| Abstract: | The supersonic flow of an inviscid gas that does not conduct heat over a cascade of planar pointed profiles is considered in the case when the component of the velocity vector of the undisturbed flow normal to the cascade front is subsonic. The investigation is restricted to regimes without separation and shock waves attached to the leading edges of the profiles and fairly dense cascades, for which the characteristics or shock waves leaving the trailing edges do not enter the region in front of the cascade. In such cases, the conditions behind the cascade do not influence the flow in front of it. In this sense, the flow in the cascade, as in a Laval nozzle in the case of supercritical gradients is  trapped , In the hodograph plane, trapped regimes of flow over the cascade correspond to velocity vectors of the undisturbed flow that lie on a certain line (see, for example, [1–3]), which is constructed in the process of solution of the problem. This property has been called the directing influence of the cascade on the oncoming flow. Regimes with detached shocks can also be trapped if the separation of the shocks is due to the profiles being blunt. A method is proposed that for regimes with attached shocks makes it possible to calculate the entire flow field, including the wave structure at large distances from the cascade front; some results obtained by the method are also given. The study of regimes with attached shocks, for which the analysis is simplest, is, first, of interest in its own right and, second, is a stage in the creation of methods of calculation and subsequent investigation of cascades with arbitrary regimes.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 108–113, July–August, 1979.We are grateful to M. Ya. Ivanov for assistance in updating the supersonic flow calculation program of [7], to G. Yu. Stepanov for helpful comments, and to E. V. Buganov and V. A. Vostretsov for assistance in preparing the paper. |
