Limit-cycle vibrations on the aero-stable wing (experiment in the transonic wind tunnel in Göttingen)
In 2001/2002 the Institute of Aeroeleasticity carried out a series of tests in the Transonic Windtunnel Göttingen within the scope of the HGF-project Aerostability. Among other things, the flutter behaviour of a swept, 3D wing with a wingspan of 60 centimetres that was affixed on one side to the wind tunnel and made out of fibre-reinforced plastic (aerostable wing) was investigated. For this purpose, the flutter limit was deliberately exceeded several times, without resulting in structural failure. Stable limit cycle vibrations with a small amplitude, the so-called LCOs, could be observed.
Larger computing capacities and improved methods in the field of flow-structure coupling have been used since 2010 to retake the numerical modelling of the limit cycle vibration problems. The first challenge lay in reproducing the steady aeroelastic equilibrium state as it had occurred during the experiment. At this time, the measured pressure distribution in the three wing sections was available; however, there were no reliable deformation measurements of the deformed wing geometry under load. The 1D beam models of the wing structure used so far in the coupled simulation led to completely different pressure distributions as compared to the experiment. A breakthrough was achieved by using the new 3D Finite Elements Shell model of the wing. This model was created with the MOdGen generator on the basis of the original layer structure plan, and by completely taking into account the wind tunnel walls of the adaptive measuring section of the TWG in the CFD-simulation. It turned out that a previously excluded, but significant, deformation of the profile geometry in the form of a bulge on the upper side was responsible for the observed excessive acceleration of the flow (see figure, top right).
As part of the DLR project iGREEN, this hypothesis could be experimentally confirmed through the deformation measurements of the newly acquired stereo-photogrammetric measurement system PicColor, and the new structural model could be extensively validated – both statically and dynamically.
This was the starting point for steady-state flow-structure coupled time domain simulations, which among other things, led to the results shown in the middle figure to the right. The time signals of the shifting of a reference point in the wingtip can be seen both in the experimental data as well as in the data of two different simulations with different starting conditions. The amplitudes of the observed limit cycles show a remarkably good compliance taking the complexity of the problem into account.
The non-linear aeroelastic model thus considered to be validated next served as the starting point for the examination of the aerodynamic non-linearity or of the amplitude limiting mechanism. The figure at the bottom right shows the local net energy input during the LCO vibration period. Clearly apparent on the wingtip is the increasing effect of a weak and strong shock wave in the corresponding (unstable) steady solution. This fomentation is ultimately a consequence of the above mentioned steady profile deformation under a load.