Abstract
In this paper, the inception of tip vortex cavitation in weak water has been predicted using a numerical simulation, and a new scaling concept with variable exponent has also been suggested for cavitation inception index. The numerical simulations of the cavitating flows over an elliptic planform hydrofoil were performed by using the RANS approach with a Eulerian cavitation model. To ensure the accuracy of the present simulations, the effects of the turbulence model and grid resolution on the tip vortex flows were investigated. The turbulence models behaved differently in the boundary layer of the tip region where the tip vortex is developed, which resulted in different pressure and velocity fields in the vortex region. Furthermore, the Reynolds stress model for the finest grid showed a better agreement with the experimental data. The tip vortex cavitation inception numbers for the foil, predicted by using both wetted and cavitating flow simulation approaches, were compared with the measured cavitation index values, showing a good correlation. The current cavitation scaling study also suggested new empirical relations as a function of the Reynolds number substitutable for the two classic constant scaling exponents. This scaling concept showed how the scaling law changes with the Reynolds number and provided a proper scaling value for any given Reynolds numbers under turbulent flow conditions.
Highlights
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 current study confirms that the Reynolds averaged Navier–Stokes (RANS) method using the Reynolds stress model (RSM) can achieve an accurate representation of this kind of tip vortex flows and can adequately explain the flow physics involved
The tip vortex flows around an elliptic hydrofoil were described by the RANS equations in which the flow quantities are split into an average and a fluctuating part
Summary
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. Some past studies reported that the RANS methods have been known to be inadequate in predicting the tip vortex flow accurately [18,28,29,30,31] This was because the one-equation and two-equation turbulence models used in the RANS simulations showed excessive numerical diffusion inside the tip vortex [18,23,24]. In this regard, the current study confirms that the RANS method using the Reynolds stress model (RSM) can achieve an accurate representation of this kind of tip vortex flows and can adequately explain the flow physics involved. The results of the tip vortex cavitation inception analysis on an elliptic planform foil are presented and discussed under the light of the present new scaling concept
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