Incident impact of Mach reflection wave configuration at a planar heavy/light interface

GUO Jingqi; LU Yizhan; ZHANG Enlai; ZOU Liyong

doi:10.11883/bzycj-2025-0465

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GUO Jingqi, LU Yizhan, ZHANG Enlai, ZOU Liyong. Incident impact of Mach reflection wave configuration at a planar heavy/light interface[J]. Explosion And Shock Waves. doi: 10.11883/bzycj-2025-0465

Citation:

GUO Jingqi, LU Yizhan, ZHANG Enlai, ZOU Liyong. Incident impact of Mach reflection wave configuration at a planar heavy/light interface[J]. Explosion And Shock Waves. doi: 10.11883/bzycj-2025-0465

GUO Jingqi, LU Yizhan, ZHANG Enlai, ZOU Liyong. Incident impact of Mach reflection wave configuration at a planar heavy/light interface[J]. Explosion And Shock Waves. doi: 10.11883/bzycj-2025-0465

Citation:

GUO Jingqi, LU Yizhan, ZHANG Enlai, ZOU Liyong. Incident impact of Mach reflection wave configuration at a planar heavy/light interface[J]. Explosion And Shock Waves. doi: 10.11883/bzycj-2025-0465

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Incident impact of Mach reflection wave configuration at a planar heavy/light interface

doi: 10.11883/bzycj-2025-0465

National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621999, Sichuan, China

Received Date: 2024-11-27
Rev Recd Date: 2025-09-01

Available Online: 2025-09-04

Abstract

Abstract

The evolution of a planar heavy/light gas interface (SF₆/N₂) subjected to a perturbed shock wave produced by diffracting a planar incident shock over a rigid cylinder is investigated by numerical and theoretical analysis, particularly focusing on the incident impact stage of Mach reflection wave configuration. While the Mach number of incident planar shock wave is 1.8, numerical schlieren images of the Mach reflection wave over a rigid cylinder are provided, and the wave evolution during the incident impact on the heavy/light interface is quantitatively analyzed. Utilizing the three-shock theory, an analytical solution describing the refraction process is derived, which accurately predicts the post-refraction shock wave shape, as well as the velocity perturbation and circulation deposition on the interface. Additionally, by drawing shock polar curves and rarefaction wave characteristic lines, the pressure changes and flow deflection across the wave configuration during the incident impact process are straightly described. Both the results of theoretical analysis and numerical simulation indicate that the differences in shock intensity and incident angles within the Mach reflection wave configuration lead to the velocity perturbation on the interface. And the tangential velocity caused by the shock impact results in circulation deposition on the interface. Velocity perturbation and circulation deposition dominate the early evolution of the heavy/light interface.
- Richtmyer-Meshkov instability,
- Mach reflection wave configuration,
- heavy/light interface,
- three-shock theory

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References(34)

References

[1]	RICHTMYER R D. Taylor instability in shock acceleration of compressible fluids [J]. Communications on Pure and Applied Mathematics, 1960, 13(2): 297–319. DOI: 10.1002/cpa.3160130207.
[2]	MESHKOV E E. Instability of the interface of two gases accelerated by a shock wave [J]. Fluid Dynamics, 1969, 4(5): 101–104. DOI: 10.1007/BF01015969.
[3]	KIFONIDIS K, PLEWA T, SCHECK L, et al. Non-spherical core collapse supernovae: II. the late-time evolution of globally anisotropic neutrino-driven explosions and their implications for SN 1987 A [J]. Astronomy and Astrophysics, 2006, 453(2): 661–678. DOI: 10.1051/0004-6361:20054512.
[4]	SMALYUK V A, WEBER C R, LANDEN O L, et al. Review of hydrodynamic instability experiments in inertially confined fusion implosions on National Ignition Facility [J]. Plasma Physics and Controlled Fusion, 2020, 62(1): 014007. DOI: 10.1088/1361-6587/ab49f4.
[5]	王立锋, 叶文华, 陈竹, 等. 激光聚变内爆流体不稳定性基础问题研究进展 [J]. 强激光与粒子束, 2021, 33(1): 012001. DOI: 10.11884/HPLPB202133.200173. WANG L F, YE W H, CHEN Z, et al. Review of hydrodynamic instabilities in inertial confinement fusion implosions [J]. High Power Laser and Particle Beams, 2021, 33(1): 012001. DOI: 10.11884/HPLPB202133.200173.
[6]	高士清, 邹立勇, 唐久棚, 等. 高马赫数激波作用下单模界面的Richtmyer-Meshkov不稳定性数值模拟 [J]. 爆炸与冲击, 2024, 44(7): 073201. DOI: 10.11883/bzycj-2023-0458. GAO S Q, ZOU L Y, TANG J P, et al. Numerical simulation of single-mode Richtmyer-Meshkov instability caused by high-Mach number shock wave [J]. Explosion and Shock Waves, 2024, 44(7): 073201. DOI: 10.11883/bzycj-2023-0458.
[7]	王涛, 汪兵, 林健宇, 等. 柱形汇聚几何中内爆驱动金属界面不稳定性 [J]. 爆炸与冲击, 2020, 40(5): 052201. DOI: 10.11883/bzycj-2019-0150. WANG T, WANG B, LIN J Y, et al. Numerical investigations of the interface instabilities of metallic material under implosion in cylindrical convergent geometry [J]. Explosion and Shock Waves, 2020, 40(5): 052201. DOI: 10.11883/bzycj-2019-0150.
[8]	ZHOU Y. Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I [J]. Physics Reports, 2017, 720/721/722: 1–136. DOI: 10.1016/j.physrep.2017.07.005.
[9]	邹立勇, 吴强, 李欣竹. 广义Richtmyer-Meshkov不稳定性研究进展 [J]. 中国科学: 物理学力学天文学, 2020, 50(10): 104702. DOI: 10.1360/SSPMA-2020-0024. ZOU L Y, WU Q, LI X Z. Research progress of general Richtmyer-Meshkov instability [J]. Scientia Sinica Physica, Mechanica & Astronomica, 2020, 50(10): 104702. DOI: 10.1360/SSPMA-2020-0024.
[10]	THOMAS V A, KARES R J. Drive asymmetry and the origin of turbulence in an ICF implosion [J]. Physical Review Letters, 2012, 109(7): 075004. DOI: 10.1103/PhysRevLett.109.075004.
[11]	ZHOU Y. Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II [J]. Physics Reports, 2017, 723/724/725: 1-160. DOI: 10.1016/j.physrep.2017.07.008.
[12]	ZHOU Y, SADLER J D, HURRICANE O A. Instabilities and mixing in inertial confinement fusion [J]. Annual Review of Fluid Mechanics, 2025, 57: 197–225. DOI: 10.1146/annurev-fluid-022824-110008.
[13]	ISHIZAKI R, NISHIHARA K, SAKAGAMI H, et al. Instability of a contact surface driven by a nonuniform shock wave [J]. Physical Review E, 1996, 53(6): R5592–R5595. DOI: 10.1103/PhysRevE.53.R5592.
[14]	刘金宏, 邹立勇, 曹仁义, 等. 绕射激波和反射激波作用下N₂/SF₆界面R-M不稳定性实验研究 [J]. 力学学报, 2014, 46(3): 475–479. DOI: 10.6052/0459-1879-13-355. LIU J H, ZOU L Y, CAO R Y, et al. Experimentally study of the Richtmyer-Meshkov instability at N₂/SF₆ flat interfaces by diffracted incident shock waves and reshock [J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(3): 475–479. DOI: 10.6052/0459-1879-13-355.
[15]	ZOU L Y, LIU J H, LIAO S F, et al. Richtmyer-Meshkov instability of a flat interface subjected to a rippled shock wave [J]. Physical Review E, 2017, 95(1): 013107. DOI: 10.1103/PhysRevE.95.013107.
[16]	LIAO S F, ZHANG W B, CHEN H, et al. Atwood number effects on the instability of a uniform interface driven by a perturbed shock wave [J]. Physical Review E, 2019, 99(1): 013103. DOI: 10.1103/PhysRevE.99.013103.
[17]	ZOU L Y, AL-MAROUF M, CHENG W, et al. Richtmyer-Meshkov instability of an unperturbed interface subjected to a diffracted convergent shock [J]. Journal of Fluid Mechanics, 2019, 879: 448–467. DOI: 10.1017/jfm.2019.694.
[18]	HE Y F, PENG N F, LI H F, et al. Formation of the cavity on a planar interface subjected to a perturbed shock wave [J]. Physical Review Fluids, 2023, 8(6): 063402. DOI: 10.1103/PhysRevFluids.8.063402.
[19]	ZHANG E L, LIAO S F, ZOU L Y, et al. Refraction of a triple-shock configuration at planar fast-slow gas interfaces [J]. Journal of Fluid Mechanics, 2024, 984: A49. DOI: 10.1017/jfm.2024.245.
[20]	ZHANG W B, WU Q, ZOU L Y, et al. Mach number effect on the instability of a planar interface subjected to a rippled shock [J]. Physical Review E, 2018, 98(4): 043105. DOI: 10.1103/PhysRevE.98.043105.
[21]	王震, 王涛, 柏劲松, 等. 流场非均匀性对非平面激波诱导的Richtmyer-Meshkov不稳定性影响的数值研究 [J]. 爆炸与冲击, 2019, 39(4): 041407. DOI: 10.11883/bzycj-2018-0342. WANG Z, WANG T, BAI J S, et al. Numerical study of non-uniformity effect on Richtmyer-Meshkov instability induced by non-planar shock wave [J]. Explosion And Shock Waves, 2019, 39(4): 041407. DOI: 10.11883/bzycj-2018-0342.
[22]	ZHANG Y M, ZHAO Y, DING J C, et al. Richtmyer-Meshkov instability with a rippled reshock [J]. Journal of Fluid Mechanics, 2023, 968: A3. DOI: 10.1017/jfm.2023.491.
[23]	张崇玉, 胡海波, 王翔, 等. 铅飞层中斜冲击波对碰马赫反射行为实验研究 [J]. 爆炸与冲击, 2019, 39(4): 043102. DOI: 10.11883/bzycj-2017-0441. ZHANG C Y, HU H B, WANG X, et al. Experimental study of Mach reflection induced by collision of oblique shock waves in a lead plate [J]. Explosion and Shock Waves, 2019, 39(4): 043102. DOI: 10.11883/bzycj-2017-0441.
[24]	张崇玉, 胡海波, 王翔. 平面金属飞层对碰区速度剖面的精密测试 [J]. 爆炸与冲击, 2016, 36(4): 557–561. DOI: 10.11883/1001-1455(2016)04-0557-05. ZHANG C Y, HU H B, WANG X. Precision test of velocity profile in collision region of plane metal flying layer [J]. Explosion and Shock Waves, 2016, 36(4): 557–561. DOI: 10.11883/1001-1455(2016)04-0557-05.
[25]	陈大伟, 秦承森, 王裴, 等. 凝聚介质中斜激波的反射 [J]. 计算物理, 2011, 28(6): 791–796. DOI: 10.3969/j.issn.1001-246X.2011.06.001. CHEN D W, QIN C S, WANG P, et al. Oblique shock wave reflection in condensed matter [J]. Chinese Journal of Computational Physics, 2011, 28(6): 791–796. DOI: 10.3969/j.issn.1001-246X.2011.06.001.
[26]	WOODWARD P, COLELLA P. The numerical simulation of two-dimensional fluid flow with strong shocks [J]. Journal of Computational Physics, 1984, 54(1): 115–173. DOI: 10.1016/0021-9991(84)90142-6.
[27]	ZHENG H W, SHU C, CHEW Y T, et al. A solution adaptive simulation of compressible multi-fluid flows with general equation of state [J]. International Journal for Numerical Methods in Fluids, 2011, 67(5): 616–637. DOI: 10.1002/fld.2380.
[28]	LI L F, JIN T, ZOU L Y, et al. Numerical study of Richtmyer–Meshkov instability of a flat interface driven by perturbed and reflected shock waves [J]. Physics of Fluids, 2023, 35(2): 026104. DOI: 10.1063/5.0137389.
[29]	SUTHERLAND W. LII. The viscosity of gases and molecular force [J]. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1893, 36(223): 507–531. DOI: 10.1080/14786449308620508.
[30]	BEN-DOR G. Shock wave reflection phenomena [M]. 2nd ed. Heidelberg: Springer, 2007. DOI: 10.1007/978-3-540-71382-1.
[31]	HENDERSON L F, LOZZI A. Experiments on transition of Mach reflexion [J]. Journal of Fluid Mechanics, 1975, 68(1): 139–155. DOI: 10.1017/S0022112075000730.
[32]	王继海. 爆轰波在物质介面上的折射 [J]. 爆炸与冲击, 1981, 1(2): 1–11. DOI: 10.11883/1001-1455(1981)02-0001-11. WANG J H. Refraction of detonation waves on material interface [J]. Explosion and Shock Waves, 1981, 1(2): 1–11. DOI: 10.11883/1001-1455(1981)02-0001-11.
[33]	ANDERSON JR J D. Fundamentals of aerodynamics [M]. 6th ed. New York: McGraw Hill, 2016: 978-1259129919.
[34]	SAMTANEY R, ZABUSKY N J. Circulation deposition on shock-accelerated planar and curved density-stratified interfaces: models and scaling laws [J]. Journal of Fluid Mechanics, 1994, 269: 45–78. DOI: 10.1017/S0022112094001485.