Towards extending the aircraft flight envelope by mitigating transonic airfoil buffet

Abstract

In the age of globalization, commercial aviation plays a central role in maintaining our international connectivity by providing fast air transport services for passengers and freight. However, the upper limit of the aircraft flight envelope, i.e., its operational limit in the high-speed (transonic) regime, is usually fixed by the occurrence of transonic aeroelastic effects. These harmful structural vibrations are associated with an aerodynamic instability called transonic buffet. It refers to shock wave oscillations occurring on the aircraft wings, which induce unsteady aerodynamic loads acting on the wing structure. Since the structural response can cause severe structural damage endangering flight safety, the aviation industry is highly interested in suppressing transonic buffet to extend the flight envelope to higher aircraft speeds. In this contribution, we demonstrate experimentally that the application of porous trailing edges substantially attenuates the buffet phenomenon. Since porous trailing edges have the additional benefit of reducing acoustic aircraft emissions, they could prospectively provide faster air transport with reduced noise emissions.

Fig. 1. Transonic buffet attenuation and flight envelope extension by porous trailing edges.

In the transonic flight regime, an aerodynamic instability called transonic buffet occurs at specific flow conditions. This phenomenon describes self-sustained shock wave oscillations along the suction side, i.e., the upper side, of the airfoil. Due to the fluid-structure interaction, certain aerodynamic and aeroelastic instabilities are coupled. Thus, the presence of transonic buffet is usually accompanied by structural instabilities, which potentially result in a structural failure of the aircraft wing. Therefore, the typical aircraft flight envelope is limited to lower aircraft speeds. We demonstrate experimentally that the installation of porous trailing edges attenuates the buffet phenomenon substantially. This allows an extension of the flight envelope to higher velocities without hazarding the aircraft’s structural integrity. Such an extension is marked in the flight envelope diagram (upper right) by dashed lines and arrows. Moreover, porous trailing edges have been shown to reduce the trailing edge noise. Thus, our approach can lead to faster and safer aircraft operation with reduced noise emission.

Fig. 2. Experimental setup.

a The experiments are conducted in the transonic measurement section equipped with a rigid airfoil model. The flow field around the airfoil is visualized by two synchronized measurement systems. The PIV setup captures the velocity field and the BOS setup measures density gradients, the latter allowing a precise localization of the oscillating shock wave. b Pictures of the airfoil model and the exchangeable trailing edges. Two types of porous trailing edges are tested: PTE1 is based on a three-dimensional lattice structure, and PTE2 comprises stacked gyroid cubes.

Fig. 3. Fully developed transonic airfoil buffet of the reference (REF) configuration.

A sketch of the shock wave oscillation along the airfoil is given in a, while (b–d) show measurement data related to the shock wave movement. The instantaneous shock wave position normalized by the chord length x_s/c is given in c as a function of time t and its PDF in d, where $\mathcal{D}$ denotes the probability density. The power spectrum $\mathcal{PS}$ of the shock wave position obtained by applying a Fourier transform is provided in b as a function of frequency f and non-dimensional Strouhal number St. It reveals that the shock wave oscillates at a dominant buffet frequency of f ≈ 180 Hz and St = fc/u_∞ ≈ 0.11. Source data are provided as a Source Data file.

Fig. 4. Damping shock wave oscillations in fully developed buffet conditions using porous trailing edges.

The instantaneous shock wave position normalized by the chord length x_s/c is given in a as a fucntion of time t for both PTEs and the reference case (REF), while the corresponding PDFs are shown in b. Here, $\mathcal{D}$ denotes the probability density. Both representations convincingly demonstrate that both PTE designs successfully attenuate the shock wave movement. The power spectra $\mathcal{PS}$ of the shock wave positions obtained by applying a Fourier transform are provided in (c–e) as a function of frequency f and non-dimensional Strouhal number St. They clearly reveal that both PTEs (d, e) substantially reduce the energy contained in the shock wave movement, i.e., they damp shock oscillations and eliminate the frequency peak usually associated with transonic airfoil buffet. Source data are provided as a Source Data file.

Fig. 5. Modification of the boundary layer characteristics in fully developed buffet conditions using porous trailing edges.

The PDFs, with $\mathcal{D}$ being the probability density, of the boundary layer thickness normalized by the chord length δ/c of both PTEs and the reference case (REF) are depicted in a and clearly reveal the reduced boundary layer breathing in the presence of PTEs. PDFs of the streamwise u (b) and the vertical v (c) velocity components within the boundary layer show the substantial modifications induced by the PTEs. A comparison to the streamwise velocity PDFs of the reference configuration at different Mach numbers Ma (d) reveals that the PTEs induce a streamwise velocity distribution similar to pre-buffet conditions (Ma ≤0.72). Source data are provided as a Source Data file.

Fig. 6. Model design choices that optimize the aerodynamic performance of the porous trailing edge configurations.

When mitigating transonic airfoil buffet to extend the flight envelope in the high-speed regime, it is important to consider the effects of the respective airfoil modifications on the aerodynamic performance. To prevent a lift loss, an impermeable solid layer is added at the centerline. This blockage inhibits a mass flux between the pressure and suction side, which would yield a pressure compensation degrading the aircraft’s lift force. Moreover, a perforated surface layer is added on both sides of the porous trailing edges. Since the porous material constitutes very rough surfaces, it typically disturbs the near-wall flow field massively resulting in increased turbulence intensity. This additional viscous drag would increase the overall aircraft’s drag requiring a higher fuel consumption. Thus, both design choices aim at counteracting the aerodynamic performance penalties in the presence of porous trailing edges. The figure shows two representations of the PTE2 configuration, i.e., the Computer-Aided Design (CAD) model and photographs of the titanium model.

Fig. 7. Pressure distribution along the airfoil and lift and drag contributions.

a time-averaged pressure coefficient distribution c_p along the reference airfoil at Ma = 0.73 with the streamwise location x being normalized by the chord length c. The derived pressure distribution is compared with surface pressure sensor measurements of a previous study by Feldhusen et al. to verify the physical correctness of the pressure calculation. b time-averaged pressure coefficient distribution c_p at Ma = 0.76 for all three configurations. Reliable data is not available in the leading edge region and along the non-porous part of the pressure side due to optical constraints of the measurement section. However, the porous trailing edges are not expected to change the flow field in the excluded regions significantly. A substantial deviation from the reference distribution is observed for PTE1 on the suction side. PTE2 follows the reference data quite well with a small deviation at the shock position. c Contributions to the overall lift and drag coefficients based on the pressure distributions given in b. The left-hand side displays physical values and the right-hand side provides the percentage deviation of the PTE configurations from the reference case. Arrows indicate if the deviation is positive or negative. PTE1 induces a strong reduction of the lift coefficient and an increase of the drag coefficient. On the contrary, PTE2 yields a small lift increase with a negligible variation of the drag coefficient. Source data are provided as a Source Data file.

Fig. 8. Schematic diagram explaining how porous trailing edges interact with the flow field to mitigate the shock wave oscillations of transonic airfoil buffet.

In the presence of PTEs, fluid penetrates the porous material, which results in a reduction of the kinetic energy of the flow. Consequently, the recirculation region enlarges and the boundary layer thickness increases. Therefore, the boundary layer has an increased resistance to incoming disturbances, which provokes two different effects. First, the boundary layer breathing is reduced, which damps the pressure fluctuations in the trailing edge region. Second, the recirculation region acts as a buffer at the shock foot, i.e., it damps instabilities associated with the shock wave. Both effects cause an overall reduction of the shock wave oscillations. Consequently, the physical connection between the boundary layer downstream of the shock wave and the shock wave itself enables a mitigation of the shock wave movement via porous trailing edges, although the location of such trailing edge devices inhibits a direct interaction with the shock wave. Please note that the physical processes sketched in this figure are simplified and exaggerated to illustrate the respective phenomena more clearly.

Fig. 9. Pressure field derivation to calculate aerodynamic performance measures based on the time-averaged flow field information at Ma = 0.73.

An integration of the density gradient fields provides the density field ρ as a function of streamwise x and vertical y location as shown in a. The temperature field T given in b is derived from the velocity data and the energy equation. Finally, the ideal gas law is used to provide the pressure field p shown in c. A comparison of the pressure distribution close to the wall with surface pressure measurements conducted by Feldhusen et al. in d shows that the present approach is able to derive physically meaningful pressure coefficient values c_p, which is of utmost importance for the subsequent calculation of the aerodynamic quantities. Source data are provided as a Source Data file.