quantitative results differ substantially. A recent paper dealing with the flow around a surface piercing blunt body by Zhang and Stern (7) contains mostly results of a numerical analysis, but also some surface elevation measurements at the intersection with the model. They predict that separation with reverse flow occurs at virtually all Froude numbers, and that the separation is limited to a region near the free surface for FrL≤0.55. Some of their trends will be compared later to the present results. To the best of our knowledge, there isn't any other source that provides data on the velocity distribution and vorticity structure around a surface piercing blunt body with a long draft. Due to the occurrence of flow separation and the formation of a bubbly wake at the trough of the bow wave (even in full scale models, such as catamarans and SWATH), they represent a unique problem. The present paper deals with such a flow.
The experiments were performed in the 140 ft towing tank located at the David Taylor Model Basin. The facility is 152 cm deep, 305 cm wide, and 4270 cm long. The experimental setup and model are shown in Figure 1. The model draft is 1.37 m. Experiments are performed at 0° incidence, at Froude numbers based on model length, FrL, ranging between 0.051 and 0.51. The corresponding range of Reynolds numbers is 1.39×105 to 1.39×106, respectively.
PIV measurements are conducted with three orientations of the laser sheet: a vertical plane inclined 115° to the streamwise direction (Figure 1c), a sheet inclined 59° to the streamwise direction and tilted 9° to the vertical (Figure 1b), accounting for the majority of presented data, as well as a sheet inclined 34° and tilted 9° to the vertical. The slight vertical tilt facilitates observations of the wave crest by avoiding any blockage caused by the wave trough. As shown in Figure 1, the primed coordinates (x', y', z') refer to the plane of a given image. Note that the axial position, x/L, varies across any given image. The reference to a specific x/L for an image indicates the position of the origin of the (x,y',z') frame on the center line of the model.
The 6 mm thick laser sheet is generated by a 15W, air cooled, copper vapor laser. The optical setup is sketched in Figure 1b. Data is recorded using a 35 mm film camera, equipped with a 90 mm lens, that has a maximum recording rate of 65 frames per second. The actual rate is approximately 10 frames per second, in order to allow adequate time delays between laser pulses while recording a single photograph. Each image consists of three exposures, with delays ranging from 3 to 15 ms. The images are recorded on Kodak TMAX ASA 3200 B&W film. The acrylic particle tracers are 40 to 60 µm diameter, neutrally buoyant (specific gravity ranging from 0.95 to 1.05), and fluorescing (they respond in the 550 to 560 nm range when subjected to green excitation), as described by Dong, et al. (9). The water is seeded with particles prior to each run. Fine aluminum powder is added to the free surface before some of the runs to improve the visualization of the free surface. Comparison of data with and without the aluminum powder confirms that the presence of the powder has an insignificant impact on the flow. A band-pass filter is inserted in front of the camera to reduce glare caused by the reflection of the light sheet from the model, free surface, and large entrained bubbles. It partially eliminates the green reflections without significantly affecting the fluorescence from the particles. A sample image is shown in Figure 2.
Photographic images are digitized using a Nikon LS3500 slide scanner, at magnifications ranging between 8–22 pixels/mm of fluid, as needed. The digitized images are enhanced and particularly bright objects, such as the model and the free surface, are removed. Velocities are computed using in-house auto-correlation software, as described by Dong et al. (8), and Roth et al.(9). The interrogation window size is 64×64 pixels, and the distance between adjacent windows is 32 pixels (i.e., 50% overlap). The typical uncertainty level is about 0.4 pixels, which for a typical 20 pixel displacement yields a characteristic uncertainty of 2%. The free surface contour for each vector map is measured directly from the digitized image. Video images, recorded with a submerged camera are also used for mapping the free surface elevation and for qualitative observations on the flow structure.
Sample photographs of the free surface at different Froude numbers are presented in Figure 3. They clearly show the increase in elevation of the bow wave with Froude number and the generation of bubbles (splashing) within the trough behind the bow wave. This splashing occurs at FrL≥0.15 and curiously, it begins near x/L=0.41, regardless of Froude number. At FrL=0.205 (Figure 3a) it is possible to identify several additional waves behind the bubbly trough. At FrL=0.255 the second shoulder wave crest is pushed further downstream, and at FrL=0.36 the flow becomes extremely unsteady, violent, and turbulent, without any additional steady crests. However, the front of the bubbly region involves an abrupt change in surface elevation, much like a hydraulic jump. For all FrL≥0.25, the shoulder