# Scale-Adaptive Simulation of Unsteady Cavitation Around a Naca66 Hydrofoil
## 1 Introduction  
Studies of unsteady cavitating flow around hydrofoils are important to understand the cavitation dynamic behavior and its impact in hydraulic machinery [1; 2]. Experimental studies have shown limitations such as: equipment uncertainty, costs and experiments calibration [3]. Therefore, CFD is an alternative way to study the aforementioned phenomenon based on numerical models [4]. One of the main characteristics of cavitating flows around foil or blade is the detachment process of the cavities, which should be related to eddies of the flow field [5]. In previous studies, large eddy simulation (LES) has been used to reproduce the unsteady behavior [6; 7; 8]. LES can be applied using explicit or implicit methods to estimate the subgrid tensor and consequently large and small eddies [9]. Based on previous studies of [PERSON] et al. [10], [PERSON] et al. [4] applied implicit large eddy simulation (ILES) for the numerical simulation of unsteady cavitating flows around a plane-convex hydrofoiland results showed that the main characteristics of the cavitation phenomenon were reproduced fairly well. However, LES models are more complex than RANS, and they have been underutilized to estimate the regular growth of the leading edge cavity at the beginning of the cavitation phenomenon. Considering that point of view, researchers such as [PERSON] et al. [11] and [PERSON] et al. [12] applied the partially averaged Navier-Stokes method (PANS) for the numerical simulation of turbulent cavitating flows based on [PERSON] ideas [13]. PANS is a hybrid turbulence model, which conducts the simulation from Reynold average Navier-Stokes (RANS) to direct numerical simulation, DNS. It is based on unresolved total ratios of kinetic energy, \(f_{k}\), and dissipation, \(f_{c}\). Nevertheless, those ratios can only be found by a subgrid independence analysis and they are not easily estimated [13; 14]. Other authors as [PERSON] et al. [15], applied the unsteady RANS (URANS) to achieve the unstable behavior of the cavitation phenomenon. The URANS averages out all turbulent fluctuations and resolves only frequencies far lower than those of the turbulent fluctuations, which are resulting from geometry variations or boundary conditions and typically only reproduce the single vortex shedding frequency [16; 17]. Thus, the cavitation shedding and the detached cavity are not fully reproduced in [PERSON]'s studies [15]. In this context, a hybrid model RANS-LES can be applied to reproduce the attached cavity and the flow separation. The detached eddy simulation (DES) mixes the computational cost of RANS in the attached boundary layer and of LES in the separation region [18; 19]. However, the grid should be highly refined in a region of particular interest, and the simulation depends in a great percentage of the grid mesh as in a similar way to LES. In contrast, [PERSON] and [PERSON]. [17] proposed a RANS-LES turbulence model called scale adaptive simulation (SAS) which is based on previous studies carried out by [PERSON] [20; 21]. The turbulence model is similar to DES, but without an explicit influence of the grid mesh at the RANS mode of the model, and it changes smoothly from a LES model back to steady RANS. Moreover, SAS presents benefits in comparison to URANS due to the spectral content of turbulent flows [17; 19]. After all, the use of SAS for numerical simulations of unsteady cavitating flows around hydrofoils has not been widely explored yet, and the model mechanics of the scale-adaptive characteristics in regions as the detached process of cavities is not fully understood [19]. Therefore, the present study is focused on the application of SAS to research unsteady cloud cavitation flows around a NACA66 hydrofoil with experimental validation based on [22]. Moreover, for a better understanding of the SAS model and to capture major trends, ILES has also been carried out for the numerical simulation of unsteady cloud cavitation flows around a NACA66 hydrofoil.