Transient leading-edge vortex development on a wing rolling in uniform flow

Abstract

Plenoptic particle image velocimetry and surface pressure measurements were used to analyse the early development of leading-edge vortices (LEVs) created by a flat-plate wing of aspect ratio 2 rolling in a uniform flow parallel to the roll axis. Four cases were constructed by considering two advance coefficients, $J=0.54$ and 1.36, and two wing radii of gyration, $R_g/c=2.5$ and 3.25. In each case, the wing pitch angle was articulated such as to achieve an angle of attack of $33^{\circ }$ at the radius of gyration of the wing. The sources and sinks of vorticity were quantified for a chordwise rectangular control region, using a vorticity transport framework in a non-inertial coordinate system attached to the wing. Within this framework, terms associated with Coriolis acceleration provide a correction to tilting and spanwise convective fluxes measured in the rotating frame and, for the present case, have insignificant values. For the baseline case ( $J=0.54, R_g/c=3.25$ ), three distinct spanwise regions were observed within the LEV, with distinct patterns of vortex evolution and vorticity transport mechanisms in each region. Reducing the radius of gyration to $R_g/c=2.5$ resulted in a more stable vortex with the inboard region extending over a broader spanwise range. Increasing advance ratio eliminated the conical vortex, resulting in transport processes resembling the mid-span region of the baseline case. Although the circulation of the LEV system was generally stronger at the larger advance coefficient, the shear-layer contribution was diminished.

Inflow-Velocity and Rotational Effects on Revolving and Translating Wings

“…The rotational motion of wings and blades is known to be associated with greater LEV stability and higher sectional lift coefficients. By varying both aspects of rotational motion on simulations conducted with rotating and translating wings, it was demonstrated when and how each aspect analysis within a comprehensive circulation budget demonstrated that the Coriolis tilting is not an important contributor, consistent with the observations of Wabick et al 27 .…”

“…Werner et al 26 verified the process through experimental measurements, and attributed the effect to the tilting of vorticity, as observed within the rotating coordinate system, by a vertical gradient of Coriolis acceleration. However, Wabick et al 27 found the Coriolis tilting contribution to be negligible on a wing rolling in a uniform flow, in comparison with other mechanisms of vorticity transport.…”

“…A vorticity transport analysis framework, developed by Wabick et al 27 , quantifies the sources and sinks of vorticity in a finite control region adjacent to the suction surface of the wing. The vorticity transport budget is used to understand the associations between LEV behavior, the underlying transport processes, and the existence or absence of inflow velocity gradient and rotational accelerations.…”

“…The present paper utilizes and advances the transport framework derived by Eslam Panah et al 23 and extended to a non-inertial, rotating reference frame by Wabick et al 27 . The rate of change of circulation, with constant-reference-frame angular velocity Ω = (Ω x , Ω y , Ω z ), is given by:…”

“…Since the primary focus of the study is the growth of the LEV, boundary 3 was positioned upstream of the trailing edge to minimize influence of the TEV on the circulation. Other studies employ either a rectangular control region of smaller chordwise extent, such as to contain only the LEV system 23,24,27 , or a control region with boundaries that conform to the vortex 5,19,20 . In the present work, a rectangular control region was selected to capture the diffusive flux of vorticity generated on the suction surface of the wing, and its size results from a compromise between exclusion of the TEV and maximum inclusion of the LEV (which is unstable in some cases).…”