|
|
|
KTH /
Engineering Sciences /
Mechanics /
Research /
Publication list /
Publication information
Article information
The use of global modes to understand transition and perform flow control
| Authors: |
Henningson, D.S.H.,
Åkervik, E.Å.,
|
| Type: |
Article |
| Pubstate: |
Published |
| Journal: |
Physics of Fluids |
| Volume: |
20
031302 |
| Year: |
2008 |
Abstract
The stability of non-parallel 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 wavepackets. 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 wavepacket 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 wavepacket upstream through a global pressure
pulse. Second, we consider two-dimensional disturbances in the Blasius
boundary layer. It is found that a wavepacket 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
wavepacket 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 equations time integration and it is shown to damp out the global
oscillations.
|
|
|
