State estimation of wall bounded flow systems. Part 1. Laminar flows

Authors: Hoepffner, J.P.J., Chevalier, M.C., Bewley, T. R., Henningson, D.S.H.
Document Type: Article
Pubstate: Published
Journal: J. Fluid Mech.
Volume: 534   263--294
Year: 2005


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.