Bernardo Galletti

Low-order modelling of laminar flow regimes past a confined square cylinder

A proper orthogonal decomposition based model is considered for two-dimensional vortex shedding past a confined square cylinder. The aim is to study the validity of such a model for Reynolds numbers and blockage ratios that are different from those for which the model was derived. Using a calibration procedure it is shown that reliable results can be obtained in terms of short-term (one period) dynamics. Long-term dynamics are accurately captured with a variation of the Reynolds number, whereas the error becomes large when the blockage ratio changes. The controllability and observability of vortex shedding at a slightly supercritical Reynolds number is investigated relying on the accurate low-order models obtained

Large-scale secondary structures in duct flow

The spatial growth of small perturbations developing on a fully developed base flow in a duct with two inhomogeneous cross-flow directions is examined. For a laminar mean flow it is shown that optimally configured vortices at an upstream cross-section induce large transient amplification of a disturbance energy norm downstream. Such a linear growth is a likely initial stage of transition in ducts for which the cross-section is square or of moderate aspect ratio, asymptotically stable according to conventional eigen-analyis. With the increase of the cross-sectional aspect ratio the transient growth results of the plane channel flow case are approached. The optimization methodology is then employed to study the transient amplification of large-scale secondary structures developing in a square duct for which the unidirectional base motion has a turbulent-like profile. Under the hypothesis that fine-scale turbulence does not affect the growth of large-scale secondary flows, it is shown that cross-stream vortices are sustained by the mean flow and grow maximally over a streamwise distance of several thousand viscous units of length.

Trapped vortices and a favourable pressure gradient

It is shown that there exist bodies such that in two-dimensional steady inviscid incompressible flow the pressure gradient is favourable over the entire surface of the body, and the lift is non-zero, if the body is immersed in a uniform stream and there are also two trapped point vortices.

Formation of Secondary Vortices in Turbulent Square-Duct Flow

A linear approach, inspired by hydrodynamic stability theory, is used to describe the formation of large-scale coherent vortices for the turbulent flow that develops in a duct of square cross section. A set of equations for small-amplitude coherent motion is derived and closed with a simple mixing-length strategy. The initial condition that maximizes a chosen functional (related to either the kinetic energy of the coherent motion or the rate of turbulence production) is found through a direct/adjoint numerical approach borrowed from optimal control theory. It is found that different kinds of secondary flows can appear in the duct cross section, sustained by the mean shear. Some of these optimal states display a symmetry about the bisectors and the diagonals of the duct, in agreement with experimental observations and direct numerical simulations.

Secondary Vortices in Turbulent Square Duct Flow (invited)

A linear approach, inspired by hydrodynamic stability theory, is used to describe the presence of large scale coherent vortices for the turbulent flow in a duct of square crosssection. A set of equations for the small-amplitude coherent motion is derived and closed with a simple mixing length strategy. The initial condition that maximizes a chosen functional (related to either the kinetic energy of the coherent motion or the rate of turbulence production) is found through a direct/adjoint numerical approach borrowed from optimal control theory. It is found that different kinds of secondary flows can appear in the duct cross-section, sustained by the mean shear. Some of these optimal states display a symmetry about the bisectors and the diagonals of the duct, in agreement to experimental observations and direct numerical simulations.

Nonlinear Analysis and Control of Detached Model Flows

In this paper we discuss some aspects related to feed-back control of detached flows. We use a very crude model, a single point vortex of variable intensity, to describe the massive separation region past a cusp followed by a smooth cavity. Then we investigate the controllability and the observabilty of the system by standard nonlinear control techniques. We concentrate on the possibility of controlling such a model by a feed-back controller and define the conditions under which the vortex can be asymptotically stabilized about unstable equilibria.Copyright