Illuminating the complex role of the added mass during vortex induced vibration

2021 ◽  
Vol 33 (8) ◽  
pp. 085120
Author(s):  
Zhicheng Wang ◽  
Dixia Fan ◽  
Michael S. Triantafyllou
Keyword(s):  
Added Mass ◽  
Vortex Induced Vibration

scholarly journals On the role of added mass and vorticity release for self-propelled aquatic locomotion

2021 ◽  
Vol 918 ◽  
Author(s):  
D. Paniccia ◽  
G. Graziani ◽  
C. Lugni ◽  
R. Piva
Keyword(s):  
Added Mass ◽  
Aquatic Locomotion

Abstract

A Double Birkhoff Wake Oscillator for the Modeling of Vortex-Induced Vibration

2011 ◽  
Author(s):  
R. H. M. Ogink
Keyword(s):  
Free Vibration ◽  
Added Mass ◽  
Mass Force ◽  
Near Wake ◽  
Vibration Measurements ◽  
Vortex Induced Vibration ◽  
Fluid Forces ◽  
Wake Oscillator ◽  
Model Equations ◽  
Far Wake

A double Birkhoff wake oscillator for the modeling of vortex-induced vibration is presented in which the oscillating variables are assumed to be associated with the boundary layer/near wake and the far wake. The fluid forces are assumed to consist of a potential added mass force and a force due to vortex shedding. In the limit of vanishing incoming flow velocity, the model equations reduce to a form similar to the Morison equation. The results of the double wake oscillator have been compared with forced vibration measurements and free vibration measurements over a range of mass and damping ratios. The model is capable of describing the most important trends in both the forced and free vibration experiments. Specifically, the double wake oscillator is able to model both the upper and lower branch of free vibration.

Unsteady swimming of small organisms

2012 ◽  
Vol 702 ◽  
pp. 286-297 ◽  
Author(s):  
S. Wang ◽  
A. M. Ardekani
Keyword(s):  
Reynolds Number ◽  
Low Reynolds Number ◽  
Fundamental Equation ◽  
Added Mass ◽  
Natural Environments ◽  
Mean Velocity ◽  
Unsteady Forces ◽  
Uniform Background ◽  
Low Reynolds

AbstractSmall planktonic organisms ubiquitously display unsteady or impulsive motion to attack a prey or escape a predator in natural environments. Despite this, the role of unsteady forces such as history and added mass forces on the low-Reynolds-number propulsion of small organisms, e.g. Paramecium, is poorly understood. In this paper, we derive the fundamental equation of motion for an organism swimming by means of the surface distortion in a non-uniform background flow field at a low-Reynolds-number regime. We show that the history and added mass forces are important as the product of Reynolds number and Strouhal number increases above unity. Our results for an unsteady squirmer show that unsteady inertial effects can lead to a non-zero mean velocity for the cases with zero streaming parameters, which have zero mean velocity in the absence of inertia.

scholarly journals On the development of a nonlinear time-domain numerical method for describing vortex-induced vibration and wake interference of two cylinders using experimental results

2021 ◽  
Author(s):  
Milad Armin ◽  
Sandy Day ◽  
Madjid Karimirad ◽  
Mahdi Khorasanchi
Keyword(s):  
Time Domain ◽  
Hydrodynamic Force ◽  
Maximum Amplitude ◽  
Added Mass ◽  
Duffing Equation ◽  
Experimental Results ◽  
Interference Phenomenon ◽  
Vortex Induced Vibration ◽  
Coupled Equations ◽  
Wake Interference

AbstractA nonlinear mathematical model is developed in the time domain to simulate the behaviour of two identical flexibly mounted cylinders in tandem while undergoing vortex-induced vibration (VIV). Subsequently, the model is validated and modified against experimental results. Placing an array of bluff bodies in proximity frequently happens in different engineering fields. Chimney stacks, power transmission lines and oil production risers are few engineering structures that may be impacted by VIV. The coinciding of the vibration frequency with the structure natural frequency could have destructive consequences. The main objective of this study is to provide a symplectic and reliable model capable of capturing the wake interference phenomenon. This study shows the influence of the leading cylinder on the trailing body and attempts to capture the change in added mass and damping coefficients due to the upstream wake. The model is using two coupled equations to simulate the structural response and hydrodynamic force in each of cross-flow and stream-wise directions. Thus, four equations describe the fluid–structure interaction of each cylinder. A Duffing equation describes the structural motion, and the van der Pol wake oscillator defines the hydrodynamic force. The system of equations is solved analytically. Two modification terms are added to the excitation side of the Duffing equation to adjust the hydrodynamic force and incorporate the effect of upstream wake on the trailing cylinder. Both terms are functions of upstream shedding frequency (Strouhal number). Additionally, the added mass modification coefficient is a function of structural acceleration and the damping modification coefficient is a function of velocity. The modification coefficients values are determined by curve fitting to the difference between upstream and downstream wake forces, obtained from experiments. The damping modification coefficient is determined by optimizing the model against the same set of experiments. Values of the coefficients at seven different spacings are used to define a universal function of spacing for each modification coefficient so that they can be obtained for any given distance between two cylinders. The model is capable of capturing lock-in range and maximum amplitude.

scholarly journals Drag cancellation by added-mass pumping

2016 ◽  
Vol 798 ◽  
Author(s):  
F. Giorgio-Serchi ◽  
G. D. Weymouth
Keyword(s):  
Shape Change ◽  
Stokes Number ◽  
Added Mass ◽  
Navier Stokes ◽  
Viscous Damping ◽  
Size Change ◽  
Biologically Inspired ◽  
Sustained Oscillations ◽  
Submerged Body

A submerged body subject to a sudden shape change experiences large forces due to the variation of added-mass energy. While this phenomenon has been studied for single actuation events, application to sustained propulsion requires the study of periodic shape change. We do so in this work by investigating a spring–mass oscillator submerged in quiescent fluid subject to periodic changes in its volume. We develop an analytical model to investigate the relationship between added-mass variation and viscous damping, and demonstrate its range of application with fully coupled fluid–solid Navier–Stokes simulations at large Stokes number. Our results demonstrate that the recovery of added-mass kinetic energy can be used to completely cancel the viscous damping of the fluid, driving the onset of sustained oscillations with amplitudes as large as four times the average body radius $r_{0}$. A quasi-linear relationship is found to link the terminal amplitude of the oscillations $X$ to the extent of size change $a$, with $X/a$ peaking at values from 4 to 4.75 depending on the details of the shape-change kinematics. In addition, it is found that pumping in the frequency range of $1-a/2r_{0}<{\it\omega}^{2}/{\it\omega}_{n}^{2}<1+a/2r_{0}$, with ${\it\omega}/{\it\omega}_{n}$ being the ratio between frequency of actuation and natural frequency, is required for sustained oscillations. The results of this analysis shed light on the role of added-mass recovery in the context of shape-changing bodies and biologically inspired underwater vehicles.

Vortex-induced vibration of a rising and falling cylinder

2010 ◽  
Vol 662 ◽  
pp. 352-383 ◽  
Author(s):  
M. HOROWITZ ◽  
C. H. K. WILLIAMSON
Keyword(s):  
Degrees Of Freedom ◽  
Critical Mass ◽  
Vortex Formation ◽  
Small Mass ◽  
Added Mass ◽  
The Body ◽  
Spring Stiffness ◽  
Mass Ratio ◽  
Vortex Induced Vibration ◽  
Direct Measurements

In this study, we investigate the dynamics of a freely rising and falling cylinder. This is, in essence, a vortex-induced vibration (VIV) system comprising both transverse (Y) and streamwise (X) degrees-of-freedom (d.o.f.), but with zero spring stiffness and zero damping. This problem represents a limiting case among studies in VIV, and is an extension of recent research of elastically mounted bodies having very low spring stiffness, as well as bodies with very low mass and damping. We find that if the mass ratio (where m* = cylinder mass/displaced fluid mass) is greater than a critical value, m*crit = 0.545, the body falls or rises with a rectilinear trajectory. As the mass ratio is reduced below m*crit = 0.545, the cylinder suddenly begins to vibrate vigorously and periodically, with a 2P mode of vortex formation, as reported in the preliminary study of Horowitz & Williamson (J. Fluids Struct. vol. 22, 2006, pp. 837–843). The similarity in critical mass between freely rising and elastically mounted bodies is unexpected, as it is known that the addition of streamwise vibration can markedly affect the response and vortex formation in elastically mounted systems, which would be expected to modify the critical mass. However, we show in this paper that the similarity in vortex formation mode (2P) between the freely rising body and the elastically mounted counterpart is consistent with a comparable phase of vortex dynamics, strength of vortices, amplitudes and frequencies of motion and effective added mass (CEA). All of these similarities result in comparable values of critical mass. The principal fact that the 2P mode is observed for the freely rising body is an interesting and consistent result; based on the previous VIV measurements, this is the only mode out of the known set {2S, 2P, 2T} to yield negative effective added mass (CEA < 0), which is a condition for vibration of a freely rising body. In this paper, we deduce that there exists only one possible two degree-of-freedom elastically mounted cylinder system, which can be used to predict the dynamics of freely rising bodies. Because of the symmetry of the vortex wake, this system is one for which the natural frequencies are fNX = 2fNY. Although this seems clear in retrospect, previous attempts to predict critical mass did not take this into account. Implementing such an elastic system, we are able to predict vibration amplitudes and critical mass (m*crit = 0.57) for a freely rising cylinder in reasonable agreement with direct measurements for such a rising body, and even to predict the Lissajous figures representing the streamwise–transverse vibrations for a rising body with very small mass ratios (down to m* = 0.06), unobtainable from our direct measurements.

scholarly journals Study on Vortex-Induced Vibration of Deep-Water Marine Drilling Risers in Linearly Sheared Flows in consideration of Changing Added Mass

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Guanghai Gao ◽  
Xiao Cong ◽  
Yunjing Cui ◽  
Xingqi Qiu
Keyword(s):  
Deep Water ◽  
Nonlinear Partial Differential Equations ◽  
Cross Flow ◽  
Added Mass ◽  
Flow Speed ◽  
Vortex Induced Vibration ◽  
Sheared Flows ◽  
Heave Motion ◽  
Improved Model ◽  
The Impact

In order to more accurately predict the coupled in-line and cross-flow vortex-induced vibration (VIV) response of deep-water marine drilling risers in linearly sheared flows, an improved three-dimensional time-domain coupled model based on van der Pol wake oscillator models was established in this paper. The impact of the in-line and cross-flow changing added mass coefficients was taken into account in the model. The finite element, Newmark-β, and Newton–Raphson methods were adopted to solve the coupled nonlinear partial differential equations. The entire numerical solution process was realized by a self-developed program based on MATLAB. Comparisons between the numerical calculations and the published experimental tests showed that the improved model can more accurately predict some main features of the coupled in-line and cross-flow VIV of long slender flexible risers in linearly sheared flows to some extent. The coupled in-line and cross-flow VIV of a real-size marine drilling riser, usually used in the deep-water oil/gas industry in the South China Sea, was analyzed. The influence of top tension force and seawater flow speed, as well as platform heave amplitude and frequency, on the riser in-line and cross-flow VIV was also discussed. The results show that the platform heave motion increases the VIV displacements and changes the magnitudes of peak frequencies as well as the components of frequencies. The platform heave motion also has a significant influence on the vibration modes of the middle and upper sections of the riser. The impact level of each factor on the in-line and cross-flow VIV response of the riser is different. The improved model and the results of this paper can be used as a reference for the engineering design of deep-water marine drilling risers.

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