Experimental Comparison of Two Degrees-of-Freedom Vortex-Induced Vibration on High and Low Aspect Ratio Cylinders with Small Mass Ratio

Vortex-induced motion (VIM) is a specific way for naming the vortex-induced vibration (VIV) acting on floating units. The VIM phenomenon can occur in monocolumn production, storage and offloading system (MPSO) and spar platforms, structures presenting aspect ratio lower than 4 and unity mass ratio, i.e., structural mass equal to the displaced fluid mass. These platforms can experience motion amplitudes of approximately their characteristic diameters, and therefore, the fatigue life of mooring lines and risers can be greatly affected. Two degrees-of-freedom VIV model tests based on cylinders with low aspect ratio and small mass ratio have been carried out at the recirculating water channel facility available at NDF-EPUSP in order to better understand this hydro-elastic phenomenon. The tests have considered three circular cylinders of mass ratio equal to one and different aspect ratios, respectively L/D = 1.0, 1.7, and 2.0, as well as a fourth cylinder of mass ratio equal to 2.62 and aspect ratio of 2.0. The Reynolds number covered the range from 10 000 to 50 000, corresponding to reduced velocities from 1 to approximately 12. The results of amplitude and frequency in the transverse and in-line directions were analyzed by means of the Hilbert-Huang transform method (HHT) and then compared to those obtained from works found in the literature. The comparisons have shown similar maxima amplitudes for all aspect ratios and small mass ratio, featuring a decrease as the aspect ratio decreases. Moreover, some changes in the Strouhal number have been indirectly observed as a consequence of the decrease in the aspect ratio. In conclusion, it is shown that comparing results of small-scale platforms with those from bare cylinders, all of them presenting low aspect ratio and small mass ratio, the laboratory experiments may well be used in practical investigation, including those concerning the VIM phenomenon acting on platforms. [DOI: 10.1115/1.4006755]

Two-degree-of-freedom vortex-induced vibration of circular cylinders with very low aspect ratio and small mass ratio

The investigation of vortex-induced vibration on very short cylinders with two degrees of freedom has drawn the attention of a large number of researchers. Some investigations on such a problem are carried out in order to have a better understanding of the physics involved in vortex-induced motions of floating bodies such as offshore platforms. In this paper, experiments were carried out in a recirculating water channel over the range of Reynolds number 6000small mass ratios (m⁎=1.00; 2.62 and 4.36) and very low aspect ratios (0.3≤L/D≤2.0) were shown and the results were discussed in depth. Conversely to what would be expected for cylinders with very low aspect ratio, the results showed large motions in the transverse direction with maximum amplitudes around 1.5 diameters for cylinders with L/D=2.0, despite being smaller when the aspect ratio is reduced. Moreover, the response amplitudes presented high values around 0.4 diameters in the in-line direction. In fact, the large transverse motions were related to a strong coupling with the in-line responses, visibly identified in the plots of nondimensional frequency, as well as by the trajectories in the XY-plane, Lissajous figures, particularly in the case of m⁎=1.00 and L/D=2.0, when 8-shape trajectories were clearly observed. The case of m⁎=1.00 deserves more attention because of its smaller amplitude compared to the cases with the same aspect ratio and a larger mass ratio. This counter-intuitive behavior seems to be related to the energy transferring process from the steady stream to the oscillatory hydroelastic system. Finally, it is noteworthy that the characteristic of the “Strouhal-like” number decreases when the aspect ratio decreases, as also observed in previous works available in the literature, most of them for stationary cylinders.

Two-degree-of-freedom vortex-induced vibration of circular cylinders with very low aspect ratio and small mass ratio

The investigation of vortex-induced vibration on very short cylinders with two degrees of freedom has drawn the attention of a large number of researchers. Some investigations on such a problem are carried out in order to have a better understanding of the physics involved in vortex-induced motions of floating bodies such as offshore platforms. In this paper, experiments were carried out in a recirculating water channel over the range of Reynolds number 6000small mass ratios (m⁎=1.00; 2.62 and 4.36) and very low aspect ratios (0.3≤L/D≤2.0) were shown and the results were discussed in depth. Conversely to what would be expected for cylinders with very low aspect ratio, the results showed large motions in the transverse direction with maximum amplitudes around 1.5 diameters for cylinders with L/D=2.0, despite being smaller when the aspect ratio is reduced. Moreover, the response amplitudes presented high values around 0.4 diameters in the in-line direction. In fact, the large transverse motions were related to a strong coupling with the in-line responses, visibly identified in the plots of nondimensional frequency, as well as by the trajectories in the XY-plane, Lissajous figures, particularly in the case of m⁎=1.00 and L/D=2.0, when 8-shape trajectories were clearly observed. The case of m⁎=1.00 deserves more attention because of its smaller amplitude compared to the cases with the same aspect ratio and a larger mass ratio. This counter-intuitive behavior seems to be related to the energy transferring process from the steady stream to the oscillatory hydroelastic system. Finally, it is noteworthy that the characteristic of the “Strouhal-like” number decreases when the aspect ratio decreases, as also observed in previous works available in the literature, most of them for stationary cylinders.

PIV studies of large scale structures in the near field of small aspect ratio elliptic jets

The near flow field of small aspect ratio elliptic turbulent free jets (issuing from nozzle and orifice) was experimentally studied using a 2D PIV. Two point velocity correlations in these jets revealed the extent and orientation of the large scale structures in the major and minor planes. The spatial filtering of the instantaneous velocity field using Gaussian convolution kernel shows that while a single large vortex ring circumscribing the jet seems to be present at the exit of nozzle, the orifice jet exhibited a number of smaller vortex ring pairs close to jet exit. The smaller length scale observed in the case of the orifice jet is representative of the smaller azimuthal vortex rings that generate axial vortex field as they are convected. This results in the axis-switching in the case of orifice jet and may have a mechanism different from the self induction process as observed in the case of contoured nozzle jet flow.

Are superhumps good measures of the mass ratio for AM CVn systems?

We extend recent work that included the effect of pressure forces to derive the precession rate of eccentric accretion discs in cataclysmic variables to the case of double degenerate systems. We find that the logical scaling of the pressure force in such systems results in predictions of unrealistically high primary masses. Using the prototype AM CVn as a calibrator for the magnitude of the effect, we find that there is no scaling that applies consistently to all the systems in the class. We discuss the reasons for the lack of a superhump period to mass ratio relationship analogous to that known for SU UMa systems and suggest that this is because these secondaries do not have a single valued mass-radius relationship. We highlight the unreliability of mass-ratios derived by applying the SU UMa expression to the AM CVn binaries.

Superhumps, magnetic fields and the mass ratio in AM Canum Venaticorum

We show that the observed K velocities and periodicities of AM CVn can be reconciled given a mass ratio q~0.22 and a secondary star with a modest magnetic field of surface strength B~1 T. We see that the new mass ratio implies that the secondary is most likely semidegenerate. The effect of the field on the accretion disc structure is examined. The theory of precessing discs and resonant orbits is generalized to encompass higher order resonances than 3:2 and shown to retain consistency with the new mass ratio.

The effect of a single supernova explosion on the cuspy density profile of a small-mass dark matter halo

Some observations of galaxies, and in particular dwarf galaxies, indicate a presence of cored density profiles in apparent contradiction with cusp profiles predicted by dark matter N-body simulations. We constructed an analytical model, using particle distribution functions (DFs), to show how a supernova (SN) explosion can transform a cusp density profile in a small-mass dark matter halo into a cored one. Considering the fact that an SN efficiently removes matter from the centre of the first haloes, we study the effect of mass removal through an SN perturbation in the DFs. We find that the transformation from a cusp into a cored profile occurs even for changes as small as 0.5 per cent of the total energy of the halo, which can be produced by the expulsion of matter caused by a single SN explosion.

Optimal V. O2max-to-mass ratio for predicting 15 km performance among elite male cross-country skiers

The aim of this study was 1) to validate the 0.5 body-mass exponent for maximal oxygen uptake (V. O2max) as the optimal predictor of performance in a 15 km classical-technique skiing competition among elite male cross-country skiers and 2) to evaluate the influence of distance covered on the body-mass exponent for V. O2max among elite male skiers. Twenty-four elite male skiers (age: 21.4±3.3 years [mean ± standard deviation]) completed an incremental treadmill roller-skiing test to determine their V. O2max. Performance data were collected from a 15 km classicaltechnique cross-country skiing competition performed on a 5 km course. Power-function modeling (ie, an allometric scaling approach) was used to establish the optimal body-mass exponent for V . O2max to predict the skiing performance. The optimal power-function models were found to be race speed = 8.83⋅(V . O2max m-0.53) 0.66 and lap speed = 5.89⋅(V . O2max m-(0.49+0.018lap)) 0.43e0.010age, which explained 69% and 81% of the variance in skiing speed, respectively. All the variables contributed to the models. Based on the validation results, it may be recommended that V. O2max divided by the square root of body mass (mL⋅min−1 ⋅kg−0.5) should be used when elite male skiers’ performance capability in 15 km classical-technique races is evaluated. Moreover, the body-mass exponent for V . O2max was demonstrated to be influenced by the distance covered, indicating that heavier skiers have a more pronounced positive pacing profile (ie, race speed gradually decreasing throughout the race) compared to that of lighter skiers.

Theory of small aspect ratio waves in deep water

In the limit of small values of the aspect ratio parameter (or wave steepness) which measures the amplitude of a surface wave in units of its wave-length, a model equation is derived from the Euler system in infinite depth (deep water) without potential flow assumption. The resulting equation is shown to sustain periodic waves which on the one side tend to the proper linear limit at small amplitudes, on the other side possess a threshold amplitude where wave crest peaking is achieved. An explicit expression of the crest angle at wave breaking is found in terms of the wave velocity. By numerical simulations, stable soliton-like solutions (experiencing elastic interactions) propagate in a given velocities range on the edge of which they tend to the peakon solution. (c) 2005 Elsevier B.V. All rights reserved.