On the optimal size of square-lobed trailing edges in transonic flow over a backward-facing step

Controlling flow separation and reattachment in transonic conditions over a backward‐facing step (BFS) is a critical challenge with significant implications for drag, noise, and structural stability. Square‐lobed trailing edges have emerged as a promising passive flow control strategy. In this study, we extend previous research by investigating an unprecedented range of lobe protrusion heights (LPH), from the traditional 0.4ℎ up to 1.0ℎ. To determine whether larger geometries offer additional performance benefits. Using a combination of Reynolds-Averaged Navier–Stokes (RANS) and Detached Eddy Simulation (DES) at a transonic Mach number of 0.8 and a Reynolds number of 1.8 × 10⁵, we analyse the influence of LPH on reattachment lengths and three-dimensional flow dynamics. For clarity, we differentiate between the “peak” region (upper edge) and the “valley” region (lower edge) of the step. The results indicate a significant reduction in the valley reattachment length as LPH increases, while the shortest reattachment length in the peak region occurs at LPH = 0.6ℎ, with less pronounced differences at higher LPH values. DES reveals that larger LPH configurations enhance the stability and organisation of lateral vortices, reducing chaotic flow behaviours compared to the baseline BFS.