用学术研讨会, 中国北京, 2016年11月26日]

Cited By

[1]	Rayleigh L 1882 Proc. London Math. Soc. s1-14 170
[2]	Lamb H 1932 Hydrodynamics (6th Ed.) (London:Cambridge University press) p501
[3]	Taylor G 1950 Proc. R. Soc. London A 201 192
[4]	Betti R, Goncharov V, McCrory R, Verdon C 1998 Phys. Plasmas (1994-present) 5 1446
[5]	Wang L F, Ye W H, Wu J F, Liu J, Zhang W Y, He X T 2016 Phys. Plasmas 23 052713
[6]	Wang L F, Ye W H, He X T, Wu J F, Fan Z F, Xue C, Guo H Y, Miao W Y, Yuan Y T, Dong J Q, Jia G, Zhang J, Li Y J, Liu J, Wang L M, Ding Y K, Zhang W Y 2017 Sci. China:Phys. Mech. Astron. 60 055201
[7]	Cabot W, Cook A 2006 Nat. Phys. 2 562
[8]	Berthoud G 2000 Annu. Rev. Fluid Mech. 32 573
[9]	Barber J L, Kadau K, Germann T C, Alder B J 2008 Eur. Phys. J. B 64 271
[10]	Celani A, Mazzino A, Vozella L 2006 Phys. Rev. L. 96 134504
[11]	Moin P 1991 Comput. Meth. Appl. Mech. Eng. 87 329
[12]	Succi S 2001 The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (New York:Oxford University Press) pp179-255
[13]	He X Y, Chen S Y, Zhang R Y 1999 J. Comput. Phys. 152 642
[14]	Li Q, Luo K H, Gao Y J, He Y L 2012 Phys. Rev. E 85 026704
[15]	Liu G J, Guo Z L 2013 Int. J. Numer. Method H. 23 176
[16]	Scagliarini A, Biferale L, Sbragaglia M, Sugiyama K, Toschi F 2010 Phys. Fluids 22 055101
[17]	Xu A G, Zhang G C, Gan Y B, Chen F, Yu X J 2012 Front. Phys. 7 582
[18]	Xu A G, Zhang G C, Gan Y B 2016 Mech. Eng. 38 361 (in Chinese)[许爱国, 张广财, 甘延标 2016 力学与实践 38 361]
[19]	Gan Y B, Xu A G, Zhang G C, Yu X J, Li Y J 2008 Physica A 387 1721
[20]	Gan Y B, Xu A G, Zhang G C, Li Y J 2011 Phys. Rev. E 83 056704
[21]	Gan Y B, Xu A G, Zhang G C, Li Y J, Li H 2011 Phys. Rev. E 84 046715
[22]	Yan B, Xu A G, Zhang G C, Ying Y J, Li H 2013 Front. Phys. 8 94
[23]	Xu A G, Zhang G C, Li Y J, Li H 2014 Prog. Phys. 34 136 (in Chinese)[许爱国, 张广财, 李英骏, 李华 2014 物理学进展 34 136]
[24]	Xu A G, Zhang G C, Ying Y J 2015 Acta Phys. Sin. 64 184701 (in Chinese)[许爱国, 张广财, 应阳君 2015 物理学报 64 184701]
[25]	Xu A G, Zhang G C, Ying Y J, Wang C 2016 Sci. China:Phys. Mech. Astron. 59 650501
[26]	Lin C D, Xu A G, Zhang G C, Li Y J, Succi S 2014 Phys. Rev. E 89 013307
[27]	Lai H L, Xu A G, Zhang G C, Gan Y B, Ying Y J, Succi S 2016 Phys. Rev. E 94 023106
[28]	Liu H, Kang W, Zhang Q, Zhang Y, Duan H L, He X T 2016 Front. Phys. 11 115206
[29]	Gan Y B, Xu A G, Zhang G C, Yang Y 2013 Europhys. Lett. 103 24003
[30]	Gan Y B, Xu A G, Zhang G C, Succi S 2015 Soft Matter 11 5336
[31]	Watari M, Tsutahara M 2004 Phys. Rev. E 70 016703
[32]	Zhang H X 1988 Acta Aerodyn. Sin. 6 43 (in Chinese)[张涵信 1988 空气动力学学报 6 43]
[33]	Guo Z L, Zheng C G, Shi B C 2002 Phys. Fluids 14 2007
[34]	Xu A G, Zhang G C 2016 The 9th National Conference on Fluid Mechanics Nanjing, China Oct. 20-23, 2016 (in Chinese)[许爱国, 张广财 2016 第九届全国流体力学学术会议, 南京, 2016年10月20–23 日]
[35]	Xu A G, Zhang G C 2016 Special Academic Report of Electromechanical College of Nanjing Forestry University Nanjing, China, Oct. 25, 2016 (in Chinese)[许爱国, 张广财 2016 南京林业大学机电学院专题学术报告, 中国南京, 2016年10月25日]
[36]	Xu A G, Zhang G C 2016 Academic Report on Physics Department of Renmin University of China Beijing, China, Nov. 23, 2016 (in Chinese)[许爱国, 张广财 2016 中国人民大学物理系专题学术报告, 中国北京, 2016 年11 月23日]
[37]	Xu A G, Zhang G C 2016 The 4th Academic Seminar of LBM and Its Applications Beijing, China, Nov. 26, 2016 (in Chinese)[许爱国, 张广财 2016 第四届LBM及其应用学术研讨会, 中国北京, 2016年11月26日]

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Vol. 67, Issue 8 - 2018-04-20

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