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 (Rec) of the flow Reynolds number. Conversely, for Reynolds numbers lower than Rec, 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

T-mixer operating with water at different temperatures: Simulation and stability analysis

In this paper we investigate the transition from the vortex to the engulfment regime in a T-mixer when the two entering flows have different viscosity. In particular we consider as working fluid water entering the two inlet channels of the mixer at two different temperatures. Contrary to the isothermal case, at low Reynolds numbers the vortex regime shows only a single reflectional symmetry, due to the nonhomogeneous distribution of the viscosity. Increasing the Reynolds number, a symmetry-breaking bifurcation drives the system to a new steady flow configuration, usually called the engulfment regime, similar to what it is possible to observe in an isothermal case. This flow regime is associated with an increase of the mixing between the two inlet streams. It is shown by direct numerical simulation (DNS) and by stability analysis that the engulfment regime is promoted by the temperature difference. Starting from the DNSs, the resulting flow fields are analyzed in detail considering different temperature jumps between the two inlet boundaries. Furthermore, dedicated linear stability analyses are carried out to investigate the instability mechanism associated with the occurrence of the engulfment regime. In particular, similarly to the case without temperature differences, the onset of engulfment is driven by the momentum equation, and the temperature field does not lead to any additional instability mechanism. However, the existence of a temperature field leads to quantitative changes of the stability characteristics and of the resulting flow fields via a variation of the viscosity coefficient

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 expanding 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 give the best approximation to the available measurements and that at the same time they satisfy as close as possible the non-linear low-order model. The practical use may range from feedback flow control to 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 laminar flow regimes. Comparisons are provided. with existing linear and non-linear estimation techniques

Suppression of von Kármán 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 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 nondimensional permeability allows us 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

Flow dynamics of a dandelion pappus: A linear stability approach

The study and control of flow instabilities is a key problem in aerodynamics. Aircrafts are designed not only to generate the lift force needed to balance their weight but, more importantly, to be stable and reasonably steady when in cruise conditions. Similar flow stability properties are naturally achieved by biological flying objects such as the dandelion seeds that are transported by the wind owing to a disklike structure called a pappus. The pappus creates a parachute flow configuration and is a remarkable prototype of how the wake, which would be unsteady if the pappus was completely impermeable, can be stabilized by changing the body structure so as to allow the flow to pass through. We approach the problem using the approximation of an anisotropic and nonhomogeneous rigid porous disk, combined with the linear stability analysis technique. The results show the presence of a mean porosity threshold beyond which the flow is always characterized by a separated, steady, and axisymmetric recirculating vortex ring. We compare our results with those of real dandelion pappi. The threshold is very close to the experimentally observed values of porosity, explaining why the morphology of the pappus promotes a steady wake regime

Linear stability analysis of wind turbine wakes performed on wind tunnel measurements

Wind tunnel measurements were performed for the wake produced by a three-bladed wind turbine immersed in uniform flow. These tests show the presence of a vorticity structure in the near-wake region mainly oriented along the streamwise direction, which is denoted as the hub vortex. The hub vortex is characterized by oscillations with frequencies lower than that connected to the rotational velocity of the rotor, which previous works have ascribed to wake meandering. This phenomenon consists of transversal oscillations of the wind turbine wake, which might be excited by the vortex shedding from the rotor disc acting as a bluff body. In this work, temporal and spatial linear stability analyses of a wind turbine wake are performed on a base flow obtained with time-averaged wind tunnel velocity measurements. This study shows that the low-frequency spectral component detected experimentally matches the most amplified frequency of the counter-winding single-helix mode downstream of the wind turbine. Then, simultaneous hot-wire measurements confirm the presence of a helicoidal unstable mode of the hub vortex with a streamwise wavenumber roughly equal to that predicted from the linear stability analysi

Permeability sets the linear path instability of buoyancy-driven disks

The prediction of trajectories of buoyancy-driven objects immersed in a viscous fluid is a key problem in fluid dynamics. Simple-shaped objects, such as disks, present a great variety of trajectories, ranging from zig-zag to tumbling and chaotic motions. Yet, similar studies are lacking when the object is permeable. We perform a linear stability analysis of the steady vertical path of a thin permeable disk, whose flow through the microstructure is modelled via a stress-jump model based on homogenization theory. The relative velocity of the flow associated with the vertical steady path presents a recirculation region detached from the body, which shrinks and eventually disappears as the disk becomes more permeable. In analogy with the solid disk, one non-oscillatory and several oscillatory modes are identified and found to destabilize the fluid-solid coupled system away from its straight trajectory. Permeability progressively filters out the wake dynamics in the instability of the steady vertical path. Modes dominated by wake oscillations are first stabilized, followed by those characterized by weaker, or absent, wake oscillations, in which the wake is typically a tilting induced by the disk inclined trajectory. For sufficiently large permeabilities, the disk first undergoes a non-oscillatory divergence instability, which is expected to lead to a steady oblique path with a constant disk inclination, in the nonlinear regime. A further permeability increase reduces the unstable range of all modes until quenching of all linear instabilities

An Overview of Flow Features and Mixing in Micro T and Arrow Mixers

An overview of the mixing performances of micro T mixers operating with a single fluid is presented. The focus is on the relationship between the flow features and mixing. Indeed, T mixers are characterized by a variety of regimes for increasing Reynolds numbers; they are briefly described, in particular in terms of the three-dimensional vorticity field, which can explain the different mixing performances. The effects of changes in the aspect ratio of the channels are also reviewed. The role of instability and sensitivity analyses in highlighting the mechanisms of the onsets of the different regimes is then described. These analyses also suggest possible geometrical modifications to promote mixing. We focus on that consisting of the downward tilting of the inlet channels (arrow mixers). Arrow mixers are interesting because the onset of the engulfment regime is anticipated at lower Reynolds numbers. Hence, the mixing performances of arrow mixers with varying Reynolds number are described

On the onset of breathing mode in Hall thrusters and the role of electron mobility fluctuations

Breathing mode is an ionization instability which is observed ubiquitously in the operation of Hall thrusters. It is recognized as a relatively low frequency (10-30 kHz) longitudinal oscillation of the discharge current and the plasma parameters. Although breathing instability is widely studied in the literature, the conditions for its origin are not fully understood. In this work we investigate the mechanisms responsible for the origin of the breathing mode in Hall thrusters by using a numerical model, allowing us to highlight the importance of electron mobility fluctuations for the onset and self-sustenance of the instability. Our one-dimensional, fully fluid model of the thruster channel is calibrated against the measured discharge current signal for a 5 kW-class Hall thruster operating in a condition where breathing mode is fully developed. The corresponding steady, unstable configuration (base state) is numerically computed by applying the Selective Frequency Damping (SFD) method. Then, a series of numerical tests is performed to show the existence of a feedback loop involving fluctuations around the base state of the neutral density, electron mobility, and electric field. We show that oscillations of the electron mobility are mainly caused by variations of the neutral density and are in phase with them; this, in turn, induces oscillations of the electric field, which are in phase opposition. The electric field acts simultaneously on the electron temperature and on the ion dynamics, promoting the depletion and replenishment of neutrals in the chamber