Curvature effect on stabilization of cellular detonations in channel, circular arc and spherical shell geometries

The stability and propagation characteristics of gaseous detonations are numerically investigated, specifically in configurations where global front surface curvature plays a significant role. The simulations use idealized constitutive models representing a weakly unstable mixture and the simulated geometries include both two-dimensional arc and spherical shell sections with rigid walls and a straight channel geometry with compliant confinement. Depending on the inner and outer arc radius, differing levels of curvature can be imparted on the propagating wave in the two curved geometries. For thinner explosive regions, cellular type instabilities develop as the wave propagates around the arc and shell. However, as the thickness of the explosive increases and progressively greater surface curvature is imposed, laminar flow regions develop which can coexist with regions dominated by unstable cellular propagation. Here, the appearance and persistence of this laminar zone is shown to coincide with a critical level of surface curvature for both the arc and shell geometries. This critical curvature concept is also tested in the corresponding straight channel configuration with a compliant confiner, which similarly produces global surface curvature on the propagating detonation front but now as function of imposed wall divergence. Similarly, the propagation in the channel is found to stabilize when the maximum surface curvature exceeds a certain critical value that is close to the analog from the curved geometries. These results support the likely existence of a critical surface curvature mechanism or criterion that ensures the stabilization of a nominally unstable cellular detonation.