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Twenty-First Symposium on NAVAL HYDRODYNAMICS
diameter of 30 µm. The light sheet had an average thickness of 1 mm and was positioned parallel to the mean flow direction with maximum intensity near the closure region of the cavity. Two cameras were placed on opposite sides of the sheet to record images of the light sheet. One camera recorded all the scattered light from the bubbles and particles within the sheet, and the second camera was equipped with a filter to block the scattered laser light while recording the fluorescent return of the particles. Thus, it was possible to detect only the motion of the particle tracers as they flowed in the bubbly region behind the cavity. The double pulsed images recorded on the photographs were digitized and processed to determine particle pairs.
Flow Field Near the Leading Edge of a Ventilated Cavity: Developed attached cavitation results from the detachment of the flow from either a smooth surface or at a discontinuity of the slope on the surface. It is often not clear where a cavity will separate from a smooth surface simply from examination of the fully wetted flow. Brennen (1969a and 1969b) examined the fully developed cavity flows over a sphere and cylinder, and Arakeri and Acosta (1973) and Arakeri (1975) studied flows over a variety of headforms. These studies revealed that the viscous flow near the surface strongly influences the inception and location of cavity detachment.
Arakeri (1975) studied the relationship between laminar boundary layer separation and cavity detachment. Cavities were shown to be preceded by laminar boundary layer separation in the non-cavitating flow, yet the location of the cavity detachment was not necessarily near the non-cavitating separation point. Figure 3 shows a schematic drawing of the cavity detachment for a nominally two dimensional cavity, as presented by Arakeri. The boundary layer is observed to separate upstream of the cavity detachment, and the cavity interface is observed to curve into the solid surface. Arakeri offered correlations to predict the location of boundary layer separation upstream of the cavity and the distance between the boundary layer separation and the cavity detachment, λ. The position of boundary layer separation was found to be a weak function of Reynolds number and a strong function of cavitation number. λ was related to the Taylor-Saffman number, µUo/T (where µ is the dynamic viscosity of the fluid, T is the surface tension, and Uo is the freestream velocity), and to the momentum thickness of the non-cavitating boundary layer near the point of boundary layer separation.
Franc and Michel (1985) also significantly expanded the work of Arakeri with examination of the flow over a series of bodies, including hydrofoils. Franc and Michel also recognized the relationship between the presence of non-cavitating laminar boundary layer separation and the formation of attached cavitation, and they proposed a method to predict the location of cavity detachment on smooth surfaces. Their method recognizes that the presence of a cavity will alter the pressure distribution around the cavitating object, and this will modify the growth of the boundary layer upstream of the point of cavity detachment. It was shown that a cavity will detach if the modified boundary layer separates upstream of the cavity.
Franc and Michel point out the “cavity detachment paradox.” A cavity must be preceded by laminar boundary layer separation. However, the cavity pressure may be the lowest pressure of the flow, and this would result in a favorable pressure gradient just upstream of the cavity. Thus, laminar separation would not be expected to occur. Need the region upstream of the cavity be in tension (or have pressure lower than the cavity pressure, in the case of a
Figure 3: Schematic drawing of the cavity detachment region (after Arakeri, 1975).