Mach reflection of cellular detonations

Abstract

The present paper reports the results of an experimental study of the Mach reflection of cellular detonations. Mixtures representing regular smoked foil pattern (C2H2+2.5O2+70%Ar) and irregular pattern (C2H2+2.5O2, C3H8+5O2) are used in the experiments. The range of the initial pressures used is 3kPa<Po<20kPa which provide a range of cell sizes of the detonation front. Schlieren photographs as well as smoked foils are used to observe the phenomenon. Wedges of angles ranging from 10°<θ<40° are used. Measurement of the Mach stem height with distance traveled from schlieren photographs and smoked foils indicate that the triple point lies on a curved trajectory instead of a straight line from the wedge apex as obtained from self-similar three shock theory. This is due to the finite thickness of the detonation front presenting a characteristic length scale that renders the self-similar three shock theory invalid. Following the work of Hornung and Shepherd et al., the present results are analyzed according to the so called frozen and equilibrium limits. The results do seem to agree with the frozen limit for the initial propagation of the Mach stem near the apex of the wedge when the distance traveled by the Mach stem is small compared to the characteristic length of the detonation front (e.g. cell size “λ”, hydrodynamic thickness, etc.). In the asymptotic far field region when the distance traveled is large compared to the effective detonation thickness, the present results appear to approach the prediction using three shock theory based on a discontinuous detonation front. Thus in spite of the transient three dimensional structure of a cellular detonation front, the frozen and equilibrium limit concept based on a global quasi-steady reaction zone thickness of the detonation front appears to provide a useful scheme to interpret the results. Examination of the smoked foils indicate that the interaction of the transverse waves of cellular instability with the reflected shock and shear layer of the Mach reflection play an important role in the description of the triple point region.