Formation and evolution of Mach disk in axisymmetric internal conical flow

The Mach reflection in axisymmetric flows, which is compressed by an internal cone, is investigated by using a combination of numerical simulations and theoretical analyses at a free-stream Mach number of 6. The effects of the leading-edge angle and cone length on the convergence behaviour of incident shocks and the flow downstream of Mach disk are examined. The results show that the leading-edge angle determines the point of von Neumann strength of the convergent incident shock, and also the location of the Mach disk. In addition to the shock convergence, the position of Mach disk is influenced by the downstream flow as well. According to whether the sonic throat of the stream tube downstream of the Mach disk is affected by the expansion waves generated from the trailing edge of the wall or not, two types of flow patterns downstream of the Mach disk can be classified depending on the leading-edge angle and the cone length. When the sonic throat is independent of the expansion waves, the pressure upstream of the sonic throat is balanced by the post-shock pressure of the reflected shock, and the position of Mach disk will not shift even if the cone length changes. On the other hand, when the sonic throat depends on the expansion waves, the stream tube upstream of the sonic throat needs to match the change of the pressure resulting from expansion waves. The position of Mach disk can be theoretically predicted based on the matching relations between the flow downstream of reflected shocks and the flow downstream of Mach disk.