Matrix-free methods for the stability and control of boundary layers
2009 (English)In: AIAA Journal, ISSN 0001-1452, E-ISSN 1533-385X, Vol. 47, no 5, 1057-1068 p.Article in journal (Refereed) Published
This paper presents matrix-free methods for the stability analysis and control design of high-dimensional systems arising from the discretized linearized Navier-Stokes equations. The methods are applied to the two-dimensional spatially developing Blasius boundary-layer. A critical step in the process of systematically investigating stability properties and designing feedback controllers is solving very large eigenvalue problems by storing only velocity fields at different times instead of large matrices. For stability analysis, where the entire dynamics of perturbations in space and time is of interest, iterative and adjoint-based optimization techniques are employed to compute the global eigenmodes and the optimal initial conditions. The latter are the initial conditions yielding the largest possible energy growth over a finite time interval. The leading global eigenmodes take the shape of Tollmien-Schlichting wavepackets located far downstream in streamwise direction, whereas the leading optimal disturbances are tilted structures located far upstream in the boundary layer. For control design on the other hand, the input-output behavior of the system is of interest and the snapshot-method is employed to compute balanced modes that correctly capture this behavior. The inputs are external disturbances and wall actuation and the outputs are sensors that extract wall shear stress. A low-dimensional model that capture the input-output behavior is constructed by projection onto balanced modes. The reduced-order model is then used to design a feedback control strategy such that the growth of disturbances are damped as they propagate downstream.
Place, publisher, year, edition, pages
2009. Vol. 47, no 5, 1057-1068 p.
Adjoint-based optimization, Blasius boundary layer, Control design, Critical steps, Eigen modes, Eigenvalue problem, Energy growth, External disturbances, Feedback control strategies, Feedback controller, Finite time intervals, High-dimensional systems, Initial conditions, Input-output behavior, Linearized navier-stokes equations, Low-dimensional models, matrix, Optimal disturbances, Reduced order models, Snapshot method, Space and time, Stability analysis, Stability and control, Stability properties, Streamwise directions, Tollmien-schlichting wave packets, Velocity field, Wall shear stress, Aerodynamics, Boundary layers, Eigenvalues and eigenfunctions, Feedback control, Flow separation, Navier Stokes equations, Optimization, System stability
Fluid Mechanics and Acoustics
IdentifiersURN: urn:nbn:se:kth:diva-9546DOI: 10.2514/1.41365ISI: 000265586200001ScopusID: 2-s2.0-67649170531OAI: oai:DiVA.org:kth-9546DiVA: diva2:117430
QC 20100927 AIAA 5th Theoretical Fluid Mechanics Meeting, Seattle, WA, JUN 23-26, 20082008-11-122008-11-122011-03-29Bibliographically approved