Numerical resolution of pulsating detonation waves

The canonical problem of the one-dimensional, pulsating, overdriven detonation wave has been studied for over 30 years, not only for its phenomenological relation to the evolution of multidimensional detonation instabilities, but also to provide a robust, reactive, high-speed flowfield with which to test numerical schemes. The present study examines this flowfield using high-order, essentially non-oscillatory schemes, systematically varying the level of resolution of the reaction zone, the size and retention of information in the computational domain, the initial conditions, and the order of the scheme. It is found that there can be profound differences in peak pressures as well as in the period of oscillation, not only for cases in which the reaction front is under-resolved, but for cases in which the computation is corrupted due to a too-small computational domain. Methods for estimating the required size of the computational domain to reduce costs while avoiding erroneous solutions are proposed and tested.

[1]  W. Döring,et al.  Über den Detonationsvorgang in Gasen , 1943 .

[2]  Ronald Fedkiw,et al.  High Accuracy Numerical Methods for Thermally Perfect Gas Flows with Chemistry , 1997 .

[3]  S. Osher,et al.  Some results on uniformly high-order accurate essentially nonoscillatory schemes , 1986 .

[4]  J. Neuman,et al.  Theory of Detonation Waves , 1942 .

[5]  Elaine S. Oran,et al.  Detailed structure and propagation of three-dimensional detonations , 1996 .

[6]  J. Erpenbeck,et al.  Stability of Steady‐State Equilibrium Detonations , 1962 .

[7]  J. Erpenbeck,et al.  STABILITY OF IDEALIZED ONE-REACTION DETONATIONS , 1964 .

[8]  W. Fickett,et al.  Flow Calculations for Pulsating One‐Dimensional Detonations , 1966 .

[9]  Y. Zeldovich,et al.  On the theory of the propagation of detonation in gaseous systems , 1950 .

[10]  The Rate of Explosion in Gases , 2022, Nature.

[11]  Donald Scott Stewart,et al.  Calculation of linear detonation instability: one-dimensional instability of plane detonation , 1990, Journal of Fluid Mechanics.

[12]  D. Chapman,et al.  VI. On the rate of explosion in gases , 1899 .

[13]  Donald Whitley Woodhead,et al.  CCCCI.—The ignition of gases by an explosion-wave. Part I. Carbon monoxide and hydrogen mixtures , 1926 .

[14]  Miltiadis Papalexandris,et al.  Unsplit Schemes for Hyperbolic Conservation Laws with Source Terms in One Space Dimension , 1997 .

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

[16]  G. D. Byrne,et al.  VODE: a variable-coefficient ODE solver , 1989 .

[17]  Andrew J. Majda,et al.  Theoretical and numerical structure for unstable one-dimensional detonations , 1991 .

[18]  P. Clavin,et al.  Stability and nonlinear dynamics of one-dimensional overdriven detonations in gases , 1996, Journal of Fluid Mechanics.

[19]  J. Erpenbeck,et al.  Nonlinear Theory of Unstable Two‐Dimensional Detonation , 1967 .

[20]  J. Erpenbeck.  STRUCTURE AND STABILITY OF THE SQUARE-WAVE DETONATION , 1963 .

[21]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[22]  Donald Whitley Woodhead,et al.  CCVII.—Striated photographic records of explosion-waves , 1927 .

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