Analisi numerica del flusso attorno a un cilindro circolare libero di muoversi in un fluido

L'elaborato si occupa dello studio numerico del flusso attorno a un cilindro circolare libero di muoversi in un fluido. Si analizza prima il caso del cilindro circolare libero di ruotare immerso in una corrente fluida uniforme e in secondo luogo il caso del cilindro circolare che cade o galleggia, in funzione del rapporto di massa selezionato, in un fluido in quiete

Suppression of von K\'arm\'an vortex streets past porous rectangular cylinders

Although the stability properties of the wake past impervious bluff bodies have been widely examined in the literature, similar analyses regarding the flow around and through porous ones are still lacking. In this work, the effect of the porosity and permeability on the wake patterns of porous rectangular cylinders is numerically investigated at low to moderate Reynolds numbers in the framework of direct numerical simulation combined with local and global stability analyses. A modified Darcy-Brinkman formulation is employed here so as to describe the flow behavior inside the porous media, where also the convective terms are retained to correctly account for the inertial effects at high values of permeability. Different aspect ratios of the cylinder are considered, varying the thickness-to-height ratios, t/d, from 0.01 (flat plate) to 1.0 (square cylinder). The results show that the permeability of the bodies has a strong effect in modifying the characteristics of the wakes and of the associated flow instabilities, while the porosity weakly affects the resulting flow patterns. In particular, the fluid flows through the porous bodies and, thus, as the permeability is progressively increased, the recirculation regions, initially attached to the rear part of the bodies, at first detach from the body and, eventually, disappear even in the near wakes. Global stability analyses lead to the identification of critical values of the permeability above which any linear instability is prevented. Moreover, a different scaling of the non-dimensional permeability allows to identify a general threshold for all the configurations here studied that ensures the suppression of vortex shedding, at least in the considered parameter space.Comment: 31 pages and 17 figure

Stability analysis of boundary layers controlled by miniature vortex generators

It is currently known that Tollmien–Schlichting (TS) waves can be attenuated by the introduction of spanwise mean velocity gradients in an otherwise two-dimensional boundary layer (BL). The stabilizing effect, associated with an extra turbulence production term, is strong enough to obtain a delay in transition to turbulence induced by TS waves, with the implication of reducing skin-friction drag. Miniature vortex generators (MVGs), mounted in an array, have successfully been used to obtain velocity modulations by the generation of alternating high- and low-speed streaks in the spanwise direction to control the BL. Experimentally, an initial amplification of the TS waves has been reported, which takes place in the near-wake region of the MVG array. The higher the streak amplitude, the stronger the downstream stabilizing effect becomes, but with the drawback of experiencing an even stronger initial amplification. This can lead to a sub-critical transitional Reynolds number, which would not only mean that the control has failed but, even worse, also lead to an advancement of the transition location. Here, direct numerical simulations and a local spatial stability analysis have been performed in order to reach a deeper understanding of this behaviour. The results agree well with experiments and we propose an explanation of the described behavior in terms of stability properties of the controlled BL. This important knowledge can be used in future designs of BL modulators, which can lead to improved stability of the control and to an extended region of laminar flow

Boundary layer stabilization using free-stream vortices

In this numerical investigation we explore the possibility of applying free-stream vortices as a passive flow control method for delaying the transition to turbulence. The work is motivated by previous experimental studies demonstrating that stable streamwise boundary layer (BL) streaks can attenuate both two- and three-dimensional disturbances inside the BL, leading to transition delay, with the implication of reducing skin-friction drag. To date, successful control has been obtained using physical BL modulators mounted on the surface in order to generate stable streaks. However, surface mounted BL modulators are doomed to failure when the BL is subject to free-stream turbulence (FST), since a destructive interaction between the two is inevitable. In order to tackle free-stream disturbances, such as FST, a smooth surface is desired, which has motivated us to seek new methods to induce streamwise streaks inside the BL. A first step, in a systematic order, is taken in the present paper to prove the control idea of generating free-stream vortices for the attenuation of ordinary Tollmien–Schlichting waves inside the BL. In this proof-of-concept study we show that, by applying a spanwise array of counter-rotating free-stream vortices, inducing streamwise BL streaks further downstream, it is possible to alter the BL stability characteristics to such a degree that transition delay may be accomplished. For the demonstration we use direct numerical simulations along with stability analysis

Effect of geometry modifications on the engulfment in micromixers: Numerical simulations and stability analysis

The effect of geometry variations on the engulfment regime in micromixers is investigated. The engulfment regime is a steady flow regime resulting from a symmetry-breaking pitchfork bifurcation as the Reynolds number (based on the hydraulic diameter and bulk velocity of the outlet conduit) is increased above a critical value. This flow regime is particularly interesting because it leads to an increase of mixing in micromixers. Here, starting from a T-mixer, the inclination α of the inlet channels is systematically varied, considering both arrow-like (α<0) and Y-mixers (α>0), α=0° denoting a T-mixer. It is shown by direct numerical simulations (DNS) that the engulfment regime is present in all the considered geometries and it starts at progressively lower values of the Reynolds number as α is decreased. The main differences in the flow topology are limited and mainly confined at the confluence region between the two incoming flows. The instability leading to the engulfment regime is further investigated by linear stability analysis. This allows a more accurate prediction of the critical Reynolds number for the onset of engulfment as α is varied and, through an adjoint-based sensitivity analysis, the localization of the corresponding instability core

Mixing performance of arrow-shaped micro-devices.

The process of liquid laminar mixing in arrow-shaped micro-devices is studied by direct numerical simulations. Two different CFD codes, i.e. Fluent (based on finite volume method) and Nek5000 (based on spectral element method) have been used to investigate the flow and concentration fields. Unexpectedly we observe that within the engulfment regime, the degree of mixing first increases and then diminishes as the inlet flow rate is increased. Such reduction in the degree of mixing, not observed in T-shaped mixers, can be imputed to the presence of a strong vortical structure at the center of the mixing channel. This result is important for control operations, as it shows that on one hand arrow type mixers are characterized by higher degree of mixing with respect to T-shaped mixers, but on the other hand they present a narrower range of optimal conditions

Stability and sensitivity analysis of the secondary instability in the sphere wake

The three-dimensional flow past a fixed sphere placed within a uniform stream is investigated. This paper focuses on the second bifurcation, which is responsible for the onset of the unsteadiness. Using the highly efficient Nek5000 parallel solver together with a recently developed numerical algorithm to stabilize and accelerate the numerical solution, it was possible to identify the three-dimensional eigenmode responsible for the second bifurcation. The characteristics of this eigenmode are analyzed in detail. The value of the critical Reynolds number ReIIcr=271.8, as well as the Strouhal number of the arising limit cycle, agree well with previous experimental and numerical investigations. To further assess the nature of the instability, an adjoint-based sensitivity analysis is carried out. The structure of the direct and adjoint modes are discussed, and then the core of the instability is localized. Finally, the sensitivity of the instability to a generic base flow modification is investigated

Stability and sensitivity analysis for flow control

Wakes, jets and boundary layers are examples of open flows, where fluid particles are convected downstream outside the physical domain of interest. These flows can exhibit several types of instabilities, depending on the considered geometry and flow conditions. A common classification in open flows is made according to the features of their instabilities. Flows are called noise amplifiers, or amplifiers, when the instabilities are the result of strong amplifications of external disturbances, that also define their characteristics. Conversely, oscillators are flows that show an intrinsic dynamics and, under specific conditions, synchronised self-sustained oscillations occur. The characterization of the instability mechanisms is the fundamental stage to design effective and efficient control strategies. In this thesis, the study of amplifiers and oscillators is carried out in the framework of the linear stability analysis. Concerning the amplifiers, the study is here addressed to investigate passive methods for transition delay in a Blasius boundary layer, aimed at a reduction of the friction drag. All the control strategies here considered are based on the methods of the spanwise mean velocity gradient, where the laminar-turbulent transition is delayed through a modulation of the velocity inside the boundary layer in spanwise direction. Different control devices are investigated in detail through the use of direct numerical simulations and local stability analyses. The results of the stability problem are summarized in neutral stability curves, that allow to identify promising configurations in terms of stabilization of the Blasius unstable mode. The study of oscillators is here conducted characterizing the leading global unstable modes that define the flow behaviours. The flow in micromixers is first of all investigated using global stability analysis. In particular, starting from the well documented T-junction configuration, variations in geometry and fluid properties are here considered to assess their effects on the onset of different flow regimes. Moreover, the global stability approach is also applied to the flow past a sphere, in order to characterize its second bifurcation that drives the system from a steady asymmetric solution towards an unsteady flow state. Finally, a theoretical work is presented, in which an accurate estimation of the global stability modes and of the characteristics of wakes, under assumption of slowly non-parallel flow, is obtained by a higher-order correction term in the WKBJ asymptotic approximation

Investigation of the symmetry-breaking instability in a T-mixer with circular cross section

This paper investigates the laminar flow inside a T-mixer composed of three pipes with a circular cross section. The flow enters the mixer symmetrically from the two aligned pipes and leaves the device from the third pipe. In similar devices, but involving rectangular channels instead of pipes, an important regime for mixing has been identified, denoted as engulfment. Despite the symmetries of the flow and of the geometry, engulfment is an asymmetric steady regime, which is observed above a critical value (Re-c) of the flow Reynolds number. Conversely, for Reynolds numbers lower than Re-c, the flow regime is steady and symmetric, and it is usually denoted as the vortex regime. In this paper, both the vortex and the engulfment regimes are identified for the considered geometry, and they are characterized in detail by dedicated direct numerical simulations (DNSs). Despite an apparent similitude with the behavior of T-mixers employing rectangular channels, which are the most investigated T-mixers in the literature, substantial differences are observed and highlighted here concerning both regimes, i.e., the vortex and the engulfment ones, and concerning transition between the two. Global stability analysis is finally used in synergy with DNS to investigate the onset of the engulfment regime, which is shown to be related to a symmetry-breaking bifurcation of the vortex regime