The Effect of Reynolds Number on a Developed Tip-Vortex Cavity and its Radiated Noise

It is well known that the inception of tip-vortex cavitation on wings and ship propellers is delayed in model tests when compared to sea trials due to the lower Reynolds number in the model test. There is, however, a lack of knowledge on the effect of Reynolds number on the vortex cavity when it becomes more developed. The present paper aims to
fill this gap by presenting a method to correct underwater radiated noise levels and broadband hull pressure fluctuations due to tip-vortex cavitation on ship propellers for lower Reynolds numbers present in measurements in cavitation test facilities.
The method assumes that the noise by vortex cavitation scales with the cavity radius according to a semi-empirical formulation that was developed by Raestad (1996) and Bosschers (2018b). The method makes use of a vortex model that relates the cavity radius, or cavity size, to cavitation number. Using an analytically derived solution for a 2-D cavitating vortex, it was shown in Bosschers (2018a) that the ratio of cavity size and viscous core size becomes independent of the vortex strength when presented as function of the ratio of cavitation number and cavitation number at inception. As the Reynolds number has an effect on both cavitation number at inception and viscous core size, this relation can be used to predict the effect of Reynolds number on cavity size. The method requires knowledge of the cavitation number at inception of vortex cavitation in the model test.
The behavior of the formulations in the limit for very small cavity size shows that the cavity size depends on the cavitation number at inception and thereby on the Reynolds number. However, in the limit of very large cavity size, the cavity size becomes independent of the cavitation number at inception and therefore also independent on Reynolds number. The relevant parameter is the ratio of cavity size and viscous core size.
The methodology can be used to adjust the cavitation number in the model test, to correct the measured noise levels, or a combination of the two. The method is applied to a number of test-cases in which the vortex cavity size in the model test varied from close to inception to fully developed. The results show an improvement of the predictions of the model test but more studies are required to validate and refine the procedure.