Simone Camarri

Low-dimensional modelling of a confined three-dimensional wake flow

The laminar flow past a square cylinder symmetrically placed between two parallel walls is considered. A classical vortex wake is shed from the cylinder, but three-dimensional instabilities are present and they develop in complicated flow patterns. The possibility of extracting an accurate low-order model of this flow is explored.

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.

Investigation of the steady engulfment regime in a three-dimensional T-mixer

The steady engulfment regime in a fully three-dimensional micro T-mixer is investigated. This regime is of significant interest for applications since it implies high mixing between the flow streams entering the device. Direct numerical simulations are first used to characterize this regime. In particular, the main vortical structures typical of the engulfment regime and their effects on mixing are investigated. Three-dimensional linear stability analysis is successively applied to the characterization of the instability leading to the engulfment regime. The critical Reynolds number and the global unstable mode are first computed for a configuration characterized by fully-developed inlet velocity conditions. The sensitivity of this instability to a generic modification of the base flow is then investigated, thanks to the computation of the mode adjoint to the direct unstable one. Finally, this kind of analysis is specialized to investigate the effect of a perturbation of the velocity distribution at the i...

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.

Stability analysis and control of the flow in a symmetric channel with a sudden expansion

The laminar flow in two-dimensional diffusers may produce either symmetric or nonsymmetric steady solutions, depending on the value of the Reynolds number as compared with some critical value. The stability properties of the flow are studied in the context of linear theory. In this context, a sensitivity analysis of the flow instability is carried out with respect to perturbations that may be produced by a realistic passive control, thus providing qualitative hints and quantitative information for the control design. Following the so-obtained information, a passive control is built by introducing a small cylinder in the flow with the aim of stabilizing the unstable symmetric flow configuration in the diffuser. The effectiveness of this control is finally assessed by direct numerical simulation. It is shown that the introduction of the cylinder, placed following the indications of the linear sensitivity analysis in the stable asymmetric flow configuration, allows a steady completely symmetric or less asymm...

Feedback control by low-order modelling of the laminar flow past a bluff body

In this work a two-dimensional laminar flow past a square cylinder is considered. Actuators placed on the cylinder enable active control by blowing and suction. Proportional feedback control is then applied using velocity measurements taken in the cylinder wake. Projection onto an empirical subspace is combined with a calibration technique to build a low-order model of the incompressible Navier-Stokes equations. This model is used within an optimization method to determine a set of feedback gains which reduces the unsteadiness of the wake at Re = 150. The resulting controlled flows are further characterized by computing the critical Reynolds numbers for the onset of the vortex shedding instability.

Feedback control of the vortex-shedding instability based on sensitivity analysis

In the present work, a simple proportional feedback control is designed to suppress the vortex-shedding instability in the wake of a prototype bluff-body flow, i.e., the flow around a square cylinder confined in a channel with an incoming Poiseuille flow. Actuation is provided by two jets localized on the cylinder surface and velocity sensors are used for feedback control. This particular configuration is a pretext to propose a more general strategy for designing a controller, which is independent of the type of actuation and sensors. The method is based on the linear stability analysis of the flow, carried out on the unstable steady solution of the equations, which is also the target flow of the control. The idea is to use sensitivity analysis to predict the displacement in the complex plane of some selected eigenvalues, found by the linear stability analysis of the flow, as a function of the control design parameters. In this paper, it is shown that the information provided by only sensitivity analysis ...

Unsteady asymmetric engulfment regime in a T-mixer

Unsteady flow regimes in a micro T-mixer are investigated. Direct numerical simulations (DNS) show that, in agreement with experimental and numerical results in the literature, when the Reynolds number is increased above a critical value larger than those typical of the steady engulfment regime, the flow remains asymmetric in the mean but becomes periodic in time. The dynamics of this regime is characterized by analyzing the evolution of the three-dimensional vortical structures forming at the confluence of the two inlet flow streams. As the Reynolds number is further increased, the flow remains time-periodic but it continuously switches between a symmetric configuration, similar to that of the vortical regime, and an asymmetric one, close to the engulfment configuration. Three-dimensional linear stability analysis is successively used to characterize the instability leading to the unsteady asymmetric regime, which is also interesting for applications due to its high mixing efficiency. The critical Reynol...

A non-linear observer for unsteady three-dimensional flows

A method is proposed to estimate the velocity field of an unsteady flow using a limited number of flow measurements. The method is based on a non-linear low-dimensional model of the flow and on an expansion of the velocity field in terms of empirical basis functions. The main idea is to impose that the coefficients of the modal expansion of the velocity field gives the best approximation of the available measurements, while at the same time satisfying the non-linear low-order model as closely as possible. Practical applications may range from feedback flow control to the monitoring of the flow in non-accessible regions. The proposed technique is applied to the flow around a confined square cylinder, both in two- and three-dimensional flow regimes. Comparisons are provided with existing linear and non-linear estimation techniques.