Instabilities in the flow over a spinning disk at angle of attack

Three-dimensional laminar flow over an inclined spinning disk is investigated at a Reynolds number of ${\textit{Re}} = 500$ and an angle of attack of $\alpha = 25^\circ$ , for tip-speed ratios up to 3. Numerical simulations are performed to investigate the effect of spin on the aerodynamics and characterise the instabilities that occur. Increasing tip-speed ratio significantly increases both lift and drag monotonically. Several distinct wake regimes are observed, including vortex shedding in the non-spinning case, vortex-shedding suppression at moderate tip-speed ratios and a distinct corkscrew-like short-wavelength instability in the advancing tip vortex at higher tip-speed ratios. Vorticity generated by the spinning disk strengthens the advancing tip vortex, inducing a spanwise stretching in the trailing-edge vortex sheet. This helps to dissipate the vorticity, which in turn prevents roll up and suppresses vortex shedding. The short-wavelength instability shows qualitative and quantitative matches to the $(-2,0,1)$ principal mode of the elliptic instabilities seen in pairs of counter-rotating Batchelor vortices. The addition of vorticity from the disk rotation significantly alters the circulation and axial velocity in the tip vortices, giving rise to elliptic instability despite its absence in the non-spinning case. In select cases, lock-in between the frequency of the elliptic instability and twice the spin frequency is observed, indicating that disk rotation acts as an additional forcing for the elliptic instability. Additional simulations at different Reynolds numbers and angle of attacks are considered to examine the robustness of observed phenomena across different parameter combinations.