Instability and Bifurcation of Transonic Flow Over Airfoils (invited)

Bifurcations and buffet of transonic flow past flattened surfaces

“…Each domain corresponds to a flow field with two, three or four local supersonic regions as sketched at the periphery of the figure. The realization of the certain flow structure depends on initial data and time history of freestream conditions [14,16]. For example, Fig.…”

“…The bifurcations are caused by instability which accompanies the coalescence/rupture of supersonic regions on the surfaces with a small local curvature [15]. Another type of instability of the flow structure, which is irrelative to the coalescence/rupture of supersonic regions but also manifests abrupt changes of the flow field, was found by Kuz'min [14] at positive angles of attack for the airfoil (2) with c ¼ 16, i.e.,…”

“…When c P 8:5 the inviscid transonic flow past the airfoil (2) at zero angle of attack exhibits bifurcations in a range of freestream Mach numbers [12][13][14]. The bifurcations are caused by instability which accompanies the coalescence/rupture of supersonic regions on the surfaces with a small local curvature [15].…”

Instabilities of Transonic Turbulent Flow over a Flat-Sided Wedge

“…Section 5 addresses multiple regimes at the vanishing angle of attack α in a band of M∞. Finally, in Section 6 we discuss a surface illustrating the lift coefficient as a function of α and M∞, which is similar to the surface discussed in (Kuzmin 2005) for a smooth airfoil and inviscid flow.…”

“…Then non-unique flow regimes and high sensitivity to free-stream Mach number were revealed for symmetric airfoils at the vanishing angle of attack (McGrattan 1992;Guo 1999a, 1999b). Kuzmin (2005) suggested that the hysteresis and non-uniqueness occur if an airfoil involves a straight segment or nearly flat arc. Such a segment/arc provokes the arising of two local supersonic regions on the same side of airfoil.…”