On the frequency selection mechanism of the low-Re flow around rectangular cylinders

2022 ◽  
Vol 933 ◽  
Author(s):  
A. Chiarini ◽  
M. Quadrio ◽  
F. Auteri
Keyword(s):  
Aspect Ratio ◽  
Strouhal Number ◽  
Leading Edge ◽  
Stream Velocity ◽  
Frequency Locking ◽  
Trailing Edge ◽  
Aspect Ratios ◽  
Nonlinear Simulations ◽  
Edge Vortex ◽  
Rectangular Cylinders

In the flow past elongated rectangular cylinders at moderate Reynolds numbers, vortices shedding from the leading- and trailing-edge corners are frequency locked by the impinging leading-edge vortex instability. The present work investigates how the chord-based Strouhal number varies with the aspect ratio of the cylinder at a Reynolds number (based on the cylinder thickness and the free-stream velocity) of $Re=400$ , i.e. when locking is strong. Several two-dimensional, nonlinear simulations are run for rectangular and D-shaped cylinders, with the aspect ratio ranging from $1$ to $11$ , and a global linear stability analysis of the flow is performed. The shedding frequency observed in the nonlinear simulations is predicted fairly well by the eigenfrequency of the leading eigenmode. The inspection of the structural sensitivity confirms the central role of the trailing-edge vortex shedding in the frequency locking, as already assumed by other authors. Surprisingly, however, the stepwise increase of the Strouhal number with the aspect ratio reported by several previous works is not fully reproduced. Indeed, with increasing aspect ratio, two distinct flow behaviours are observed, associated with two flow configurations where the interaction between the leading- and trailing-edge vortices is different. These two configurations are fully characterised, and the mechanism of selection of the flow configuration is discussed. Lastly, for aspect ratios close to the jump between two consecutive shedding modes, the Strouhal number is found to present hysteresis, implying the existence of multiple stable configurations. Continuing the lower shedding-mode branch by increasing the aspect ratio, we found that the periodic configuration loses stability via a Neimark–Sacker bifurcation leading to different Arnold tongues. This hysteresis can explain, at least partially, the significant scatter of existing experimental and numerical data.

Linear stability of the steady flow past rectangular cylinders

2021 ◽  
Vol 929 ◽  
Author(s):  
A. Chiarini ◽  
M. Quadrio ◽  
F. Auteri
Keyword(s):  
Aspect Ratio ◽  
Critical Reynolds Number ◽  
Leading Edge ◽  
Curvature Radius ◽  
Trailing Edge ◽  
Aspect Ratios ◽  
A Value ◽  
Flow Past ◽  
Rectangular Cylinders ◽  
Primary Instability

The primary instability of the flow past rectangular cylinders is studied to comprehensively describe the influence of the aspect ratio $AR$ and of rounding the leading- and/or trailing-edge corners. Aspect ratios ranging between $0.25$ and $30$ are considered. We show that the critical Reynolds number ( $\textit {Re}_c$ ) corresponding to the primary instability increases with the aspect ratio, starting from $\textit {Re}_c \approx 34.8$ for $AR=0.25$ to a value of $\textit {Re}_c \approx 140$ for $AR = 30$ . The unstable mode and its dependence on the aspect ratio are described. We find that positioning a small circular cylinder in the flow modifies the instability in a way strongly depending on the aspect ratio. The rounded corners affect the primary instability in a way that depends on both the aspect ratio and the curvature radius. For small $AR$ , rounding the leading-edge corners has always a stabilising effect, whereas rounding the trailing-edge corners is destabilising, although for large curvature radii only. For intermediate $AR$ , instead, rounding the leading-edge corners has a stabilising effect limited to small curvature radii only, while for $AR \geqslant 5$ it has always a destabilising effect. In contrast, for $AR \geqslant 2$ rounding the trailing-edge corners consistently increases $\textit {Re}_c$ . Interestingly, when all the corners are rounded, the flow becomes more stable, at all aspect ratios. An explanation for the stabilising and destabilising effect of the rounded corners is provided.

scholarly journals Leading-Edge Vortex Characteristics of Low-Aspect-Ratio Sweptback Plates at Low Reynolds Number

2021 ◽  
Vol 11 (6) ◽  
pp. 2450
Author(s):  
Jong-Seob Han ◽  
Christian Breitsamter
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Leading Edge ◽  
Flapping Wing ◽  
Flat Plates ◽  
Leading Edge Vortex ◽  
Low Aspect Ratio ◽  
Aspect Ratios ◽  
Oil Flow ◽  
Edge Vortex

A sweptback angle can directly regulate a leading-edge vortex on various aerodynamic devices as well as on the wings of biological flyers, but the effect of a sweptback angle has not yet been sufficiently investigated. Here, we thoroughly investigated the effect of the sweptback angle on aerodynamic characteristics of low-aspect-ratio flat plates at a Reynolds number of 2.85 × 104. Direct force/moment measurements and surface oil-flow visualizations were conducted in the wind-tunnel B at the Technical University of Munich. It was found that while the maximum lift at an aspect ratio of 2.03 remains unchanged, two other aspect ratios of 3.13 and 4.50 show a gradual increment in the maximum lift with an increasing sweptback angle. The largest leading-edge vortex contribution was found at the aspect ratio of 3.13, resulting in a superior lift production at a sufficient sweptback angle. This is similar to that of a revolving/flapping wing, where an aspect ratio around three shows a superior lift production. In the oil-flow patterns, it was observed that while the leading-edge vortices at aspect ratios of 2.03 and 3.13 fully covered the surfaces, the vortex at an aspect ratio of 4.50 only covered up the surface approximately three times the chord, similar to that of a revolving/flapping wing. Based on the pattern at the aspect ratio of 4.50, a critical length of the leading-edge vortex of a sweptback plate was measured as ~3.1 times the chord.

Aspect-ratio effects on rotating wings: circulation and forces

2015 ◽  
Vol 767 ◽  
pp. 497-525 ◽  
Author(s):  
Zakery R. Carr ◽  
Adam C. DeVoria ◽  
Matthew J. Ringuette
Keyword(s):  
Aspect Ratio ◽  
Lift Force ◽  
Slow Growth ◽  
Lift Coefficient ◽  
Leading Edge ◽  
Tip Vortex ◽  
Trailing Edge ◽  
Data Set ◽  
Edge Vortex ◽  
Total Circulation

AbstractWe employ experiments to study aspect ratio ($\def\AR{A\mkern-8muR}\AR$) effects on the vortex structure, circulation and lift force for flat-plate wings rotating from rest at 45° angle of attack, which represents a simplified hovering-wing half-stroke. We use the time-varying, volumetric $\AR =2$ data of Carr et al. (Exp. Fluids, vol. 54, 2013, pp. 1–26), reconstructed from phase-locked, phase-averaged stereoscopic digital particle image velocimetry (S-DPIV), and an $\AR =4$ volumetric data set matching the span-based Reynolds number ($\mathit{Re}$) of $\AR =2$. For $\AR =1{-}4$ and $\mathit{Re}_{\mathit{span}}$ of $O$($10^{3}$–$10^{4}$), we directly measure the lift force. The total leading-edge-region circulation for $\AR =2$ and 4 compares best overall using a span-based normalization and for matching rotation angles. The total circulation increases across the span to the tip region, and is larger for $\AR =2$. After the startup, the total circulation for each $\AR$ has a similar slope and a slow growth. The first leading-edge vortex (LEV) and the tip vortex (TV) for $\AR =4$ move past the trailing edge, followed by substantial breakdown. For $\AR =2$ the outboard, aft-tilted LEV merges with the TV and resides over the tip, although breakdown also occurs. Where the LEV is ‘stable’ inboard, its circulation saturates for $\AR =2$ and the growth slows for $\AR =4$. Aft LEV tilting reduces the spanwise LEV circulation for each $\AR$. Both positive and negative axial flow are found in the first LEV for $\AR =2$ and 4, with the positive component being somewhat larger. This yields a generally positive (outboard) average vorticity flux. The average lift coefficient is essentially constant with $\AR$ from 1 to 4 during the slow growth phase, although the large-time behaviour shows a slight decrease in lift coefficient with increasing $\AR$. The S-DPIV data are used to obtain the lift impulse and the spanwise and streamwise components contributing to the lift coefficient. The spanwise contribution is similar for $\AR =2$ and 4, due to similar trailing-edge vortex interactions, LEV saturation behaviour and total circulation slopes. However, for $\AR =2$ the streamwise contribution is much larger, because of the stronger, coherent TV and aft-tilted LEV, which will create a relatively lower-pressure region over the tip.

The role of advance ratio and aspect ratio in determining leading-edge vortex stability for flapping flight

2014 ◽  
Vol 751 ◽  
pp. 71-105 ◽  
Author(s):  
R. R. Harbig ◽  
J. Sheridan ◽  
M. C. Thompson
Keyword(s):  
Aspect Ratio ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Leading Edge Vortex ◽  
Aspect Ratios ◽  
Edge Vortex ◽  
Advance Ratio ◽  
Vorticity Production ◽  
The Stability

AbstractThe effects of advance ratio and the wing’s aspect ratio on the structure of the leading-edge vortex (LEV) that forms on flapping and rotating wings under insect-like flight conditions are not well understood. However, recent studies have indicated that they could play a role in determining the stable attachment of the LEV. In this study, a numerical model of a flapping wing at insect Reynolds numbers is used to explore the effects of these parameters on the characteristics and stability of the LEV. The word ‘stability’ is used here to describe whether the LEV was attached throughout the stroke or if it was shed. It is demonstrated that increasing the advance ratio enhances vorticity production at the leading edge during the downstroke, and this results in more rapid growth of the LEV for non-zero advance ratios. Increasing the wing aspect ratio was found to have the effect of shortening the wing’s chord length relative to the LEV’s size. These two effects combined determine the stability of the LEV. For high advance ratios and large aspect ratios, the LEV was observed to quickly grow to envelop the entire wing during the early stages of the downstroke. Continued rotation of the wing resulted in the LEV being eventually shed as part of a vortex loop that peels away from the wing’s tip. The shedding of the LEV for high-aspect-ratio wings at non-zero advance ratios leads to reduced aerodynamic performance of these wings, which helps to explain why a number of insect species have evolved to have low-aspect-ratio wings.

Particle image velocimetry and visualization of natural and forced flow around rectangular cylinders

2003 ◽  
Vol 478 ◽  
pp. 299-323 ◽  
Author(s):  
RICHARD MILLS ◽  
JOHN SHERIDAN ◽  
KERRY HOURIGAN
Keyword(s):  
Particle Image Velocimetry ◽  
Flow Visualization ◽  
Vortex Shedding ◽  
Particle Image ◽  
Leading Edge ◽  
Trailing Edge ◽  
Image Velocimetry ◽  
Edge Vortex ◽  
Rectangular Cylinders ◽  
Leading Edge Vortices

Particle image velocimetry (PIV) measurements and flow visualization in a water tunnel show that vortex shedding at the leading and trailing edges of rectangular cylinders can be simultaneously phase-locked to transverse velocity perturbations when the applied perturbation Stp is close to an impinging leading-edge vortex/trailing-edge vortex shedding (ILEV/TEVS) frequency. The transverse perturbations, analogous to β-mode duct acoustic resonances, are generated through harmonic oscillations of the sidewalls. When this occurs, the leading-edge vortices are found always to pass the trailing edge at the same phase in the perturbation cycle regardless of the chord-to-thickness (c/t) ratio. Applying perturbations at an Stp not equal to the natural global frequency also results in phase-locked vortex shedding from the leading edge, and a near wake with a frequency equal to the perturbation frequency. This is consistent with previous experimental findings. However, vortex shedding at the trailing edge is either weaker or non-existent. PIV results and flow visualization showed trailing-edge vortex growth was weaker because leading-edge vortices arrive at the trailing edge at a phase in the perturbation cycle where they interfere with trailing-edge shedding. The frequencies at which trailing-edge vortices form for different c/t ratios correspond to the natural ILEV/TEVS frequencies. As in the case of natural shedding, peaks in base suction occur when the leading-edge vortices pass the trailing edge at the phase in the perturbation cycle (and thus in the leading-edge shedding cycle) that allows strong trailing-edge shedding. This is the reason for the similarity in the Stvs.c/t relationship for three seemingly different sets of experiments.

scholarly journals On the lift-optimal aspect ratio of a revolving wing at low Reynolds number

2018 ◽  
Vol 15 (143) ◽  
pp. 20170933 ◽  
Author(s):  
T. Jardin ◽  
T. Colonius
Keyword(s):  
Aspect Ratio ◽  
Lift Coefficient ◽  
Leading Edge ◽  
Rossby Number ◽  
Subsequent Work ◽  
High Lift ◽  
Low Aspect Ratio ◽  
Axis Of Rotation ◽  
Edge Vortex ◽  
Convergent Solution

Lentink & Dickinson (2009 J. Exp. Biol. 212 , 2705–2719. ( doi:10.1242/jeb.022269 )) showed that rotational acceleration stabilized the leading-edge vortex on revolving, low aspect ratio (AR) wings and hypothesized that a Rossby number of around 3, which is achieved during each half-stroke for a variety of hovering insects, seeds and birds, represents a convergent high-lift solution across a range of scales in nature. Subsequent work has verified that, in particular, the Coriolis acceleration plays a key role in LEV stabilization. Implicit in these results is that there exists an optimal AR for wings revolving about their root, because it is otherwise unclear why, apart from possible morphological reasons, the convergent solution would not occur for an even lower Rossby number. We perform direct numerical simulations of the flow past revolving wings where we vary the AR and Rossby numbers independently by displacing the wing root from the axis of rotation. We show that the optimal lift coefficient represents a compromise between competing trends with competing time scales where the coefficient of lift increases monotonically with AR, holding Rossby number constant, but decreases monotonically with Rossby number, when holding AR constant. For wings revolving about their root, this favours wings of AR between 3 and 4.

Separating and Reattaching Flow Structure in a Suddenly Expanding Rectangular Duct

1995 ◽  
Vol 117 (1) ◽  
pp. 17-23 ◽  
Author(s):  
G. Papadopoulos ◽  
M. V. O¨tu¨gen
Keyword(s):  
Aspect Ratio ◽  
Flow Structure ◽  
Three Dimensional ◽  
Side Wall ◽  
Stream Velocity ◽  
Rectangular Duct ◽  
Mean Flow ◽  
Wall Effects ◽  
Velocity Measurements ◽  
Aspect Ratios

The incompressible turbulent flow over a backward-facing step in a rectangular duct was investigated experimentally. The side wall effects on the core flow were determined by varying the aspect ratio (defined as the step span-to-height ratio) from 1 to 28. The Reynolds number, based on the step height and the oncoming free-stream velocity, was 26,500. Detailed velocity measurements were made, including the turbulent stresses, in a region which extended past the flow reattachment zone. Wall static pressure was also measured on both the step and flat walls. In addition, surface visualizations were obtained on all four walls surrounding the separated flow to supplement near-wall velocity measurements. The results show that the aspect ratio has an influence on both the velocity and wall pressure even for relatively large aspect ratios. For example, in the redevelopment region downstream of reattachment, the recovery pressure decreases with smaller aspect ratios. The three-dimensional side wall effects tend to slow down the relaxation downstream of reattachment for smaller aspect ratios as evidenced by the evolution of the velocity field. For the two smallest aspect ratios investigated, higher centerplane streamwise and transverse velocities were obtained which indicate a three-dimensional mean flow structure along the full span of the duct.

An Investigation of the Flow around Rectangular Cylinders

1972 ◽  
Vol 23 (3) ◽  
pp. 229-237 ◽  
Author(s):  
P W Bearman ◽  
D M Trueman
Keyword(s):  
Drag Coefficient ◽  
Strouhal Number ◽  
Pressure Coefficient ◽  
Base Pressure ◽  
Trailing Edge ◽  
Rectangular Cylinders

SummaryMeasurements are presented of the base pressure coefficient, drag coefficient and Strouhal number of rectangular cylinders. The results confirm a finding in Japan that the drag coefficient rises to nearly 3 when the depth of the section is just over half the width. The flow around the sections is found to be strongly influenced by the presence of the trailing-edge corners.

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