Bifurcation of a transonic ideal-gas flow around a symmetric airfoil with a concavity

Abstract

A transonic flow around a symmetric airfoil with a concavity in its central part has been numerically investigated. The dependences of the lift coefficient on the Mach number of the incident flow M∞ and on the angle of attack α were determined. It is shown that, depending on M∞, in the flow past the upper part of the indicated airfoil there can arise one or two supersonic-flow regions. It has been established that, at fairly large angles of attack, the coalescence and separation of supersonic-flow regions are realized in a discrete way. For these angles of attack, singular Mach numbers Ms, in the neighborhood of which the structure of the flow is transformed, were determined and the physical processes occurring in this case were analyzed. It was found that the flow being considered is characterized by a large hysteresis in M∞.