Experimental and CFD Study of KCS Turning Circles in Waves

Experiments and CFD are used to explain the physics of turning circles (TCs) in waves. The trajectories collapse onto a single circle if transformed using the wave drift distance H_D and direction µ_D, as do the time series when synchronized/averaged by each turn. The CFD 6DoF equation balances are satisfied for all TCs, for the synchronized/averaged data and linearly for the total, mean, and unsteady responses. The time mean and unsteady CFD validation variable errors are comparable with the multiple facility standard deviation. The TC 3DoF equation balances (heave, roll and pitch are negligible) for the calm water and the time mean in waves are similar, except that the latter have larger magnitudes: the physics are the same with added Coriolis terms, forces, and moments. In the earth-fixed system, the running mean trajectory follows µ_D and H_D, and the time mean resultant velocity follows µ_D, and its integration is comparable to H_D; and the sector averaged time mean horizontal plane velocity components show the same trends as their time mean values, and the angle of the ratio of the time mean surge X and sway Y force components is the same as µ_D. The 6DoF equation balance for the unsteady response is much simpler than the time-mean response. The unsteady responses show strong correlations with wave direction that are revealed via polar plots of which the envelope corresponds to the Hilbert Transform instantaneous amplitude and the midpoint corresponds to the low frequency (yaw angle averaged) analysis. The time-mean volume flow field shows similar trends as the calm water TC with increased magnitudes; and the unsteady response oscillates about the time mean. The physics of the TCs in waves are best explained using inverse dynamics: wave induced motions (mainly, pitch and heave) result in oscillating X and Y forces (mainly, added resistance X_H/X_W, and side forces Y_H/Y_W), which produce the oscillating u, v, drift angle (hull vortices), and propeller and rudder loads; all of which combine as the time mean and unsteady responses, and wave drift direction and distance.