Phase-Averaged PIV for the Nominal Wake of a Surface Ship in Regular Head Waves

Abstract

Phase-averaged organized oscillation velocities (U,V,W) and random fluctuation Reynolds stresses (uu¯,vv¯,ww¯,uv¯,uw¯) are presented for the nominal wake of a surface ship advancing in regular head (incident) waves, but restrained from body motions, i.e., the forward-speed diffraction problem. A 3.048×3.048×100m towing tank, plunger wave maker, and towed, 2D particle-image velocimetry (PIV) and servo mechanism wave-probe measurement systems are used. The geometry is DTMB model 5415 (L=3.048m, 1∕46.6 scale), which is an international benchmark for ship hydrodynamics. The conditions are Froude number Fr=0.28, wave steepness Ak=0.025, wavelength λ∕L=1.5, wave frequency f=0.584Hz, and encounter frequency fe=0.922Hz. Innovative data acquisition, reduction, and uncertainty analysis procedures are developed for the phase-averaged PIV. The unsteady nominal wake is explained by interactions between the hull boundary layer and axial vortices and incident wave. There are three primary wave-induced effects: pressure gradients 4%Uc, orbital velocity transport 15%Uc, and unsteady sonar dome lifting wake. In the outer region, the uniform flow, incident wave velocities are recovered within the experimental uncertainties. In the inner, viscous-flow region, the boundary layer undergoes significant time-varying upward contraction and downward expansion in phase with the incident wave crests and troughs, respectively. The zeroth harmonic exceeds the steady-flow amplitudes by 5–20% and 70% for the velocities and Reynolds stresses, respectively. The first-harmonic amplitudes are large and in phase with the incident wave in the bulge region (axial velocity), damped by the hull and boundary layer and mostly in phase with the incident wave (vertical velocity), and small except near the free surface-hull shoulder (transverse velocity). Reynolds stress amplitudes are an order-of-magnitude smaller than for the velocity components showing large values in the thin boundary layer and bulge regions and mostly in phase with the incident wave.