Low-Dimensional Models for Control of Leading-Edge Vortices: Equilibria and Linearized Models

Ahuja, Sunil; Rowley, Clarence W.; Kevrekidis, Ioannis G.; Wei, Mingjun; Colonius, Tim; Tadmor, Gilead

doi:10.2514/6.2007-709

Cited by 30 publications

(32 citation statements)

References 23 publications

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“…The change in the dynamics between the shaded (sub-critical) and unshaded (super-critical) regions can be viewed as an extension of the two-dimensional stability boundary. We claim that the change in the dynamics is attributed to a Hopf-bifurcation, as shown by Ahuja et al (2007) for the two-dimensional case. For lower aspect ratios, the vortex sheet emanating from the trailing edge forms and sheds hairpin vortices repeatedly.…”

Section: Flows At Higher Reynolds Numbermentioning

confidence: 99%

Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers

2009

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Three-dimensional flows over impulsively translated low-aspect-ratio flat plates are investigated for Reynolds numbers of 300 and 500, with a focus on the unsteady vortex dynamics at post-stall angles of attack. Numerical simulations, validated by an oil tow-tank experiment, are performed to study the influence of aspect ratio, angle of attack and planform geometry on the wake vortices and the resulting forces on the plate. Immediately following the impulsive start, the separated flows create wake vortices that share the same topology for all aspect ratios. At large time, the tip vortices significantly influence the vortex dynamics and the corresponding forces on the wings. Depending on the aspect ratio, angle of attack and Reynolds number, the flow at large time reaches a stable steady state, a periodic cycle or aperiodic shedding. For cases of high angles of attack, an asymmetric wake develops in the spanwise direction at large time. The present results are compared to higher Reynolds number flows. Some non-rectangular planforms are also considered to examine the difference in the wakes and forces. After the impulsive start, the time at which maximum lift occurs is fairly constant for a wide range of flow conditions during the initial transient. Due to the influence of the tip vortices, the three-dimensional dynamics of the wake vortices are found to be quite different from the two-dimensional von Kármán vortex street in terms of stability and shedding frequency.

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Section: Flows At Higher Reynolds Numbermentioning

confidence: 99%

Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers

2009

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“…Then, the linear first-order set of equations with impulse input as the boundary condition should be solved for the flow variables u 1 , p 1 . Finally, the flow field with an arbitrary control input ε p can be estimated by Equation 17. The accuracy of the perturbation method will be investigated in Section 5.2.…”

Section: Zero-order Set Of Equations (Have Nominated As Equations A)mentioning

confidence: 99%

Feedback control of laminar flow separation on NACA23012 airfoil by POD analysis and using perturbed Navier‐Stokes equations

Zare

Emdad

Rad

2017

Numerical Methods in Fluids

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Summary The main purpose of this article is to develop a forced reduced‐order model based on the proper orthogonal decomposition (POD)/Galerkin projection (on isentropic Navier‐Stokes equations) and perturbation method on the compressible Navier‐Stokes equations. The resulting forced reduced‐order model will be used in optimal control of the separated flow over a NACA23012 airfoil at Mach number of 0.2, Reynolds number of 800, and high incidence angle of 24°. The main disadvantage of the POD/Galerkin projection method for control purposes is that controlling parameters do not show up explicitly in the resulting reduced‐order system. The perturbation method and POD/Galerkin projection on the isentropic Navier‐Stokes equations introduce a forced reduced‐order model that can predict the time varying influence of the controlling parameters and the Navier‐Stokes response to external excitations. An optimal control theory based on forced reduced‐order system is used to design a control law for a nonlinear reduced‐order system, which attempts to minimize the vorticity content in the flow field. The test bed is a laminar flow over NACA23012 airfoil actuated by a suction jet at 12% to 18% chord from leading edge and a pair of blowing/suction jets at 15% to 18% and 24% to 30% chord from leading edge, respectively. The results show that wall jet can significantly influence the flow field, remove separation bubbles, and increase the lift coefficient up to 22%, while the perturbation method can predict the flow field in an accurate manner.

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“…The simple model problem described here is part of a larger research program 3 that includes three-dimensional flow simulations, 4 experiments, 5 and reduced-order modeling. 6 Unsteady actuation has been used in the past for separation control. 7,8 Several studies have demonstrated that unsteady actuation near the separation point can reattach the flow, shorten the separation bubble, or suppress vortex shedding to reduce drag.…”

Section: Introductionmentioning

confidence: 99%

Closed-Loop Control of Vortex Shedding on a Two-Dimensional Flat-Plate Airfoil at a Low Reynolds Number

Joe

Taira

Colonius

et al. 2008

46th AIAA Aerospace Sciences Meeting and Exhibit

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Open-and closed-loop control of vortex shedding in two-dimensional flow over a flat plate at high angles of attack is numerically investigated at a Reynolds number of 300. Unsteady actuation is modeled as a body force near the leading or trailing edge, and is directed either upstream or downstream. For moderate angles of attack, sinusoidal forcing at the natural shedding frequency results in phase locking, with a periodic variation of lift at the same frequency. However, at sufficiently high angles of attack, subharmonics of the forcing frequency are also excited and the average lift over the forcing period varies from cycle to cycle in a complex manner. It is observed that the periods with the highest averaged lift are associated with particular phase difference between the forcing and the lift. We design a feedback algorithm to lock the forcing with the phase shift associated with the highest period-averaged lift. It is shown that the compensator results in a stable phaselocked limit cycle for a larger range of forcing frequencies than the open-loop control, and that it is able to stabilize otherwise unstable high-lift limit cycles that cannot be obtained with open-loop control. For example at an angle of attack of 40 • , the feedback controller can increase the averaged lift coefficient from 1.35 to 2.43, an increase of 80%.

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Low-Dimensional Models for Control of Leading-Edge Vortices: Equilibria and Linearized Models

Cited by 30 publications

References 23 publications

Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers

Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers

Feedback control of laminar flow separation on NACA23012 airfoil by POD analysis and using perturbed Navier‐Stokes equations

Closed-Loop Control of Vortex Shedding on a Two-Dimensional Flat-Plate Airfoil at a Low Reynolds Number

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