Unsteady Flow and Force Development in the case of a Circular Cylinder


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The time varying nature of many real flows has a strong effect on the resulting force experienced by aerodynamic bodies, where the transient force response can readily exceed the steady-state equivalent. This therefore poses a significant threat to small drones as well as larger aircraft that can be subjected to highly unsteady flow fields. Sensing the flow and using predictive modelling to mitigate the unsteady forces shows potential, yet requires a detailed knowledge of the aerodynamic principles at play. This work is a fundamental study into the underlying mechanisms involved in low Reynolds number unsteady aerodynamics to help facilitate future low order models (LOMs). Specifically, the focus is on the development of the unsteady force, by exploring the origin and evolution of boundary layer vorticity as well as the impact of free vorticity located in the flow.

Four sets of experiments are conducted in the towing tank facilities at the University of Cambridge using a rotating and translating circular cylinder as well as a flat plate. To capture the fluid dynamic response, force balance and planar particle image velocimetry (PIV) measurements are acquired in combination, at Reynolds numbers between 4000 and 20000. It is found that whilst the potential flow `added mass' vortex sheet distribution around a stationary object immersed in an accelerating freestream is correct in shape, it ascribes the vortex sheet to the wrong origin. Instead, the vortex sheet is found to develop as a result of external vorticity that is created at the interface between the moving freestream and the quiescent surrounding. Moreover, the evolution of the boundary layer vortex sheet is investigated around a translating and rotating cylinder. The vortex sheet contributions due to kinematics and free vorticity are experimentally recovered. It is further proposed that the vortex sheet contribution due to free vorticity can be decomposed into a local and far-field component. Examining the vortex sheet strength at the unsteady separation point, which has been used in literature explicitly or implicitly to predict unsteady separation, shows that it is strongly affected by the instantaneous velocity, rotation rate and far-field vorticity. Accounting for these contributions collapses the strength of the vortex sheet at the unsteady separation point for the kinematics studied, even as the flow field evolves. In future this may provide avenues with which to predict unsteady separation. Furthermore, the rate at which vorticity sheds from the surface of an object is linked to the boundary layer vortex sheet components. When the unsteady separation point is known, this makes it possible to predict the vorticity shedding rate only from the motion kinematics and the boundary layer vortex sheet.

To minimise computational effort for LOMs, only the most dominant flow physics are ideally modelled. To help determine which flow features therefore need to be incorporated in an LOM, a methodology to approximate the force due to an individual flow structure is proposed. A study of a cylinder encountering a sharp-edged transverse gust explores the force caused by external vorticity located within the gust shear layers. The rigid shear layer assumption inherent in Küssner's model is found to overestimate the related non-circulatory gust force. However, the discrepancy remains small compared to the total force.

Babinsky, Holger
Fluid Dynamics, Vortex Sheets, Unsteady Forces, Unsteady Flow, Added Mass, Unsteady Separation
Awarding Institution
University of Cambridge
EPSRC (1947089)