Effect of the vortical structures on the hydrodynamic performance of a pitching hydrofoil

The objective is to study the vortical structural behaviors of a transient pitching hydrofoil and their effects on the hydrodynamic performance. The pitching motion of the hydrofoil is set to pitch up with an almost constant rate from 5° to 15° and then back to 5°, with the Reynolds number 4.4×10^(5) and the frequency 2 Hz. The results show that the main coherent structures around the pitching hydrofoil include small-scale laminar separation bubble (LSB), large-scale second vortex (SV) and trailing edge vortex (TEV) which are all vortical. The relationship between the vortical structure and the lift is investigated with the finite-domain impulse theory. It indicates that the major part of the lift is contributed by the LSB, whereas the shedding and the formation of the SV and TEV cause the fluctuation of the lift. The proper orthogonal decomposition (POD) method is applied to capture the most energetic modes, revealing that the LSB mode occupies a large amount of energy in the flow field. The dynamic mode decomposition (DMD) method accurately extracts the dominant frequency and modal characteristics, with the first mode corresponding to the mean flow, the second mode corresponding to the LSB structure and the third and fourth modes corresponding to the vortex shedding.

Numerical simulation of unsteady cavitating flows around a transient pitching hydrofoil

The objective of this paper is to improve the understanding of the influence of multiphase flow on the turbulent closure model, the interplay between vorticity fields and cavity dynamics around a pitching hydrofoil. The effects of pitching rate on the sub- cavitating and cavitating response of the pitching hydrofoil are also investigated. In particular, we focus on the interactions between cavity inception, growth, and shedding and the vortex flow structures, and their impacts on the hydrofoil performance. The calculations are 2-D and performed by solving the incompressible, multiphase Unsteady Reynolds Averaged Navier Stokes （URANS） equations via the commercial CFD code CFX. The k-co SST （Shear Stress Transport） turbulence model is used along with the transport equation-based cavitation models. The density correction function is considered to reduce the eddy viscosity according to the computed local fluid mixture density. The calculation results are validated with experiments conducted by Ducoin et al. （see Computational and experimental investigation of flow over a transient pitching hydrofoil, Eur J Mech/B Fluids, 2009, 28：728-743 and An experimental analysis of fluid structure interaction of a flexible hydrofoil in vari- ous flow regimes including cavitating flow, Eur J Mech B/fluids, 2012, 36： 63-74）. Results are shown for a NACA66 hydro- foil subject to slow （quasi static, t2=6~/s, ＆＊ =0.18） and fast （dynamic, ＆=63~/s, dr＂ =1.89） pitching motions from a =0~ to a =15~. Both subcavitaing （or =8.0） and cavitating （cr=3.0） flows are considered. For subcavitating flow （or=8.0）, low frequency fluctuations have been observed when the leading edge vortex shedding occurs during stall, and delay of stall is ob- served with increasing pitching velocity. For cavitating flow （tr=3.0）, small leading edge cavities are observed with the slow pitching case, which significantly modified the vortex dynamics at high angles of attack, leading to high frequency fluctuations of the hydrodynamic coefficients and different stall behaviors compared to the subcavitating flow at the same pitching rate. On the other hand, for the fast pitching case at or=3.0, large-scale sheet/cloud cavitation is observed, the cavity behavior is un- steady and has a strong impact on the hydrodynamic response, which leads to high amplitude fluctuations of the hydrodynamic coefficients, as well as significant changes in the stall and post-stall behavior. The numerical results also show that the local density modification helps to reduce turbulent eddy viscosity in the cavitating region, which significantly modifies the cavity lengths and shedding frequencies, particularly for the fast pitching case. In general, compared with the experimental visualiza- tions, the numerical results with local density correction have been found to agree well with experimental measurements and observations for both slow and fast transient pitching cases.

Investigation of hysteresis effect of cavitating flow over a pitching Clark-Y hydrofoil

The objective of this paper is to investigate the hysteresis effect of cavitating flow over a Clark-Y hydrofoil undergoing a transient pitching motion at Reynolds number Re=4.55×105,cavitation numberσ=1.33,pitching frequency f*=2 Hz via combined experimental and numerical studies.A hysteresis phenomenon is observed in the hydrodynamic curve and cavity area in increasing and decreasing of the angle of attackα.The hydrodynamic curves are divided into three regions:Regions A,B and C.For Region A,the lift coefficient of downstroke is lower than that of the upstroke,and the lift coefficient curve of the downstroke is more unstable.The formation and development of counterclockwise trailing edge vortex(TEV)are responsible for the decline and fluctuation of lift during the downstroke,thus leading to the increase of the hysteresis loop.Compared with the upstroke,the hydrodynamic curve in downstroke is shifted laterally to some extent in Region B.The delay effect is the main factor leading to the shift of the hydrodynamic curve,which corresponds to the minimum hysteresis loop.In Region C,the hysteresis loop is maximum and the evolution trend of the hydrodynamic curve is peak-valley opposites.When the direction of oscillation changes,the detachment and dwell time of the cavity are advanced,thus leading to the difference of hydrodynamic curve and the increase of hysteresis loop.