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Adaptive separation control of a laminar boundary layer using online dynamic mode decomposition

Published online by Cambridge University Press:  23 September 2020

Eric A. Deem ,
Louis N. Cattafesta III Open the ORCID record for Louis N. Cattafesta III [Opens in a new window] ,
Maziar S. Hemati Open the ORCID record for Maziar S. Hemati [Opens in a new window] ,
Hao Zhang ,
Clarence Rowley Open the ORCID record for Clarence Rowley [Opens in a new window]  and
Rajat Mittal Open the ORCID record for Rajat Mittal [Opens in a new window]
Eric A. Deem
Affiliation:
Mechanical Engineering, Florida State University, Tallahassee, FL32310, USA
Louis N. Cattafesta III*
Affiliation:
Mechanical Engineering, Florida State University, Tallahassee, FL32310, USA
Maziar S. Hemati
Affiliation:
Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN55455, USA
Hao Zhang
Affiliation:
Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA
Clarence Rowley
Affiliation:
Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA
Rajat Mittal
Affiliation:
Mechanical Engineering, Johns Hopkins University, Baltimore, MD21218, USA
*
†Email address for correspondence: lcattafesta@eng.famu.fsu.edu
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Abstract

Adaptive control of flow separation based on online dynamic mode decomposition (DMD) is formulated and implemented on a canonical separated laminar boundary layer via a pulse-modulated zero-net mass-flux jet actuator located just upstream of separation. Using a linear array of thirteen flush-mounted microphones, dynamical characteristics of the separated flow subjected to forcing are extracted by online DMD. This method provides updates of the modal characteristics of the separated flow while forcing is applied at a rate commensurate with the characteristic time scales of the flow. In particular, online DMD provides a time-varying linear estimate of the nonlinear evolution of the controlled flow without any prior knowledge. Using this adaptive model, feedback control is then implemented in which the linear quadratic regulator gains are computed recursively. This physics-based, autonomous approach results in more efficient flow reattachment compared with commensurate open-loop control. Four Reynolds numbers are tested to assess robustness, $Re_c = 0.9\times 10^5$, $Re_c = 1\times 10^5$, $Re_c = 1.1\times 10^5$ and $Re_c = 1.25\times 10^5$. All controlled cases exhibit a significant reduction in mean separation bubble height, requiring approximately 10 characteristic time periods to establish control.

JFM classification

Boundary Layers: Boundary layer separation Boundary Layers: Boundary layer control

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JFM Papers
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Journal of Fluid Mechanics , Volume 903 , 25 November 2020 , A21
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© The Author(s), 2020. Published by Cambridge University Press

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References

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