scholarly journals Flow-excited membrane instability at moderate Reynolds numbers

2021 ◽  
Vol 929 ◽  
Author(s):  
Guojun Li ◽  
Rajeev Kumar Jaiman ◽  
Boo Cheong Khoo
Keyword(s):  
Dynamic Balance ◽  
Reynolds Numbers ◽  
Aerodynamic Performance ◽  
Mass Ratio ◽  
Flexible Membrane ◽  
Structure Interaction ◽  
Balance State ◽  
Vortex Shedding Frequency ◽  
Shedding Frequency ◽  
Lock In

In this paper, we study the fluid–structure interaction of a three-dimensional (3-D) flexible membrane immersed in an unsteady separated flow at moderate Reynolds numbers. We employ a body-conforming variational fluid–structure interaction solver based on the recently developed partitioned iterative scheme for the coupling of turbulent fluid flow with nonlinear structural dynamics. Of particular interest is to understand the flow-excited instability of a 3-D flexible membrane as a function of the non-dimensional mass ratio ( $m^{*}$ ), Reynolds number ( $Re$ ) and aeroelastic number ( $Ae$ ). For a wide range of parameters, we examine two distinct stability regimes of the fluid–membrane interaction: deformed steady state (DSS) and dynamic balance state (DBS). We propose stability phase diagrams to demarcate the DSS and DBS regimes for the parameter space of mass ratio versus Reynolds number ( $m^{*}$ - $Re$ ) and mass ratio versus aeroelastic number ( $m^{*}$ - $Ae$ ). With the aid of the global Fourier mode decomposition technique, the distinct dominant vibrational modes are identified from the intertwined membrane responses in the parameter space of $m^{*}$ - $Re$ and $m^{*}$ - $Ae$ . Compared to the deformed steady membrane, the flow-excited vibration produces relatively longer attached leading-edge vortices which improve the aerodynamic performance when the coupled system is near the flow-excited instability boundary. The optimal aerodynamic performance is achieved for lighter membranes with higher $Re$ and larger flexibility. Based on the global aeroelastic mode analysis, we observe a frequency lock-in phenomenon between the vortex-shedding frequency and the membrane vibration frequency causing self-sustained vibrations in the dynamic balance state. To characterize the origin of the frequency lock-in, we propose an approximate analytical formula for the nonlinear natural frequency by considering the added mass effect and employing a large deflection theory for a simply supported rectangular membrane. Through our systematic high-fidelity numerical investigation, we find that the onset of the membrane vibration and the mode transition has a direct dependence on the frequency lock-in between the natural frequency of the tensioned membrane and the vortex-shedding frequency or its harmonics. These findings on the fluid-elastic instability of membranes have implications for the design and development of control strategies for membrane wing-based unmanned systems and drones.

Numerical Solution for Laminar Two Dimensional Flow About a Cylinder Oscillating in a Uniform Stream

1982 ◽  
Vol 104 (2) ◽  
pp. 214-220 ◽  
Author(s):  
S. E. Hurlbut ◽  
M. L. Spaulding ◽  
F. M. White
Keyword(s):  
Reynolds Numbers ◽  
Quantitative Agreement ◽  
Two Dimensional ◽  
Inertia Effects ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Vortex Shedding Frequency ◽  
Shedding Frequency ◽  
Lock In ◽  
Uniform Stream

A finite difference model is presented for viscous two dimensional flow of a uniform stream past an oscillating cylinder. A noninertial coordinate transformation is used so that the grid mesh remains fixed relative to the accelerating cylinder. Three types of cylinder motion are considered: oscillation in a still fluid, oscillation parallel to a moving stream, and oscillation transverse to a moving stream. Computations are made for Reynolds numbers between 1 and 100 and amplitude-to-diameter ratios from 0.1 to 2.0. The computed results correctly predict the lock-in or wake-capture phenomenon which occurs when cylinder oscillation is near the natural vortex shedding frequency. Drag, lift, and inertia effects are extracted from the numerical results. Detailed computations at a Reynolds number of 80 are shown to be in quantitative agreement with available experimental data for oscillating cylinders.

An Experimental Study on the Vertical Flow Past a Finite-Length Horizontal Cylinder at Low Reynolds Numbers

2014 ◽  
Vol 493 ◽  
pp. 68-73 ◽  
Author(s):  
Willy Stevanus ◽  
Yi Jiun Peter Lin
Keyword(s):  
Finite Length ◽  
Vortex Shedding ◽  
Vortex Formation ◽  
Reynolds Numbers ◽  
Horizontal Cylinder ◽  
Vortex Street ◽  
Vertical Flow ◽  
Low Reynolds Numbers ◽  
Vortex Shedding Frequency ◽  
Shedding Frequency

The research studies the characteristics of the vertical flow past a finite-length horizontal cylinder at low Reynolds numbers (ReD) from 250 to 1080. The experiments were performed in a vertical closed-loop water tunnel. Flow fields were observed by the particle tracer approach for flow visualization and measured by the Particle Image Velocimetry (P.I.V.) approach for velocity fields. The characteristics of vortex formation in the wake of the finite-length cylinder change at different regions from the tip to the base of it. Near the tip, a pair of vortices in the wake was observed and the size of the vortex increased as the observed section was away from the tip. Around a distance of 3 diameters of the cylinder from its tip, the vortex street in the wake was observed. The characteristics of vortex formation also change with increasing Reynolds numbers. At X/D = -3, a pair of vortices was observed in the wake for ReD = 250, but as the ReD increases the vortex street was observed at the same section. The vortex shedding frequency is analyzed by Fast Fourier Transform (FFT). Experimental results show that the downwash flow affects the vortex shedding frequency even to 5 diameters of the cylinder from its tip. The interaction between the downwash flow and the Von Kármán vortex street in the wake of the cylinder is presented in this paper.

Vortex Shedding Induced Dynamic Response of Marine Risers

1984 ◽  
Vol 106 (2) ◽  
pp. 214-221 ◽  
Author(s):  
F. Rajabi ◽  
M. F. Zedan ◽  
A. Mangiavacchi
Keyword(s):  
Dynamic Response ◽  
Vortex Shedding ◽  
Equation Of Motion ◽  
Continuous Beam ◽  
Regular Waves ◽  
Empirical Correlations ◽  
Fluid Resistance ◽  
Vortex Shedding Frequency ◽  
Shedding Frequency ◽  
Lock In

An analytical model to predict the dynamic response of a riser in regular waves or in current to vortex shedding-induced lift forces is described. The riser is treated as a continuous beam under tension. A modal superposition scheme is used to solve the linearized equation of motion in the frequency domain. The excitation lift force is represented by a harmonic function with a frequency equal to the dominant vortex shedding frequency. Empirical correlations are used to determine the lift coefficients and shedding frequencies along the riser. Lift amplification is considered at or near the “lock-in” conditions. The fluid resistance to riser oscillations is represented by a Morison’s equation-type expression.

Numerical Simulation of Vortex Shedding and Lock-in Characteristics for a Thin Cambered Blade

2007 ◽  
Vol 129 (10) ◽  
pp. 1297-1305 ◽  
Author(s):  
Baoshan Zhu ◽  
Jun Lei ◽  
Shuliang Cao
Keyword(s):  
Numerical Simulation ◽  
Vortex Shedding ◽  
Forced Oscillation ◽  
Tvd Scheme ◽  
Convective Term ◽  
Variation Diminishing ◽  
Vortex Shedding Frequency ◽  
Shedding Frequency ◽  
Lock In ◽  
Phase Differences

In this paper, vortex-shedding patterns and lock-in characteristics that vortex-shedding frequency synchronizes with the natural frequency of a thin cambered blade were numerically investigated. The numerical simulation was based on solving the vorticity-stream function equations with the fourth-order Runge–Kutta scheme in time and the Chakravaythy–Oscher total variation diminishing (TVD) scheme was used to discretize the convective term. The vortex-shedding patterns for different blade attack angles were simulated. In order to confirm whether the vortex shedding would induce blade self-oscillation, numerical simulation was also carried out for blade in a forced oscillation. By changing the pitching frequency and amplitude, the occurrence of lock-in at certain attack angles was determined. Inside the lock-in zone, phase differences between the blade’s pitching displacement and the torque acting on the blade were used to infer the probability of the blade self-oscillation.

Computational Determination of the Modified Vortex Shedding Frequency for a Rigid, Truncated, Wall-Mounted Cylinder in Cross Flow

2014 ◽  
Author(s):  
Aimie Faucett ◽  
Todd Harman ◽  
Tim Ameel
Keyword(s):  
Vortex Shedding ◽  
Cross Flow ◽  
Classical Case ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
End Effects ◽  
Dimensional Solution ◽  
Horseshoe Vortices ◽  
Vortex Shedding Frequency ◽  
Shedding Frequency

Flow around a rigid, truncated, wall-mounted cylinder with an aspect ratio of 5 is examined computationally at various Reynolds numbers Re to determine how the end effects impact the vortex shedding frequency. The existence of the wall and free end cause a dampening of the classical shedding frequency found for a semi-infinite, two-dimensional cylinder, as horseshoe vortices along the wall and flow over the tip entrain into the shedding region. This effect was observed for Reynolds numbers in the range of 50 to 2000, and quantified by comparing the modified Strouhal numbers to the classical (two-dimensional) solution for Strouhal number as a function of Reynolds number. The range of transition was found to be 220 < Re < 300, versus 150 < Re < 300 for the classical case. Vortex shedding started at Re ≈ 100, significantly above Re = 50, where shedding starts for the two-dimensional case.

A Study on Vortex Shedding From Spheres in a Uniform Flow

1990 ◽  
Vol 112 (4) ◽  
pp. 386-392 ◽  
Author(s):  
H. Sakamoto ◽  
H. Haniu
Keyword(s):  
Reynolds Number ◽  
Strouhal Number ◽  
Vortex Shedding ◽  
Water Channel ◽  
Reynolds Numbers ◽  
Uniform Flow ◽  
Freestream Velocity ◽  
Vortex Shedding Frequency ◽  
Shedding Frequency ◽  
Visualization Experiments

Vortex shedding from spheres at Reynolds numbers from 3 × 102 to 4 × 104 in a uniform flow was investigated experimentally. Standard hot-wire technique were used to measure the vortex shedding frequency from spheres in a low-speed wind tunnel. Flow-visualization experiments were carried out in a water channel. Important results from the investigation were that (i) the variation of the Strouhal number St (=fD/U0, U0: freestream velocity, D: diameter of the sphere, f: vortex shedding frequency) with the Reynolds number (= U0D/v, v: kinematic viscosity) can be classified into four regions, (ii) the Reynolds number at which the hairpinshaped vortices begin to change from laminar to turbulent vortices so that the wake structure behind the sphere is not shown clearly when a Reynolds number of about 800 is reached, and (vi) at Reynolds numbers ranging from 8X102 to 1.5X104, the higher and lower frequency modes of the Strouhal number coexist.

Cavitation Influence on von Kármán Vortex Shedding and Induced Hydrofoil Vibrations

2007 ◽  
Vol 129 (8) ◽  
pp. 966-973 ◽  
Author(s):  
Philippe Ausoni ◽  
Mohamed Farhat ◽  
Xavier Escaler ◽  
Eduard Egusquiza ◽  
François Avellan
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Trailing Edge ◽  
Cavitation Inception ◽  
Structure Interaction ◽  
New Correlation ◽  
Von Karman ◽  
Vortex Shedding Frequency ◽  
Shedding Frequency ◽  
Von Kármán

The present study deals with the shedding process of the von Kármán vortices at the trailing edge of a 2D hydrofoil at high Reynolds number Reh=25×103–65×103. This research focuses mainly on the effects of cavitation and fluid-structure interaction on the mechanism of the vortex generation. The vortex shedding frequency, derived from the flow-induced vibration measurement, is found to follow the Strouhal law provided that no hydrofoil resonance frequencies are excited, i.e., lock-off. For such a regime, the von Kármán vortices exhibit strong spanwise 3D instabilities and the cavitation inception index is linearly dependent on the square root of the Reynolds number. In the case of resonance, the vortex shedding frequency is locked onto the hydrofoil eigenfrequency and the spatial coherence is enhanced with a quasi-2D shape. The measurements of the hydrofoil wall velocity amplitude and phase reveal the first torsion eigenmotion. In this case, the cavitation inception index is found to be significantly increased compared to lock-off conditions. It makes clear that the vortex roll-up is amplified by the phase locked vibrations of the trailing edge. For the cavitation inception index, a new correlation relationship that encompasses the entire range of Reynolds numbers, including both the lock-off and the lock-in cases, is proposed and validated. In contrast to the earlier models, the new correlation takes into account the trailing edge displacement velocity. In addition, it is found that the transverse velocity of the trailing edge increases the vortex strength linearly. This effect is important in the context of the fluid-structure interaction, since it implies that the velocity of the hydrofoil trailing edge increases the fluctuating forces on the body. It is also demonstrated that cavitation developing in the vortex street cannot be considered as a passive agent for the turbulent wake flow. In fact, for fully developed cavitation, the vortex shedding frequency increases up to 15%, which is accompanied by the increase of the vortex advection velocity and reduction of the streamwise vortex spacing. In addition, a significant increase of the vortex-induced vibration level is found at cavitation onset. These effects are addressed and thought to be a result of the increase of the vorticity by cavitation.

Flow-Induced Streamwise Vibration of a Flexibly-Mounted Cantilevered Cylinder in Steady and Pulsating Crossflow

2009 ◽  
Author(s):  
Joseph Sherwood ◽  
Jonathan Dusting ◽  
Efstathios Konstantinidis ◽  
Stavroula Balabani
Keyword(s):  
Steady Flow ◽  
Excitation Frequency ◽  
Reynolds Numbers ◽  
Pulsation Frequency ◽  
Plate Spring ◽  
Low Mass ◽  
Vortex Shedding Frequency ◽  
Shedding Frequency ◽  
Low Mass Ratio ◽  
Fixed Cylinder

This paper describes an experimental study of the response of a freely vibrating cylinder with low mass ratio and high damping to steady and pulsating crossflow for Reynolds numbers in the range 120–2900. A rigid circular cylinder was cantilevered by means of a plate spring allowing it to oscillate in the stream-wise direction only. A camera-based technique was employed for tracking the cylinder vibration while the wake fluctuations were measured by a laser-Doppler system. The results show that the forced excitation from pulsating flow can take over control of the wake and/or the cylinder oscillations in a complex manner. The overall response depends strongly on two main parameters: the ratios of the pulsation frequency to the structural frequency and to the vortex shedding frequency from a fixed cylinder in steady flow. When the excitation frequency from both the wake and the external pulsation coincided with the natural frequency of the structure, the r.m.s. amplitude of the cylinder vibration increased up to 400% compared to that for the same reduced velocity in steady flow. In this case, maximum end displacements exceeded 35% of the cylinder diameter.

Universal Similarity in the Wakes of Stationary and Vibrating Bluff Structures

1981 ◽  
Vol 103 (1) ◽  
pp. 52-58 ◽  
Author(s):  
Owen M. Griffin
Keyword(s):  
Vortex Formation ◽  
Reynolds Numbers ◽  
Bluff Bodies ◽  
Characteristic Parameters ◽  
Incident Flow ◽  
Mean Velocity ◽  
Pressure Drag ◽  
Vortex Shedding Frequency ◽  
The Mean ◽  
Shedding Frequency

A universal wake Strouhal number, St* =fsd′/Ub, has been proposed and is based upon the Strouhal frequency fs of the incident flow, the measured wake width d′ at the end of the vortex formation region, and the mean velocity Ub at the edge of the separated boundary layer. This universal parameter collapses these characteristic parameters for bluff bodies onto a single curve for wake Reynolds numbers between Re* = 100 and 107. The pressure drag, vortex shedding frequency and base pressure are related through an inverse dependence between St* and a wake drag coefficient CD* = CD/(d′/d) K2, where K = (1−Cpb)1/2. The product St* CD* is equal to a constant value of 0.073 ± 0.005 for Re* in this same range of Reynolds numbers.

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