On the Co-existence of Transonic Buffet and Separation-Bubble Modes for the OALT25 Laminar-Flow Wing Section

Abstract

Transonic buffet is an unsteady flow phenomenon that limits the safe flight envelope of modern aircraft. Scale-resolving simulations with span-periodic boundary conditions are capable of providing new insights into its flow physics. The present contribution shows the co-existence of multiple modes of flow unsteadiness over an unswept laminar-flow wing section, appearing in the following order of increasing frequency: (a) a low-frequency transonic buffet mode, (b) an intermediate-frequency separation bubble mode, and (c) high-frequency wake modes associated with vortex shedding. Simulations are run over a range of Reynolds and Mach numbers to connect the lower frequency modes from moderate to high Reynolds numbers and from pre-buffet to established buffet conditions. The intermediate frequency mode is found to be more sensitive to Reynolds-number effects compared to those of Mach number, which is the opposite trend to that observed for transonic buffet. Spectral proper orthogonal decomposition is used to extract the spatial structure of the modes. The buffet mode involves coherent oscillations of the suction-side shock structure, consistent with previous studies including global mode analysis. The laminar separation-bubble mode at intermediate frequency is fundamentally different, with a phase relationship between separation and reattachment that does not correspond to a simple ‘breathing’ mode and is not at the same Strouhal number observed for shock-induced separation bubbles. Instead, a Strouhal number based on separation bubble length and reverse flow magnitude is found to be independent of Reynolds number within the range of cases studied.

Connecting transonic buffet with incompressible low-frequency oscillations on aerofoils

“…Note that the LES result at Re = 5 × 10 5 using V2C's equivalent grid to grid 1 has been shown to match well with a direct numerical simulation employing a refined grid (Zauner & Sandham 2020). Additionally, the grid for OALT25 that is equivalent to grid 1 has also been shown to capture buffet frequency accurately for Re = 3 × 10 6 (see the comparison with LES of Dandois et al (2018) and experiments of Brion et al (2020) reported in Zauner et al 2023). Thus, the present choices of grid distributions in the x-y plane associated with grid 1 and grid 0 (which is even further resolved) are considered more than adequate to capture features at a relatively lower Reynolds number of Re = 5 × 10 4 .…”

“…The methodology adopted here is similar to that used and extensively discussed in previous studies (Zauner & Sandham 2020;Moise et al 2022a;Zauner et al 2023), highlights of which are provided below. We have chosen to perform LES and analyse buffet features using a SPOD of the simulation results in lieu of the more common approach of performing simulations using a RANS framework and global linear stability analysis.…”

“…The simulations are performed using SBLI, an in-house, scalable, high-order, multi-block, compressible flow solver with shock-capturing capabilities (Yao et al 2009). This solver has been extensively used to study transonic buffet (Zauner, De Tullio & Sandham 2019;Zauner & Sandham 2020;Moise et al 2022a,b;Zauner et al 2023) and LFO (Almutairi et al 2010;Almutairi & AlQadi 2013) for various flow conditions. Fourth-order and third-order finite-difference schemes are used for spatial and temporal discretisation, respectively.…”

“…Since this code generates the grid-point positions in the x-y plane based on spacing requirements, curvature, etc., it can be easily adapted to generate grids with similar characteristics for different aerofoils. Here, for grid 1, we use a similar distribution in the x-y plane as that used for LES of flow over Dassault Aviation's V2C aerofoil and ONERA's OALT25 in previous studies (Zauner & Sandham 2020;Moise et al 2022a;Zauner et al 2023). The three-dimensional grids based on grid 0 and grid 1 contain approximately 82 and 75 million points, respectively.…”

“…Interest in studying laminar aerofoils with applications towards improving aircraft performance and reducing skin-friction drag has led to several recent studies (Dandois et al 2018;Brion et al 2020;Zauner & Sandham 2020). Although initially considered to have a distinct mechanism as opposed to turbulent transonic buffet, it has been shown recently in several studies (Moise et al 2022a,b;Zauner, Moise & Sandham 2023) that the spatio-temporal characteristics strongly resemble each other (compare figure 14a and figure 14b in Moise et al 2022b), suggesting similar underlying mechanisms. It was also shown in these studies that in contrast to a single shock wave that is commonly observed in transonic flows around aerofoils, multiple shock waves can develop if the free-stream Reynolds number is sufficiently low and transition occurs naturally.…”