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

Abstract

A turbulent flow past two symmetric airfoils, whose bow and aft portions are circular arcs, whereas midparts are flat, is studies numerically. The amplitude of lift coefficient oscillations versus the free-stream Mach number M ∞ is analyzed at zero angle of attack. Ranges of M ∞ in which there exist flow bifurcations are determined.

Bifurcations of transonic flow past simple airfoils with elliptic and wedge-shaped noses

“…Figure 3 shows the asymmetric flow field (with three local supersonic regions) obtained at an instant t for M ∞ = 0.857 and α = 0 • . In the proximity of the trailing edge, the flow pattern with the boundary layer separation differs only slightly from that studied in [4]. The Reynolds number based on the airfoil chord length of 0.5 m and M ∞ ≈ 0.86 is 1.1 · 10 7 .…”

“…Solutions of the initial-value problem for the system of Navier-Stokes equations endowed with the SST-k-ω turbulence model were obtained with a finite-volume solver [4]. in the boundary layer, we chose such positions for the nearest nodes to the airfoil that the dimensionless distance y + was less than unity [6].…”

“…The total number of mesh nodes was approximately 1.8 · 10 5 . The solver was validated by running a few benchmark problems on transonic buffet [4].…”

“…Figure 2 demonstrates the maximum values C L,max and minimum values C L,min of the lift coefficient for periodic self-sustained oscillations at various values of M ∞ . The realization of symmetric or asymmetric flow regimes depends on the initial data and time history of the parameters M ∞ and α [4,5]. The domains I and IV in Fig.…”

“…The existence of bifurcations of a transonic flow past symmetric and asymmetric airfoils having lengthy portions with a small or zero curvature was established in a number of studies on the basis of the Navier-Stokes equations [1][2][3]. In [4,5], we obtained and analyzed regimes of transonic buffet and bifurcations of the flow past simple airfoils whose nose and tail are circular arcs. In this work, the above-mentioned phenomena are studied for other simple airfoils.…”