Steady three-dimensional Streaks and their Optimal Growth in a Laminar Separation Bubble

Author(s):  
O. Marxen ◽  
U. Rist ◽  
D. Henningson
2010 ◽  
Vol 655 ◽  
pp. 280-305 ◽  
Author(s):  
D. RODRÍGUEZ ◽  
V. THEOFILIS

The topology of the composite flow fields reconstructed by linear superposition of a two-dimensional boundary layer flow with an embedded laminar separation bubble and its leading three-dimensional global eigenmodes has been studied. According to critical point theory, the basic flow is structurally unstable; it is shown that in the presence of three-dimensional disturbances the degenerate basic flow topology is replaced by a fully three-dimensional pattern, regardless of the amplitude of the superposed linear perturbations. Attention has been focused on the leading stationary eigenmode of the laminar separation bubble discovered by Theofilis et al. (Phil. Trans. R. Soc. Lond. A, vol. 358, 2000, pp. 3229–3324); the composite flow fields have been fully characterized with respect to the generation and evolution of their critical points. The stationary global mode is shown to give rise to a three-dimensional flow field which is equivalent to the classical U-shaped separation, defined by Hornung & Perry (Z. Flugwiss. Weltraumforsch., vol. 8, 1984, pp. 77–87), and induces topologies on the surface streamlines that are resemblant to the characteristic stall cells observed experimentally.


Author(s):  
Paul Ziadé ◽  
Pierre E. Sullivan

Large-eddy simulation and linear stability analysis were performed on a NACA 0025 airfoil at a chord Reynolds number of 105 and four angles of attack. The computations showed that the initial vortex roll-up quickly breaks down to three-dimensional turbulence. Flow separation was observed at all angles, whereas only the lowest angle of attack formed a laminar separation bubble due to flow transition occuring close to the airfoil surface. A Chebyshev collocation method was employed to solve the viscous and inviscid stability equations. Linear stability analysis demonstrated that high-frequency disturbances occur in the laminar separation bubble case, whereas lower frequencies are present for the fully separated angles of attack. The maximum disturbance growth rates were dampened with the addition of viscosity but negligible change in peak frequency was noted.


2021 ◽  
Vol 929 ◽  
Author(s):  
Connor E. Toppings ◽  
Serhiy Yarusevych

The three-dimensional flow topology of a laminar separation bubble forming on the suction surface of a semispan wing with an aspect ratio of $2.5$ and NACA 0018 airfoil section is characterised experimentally using surface pressure measurements and particle image velocimetry at a chord Reynolds number of $125\ 000$ . In the inboard region of the wing, the separation bubble is essentially two-dimensional, and the transition process in the separated shear layer leads to periodic vortex shedding, which dominates the bubble dynamics, similar to two-dimensional separation bubbles. However, progressive spanwise changes in the mean structure and vortex dynamics occur near the wingtip, leading to an open separation and eventual suppression of the bubble. In the immediate proximity of the wingtip, the boundary layer remains attached, no vortex shedding occurs and the flow remains laminar, terminating separation bubble formation. Despite variations in the mean separation bubble topology and vortex dynamics along the span, the fundamental shedding characteristics remain nearly invariant across the portion of the wing where vortex shedding occurs, and the flow appears to lock onto a common instability mode across the span, leading to minimal changes in the mean bubble characteristics despite notable changes in the effective angle of attack along the span. A comparison with available surface flow visualisations from previous studies indicates that the observed changes to the mean bubble footprint along the span of the wing are similar across different geometries and flow characteristics, suggesting similarities in the three-dimensional bubble topology and dynamics on finite wings.


2010 ◽  
Vol 648 ◽  
pp. 257-296 ◽  
Author(s):  
L. E. JONES ◽  
R. D. SANDBERG ◽  
N. D. SANDHAM

Stability characteristics of aerofoil flows are investigated by linear stability analysis of time-averaged velocity profiles and by direct numerical simulations with time-dependent forcing terms. First the wake behind an aerofoil is investigated, illustrating the feasibility of detecting absolute instability using these methods. The time-averaged flow around an NACA-0012 aerofoil at incidence is then investigated in terms of its response to very low-amplitude hydrodynamic and acoustic perturbations. Flow fields obtained from both two- and three-dimensional simulations are investigated, for which the aerofoil flow exhibits a laminar separation bubble. Convective stability characteristics are documented, and the separation bubble is found to exhibit no absolute instability in the classical sense; i.e. no growing disturbances with zero group velocity are observed. The flow is however found to be globally unstable via an acoustic-feedback loop involving the aerofoil trailing edge as a source of acoustic excitation and the aerofoil leading-edge region as a site of receptivity. Evidence suggests that the feedback loop may play an important role in frequency selection of the vortex shedding that occurs in two dimensions. Further simulations are presented to investigate the receptivity process by which acoustic waves generate hydrodynamic instabilities within the aerofoil boundary layer. The dependency of the receptivity process to both frequency and source location is quantified. It is found that the amplitude of trailing-edge noise in the fully developed simulation is sufficient to promote transition via leading-edge receptivity.


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