The structural instability of transonic flow associated with amalgamation/splitting of supersonic regions

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

“…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].…”

“…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 and buffet of transonic flow past flattened surfaces

“…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.,…”

Transonic flow instability in the entrance region of a channel with breaks of walls

“…The approach and coalescence of supersonic regions inside the flow (Fig. 7a) develop gradually and do not provoke the instability [7]. Figure 9 illustrates shock positions in the channel as functions of the angle of attack.…”