Marco Carini

Global stability and control of the confined turbulent flow past a thick flat plate

This article investigates the structural stability and sensitivity properties of the confined turbulent wake behind an elongated D-shaped cylinder of aspect-ratio 10 at Re = 32 000. The stability analysis is performed by linearising the incompressible Navier-Stokes equations around the numerically computed and the experimentally measured mean flows. We found that the vortex-shedding frequency is very well captured by the leading unstable global mode, especially when the additional turbulent diffusion is modelled in the stability equations by means of a frozen eddy-viscosity approach. The sensitivity maps derived from the computed and the measured mean flows are then compared, showing a good qualitative agreement. The careful inspection of their spatial structure highlights that the highest sensitivity is attained not only across the recirculation bubble but also at the body blunt-edge, where tiny pockets of maximum receptivity are found. The impact of the turbulent diffusion on the obtained results is investigated. Finally, we show how the knowledge of the unstable adjoint global mode of the linearised mean-flow dynamics can be exploited to design an active feedback control of the unsteady turbulent wake, which leads, under the adopted numerical framework, to completely suppress its low-frequency oscillation.

Secondary Instability of the Flow Past Two Side-by-side Cylinders

In this work the flip-flop instability occurring in the flow past two side-by-side circular cylinders is numerically investigated at a fixed nondimensional gap spacing of \(g=0.7\) and within the range of Reynolds numbers \(60< \textit{Re}\le 90\). The inherent two-dimensional flow pattern is characterized by an asymmetric unsteady wake (with respect to the horizontal axis of symmetry) and the gap flow is deflected alternatively toward one of the cylinders. Such behaviour has been ascribed by other authors to a bi-stability of the flow, and therefore termed flip-flop. On the contrary, the simulations performed herein provide new evidence that at low Reynolds numbers the flip-flopping state develops through an instability of the in-phase synchronized vortex shedding between the two cylinder wakes. This new scenario is confirmed and explained by means of a global linear stability investigation of the in-phase periodic base flow. The Floquet analysis reveals indeed that a pair of complex-conjugate multipliers becomes unstable above the critical threshold of \(\textit{Re}=61.74\) having the same low frequency as the gap flow flip-over.

Direct-numerical-simulation-based measurement of the mean impulse response of homogeneous isotropic turbulence

A technique for measuring the mean impulse response function of stationary homogeneous isotropic turbulence is proposed. Such a measurement is carried out here on the basis of direct numerical simulation (DNS). A zero-mean white-noise volume forcing is used to probe the turbulent flow, and the response function is obtained by accumulating the space-time correlation between the white forcing and the velocity field. This technique to measure the turbulent response in a DNS numerical experiment is a research tool in that field of spectral closures where the linear-response concept is invoked either by resorting to renormalized perturbations theories or by introducing the well-known fluctuation-dissipation relation (FDR). Although the results obtained in the present work are limited to relatively low values of the Reynolds number, a preliminary analysis is possible. Both the characteristic form and the time scaling properties of the response function are investigated in the universal subrange of dissipative wave numbers; a comparison with the response approximation given by the FDR is proposed through the independent DNS measurement of the correlation function. Very good agreement is found between the measured response and Kraichnans description of random energy-range advection effects.

Cylinder Wake Stabilization Using a Minimal Energy Compensator

In the present work a linear feedback control strategy is used to control and suppress the cylinder vortex-shedding at low Reynolds numbers. The classical minimal control energy or small gain solution of the optimal control and estimation problems is exploited in order to design a full-dimensional stabilizing compensator of the linearized Navier–Stokes equations. Both feedback and observer gains are efficiently computed based solely on the knowledge of the unstable adjoint and direct global modes, respectively. In our control setup, the actuation is realized by means of angular oscillations of the cylinder surface while a single velocity sensor is employed for the state estimation. For \(\text {Re}=50\) the derived compensator is shown to be able to drive the flow from the natural limit cycle to the unstable steady state which is finally restored. Then the sensitivity of the control performance to the sensor placement and the Reynolds number is investigated.

Global linear stability analysis of the flow around a superhydrophobic circular cylinder

Over the last few years, superhydrophobic (SH) surfaces have been receiving an increasing attention in many scientific areas by virtue of their ability to enhance flow slip past solid walls and reduce the skin-friction drag. In the present study, a global linear-stability analysis is employed to investigate the influence of the SH-induced slip velocity on the primary instability of the 2D flow past a circular cylinder. The flow regions playing the role of ‘wavemaker’ are identified by considering the structural sensitivity of the unstable mode, thus highlighting the effect of slip on the global instability of the considered flow. In addition, a sensitivity analysis to slip-induced base-flow modifications is performed, revealing which areas of the cylinder surface provide a stabilising/destabilising effect when treated with a SH coating.