The Effect of Pitching Frequency on the Hydrodynamics of Oscillating Foils

2019 ◽  
Vol 86 (10) ◽  
Author(s):  
Arman Hemmati ◽  
Alexander J. Smits
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Strouhal Number ◽  
Vortex Formation ◽  
Free Swimming ◽  
Trailing Edge ◽  
Wake Structure ◽  
Abrupt Transition ◽  
Vortex Streets ◽  
Karman Street

Abstract The effects of two different pitching frequencies (that is, Strouhal number, St) on the wake structure generated by two foils of aspect ratio 1.0 are examined numerically at a Reynolds number of 10,000. Strouhal numbers of 0.5 and 0.2 were studied, the first corresponding approximately to the peak in efficiency and the second corresponding to the point where the thrust is equal to the drag (the free-swimming condition). The two foils have either a square trailing edge or a convex trailing edge that mimics the shape of the caudal fin exhibited by certain species of fish. In previous works, the convex trailing edge panel was found to have higher thrust and efficiency compared with the square panel trailing edge. Here, these differences are related to their characteristic vortex formation and detachment processes leading to differences in wake coherence and extension. The wake of the square panel at St = 0.2 transitions slowly from a reverse von Kármán street (2S) pattern to a paired (2P) system as the wake develops downstream, whereas at St = 0.5, the wake almost immediately takes on a 2P form with an attendant split in the wake structure. For the convex panel, the transition from a 2S to a 2P structure at St = 0.2 is slower than that seen for the square panel, and for St = 0.5, the wake undergoes an abrupt transition leading to two distinct vortex streets that evolve at a considerably slower rate than seen for the square panel.

Reynolds Number–Strouhal Number Relationship for Cylindrical Bluff Body with Variation of Aspect Ratio in High Reynolds Number

2014 ◽  
Vol 69 (3) ◽  
Author(s):  
Nor Azwadi Che Sidik ◽  
Tey Wah Yen
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Strouhal Number ◽  
Bluff Body ◽  
Flow Parameters ◽  
Ansys Cfx ◽  
Sst Model ◽  
Model Equations ◽  
High Reynolds ◽  
Volume Method

The effect between Reynolds number and bluff body aspect ratio to the flow parameters such as Strouhal number and drag coefficient are studied. The range of Reynolds number applied is within 10000 and 200000 while three aspect ratio (Ar) where Ar = 1.0, 1.5 and 2.0 are implemented. Finite volume method with the aid of ANSYS CFX codes is deployed using the turbulence SST model. Equations of Re-St relationship for Ar 1.0 and 1.5 are then hypothesized as well in this paper for the range of 10000<Re<100000.

The wake from a cylinder subjected to amplitude-modulated excitation

1993 ◽  
Vol 247 ◽  
pp. 79-110 ◽  
Author(s):  
M. Nakano ◽  
D. Rockwell
Keyword(s):  
Reynolds Number ◽  
Modulation Frequency ◽  
Low Reynolds Number ◽  
Vortex Formation ◽  
Near Wake ◽  
Proper Selection ◽  
Wake Structure ◽  
Far Wake ◽  
Stream Direction ◽  
Selection Of

Controlled, amplitude-modulated excitation of a cylinder at low Reynolds number (Re equals; 136) in the cross-stream direction generates several states of response of the near wake including: a locked-in wake structure, which is periodic at the modulation frequency; a period-doubled wake structure, which is periodic at a frequency half the modulation frequency; and a destabilized structure of the wake, which is periodic at the modulation frequency, but involves substantial phase modulations of the vortex formation relative to the cylinder displacement. The occurrence of each of these states depends upon the dimensionless modulation frequency, as well as the nominal frequency and amplitude of excitation. Transition through states of increasing disorder can be attained by either decreasing the modulation frequency or increasing the amplitude of excitation at a constant value of nominal frequency. These states of response in the near wake are crucial in determining whether the far wake is highly organized or incoherent. Both of these extremes are attainable by proper selection of the parameters of excitation.

scholarly journals The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel

2008 ◽  
Vol 603 ◽  
pp. 331-365 ◽  
Author(s):  
JAMES H. J. BUCHHOLZ ◽  
ALEXANDER J. SMITS
Keyword(s):  
Aspect Ratio ◽  
Strouhal Number ◽  
Three Dimensional ◽  
Leading Edge ◽  
Horseshoe Vortex ◽  
Dimensional Structure ◽  
Peak Efficiency ◽  
Thrust Coefficient ◽  
Wake Structure ◽  
Thrust Performance

Thrust performance and wake structure were investigated for a rigid rectangular panel pitching about its leading edge in a free stream. For ReC = O(104), thrust coefficient was found to depend primarily on Strouhal number St and the aspect ratio of the panel AR. Propulsive efficiency was sensitive to aspect ratio only for AR less than 0.83; however, the magnitude of the peak efficiency of a given panel with variation in Strouhal number varied inversely with the amplitude to span ratio A/S, while the Strouhal number of optimum efficiency increased with increasing A/S. Peak efficiencies between 9% and 21% were measured. Wake structures corresponding to a subset of the thrust measurements were investigated using dye visualization and digital particle image velocimetry. In general, the wakes divided into two oblique jets; however, when operating at or near peak efficiency, the near wake in many cases represented a Kármán vortex street with the signs of the vortices reversed. The three-dimensional structure of the wakes was investigated in detail for AR = 0.54, A/S = 0.31 and ReC = 640. Three distinct wake structures were observed with variation in Strouhal number. For approximately 0.20 < St < 0.25, the main constituent of the wake was a horseshoe vortex shed by the tips and trailing edge of the panel. Streamwise variation in the circulation of the streamwise horseshoe legs was consistent with a spanwise shear layer bridging them. For St > 0.25, a reorganization of some of the spanwise vorticity yielded a bifurcating wake formed by trains of vortex rings connected to the tips of the horseshoes. For St > 0.5, an additional structure formed from a perturbation of the streamwise leg which caused a spanwise expansion. The wake model paradigm established here is robust with variation in Reynolds number and is consistent with structures observed for a wide variety of unsteady flows. Movies are available with the online version of the paper.

A study of three-dimensional aspects of vortex shedding from a bluff body with a mild geometric disturbance

1997 ◽  
Vol 330 ◽  
pp. 85-112 ◽  
Author(s):  
N. TOMBAZIS ◽  
P. W. BEARMAN
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Bluff Body ◽  
Vortex Formation ◽  
Three Dimensional ◽  
Base Pressure ◽  
Trailing Edge ◽  
Blunt Trailing Edge ◽  
Trailing Edges ◽  
Mode Transitions

Experiments have been carried out to study the three-dimensional characteristics of vortex shedding from a half-ellipse shape with a blunt trailing edge. In order to control the occurrence of vortex dislocations, the trailing edges of the models used were constructed with a series of periodic waves across their spans. Flow visualization was carried out in a water tunnel at a Reynolds number of 2500, based on trailing-edge thickness. A number of shedding modes were observed and the sequence of mode transitions recorded. Quantitative data were obtained from wind tunnel measurements performed at a Reynolds number of 40000. Two shedding frequencies were recorded with the higher frequency occurring at spanwise positions coinciding with minima in the chord. At these same positions the base pressure was lowest and the vortex formation length longest. Arguments are put forward to explain these observations. It is shown that the concept of a universal Strouhal number holds, even when the flow is three-dimensional. The spanwise variation in time-average base pressure is predicted using the estimated amount of time the flow spends at the two shedding frequencies.

Three-dimensional simulation of a flapping flag in a uniform flow

2010 ◽  
Vol 653 ◽  
pp. 301-336 ◽  
Author(s):  
WEI-XI HUANG ◽  
HYUNG JIN SUNG
Keyword(s):  
Reynolds Number ◽  
Strouhal Number ◽  
Three Dimensional ◽  
Uniform Flow ◽  
Positive Pressure ◽  
Spanwise Direction ◽  
Trailing Edge ◽  
Vortical Structures ◽  
Significant Difference ◽  
Stabilization Effect

A three-dimensional computational model is developed for simulating the flag motion in a uniform flow. The nonlinear dynamics of the coupled fluid–flag system after setting up of flapping is investigated by a series of numerical tests. At low Reynolds numbers, the flag flaps symmetrically about its centreline when gravity is excluded, and the bending in the spanwise direction is observed near the corners on the trailing edge. As the Reynolds number increases, the spanwise bending is flattened due to the decrease of the positive pressure near the side edges as well as the viscous force of the fluid. At a certain critical Reynolds number, the flag loses its symmetry about the centreline, which is shown to be related to the coupled fluid–flag instability. The three-dimensional vortical structures shed from the flag show a significant difference from the results of two-dimensional simulations. Hairpin or O-shaped vortical structures are formed behind the flag by connecting those generated at the flag side edges and the trailing edge. Such vortical structures have a stabilization effect on the flag by reducing the pressure difference across the flag. Moreover, the positive pressure near the side edges is significantly reduced as compared with that in the center region, causing the spanwise bending. The Strouhal number defined based on the flag length is slightly dependent on the Reynolds number and the flag width, but scales with the density ratio as St ~ ρ−1/2). On the other hand, the flapping-amplitude-based Strouhal number remains close to 0.2, consistent with the values reported for flying or swimming animals. A flag flapping under gravity is then simulated, which is directed along the negative spanwise direction. The sagging down of the flag and the rolling motion of the upper corner are observed. The dual effects of gravity are demonstrated, i.e. the destabilization effect like the flag inertia and the stabilization effect by increasing the longitudinal tension force.

scholarly journals Vortex shedding from a blunt trailing edge with equal and unequal external mean velocities

1976 ◽  
Vol 75 (4) ◽  
pp. 721-735 ◽  
Author(s):  
D. R. Boldman ◽  
P. F. Brinich ◽  
M. E. Goldstein
Keyword(s):  
Steady State ◽  
Flow Visualization ◽  
Strouhal Number ◽  
Vortex Shedding ◽  
Free Stream ◽  
Theoretical Calculations ◽  
Vortex Formation ◽  
Trailing Edge ◽  
Blunt Trailing Edge ◽  
Good Agreement

A flow-visualization study has shown that strong Kármán vortices develop behind the blunt trailing edge of a plate when the free-stream velocities over both surfaces are equal and that the vortices tend to disappear when the surface velocities are unequal. This observation provides an explanation for the occurrence and disappearance of certain discrete tones often found to be present in the noise spectra of coaxial jets. Both the vortex formation and the tones occur at a Strouhal number based on the lip thickness and the average of the external steady-state velocities of about 0.2.Results from theoretical calculations of the vortex formation, based on an inviscid incompressible analysis of the motion of point vortices, were in good agreement with the experimental observations.

Dynamics of Wake Behind a Low Aspect Ratio Pitching Plate

2011 ◽  
Author(s):  
A. K. De
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Vortex Shedding ◽  
Separation Bubble ◽  
Time Integration ◽  
Low Aspect Ratio ◽  
Unsteady Wake ◽  
Lower Reynolds Number ◽  
Vortex Streets ◽  
Predictor Corrector

Vectorized numerical simulations of unsteady wake behind a low-aspect ratio (double amplitude to span ratio 0.3) sinusoidally pitching plate (Strouhal number 0.4 and 0.5) are carried out for the Reynolds number, Re = 150,300. A non-staggered finite volume based predictor-corrector type of algorithm employing 2nd-order time integration and spatial schemes is used. The first sign of instability appears on the plate promoting separation which becomes more vigorous with the increase in Reynolds number. At low Reynolds number, the separation bubble originating near the plate diffuses in the near wake region and the whole wake oscillates with the plate. Fully developed vortex shedding from the rear edge of the plate is observed at a higher Reynolds number. The shed vortices are slowly convected and eventually diffuses completely at a large downstream distance. At a higher forced frequency the wake does not alter significantly at a lower Reynolds number. However, vigorous vortex shedding leading to two layers of vortex streets from both the sides of the plate is observed at a higher Reynolds number.

scholarly journals Numerical Computations of Vortex Formation Length in Flow Past an Elliptical Cylinder

Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 157
Author(s):  
Matthew Karlson ◽  
Bogdan G. Nita ◽  
Ashwin Vaidya
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Vortex Shedding ◽  
Critical Reynolds Number ◽  
Vortex Formation ◽  
Project Based Learning ◽  
Unsteady Regime ◽  
Karman Vortex ◽  
Elliptical Cylinders ◽  
Asymmetric Configuration

We examine two dimensional properties of vortex shedding past elliptical cylinders through numerical simulations. Specifically, we investigate the vortex formation length in the Reynolds number regime 10 to 100 for elliptical bodies of aspect ratio in the range 0.4 to 1.4. Our computations reveal that in the steady flow regime, the change in the vortex length follows a linear profile with respect to the Reynolds number, while in the unsteady regime, the time averaged vortex length decreases in an exponential manner with increasing Reynolds number. The transition in profile is used to identify the critical Reynolds number which marks the bifurcation of the Karman vortex from steady symmetric to the unsteady, asymmetric configuration. Additionally, relationships between the vortex length and aspect ratio are also explored. The work presented here is an example of a module that can be used in a project based learning course on computational fluid dynamics.

Wake Structure and Dynamic Thrust of an Unsteady Airfoil

2005 ◽  
Author(s):  
Masaki Fuchiwaki ◽  
Kazuhiro Tanaka
Keyword(s):  
Reynolds Number ◽  
Dynamic Behavior ◽  
Hysteresis Loops ◽  
Water Tunnel ◽  
Trailing Edge ◽  
Wake Structure ◽  
Velocity Increase ◽  
Pitching Airfoil ◽  
Thrust Efficiency ◽  
Maximum Thrust

The detailed wake structure behind pitching airfoil and heaving airfoil at a low Reynolds number region was measured by PIV. Moreover, dynamic thrust acting on them in water tunnel was measured by a six-axes sensor. At the high non-dimensional trailing edge velocity and the non-dimensional heaving velocity, the thrust producing vortex street is formed clearly. Moreover, it has been founded that not only the distance between vortices becomes narrow but also vorticity increases as the non-dimensional trailing edge velocity and the non-dimensional heaving velocity increase. The averaged dynamic thrust acting on a pitching airfoil and a heaving airfoil increases as the non-dimensional trailing edge velocity and the non-dimensional heaving velocity increase. The hysteresis loops of dynamic thrust acting on a pitching airfoil and a heaving airfoil show reentrant and convexity shapes characteristics. The dynamic behavior of dynamic thrust acting on a heaving airfoil is different from that on a pitching airfoil. The thrust efficiency of a pitching airfoil increased up to Vp = 0.7 rapidly and maximum thrust efficiency was 0.34. The thrust efficiency of a heaving airfoil increased up to Vp = 0.5 rapidly and the maximum thrust efficiency was 0.20.

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