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Research Papers: Ocean Engineering

# Simultaneous Measurement of Free Surface Elevation and Three-Component Velocity Field Around a Translating Surface-Piercing Foil

[+] Author and Article Information
James Schock

Engineering Department (den),
31 Mohegan Avenue,
New London, CT 06320
e-mail: jjschock@gmail.com

Jason Dahl

Department of Ocean Engineering,
University of Rhode Island,
217 Sheets Building Narragansett Bay Campus,
Narragansett, RI 02882
e-mail: jmdahl@uri.edu

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received April 6, 2017; final manuscript received November 16, 2017; published online January 2, 2018. Assoc. Editor: Yin Lu Young.

J. Offshore Mech. Arct. Eng 140(3), 031103 (Jan 02, 2018) (11 pages) Paper No: OMAE-17-1053; doi: 10.1115/1.4038586 History: Received April 06, 2017; Revised November 16, 2017

## Abstract

Two methods are investigated to simultaneously obtain both three-dimensional (3D) velocity field and free surface elevations (FSEs) measurements near a surface piercing foil, while limiting the equipment. The combined velocity field and FSE measurements are obtained specifically for the validation of numerical methods requiring simultaneous field data and free surface measurements for a slender body shape. Both methods use stereo particle image velocimetry (SPIV) to measure three component velocities in the flow field and both methods use an off the shelf digital camera with a laser intersection line to measure FSEs. The first method is performed using a vertical laser sheet oriented parallel to the foil chord line. Through repetition of experiments with repositioning of the laser, a statistical representation of the three-dimensional flow field and surface elevations is obtained. The second method orients the vertical laser sheet such that the foil chord line is orthogonal to the laser sheet. A single experiment is performed with this method to measure the three-dimensional three component (3D3C) flow field and free surface, assuming steady flow conditions, such that the time dimension is used to expand the flow field in 3D space. The two methods are compared using dynamic mode decomposition and found to be comparable in the primary mode. Utilizing these methods produces results that are acceptable for use in numerical methods verification, at a fraction of the capital and computing cost associated with two plane or tomographic particle image velocimetry (PIV).

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## References

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## Figures

Fig. 1

Experimental test tank and model. The test foil is connected to the top carriage. High-speed cameras shown in the foreground are mounted to a bottom carriage which traverses the tank at the same speed as the top carriage. The green laser sheet shines through the glass bottom of the tank.

Fig. 2

Method 1: SPIV setup for longitudinal (streamwise) slicing. The field of view of the SPIV cameras covered an area from the free surface to one chord length below the surface. The off-the-shelf digital camera field of view focused on the intersection of the laser plane with the free surface with the foil at the center. Foil movement is parallel to the X axis.

Fig. 3

SPIV camera positions for the two experimental methods. Cameras are separated by an angle of approximately 30 deg in both cases. For longitudinal slicing, the cameras are centered on the chord of the foil. To perform transverse slicing, the cameras are placed at the end of the tow tank. One camera is placed just to the left of the centerline of the tank and the other camera is placed as far to the left as possible while maintaining a clear view of the area of interrogation.

Fig. 4

Method 2: SPIV setup for 2D + T transverse slicing method. The laser plane and cameras are fixed in space with a fixed field of view in y–z plane. Foil movement is parallel to the X axis.

Fig. 5

This figure demonstrates the positioning of the GoPro camera in relation to the foil. The camera was mounted just slightly above the still water free surface to avoid the camera from interfering in the wave field. (A) Camera, (B) camera field of view, (C) laser plane intersecting the free surface, and (D) foil.

Fig. 6

Arrangement of vertical tracking lines and the free surface. The laser plane intersecting the free surface is the high-intensity horizontal line of approximately 10 pixels in thickness. Vertical colored lines are 1D tracking lines, where peak intensity is tracked as a function of time.

Fig. 7

Longitudinal locations of velocity field measurements. The slices, obtained in separate, random order experiments, are combined to obtain the 3D average velocities within the volume.

Fig. 8

Nondimensional velocities for directional velocity components U-component (top row), V-component (middle row), and W-component (bottom row) for Froude numbers 0.37 and 0.55, taken at a representative height of y/c = −0.334 below the free surface using the longitudinal slicing method. Velocity field components are time-averaged. Field velocities are normalized by the forward speed of the carriage.

Fig. 9

FSEs obtained through longitudinal slicing of the free surface for varying Froude number. Contours show the FSE normalized by the chord length of the foil.

Fig. 10

In the transverse slicing method, the location of the light sheet varies in time due to the forward motion of the foil. Knowing the frame rate of the obtained SPIV images, the flow field may be reconstructed assuming a steady flow where the time variation is equivalent to spatial variation in the x-dimension.

Fig. 11

Depthwise variation in velocity components for U, V, and W velocities corresponding to Fr = 0.37. Plots at increasing depth along the chord of the foil, starting near the mean free surface and extending to one chord length below the free surface. Contours show the field velocity components normalized by the forward speed of the carriage.

Fig. 12

Velocity field components obtained through transverse slicing method for Froude number 0.37 at a depth y/c = −0.334. Velocity components are instantaneous at each x-location and are not time-averaged. Field velocities are normalized by the forward speed of the carriage.

Fig. 13

At Froude number 0.37; Top: FSEs measured using the longitudinal slicing method. Middle: FSEs measured using the transverse slicing method. Elevations are nondimensionalized by the chord length of the foil. Bottom: RMSD (%) between the two methods.

Fig. 14

Nondimensional RMS (in %) for all directional components and Froude numbers investigated with the longitudinal slicing method for y/c = –.334. Velocities are nondimensionalized by forward speed of the carriage.

Fig. 15

Measured free surface from digital camera and light sheet intersection with free surface (dotted line) overlaid on raw image obtained from SPIV camera. Slice is located 0.11 chord lengths from the center line of foil for Fr = 0.37.

Fig. 16

U-component of velocity field with free surface. Slice located at z/c = 0.11 for Fr = 0.37. Field velocities are normalized by the forward speed of the carriage.

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