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The contribution of shock tubes to simplified analysis of gas filtration through granular media

Published online by Cambridge University Press:  14 August 2007

A. BRITAN ,
H. SHAPIRO  and
G. BEN-DOR
A. BRITAN
Affiliation:
Pearlstone Center for Aeronautical Engineering Studies, Protective Technologies R&D Center, Department of Mechanical Engineering, Faculty of Engineering Sciences, Ben-Gurion University of the Negev, Beer-Sheva, Israel
H. SHAPIRO
Affiliation:
Pearlstone Center for Aeronautical Engineering Studies, Protective Technologies R&D Center, Department of Mechanical Engineering, Faculty of Engineering Sciences, Ben-Gurion University of the Negev, Beer-Sheva, Israel
G. BEN-DOR
Affiliation:
Pearlstone Center for Aeronautical Engineering Studies, Protective Technologies R&D Center, Department of Mechanical Engineering, Faculty of Engineering Sciences, Ben-Gurion University of the Negev, Beer-Sheva, Israel
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Abstract

A hybrid method for the problem of transient shock-induced filtration of the gas flow through granular media is developed. The hybrid method combines a controlled shock-tube test and Morrison's simplified approach to the problem of gas filtration. It is demonstrated that most pressure traces that have been recorded in various laboratories with a large variety of granular material samples and under different conditions are limited to situations in which the pressure losses in the flow are dominated by the Forchheimer mechanism. The hybrid method enables these results to be described by a single, universal pressure curve, and specification of the Forchheimer coefficient which is one of the two key parameters responsible for the correct simulation of the filtration-flow behaviour. The second key parameter, the Darcy coefficient, cannot be evaluated by the available experimental results. To overcome this shortcoming, a new controlled laboratory test that provides a wider range of the flow conditions, from the Forchheimer to the developed mixed flow, was conducted. In turn, a comprehensive gas dynamic analysis of the transient flow inside the shock tube enables us to define, from the single controlled laboratory test, the two coefficients of the Forchheimer resistance law, a and b.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 586 , 10 September 2007 , pp. 147 - 176
Copyright
Copyright © Cambridge University Press 2007

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References

Antohe, B. V., Lage, J. L., Price, D. C. & Weber, R. M. 1997 Experimental determination of permeability and inertia coefficients of mechanically compressed aluminum porous matrices. Trans. ASME: J. Fluids Engng 119, 404–412.Google Scholar
Asay, B. W., Son, S. F. & Bdzil, J. B. 1996 The role of gas permeation in convective burning. Intl J. Multiphase Flow 22, 923–952.CrossRefGoogle Scholar
Britan, A., Ben-Dor, G., Elperin, T., Igra, O. & Jiang, J. P. 1997 Gas filtration during the impact of weak shock waves on granular columns. Intl J. Multiphase Flow 23, 473–491.CrossRefGoogle Scholar
Britan, A., Ben-Dor, G., Igra, O. & Shapiro, H. 2001 a Shock waves attenuation by granular filters. Intl J. Multiphase Flow 27, 617–634.CrossRefGoogle Scholar
Britan, A., Ben-Dor, G., Igra, O. & Shapiro, H. 2006 Development of a general approach for predicting the pressure fields of unsteady gas flows through granular media. J. Appl. Phys. 99 (9), 093519.CrossRefGoogle Scholar
Britan, A., Ben-Dor, G. & Shapiro, H. 2001 b Numerical and analytical investigations of the head-on interaction of shock waves with granular layers. In Proc. 23rd Intl Symp. Shock Waves, Univ. Texas, Arlington, USA, p. 210.Google Scholar
Britan, A. & Levy, A. 2001 Weak shock wave interaction with inert granular media. In Handbook of Shock Waves (ed. Ben-Dor, G., Igra, O. & Elperin, T.), vol. 2, pp. 597–666. Academic.CrossRefGoogle Scholar
Britan, A., Vasiliev, E. I. & Zinovik, I. 1992 a Reflection of a blast profile shock wave from the end-wall of a shock tube. Fluid Dyn. USSR 3, 412–417.Google Scholar
Britan, A., Vasiliev, E. I. Zinovik, I. & Kaminin, I. 1992 b Reflection of blast-profile shock wave from the end wall of a shock tube. Fluid Dyn. 3, 412–417.Google Scholar
Engebretsen, T., Bakken, J., Hansen, E. W. M. & Lysberg, I. 1996 Shock waves and gas flow through granular materials. In Proc. Workshop Explosion Effects in Granular Materials (ed. Jenssen, A., Langberg, H. & Madshus, C.), Oslo, Norway, pp. 111–131.Google Scholar
Ergun, S. 1952 Fluid flow through packed columns. Chem. Engng Prog 48, 89–73.Google Scholar
Gelfand, B. E., Medvedev, S. P., Borisov, A. A., Polenov, A. N., Frolov, S. M. & Tsyganov, S. A. 1989 Shock loading of stratified dusty system. Combustion 9, 153–165.Google Scholar
van der Grinten, J. G. M., van Dongen, M. E. H. & van der Kogel, H. 1985 A shock-tube technique for studying pore-pressure propagation in dry and water-saturated porous medium. J. Appl. Phys. 58, 2937–2942.CrossRefGoogle Scholar
Holman, J. P. 1994 Experimental Methods for Engineers, 6th Edn. McGraw-Hill.Google Scholar
Lage, J. L. 1998 The fundamental theory of flow through permeable media. From Darcy to turbulence. In Transport Phenomena in Porous Media (ed. Ingham, D. B. & Pop, I.), pp. 1–30. Pergamon.Google Scholar
Lage, J. L. & Antohe, B. V. 2000 Darcy's experiments and the deviation to nonlinear flow regime. Trans. ASME. J. Fluids Engng 122, 619–625.CrossRefGoogle Scholar
Levy, A. 1999 Shock wave interaction with granular materials. Powder Tech. 103, 212–219.CrossRefGoogle Scholar
Levy, A., Ben Dor, G. & Sorek, S. 1993 Head on collision of normal shock waves with rigid porous materials. Exps. Fluids 15, 183–190.CrossRefGoogle Scholar
Levy, A., Ben Dor, G. & Sorek, S. 1996 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
Levi, A., Levi-Hevroni, D., Sorek, S. & Ben-Dor, G. 1999 Derivation of Forchheimer terms and their verification by application to waves propagation in porous media. Intl J. Multiphase Flow 25, 683–704.CrossRefGoogle Scholar
Liang, S-F. & Chao, Z. 1998 Principles of Gas-Solid Flows. Cambridge University Press.Google Scholar
Macdonald, M. S., El-Sayed, M. S., Mourg, K. & Dullien, F. A. L. 1979 Flow-through porous media – the Ergun equation revisited. Ind. Engng Chem. Fundam. 18, 199–208.CrossRefGoogle Scholar
Medvedev, S. P., Frolov, S. M. & Gelfand, B. E. 1990 Shock wave attenuation by screens composed of granular materials. Engng Phys. J. (USSR), 55 (6), 924–928 (in Russian).Google Scholar
Mikami, H., Kanada, T., Sakumara, Y. & Susuki, T. 2001 Pressure waves in a shock loaded dust layer. In Proc. 23rd Intl Symp. Shock Waves, Univ. Texas, Arlington, USA, pp. 834–840.Google Scholar
Morrison, F. A. 1972 Transient gas flow in a porous column. Ind. Engng Chem. Fundam. 11 (2), 191–197.CrossRefGoogle Scholar
Morrison, F. A. 1976 Similarity in transient high-speed gas flow through porous media. Trans. ASME: J. Fluids Engng 8, 567–568.Google Scholar
Morrison, F. A. 1977 Transient non-Darcy gas flow in a finite porous bed. Trans. ASME: J. Fluids Engng 12, 779–781.Google Scholar
Nishida, M. 2001 Shock Tubes. In Handbook of Shock Waves (ed. Ben-Dor, G., Igra, O. & Elperin, T.), vol. 1, pp. 553–585. Academic.CrossRefGoogle Scholar
Rogg, B., Hermann, D. & Adomeit, G. 1985 Shock induced flow in regular arrays of cylinders and packed beds. Intl J. Heat Mass Transfer 28, 2285–2287.CrossRefGoogle Scholar
Sakakita, H. & Hayashi, K. 1992 Study on pressure profiles in a powder layer using a vertical shock tube. In Proc. Natl Symp. On Shock Waves 92, Japan, pp. 655–660.Google Scholar
Sen, S., Mohan, T. R. K., Visco, D. P., Swaminathan, S., Sokolow, A., Avanos, E. & Nakagawa, M. 2005 Using mechanical energy as a probe for the detection and imaging of shallow buried inclusions in dry granular beds. Intl J. Mod. Phys. B19 (18), 2951–2974.CrossRefGoogle Scholar
Smeulders, D. M. J., van Dongen, M. E. H. & Wisse, C. J. 1997 Acoustic slow wave transition in air-saturated porous media. Proc. 21st Intl Symp. Shock Waves, Great Keppel Island, Australia, Paper 6911.Google Scholar
Sodre, J. & Parise, J. 1998 Fluid flow pressure drop through an annular bed of spheres with wall effects. Expl Thermal Fluid Sci. 17, 265–275.CrossRefGoogle Scholar