Effect of Tripping and Domain-Width on Transonic Buffet on Periodic NASA-CRM Airfoils

Abstract: Transonic buffet is an instability characterized by shock-oscillations and separated boundary-layers. High-fidelity simulations have typically been limited to narrow domains to be computationally feasible, overly constraining the flow and introducing modelling errors. Depending on the boundary-layer state upstream of the interaction, different buffet features are observed. High-fidelity simulations were performed on the periodic NASA-CRM wing at moderate Reynolds number to assess sensitivity of the two-dimensional transonic buffet to boundary-layer state and domain width. Simulations were cross-validated against RANS/URANS and global stability analysis and excellent agreement was found near the onset. By varying the boundary-layer tripping amplitude, laminar, transitional, and turbulent buffet interactions were obtained. All cases consisted of a single shock and low-frequency oscillations $(St \approx 0.07)$. The transitional interaction also exhibited reduced shock movement, a $15\%$ increase in $\overline{C_L}$, and energy content at higher frequencies $(St \approx 1.3)$. Span-wise domain studies showed sensitivity at the shock location and near the trailing edge. We conclude that the span-width must be greater than the trailing-edge boundary-layer thickness to obtain span-independent solutions. For largely separated cases, the sensitivity to span-width increased and variations across the span were observed. This was found to be associated to a loss of two-dimensionality of the flow.