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A simple constitutive model for predicting the pressure histories developed behind rigid porous media impinged by shock waves

Published online by Cambridge University Press:  08 February 2013

O. Ram  and
O. Sadot
O. Ram
Affiliation:
Pearlstone Center for Aeronautical Engineering Studies, Protective Technologies R&D Center, Department of Mechanical Engineering, Ben-Gurion University of the Negev, 84105 Beer Sheva, Israel
O. Sadot*
Affiliation:
Pearlstone Center for Aeronautical Engineering Studies, Protective Technologies R&D Center, Department of Mechanical Engineering, Ben-Gurion University of the Negev, 84105 Beer Sheva, Israel
*
†Email address for correspondence: [email protected]
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Abstract

Shock wave attenuation by means of rigid porous media is often applied when protective structures are dealt with. The passage of a shock wave through a layer of porous medium is accompanied by diffractions and viscous effects that attenuate and weaken the transmitted shock, thus reducing the load that develops on the target wall that is placed behind the protective layer. In the present study, the parameters governing the pressure build-up on the target wall are experimentally investigated using a shock tube facility. Different porous samples are impinged by normal shock waves of various strengths and the subsequent pressure histories that are developed on the target wall are recorded. In addition, different standoff distances from the target wall are investigated. Assuming that the flow through the porous medium is close to being isentropic enabled us to develop a general constitutive model for predicting the pressure history developed on the target wall. This model can be applied to predict the pressure build-up on the target wall for any pressure history that is imposed on the front face of the porous sample without the need to conduct numerous experiments. Results obtained by other investigators are found to be in very good agreement with the predictions of the presently developed constitutive model.

JFM classification

Compressible Flows: Compressible Flows Complex Fluids: Foams Compressible Flows: Shock waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 718 , 10 March 2013 , pp. 507 - 523
Copyright
©2013 Cambridge University Press

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References

Andreopoulos, Y., Xanthos, S. & Subramaniam, K. 2007 Moving shocks through metallic grids: their interaction and potential for blast wave mitigation. Shock Waves 16, 455–466.Google Scholar
Bachmat, Y. & Bear, J. 1986 Macroscopic modelling of transport phenomena in porous media. 1: The continuum approach. Transp. Porous Med. 1, 213–240.CrossRefGoogle Scholar
Baer, M. R. 1992 A numerical study of shock wave reflections on low density foam. Shock Waves 2, 121–124.Google Scholar
Ben-Dor, G, Britan, A., Elprin, T., Igra, O. & Jiang, J. P. 1997 Experimental investigation of the interaction between weak shock waves and granular layers. Exp. Fluids 22, 432–443.Google Scholar
Biot, M. A. 1941 General theory of three-dimensional consolidation. J. Appl. Phys. 12, 155–164.Google Scholar
Britan, A. & Ben-Dor, G. 2006 Shock tube study of the dynamical behaviour of granular materials. Intl J. Multiphase Flow 32, 623–642.Google Scholar
Britan, A., Ben-Dor, G., Elperin, T., Igra, O. & Jiang, J. P. 1997a Mechanism of compressive stress formation during weak shock waves impact with granular layer. Exp. Fluids 22, 507–518.Google Scholar
Britan, A., Ben-Dor, G., Igra, O. & Shapiro, H. 2001 Shock waves attenuation by granular filters. Intl J. Multiphase Flow 27, 617–634.CrossRefGoogle Scholar
Britan, A., Igra, O., Ben-Dor, G. & Shapiro, H. 2006 Shock wave attenuation by grids and orifice plates. Shock Waves 16 (10), 1–15.Google Scholar
Britan, A., Jiang, J. P., Igra, O., Elperin, T. & Ben-Dor, G. 1997b Gas filtration during the impact on weak shock waves on granular layers. Intl J. Multiphase Flow 23 (3), 473–491.Google Scholar
Britan, A., Shapiro, H. & Ben-Dor, G. 2007 The contribution of shock tubes to simplified analysis of gas filtration through granular media. J. Fluid Mech. 586, 147–176.Google Scholar
Dutton, J. C. & Coverdill, R. E. 1997 Experiments to study the gaseous discharge and filling of vessels. Intl J. Engng Ed. 13 (2), 123–134.Google Scholar
Gibson, L. & Ashby, H. 1988 Cellular Solids: Structure and Properties. Pergamon.Google Scholar
Hattingh, T. S. & Skews, B. W. 2001 Experimental investigation of the interaction of shock waves with textiles. Shock Waves 11, 115–123.Google Scholar
Kazemi-Kamyab, V., Subramaniam, K. & Andreopoulos, Y. 2011 Stress transmission in porous materials impacted by shock waves. J. Appl. Phys. 109, 013523.Google Scholar
Kitagawa, K., Yasuhara, M. & Takayama, K. 2006 Attenuation of shock waves propagating in polyurethane foams. Shock Waves 15, 437–445.CrossRefGoogle Scholar
Levi-Hevroni, D., Levy, A., Ben-Dor, G. & Sorek, S. 2002 Numerical investigation of the propagation of planar shock waves in saturated flexible porous materials: development of the computer code and comparison with experimental results. J. Fluid Mech. 462, 285–306.Google Scholar
Levi-Hevroni, D., Levy, A., Ben-Dor, G. & Sorek, S. 2006 The interaction of planar shock waves with multiphase saturated flexible porous materials – a numerical investigation. J. Fluid Mech. 563, 159–188.CrossRefGoogle Scholar
Levy, A., Ben-Dor, G., Skews, B. W. & Sorek, S. 1993 Head-on collision of normal shock waves with rigid porous materials. Exp. Fluids 15, 183–190.Google Scholar
Levy, A., Ben-Dor, G. & Sorek, S. 1996a Numerical investigation of the propagation of shock waves in rigid porous materials: development of the computer code and comparison with experimental results. J. Fluid Mech. 324, 163–179.CrossRefGoogle Scholar
Levy, A., Ben-Dor, G. & Sorek, S. 1998 Numerical investigation of the propagation of shock waves in rigid porous materials: flow field behaviour and parametric study. Shock Waves 8 (3), 127–137.CrossRefGoogle Scholar
Levy, A., Levy-Hevroni, D., Sorek, S. & Ben-Dor, G. 1999 Derivation of Forchheimer terms: application to compaction waves propagation in porous media. Intl J. Multiphase Flow 25, 683–704.Google Scholar
Levy, A., Sorek, S., Ben-Dor, G. & Skews, B. W. 1996b Wave propagation in saturated rigid porous media: analytical model and comparison with experimental results. Fluid Dyn. Res. 17, 49–65.Google Scholar
Li, H., Levy, A. & Ben-Dor, G. 1995 Head-on interaction of planar shock waves with ideal rigid open-cell porous materials – analytical model. Fluid Dyn. Res. 16 (4), 203–215.Google Scholar
Mazor, G., Ben-Dor, G., Igra, O & Sorek, S. 1994a Shock wave interaction with cellular materials. I. Analytical investigation and governing equations. Shock Waves 3 (3), 159–165.Google Scholar
Mazor, G., Ben-Dor, G., Igra, O., Sorek, S. & Onodera, H. 1994b. Shock wave interaction with cellular materials: II. Open cell foams: experimental and numerical results. Shock Waves 3 (3), 167–179.Google Scholar
Seeraj, S. & Skews, B. W. 2009 Dual-element directional shock wave attenuators. Exp. Therm. Fluid Sci. 33, 503–516.Google Scholar
Seitz, M. W. & Skews, B. W. 2006 Effect of compressible foam properties on pressure amplification during shock wave impact. Shock Waves 15, 177–197.Google Scholar
Seitz, M. W. & Skews, B. W. 1996 Shock impact on porous plugs with a fixed gap between the plug and a wall. In Proceedings of the 20th International Symposium on Shock Waves (ed. Sturtevant, B., Shepherd, J. E. & Hornung, H. G.). pp. 1381–1386. World Scientific.Google Scholar
Shapiro, A. H. 1953 The Dynamics and Thermodynamics of Compressible Fluid Flow. Wiley.Google Scholar
Skews, B. W. 1991 The reflected pressure field in the interaction of weak shock waves with a compressible foam. Shock Waves 1, 205–211.CrossRefGoogle Scholar
Sorek, S., Levi-Hevroni, D., Levy, A. & Ben-Dor, G. 2005 Extensions to the macroscopic Navier–Stokes equation. Transp. Porous Med. 61, 215–223.Google Scholar