Flavio Giannetti

Structural sensitivity of the first instability of the cylinder wake

The stability properties of the flow past an infinitely long circular cylinder are studied in the context of linear theory. An immersed-boundary technique is used to represent the cylinder surface on a Cartesian mesh. The characteristics of both direct and adjoint perturbation modes are studied and the regions of the flow more sensitive to momentum forcing and mass injection are identified. The analysis shows that the maximum of the perturbation envelope amplitude is reached far downstream of the separation bubble, where as the highest receptivity is attained in the near wake of the cylinder, close to the body surface. The large difference between the spatial structure of the two-dimensional direct and adjoint modes suggests that the instability mechanism cannot be identified from the study of either eigenfunctions separately. For this reason a structural stability analysis of the problem is used to analyse the process which gives rise to the self-sustained mode. In particular, the region of maximum coupling among the velocity components is localized by inspecting the spatial distribution of the product between the direct and adjoint modes. Results show that the instability mechanism is located in two lobes placed symmetrically across the separation bubble, confirming the qualitative results obtained through a locally plane-wave analysis. The relevance of this novel technique to the development of effective control strategies for vortex shedding behind bluff bodies is illustrated by comparing the theoretical predictions based on the structural perturbation analysis with the experimental data of Strykowski & Sreenivasan ( J. Fluid Mech. vol. 218, 1990, p. 71).

Instability and sensitivity of the flow around a rotating circular cylinder

The two-dimensional flow around a rotating circular cylinder is studied at Re = 100. The instability mechanisms for the first and second shedding modes are analysed. The region in the flow with a r ...

Effect of confinement on three-dimensional stability in the wake of a circular cylinder

This paper investigates the three-dimensional stability of the wake behind a symmetrically confined circular cylinder by a linear stability analysis. Emphasis has been placed on discussing analogies and differences with the unconfined case to highlight the role of the inversion of the von Karman street in the nature of the three-dimensional transition. Indeed, in this flow, the vortices of opposite sign that are alternately shed from the body into the wake cross the symmetry line further downstream and they assume a final configuration which is inverted with respect to the unconfined case. It is shown that the transition to a three-dimensional state has the same space-time symmetries of the unconfined case, although the shape of the linearly unstable modes is affected by the inversion of the wake vortices. A possible interpretation of this result is given here.

On the inversion of the von Kármán street in the wake of a confined square cylinder

This paper considers the incompressible two-dimensional laminar flow around a square cylinder symmetrically positioned in a channel. In this type of flow, even if vortices of opposite sign are alternately shed from the body into the wake as in the unconfined case, an inversion of their position with respect to the flow symmetry line takes place further downstream. A numerical analysis is carried out to investigate the physical origin of this phenomenon and to characterize the position in the wake at which the vortices cross the symmetry line. It is shown that, for low to moderate blockage ratios, the fundamental cause of the inversion of the vortices is the amount of vorticity present in the incoming flow, and a dynamic interpretation in terms of vorticity interference in the wake is given. Further insight is gained through a linear stability analysis of the vortex shedding instability.

Structural sensitivity of the secondary instability in the wake of a circular cylinder

The sensitivity of the three-dimensional secondary instability of a circular-cylinder wake to a structural perturbation of the associated linear equations is investigated. In particular, for a given flow condition, the region of maximum coupling between the velocity components is localized by using the most unstable Floquet mode and its adjoint mode. The variation of this region in time is also found by considering a structural perturbation which is impulsively applied in time at a given phase of the vortex-shedding process. The analysis is carried out for both mode A and mode B types of transition in the wake of a circular cylinder using a finite-difference code. The resulting regions identified as the core of the instability are in full agreement with the results reported in the literature and with the a posteriori checks documented here.

Structural Sensitivity of the Finite-Amplitude Vortex Shedding Behind a Circular Cylinder

In this paper we study the structural sensitivity of the nonlinear periodic oscillation arising in the wake of a circular cylinder for Re47. The sensibility of the periodic state to a spatially localised feedback from velocity to force is analysed by performing a structural stability analysis of the problem. The sensitivity of the vortex shedding frequency is analysed by evaluating the adjoint eigenvectors of the Floquet transition operator. The product of the resulting neutral mode with the nonlinear periodic state is then used to localise the instability core. The results obtained with this new approach are then compared with those derived by Giannetti & Luchini [8]. An excellent agreement is found comparing the present results with the experimental data of Strykowski & Sreenivasan [7].

Global stability and sensitivity analysis of boundary-layer flows past a hemispherical roughness element

We study the full three-dimensional instability mechanism past a hemispherical roughness element immersed in a laminar Blasius boundary layer. The inherent three-dimensional flow pattern beyond the Hopf bifurcation is characterized by coherent vortical structures usually called hairpin vortices. Direct numerical simulation results are used to analyze the formation and the shedding of hairpin vortices inside the shear layer. The first bifurcation is investigated by global-stability tools. We show the spatial structure of the linear direct and adjoint global eigenmodes of the linearized Navier-Stokes equations and use the structural-sensitivity field to locate the region where the instability mechanism acts. The core of this instability is found to be symmetric and spatially localized in the region immediately downstream of the roughness element. The effect of the variation of the ratio between the obstacle height k and the boundary layer thickness δk∗ is also considered. The resulting bifurcation scenario ...

Characterization of the three-dimensional instability in a lid-driven cavity by an adjoint based analysis

In this paper we investigate the three-dimensional stability of the 2D flow generated in a cavity by the motion of two facing walls. An adjoint-based analysis of the most unstable global mode will be performed in order to localize the core of the instability.

Stability and Sensitivity Analysis of Non-Newtonian Flow through an Axisymmetric Expansion

This paper deals with a linear stability analysis of the flow in a circular pipe with a sudden expansion. We consider both Newtonian and non-Newtonian fluid models and a thorough comparison is presented. The stability analysis is completed by an adjoint-based investigation on the sensitivity characteristics of perturbations. The results are discussed and compared, when it is possible, to those already published in the pertinent literature.

Three-dimensional stability, receptivity and sensitivity of non-Newtonian flows inside open cavities

We investigate the stability properties of flows over an open square cavity for fluids with shear-dependent viscosity. Analysis is carried out in context of the linear theory using a normal-mode decomposition. The incompressible Cauchy equations, with a Carreau viscosity model, are discretized with a finite-element method. The characteristics of direct and adjoint eigenmodes are analyzed and discussed in order to understand the receptivity features of the flow. Furthermore, we identify the regions of the flow that are more sensitive to spatially localized feedback by building a spatial map obtained from the product between the direct and adjoint eigenfunctions. Analysis shows that the first global linear instability of the steady flow is a steady or unsteady three-dimensionl bifurcation depending on the value of the power-law index n. The instability mechanism is always located inside the cavity and the linear stability results suggest a strong connection with the classical lid-driven cavity problem.