Scale effects of the tip-leakage flow with and without cavitation: A numerical study in OpenFOAM

Large eddy simulations of the tip-leakage vortex (TLV) flow around the NACA0009 hydrofoil are performed in OpenFOAM to study the scale effects of the tip-leakage vortex profile with and without cavitation. An incompressible single-phase solver and an in-house advanced compressible cavitating flow solver are employed to reproduce the evolution of the TLV and tip-leakage vortex cavitation (TLVC), respectively. By changing the incoming velocity and the hydrofoil size, six cases are divided into three different flow conditions: velocity scale, size scale and Reynolds number similarity. Comparing the predicted results with the experimental data from literature, a satisfying agreement is obtained. Some crucial flow characteristics, e.g. vortex structures, vortex intensity, vortex trajectory and wandering, velocity distribution, fluctuation features, and TLVC evolution, are studied in detail and the scale effects of them are significant. With the increasing incoming velocity or scale ratio, more pronounced vortex fusion occurs and makes the TLV maintain a higher intensity downstream. The greater the incoming velocity or scale ratio, the more the TLV is pulled away from the hydrofoil and the weaker the amplitude of TLV wandering. Moreover, the transition of axial flow profile from jet-like to wake-like is delayed by increasing the incoming velocity/scale ratio. An increase in incoming velocity or scale ratio leads to an increase in circulation and a decrease in the radius of TLV core, facilitating the occurrence of TLVC. With equal Reynolds number and cavitation number, the scale effects of tip-leakage flows can be neglected.