In order to decrease fuel consumption and thus CO2 emissions, more and more aircraft are designed with highly flexible wings, which exhibit large deformations during flight. But how large can the elastic deformation of a wing become? Which special effects occur at very large deformations? And how do these effects influence the aeroelastic stability of the wing? These questions are addressed by the Institute of Aeroelasticity in collaboration with Technion, Imperial College, University of Michigan, TU Delft and NASA.
Flexibility due to lightweight construction
Nowadays, the development of modern aircraft wings focuses on two criteria. First, the weight must be reduced as much as possible, which is enabled by using new construction methods in combination with lightweight materials (e.g. fiber-reinforced plastics like CFRP). Second, the reduced drag must be minimized, which requires a slender wing with a large span and high aspect ratio. In combination, both measures lead to a very soft and elastic wing structure and, as a consequence, to large deflections under certain flight conditions. The resulting large deformations, however, prohibit the application of common computational methods. These so-called linear methods are based on simplifying structural dynamic and aerodynamic assumptions that are not fulfilled anymore at large deformations.
The Pazy wing test case of the Aeroelastic Prediction Workshop
Therefore, new and more complex methods have to be developed for the calculation of highly flexible wings. An important part of the development is the comparison of computational results with experimental data. For this purpose, a highly flexible wind tunnel model, the Pazy wing, is being investigated in NASA’s 3rd Aeroelastic Prediction Workshop (AePW3). The wing itself is developed and experimentally tested at the Technion – Israel Institute of Technology. Due to the special design, very large deformations can be investigated in the wind tunnel for the first time. The construction is intentionally kept very simple so that scientists involved can create simulation models and, if required, quickly and inexpensively reproduce the model themselves.
Deformations up to 50 percent of the wing span
The wind tunnel tests are conducted at the Technion, while DLR and other groups of the AePW3 provide the corresponding simulation results. A simulation tool developed at DLR is used to determine the deformations of the wing at static aeroelastic equilibrium. The calculation of the aerodynamic forces is performed using a geometrically nonlinear vortex-lattice method. The forces obtained are then passed to a nonlinear finite element program, which computes the resulting deformations. The application of nonlinear methods is necessary, amongst others, because linear methods would lead to an artificial elongation of the wing. This is especially important in the case of the Pazy wing, since it exhibits vertical displacements of up to 50 percent with respect to the wing span at high flow velocities. In comparison: The Boeing 787, currently the most flexible commercial airliner, reaches a maximum deflection of 28 percent under extreme flight conditions. The simulation results are in very good agreement with data provided by other members of the workshop.
Comparison of a linear and a nonlinear finite element simulation of a generic beam with loading at the beam tip
The artificial elongation of the beam in the linear simulation is clearly visible.
Large deformations affect the aeroelastic stability
In addition to the deformations, the dynamic stability of the wing is also to be investigated. Commercial software packages for determining the aeroelastic stability or, respectively, the flutter speed usually only consider the undeformed shape of a wing. Therefore, a method for the stability analysis of highly flexible wings was developed as part of a master’s thesis. It was found, that the modal properties, such as the natural vibrations of the structure strongly change due to the deformations. This has a significant impact on the aeroelastic stability. The more the wing bends, the smaller the so-called flutter speed becomes and thus the velocity range in which the wing can be operated safely.
Dependency of the flutter velocity on the deformation at the wing tip
