Skip to main content

Numerical investigation of shock wave attenuation in channels using water obstacles

Abstract

Here, short duration direct numerical simulations of shock water cylinder interaction in a two-dimensional channel are conducted to study shock wave attenuation at time scales smaller than the cylinder convection time. Four different cylinder configurations, i.e., 1 \(\times \) 1, 2 \(\times \) 2, 3 \(\times \) 3, and 4 \(\times \) 4, are considered, where the total volume of water is kept constant throughout all the cases. Meanwhile, the incident shock Mach number was varied from 1.1 to 1.4. The physical motion of the water cylinders is quantitatively studied. Results show that the center-of-mass velocity increases faster for the cases with more cylinders. In the early stage of breakup, the transfer rate of kinetic energy from the shock-induced flow to the water cylinders increases as the number of cylinders increases. Further, comparing the cases of different incident shock Mach numbers, higher center-of-mass velocity is induced for the cases of lower incident shock Mach numbers. Moreover, the pressure and impulse changes upstream and downstream of the cylinder matrices are tracked as a quantitative evaluation of the shock attenuation.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

References

  • Abgrall R, Karni S (2001) Computations of compressible multifluids. J Comput Phys 169(2):594–623

    MathSciNet  MATH  Article  Google Scholar 

  • Chaudhuri A, Hadjadj A, Sadot O, Ben-Dor G (2013) Numerical study of shock-wave mitigation through matrices of solid obstacles. Shock Waves 23(1):91–101

    Article  Google Scholar 

  • Chauvin A, Jourdan G, Daniel E, Houas L, Tosello R (2011) Experimental investigation of the propagation of a planar shock wave through a two-phase gas-liquid medium. Phys Fluids 23(11):113301

    Article  Google Scholar 

  • Chen H (2008) Two-dimensional simulation of stripping breakup of a water droplet. AIAA J 46(5):1135–1143

    Article  Google Scholar 

  • Cirak F, Deiterding R, Mauch S (2007) Large-scale fluid-structure interaction simulation of viscoplastic and fracturing thin-shells subjected to shocks and detonations. Comput Struct 85(11):1049–1065

    Article  Google Scholar 

  • Deiterding R (2005) An adaptive Cartesian detonation solver for fluid-structure interaction simulation on distributed memory computers. In: Parallel computational fluid dynamics-theory and application, Proc. Parallel CFD 2005 Conference, pp 333–340

  • Deiterding R (2009) A parallel adaptive method for simulating shock-induced combustion with detailed chemical kinetics in complex domains. Comput Struct 87(11):769–783

    Article  Google Scholar 

  • Deiterding R (2011) Block-structured adaptive mesh refinement-theory, implementation and application. ESAIM Proc 34:97–150

    MathSciNet  MATH  Article  Google Scholar 

  • Deiterding R, Cirak F, Mauch S (2009) Efficient fluid–structure interaction simulation of viscoplastic and fracturing thin-shells subjected to underwater shock loading. In: Hartmann S, Meister A, Schäfer M, Turek S (eds) International workshop on fluid–structure interaction, theory, numerics and applications

  • Flåtten T, Morin A, Munkefjord ST (2011) On solutions to equilibrium problems for systems of stiffened gases. SIAM J Appl Math 71(1):41–67

    MathSciNet  MATH  Article  Google Scholar 

  • Gelfand B (1996) Droplet breakup phenomena in flows with velocity lag. Prog Energy Combust Sci 22(3):201–265

    Article  Google Scholar 

  • Guildenbecher D, López-Rivera C, Sojka P (2009) Secondary atomization. Exp Fluids 46(3):371

    Article  Google Scholar 

  • Igra D, Takayama K (2001a) Numerical simulation of shock wave interaction with a water column. Shock Waves 11(3):219–228

    MATH  Article  Google Scholar 

  • Igra D, Takayama K (2001b) A study of shock wave loading on a cylindrical water column. Technical report, Report of the Institute of Fluid Science, Tohoku University

  • Igra D, Takayama K (2003) Experimental investigation of two cylindrical water columns subjected to planar shock wave loading. J Fluids Eng 125:325–331

    Article  Google Scholar 

  • Jourdan G, Biamino L, Mariani C, Blanchot C, Daniel E, Massoni J, Houas L, Tosello R, Praguine D (2010) Attenuation of a shock wave passing through a cloud of water droplets. Shock Waves 20(4):285–296

    MATH  Article  Google Scholar 

  • Kailasanath K, Tatem P, Mawhinney J (2002) Blast mitigation using water—a status report. Technical report, NRL/MR/6400-02-8606, US Naval Research Laboratory

  • LeVeque R (2002) Finite volume methods for hyperbolic problems. Cambridge University Press, Cambridge

    MATH  Book  Google Scholar 

  • Meng J, Colonius T (2015) Numerical simulations of the early stages of high-speed droplet breakup. Shock Waves 25(4):399–414

    Article  Google Scholar 

  • Nomura K, Koshizuka S, Oka Y, Obata H (2001) Numerical analysis of droplet breakup behavior using particle method. J Nucl Sci Technol 38(12):1057–1064

    Article  Google Scholar 

  • Perotti L, Deiterding R, Inaba K, Shepherd J, Ortiz M (2013) Elastic response of water-filled fiber composite tubes under shock wave loading. Int J Solids Struct 50(3):473–486

    Article  Google Scholar 

  • Pilch M, Erdman C (1987) Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop. Int J Multiph Flow 13(6):741–757

    Article  Google Scholar 

  • Ranger A, Nicholls J (1969) Aerodynamic shattering of liquid drops. AIAA J 7(2):285–290

    Article  Google Scholar 

  • Sembian S, Liverts M, Tillmark N, Apazidis N (2016) Plane shock wave interaction with a cylindrical water column. Phys Fluids 28(5):056102

    Article  Google Scholar 

  • Shin Y, Lee M, Lam K, Yeo K (1998) Modeling mitigation effects of watershield on shock waves. Shock Vib 5(4):225–234

    Article  Google Scholar 

  • Shyue K-M (1998) An efficient shock-capturing algorithm for compressible multicomponent problems. J Comput Phys 142(1):208–242

    MathSciNet  MATH  Article  Google Scholar 

  • Shyue K-M (2006) A volume-fraction based algorithm for hybrid barotropic and non-barotropic two-fluid flow problems. Shock Waves 15(6):407–423

    MATH  Article  Google Scholar 

  • Theofanous T (2011) Aerobreakup of newtonian and viscoelastic liquids. Annu Rev Fluid Mech 43:661–690

    MATH  Article  Google Scholar 

  • Toro E, Spruce M, Speares W (1994) Restoration of the contact surface in the HLL-Rriemann solver. Shock Waves 4(1):25–34

    MATH  Article  Google Scholar 

  • Wan Q, Eliasson V (2015) Numerical study of shock wave attenuation in two-dimensional ducts using solid obstacles: how to utilize shock focusing techniques to attenuate shock waves. Aerospace 2(2):203–221

    Article  Google Scholar 

  • Wan Q, Jeon H, Deiterding R, Eliasson V (2017) Numerical and experimental investigation of oblique shock wave reflection off a water wedge. J Fluid Mech 826:732–758

    MathSciNet  Article  Google Scholar 

  • Wierzba A, Takayama K (1988) Experimental investigation of the aerodynamic breakup of liquid drops. AIAA J 26(11):1329–1335

    Article  Google Scholar 

  • Yoshida T, Takayama K (1990) Interaction of liquid droplets with planar shock waves. J Fluids Eng 112(4):481–486

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the High Performance Computing Center at University of Southern California for providing free access to computing resources.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Veronica Eliasson.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This study was supported by the National Science Foundation (NSF) under Grant no. CBET-1437412.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Wan, Q., Deiterding, R. & Eliasson, V. Numerical investigation of shock wave attenuation in channels using water obstacles. Multiscale and Multidiscip. Model. Exp. and Des. 2, 159–173 (2019). https://doi.org/10.1007/s41939-018-00041-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41939-018-00041-y

Keywords

  • Shock–water interaction
  • Multi-phase flow
  • Shock attenuation
  • Impulse