The Onset of Bubble-Ring Cavitation on Hemispherical Headforms

Abstract

An approximate theory is developed to predict the onset of cavitation on hemispherical headforms for Reynolds numbers at which laminar separation is known to occur. Insofar as it is possible, the theory is based upon first principles. Fairly good agreement is obtained between the cavitation desinence trends recently measured by Holl and Carroll and the present theory. It is also found that the onset cavitation number should be less than the magnitude of the pressure coefficient at the laminar separation point and that the cavitation number increases with freestream velocity. As long as there is an appreciable concentration of dissolved air in the water, it is also found, in agreement with experiment, that the onset of bubblering cavitation is practically independent of air content. Moreover, the observed occurrence of a lowest speed for “bubble-ring” cavitation, which is the only cavitation form considered here, and the range of “cutoff” speeds predicted by the present asymptotic theory show very encouraging agreement. The present theory suggests that this cutoff speed and its accompanying cutoff cavitation number can also depend on the temperature of the water, provided that the initial size attributed to a “typical” spherical free-stream air bubble nucleus also varies with the temperature. At 80° F (26.6°C) it is estimated that the typical nucleus from which bubble-ring cavitation originates has a radius of about seven μm. At higher temperatures the nucleus radius decreases from this value while at lower temperatures the initial radius exceeds the value noted.