Tip vortices generated by marine lifting surfaces such as propeller blades, ship rudders, hydrofoil wings, and antiroll fins can lead to cavitation. Prediction of the onset of this cavitation depends on model tests at Reynolds numbers much lower than those for the corresponding full-scale flows. The effect of Reynolds number variations on the scaling of tip vortex cavitation inception is investigated using a theoretical flow similarity approach. The ratio of the circulations in the full-scale and model-scale trailing vortices is obtained by assuming that the spanwise distributions of the section lift coefficients are the same between the model-scale and the full-scale. The vortex pressure distributions and core sizes are derived using the Rankine vortex model and McCormick’s assumption about the dependence of the vortex core size on the boundary layer thickness at the tip region. Using a logarithmic law to describe the velocity profile in the boundary layer over a large range of Reynolds number, the boundary layer thickness becomes dependent on the Reynolds number to a varying power. In deriving the scaling of the cavitation inception index as the ratio of Reynolds numbers to an exponent , the values of are not constant and are dependent on the values of the model- and full-scale Reynolds numbers themselves. This contrasts traditional scaling for which is treated as a fixed value that is independent of Reynolds numbers. At very high Reynolds numbers, the present theory predicts the value of to approach zero, consistent with the trend of these flows to become inviscid. Comparison of the present theory with available experimental data shows promising results, especially with recent results from high Reynolds number tests. Numerical examples of the values of are given for different model- to full-scale sizes and Reynolds numbers.
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e-mail: young.shen@navy.mil
e-mail: scott.gowing@navy.mil
e-mail: stuart.jessup@navy.mil
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July 2009
Research Papers
Tip Vortex Cavitation Inception Scaling for High Reynolds Number Applications
Young T. Shen,
Young T. Shen
Carderock Division,
e-mail: young.shen@navy.mil
Naval Warfare Center
, Code 5800, West Bethesda, MD 20817
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Scott Gowing,
Scott Gowing
Carderock Division,
e-mail: scott.gowing@navy.mil
Naval Warfare Center
, Code 5800, West Bethesda, MD 20817
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Stuart Jessup
Stuart Jessup
Carderock Division,
e-mail: stuart.jessup@navy.mil
Naval Warfare Center
, Code 5030, West Bethesda, MD 20817
Search for other works by this author on:
Young T. Shen
Carderock Division,
Naval Warfare Center
, Code 5800, West Bethesda, MD 20817e-mail: young.shen@navy.mil
Scott Gowing
Carderock Division,
Naval Warfare Center
, Code 5800, West Bethesda, MD 20817e-mail: scott.gowing@navy.mil
Stuart Jessup
Carderock Division,
Naval Warfare Center
, Code 5030, West Bethesda, MD 20817e-mail: stuart.jessup@navy.mil
J. Fluids Eng. Jul 2009, 131(7): 071301 (6 pages)
Published Online: June 1, 2009
Article history
Received:
May 12, 2008
Revised:
February 4, 2009
Published:
June 1, 2009
Citation
Shen, Y. T., Gowing, S., and Jessup, S. (June 1, 2009). "Tip Vortex Cavitation Inception Scaling for High Reynolds Number Applications." ASME. J. Fluids Eng. July 2009; 131(7): 071301. https://doi.org/10.1115/1.3130245
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