Abstract
In this paper, we combine the pseudo arc-length numerical method with the mathematical model of multiphase compressible flow for simulating the shock wave interaction with a deformable particle. Firstly, an arc-length parameter is introduced to weaken the discontinuous singularity of governing equations, and an efficient pseudo arc-length numerical method of multiphase compressible flow is proposed. Then the accuracy and adaptive moving mesh property of this algorithm are tested. Finally, the multiphase pseudo arc-length numerical method is applied to the problem of interaction between shock wave and the deformable particle. Through the flow flied change and data analysis of key points, it can be found the complex wave structures are presented after the interactions between the planar incident shock wave and the metal particle, and all these wave interactions lead to the movement and deformation of metal particle, and then the deformed particle will affect the transmitted shock wave back. According to the discussion, the deformation of particle and shock wave propagation in the particle are determined by the shock wave impedance of each medium and shock speed, so the interaction between shock wave and the deformable particle can be studied on the basis of physical properties of explosive mediums.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Frost D L, Ornthanalai C, Zarei Z, et al. Particle momentum effects from the detonation of heterogeneous explosives. J Appl Phys, 2007, 101: 113529
Lee J H S. The Detonation Phenomenon. New York: Cambridge University Press, 2008
Baer M, Nunziato J. A two-phase mixture theory for the deflagrationto- detonation transition (DDT) in reactive granular materials. Int J Multiphase Flow, 1986, 12: 861–889
Ripley R C. Acceleration and heating of metal particles in condensed matter detonation. Dissertation of Doctor Degree. Waterloo: University of Waterloo, 2010
Ning J G, Liu H F, Shang L. Dynamic mechanical behavior and the constitutive model of concrete subjected to impact loadings. Sci China Ser G Phys Mech Astron, 2008, 51: 1745–1760
Ning J G, Chen L W. Fuzzy interface treatment in Eulerian method. Sci China Ser E Tech Sci, 2004, 47: 550–568
Britan A, Elperin T, Igra O, et al. Acceleration of a sphere behind planar shock waves. Exp Fluids, 1995, 20: 84–90
Parmar M, Haselbacher A, Balachandar S. Improved drag correlation for spheres and application to shock-tube experiments. AIAA J, 2010, 48: 1273–1276
Ripley R C, Zhang F, Lien F S. Shock interaction of metal particles in condensed explosive detonation. AIP Conf Proc, 2006, 845: 499–502
Sun Q, Li Y H, Cui W, et al. Shock wave-boundary layer interactions control by plasma aerodynamic actuation. Sci China Tech Sci, 2014, 55: 1335–1341
Ling Y, Haselbacher A, Balachandar S, et al. Shock interaction with a deformable particle: Direct numerical simulation and point-particle modeling. J Appl Phys, 2013, 113: 013504
Li J, Ren H L, Ning J G. Additive Runge-Kutta methods for H2/O2/Ar detonation with a detailed elementary chemical reaction model. Chin Sci Bull, 2013, 58: 1216–1227
Wang X, Ma T B, Ning J G. A pseudo arc-length method numerical simulation of shock wave. Chin Phys Lett, 2014, 31: 030201
Wang X, Ma T B, Ren H L, et al. A local pseudo arc-length method for hyperbolic conservation laws. Acta Mech Sinica, 2014, 30: 956–965
Riks E. An incremental approach to the solution of snapping and buckling problems. Int J Solids Struct, 1979, 15: 529–551
Crisfield M S. A fast incremental iterative solution procedure that handles ‘snap through’. Comput Struct, 1981, 13: 55–62
Wu J K, Hui W H, Ding H L. A kind of arc-length method for ordinary differential equations. Commun Nonlinear Sci, 1997, 2: 145–150
Abgrall R. How to prevent pressure oscillations in multicomponent flow calculations: A quasi conservative approach. J Comput Phys, 1996, 125: 150–160
Shyue K M. A high-resolution mapped grid algorithm for compressible multiphase flow problems. J Comput Phys, 2010, 229: 8780–8801
Menikoff R, Plohr B J. The Riemann problem for fluid flow of real materials. Rev Mod Phys, 1989, 61: 75–130
Van L B. Towards the ultimate conservative difference scheme: A second order sequel to Godunov’s method. J Comput Phys, 1979, 32: 101–132
Jiang G S, Shu C W. Efficient implementation of weighted ENO schemes. J Comput Phys, 1996, 126: 202–228
Ling Y, Wagner J L, Beresh S J, et al. Interaction of a planar shock wave with a dense particle curtain: Modeling and experiments. Phys Fluids, 2012, 24: 113301
Layes G, Jourdan G, Houas L. Distortion of a spherical gaseous interface accelerated by a plane shock wave. Phys Rev Lett, 2003, 91: 174502
Wu M, Sun Z F, Zhang L M, et al. The effects of shock wave and quasi-traveling wave in the mechanical impact test. Sci China Tech Sci, 2010, 53: 2528–2534
Henderson L F. On the refraction of shock waves. J Fluid Mech, 1989, 198: 365–386
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ning, J., Wang, X., Ma, T. et al. Numerical simulation of shock wave interaction with a deformable particle based on the pseudo arc-length method. Sci. China Technol. Sci. 58, 848–857 (2015). https://doi.org/10.1007/s11431-015-5800-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11431-015-5800-9