Numerical study on wetted and cavitating tip-vortical flows around an elliptical hydrofoil: Interplay of cavitation, vortices, and turbulence

Abstract

Cavitation in a tip vortex remains a challenging issue in a variety of engineering problems. In this study, we perform large eddy simulation of wetted and cavitating flows around a stationary elliptical hydrofoil with the cross section of NACA (National Advisory Committee for Aeronautics) 16–020. The Schnerr–Sauer cavitation model is adopted for phase transport. The numerical results are verified by comparing with the experimental measurements. Instantaneous vorticity and pressure in both wetted and cavitating flows are studied. It is found that the cavitation promotes the production of vorticity and increases the boundary layer thickness. To further analyze the influence of cavitation on the tip vortices, each term in the transport equation of enstrophy is examined. In the cavitating flow, the dilatation and baroclinic torque terms are promoted to be equally dominant as the vortex stretching term, while in the wetted flow the stretching term is the only dominant one. The axial and azimuthal velocities in the cavity are smaller than those in wetted tip-vortical flow, while the pressure inside is nearly equal to the constant saturation pressure. A tip vortex model with four regions in cavitating flow is built and compared to the wetted flow model. A weakly meandering motion of the tip vortex is observed in the near field. To study the surface wave behaviors of the tip vortex, the space-time velocity correlation analysis is carried out. The surface wave moves at a speed smaller than the incoming flow. A dominating helical mode is found and is consistent with the analytical and experimental results.

Dynamics of cavitating tip vortex

“…For the wetted flow case in figure 10, wavy motion develops over the cylindrical-shaped tip vortex surface (figure 10c), similar to the observation of previous numerical simulations (Asnaghi et al 2020a;Cheng et al 2021;Xie et al 2021). Vortex shedding appears over the suction side of the hydrofoil due to flow separation (figure 10(a,b) side and top view).…”

“…For breathing mode cavitation, the tip vortex deforms from the cylindrical shape downstream of the tip due to the volume and diameter variation of the vortex cavity (figures 5b and 6bii-biv). The vorticity magnitude is significantly lower due to the onset of cavitation (Dreyer 2015;Pennings et al 2015b;Xie et al 2021), yielding a maximum value of ω *…”

“…The presence of the cavity increases the vortex radius, accompanied by a pressure increase around the cavity and a decrease in velocity excess (Batchelor 1964;Garmann & Visbal 2017a). The pressure in the cavity is approximately equal to the vapour pressure, thus reducing the axial pressure gradient (Xie et al 2021). On the other hand, the velocity deficit regions evolve downstream with comparable intensity to the wetted flow condition.…”

“…The nuclei caught in the vortex filament grow rapidly at the centre with minimum pressure, resulting in a continuous cavity structure or intermittent elongated bubbles (Rood 1991). The onset of cavitation further weakens the pressure gradient in the vortex core, resulting in a reduction in axial velocity (Park et al 2021;Xie et al 2021). The inception of cavitation depends on the distribution of the nuclei and the local pressure.…”

An experimental study on near-field tip vortex of an elliptical hydrofoil using tomographic particle image velocimetry

“…The vortex center is detected by | λ ci,x | max , the local maximum of | λ ci,x |, which indicates the point with the highest swirling strength along the freestream direction. As for the vortex core identification, the core periphery could be delineated by finding discrete positions with peak tangential velocity (Pennings et al, 2015;Dreyer, 2015;Xie et al, 2021). In the present work, an enclosed area bounded by a continuous line with an appropriate threshold, the λ ci,x contour with the threshold | λ ci,x | / | λ ci,x | max = 0.125, is used to determine the core periphery.…”