Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-27T06:11:17.068Z Has data issue: false hasContentIssue false
  • English
  • Français

High Order Numerical Simulation of Detonation Wave Propagation Through Complex Obstacles with the Inverse Lax-Wendroff Treatment

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Shock waves and blast waves

Published online by Cambridge University Press:  23 November 2015

Cheng Wang ,
Jianxu Ding ,
Sirui Tan  and
Wenhu Han
Cheng Wang*
Affiliation:
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, 100081, P.R. China
Jianxu Ding
Affiliation:
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, 100081, P.R. China
Sirui Tan
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
Wenhu Han
Affiliation:
Center for Combustion Energy, Tsinghua University, Beijing, 100084, P.R. China
*
*Corresponding author. Email address:[email protected] (C. Wang)
Get access

Abstract

The high order inverse Lax-Wendroff (ILW) procedure is extended to boundary treatment involving complex geometries on a Cartesian mesh. Our method ensures that the numerical resolution at the vicinity of the boundary and the inner domain keeps the fifth order accuracy for the system of the reactive Euler equations with the two-step reaction model. Shock wave propagation in a tube with an array of rectangular grooves is first numerically simulated by combining a fifth order weighted essentially non-oscillatory (WENO) scheme and the ILW boundary treatment. Compared with the experimental results, the ILW treatment accurately captures the evolution of shock wave during the interactions of the shock waves with the complex obstacles. Excellent agreement between our numerical results and the experimental ones further demonstrates the reliability and accuracy of the ILW treatment. Compared with the immersed boundary method (IBM), it is clear that the influence on pressure peaks in the reflected zone is obviously bigger than that in the diffracted zone. Furthermore, we also simulate the propagation process of detonation wave in a tube with three different widths of wall-mounted rectangular obstacles located on the lower wall. It is shown that the shock pressure along a horizontal line near the rectangular obstacles gradually decreases, and the detonation cellular size become large and irregular with the decrease of the obstacle width.

Keywords

Boundary treatmentdetonationinverse Lax-Wendrofftwo-step reaction modelWENO scheme.

MSC classification

Secondary: 65M06: Finite difference methods 76L05: Shock waves and blast waves
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 5 , November 2015 , pp. 1264 - 1281
Copyright
Copyright © Global-Science Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Bohachevsky, I. O., A direct method for computation of nonequilibrium flows with detached shock waves, AIAA, 4 (1966), 600–607.Google Scholar
[2]Moretti, G., Importance of boundary conditions in the numerical treatment of hyperbolic equations, Phys. Fluids, II (1969), 13–20.Google Scholar
[3]Peskin, C. S.Flow patterns around heart values, A numerical method, J. Comput. Phys., 10 (1972), 252–271.Google Scholar
[4]Sjögreen, B., Petersson, N., A Cartesian embedded boundary method for hyperbolic conservation laws, Commun. Comput. Phys., 2 (2007), 1199–1219.Google Scholar
[5]Chaudhuri, A., Hadjadj, A., Chinnayya, A., On the use of immersed boundary methods for shock/obstacle interactions, J. Comput. Phys., 230 (2011), 1731–1748.Google Scholar
[6]Farooq, M. A., Skien, A. A., Müller, B., Cartesian grid method for the compressible Euler equations using simplified ghost points treatments at embedded boundaries, Comput Fluids, 82 (2013), 50–62.Google Scholar
[7]Tan, S., Shu, C.-W., Inverse Lax-Wendroff procedure for numerical boundary conditions of conservation laws, J. Comput. Phys., 229 (2010), 8144–8166.Google Scholar
[8]Tan, S., Wang, C., Shu, C.-W., Ning, J., Efficient implementation of high order inverse Lax-Wendroff boundary treatment for conservation laws, J. Comput. Phys., 231 (2012), 2510–2517.Google Scholar
[9]Vilar, F., Shu, C.-W., Development and stability analysis of the inverse Lax-Wendroff boundary treatment for central compact schemes, Math. Model Num., 49 (2015), 39–67.Google Scholar
[10]Guo, C. M., Wang, C. J., Xu, S. L., Zhang, H. H., Cellular pattern evolution in gaseous detonation diffraction in a 90°-branched channel, Combust. Flame, 148 (2007), 89–99.Google Scholar
[11]Starr, A., Lee, J. H. S., Ng, H. D., Detonation limits in rough walled tubes, Proc. Combust. Inst., 35 (2015), 1989–1996.Google Scholar
[12]Zhu, C. J., Lin, B. Q., Ye, Q., Zhai, C., Effect of roadway turnings on gas explosion propagation characteristics in coal mines, J. China U. Min. Techno., 21 (2012), 365–369.Google Scholar
[13]Zhang, P. L., Du, Y., Zhou, Yi.et al., Explosions of gasoline-air mixture in the tunnels containing branch configuration, J. Loss. Prevent Proc., 26 (2013), 1279–1284.Google Scholar
[14]Frolov, S. M., Aksenov, V. S., Shamshin, I. O., Reactive shock and detonation propagation in U-bend tubes, J. Loss. Prevent Proc., 20 (2007), 501–508.CrossRefGoogle Scholar
[15]Hou, W., Qu, Z. M., Pian, L. J., Numerical simulation on propagation and attenuation of shock waves in simplex turn roadway during gas explosion, J. China Coal Soc., 3 (2009), 509–513.Google Scholar
[16]Wang, C., Ma, T. B., Lu, J., Influence of obstacle disturbance in a duct on explosion characteristics of coal gas, Sci. China Phys. Mech., 2 (2010), 269–278.Google Scholar
[17]Li, J., Ren, H. L., Ning, J. G., Numerical application of additive Runge-Kutta methods on detonation interaction with pipe bends, Int.J. Hydrogen Energ., 38 (2013), 9016–9027.CrossRefGoogle Scholar
[18]Taki, S., Fujiwara, T., Numeical analysis of two-dimensional nonsteady detonation, AIAA, 16 (1978), 73–77.Google Scholar
[19]Wang, C., Han, W. H., Ning, J. G., Design and development of dynamic parallel computing code for three-dimensional gaseous detonation, Chinese J. Comput. Mech., 29 (2012), 948–953.Google Scholar
[20]Jiang, G. S., Shu, C.-W., Efficient implementation of weighted ENO schemes, J. Comput. Phys., 126 (1996), 202–228.CrossRefGoogle Scholar
[21]Gongora-Orozco, N., Zare-Behtash, H., Kontis, K., Experimental Studies on Shock Wave Propagating Through Junction with Grooves, Proceedings of the 47th AIAA Aerospace Sciences Meeting Including New Horizons Forum and Aerospace Exposition, Florida, USA: American Institute of Aeronautics and Astronautics, 2009, 5–8.Google Scholar
[22]Bourlioux, A., Majda, A. J., Theoretical and numerical structure of unstable detonations, Philosophical Transactions of the Royal Society of London A, 350 (1995), 2968.Google Scholar
[23]Zhang, Z. C., Yu, S. T. J., He, H., Chang, S. C., Direct calculations of two- and three-dimensional detonations by an extended CE/SE method, AIAA, No. 2001-0476.Google Scholar