Spatial development of trailing vortices behind a delta wing, in and out of ground effect

Abstract

In this research, we study the dynamics of vortex pairs both in and out of ground effect. Trailing vortices are generated by towing a 75 $$^\circ$$ leading-edge sweep-angle delta wing in an XY-towing tank, at 15 $$^\circ$$ angle of attack. As the delta wing is towed, it generates a spatially developing vortex pair with the axial (streamwise) flow in the vortex cores. Particle image velocimetry is used to determine the transverse velocity field, and the vortex pair is found to be well-characterized by the superposition of two Lamb–Oseen vortices. The axial flow is captured using a longitudinal light sheet. To ensure we capture the vortex core, a technique is used wherein the light sheet is set such that it is slightly oblique to the length of the vortex. Using this technique allows the axial flow to be measured in the vortex core more than 20 chord-lengths downstream of the delta wing, capturing data at a resolution as close as 0.03 chord-lengths apart. This technique is unaffected by displacements of the vortex core, allowing us to analyze the axial flow profile both in and out of ground effect. A Gaussian velocity profile with a wake-like velocity deficit (flow upstream) is observed in the far-wake of the delta wing in both cases. We also trigger the long-wavelength instability (Crow AIAA J 8:2172–2179, 1970) in the vortices, and compare the measured growth rate of the instability to theoretical growth rate predictions using the theory of Widnall and Bliss (J Fluid Mech 50:335–353, 1971) in a similar manner to Leweke et al. (Annu Rev Fluid Mech 48:1–35, 2016) and Fabre (Ph.D Thesis, 2000). This work is limited to a chord-based Reynolds number of 5000.