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State estimation in wall-bounded flow systems. Part 3. The ensemble Kalman filter

Published online by Cambridge University Press:  03 August 2011

C. H. COLBURN ,
J. B. CESSNA  and
T. R. BEWLEY
C. H. COLBURN*
Affiliation:
Department of Mechanical Engineering, University of California, San Diego La Jolla, CA 92093, USA
J. B. CESSNA
Affiliation:
Numerica Corporation, 4850 Hahns Peak Drive, Suite 200, Loveland, CO 80538, USA
T. R. BEWLEY
Affiliation:
Department of Mechanical Engineering, University of California, San Diego La Jolla, CA 92093, USA
*
†Email address for correspondence: ccolburn@ucsd.edu
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Abstract

State estimation of turbulent near-wall flows based on wall measurements is one of the key pacing items in model-based flow control, with low-Re channel flow providing the canonical testbed. Model-based control formulations in such settings are often separated into two subproblems: estimation of the near-wall flow state via skin friction and pressure measurements at the wall, and (based on this estimate) control of the near-wall flow field fluctuations via actuation of the fluid velocity at the wall. In our experience, the turbulent state estimation sub-problem has consistently proven to be the more difficult of the two. Though many estimation strategies have been tested on this problem (by our group and others), none have accurately captured the turbulent flow state at the outer boundary of the buffer layer (5 ≤ y+ ≤ 30), which is deemed to be an important milestone, as this is the approximate range of the characteristic near-wall turbulent structures, the accurate estimation of which is important for the control problem. Leveraging the ensemble Kalman filter (an effective variant of the Kalman filter which scales well to high-dimensional systems), the present paper achieves at least an order of magnitude improvement (in the near-wall region) over the best results available in the published literature on the estimation of low-Reynolds number turbulent channel flow based on wall information alone.

JFM classification

Flow Control: Control theory Turbulent Flows: Turbulence control
Type
Papers
Information
Journal of Fluid Mechanics , Volume 682 , 10 September 2011 , pp. 289 - 303
Copyright
Copyright © Cambridge University Press 2011

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