Transverse waves in numerical simulations of cellular detonations

In this paper the structure of strong transverse waves in two-dimensional numerical simulations of cellular detonations is investigated. Resolution studies are performed and it is shown that much higher resolutions than those generally used are required to ensure that the flow and burning structures are well resolved. Resolutions of less than about 20 numerical points in the characteristic reaction length of the underlying steady detonation give very poor predictions of the shock configurations and burning, with the solution quickly worsening as the resolution drops. It is very difficult and dangerous to attempt to identify the physical structure, evolution and effect on the burning of the transverse waves using such under-resolved calculations. The process of transverse wave and triple point collision and reflection is then examined in a very high-resolution simulation. During the reflection, the slip line and interior triple point associated with the double Mach configuration of strong transverse waves become detached from the front and recede from it, producing a pocket of unburnt gas. The interaction of a forward facing jet of exploding gas with the emerging Mach stem produces a new double Mach configuration. The formation of this new Mach configuration is very similar to that of double Mach reflection of an inert shock wave reflecting from a wedge.

[1]  Andrew J. Majda,et al.  Theoretical and numerical structure for unstable two-dimensional detonations , 1992 .

[2]  James J. Quirk,et al.  Godunov-Type Schemes Applied to Detonation Flows , 1994 .

[3]  I. I. Glass,et al.  A numerical study of oblique shock-wave reflections with experimental comparisons , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[4]  G. Sharpe,et al.  One-dimensional numerical simulations of idealized detonations , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[5]  F. Sharpe,et al.  Two-dimensional numerical simulations of idealized detonations , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[6]  S. Falle.  Self-similar jets , 1991 .

[7]  E. S. Oran,et al.  Analysis of the shock structures in a regular detonation , 1995 .

[8]  John H. S. Lee,et al.  Dynamic Parameters of Gaseous Detonations , 1984 .

[9]  G. Sharpe,et al.  Numerical simulations of pulsating detonations: I. Nonlinear stability of steady detonations , 2000 .

[10]  M. Lefebvre,et al.  Experiments on spinning detonations with detailed analysis of the shock structure , 2000 .

[11]  Gary J. Sharpe,et al.  Linear stability of idealized detonations , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[12]  Elaine S. Oran,et al.  A study of detonation structure: The formation ofunreacted gas pockets , 1982 .

[13]  V. Subbotin.  Two kinds of transverse wave structures in multifront detonation , 1975 .

[14]  J. Dold,et al.  Comparison between shock initiations of detonation using thermally-sensitive and chain-branching chemical models , 1991 .

[15]  Mark Short,et al.  On the nonlinear stability and detonability limit of a detonation wave for a model three-step chain-branching reaction , 1997, Journal of Fluid Mechanics.

[16]  J. Quirk.  A Contribution to the Great Riemann Solver Debate , 1994 .