The use of global modes to understand transition and performflow control

• Published in: Physics of fluids (1994) Vol. 20; no. 3; pp. 031302 - 031302-15
• Main Authors: Henningson, Dan S., Åkervik, Espen
• Format: Journal Article
• Published: American Institute of Physics 12.03.2008
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.2832773

The stability of nonparallel flows is considered using superposition of global modes. When perturbed by the worst case initial condition, these flows often exhibit a large transient growth associated with the development of wave packets. The global modes of the systems also provide a good starting point for the design of reduced order models used to control the growing disturbances. Three recent investigations are reviewed. The first example is the growth of a wave packet on a falling liquid sheet. The optimal perturbation analysis shows that the worst case initial condition is a localized disturbance that creates a propagating wave packet that hits the downstream end, regenerating a wave packet upstream through a global pressure pulse. Second, we consider two-dimensional disturbances in the Blasius boundary layer. It is found that a wave packet is optimally excited by an initial condition consisting of localized backward leaning Orr structures. Finally, the control of a globally unstable boundary-layer flow along a shallow cavity is considered. The disturbance propagation is associated with the development of a wave packet along the cavity shear layer, unstable to the Kelvin-Helmholtz mechanism, followed by a global cycle related to the two unstable global modes. Direct numerical simulations of this flow are coupled to a measurement feedback controller, which senses the wall shear stress at the downstream lip of the cavity and provides the actuation at the upstream lip. A reduced order model for the control is obtained by a projection on the least stable global eigenmodes. The linear-quadratic-Gaussian controller is run in parallel to the Navier-Stokes time integration and it is shown to damp out the global oscillations.