Critical conditions for detonation propagation through mixture with decreasing reaction rate

Abstract

A problem of detonation propagation through decreasing reaction rate gradient is examined. To estimate corresponding critical conditions, a simplified problem is considered where the width of reaction zone increases linearly with distance. The stationary solution for this self-similar problem exists only if the gradient of reactivity is below a certain critical value. The critical conditions are found analytically for a one-step Arrhenius kinetic model with larger activation energy. The critical gradient is expressed through the characteristic reaction zone width, its dependence on temperatue, and thermodynamic properties of the mixture. In the cases of expanding waves (cylindrical or spherical symmetry), superposition of limitations imposed by the gradient and by the wave curvature is observed. The critical gradient decreases with an increase of E a /T ooN (E a , activation energy; T OoN , von Neumann temperature for stationary detonation wave) and with the change of the wave symmetry from planar to spherical. Numerical integration of the self-similakr system of flow equations for a wide range of E a /T OoN is presented. the results show that the analytical solution can be applied for moderate values of effective activation energy as well. The critical conditions are also examined by time-dependent numerical simulation. The results are in agreement with the analytical solution if E a /T OoN is less than 6–8. For higher E a / T ooN , longitudinal instability of the detonation wave becomes the most important factor.