多模态瑞利-泰勒不稳定性的离散玻尔兹曼数值研究

陈璐; 赖惠林; 林传栋; 李德梅

doi:10.7638/kqdlxxb-2021.0345

欢迎来到能源电力期刊网！

English Version 期刊登录

您当前的位置：

首页 >

文章列表页 >

多模态瑞利-泰勒不稳定性的离散玻尔兹曼数值研究

专栏——格子玻尔兹曼方法及应用 | 更新时间：2026-05-28

- 多模态瑞利-泰勒不稳定性的离散玻尔兹曼数值研究
- Numerical study of multimode Rayleigh-Taylor instability by using the discrete Boltzmann method
- 空气动力学学报 2022年40卷第3期页码：140-150
- 作者机构：
  
  1. 福建师范大学数学与统计学院,福州,350117
  2. 福建师范大学福建省分析数学及应用重点实验室,福州,350117
  3. 福建师范大学福建省应用数学研究中心,福州,350117
  4. 中山大学中法核工程与技术学院,珠海,519082
- 作者简介：
  
  陈璐（1998-），女，河南许昌人，硕士研究生，研究方向：可压缩流体RT不稳定性的动理学数值研究. E-mail：chenlu9801@163.com
  赖惠林*（1982-），男，福建平和人，副教授，研究方向：多尺度复杂物理系统建模与模拟，流体力学中的数值计算，微分方程数值计算，湍流与流动稳定性，等. E-mail：hllai@fjnu.edu.cn
  林传栋*（1985-），男，山东临沂人，副教授，研究方向：高超声速空气动力学，流体不稳定性，多相流，爆轰，离散玻尔兹曼方法，格子玻尔兹曼方法，等. E-mail：linchd3@mail.sysu.edu.cn
- 基金信息：
  
  国家自然科学基金（51806116，11875001）;福建省自然科学基金（2021J01652，2021J01655）
- DOI：10.7638/kqdlxxb-2021.0345
  中图分类号： O359
- 纸质出版：2022
- 稿件说明：
移动端阅览
陈璐, 赖惠林, 林传栋, 等. 多模态瑞利-泰勒不稳定性的离散玻尔兹曼数值研究[J]. 空气动力学学报, 2022, 40(3): 140−150.

CHEN Lu, LAI Huilin, LIN Chuandong, et al. Numerical study of multimode Rayleigh-Taylor instability by using the discrete Boltzmann method[J]. 2022, 40(3): 140-150.
陈璐, 赖惠林, 林传栋, 等. 多模态瑞利-泰勒不稳定性的离散玻尔兹曼数值研究[J]. 空气动力学学报, 2022, 40(3): 140−150. DOI： 10.7638/kqdlxxb-2021.0345

CHEN Lu, LAI Huilin, LIN Chuandong, et al. Numerical study of multimode Rayleigh-Taylor instability by using the discrete Boltzmann method[J]. 2022, 40(3): 140-150. DOI： 10.7638/kqdlxxb-2021.0345.

摘要

瑞利-泰勒（Rayleigh-Taylor，RT）不稳定性广泛存在于自然界和工程领域，认清RT不稳定性演化过程中的物理机理具有重要的理论意义和实用价值。本文利用离散玻尔兹曼方法模拟了可压缩流体的RT不稳定性现象，并利用该方法对界面连续的随机多模初始扰动的可压缩RT不稳定性进行了数值研究。研究结果表明，在温度梯度的影响下，与热通量相关的热力学非平衡强度呈现先增大后减小的趋势；在热扩散作用下，界面上的热力学非平衡强度先减小后增大，继而影响热力学非平衡区域的占比，使之呈现相同的变化趋势。最后，分析了全局平均热力学非平衡强度随时间的演化规律，发现在宏观物理量梯度和热力学非平衡面积的共同作用下，全局平均热力学非平衡强度先增后减，最后趋于稳定。不仅如此，热力学非平衡区域面积的增大（减小）会增强（减弱）热力学非平衡的强度；同时，物质界面物理量梯度的增大（减小）对全局平均热力学非平衡强度也有相同的影响，二者相互作用、相互竞争。

Abstract

Rayleigh-Taylor (RT) instability phenomenon exists widely in nature and engineering fields. It is of great theoretical significance and practical value to clearly understand the physical mechanism of the RT instability. In this paper

the compressible RT instability is simulated by the discrete Boltzmann method (DBM)

and the compressible RT instability with random multimode initial perturbations at continuous interfaces is numerically investigated by means of the DBM. The results show that with the influence of temperature gradient

the thermodynamic non-equilibrium strength related to heat flux firstly increases and then decreases. Under the action of thermal diffusion

the thermodynamic non-equilibrium strength at the interface firstly decreases and then increases

which affects the time evolution of proportion of the thermodynamic non-equilibrium region. In this respect

effects of temperature gradient and thermal diffusion on the time evolution trend of non-equilibrium strength at the interface are the same. Finally

we analyze the time evolution of the global average thermodynamic non-equilibrium strength

and find that under the joint action of macroscopic physical gradients and thermodynamic non-equilibrium area

the global average thermodynamic non-equilibrium strength firstly increases

then decreases

and finally tends to be stable. On the one hand

the increase (decrease) of the area of thermodynamic non-equilibrium region will increase (decrease) the strength of thermodynamic non-equilibrium. On the other hand

the increase (decrease) of physical gradients at the material interface also has the same effect on the global average thermodynamic non-equilibrium strength. The two physical mechanisms interact and compete with each other.

关键词

Keywords

references

RAYLEIGH L. Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density[J]. Proceedings of the London Mathematical Society, 1882, s1-14(1): 170-177. DOI:10.1112/plms/s1-14.1.170

TAYLOR G I. . The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I[J]. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences, 1950, 201(1065): 192-196. DOI:10.1098/rspa.1950.0052

WOO K M, BETTI R, SHVARTS D, et al. Effects of residual kinetic energy on yield degradation and ion temperature asymmetries in inertial confinement fusion implosions[J]. Physics of Plasmas, 2018, 25(5): 052704. DOI:10.1063/1.5026706

MAEDER A, MEYNET G, LAGARDE N, et al. The thermohaline, Richardson, Rayleigh-Taylor, Solberg–Høiland, and GSF criteria in rotating stars[J]. Astronomy Astrophysics, 2013, 553: A1. DOI:10.1051/0004-6361/201220936

SHIOKAWA K, NAKAJIMA A, IEDA A, et al. Rayleigh-Taylor type instability in auroral patches[J]. Journal of Geophysical Research: Space Physics, 2010, 115(A2): A02211. DOI:10.1029/2009ja014273

MARTIN J, XILOURIS K, SOKER N. The early interaction of the planetary nebula NGC 40 with the interstellar medium[J]. Astronomy Astrophysics, 2002, 391(2): 689-692. DOI:10.1051/0004-6361: 20020848

ABARZHI S I, BHOWMICK A K, NAVEH A, et al. Supernova, nuclear synthesis, fluid instabilities, and interfacial mixing[J]. Proceedings of the National Academy of Sciences, 2019, 116(37): 18184-18192. DOI:10.1073/pnas.1714502115

AKULA B, SUCHANDRA P, MIKHAEIL M, et al. Dynamics of unstably stratified free shear flows: an experimental investigation of coupled Kelvin–Helmholtz and Rayleigh–Taylor instability[J]. Journal of Fluid Mechanics, 2017, 816: 619-660. DOI:10.1017/jfm.2017.95

POLAVARAPU R, ROACH P, BANERJEE A. Rayleigh-Taylor-instability experiments with elastic-plastic materials[J]. Physical Review E, 2019, 99(5-1): 053104. DOI:10.1103/physreve.99.053104

XUE C, YE W H. Destabilizing effect of compressibility on Rayleigh-Taylor instability for fluids with fixed density profile[J]. Physics of Plasmas, 2010, 17(4): 042705. DOI:10.1063/1.3360295

ZHANG Y S, RUAN Y C, XIE H S, et al. Mixed mass of classical Rayleigh-Taylor mixing at arbitrary density ratios[J]. Physics of Fluids, 2020, 32(1): 011702. DOI:10.1063/1.5131495

MESHKOV E E, ABARZHI S I. Group theory and jelly's experiment of Rayleigh–Taylor instability and Rayleigh–Taylor interfacial mixing[J]. Fluid Dynamics Research, 2019, 51(6): 065502. DOI:10.1088/1873-7005/ab3e83

TAO Y S, WANG L F, YE W H, et al. The bubble velocity research of Rayleigh-Taylor and Richtmyer-Meshkov instabilities at arbitrary Atwood numbers[J]. Acta Physica Sinica, 2012, 61(7): 314-320. (in Chinese)

GALLIS M A; KOEHLER T P; TORCZYNSKI J R, et al. Direct simulation Monte Carlo investigation of the Rayleigh-Taylor instability[J]. Physical Review Fluids, 2016, 1(4): 043403. Doi: 10.1103/PhysRevFluids.1.043403

WEI Y K, DOU H S, QIAN Y H, et al. A novel two-dimensional coupled lattice Boltzmann model for incompressible flow in application of turbulence Rayleigh-Taylor instability[J]. Computers Fluids, 2017, 156: 97-102. DOI:10.1016/j.compfluid.2017.07.003

LIANG H, HU X L, HUANG X F, et al. Direct numerical simulations of multi-mode immiscible Rayleigh-Taylor instability with high Reynolds numbers[J]. Physics of Fluids, 2019, 31(11): 112104. DOI:10.1063/1.5127888

LYUBIMOVA T, VOROBEV A, PROKOPEV S. Rayleigh-Taylor instability of a miscible interface in a confined domain[J]. Physics of Fluids, 2019, 31(1): 014104. DOI:10.1063/1.5064547

WIELAND S A, HAMLINGTON P E, RECKINGER S J, et al. Effects of isothermal stratification strength on vorticity dynamics for single-mode compressible Rayleigh-Taylor instability[J]. Physical Review Fluids, 2019, 4(9): 093905. DOI:10.1103/physrevfluids.4.093905

LI Z Y, WANG L F, WU J F, et al. Interface coupling effects of weakly nonlinear Rayleigh–Taylor instability with double interfaces[J]. Chinese Physics B, 2020, 29(3): 034704. DOI: 10.1088/1674-1056/ab6965

LUO T F, WANG J C, XIE C Y, et al. Effects of compressibility and Atwood number on the single-mode Rayleigh-Taylor instability[J]. Physics of Fluids, 2020, 32(1): 012110. DOI:10.1063/1.5131585

LIVESCU D, WEI T, BRADY P T. Rayleigh-Taylor instability with gravity reversal[J]. Physica D: Nonlinear Phenomena, 2021, 417: 132832. DOI:10.1016/j.physd.2020.132832

BANERJEE A, ANDREWS M J. 3D Simulations to investigate initial condition effects on the growth of Rayleigh-Taylor mixing[J]. International Journal of Heat and Mass Transfer, 2009, 52(17-18): 3906-3917. DOI:10.1016/j.ijheatmasstransfer.2009.03.032

BURTON G C. Study of ultrahigh Atwood-number Rayleigh-Taylor mixing dynamics using the nonlinear large-eddy simulation method[J]. Physics of Fluids, 2011, 23(4): 045106. DOI:10.1063/1.3549931

ZHANG H, BETTI R, YAN R, et al. Self-similar multimode bubble-front evolution of the ablative Rayleigh-Taylor instability in two and three dimensions[J]. Physical Review Letters, 2018, 121(18): 185002. DOI:10.1103/physrevlett.121.185002

YILMAZ I. Analysis of Rayleigh-Taylor instability at high Atwood numbers using fully implicit, non-dissipative, energy-conserving large eddy simulation algorithm[J]. Physics of Fluids, 2020, 32(5): 054101. DOI:10.1063/1.5138978

HAMZEHLOO A, BARTHOLOMEW P, LAIZET S. Direct numerical simulations of incompressible Rayleigh-Taylor instabilities at low and medium Atwood numbers[J]. Physics of Fluids, 2021, 33(5): 054114. DOI:10.1063/5.0049867

DING J C, SUN P Y, HUANG S H, et al. Single- and dual-mode Rayleigh-Taylor instability at microscopic scale[J]. Physics of Fluids, 2021, 33(4): 042102. DOI:10.1063/5.0042505

LIU H, ZHANG Y, KANG W, et al. Molecular dynamics simulation of strong shock waves propagating in dense deuterium, taking into consideration effects of excited electrons[J]. Physical Review E, 2017, 95(2-1): 023201. DOI:10.1103/physreve.95.023201

XU A G, ZHANG G C, YING Y J. Progess of discrete Boltzmann modeling and simulation of combustion system[J]. Acta Physica Sinica, 2015, 64(18): 35-60. (in Chinese)

XU A G, ZHANG G C, ZHANG Y D. Discrete Boltzmann modeling of compressible flows[M]// KYZAS G Z, MITROPOULOS A C, edited. Kinetic Theory: Chapter 2. Croatia: InTech, 2018. https://www.intechopen.com/chapters/56964 doi: 10.5772/intechopen.70748

XU A G, ZHANG G C, GAN Y B, et al. Lattice Boltzmann modeling and simulation of compressible flows[J]. Frontiers of Physics, 2012, 7(5): 582-600. DOI:10.1007/s11467-012-0269-5

XU A G, CHEN J, SONG J H, et al. Progress of discrete Boltzmann study on multiphase complex flows[J]. Acta Aerodynamica Sinica, 2021, 39(3): 138-169. (in Chinese)

XU A G, SONG J H, CHEN F, XIE K, YING Y J. Modeling and analysis methods for complex fields based on phase space[J]. Chinese Journal of Computational Physics, 2021, 38(6): 631-660(in Chinese).

LAI H L, XU A G, ZHANG G C, et al. Nonequilibrium thermohydrodynamic effects on the Rayleigh-Taylor instability in compressible flows[J]. Physical Review E, 2016, 94(2): 023106. DOI:10.1103/physreve.94.023106

LI D M, LAI H L, XU A G, et al. Discrete Boltzmann simulation of Rayleigh-Taylor instability in compressible flows[J]. Acta Physica Sinica, 2018, 67(8): 080501. (in Chinese)

CHEN F, XU A G, ZHANG G C. Viscosity, heat conductivity, and Prandtl number effects in the Rayleigh-Taylor Instability[J]. Frontiers of Physics, 2016, 11(6): 114703. DOI:10.1007/s11467-016-0603-4

CHEN F, XU A G, ZHANG G C. Collaboration and competition between Richtmyer-Meshkov instability and Rayleigh-Taylor instability[J]. Physics of Fluids, 2018, 30(10): 102105. DOI:10.1063/1.5049869

GAN Y B, XU A G, ZHANG G C, et al. Nonequilibrium and morphological characterizations of Kelvin-Helmholtz instability in compressible flows[J]. Frontiers of Physics, 2019, 14(4): 1-17. DOI:10.1007/s11467-019-0885-4

LIN C D, LUO K H, GAN Y B, et al. Kinetic simulation of nonequilibrium Kelvin-Helmholtz instability[J]. Communications in Theoretical Physics, 2019, 71(1): 132. DOI:10.1088/0253-6102/71/1/132

CHEN F, XU A G, ZHANG Y D, et al. Morphological and non-equilibrium analysis of coupled Rayleigh-Taylor-Kelvin-Helmholtz instability[J]. Physics of Fluids, 2020, 32(10): 104111. DOI:10.1063/5.0023364

YE H Y, LAI H L, LI D M, et al. Knudsen number effects on two-dimensional Rayleigh–Taylor instability in compressible fluid: Based on a discrete Boltzmann method[J]. Entropy, 2020, 22(5): 500. DOI:10.3390/e22050500

CHEN L, LAI H L, LIN C D, et al. Specific heat ratio effects of compressible Rayleigh—Taylor instability studied by discrete Boltzmann method[J]. Frontiers of Physics, 2021, 16(5): 1-12. DOI:10.1007/s11467-021-1096-3

ZHANG G, XU A G, ZHANG D J, et al. Delineation of the flow and mixing induced by Rayleigh-Taylor instability through tracers[J]. Physics of Fluids, 2021, 33(7): 076105. DOI:10.1063/5.0051154

GAN Y B, XU A G, ZHANG G C, et al. Physical modeling of multiphase flow via lattice Boltzmann method: Numerical effects, equation of state and boundary conditions[J]. Frontiers of Physics, 2012, 7(4): 481-490. DOI:10.1007/s11467-012-0245-0

GAN Y B, XU A G, ZHANG G C, et al. Discrete Boltzmann modeling of multiphase flows: hydrodynamic and thermodynamic non-equilibrium effects[J]. Soft Matter, 2015, 11(26): 5336-5345. DOI:10.1039/c5sm01125f

LIN C D, LUO K H, FEI L L, et al. A multi-component discrete Boltzmann model for nonequilibrium reactive flows[J]. Scientific Reports, 2017, 7: 14580. DOI:10.1038/s41598-017-14824-9

LIN C D, LUO K H. MRT discrete Boltzmann method for compressible exothermic reactive flows[J]. Computers Fluids, 2018, 166: 176-183. DOI:10.1016/j.compfluid.2018.02.012

LIN C D, LUO K H. Discrete Boltzmann modeling of unsteady reactive flows with nonequilibrium effects[J]. Physical Review E, 2019, 99: 012142. DOI:10.1103/physreve.99.012142

LIN C D, SU X L, ZHANG Y D. Hydrodynamic and thermodynamic nonequilibrium effects around shock waves: based on a discrete Boltzmann method[J]. Entropy, 2020, 22(12): 1397. DOI:10.3390/e22121397

YAN B, XU A G, ZHANG G C, et al. Lattice Boltzmann model for combustion and detonation[J]. Frontiers of Physics, 2013, 8(1): 94-110. DOI:10.1007/s11467-013-0286-z

LIN C D, XU A G, ZHANG G C, et al. Polar coordinate Lattice Boltzmann Kinetic modeling of detonation phenomena[J]. Communications in Theoretical Physics, 2014, 62(5): 737-748. DOI:10.1088/0253-6102/62/5/18

ZHANG Y D, XU A G, ZHANG G C, et al. Kinetic modeling of detonation and effects of negative temperature coefficient[J]. Combustion and Flame, 2016, 173: 483-492. DOI:10.1016/j.combustflame.2016.04.003

LIN C D, XU A G, ZHANG G C, et al. Double-distribution-function discrete Boltzmann model for combustion[J]. Combustion and Flame, 2016, 164: 137-151. DOI:10.1016/j.combustflame.2015.11.010

LIN C D, LUO K H. Mesoscopic simulation of nonequilibrium detonation with discrete Boltzmann method[J]. Combustion and Flame, 2018, 198: 356-362. DOI:10.1016/j.combustflame.2018.09.027

ZHANG Y D, XU A G, ZHANG G C, et al. A one-dimensional discrete Boltzmann model for detonation and an abnormal detonation phenomenon[J]. Communications in Theoretical Physics, 2019, 71(1): 117. DOI:10.1088/0253-6102/71/1/117

LIN C D, LUO K H. Kinetic simulation of unsteady detonation with thermodynamic nonequilibrium effects[J]. Combustion, Explosion, and Shock Waves, 2020, 56(4): 435-443. DOI:10.1134/S0010508220040073

GIMELSHEIN S F, WYSONG I J. Nonequilibrium air flow predictions with a high-fidelity direct simulation Monte Carlo approach[J]. Physical Review Fluids, 2019, 4(3): 033405. DOI:10.1103/physrevfluids.4.033405

ZHANG Y D, XU A G, ZHANG G C, et al. Discrete Boltzmann method for non-equilibrium flows: Based on Shakhov model[J]. Computer Physics Communications, 2019, 238: 50-65. DOI:10.1016/j.cpc.2018.12.018

ZHANG H X, ZHUANG F G. NND schemes and their applications to numerical simulation of two- and three-dimensional flows[J]. Advances in Applied Mechanics, 1991, 29: 193-256. DOI:10.1016/S0065-2156(08)70165-0

NOURGALIEV R R, THEOFANOUS T G. High-fidelity interface tracking in compressible flows: unlimited anchored adaptive level set[J]. Journal of Computational Physics, 2007, 224(2): 836-866. DOI:10.1016/j.jcp.2006.10.031

RAHMAN S, SAN O. A relaxation filtering approach for two-dimensional Rayleigh–Taylor instability-induced flows[J]. Fluids, 2019, 4(2): 78. DOI:10.3390/fluids4020078

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

多相流系统的离散玻尔兹曼研究进展

基于神经网络与遗传算法的热气防冰结构优化

离心通风机降噪研究进展

风扇叶片颗粒侵蚀特性的多因素分析与模拟

基于LBM方法的LAGOON起落架噪声预测与降噪方法研究