Experimental and theoretical study on the vortex system of a tubercled wing: from leading-edge vortex to stall cells

Abstract

Wings with leading-edge (LE) tubercles have gained increasing attention over the past decade. Despite their impressive aerodynamic performance, the underlying flow control mechanisms of tubercles remain controversial. In this thesis, both experimental and theoretical approaches are employed to investigate the flow patterns of a tubercled wing at pre-stall and post-stall angles of attack (AoAs).

In the experimental study, 2D Particle Image Velocimetry (PIV) was used to measure flow patterns at cross-flow planes along the chord. At a pre-stall AoA, high-vorticity regions generated by the tubercles appear in an alternating pattern near the LE. A quantitative comparison was conducted to examine the similarities between a tubercle and a delta wing. The results show that tubercles cannot be regarded as small delta wings in terms of vortex generation. The leading-edge vortex (LEV) sheets are convected downstream, where they interact with laminar separation bubbles (LSBs), creating complex flow patterns in the downstream regions. At a post-stall AoA, stall cells (SCs) appear along the span, with their formation dependent on both Reynolds number (Re) and tubercle amplitude. However, the spacing of SCs is relatively independent of AoA, Re, and amplitude, consistently ranging between 5 to 7 tubercle wavelengths.

In the theoretical study, the lifting line theory (LLT) approach was first used to predict the LEV strength but proved ineffective due to the absence of thickness effects. A subsequent analysis using the panel method in xflr5 showed that the Kutta condition should also be applied to the leading edge (LE) rather than only to the trailing edge (TE). Crow’s model was adapted by taking LEVs into consideration. However, a global description of the instability was not obtained due to difficulties in representing LEVs and related mathematical challenges.

This thesis contributes to a further understanding of the tubercle’s role in flow control. The LEVs generated by the tubercles are identified as key factors influencing flow evolution, yet these effects are not captured by LLT-based models or a conventional panel method. Future reduced-order models (ROMs) should account for the influence of LEVs to provide accurate representations of tubercled wing flow dynamics.