Abstract
The problem of planar shock wave–dense particle cloud interaction is solved using two approaches. In the first one, the two-dimensional gas dynamics modeling of the interaction of the planar shock wave with Mach number 1.67 with the set of cylinders is carried out. The original author’s numerical algorithm of the Cartesian grid method is used. The set of cylinders models the dense particles cloud with the volume fraction 0.15. As a result of interaction, the collective reflected and transmitted waves are formed. In the second approach, the one-dimensional system of equations for the description of the dense two-phase flows is solved. Results of one-dimensional modeling are matched with the cross-section averaged pressure distribution from the two-dimensional calculation. The quantitative agreement is achieved. The specific features of the process are discussed. We formulate the idea of complex approach to the investigation of the shock wave–dense particle cloud interaction that is based on the getting of the drag coefficient of the particles bed from the results of the multidimensional calculations and the comparison of those results with the calculation using the two-phase model.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
J.D. Regele, J. Rabinovitch, T. Colonius, G. Blanquart, Int. J. Multiphase Flow 61, 1 (2014)
V.M. Boiko, V.P. Kiselev, S.P. Kiselev, A.N. Papyrin, S.V. Poplavsky, V.M. Fomin, Shock Waves 7, 275 (1997)
S.N. Medvedev, S.M. Frolov, B.E. Gel’fand, J. Phys. Eng. 58, 924 (1990)
R.W. Houim, E.S. Oran, J. Fluid Mech. 789, 166 (2016)
T.P. McGrath II, J.G.St. Clair, S. Balachandar, J. Appl. Phys. 119, Paper 174903 (2016)
I.A. Bedarev, A.V. Fedorov, V.M. Fomin, Comb., Expl. Shock Waves. 48, 446 (2012)
I.A. Bedarev, A.V. Fedorov, J. Appl. Mech. Tech. Phys. 56, 750 (2015)
M. Berger, C. Helzel, SIAM J. Sci. Comp. 34, A861 (2012)
R. Saurel, R. Abgrall, J. Comput. Phys. 150, 425 (1999)
D.A. Sidorenko, P.S. Utkin, Num. Meth. Programm. 17, 353 (2016)
E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, 3rd ed. (Springer, 2009)
Y.-X. Ren, Comput. Fluids 32, 1379 (2003)
H.M. Glaz, P. Colella, I.I. Glass, R.L. Deschambault, Proc. Royal Soc. London A. 298, 117 (1985)
K. Takayama, K. Itoh, Proc. 15th Int. Symp. on Shock Waves and Shock Tubes 439 (1985)
Y. Tanino, H.M. Nepf, J. Hydraul. Eng. 134, 34 (2008)
S. Ergun, Chem. Eng. Prog. 48, 89 (1952)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Sidorenko, D., Utkin, P. (2019). To the Complex Approach to the Numerical Investigation of the Shock Wave: Dense Particle Bed Interaction. In: Sasoh, A., Aoki, T., Katayama, M. (eds) 31st International Symposium on Shock Waves 2. ISSW 2017. Springer, Cham. https://doi.org/10.1007/978-3-319-91017-8_82
Download citation
DOI: https://doi.org/10.1007/978-3-319-91017-8_82
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-91016-1
Online ISBN: 978-3-319-91017-8
eBook Packages: EngineeringEngineering (R0)