# Numerical Study on Tip Vortex Cavitation Inception on a Foil
## 1 Introduction  
Experimental and numerical analyses of vortex cavitation on hydrofoil-shaped control fins and energy saving devices, rudders and propellers are of crucial importance in naval hydrodynamic problems since this type of cavitation often occurs first and leads to performance deterioration, cavitation erosion damages and cavitation induced noise. The essence of the analyses should be the proper understanding and modeling of the detailed flow physics into the vortex cavitation inception process of a vortex flow. In addition, one of the practical purposes of cavitation analysis is the upscaling of vortex cavitation inception from the model scale data to full scale designs. Although experiments and numerical analyses have their own shortcomings, mutually complementary studies are needed to more accurately and effectively solve cavitation scaling problems. Experimental approaches, analytical methods and numerical schemes for the investigation of the complicated physics involved in cavitating flows have been developed, and these have produced an enormous amount of data on the subject of cavitation. Representative reviews for the subject can be found in [PERSON] and [PERSON] [1], [PERSON] [2, 3], [PERSON] [4] and [PERSON] [5]. The mechanism of development of tip vortex flow and the appearance characteristics of tip vortex cavitation were examined and reported by [PERSON] and [PERSON] [6], [PERSON] et al. [7], [PERSON] and [PERSON] [8] and [PERSON] and [PERSON] [9]. The complicatedness of tip vortex flows is made known to be brought about by the turbulence and sharp changes of the pressure and velocity across the vortex core [10]. Several observations in relation tocavitation in a tip vortex trailing from an elliptic hydrofoil can be found in [PERSON] et al. [7]. This experimental study shows the dependency of the cavitation number associated with tip vortex cavitation inception on the Reynolds number and gas content value and detailed LDV data of the velocity field inside the tip vortex. As for the detailed mechanism of vortex cavitation inception, the role of nuclei reaching the vortex core as a trigger of cavitation occurrence was investigated by [PERSON] et al. [11], and afterward, the sensitivity of the tip vortex cavitation developing on a blade to the nuclei distribution was found by [PERSON] et al. [12]. The cavitation inception point is usually determined by visual observations of cavitation appearance [8]. Recently, acoustic measurement schemes have been utilized as another alternative to detect the cavitation inception by using a signal analysis [13; 14; 15]. However, as discussed in [PERSON] et al. [16], since all relevant flow features cannot be measured in the experimental approaches because of small scales of flow dynamics, numerical simulations can be used as a complementary tool to obtain further insights into tip vortex properties [17; 18; 19]. It should be noted that it is still a challenging problem for the experimental methods as well as the numerical methods to accurately predict the vortex flows getting complicated by the turbulence, steep pressure and velocity gradients. These flows become more complicated by the presence of phase change [20; 21]. The numerical methods to predict the cavitation inception are well classified and explained in [PERSON] et al. [16]. The wetted flow approach without considering cavitation occurrence utilizes the minimum pressure to determine the cavitation inception point, in which cavitation occurrence is expected when the minimum pressure reaches the saturation pressure. The empirical relations obtained from the experimental data showing the dependency of the tip vortex cavitation on the Reynolds number can also be used with the wetted flow simulations [5; 8; 22]. As a direct simulation approach, in the Eulerian cavitation simulation approach, the cavitation inception number is determined when the computed vapor volume shows similar with a detectable minimum vapor volume at the cavitation inception point [16; 18; 19; 23].