On the Nonlinear Geometric Behaviour of Flared Folding Wingtips

Abstract

Recent studies have considered the use of flared folding wingtips (FFWTs) to enable higher aspect ratios -reducing overall induced drag -whilst reducing gust loading and meeting airport operational requirements. The majority of these analyses have been conducted using linear assumptions despite the presence of large wingtip deformations. The aim of this work is to assess the effect of geometric nonlinearities introduced by an FFWT on the static and dynamic aeroelastic response of a wing. In this paper, a geometrically exact expression was formulated to describe the change in both the local Angle of Attack (AoA) and sideslip angle across all fold angles. This expression highlighted that the aerodynamic stiffness of an FFWT, and therefore quantities such as the linear flutter speed, are a function of the fold angle and therefore, the attitude of the wing. This effect was then verified using both: a wind tunnel model of a flexible semi-span wing incorporating an Flared Folding Wingtip (FFWT), and a new numerical modelling technique, utilising MSC Nastran, which linearised the model about the equilibrium position of the wingtip. The results of these experiments show that the geometric nonlinearities introduced due to the large deformations of FFWTs can significantly affect the dynamics of the system, with flutter speeds varying by over 25%, simply by changing the root angle of attack of the model. Furthermore, good agreement was found between the experimental results and numerical predictions.

Nonlinear Stability Analysis and Experimental Exploration of Limit Cycle Oscillations with Flared Folding Wingtips

“…The mechanism for this variation in both the aerodynamic stiffness of the FFWT and the change in the linear flutter boundary with root AoA, are described in detail in [19], in which the authors developed a methodology to linearise an MSC Nastran model of the same wing presented in this paper about different coast angles to predict the linear flutter boundary. As illustrated in Fig.…”

“…For the inner wing = ( , ). For the FFWT the local geometric AoA is approximated as , which is defined using a geometrically exact representation of the local AoA as presented by Healy et al [19]. This formulations uses a set of rotation matrices to calculate the local velocity vector in a reference frame centred about the FFWT, such that…”

“…One such device is the Flared Folding Wingtip (FFWT) [10][11][12][13][14][15][16][17][18][19][20]. As illustrated in Fig.…”

“…Such large deformations are analogous to those seen in the modelling of highly flexible wings [22], and can introduce geometric and aerodynamic nonlinearities that significantly affect the overall system behaviour, which cannot be adequately predicted using linear methods. Such nonlinearities have been found to have a significant effect on the behaviour of systems including FFWTs, with the authors in [19] highlighting that when the primary flutter mechanism incorporates the motion of the FFWT, the linear flutter boundary is dependent on the attitude of the aircraft. With wind tunnel experiments demonstrating a 25% change in the linear flutter boundary.…”

Experimental Analysis of the Dynamics of Flared Folding Wingtips via a Novel Tethered Flight Test

“…One such device, the Flared Folding Wingtip (FFWT) concept, has received significant research effort [17][18][19][20][24][25][26][27][28][29][30]. As illustrated in Fig.…”