Wake instability issues: From circular cylinders to stalled airfoils

Meneghini, Júlio Romano; Carmo, Bruno Souza; Tsiloufas, Stergios Pericles; Gioria, Rafael dos Santos; Aranha, José Augusto Penteado

doi:10.1016/j.jfluidstructs.2011.03.018

Cited by 15 publications

(13 citation statements)

References 9 publications

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“…reflectional symmetry about the centreline). We note that the present finding of the first unstable mode agrees with that found by Meneghini et al (2011), Deng et al (2017 and He et al (2017), even though those studies were conducted at a fixed α = 20 • and with an objective of finding the critical Re 3D at which the flow becomes three-dimensionally unstable at a high post-stall angle of attack. Thus, by combining the present results with those from the literature, we conclude that mode C is the first 3-D unstable mode that emerges in the wake of an airfoil by altering either of the fluid's governing parameters (α, Re), which contrasts to mode A appearing first in a circular cylinder's wake.…”

Section: The Critical Angle Of Attack α 3d For 3-d Transitionsupporting

confidence: 89%

“…Concerning stability analysis of an airfoil wake, fewer studies have been reported discussing the role of the various governing parameters (discussed above) on the onset of wake three-dimensionality. Meneghini et al (2011) investigated the significance of one of these flow parameters, Re, for a NACA0012 airfoil at fixed α = 20 • for 400 ≤ Re ≤ 1000. They noticed that the flow becomes three-dimensionally unstable at a critical Re 3D = 456 through a subharmonic mode (mode C) of wavelength λ/C = 0.57.…”

Section: Prediction Of the Onset Of Three Dimensionality In Wakesmentioning

confidence: 99%

“…Meneghini et al. (2011) investigated the significance of one of these flow parameters, , for a NACA0012 airfoil at fixed for . They noticed that the flow becomes three-dimensionally unstable at a critical through a subharmonic mode (mode C) of wavelength .…”

Section: Introductionmentioning

confidence: 99%

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Two- and three-dimensional wake transitions of a NACA0012 airfoil

et al. 2023

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Flow transitions are an important fluid-dynamic phenomena for many reasons, including the direct effect on the aerodynamic forces acting on the body. In the present study, two-dimensional (2-D) and three-dimensional (3-D) wake transitions of a NACA0012 airfoil are studied for angles of attack in the range $0^\circ \leq \alpha \leq 20^\circ$ and Reynolds numbers $500 \leq {\textit {Re}} \leq 5000$ . The study uses water-channel experiments and 2-D and 3-D numerical simulations based on the nodal spectral-element method, level-set function-based immersed-interface method and Floquet stability analysis. The different wake states are categorised based on the time-instantaneous wake structure, non-dimensional frequency and aerodynamic force coefficients. The wake states and transition boundaries are summarised in a wake regime map. The critical angle of attack and Reynolds number for the supercritical Hopf bifurcation (i.e. steady to periodic wake transition) varies as $\alpha _1 {\sim} {\textit {Re}}^{-0.65}$ , while the critical angle of attack for the onset of three dimensionality varies as $\alpha _{3D} {\sim} {\textit {Re}}^{-0.5}$ . Over the entire Reynolds number range, the transition to 3-D flow occurs through a mode C (subharmonic) transition. Beyond this initial transition, further instabilities of the 2-D periodic base flow arise and are investigated. For instance, at $ {\textit {Re}}=2000$ and $\alpha _{3D,2}=11.0^\circ$ , mode C coexists together with modes related to modes A and QP seen in a stationary circular cylinder wake. In contrast, at $ {\textit {Re}}=5000$ and $\alpha _{3D,2}=8.0^\circ$ , the dominant mode C coexists with mode QP. Three-dimensional simulations well beyond critical angles indicate that 2-D vortex-street transitions are approximately maintained in the fully saturated 3-D wakes in a spanwise-averaged sense.

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Section: The Critical Angle Of Attack α 3d For 3-d Transitionsupporting

confidence: 89%

Section: Prediction Of the Onset Of Three Dimensionality In Wakesmentioning

confidence: 99%

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Two- and three-dimensional wake transitions of a NACA0012 airfoil

et al. 2023

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“…Investigations have also been conducted on the flow fields around bluff bodies with noncircular sections, such as those around bluff elongated cylinders [9] and stalled airfoils [10]. For a cylinder of square cross section, "mode S" was found to be critical within 150 < Re < 225, but only after the other modes had already undergone transition, and therefore may not be observed experimentally.…”

Section: Introductionmentioning

confidence: 99%

“…It is noted that a real harmonic mode cannot be physically realized unless the Z2 spatiotemporal symmetry in the wake is broken. This can be achieved in two ways: (i) in geometries without reflection symmetry, such as a circular cylinder with a tripwire placed adjacent to the cylinder but not on the symmetry plane [12], inclined flat plates [13], inclined square cylinders [14], and stalled airfoils [10]; (ii) by a transversely oscillating cylinder which can also change the spatiotemporal symmetry of the two-dimensional wake [15,16], At high oscillation amplitudes, the wake takes on the "P + S" configuration, with a pair of vortices on one side ol the wake and a single vortex on the other side for each oscillation cycle. As a result of the asymmetry about the center line, a real subharmonic "mode C" instability emerges, or more specifically for oscillating cylinders two subharmonic modes, "S L " and "55'," appear, with long and short wavelengths respectively.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional transition after wake deflection behind a flapping foil

Deng

Caulfield

2015

Phys. Rev. E

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We report the inherently three-dimensional linear instabilities of a propulsive wake, produced by a flapping foil, mimicking the caudal fin of a fish or the wing of a flying animal. For the base flow, three sequential wake patterns appear as we increase the flapping amplitude: Bénard-von Kármán (BvK) vortex streets; reverse BvK vortex streets; and deflected wakes. Imposing a three-dimensional spanwise periodic perturbation, we find that the resulting Floquet multiplier |μ| indicates an unstable "short wavelength" mode at wave number β=30, or wavelength λ=0.21 (nondimensionalized by the chord length) at sufficiently high flow Reynolds number Re=Uc/ν≃600, where U is the upstream flow velocity, c is the chord length, and ν is the kinematic viscosity of the fluid. Another, "long wavelength" mode at β=6 (λ=1.05) becomes critical at somewhat higher Reynolds number, although we do not expect that this mode would be observed physically because its growth rate is always less than the short wavelength mode, at least for the parameters we have considered. The long wavelength mode has certain similarities with the so-called mode A in the drag wake of a fixed bluff body, while the short wavelength mode appears to have a period of the order of twice that of the base flow, in that its structure seems to repeat approximately only every second cycle of the base flow. Whether it is appropriate to classify this mode as a truly subharmonic mode or as a quasiperiodic mode is still an open question however, worthy of a detailed parametric study with various flapping amplitudes and frequencies.

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