Showing papers on "Vortex-induced vibration published in 2016"

Large-amplitude flapping of an inverted flag in a uniform steady flow – a vortex-induced vibration

Abstract: The dynamics of a cantilevered elastic sheet, with a uniform steady flow impinging on its clamped end, have been studied widely and provide insight into the stability of flags and biological phenomena. Recent measurements by Kim et al. (J. Fluid Mech., vol. 736, 2013, R1) show that reversing the sheet’s orientation, with the flow impinging on its free edge, dramatically alters its dynamics. In contrast to the conventional flag, which exhibits (small-amplitude) flutter above a critical flow speed, the inverted flag displays large-amplitude flapping over a finite band of flow speeds. The physical mechanisms giving rise to this flapping phenomenon are currently unknown. In this article, we use a combination of mathematical theory, scaling analysis and measurement to establish that this large-amplitude flapping motion is a vortex-induced vibration. Onset of flapping is shown mathematically to be due to divergence instability, verifying previous speculation based on a two-point measurement. Reducing the sheet’s aspect ratio (height/length) increases the critical flow speed for divergence and ultimately eliminates flapping. The flapping motion is associated with a separated flow – detailed measurements and scaling analysis show that it exhibits the required features of a vortex-induced vibration. Flapping is found to be periodic predominantly, with a transition to chaos as flow speed increases. Cessation of flapping occurs at higher speeds – increased damping reduces the flow speed range where flapping is observed, as required. These findings have implications for leaf motion and other biological processes, such as the dynamics of hair follicles, because they also can present an inverted-flag configuration.

Lock-in in vortex-induced vibration

Abstract: The phenomenon of lock-in in vortex-induced vibration of a circular cylinder is investigated in the laminar flow regime ( ). Direct time integration (DTI) and linear stability analysis (LSA) of the governing equations are carried out via a stabilized finite element method. Using the metrics that have been proposed in earlier studies, the lock-in regime is identified from the results of DTI. The LSA yields the eigenmodes of the coupled fluid–structure system, the associated frequencies ( ) and the stability of the steady state. A linearly unstable system, in the absence of nonlinear effects, achieves large oscillation amplitude at sufficiently large times. However, the nonlinear terms saturate the response of the system to a limit cycle. For subcritical , the occurrence of lock-in coincides with the linear instability of the fluid–structure system. The critical is the Reynolds number beyond which vortex shedding ensues for a stationary cylinder. For supercritical , even though the aeroelastic system is unstable for all reduced velocities ( ) lock-in occurs only for a finite range of . We present a method to estimate the time beyond which the nonlinear effects are expected to be significant. It is observed that much of the growth in the amplitude of cylinder oscillation takes place in the linear regime. The response of the cylinder at the end of the linear regime is found to depend on the energy ratio, , of the unstable eigenmode. is defined as the fraction of the total energy of the eigenmode that is associated with the kinetic and potential energy of the structure. DTI initiated from eigenmodes that are linearly unstable and whose energy ratio is above a certain threshold value lead to lock-in. Interestingly, during lock-in, the oscillation frequency of the fluid–structure system drifts from towards a value that is closer to the natural frequency of the oscillator in vacuum ( ). In the event of more than one eigenmode being linearly unstable, we investigate which one is responsible for lock-in. The concept of phase angle between the cylinder displacement and lift is extended for an eigenmode. The phase angle controls the direction of energy transfer between the fluid and the structure. For zero structural damping, if the phase angle of all unstable eigenmodes is less than 90°, the phase angle obtained via DTI evolves to a value that is close to 0°. If, on the other hand, the phase angle of any unstable eigenmode is more than 90°, it settles to 180°, approximately in the limit cycle. A new approach towards classification of modes is presented. The eigenvalues are tracked over a wide range of while keeping and mass ratio ( ) fixed. In general, for large values of , the eigenmodes corresponding to the two leading eigenvalues exhibit a decoupled behaviour with respect to . They are classified as the fluid and elastic modes. However, for relatively low such a classification is not possible. The two leading modes are coupled and are referred to as fluid–elastic modes. The regime of such occurrence is shown on the parameter space.

Interaction dynamics of gap flow with vortex-induced vibration in side-by-side cylinder arrangement

Abstract: A numerical investigation of the vortex-induced vibration (VIV) in a side-by-side circular cylinder arrangement has been performed in a two-dimensional laminar flow environment. One of the cylinders is elastically mounted and only vibrates in the transverse direction, while its counterpart remains stationary in a uniform flow stream. When the gap ratio is sufficiently small, the flip-flopping phenomenon of the gap flow can be an additional time-dependent interference to the flow field. This phenomenon was reported in the experimental work of Bearman and Wadcock [“The interaction between a pair of circular cylinders normal to a stream,” J. Fluid Mech. 61(3), 499–511 (1973)] in a side-by-side circular cylinder arrangement, in which the gap flow deflects toward one of the cylinders and switched its sides intermittently. Albeit one of the two cylinders is free to vibrate, the flip-flop of a gap flow during VIV dynamics can still be observed outside the lock-in region. The exact moments of the flip-flop phenom...

On the Stability of Spinning Functionally Graded Cantilevered Pipes Subjected to Fluid-Thermomechanical Loading

Abstract: This paper studies the thermomechanical stability of a cantilevered pipe spinning along its longitudinal axis and carrying an internal axial flow. The pipe, made of functionally graded materials (FGMs), is subjected to an axial force at the free end operating in a high temperature environment. It is modeled by the Rayleigh beam theory and is considered as a hollow thin-walled beam. The equation of motion, along with the boundary conditions, for the pipe is derived by using the extended Hamilton’s principle. Further, the extended Galerkin’s method (EGM) in conjunction with a proper representation of the displacements of the pipe is used to solve the eigenvalue problem. Depending upon the nature of the eigenvalues, i.e. real or complex-conjugate, the conditions for occurrence of instability by flutter or by divergence are derived. The effects of spin rate and velocity of fluid flow are studied on the stability regions, i.e. the critical flutter and divergence boundary, by the numerical method. Also, the effects of parameters, such as fluid mass ratio, compressive axial force, volume fraction index of the FGM and temperature gradient through the pipe thickness, are considered in developing the stability map for the spinning cantilever pipe. The results are compared with those available in the literature and good agreement has been achieved.

Multi-modes approach to modelling of vortex-induced vibration

Abstract: In this work the fluid–structure interactions are considered by investigating a straight but slender pipe interacting with uniform water flow. Two configurations are studied, namely vertically and horizontally positioned pipes, which are modelled as an Euler–Bernoulli beam with flexural stiffness. Both pretension and length-wise mass distribution are considered. The structure is assumed to be moving only in the direction normal to flow (cross-flow motion) hence its in-line motion is neglected. The external fluid force acting on the structure is the result of the action of sectional vortex-induced drag and lift forces. Only mean drag force is considered, with time varying lift force modelled using a non-linear oscillator equation of the Van der Pol type. The obtained coupled system of non-linear partial differential equations is simplified employing Galerkin-type discretisation. The resulting ordinary differential equations are solved numerically providing multi-mode approximations of cross-flow displacement and non-dimensional lift coefficient. The comparison between the responses of vertical and horizontal structures shows that, as expected, due to a balancing between pretension and weight, in general a higher amplitude of vibration is observed for the vertical configuration than in the same location along the pipe for the horizontal configuration in the lower part of the structure. However, lower amplitudes are obtained in the upper part of the pipe. The horizontal configuration solutions are identical in symmetrical locations along the pipe due to constant pretension. The influence of the wake equation coefficients and the fluid force coefficients on the response amplitudes has been also considered together with the length of the pipe and pretension level, and the appropriate response curves are included. Finally, for the higher mode approximations it has been shown that the vibrations level at lower frequencies is predicted reasonably well by retaining only a small subset of modes.

Suppression of vortex-induced vibration of a circular cylinder using thermal effects

Abstract: Transverse vortex-induced vibration (VIV) of a cylinder with various body-to-fluid density ratio and stiffness is studied. The cylinder is elastically mounted and heated, and the flow direction is aligned with the direction of the thermal induced buoyancy force. Amplitude of VIV can be reduced as the thermal control parameter Richardson number (Ri) increases, or even be fully suppressed when Ri is above a critical value. This critical Richardson number depends on both body-to-fluid density and structural stiffness. A higher critical Richardson is required to fully suppress the VIV of a structure with smaller density ratio. With the same density or mass, a structure with intermediate stiffness vibrating in lock-in regime needs higher critical Ri to suppress VIV than either rigid or flexible structures. Drag experienced by the body is also studied. It is found that for a flexible body, drag gradually increases with the Richardson number. For a body with intermediate stiffness, both drag and amplitude of VIV...

Vortex Induced Vibration and Frequency Lock-in of an Airfoil at High Angles of Attack

Abstract: Vortex-induced vibration is a fluid instability where vortices due to secondary flows exert a periodic unsteady force on the elastic structure. Under certain circumstances, the shedding frequency can lock into the structure natural frequency and lead to limit cycle oscillations. These vibrations may cause material fatigue and are a common source of structural failure. This work uses a frequency domain, harmonic balance (HB) computational fluid dynamics (CFD) code to predict the natural shedding frequency and lock-in region of an airfoil at very high angles of attack. The numerical results are then successfully compared to experimental data from wind tunnel testings.