Unsteady shock-boundary-layer interaction on the lower surface of a transport-aircraft wing can be caused or amplified by ultrahigh-bypass-ratio underwing nacelle installation. This work analyzes the resulting buffet dynamics on the Airbus XRF-1 configuration at a Mach number of $0.84$, a Reynolds number of $3.3\times 10^6$, and $-4^\circ$ angle of attack using scale-resolving delayed detached eddy simulations and unsteady pressure-sensitive paint measurements. Coherent structures are extracted employing a data-efficient multi-taper spectral POD. Dominant modes occur in the Strouhal number range $St \in [0.1,0.3]$. Surface modes reveal wave-like shock motions that originate near the pylon-wing intersection and propagate inboard towards the fuselage. These shock oscillations are linked to unsteady flow separation downstream of the shock. Additional dominant modes show spanwise oscillations of the separated flow region and shock oscillations phase-linked to shear layer instabilities. The modal analysis of volume data reveals pressure waves connected to these modes traveling upstream above and below the wing.
Modern transport aircraft design has to maximize efficiency to mitigate its climate impact and be competitive in the global market. However, uncertainties associated with transonic shock buffet at the high-speed border of the flight envelope necessitate significant safety margins during aircraft design. These additional margins directly contribute to increased aircraft empty weight, leading to higher fuel consumption and reduced payload capacity. A detailed understanding of the buffet phenomenon will enable informed design recommendations for future aircraft, improving efficiency while maintaining high levels of safety.
Although many decades have passed since the first description of the buffet phenomenon by Hilton and Fowler [1], the field of buffet research is still very active. While these early studies approached the problem primarily by means of experiments on 2D airfoils, numerical investigations have become increasingly important over the years. Experimental investigations and wind tunnel tests continue to play an important role, as they provide indispensable validation data for simulations. The configurations investigated became more and more complex over time, including finite span unswept [2] and swept wing models [3,4] up to full wing-body configurations [5,6,7,8], until today, highly accurate simulations and wind tunnel tests are carried out on entire aircraft models, including nacelles and tailplane [9].
Buffet analysis is challenging due to the generation of broadband, threedimensional signals that are difficult to decouple. Consequently, isolating the underlying physical mechanisms driving the phenomenon is hard. In the past decade, modal analysis techniques emerged as a promising approach to support the analysis and visualization of spatially and temporally resolved snapshot data. The most commonly employed techniques are proper orthogonal decomposition (POD), discrete Fourier transformation (DFT), dynamic mode decomposition (DMD), spectral POD (SPOD), and resolvent analysis. Taira et al. [10] provide an introduction and overview. A theoretical connection between SPOD, DMD, and resolvent analysis is established in [11]. While the POD is straightforward to compute and analyze, the modes may contain a mixture of phenomena associated with different frequencies or frequency bands, since POD modes maximize variance but not necessarily coherence [12]. This spectral mixing can make the physical interpretation of modes more challenging. The DMD builds on the POD by fitting a linear dynamics model within an approximately invariant subspace spanned by the leading POD modes. The resulting decomposition is more interpretable since each spatial mode is associated with a unique frequency and growth rate. However, in practice, DMD computations are very sensitive to imperfections in the data (noise, nonlinear dynamics, limited number of snapshots), leading to spuriously decaying or growing dynamics [13,14]. The SPOD according to [11] combines DFT and POD. In the vanilla SPOD algorithm, spectral estimates are obtained by computing the DFT of temporally overlapping blocks of snapshots. A POD of the estimates for each frequency bin yields the sorted SPOD modes and their energies. Applying the standard SPOD to simulation data is challenging due to the enormous volume of data that must be processed and stored. Moreover, the sequence length and hence the DFT frequency resolution of simulation data are often very limited. The frequency resolution is reduced further when splitting the sequence into blocks. More recent SPOD variants with taper-based spectral estimates mitigate this issue and are computationally more feasible [15,16].
The number of scientific studies employing modal analysis to buffet on full wing-body configurations is rather limited. Ohmichi et al. [17] employ POD and DMD to study buffet on the NASA Common Research Model. In the study, the authors analyze the 3D velocity field about the blank wing. The snapshots are generated using a zonal detached eddy simulation (ZDES). The dominant fluid structures oscillate in the range St ∈ [0.2, 0.6] (St = f c MAC /U ∞ -Strouhal number, f -frequency, c MAC -mean aerodynamic chord, U ∞ -free stream velocity) and propagate from mid span towards the wing tip. The propagating shock oscillations create a cellular mode shape with increasing length towards the tip. The authors also identify low-frequency disturbances with St ≈ 0.06, which modify the entire shock front nearly uniformly, similar to 2D airfoil buffet. Masini et al. [18] studied the RCB12 half model with blank wing in buffet conditions by means of unsteady pressure sensitive paint (uPSP). The authors identify two distinct phenomena dominating the flow physics, namely, low-frequency shock unsteadiness in the range St ∈ [0.05, 0.15], connected to mostly inboard traveling pressure disturbances, and broadband outboard running pressure waves in the range St ∈ [0.2, 0.5], forming the buffet cells. In a fol
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