Nonuniqueness of the Transonic Flow past an Airfoil

Bifurcations and buffet of transonic flow past flattened surfaces

“…Frequencies of the oscillations were of the same order as those documented in previous studies of transonic buffet for a circular-arc airfoil [17,18] and wavy airfoils [19]. When c 6 8 the local curvature of the airfoil (2) is not small enough in the midchord region to trigger flow bifurcations [13,20]. It is worth mentioning that expression (1) with A ¼ 0:0644; b ¼ 3:5; c ¼ 2:5; d ¼ 1 is a good approximation of NACA 0012 airfoil, though the latter is of no interest from the viewpoint of bifurcations.…”

“…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].…”

“…Transonic flow structure past the asymmetric Whitcomb and DSMA532 airfoils was shown to be unstable at negative angles of attack [12,13].…”

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].…”

Bifurcations in the transonic flow past a symmetric airfoil

“…These reasons were analyzed in [4][5][6] for a family of symmetric airfoils y(x) = ±0.06 1 − (2x − 1) 4 (1 − x m ) 2 with 10 ≤ m ≤ 12 at angles of attack up to 6 • . For nonsymmetric Whitcomb and DSMA532 airfoils, flow instability was found to exist in regimes with negative angles of attack [7].…”