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TECHNICAL PAPERS

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

[+] Author and Article Information
J. Longo, J. Shao, M. Irvine, F. Stern

IIHR-Hydroscience and Engineering, College of Engineering, University of Iowa, Iowa City, IA 52242

IIHR-Hydroscience and Engineering, University of Iowa, Iowa, IA 52242.

Italian Ship Model Basin, Rome, Italy.

Naval Surface Warfare Center/Carderock Division, Bethesda, MD.

J. Fluids Eng 129(5), 524-540 (Sep 28, 2006) (17 pages) doi:10.1115/1.2717618 History: Received November 22, 2005; Revised September 28, 2006

## 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.

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## Figures

Figure 1

DTMB model 5512

Figure 2

IIHR facility and phase-averaged nominal wake experimental setup: towing tank, wave maker, DTMB model 5512, 2D PIV system, servo wave gage. Towing tank is not to scale in the x coordinate.

Figure 3

PIV measurements at the nominal wake plane of DTMB model 5512 showing both configuration #1 xz and configuration #2 xy of the 2D PIV system. Inset #1 and #2 highlight the xz and xy measurement zones, respectively, and the convergence parameter and UA precision-limit locations.

Figure 4

Typical unsteady PIV data-reduction procedures: (a) unsorted, unfiltered data; (b) phase-sorted, unfiltered data and first stage range-filter limits; (c) first stage range-filtered data and second stage range-filter limits; (d) range- and median-filtered data with LSR curve fit and FS expansion of LSR curve fit; (e) mean axial velocity response and LSR and FS in the xz precision limit measurement area; (f) axial normal stress response and LSR and FS in the xz precision limit measurement area; (g) mean axial velocity response and LSR and FS in the external flow; (h) axial normal stress response and LSR and FS in the external flow.

Figure 5

Steady-flow mean velocities and Reynolds stresses

Figure 6

Time histories (top, solid lines) and running averages (top, dashed lines) of ζI, CT, CH, and CM for Ak=0.025, λ=4.572m, Fr=0.28. FFTs (bottom) highlight regular head wave and encounter frequencies.

Figure 7

Differences in zeroth harmonic amplitude and steady-flow variables as a percentage of the steady variable dynamic range [streaming=(X0−Xstdy)∕DX×100%]

Figure 8

First harmonic amplitude (nondimensional) for phase-averaged velocities and Reynolds stresses

Figure 9

First harmonic phase (radians) for phase-averaged velocities and Reynolds stresses

Figure 10

FS reconstruction of unsteady nominal wake U contours and VW vectors at quarter periods for total magnitude (middle) and first harmonic (bottom): (a) t∕T=0; (b) t∕T=1∕4; (c) t∕T=1∕2; (d) t∕T=3∕4. Reference vectors are color-coded to the regular head waves (top).

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