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TECHNICAL PAPERS

Linear Stability Analysis for the Wall Temperature Feedback Control of Planar Poiseuille Flows

[+] Author and Article Information
Hervé Pabiou, Jun Liu, Christine Bénard

FAST, UMR 7608 CNRS-UPMC-UPS, Ba⁁timent 502, Campus Universitaire, 91405 Orsay Cédex, France

J. Dyn. Sys., Meas., Control 124(4), 617-624 (Dec 16, 2002) (8 pages) doi:10.1115/1.1515325 History: Received April 01, 2001; Revised December 01, 2001; Online December 16, 2002
Copyright © 2002 by ASME
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References

Figures

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Expression of the velocity controller gain Kν as a function of the wall shear stress controller gain Ks. For Kν=−0.5,Ks→∞ (imposing τ(±1) goes to 0); For Ks=0.5,Kν→∞ (imposing Du(±1) goes to 0).
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Critical Reynolds number as a function of the controller gain Kν
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Critical Reynolds number as a function of the controller gain Ks
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Critical wavenumber as a function of the controller gain Kν
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Rc as a function of the controller gain Kν in the region of Kνc
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Distribution of |θ(z)| and |u(z)| for different Pr (θ(z) and u(z) are normalized by the observation Du(−1))
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Distribution of the arguments of θ(z) and u(z) (normalized by Du(−1)) for different Pr
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Evolution of D(t),P(t),C(t), and Λ(t) before control (with Kν=0 for t<100) and after control (with Kv=−0.1 for t>100) with R=5772.22,α=1.02 and Pr=5
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Evolution of D(t),P(t),C(t), and Λ(t) before control (with Kν=0 for t<100) and after control (with Kν=0.1 for t>100) with R=5772.22,α=1.02 and Pr=0.5
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The marginal stability Rc(α) for Pr=3 and the controller gain Kν=−0.19,−0.2,−0.21
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The critical Reynolds number Rc as a function of Kν for Pr=5
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Critical wavenumber αc and phase velocity cr as a function of Kν for Pr=5
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The marginal stability curve Rc(α) for Pr=5 and Kν in the neighborhood of −0.3
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Evolution of D(t),P(t),C(t), and Λ(t) before control is on (Kν=0 for t<100) and after control is on (Kν=−0.3 or Ks=−0.75 for t>100) for R=10000,α=0.94 and Pr=5
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Evolution of D(t),P(t),C(t), and Λ(t) before control is on (Kν=0 for t<100) and after control is on (Kν=0.3 or Ks=0.1875 for t>100) for R=10000,α=0.94 and Pr=0.5
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The critical Reynolds number as a function of the controller gain Kν for Pr=3
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The critical Reynolds number as a function of the controller gain Kν for Pr=5

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