Bifurcations in the transonic flow past a symmetric airfoil

Abstract

Transonic flow past an airfoil with a small curvature in its midchord region is numerically investigated. The branching of the stationary solutions of the Euler equations is established and attributed to flow instability at certain angles of attack and freestream Mach numbers. The dependence of the lift coefficient on these parameters is studied.

Self-sustained oscillations and bifurcations of transonic flow past simple airfoils

“…At the same time, physical phenomena associated with the flow past such airfoils have not been well understood. Numerical simulations based on the system of Euler equations demonstrated bifurcations of a steady inviscid flow at certain angles of attack and free-stream Mach numbers [4][5][6][7]. The bifurcations and non-uniqueness of the transonic flow are caused by an instable interaction of two local supersonic zones residing on the same surface of the airfoil [8,9].…”

“…It can be seen from Fig. 3 that there is a singular free-stream Mach number M ∞ ≈ 0.86, at which a symmetric flow (with respect to the x axis) cannot exist, because it is impossible to realize continuous coalescence of two local supersonic zones on the airfoil surfaces with a gradual increase in M ∞ [7]. In turn, the impossibility of continuous coalescence of local supersonic zones in an inviscid flow is explained by the non-existence of an intermediate steady flow with two local supersonic zones that would have a common point on the airfoil [8,9].…”