Skip to main content
Log in

Investigation of the acceleration of aluminum particles behind a shock wave using instantaneous Laser Doppler Velocimetry

  • Original Article
  • Published:
Shock Waves Aims and scope Submit manuscript

Abstract

The acceleration of aluminum particles with a 5μm diameter in the flow field behind an incident shock wave was investigated experimentally in a 10-m long and 70 mm inner diameter shock tube. By means of instantaneous Laser Doppler Velocimetry (LDV) the velocity of the particles was observed directly. The light scattered by the moving particles is Doppler shifted and sent to the laser Doppler velocimeter. The velocimeter essentially consists of a phase-stabilized Michelson interferometer used as a sensitive spectrometer. An electro-optical circuit ensures the phase stabilization that results in a voltage signal independent of the scattered light intensity and proportional to the mean velocity of the particles at the measurement point. Because of the very short response time (1μs) of the LDV system used here, the latter gives a continuous real-time signal of the particle acceleration. To avoid particle oxidation the particles were accelerated by a high-speed nitrogen gas flow. From the measured velocity the dimensionless drag coefficient was calculated. The drag coefficient is related to the fluid dynamic force exerted by the gas on the particles. The experimental data were compared to theoretical models from the literature. A significant deviation between the model and the experimental data was observed. This deviation is supposed to be induced by the shock wave, which hits the particles and breaks them into pieces of a smaller diameter. Further experiments will be carried out in the future to check the size distribution of the particles after the shock has gone past them.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Basset A.B.: Treatise on Hydrodynamics. Bell, London (1888)

    MATH  Google Scholar 

  2. Boussinesq M.J.: Sur la résistance qu’oppose un liquide indéfini en repos .... C. R. Acad. Sci. Paris 100, 935–937 (1885)

    MATH  Google Scholar 

  3. Carlson D.J., Hoglund R.F.: Particle drag and heat transfer in rocket nozzles. AIAA J. 2(11), 1980–1984 (1964)

    Article  Google Scholar 

  4. Crowe , C.T. (eds): Multiphase Flow Handbook. CRC Press, New York (2006)

    MATH  Google Scholar 

  5. Crowe C.T., Babcock W.R., Willoughby P.G.: Drag coefficient for particles in rarefied low Mach number flows. Prog. Heat Mass Transf. 6, 419–428 (1973)

    Google Scholar 

  6. Crowe C.T., Sommerfeld M., Tsuji Y.: Multiphase Flows with Droplets and Particles. CRC Press, New York (1998)

    Google Scholar 

  7. Henderson C.B.: Drag coefficients of spheres in continuum and rarefield flows. AIAA J. 14(6), 707–708 (1976)

    Article  Google Scholar 

  8. Hermsen, R.W.: Review of particle drag models. In: JANAF Performance Standardization Subcommittee 12th Meeting Minutes, p. 113, CPIA (1979)

  9. Igra, O., Takayama, K.: Shock-tube study of the drag coefficient of a sphere in a nonstationary flow. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 442(1915), 231–247 (1993)

  10. Jourdan G., Houas L., Igra O., Estivalezes J.L., Devals C., Meshkov E.E.: Drag coefficient of a sphere in a non-stationary flow: new results. Proc. R. Soc. London Ser. A Math. Phys. Eng. Sci. 463(2088), 3323–3345 (2007)

    Google Scholar 

  11. Kim S., Karrila S.J.: Microhydrodynamics: Principles and Selected Applications. Butterworth, Heinemann, Boston (1991)

    Google Scholar 

  12. Luo X., Wang G., Olivier H.: Parametric investigation of particle acceleration in high enthalpy conical nozzle flows for coating applications. Shock Waves 17, 351–362 (2008)

    Article  Google Scholar 

  13. Millikan R.A.: The general law of fall of a small spherical body through a gas and its bearing upon the nature of molecular reflection from surfaces. Phys. Rev. 22, 1–23 (1923)

    Article  Google Scholar 

  14. Oseen C.W.: Über die Stoke’s Formel, und über eine verwendte Aufgabe in der Hydrodynamik. Ark. Math. Astronom. Fys. 6(29), 1–20 (1927)

    Google Scholar 

  15. Saito T., Saba M., Sun M., Takayama K.: The effect of an unsteady drag force on the structure of a non-equilibrium region behind a shock wave in a gas-particle mixture. Shock Waves 17, 255–262 (2007)

    Article  Google Scholar 

  16. Smeets G., George A.: Instantaneous laser Doppler velocimeter using a fast wavelength tracking Michelson interferometer. Rev. Sci. Instrum. 49(11), 1589–1596 (1978)

    Article  Google Scholar 

  17. Smeets, G., Mathieu, G.: Optische Dopplermessung mit dem Michelson-Spektrometer. ISL Report R 123/83 (1983)

  18. Sommerfeld M.: The unsteadiness of shock-waves propagating through gas-particle mixtures. Exp. Fluids 3(4), 197–206 (1985)

    Article  Google Scholar 

  19. Stokes G.G.: On the effect of internal friction of fluids on the motion of pendulums. Trans. Camb. Philos. Soc. 9, 8–106 (1851)

    Google Scholar 

  20. Tanguay V., Higgins A.J., Zhang F.: A simple analytical model for reactive particle ignition in explosives. Propellants Explos. Pyrotech. 32(5), 371–384 (2007)

    Article  Google Scholar 

  21. White F.M.: Viscous Fluid Flow. McGraw Hill, New York (1974)

    MATH  Google Scholar 

  22. Yarin L.P., Hetsroni G.: Combustion of Two-Phase Reactive Media. Springer, Berlin (2004)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to G. Schlöffel.

Additional information

Communicated by O. Igra.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schlöffel, G., Bastide, M., Bachmann, S. et al. Investigation of the acceleration of aluminum particles behind a shock wave using instantaneous Laser Doppler Velocimetry. Shock Waves 19, 125–134 (2009). https://doi.org/10.1007/s00193-009-0188-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00193-009-0188-8

Keywords

PACS

Navigation