A robust method to estimate the variation of the vortex shedding frequency with the location of a single spanwise tripwire for circular cylinders in subcritical flow

For circular cylinders fitted with a single spanwise tripwire, this paper develops a mathematical estimation method to predict the variation of the vortex shedding frequency (in the form of Strouhal number (St)) with the tripwire location (θ) for a given Reynolds number (ReD) and tripwire size (d). The basis of this method comes from the experimentally-determined data of vortex shedding frequency through Constant Temperature Anemometry (CTA) measurements. During the course of these measurements, the Reynolds number is changed from ReD=5000 to 30,000, the tripwire size is varied in diameter from 2.9% to 5.9% of the cylinder diameter and the tripwire location on the cylinder surface is changed from θ=0° to 180° with respect to the forward stagnation point of the cylinder.The estimation method proposed in this study requires only the wire diameter (d), the cylinder diameter (D) and the Reynolds number (ReD) as the input variables. In the first step, the ratio of the wire size to the unperturbed boundary layer thickness is determined at a selected circumferential location on the cylinder. This non-dimensional parameter is, then, used to predict the critical wire angles, and the minimum and maximum values of St according to an experimentally determined linear functional relationship. In the second step, the similarity of the St–θ curves at different wire sizes and Reynolds numbers permits the transformation of the St–θ data to a new modified domain (called St⁎–θ⁎), which yields a universally valid quantitative relationship for any wire size and Reynolds number considered. Using this modified functional relationship in conjunction with the predicted critical wire angles and Strouhal number boundaries, the St–θ curves are constructed. Estimated St values using this method show a reasonably good agreement with the experimental data acquired in the current study.