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Research Papers

Model Based Control of Laminar Wake Using Fluidic Actuation

[+] Author and Article Information
Imran Akhtar1

Department of Engineering Science and Mechanics, Virginia Tech, MC 0219, Blacksburg, VA 24061akhtar@vt.edu

Ali H. Nayfeh

Department of Engineering Science and Mechanics, Virginia Tech, MC 0219, Blacksburg, VA 24061

1

Corresponding author. Present address: Interdisciplinary Center for Applied Mathematics, Virginia Tech, MC 0531, Blacksburg, VA 24061.

J. Comput. Nonlinear Dynam 5(4), 041015 (Aug 20, 2010) (9 pages) doi:10.1115/1.4002085 History: Received April 22, 2009; Revised April 28, 2010; Published August 20, 2010; Online August 20, 2010

Control of fluid-structure interaction is of practical importance from the perspective of wake modification and reduction of vortex-induced vibrations (VIVs). The aim of this study is to design a control to suppress vortex shedding. We perform a two-dimensional simulation of the flow past a circular cylinder using a parallel Computational Fluid Dynamics (CFD) solver. We record the velocity and pressure fields over a shedding cycle and compute the proper orthogonal decomposition (POD) modes of the divergence-free velocity and pressure, respectively. The Navier–Stokes equations are projected onto these POD modes to reduce the dynamical system to a set of ordinary-differential equations (ODEs). This dynamical system exhibits a limit cycle with negative linear damping and positive nonlinear damping. The reduced-order model is then modified by placing a pair of suction actuators and applying a control strategy using a control function method. We use the pressure POD mode distribution on the cylinder surface to optimally locate the actuators. We design a controller based on the linearized system and make it positively damped using pole-placement technique. The control-input settles to a constant value, suggesting constant suction through the actuators. We validate the results using CFD simulations in an open-loop setting and observe suppression of the hydrodynamic forces acting on the cylinder.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) A schematic of a synthetic jet actuation pair located on the cylinder surface and (b) velocity profiles for the jet: top hat (dashed), sinusoidal (solid), and sine square (dashed-dot)

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Figure 2

The velocity coefficients (a) qi=1,2 and (b) qi=3,4 at ReD=200 of the uncontrolled flow: even (solid) and odd (dashed)

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Figure 3

Normalized singular values

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Figure 4

The pressure POD modes on the cylinder surface at ReD=200, (a) i=1,2 and (b) i=3,4: even (solid) and odd (dashed)

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Figure 5

Control mode at ReD=200: (a) streamwise velocity and (b) crossflow velocity

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Figure 6

Poles of the open-loop system

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Figure 7

Time history of q1 with control actuation: (a) CL1, (b) CL2, and (c) CL3

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Figure 8

Time history of (a) γc and (b) γ for the case CL3

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Figure 9

System response q1 for CL1: solid-modified model and dashed-linear model

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Figure 10

Time histories of CL and CD with fluidic actuation obtained from reduced-order model (solid) and without reduced-order model (dashed)

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Figure 11

Spanwise vorticity contours (a) before the control at t=80 and (b) after the control actuation at t=100

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