Abstract
An experimental study on the Richtmyer–Meshkov instability (RMI) is presented, which used a new experimental facility at Texas A&M University built for conducting shock-accelerated, inhomogeneous, inclined fluid interface experiments. The RMI develops from the misalignment of the pressure and density gradients for which the inclined shock tube facility is uniquely well suited since a fluid interface can be created at a prescribed angle to the incident shock. Measurements of the evolving RMI are taken using planar laser Mie scattering images for both the pre- and post-reshock regimes, which capture the qualitative evolution of the interface. Statistical measurements demonstrate that the inclined interface initial conditions have a high degree of run-to-run repeatability. The interface mixing width is scaled using the method developed in author’s previous work and shows that the non-dimensional mixing width grows linearly in the pre-reshock regime and then levels off at the onset of reshock, after which it grows linearly again. Mie scattering images at late times exhibit the evolution of a secondary shear instability on the primary vortex feature, which has never been resolved in simulations of the inclined interface RMI. A 2D velocity field is obtained for this feature using particle image velocimetry and processed to indicate the strength of the vorticity present. Images of the interface after reshock reveal the inversion of the bubble and spike features and the decay of prominent features toward a turbulent state.
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Abakumov AI, Fadeev VY, Kholkin SI, Meshkov EE, Nikiforov VV, Nizovtzev PN, Sadilov NN, Sobolev SK, Tilkunov VA, Tochilin VO et al (1996) Studies of film effects on the turbulent mixing zone evolution in shock tube experiments. In: Young R, Glimm J, Boston B (eds) Proceedings of the fifth international workshop on compressible turbulent mixing. World Scientific, Singapore, p 118
Abd-El-Fattah AM, Henderson LF (1978) Shock waves at a slow–fast gas interface. J Fluid Mech 89:79–95
Abd-El-Fattah AM, Henderson LF (2006) Shock waves at a fast–slow gas interface. J Fluid Mech 86:15–32
Abd-El-Fattah AM, Henderson LF, Lozzi A (1976) Precursor shock waves at a slow–fast gas interface. J Fluid Mech 76:157–176
Anderson MH, Puranik BP, Oakley JG, Brooks PW, Bonazza R (2000) Shock tube investigation of hydrodynamic issues related to inertial confinement fusion. Shock Waves 10:377–387
Bailie C, McFarland JA, Greenough JA, Ranjan D (2012) Effect of incident shock wave strength on the decay of Richtmyer–Meshkov instability-introduced perturbations in the refracted shock wave. Shock Waves 22:511–519
Balasubramanian S, Orlicz GC, Prestridge KP, Balakumar BJ (2012) Experimental study of initial condition dependence on Richtmyer–Meshkov instability in the presence of reshock. Phys Fluids 24:034103
Brouillette M (2002) The Richtmyer–Meshkov instability. Annu Rev Fluid Mech 34:445–468
Chapman PR, Jacobs JW (2006) Experiments on the three-dimensional incompressible Richtmyer–Meshkov instability. Phys Fluids 18:074101
Collins BD, Jacobs JW (2002) PLIF flow visualization and measurements of the Richtmyer–Meshkov instability of an air/SF6 interface. J Fluid Mech 464:113–136
Drake RP, Doss FW, McClarren RG, Adams ML, Amato N, Bingham D, Chou CC, DiStefano C, Fidkowski K, Fryxell B, Gombosi TI, Grosskopf MJ, Holloway JP, van der Holst B, Hunting CM (2011) Radiative effects in radiative shocks in shocktubes. High Energy Density Phys 7:130–140
Erez L, Sadot O, Oron D, Erez G, Levin LA, Shvarts D, Ben-Dor G (2000) Study of the membrane effect on turbulent mixing measurements in shock tubes. Shock Waves 10:241–251
Haas JF (1993) Experiments and simulations on shock waves in non-homogeneous gases. In: Proceedings of the 19th international symposium on shock waves. Springer, Marseille, pp 27–36
Haehn N, Weber C, Oakley J, Anderson M, Ranjan D, Bonazza R (2011) Experimental investigation of a twice-shocked spherical gas inhomogeneity with particle image velocimetry. Shock Waves 21:225–231
Harding E, Hansen J, Hurricane O, Drake R, Robey H, Kuranz C, Remington B, Bono M, Grosskopf M, Gillespie R (2009) Observation of a Kelvin–Helmholtz instability in a high-energy-density plasma on the omega laser. Phys Rev Lett 103:045005
Hill DJ, Pantano C, Pullin DI (2006) Large-eddy simulation and multiscale modelling of a Richtmyer–Meshkov instability with reshock. J Fluid Mech 557:29
Hjelmfelt AT Jr, Mockros LF (1966) Motion of discrete particles in a turbulent fluid. Appl Sci Res 16:149–161
Houas L, Chemouni I (1996) Experimental investigation of Richtmyer–Meshkov instability in shock tube. Phys Fluids 8:614
Jacobs JW (1992) Shock-induced mixing of a light-gas cylinder. J Fluid Mech 234:629–649
Jahn RG (1956) The refraction of shock waves at a gaseous interface. J Fluid Mech 1:457–489
Kane J, Drake RP, Remington BA (1999) An evaluation of the Richtmyer–Meshkov instability in supernova remnant formation. Astrophys J 511:335–340
Kramer KJ, Latkowski JF, Abbott RP, Boyd JK, Powers JJ, Seifried JE (2008) Neutron transport and nuclear burnup analysis for the laser inertial confinement fusion–fission energy (LIFE) engine. Fusion Sci Technol 56:625–631
Krivets VV, Long CC, Jacobs JW, Greenough JA (2009) Shock tube experiments and numerical simulation of the single mode three-dimensional Richtmyer–Meshkov instability. In: 26th international symposium on shock waves. Springer, Gottingen, pp 1205–1210
Kucherenko YA, Pavlenko AV, Shestachenko OE, Balabin SI, Pylaev AP, Tyaktev AA (2010) Measurement of spectral characteristics of the turbulent mixing zone. J Appl Mech Tech Phys 51:299–307
Latini M, Schilling O, Don WS (2007) Effects of WENO flux reconstruction order and spatial resolution on reshocked two-dimensional Richtmyer–Meshkov instability. J Comput Phys 221:805–836
Long CC, Krivets VV, Greenough JA, Jacobs JW (2009) Shock tube experiments and numerical simulation of the single mode three-dimensional Richtmyer–Meshkov instability. Phys Fluids 21:114104
Marble FE, Zukoski EE, Jacobs JW, Hendricks GJ, Waitz IA (1990) Shock enhancement and control of hypersonic mixing and combustion. American Institute of Aeronautics and Astronautics, Orlando, FL
McFarland J, Greenough J, Ranjan D (2011) Computational parametric study of a Richtmyer–Meshkov instability for an inclined interface. Phys Rev E 84:026303
McFarland JA, Greenough JA, Ranjan D (2013) Investigation of the initial perturbation amplitude for the inclined interface Richtmyer–Meshkov instability. Phys Scr T155:014014
Melling A (1997) Tracer particles and seeding for particle image velocimetry. Meas Sci Technol 8:1406
Meshkov EE (1972) Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn 4:101–104
Mikaelian KO (1996) Numerical simulations of Richtmyer–Meshkov instabilities in finite-thickness fluid layers. Phys Fluids 8:1269–1292
Mikaelian KO (2005) Richtmyer–Meshkov instability of arbitrary shapes. Phys Fluids 17:034101
Motl B, Oakley J, Ranjan D, Weber C, Anderson M, Bonazza R (2009) Experimental validation of a Richtmyer–Meshkov scaling law over large density ratio and shock strength ranges. Phys Fluids 21:126102
Niederhaus JHJ, Ranjan D, Oakley JG, Anderson MH, Greenough JA, Bonazza R (2009) Computations in 3D for shock-induced distortion of a light spherical gas inhomogeneity. Shock Waves 28:1169–1174
Orth CD (2003) VISTA: a vehicle for interplanetary space transport application powered by inertial confinement fusion. University of California, Lawrence Livermore National Laboratory, Report UCRL-LR-110500, in final preparation
Prestridge K, Vorobieff P, Rightley PM, Benjamin RF (2000a) Validation of an instability growth model using particle image velocimetry measurements. Phys Rev Lett 84:4353–4356
Prestridge K, Rightley PM, Vorobieff P, Benjamin RF, Kurnit NA (2000b) Simultaneous density-field visualization and PIV of a shock-accelerated gas curtain. Exp Fluids 29:339–346
Ranjan D, Anderson M, Oakley J, Bonazza R (2005) Experimental investigation of a strongly shocked gas bubble. Phys Rev Lett 94:184507
Ranjan D, Niederhaus JHJ, Oakley JG, Anderson MH, Greenough JA, Bonazza R (2008) Experimental and numerical investigation of shock-induced distortion of a spherical gas inhomogeneity. Phys Scr 2008:014020
Ranjan D, Oakley J, Bonazza R (2011) Shock-bubble interactions. Annu Rev Fluid Mech 43:117–140
Richtmyer RD (1960) Taylor instability in shock acceleration of compressible fluids. Commun Pure Appl Math 13:297–319
Robey HF, Kane JO, Remington BA, Drake RP, Hurricane OA, Louis H, Wallace RJ, Knauer J, Keiter P, Arnett D, Ryutov DD (2001) An experimental testbed for the study of hydrodynamic issues in supernovae. Phys Plasmas 8:2446
Robey HF, Boehly TR, Celliers PM, Eggert JH, Hicks D et al (2012) Shock timing experiments on the National Ignition Facility: initial results and comparison with simulation. Phys Plasmas 19:042706
Samtaney R, Zabusky NJ (1994) Circulation deposition on shock-accelerated planar and curved density-stratified interfaces: models and scaling laws. J Fluid Mech 269:45–78
Smith AV, Holder DA, Barton CJ, Morris AP, Youngs DL (2001) Shock tube experiments on Richtmyer–Meshkov instability across a chevron profiled interface. In: 8th international workshop on the physics of compressible turbulent mixing, Pasedena, CA
Sturtevant B (1987) Rayleigh–Taylor instability in compressible fluids. In: 16th international symposium on shock tubes and waves. Aachen, West Germany, pp 89–100
Taylor G (1950) The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. Proc R Soc Lond A 201:192–196
Vetter M, Sturtevant B (1995) Experiments on the Richtmyer–Meshkov instability of an air/SF 6 interface. Shock Waves 4:247–252
Vorobieff P, Anderson M, Conroy J, White R, Truman CR, Kumar S (2011) Vortex formation in a shock-accelerated gas induced by particle seeding. Phys Rev Lett 106:184503
Weber C, Haehn N, Oakley J, Rothamer D, Bonazza R (2012) Turbulent mixing measurements in the Richtmyer–Meshkov instability. Phys Fluids 24:074105
White R, Conroy J, Anderson M, Vorobieff P, Truman RC, Kumar S (2011) Oblique shock interaction with a gas cylinder. Bulletin of the American Physical Society. APS, Baltimore, MD
Zhang S, Peng G, Zabusky NJ (2005) Vortex dynamics and baroclinically forced inhomogeneous turbulence for shock—planar heavy curtain interactions. J Turbul 6:1–29
Acknowledgments
This work was partially supported by the National Science Foundation Faculty Early Career Development (CAREER) Award (Grant No. CBET-1254760) and Center for Radiative Shock Hydrodynamics (CRASH). The author would like to thank the undergraduate research scholars who assisted in the design and construction of the shock tube facility over its 3-year construction time. In particular, the author would like to thank Mr. Peter Koppenberger for his friendship and help with the early design of the shock tube, and Mr. Sterling Debner for his friendship and assistance in the design and construction of the shock tube. Without the help of these talented undergraduate students and others, the shock tube design and construction would have been a much less rewarding process.
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McFarland, J., Reilly, D., Creel, S. et al. Experimental investigation of the inclined interface Richtmyer–Meshkov instability before and after reshock. Exp Fluids 55, 1640 (2014). https://doi.org/10.1007/s00348-013-1640-1
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DOI: https://doi.org/10.1007/s00348-013-1640-1