Instabilities in the Flow Over a Spinning Disk at Angle of Attack

Citation

Lee, Marcus Kuok Kuan (2022) Instabilities in the Flow Over a Spinning Disk at Angle of Attack. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/kmhn-7e49. https://resolver.caltech.edu/CaltechTHESIS:09282021-234035965

Abstract

Micro air vehicles (MAVs) face stability issues, especially as they continue to decrease in size. A spinning disk is inherently robust to external disturbances due to its spin stabilization, and therefore is a potential design for stable MAV flight. However, controlled flight of a spinning disk requires a detailed understanding of the underlying flow structures that determine the aerodynamic behavior. A spinning disk acts to rotate and propel nearby flow tangentially outwards, while drawing in fluid from above. In this way, spin acts as an additional source of both angular and linear momentum from the disk's surface, which can alter the wake structure significantly. In this thesis, we explore how spin affects the aerodynamic forces on a disk and characterize several instabilities that occur. To this end, we use the immersed-boundary Lattice Green's function (IBLGF) method to simulate flow over a spinning disk at angle of attack for Reynolds numbers of O(10²) and tip-speed ratios (non-dimensional spin rate) up to 3.

At these Reynolds numbers, the steady flow first undergoes a bifurcation associated with wake instability, giving rise to vortex shedding. Increasing tip-speed ratio leads to monotonic increases in both lift and drag, although the lift-to-drag ratio remains fairly constant. We also identify several distinct wake regimes, including a region of vortex-shedding suppression, and the appearance of a distinct corkscrew-like short-wavelength instability in the advancing tip vortex. To understand the mechanism leading to suppression of vortex shedding, we study the streamlines and vortex lines in the wake. We show that the vorticity produced by the spinning disk strengthens the tip vortices, inducing a spanwise flow in the trailing edge vortex sheet. This helps to dissipate the vorticity, which in turn prevents roll up and thus suppresses vortex shedding. For the short-wavelength instability, we use spectral proper orthogonal decomposition (SPOD) to identify the most energetic modes and compare it to elliptic instabilities seen in counter-rotating vortex pairs with axial flow. 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. We also observe lock-in between the frequency of the elliptic instability and twice the spin frequency, indicating that disk rotation acts as an additional forcing for the elliptic instability. Many of these phenomena are consistent with observations in high Reynolds number studies and for other bluff body geometries. As a result, the mechanisms proposed here may serve as a basis for understanding and predicting the changing wake structures in more complex flow configurations.

Thesis Files