Abstract
Numerical simulations of detonations in cylindrical rate-sticks of highly non-ideal explosives are performed, using a simple model with a weakly pressure-dependent rate law and a pseudo-polytropic equation of state. Some numerical issues with such simulations are investigated, and it is shown that very high resolution (hundreds of points in the reaction zone) are required for highly accurate (converged) solutions. High-resolution simulations are then used to investigate thequalitative dependences of the detonation driving zone structure on the diameter and degree of confinement of the explosive charge. The simulation results are used to show that, given the radius of curvature of the shock at the charge axis, the steady detonation speed and the axial solution are accurately predicted by a quasi-one-dimensional theory, even for cases where the detonation propagates at speeds significantly below the Chapman-Jouguet speed. Given reaction rate and equation of state models, this quasi-one-dimensional theory offers a significant improvement to Wood-Kirkwood theories currently used in industry
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
I.J. Kirby G.A. Leiper (1985) A small divergent detonation theory for intermolecular explosives In: 8th Symp (Int) on Detonation. Office of Naval Research Arlington 176–186
Howard W.M., Fried L.E., Souers P.C., Vitello P.A. (2001). Calculation of chemical detonation waves with hydrodynamics and a thermochemical equation of state. In: Furnish M.D., Thadhani N.N., Horie Y. (eds), Shock Compression of Condensed Matter. American institute of Physics pp. 161–164.
W.W. Wood J.G. Kirkwood (1954) ArticleTitleDiameter effect in condensed explosives - the relation between velocity and radius of curvature of the detonation wave J. Chem. Phys. 22 1920–1924 Occurrence Handle10.1063/1.1739940
J.B. Bdzil (1981) ArticleTitleSteady-state two-dimensional detonation J. Fluid Mech. 108 195–266
J.B. Bdzil T.D. Aslam (2000) Detonation front models: theories and methods Los Alamos National Laboratory Report LA-UR-02-942 Los Alamos 51
J.B. Bdzil W. Ficket D.S. Stewart (1989) Detonation shock dynamics: a new approach to modeling multi-dimensional detonation waves In: 9th Symp (Int) on Detonation. Office of Naval Research Arlington 730–742
G.J. Sharpe (2000) ArticleTitleThe effect of curvature on pathological detonations Combust. Flame 123 68–81 Occurrence Handle10.1016/S0010-2180(00)00156-5
G.J. Sharpe (2000) ArticleTitleThe structure of planar and curved detonation waves with reversible reactions Phys. Fluids 12 3007–3020 Occurrence Handle10.1063/1.1313389
Aslam T.D., Bdzil J.B. Numerical and theoretical investigations on detonation-inert confinement interactions. In: 12th Symp. (Int.) on Detonation. Arlington: Office of Naval Research (2002) in print.
Hill L.G., Bdzil J.B., Aslam T.D. Front curvature rate stick measurements and detonation shock dynamics calibration for PBX 9502 over a wide temperature range. In: 11th Symp. (Int.) on Detonation. Arlington: Office of Naval Research (1998) pp. 1029–1037.
D.L. Kennedy, Multi-valued normal shock velocity versus curvature relationships for highly non-ideal explosives. In: 11th Symp. (Int.) on Detonation. Arlington: Office of Naval Research (1998) pp. 181–192.
L.G. Hill, J.B. Bdzil, W.C. Davis and R. Engelke, Front curvature analysis and detonation shock dynamics calibration fro pure and sensitized nitromethane. In: M.D. Furnish, L.C. Chhabildas and R.S. Hixson (eds), Shock Compression of Condensed Matter. American institute of Physics (1999) pp. 813–816.
T.D. Aslam, J.B. Bdzil and L.G. Hill, Extensions to DSD theory: analysis of PBX 9502 rate stick data. In: 11th Symp. (Int.) on Detonation. Arlington: Office of Naval Research (1998) pp. 21–29.
R.A. Catanach and L.G. Hill, Diameter effect curve and detonation curvature measurements for ANFO. In: M.D. Furnish, N.N. Thadhani and Y. Horie (eds), Shock Compression of Condensed Matter, American institute of Physics (2001) pp. 906–909.
J.B. Bdzil, T.D. Aslam, R.A. Catanach, L.G. Hill and M. Short, DSD front models: non-ideal explosive detonation in ANFO. Los Alamos: Los Alamos National Laboratory Report LA-UR-02-4332 (2002) 11 pp.
D.S. Stewart J. Bdzil (1988) ArticleTitleThe shock dynamics of stable multidimensional detonation Combust Flame 72 311–323 Occurrence Handle10.1016/0010-2180(88)90130-7
P.C. Souers R. Garza P. Vitello (2002) ArticleTitleIgnition and growth and JWL++ detonation models in coarse zones Propell., Expl., Pyrotech. 27 62–71
V.N. Gamezo E.S. Oran (1997) ArticleTitleReaction-zone structure of a steady-state detonation wave in a cylindrical charge Combust. Flame 109 253–265 Occurrence Handle10.1016/S0010-2180(96)00154-X
J.F. Clarke S. Karni J.J. Quirk P.L. Roe L.G. Simmonds E.F. Toro (1993) ArticleTitleNumerical computation of two-dimensional unsteady detonation waves in high energy solids J. Comp. Phys. 106 215–233
T.L. Freeman I. Gladwell M. Braithwaite W. Byers Brown P.M. Lynch I.B. Parker (1991) ArticleTitleModular software for modelling the ideal detonation of explosives Math. Engng. Ind. 3 97–109
G.J. Sharpe S.A.E.G. Falle (2000) ArticleTitleOne-dimensional nonlinear stability of pathological detonations. J. Fluid Mech. 414 339–366 Occurrence Handle10.1017/S0022112000008697
G.J. Sharpe, Supplement to HSBM research report on rate stick simulations. Hybrid Stress Blast Model Project research report (2004) 5 pp.
J. Yao D.S. Stewart (1996) ArticleTitleOn the dynamics of multi-dimensional detonation J. Fluid. Mech. 309 225–275
M. Short J.B. Bdzil (2003) ArticleTitlePropagation laws for steady curved detonations with chain-branching kinetics. J. Fluid. Mech. 479 39–64 Occurrence Handle10.1017/S0022112002003300
W. Fickett W.C. Davis (1979) Detonation University of California Press Berkeley 386
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sharpe, G.J., Braithwaite, M. Steady Non-ideal Detonations in Cylindrical Sticks of Explosives. J Eng Math 53, 39–58 (2005). https://doi.org/10.1007/s10665-005-5570-7
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10665-005-5570-7