Journal
INTERNATIONAL JOURNAL OF CONTROL
Volume 84, Issue 8, Pages 1310-1325Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207179.2011.593000
Keywords
turbulence; nonlinear equations; partial differential equations; descriptor systems; model approximation; boundary conditions
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Funding
- EPSRC
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This article investigates the problem of obtaining a state-space model of the disturbance evolution that precedes turbulent flow across aerodynamic surfaces. This problem is challenging since the flow is governed by nonlinear, partial differential-algebraic equations for which there currently exists no efficient controller/estimator synthesis techniques. A sequence of model approximations is employed to yield a linear, low-order state-space model, to which standard tools of control theory can be applied. One of the novelties of this article is the application of an algorithm that converts a system of differential-algebraic equations into one of ordinary differential equations. This enables straightforward satisfaction of boundary conditions whilst dispensing with the need for parallel flow approximations and velocity-vorticity transformations. The efficacy of the model is demonstrated by the synthesis of a Kalman filter that clearly reconstructs the characteristic features of the flow, using only wall velocity gradient information obtained from a high-fidelity nonlinear simulation.
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