Matteo Chiatto

This study delves into the construction of reduced-order models (ROMs) of a flow field over a NACA 0012 airfoil at a moderate Reynolds number and an angle of attack of 8∘. Numerical simulations were computed through the finite-volume solver OpenFOAM. The analysis considers two different reduction techniques: the standard Galerkin projection method, which involves projecting the governing equations onto proper orthogonal decomposition modes (POD−ROMs), and the cluster-based network model (CNM), a fully data-driven nonlinear approach. An analysis of the topology of the dominant POD modes was conducted, uncovering a traveling wave pattern in the wake dynamics. We compared the performances of both ROM techniques regarding their prediction of flow field behavior and integral quantities. The ROM framework facilitates the practical actuation of control strategies with significantly reduced computational demands compared to the full-order approach.

The properties of the wake flow behind concave curved cylinders have been investigated analyzing simultaneously the mean velocity profiles extracted along concentric arcs parallel to the cylinder axis and the dynamically most relevant coherent structures obtained by spectral proper orthogonal decomposition. These analyzes have allowed us to determine the position, the extension, and the evolution of the different wake regimes. The velocity measurements have been obtained through the stereo particle image velocimetry (stereo-PIV) technique. The study considers various Reynolds numbers, based on cylinder diameter (240<Re<840), and curvatures. The quarter-of-ring cylinder is first analyzed. Near the cylinder root, the flow exhibits a topology dominated by an oblique vortex shedding, contrary to what is observed in the literature for similar geometric configurations. We attribute this disagreement to differences in the treatment of the free-end conditions that play a role in triggering the shedding regime. We find that the local shedding inclination is driven by the axial velocity, whereas its extension and wavelength depend mainly on the Reynolds number. The near free-end region presents, instead, two counter-rotating standing vortices that induce a cross-wise velocity directed toward the cylinder root and a tip vortex that expands evolving downstream. As the Reynolds number increases, the wake presents irregularities and the shedding spreads becoming nearly normal to the incoming flow. At smaller curvatures, the cylinder free-end becoming more inclined with respect to the incoming flow, and the free-end effects are enhanced. The interaction with the vortex sheets of the standing vortices that develop at the leeward side weakens. As a consequence, these vortices stretch in the stream-wise direction giving rise to the trailing vortices that stem from the cylinder surface and affect the cross-wise velocity distributions.

A data-driven approach to estimate the global spectrum of gravitational planar liquid jets (sheet or curtain flows) is presented in this work. The investigation is carried out by means of two-dimensional numerical simulations performed through the solver BASILISK, based on the one-fluid formulation and the volume-of-fluid approach. The dynamic mode decomposition technique is applied to extract the underlying linear operator, considering random perturbations of the base flow. The effectiveness of this procedure is first evaluated comparing results with those of a simplified one-dimensional curtain model in terms of spectrum and eigenfunctions. The methodology is then applied to a two-dimensional configuration obtaining the BiGlobal spectra for both supercritical (Weber number We > 1) and subcritical (We < 1) regimes. Results highlight that in supercritical regime, the spectrum presents three branches: the upper and lower ones exhibit a purely sinuous behavior with frequencies quite close to those predicted by the one-dimensional model; the middle branch presents a predominant varicose component, increasing with the frequency. The subcritical spectrum, instead, shows that the first two less stable eigenvalues, sorted by increasing frequency, exhibit, respectively, a sinuous and a varicose behavior, while their growth rate is almost the same. As expected, the subcritical regime does not reveal the slow branch. The effect of the density ratio, rρ, between the two phases is investigated, revealing that the flow system is unstable for rρ>0.05. Topological inspections of the leading modes in this unstable configuration show that the predominance of a varicose behavior is related to the rupture of the curtain.