State estimation in wall-bounded flow systems. Part 1. Perturbed laminar flows

• Published in: Journal of fluid mechanics Vol. 534; pp. 263 - 294
• Main Authors: HœPFFNER, JÉRÔME, CHEVALIER, MATTIAS, BEWLEY, THOMAS R., HENNINGSON, DAN S.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 10.07.2005
• Subjects: Channel flow; Exact sciences and technology; Flow measurement; Flow system; Fluid dynamics; Fundamental areas of phenomenology (including applications); Kalman filters; Physics; Pressure sensors; Stochastic models; Turbulence control; Turbulent flows, convection, and heat transfer; Wall turbulence; Digital simulation; Control systems; Stochastic method; Turbulent laminar transition; Laminar flow; Feedback; Disturbances; Modelling; Kalman filters; State estimation; Turbulence structure; Navier-Stokes equations
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112005004210

In applications involving the model-based control of transitional wall-bounded flow systems, it is often desired 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 linearized 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 parameterization of these statistics is key to obtaining well-resolved feedback kernels with appropriate spatial extent for all three types of flow measurement 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 in accelerating 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.