The role of a transversal concentration gradient in detonation propagation in a two-dimensional channel filled with an $\text{H}_{2}{-}\text{O}_{2}$ mixture is examined by high-resolution simulation. Results show that, compared to propagation in homogeneous media, a concentration gradient reduces the average detonation velocity because of the delay in reaching downstream reaction equilibrium, leading to a large amount of unreacted $\text{H}_{2}$ and hence significant species fluctuations. The transversal concentration gradient also enhances the cellular detonation instability. Steepening it reduces considerably the number of triple points on the front, lengthens the global detonation front structure on average and consequently increases the deficit of the average detonation velocity. It is further found that the interaction of the leading shock with the transversal concentration gradient influences the formation of local $\text{H}_{2}$ bump and thus the unreacted pocket behind the front, while the transverse wave causes mixing and burning of the residue fuel downstream. Nevertheless, for the steepened concentration gradient, a transverse detonation is present and consumes the fuel in the compressed and preheated zone by the leading shock; consequently, the detonation velocity deficit is not increased significantly for detonation with the single-head propagation mode close to the limit.

The numerical simulation of supersonic flow over a cone is carried out to investigate oblique detonation waves. A three-dimensional (3D) conical oblique detonation wave is studied by changing the heat release. It is found that the formation of a conical oblique detonation wave shifts from a moderate transition to an abrupt transition and the frontal structure also changes from smooth to cellular features. Moreover, the conical oblique detonation wave approaches detachment as heat release increases. A comparison of oblique detonation waves attached to a 2D wedge and a 3D cone demonstrates that, for a fixed heat release, a cone is able to moderate the transition significantly, and that detaching behavior is also delayed significantly due to curvature as heat release changes. The critical heat release for detachment of the conical oblique detonation wave is much larger than that of the wedge-induced oblique detonation wave. Moreover, we assess the difference in angles of oblique detonation waves produced by wedges and cones and find that the angle is much smaller than that of wedge-induced oblique detonation wave because of flow divergence caused by the curvature (curved front in the circumference direction of the cone).