Flag Configuration Research Articles

Multiple solutions and orbit change in energy harvesting system with a flag configuration

AbstractThe aim of this paper is to present a methodology for implementing the high-energy orbits which is still an open problem for nonlinear energy harvesters. To achieve it, this paper presents a new design of system with a flag configuration which potential function is shaped with the use of elastic elements. We have identified the lift force in FEM for wide spectrum of air velocities and used it as excitation in dimensionless mathematical model. On this basis we have conducted simulations of energy harvesting effectiveness. In the second part of the work, we focused on identifying the coexisting solutions. Due to the existence of high-energy orbits and low-energy orbits, we conducted simulations to investigate the possibility of changing the orbit. We used the Impulse Excitation Diagram here, but supplemented it with multi-colored probability distribution maps illustrating the possibility of achieving a stable orbit at given numerical values of the impulse amplitude and duration for various values of air flow velocity. The use of probability distribution maps allow to select the optimal impulse characteristics from the point of view of the energy necessary for its initiation.

Flag Fluttering‐Triggered Piezoelectric Energy Harvester at Low Wind Speed Conditions

Flow‐induced vibrations are common occurrences in various fluid–solid interaction systems existing in nature. One way to transform this vibrational mechanical energy into a usable form is through energy harvesters. This study examines the performance of a piezoelectric energy harvester, where mechanical oscillations result from the fluttering flags made of various fabrics. Flags, made of commonly encountered fabrics, are attached to a cantilever beam inside a wind tunnel with a 30 × 30 cm test section, allowing the airflow to be adjusted between 0 and 10 m s−1. The alpaca flag, with dimensions corresponding to an aspect ratio of 2, can produce meaningful electricity even at a wind speed as low as ≈3.8 m s−1. As the wind speed increases, the fluttering frequency of this flag configuration becomes 10.9 Hz at a wind speed of 5 m s−1, coinciding with the natural frequency of the first mode shape. In this specific arrangement, the structural deformation of the piezoelectric patch on the beam surface is maximized, allowing the harvester system to produce a root mean square voltage of 5 V with a relatively high maximum power of 98 μW.

Flapping dynamics of an inverted flag behind a cylinder

The inverted flag configuration is inspired by biological structures (e.g. leaves on a tree branch), showing rich dynamics associated with instabilities at lower flow speeds than the regular flag configuration. In the biological counterpart, the arrangement of leaves and twigs on foliage creates a complex interacting environment that promotes certain dynamic fluttering modes. While enabling a large amplitude response for reduced flow speeds is advantageous in emerging fields such as energy harvesting, still, little is known about the consequence of such interactions. In this work, we numerically study the canonical bio-inspired problem of the flow-structural interaction of a 2D inverted flag behind a cylindrical bluff body, mimicking a leaf behind a tree branch, to investigate its distinct fluttering regimes. The separation distance between the cylinder and flag is gradually modified to determine the effective distance beyond which small-amplitude or large-amplitude flapping occurs for different flow velocities. It is shown that the flag exhibits a periodic large amplitude−low frequency response mode when the cylinder is placed at a sufficiently large distance in front of the flag. At smaller distances, when the flag is within the immediate wake of the cylinder, the flag undergoes a high frequency−small amplitude response. Finally, the flag’s piezoelectric power harvesting capability is investigated numerically and experimentally for varying geometrical and electrical parameters associated with these two conditions. Two separate optimal response modes with the highest energy output have also been identified.

Comprehensive experimental study on bluff body shapes for vortex-induced vibration piezoelectric energy harvesting mechanisms

• Both bluff body shape and flag configuration are two crucial factors. • The bluff body shapes with higher drag coefficients can harvest more energy. • Short full active flags generate more energy in higher wind speed. • A new experimental approach in flexible VIV piezoelectric energy harvester. • Electrode pattern are as important as upstream bluff body shapes. Vortex-induced vibration (VIV) is an appropriate mechanism to harvest energy from the low-speed wind energy by flexible piezoelectric flags as transducers. To enhance the low-speed wind energy harvesting, this work proposes a novel study on finding the best possible combination of bluff body shape and flag configuration. This study considered several bluff body shapes in different cross sections and flag configurations as two crucial parameters for finding an appropriate combination. In high flexible piezoelectric flag, zero strain or electrical canceling point along the length of the flag is an important parameter that could be considered in energy harvester design. To this purpose, wind tunnel experiments were conducted to investigate the combination of proper bluff body shape and flag configuration to improve the harvester performance. The proposed bluff body shapes are classified by drag and lift coefficients which are calculated by a computational fluid dynamics (CFD) analysis. Then, several flag configurations in different active area length were clamped to these bluff bodies and tested in the wind tunnel in low wind speed range. The analysis in time and frequency domain of the acquired voltage lead to the conclusion that in low wind speed the bluff body with higher drag coefficients can excite more the longer full active piezoelectric flags, consequently generating more energy. However, for the same bluff body shapes, short full active flags generate more energy in higher wind speed. This study could develop a new experimental approach on finding the most favorable combination of bluff body shape and flag configuration which is as important as just considering bluff body shape to improve the efficiency of the low-speed wind piezoelectric energy harvesting system.

Design and Analysis of a Small-Size, Flag-Shape UWB Antenna with Dual Notch Band Using Mushroom Structure

A small-size, flag-shaped microstrip-fed printed UWB antenna with dual notch band (NB) is investigated. The essence of flag configuration is evolved from the regular hexagon where both shapes provide UWB responses. Then, the WiMAX and WLAN notch bands are created by using electromagnetic bandgap (EBG) structures for avoiding potential interference. A microstrip line-based model is employed to investigate the NB characteristics of EBG. Various parameters, surface current distribution and input impedance are analyzed to understand the effects of the mushroom. The measured operating frequency of the proposed antenna is from 2.91[Formula: see text]GHz to 10.88[Formula: see text]GHz along with excellent rejection bands of 3.2–3.54[Formula: see text]GHz and 5.13–5.6[Formula: see text]GHz, respectively, for [Formula: see text][Formula: see text]dB. The experimental result has good correlation with the simulated one. The designed antenna exhibits minimal gain variation, appreciable efficiency, stable radiation patterns, transfer function and the time-domain study results correspond well to [Formula: see text] in the pass band. Therefore, satisfactory results ensure its ability to work as a UWB antenna.

Planform geometry effects of piezoelectric wind energy harvesting composite inverted flags

Energy harvesting devices based on the inverted flag configuration have recently attracted attention as a viable option to power small electronics and remote wireless sensors from wind excitation. Despite showing high potential, relatively little research has considered how the dynamics and power generation performance of these devices vary with planform geometry. This study considers composite inverted flags constructed using flexible polyvinylidene difluoride strips as active elements sandwiching a stainless-steel shim as elastic structural support, a configuration allowing for enhanced ability to tailor mechanical and geometrical properties (and hence responses) of the flag. We explore the effect of three key parameters (planform aspect ratio, mass ratio, second moment of area) on flag dynamics (amplitude, flapping frequency) and operational characteristics (power, velocity range). Twelve flags have been manufactured and tested under controlled wind excitation, selected to cover aspect ratios in the range of 0.9–7 and mass ratios in the range of 7–14. Our results expose a number of useful insights into how these devices perform. First, we show that for a given mass ratio, flapping amplitude, frequency, power, and power density are all inversely proportional to aspect ratio and proportional to second moment of planform area. Second, we show that second moment of planform area is a better indicator parameter to assess the flags performance, as compared to the aspect ratio. Third, we show that as mass ratio increases higher power densities and wider operational velocity ranges are allowed; however, this is on the expense of the flag being more sensitive to variations in operating conditions and the possibility of experiencing some unfavourable motion behaviour such as the ‘one-sided’ low-amplitude high-frequency low-power flapping mode.

Heat transfer enhancement in a poiseuille channel flow by using multiple wall-mounted flexible flags

The flapping dynamics of multiple wall-mounted flexible flags vertically clamped in a heated channel and their effects on heat transfer performance were explored numerically. The fluid-structure-thermal interaction between the flapping flexible flags and the surrounding fluid was modeled with the penalty immersed boundary method. The vortex mixing process was examined to analyze their effects on heat transfer enhancement. The effects of varying the gap distance G/d, the reduced distance d/L, the bending rigidity γ, the channel height H/L and the Reynolds number Re on heat transfer enhancement were scrutinized to optimize cooling, where the flag length is L. The thermal enhancement factor was determined to assess both the heat transfer enhancement benefit and the pressure drop penalty. The asymmetric flag configuration G/d = 0.5 results in better cooling performance than the symmetric configuration G/d = 0 because of the resulting thermal mixing of the cold mainstream and the near-wall hot fluid. More flags can be clamped inside the channel by varying the reduced distance d/L. Multiple flags with γ = 0.04 provide the maximum convective heat transfer at Re = 600. Increasing the blockage ratio, i.e. the ratio of the cross-sectional height occupied by the flags to the channel height, enhances the friction factor.

Geometric structures and configurations of flags in orbits of real forms

This is an introduction and a survey on geometric structures modelled on closed orbits of real forms acting on spaces of flags. We focus on 3-manifolds and the flag space of all pairs of a point and a line containing it in \({\mathbb{P}}({\mathbb{C}}^3)\). It includes a description of general flag structures which are not necessarily flat and a combinatorial description of flat structures through configurations of flags in closed orbits of real forms. We also review volume and Chern–Simons invariants for those structures.

Configurations of flags in orbits of real forms

In this paper we start the study of configurations of flags in closed orbits of real forms using mainly tools of GIT. As an application, using cross ratio coordinates for generic configurations, we identify boundary unipotent representations of the fundamental group of the figure eight knot complement into real forms of $${{\,\mathrm{PGL}\,}}(4,{\mathbb {C}})$$ .

Effect of morphology on the large-amplitude flapping dynamics of an inverted flag in a uniform flow

The stability of a cantilevered elastic sheet in a uniform flow has been studied extensively due to its importance in engineering and its prevalence in natural structures. Varying the flow speed can give rise to a range of dynamics including limit cycle behaviour and chaotic motion of the cantilevered sheet. Recently, the ‘inverted flag’ configuration – a cantilevered elastic sheet aligned with the flow impinging on its free edge – has been observed to produce large-amplitude flapping over a finite band of flow speeds. This flapping phenomenon has been found to be a vortex-induced vibration, and only occurs at sufficiently large Reynolds numbers. In all cases studied, the inverted flag has been formed from a cantilevered sheet of rectangular morphology, i.e. the planform of its elastic sheet is a rectangle. Here, we investigate the effect of the inverted flag’s morphology on its resulting stability and dynamics. We choose a trapezoidal planform which is explored using experiment and an analytical theory for the divergence instability of an inverted flag of arbitrary morphology. Strikingly, for this planform we observe that the flow speed range over which flapping occurs scales approximately with the flow speed at which the divergence instability occurs. This provides a means by which to predict and control flapping. In a biological setting, leaves in a wind can also align themselves in an inverted flag configuration. Motivated by this natural occurrence we also study the effect of adding an artificial ‘petiole’ (a thin elastic stalk that connects the sheet to the clamp) on the inverted flag’s dynamics. We find that the petiole serves to partially decouple fluid forces from elastic forces, for which an analytical theory is also derived, in addition to increasing the freedom by which the flapping dynamics can be tuned. These results highlight the intricacies of the flapping instability and account for some of the varied dynamics of leaves in nature.

Positive configurations of flags in a building and limits of positive representations

Parreau compactified the Hitchin component of a closed surface S of negative Euler characteristic in such a way that a boundary point corresponds to the projectivized length spectrum of an action of $$\pi _1(S)$$ on an $${\mathbb {R}}$$ -Euclidean building. In this paper, we use the positivity properties of Hitchin representations introduced by Fock and Goncharov to explicitly describe the geometry of a preferred collection of apartments in the limiting building.

Effect of Piezo-Embedded Inverted Flag in Free Shear Layer Wake

The use of flexible inverted piezo embedded Polyvinylidene Difluoride (PVDF) as a simultaneous energy harvester and as a wake sensor is explored. The oscillation amplitude (characterized by voltage output) and oscillation frequency of the piezo-embedded PDVF was quantified in the wake of a 2D NACA 0012 model and SD7003 model at a Reynolds number of 100,000 and 67,000, respectively. The performance of the sensor was also quantified in the freestream without the presence of the wing. In order to quantify the sensor response to angle of attack and downstream distance, the amplitude and frequency of oscillations were recorded in the wing wake. Increase in angle of attack of the wing resulted in increase in oscillation frequency and amplitude of the PVDF. The results also indicated that the inverted flag configuration performed better in the wake under unsteady conditions when compared to freestream conditions. The results from Particle Image Velocimetry indicated that the wake signature was not affected by the presence of the PVDF in the wake. The root mean square voltage contours in the wake of SD7003 airfoil show remarkable free shear layer wake features such as upper and lower surface stratification and downwash angle which shows the sensitivity of the sensor to the unsteadiness in the wake. The capability of this device to act as a potential energy harvester and as a sensor has serious implications in extending the mission capabilities of small UAVs.

Configurations of flags and representations of surface groups in complex hyperbolic geometry

In this work, we describe a set of coordinates on the PU(2,1)-representation variety of the fundamental group of an oriented punctured surface Σ with negative Euler characteristic. The main technical tool we use is a set of geometric invariants of a triple of flags in the complex hyperbolic plane $${\bf H^2_{\mathbb {C}}}$$ . We establish a bijection between a set of decorations of an ideal triangulation of Σ and a subset of the PU(2,1)-representation variety of π 1(Σ).

In-Stream Hollow-Fiber Membrane Aeration

Throughout both urban and rural areas across the United States, rivers and streams periodically suffer from low dissolved oxygen concentrations. Current aeration technologies are often expensive or ineffective. Aeration with hollow-fiber membranes has been shown to have the potential to aerate these water courses more cost-effectively than current methods and may be able to provide aeration to locations where traditional technologies are not effective. To optimize mass transfer rates, hollow-fiber membranes in a fiber flag configuration were used. The fiber modules were tested in two different orientations to determine the fiber performance as a function of flow field conditions. The results are compared to more typical fiber configurations. In a second experiment the fiber modules were run continuously in diverted river water for over 1,700 h to determine the long-term performance of the membrane modules in a practical application. The extent of fouling was monitored over the course of the experiment and the fibers were examined to determine if the fouling was biological or chemical in nature. Finally, the previous results were incorporated into a cost comparison between the hollow-fiber membranes and a conventional in-stream aeration technology currently in use.