Cylinder loading in transient motion representing flow under a wave group

by T. Stallard, P.H. Taylor, C.H.K. Williamson, and A.G.L. Borthwick

Proceedings AVolume 465(2105):1467-1488

May 8, 2009

©2009 by The Royal Society

Trajectories of a fluid particle within NewWave groups defined by (a) a narrow-banded Gaussian wave spectrum and (b) a typical JONSWAP spectrum (defined by equation (2.4) with γ=3.3).

T. Stallard et al. Proc. R. Soc. A 2009;465:1467-1488

©2009 by The Royal Society

Schematic of the XY towing tank.

T. Stallard et al. Proc. R. Soc. A 2009;465:1467-1488

©2009 by The Royal Society

Calculated (a) drag and (b) added mass coefficients due to planar oscillation compared with experimental data.

T. Stallard et al. Proc. R. Soc. A 2009;465:1467-1488

©2009 by The Royal Society

Time variation of non-dimensional in-line, Cx, and transverse (lift), Cy, forces (thick curve) experienced by a cylinder undergoing one-dimensional motion equivalent to horizontal

displacement of a particle within a focused wave group defined by γ=3.3 and A...

T. Stallard et al. Proc. R. Soc. A 2009;465:1467-1488

©2009 by The Royal Society

Superposition of non-dimensional force–time histories (thin solid curves) for eight orbital trajectories defined by a JONSWAP spectrum with amplitude ratios in the range 4D<A<10D.

T. Stallard et al. Proc. R. Soc. A 2009;465:1467-1488

©2009 by The Royal Society

Morison (a) drag and (b) added mass coefficients calculated by least-squares fit to the Cartesian force components measured for orbital trajectories with amplitude ratios in the range 4D<A<10D.

T. Stallard et al. Proc. R. Soc. A 2009;465:1467-1488

©2009 by The Royal Society

Comparison of non-dimensional measured force, Ck,m (thick curve), and best fit Morison equation, Ck,p (thin curve), for orbital motion defined by a JONSWAP spectrum and with crest

amplitude A=10D1 in the (a) x- and (b) y-directions.

T. Stallard et al. Proc. R. Soc. A 2009;465:1467-1488

©2009 by The Royal Society

Comparison of measured force, Ck,m (thick curve), and best fit Morison equation, Ck,p (thin curve), for orbital motion defined by a Gaussian wave spectrum with crest amplitude A=10D1 in

the (a) x- and (b) y-directions.

T. Stallard et al. Proc. R. Soc. A 2009;465:1467-1488

©2009 by The Royal Society

Time variation of (a) CD(t) and (b) CM(t) for orbital motion corresponding to a NewWave group defined by a Gaussian wave spectrum with crest amplitude A=10D1.

T. Stallard et al. Proc. R. Soc. A 2009;465:1467-1488

©2009 by The Royal Society

Spatial variation of vortex force (Fvortex) for motion corresponding to a wave group defined by (a) JONSWAP spectrum with crest amplitude A=10D1 (Re=7620) and (b) a Gaussian spectrum

with crest amplitude A=10D1 (Re=11 400).

T. Stallard et al. Proc. R. Soc. A 2009;465:1467-1488

©2009 by The Royal Society

Flow visualization (using the surface particle technique) of vortex formation in the wake of a cylinder undergoing circular orbits at an amplitude of KC=18.

T. Stallard et al. Proc. R. Soc. A 2009;465:1467-1488

©2009 by The Royal Society

Time-varying vortex-induced radial force over the interval −1.75<t/T<1.75.

T. Stallard et al. Proc. R. Soc. A 2009;465:1467-1488

©2009 by The Royal Society

Time variation of peak frequency of radial component of vortex force over the interval −1.75<t/T<1.75.

T. Stallard et al. Proc. R. Soc. A 2009;465:1467-1488

©2009 by The Royal Society

Time-varying azimuthal force over the interval −1.75<t/T<1.75.

T. Stallard et al. Proc. R. Soc. A 2009;465:1467-1488

©2009 by The Royal Society

Comparison of measured x-direction force component, Cx,m (thick curve), and corresponding force component predicted, Cx,p (thin curve) by summation of ideal added mass force (equation

5.1) and an azimuthal force component, , where Cθ=0.875.

T. Stallard et al. Proc. R. Soc. A 2009;465:1467-1488

©2009 by The Royal Society