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[1] Rayleigh, L., Analytic solutions of the Rayleigh equation for linear density profiles. Proceedings of the London Mathematical Society, 14, pp. 170–177, 1883.
[2] Taylor, G., The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 201(1065),1 pp. 92–196, 1950. [Crossref]
[3] Richtmyer, R.D., Taylor instability in shock acceleration of compressible fluids. Communications on Pure and Applied Mathematics, 13(2), pp. 297–319, 1960. [Crossref]
[4] Markstein, G.H., Flow disturbances induced near a slightly wavy contact surface, or flame front, traversed by a shock wave, 1957.
[5] Meshkov, E.E., Instability of shock-accelerated interface between two media. Advances in Compressible Turbulent Mixing, 8810234:473, 1992.
[6] Balakrishnan, K., Ukai, S. & Menon, S., Clustering and combustion of dilute aluminum particle clouds in a post-detonation flow field. Proceedings of the Combustion Institute, 33(2), pp. 2255–2263, 2011. [Crossref]
[7] Jacobs, G.B. & Don, W-S., A high-order WENO-Z finite difference based particlesource-in-cell method for computation of particle-laden flows with shocks. Journal of Computational Physics, 228(5), pp. 1365–1379, 2009. [Crossref]
[8] Vorobieff, P., Anderson, M., Conroy, J., White, R., Truman, C.R. & Kumar, S., Analogues of Rayleigh-Taylor and Richtmyer-Meshkov instabilities in flows with nonuniform particle and droplet seeding. Computational Methods in Multiphase Flow VI, A. Mammoli, and C. Brebbia, eds., WIT Press, Ashurst, Southampton, UK, pp. 17–28, 2011.
[9] Vorobieff, P., Anderson, M., Conroy, J., White, R., Truman, C.R. & Kumar, S., Vortex formation in a shock-accelerated gas induced by particle seeding. Physical Review Letters, 106(18), p. 184503, 2011. [Crossref]
[10] Sharma, M.P. & Stock, D.E., The particle-source-in cell (PSI-CELL) model for gasdroplet flows. Journal of Fluids Engineering, 99(2), pp. 325, 1977. [Crossref]
[11] Boiko, V.M., Kiselev, V.P., Kiselev, S.P., Papyrin, A.N., Poplavsky, S.V. & Fomin, V.M., Shock wave interaction with a cloud of particles. Shock Waves, 7(5), pp. 275–285, 1997. [Crossref]
[12] Meshkov, E.E., Instability of the interface of two gases accelerated by a shock wave. Soviet Fluid Dynamics, 4(5), pp. 101–104, 1969. [Crossref]
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Open Access
Research article

Instabilities in a Shock Interaction with a Perturbed Curtain of Particles

Ricardo Gonzalez Izard1,
Sumanth Reddy Lingampally1,
Patrick Wayne1,
Gustaaf Jacobs2,
Peter Vorobieff1
1
Department of Mechanical Engineering, The University of New Mexico, Albuquerque, NM, USA
2
Department of Aerospace Engineering, San Diego State University, San Diego, CA, USA
International Journal of Computational Methods and Experimental Measurements
|
Volume 6, Issue 1, 2018
|
Pages 59-70
Received: N/A,
Revised: N/A,
Accepted: N/A,
Available online: N/A
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Abstract:

We present a two-dimensional computational study of a shock interaction with a particle-seeded curtain where particles initially comprise 4% by volume, and the rest is air. If the initial depth of the curtain in the streamwise direction is variable, numerical results predict vortex formation in both the gas phase and the dispersed phase after the shock-curtain interaction. The phenomenon is distinct from baroclinic (Richtmyer–Meshkov) instability observed on gaseous density interfaces and is caused by the changes in the particle phase number density distribution and related interphase velocity changes.

Keywords: Baroclinicity, CFD, Particle-laden flow, Richtmyer–Meshkov instability, WENO-Z
References
[1] Rayleigh, L., Analytic solutions of the Rayleigh equation for linear density profiles. Proceedings of the London Mathematical Society, 14, pp. 170–177, 1883.
[2] Taylor, G., The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 201(1065),1 pp. 92–196, 1950. [Crossref]
[3] Richtmyer, R.D., Taylor instability in shock acceleration of compressible fluids. Communications on Pure and Applied Mathematics, 13(2), pp. 297–319, 1960. [Crossref]
[4] Markstein, G.H., Flow disturbances induced near a slightly wavy contact surface, or flame front, traversed by a shock wave, 1957.
[5] Meshkov, E.E., Instability of shock-accelerated interface between two media. Advances in Compressible Turbulent Mixing, 8810234:473, 1992.
[6] Balakrishnan, K., Ukai, S. & Menon, S., Clustering and combustion of dilute aluminum particle clouds in a post-detonation flow field. Proceedings of the Combustion Institute, 33(2), pp. 2255–2263, 2011. [Crossref]
[7] Jacobs, G.B. & Don, W-S., A high-order WENO-Z finite difference based particlesource-in-cell method for computation of particle-laden flows with shocks. Journal of Computational Physics, 228(5), pp. 1365–1379, 2009. [Crossref]
[8] Vorobieff, P., Anderson, M., Conroy, J., White, R., Truman, C.R. & Kumar, S., Analogues of Rayleigh-Taylor and Richtmyer-Meshkov instabilities in flows with nonuniform particle and droplet seeding. Computational Methods in Multiphase Flow VI, A. Mammoli, and C. Brebbia, eds., WIT Press, Ashurst, Southampton, UK, pp. 17–28, 2011.
[9] Vorobieff, P., Anderson, M., Conroy, J., White, R., Truman, C.R. & Kumar, S., Vortex formation in a shock-accelerated gas induced by particle seeding. Physical Review Letters, 106(18), p. 184503, 2011. [Crossref]
[10] Sharma, M.P. & Stock, D.E., The particle-source-in cell (PSI-CELL) model for gasdroplet flows. Journal of Fluids Engineering, 99(2), pp. 325, 1977. [Crossref]
[11] Boiko, V.M., Kiselev, V.P., Kiselev, S.P., Papyrin, A.N., Poplavsky, S.V. & Fomin, V.M., Shock wave interaction with a cloud of particles. Shock Waves, 7(5), pp. 275–285, 1997. [Crossref]
[12] Meshkov, E.E., Instability of the interface of two gases accelerated by a shock wave. Soviet Fluid Dynamics, 4(5), pp. 101–104, 1969. [Crossref]
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Izard, G. L., Lingampally, S. R., Wayne, P., Jacobs, G., & Vorobieff, P. (2018). Instabilities in a Shock Interaction with a Perturbed Curtain of Particles. Int. J. Comput. Methods Exp. Meas., 6(1), 59-70. https://doi.org/10.2495/CMEM-V6-N1-59-70
G. L. Izard, S. R. Lingampally, P. Wayne, G. Jacobs, and P. Vorobieff, "Instabilities in a Shock Interaction with a Perturbed Curtain of Particles," Int. J. Comput. Methods Exp. Meas., vol. 6, no. 1, pp. 59-70, 2018. https://doi.org/10.2495/CMEM-V6-N1-59-70
@research-article{Izard2018InstabilitiesIA,
title={Instabilities in a Shock Interaction with a Perturbed Curtain of Particles},
author={Ricardo Gonzalez Izard and Sumanth Reddy Lingampally and Patrick Wayne and Gustaaf Jacobs and Peter Vorobieff},
journal={International Journal of Computational Methods and Experimental Measurements},
year={2018},
page={59-70},
doi={https://doi.org/10.2495/CMEM-V6-N1-59-70}
}
Ricardo Gonzalez Izard, et al. "Instabilities in a Shock Interaction with a Perturbed Curtain of Particles." International Journal of Computational Methods and Experimental Measurements, v 6, pp 59-70. doi: https://doi.org/10.2495/CMEM-V6-N1-59-70
Ricardo Gonzalez Izard, Sumanth Reddy Lingampally, Patrick Wayne, Gustaaf Jacobs and Peter Vorobieff. "Instabilities in a Shock Interaction with a Perturbed Curtain of Particles." International Journal of Computational Methods and Experimental Measurements, 6, (2018): 59-70. doi: https://doi.org/10.2495/CMEM-V6-N1-59-70
LZARD G L， LINGAMPALLY S R， WAYNE P， et al. Instabilities in a Shock Interaction with a Perturbed Curtain of Particles[J]. International Journal of Computational Methods and Experimental Measurements， 2018， 6(1)： 59-70. https://doi.org/10.2495/CMEM-V6-N1-59-70