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State estimation of wall bounded flow systems. Part 1. Laminar flows
Bewley, T. R.,
||J. Fluid Mech.
In applications involving the model-based control of transitional
wall-bounded flow systems, one often desires to estimate the interior
flow state based on a history of noisy measurements from an array of
flush-mounted skin-friction and pressure sensors on the wall. This
paper considers this estimation problem, using a Kalman filter based
on the linearised Navier--Stokes equations and appropriate stochastic
models for the relevant statistics of the initial conditions, sensor
noise, and external disturbances acting on the system. We show that a
physically relevant parameterisation of these statistics is key to
obtaining well resolved feedback kernels with appropriate spatial
extent for all three types of flow measurements available on the wall.
The effectiveness of the resulting Kalman and extended Kalman filters
that implement this feedback is verified for both infinitesimal and
finite-amplitude disturbances in direct numerical simulations of a
perturbed laminar channel flow. The consideration of time-varying
feedback kernels is shown to be particularly advantageous to
accelerate the convergence of the estimator from unknown initial
conditions. A companion paper (Part 2) considers the extension of
such estimators to the case of fully-developed turbulence.