27 th Symposium on Naval Hydrodynamics Seoul, Korea, 5-10 October 2008 Scaling of Tip Vortex Cavitation Inception for a Marine Open Propeller C.-T. Hsiao and G. L. Chahine (DYNAFLOW,INC., USA) ABSTRACT The tip vortex flow generated by a marine open propeller was numerically simulated for three different scales using a Reynolds Averaged Navier-Stokes (RANS) solver. The solutions of RANS were further improved by conducting a Direct Navier-Stokes Simulation (DNSS) in a reduced computational domain. This resulted in significant modifications of the minimum pressure coefficients along the tip vortex. These were analyzed and used to deduce a scaling law. Nuclei effects on the scaling law were investigated with the help of a surface-average pressure (SAP) spherical bubble dynamics model with a realistic bubble nuclei distribution. It was found that the Reynolds number power of the scaling law predicted based on the single phase flow solution is quite different from the classical value. However, the nuclei effects tend to adjust the power back to the classical value if the reference inception criterion is not stringent (higher number of events per second). 1. Introduction Scaling propeller tip vortex cavitation inception from laboratory experiments to large scale tests has not always been very successful. For example, according to experimental data by Jessup et al. (1993), the extrapolation of the cavitation inception number,  i , from their model test to the full scale condition overestimated  i with a factor of 1.5 when the classical scaling laws,  i  R e  with  = 0.4 (McCormick 1962), was used. Many recent analytical studies have revealed that  = 0.4 used in the classical scaling laws is only suitable for low Reynolds number. Based on a modified boundary layer theory Shen et al. (2003) showed that  is a function of the Reynolds number instead of a constant and decreases as the Reynolds number increases. Amromin (2006) used asymptotic analysis and gave a two-range scaling for . He suggested  = 0.4 for laminar flows and  = 0.24 for turbulent flows. Aside from the problems associated with scaling properly the flow field for a simple one-phase flow, derivation of a reliable scaling law for tip vortex cavitation inception encounters at least two more issues. One of the issues is to appropriately incorporate nuclei effects. Another issue which produces discrepancies between different studies is the actual means used to detect cavitation inception. To address these issues Hsiao and Chahine (2005) proposed a numerical experiment which enables simulation of practical methods to call cavitation inception. They used the surface-average pressure (SAP) spherical bubble dynamics model and a realistic bubble nuclei distribution to predict the cavitation inception for a tip vortex flow. The SAP spherical model was then used to track the nuclei and record the acoustic signals generated by their volume oscillations and deduce from this statistics of acoustics pressure peaks. Hsiao and Chahine (2005) applied “acoustic” criteria which define the cavitation inception by counting the number of acoustical signal peaks that exceed a certain level per unit time to deduce the cavitation inception number for different scales. They have demonstrated that larger scales tend to detect more cavitation inception events per unit time than smaller scale because a relatively larger number of nuclei are excited by the tip vortex at the larger scale due to simultaneous increase of the nuclei capture area and of the size of the vortex core. However, this scaling study was based on RANS solutions of tip vortex flows generated by a finite-span hydrofoil used as a conical problem to study tip vortex cavitation inception. It has been shown by previous studies (Dacles-Mariani et al. 1995, Hsiao and Pauley 1998, 1999) that the RANS solution is inadequate for predicting the tip vortex flow accurately. Furthermore, the results derived from the conical problem may pose another concern for practical marine propeller applications. Hsiao and Chahine (2006, 2008) found that the RANS solution of the tip-leakage vortex flow