Experiments in Fluids

, 59:98 | Cite as

Droplet and multiphase effects in a shock-driven hydrodynamic instability with reshock

  • John B. Middlebrooks
  • Constantine G. Avgoustopoulos
  • Wolfgang J. Black
  • Roy C. Allen
  • Jacob A. McFarland
Research Article


Shock-driven multiphase instabilities (SDMI) are unique physical phenomena that have far-reaching applications in engineering and science such as high energy explosions, scramjet combustors, and supernovae events. The SDMI arises when a multiphase field is impulsively accelerated by a shock wave and evolves as a result of gradients in particle-gas momentum transfer. A new shock tube facility has been constructed to study the SDMI. Experiments were conducted to investigate liquid particle and multiphase effects in the SDMI. A multiphase cylindrical interface was created with water droplet laden air in our horizontal shock tube facility. The interface was accelerated by a Mach 1.66 shock wave, and its reflection from the end wall. The interface development was captured using laser illumination and a high-resolution CCD camera. Laser interferometry was used to determine the droplet size distribution. A particle filtration technique was used to determine mass loading within an interface and verify particle size distribution. The effects of particle number density, particle size, and a secondary acceleration (reshock) of the interface were noted. Particle number density effects were found comparable to Atwood number effects in the Richtmyer–Meshkov instability for small (\(\sim 1.7~{\upmu }\)m) droplets. Evaporation was observed to alter droplet sizes and number density, markedly after reshock. For large diameter droplets (\(\sim 10.7~{\upmu }\)m), diminished development was observed with larger droplets lagging far behind the interface. These lagging droplets were also observed to breakup after reshock into structured clusters of smaller droplets. Mixing width values were reported to quantify mixing effects seen in images.



JBM would like to thank the Missouri Space Grant Consortium and The McNair Scholars Program at the University of Missouri. WJB and RCA are supported in part by the US DOE-NNSA under Contract no. DE-NA0003345. JAM would like to thank Raj Kothakapa for his help with the particle diagnostics.


  1. Anderson M, Vorobieff P, Truman CR, Corbin C, Kuehner G, Wayne P, Conroy J, White R, Kumar S (2015) An experimental and numerical study of shock interaction with a gas column seeded with droplets. Shock Waves 25(2):107–125. CrossRefGoogle Scholar
  2. Annamalai S, Rollin B, Ouellet F, Neal C, Jackson TL, Balachandar S (2016) Effects of initial perturbations in the early moments of an explosive dispersal of particles. J Fluids Eng 138(7):070903CrossRefGoogle Scholar
  3. Avgoustopoulos C (2017) The design, instrumentation, and validation of a multiphase shock tube facility. Master’s thesis, University of Missouri-Columbia, Columbia, MOGoogle Scholar
  4. Balakumar BJ, Orlicz GC, Tomkins CD, Prestridge KP (2008) Simultaneous particle-image velocimetry-planar laser-induced fluorescence measurements of Richtmyer–Meshkov instability growth in a gas curtain with and without reshock. Phys Fluids 20(124):103zbMATHGoogle Scholar
  5. Benuzzi-Mounaix A, Koenig M, Ravasio A, Vinci T, Ozaki N, Le Gloahec MR, Loupias B, Huser G, Henry E, Bouquet S et al (2006) Laser-driven shock waves for the study of extreme matter states. Plasma Phys Controll Fusion 48(12B):B347CrossRefGoogle Scholar
  6. Berglund RN, Liu BY (1973) Generation of monodisperse aerosol standards. Environ Sci Technol 7(2):147–153CrossRefGoogle Scholar
  7. Bianchi S, Schneider R (2007) Dust formation and survival in supernova ejecta. Mon Notices R Astron Soc 378(3):973–982. CrossRefGoogle Scholar
  8. Black WJ, Denissen NA, McFarland JA (2017) Evaporation effects in shock-driven multiphase instabilities. J Fluids Eng 139(7):071204. CrossRefGoogle Scholar
  9. Bordoloi AD, Martinez AA, Prestridge K (2017) Relaxation drag history of shock accelerated microparticles. J Fluid Mech 823:R4-1–R4-11CrossRefGoogle Scholar
  10. Chen CY (1955) Filtration of aerosols by fibrous media. Chem Rev 55(3):595–623CrossRefGoogle Scholar
  11. Colarossi M, Trask N, Schmidt DP, Bergander MJ (2012) Multidimensional modeling of condensing two-phase ejector flow. Int J Refrig 35(2):290–299. CrossRefGoogle Scholar
  12. 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. CrossRefzbMATHGoogle Scholar
  13. Courtney E, Courtney A, Courtney M (2014) Shock tube design for high intensity blast waves for laboratory testing of armor and combat materiel. Def Technol 10(2):245–250CrossRefGoogle Scholar
  14. Craig L, Moharreri A, Schanot A, Rogers DC, Anderson B, Dhaniyala S (2013) Characterizations of cloud droplet shatter artifacts in two airborne aerosol inlets. Aerosol Sci Technol 47(6):662–671CrossRefGoogle Scholar
  15. Dahal J, McFarland JA (2017) A numerical method for shock driven multiphase flow with evaporating particles. J Comput Phys 344:210–233. MathSciNetCrossRefzbMATHGoogle Scholar
  16. Davis SL, Dittmann TB, Jacobs GB, Don WS (2013) Dispersion of a cloud of particles by a moving shock: effects of the shape, angle of rotation, and aspect ratio. J Appl Mech Tech Phys 54(6):900–912. CrossRefGoogle Scholar
  17. Donnelly TD, Hogan J, Mugler A, Schubmehl M, Schommer N, Bernoff A, Dasnurkar S, Ditmire T (2005) Using ultrasonic atomization to produce an aerosol of micron-scale particles. Rev Sci Instrum 76(11):113301CrossRefGoogle Scholar
  18. Endo T, Masuda K, Watanabe W, Mukai T, Nagai H, Johzaki T, Matsuoka K (2016) Reduction of air flow rate for pulse-detonation-turbine-engine operation by water-droplet injection. J Therm Sci Technol 11(2):JTST0022–JTST0022CrossRefGoogle Scholar
  19. Goodridge CL, Shi WT, Lathrop DP (1996) Threshold dynamics of singular gravity-capillary waves. Phys Rev Lett 76(11):1824CrossRefGoogle Scholar
  20. Guildenbecher DR, Lpez-Rivera C, Sojka PE (2009) Secondary atomization. Exp Fluids 46(3):371–402. CrossRefGoogle Scholar
  21. Haas JF, Sturtevant B (1987) Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities. J Fluid Mech 181:41–76CrossRefGoogle Scholar
  22. Hsiang L, Faeth G (1995) Drop deformation and breakup due to shock wave and steady disturbances. Int J Multiph Flow 21(4):545–560. CrossRefzbMATHGoogle Scholar
  23. Hulst HC, van de Hulst HC (1957) Light scattering by small particles. Courier Corporation, ChelmsfordzbMATHGoogle Scholar
  24. Jacobs JW (1992) Shock-induced mixing of a light-gas cylinder. J Fluid Mech 234:629–649. CrossRefGoogle Scholar
  25. Jalaal M, Mehravaran K (2012) Fragmentation of falling liquid droplets in bag breakup mode. Int J Multiph Flow. Google Scholar
  26. Kailasanath K (2006) Liquid-fueled detonations in tubes. J Propuls Power 22(6):1261–1268CrossRefGoogle Scholar
  27. Kane J, Drake RP, Remington BA (1999) An evaluation of the Richtmyer–Meshkov instability in supernova remnant formation. Astrophys J 511:335–340CrossRefGoogle Scholar
  28. Kasahara J, Frolov S (2015) Present status of pulse and rotating detonation engine research. In: 25th international colloquium on the dynamics of explosions and reactive systems, paper, vol 304Google Scholar
  29. König G, Anders K, Frohn A (1986) A new light-scattering technique to measure the diameter of periodically generated moving droplets. J Aerosol Sci 17(2):157–167CrossRefGoogle Scholar
  30. Kothakapa R (2017) Design of experimental apparatus for generation and measurement of an aerosol. Master’s thesis, University of Missouri-Columbia, Columbia, MOGoogle Scholar
  31. Lang RJ (1962) Ultrasonic atomization of liquids. J Acoust soc Am 34(1):6–8CrossRefGoogle Scholar
  32. Lefebvre A, McDonell V (2017) Atomization and sprays. CRC Press, Boca RatonCrossRefGoogle Scholar
  33. Lu FK, Braun EM (2014) Rotating detonation wave propulsion: experimental challenges, modeling, and engine concepts. J Propuls Power 30(5):1125–1142. CrossRefGoogle Scholar
  34. Luo X, Guan B, Si T, Zhai Z, Wang X (2016) Richtmyer–Meshkov instability of a three-dimensional SF6-air interface with a minimum-surface feature. Phys Rev E 93(1):013101CrossRefGoogle Scholar
  35. Marble FE (1970) Dynamics of dusty gases. Annu Rev Fluid Mech 2(1):397–446. CrossRefGoogle Scholar
  36. Martinez AA, Orlicz GC, Prestridge KP (2015) A new experiment to measure shocked particle drag using multi-pulse particle image velocimetry and particle tracking. Exp Fluids 56(1):1854. CrossRefGoogle Scholar
  37. McFarland J, Reilly D, Creel S, McDonald C, Finn T, Ranjan D (2014) Experimental investigation of the inclined interface Richtmyer–Meshkov instability before and after reshock. Exp Fluids 55(1):1–14. CrossRefGoogle Scholar
  38. McFarland JA, Hagenmaier M (2017) Computational study of shock driven multiphase mixing in scramjet conditions. In: 23rd AIAA computational fluid dynamics conference, p 4287Google Scholar
  39. McFarland JA, Reilly D, Black W, Greenough JA, Ranjan D (2015) Modal interactions between a large-wavelength inclined interface and small-wavelength multimode perturbations in a Richtmyer–Meshkov instability. Phys Rev E. MathSciNetGoogle Scholar
  40. McFarland JA, Black WJ, Dahal J, Morgan BE (2016) Computational study of the shock driven instability of a multiphase particle-gas system. Phys Fluids 28(2):024–105CrossRefGoogle Scholar
  41. Mie G (1908) Pioneering mathematical description of scattering by spheres. Ann Phys 25:337Google Scholar
  42. Mohaghar M, Carter J, Musci B, Reilly D, McFarland JA, Ranjan D (2017) Evaluation of turbulent mixing transition in a shock-driven variable-density flow. J Fluid Mech 831:779–825. MathSciNetCrossRefGoogle Scholar
  43. 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(126):102zbMATHGoogle Scholar
  44. Nekkanti K (2010) Analysis of thrust development in a pulse detonaton engine. Master’s thesis, The University of Texas at ArlingtonGoogle Scholar
  45. Olmstead D, Wayne P, Yoo JH, Kumar S, Truman CR, Vorobieff P (2017) Experimental study of shock-accelerated inclined heavy gas cylinder. Exp Fluids 58(6):71CrossRefGoogle Scholar
  46. Parmar M, Haselbacher A, Balachandar S (2009) Prediction and modeling of shock-particle interaction. In: 47th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, p 1124Google Scholar
  47. Parmar M, Haselbacher A, Balachandar S (2010) Improved drag correlation for spheres and application to shock-tube experiments. AIAA J 48(6):1273–1276. CrossRefGoogle Scholar
  48. Paudel M, Dahal J, McFarland J (2018) Particle evaporation and hydrodynamics in a shock driven multiphase instability. Int J Multiph Flow. MathSciNetGoogle Scholar
  49. Puthenveettil BA, Hopfinger E (2009) Evolution and breaking of parametrically forced capillary waves in a circular cylinder. J Fluid Mech 633:355–379CrossRefzbMATHGoogle Scholar
  50. Ragni D, Schrijer F, Van Oudheusden B, Scarano F (2011) Particle tracer response across shocks measured by PIV. Exp Fluids 50(1):53–64CrossRefGoogle Scholar
  51. Ranjan D, Oakley J, Bonazza R (2011) Shock–bubble interactions. Annu Rev Fluid Mech 43(1):117–140. MathSciNetCrossRefzbMATHGoogle Scholar
  52. Robey HF, Kane J, Remington B, Drake R, Hurricane O, Louis H, Wallace R, Knauer J, Keiter P, Arnett D et al (2001) An experimental testbed for the study of hydrodynamic issues in supernovae. Phys Plasmas 8(5):2446–2453CrossRefGoogle Scholar
  53. Schilling O, Latini M, Don W (2007) Physics of reshock and mixing in single-mode Richtmyer–Meshkov instability. Phys Rev E 76(2):026–319. MathSciNetCrossRefGoogle Scholar
  54. Schulz JC, Gottiparthi KC, Menon S (2013) Richtmyer–Meshkov instability in dilute gas-particle mixtures with re-shock. Phys Fluids 25(11):114105. CrossRefGoogle Scholar
  55. Schwer D, Kailasanath K (2011) Numerical investigation of the physics of rotating-detonation-engines. Proc Combust Inst 33(2):2195–2202. CrossRefGoogle Scholar
  56. Tomkins C, Prestridge K, Rightley P, Marr-Lyon M, Vorobieff P, Benjamin R (2003) A quantitative study of the interaction of two Richtmyer–Meshkov-unstable gas cylinders. Phys Fluids 15(4):986–1004CrossRefzbMATHGoogle Scholar
  57. 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(18):184503CrossRefGoogle Scholar
  58. Weber C, Haehn N, Oakley J, Rothamer D, Bonazza R (2012) Turbulent mixing measurements in the Richtmyer–Meshkov instability. Phys Fluids 24(7):074105CrossRefGoogle Scholar
  59. Wilson BM, Mejia-Alvarez R, Prestridge KP (2016) Single-interface Richtmyer–Meshkov turbulent mixing at the los alamos vertical shock tube. J Fluids Eng 138(7):070901CrossRefGoogle Scholar
  60. Wohletz K, Zimanowski B, Büttner R (2013) Magma–water interactions. In: Fagents SA, Gregg TKP, Lopes RMC (eds) Modeling volcanic processes: the physics and mathematics of volcanism, Chap 11. Cambridge University Press, Cambridge, pp 230–257CrossRefGoogle Scholar
  61. Woitke P (2006) 2D models for dust-driven AGB star winds. Astron Astrophys 452(2):537–549. CrossRefGoogle Scholar
  62. Wrblewski W, Dykas S, Gardzilewicz A, Kolovratnik M (2009) Numerical and experimental investigations of steam condensation in LP part of a large power turbine. J Fluids Eng 131(4):041301. CrossRefGoogle Scholar
  63. Yang J, Kubota T, Zukoski EE (1993) Applications of shock-induced mixing to supersonic combustion. AIAA J 31(5):854–862CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • John B. Middlebrooks
    • 1
  • Constantine G. Avgoustopoulos
    • 1
  • Wolfgang J. Black
    • 1
  • Roy C. Allen
    • 1
  • Jacob A. McFarland
    • 1
  1. 1.Mechanical and Aerospace EngineeringUniversity of MissouriColumbiaUSA

Personalised recommendations