On the theory of axisymmetric conical flows and their one-dimensional unsteady analogues

Axisymmetric conical flows (CF) without swirling and their unsteady cylindrically and spherically symmetric self-similar analogues with a self-similarity exponent of unity are considered in the approximation of an ideal (inviscid and non-heat-conducting) perfect gas. In the flows considered, Chapman–Jouguet detonation waves (DWJ) are allowed together with shock waves within the limits of the classical model (heat release is instantaneous, on both sides of a discontinuity of zero thickness there is a perfect gas with dissimilar adiabatic exponents in the general case). The main new elements associated with CF are the introduction of DWJ into known flows and the merge of several CF into one. The construction and analysis of a number of new solutions are prefaced with the merge of unsteady self-similar analogues of CF. All the merges of the unsteady analogues are also original. The systemization of the approaches used and the theoretical analysis based on them are illustrated by examples of the numerical construction of the flows in the planes of their independent variables. The illustrations include streamlines (for CF), particle trajectories (for the unsteady analogues), the C+- and C−- characteristics and their envelope, shock waves and DWJ.