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Adjoint-based phase reduction analysis of incompressible periodic flows

Yoji Kawamura1,*, Vedasri Godavarthi2,†, and Kunihiko Taira2,‡

  • 1Center for Mathematical Science and Advanced Technology, Japan Agency for Marine-Earth Science and Technology, Yokohama 236-0001, Japan
  • 2Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, California 90095, USA

  • *ykawamura@jamstec.go.jp
  • †vedasrig@g.ucla.edu
  • ‡ktaira@seas.ucla.edu
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Phys. Rev. Fluids 7, 104401 – Published 6 October, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.104401

Abstract

We establish the theoretical framework for adjoint-based phase reduction analysis for incompressible periodic flows. Through this adjoint-based method, we obtain spatiotemporal phase sensitivity fields through a single pair of forward and backward direct numerical simulations, as opposed to the impulse-based method that requires a very large number of simulations. Phase-based analysis involves perturbation analysis about a periodically varying base state and hence is tailored for the analysis of periodic flows. We formulate the phase description of periodic flows with respect to the potential and vortical perturbations in the flow field. The current phase-reduction analysis can also be implemented consistently in the immersed boundary projection method, which facilitates the analysis over arbitrarily shaped bodies. We demonstrate the strength of the phase-based analysis for periodic flows over circular cylinder and symmetric airfoils at high incidence angles. The critical regions for phase modification in the cylinder flow are investigated, and the locations of flow separation are shown to be the most sensitive regions. Further, the results reveal the influence of the angle of attack and airfoil thickness on the phase-sensitivity distribution of flows over various airfoils. The phase for such flows is defined based on the lift coefficient, and hence it is influenced by the vortical structures responsible for lift production. The present framework sheds light on the connection between phase sensitivity and vortex formation dynamics.

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Phys. Rev. Fluids 7, 104401– Published 6 October, 2022
  • Received 19 April 2022
  • Accepted 29 August 2022
Article part of CHORUS
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