Nonlinearc Aeroelastic Analysis of an Airfoil Using CFD-Based Indicial Approach

Bifurcation analysis and limit cycle oscillation amplitude prediction methods applied to the aeroelastic galloping problem

“…Lee (1986) and Conner et al (1997)] and, more recently, nonlinear aerodynamics [e.g. Thomas et al (2004), Kholodar et al (2004), Attar et al (2005) and Kim et al (2005)]. Other types of nonlinearities have been investigated such as nonlinearities in the control system (Dimitriadis and Cooper, 2000), due to external stores (Nam et al, 2001) and due to large deformations (Patil et al, 2001).…”

Development of an indicial function approach for the two-dimensional incompressible/compressible aerodynamic load modelling

“…The expressions in the time domain of the unsteady lift can be determined by adding equations (7) and (10), whereas the aerodynamic moment about the axis at x = ab, rearward from the mid-chord, by taking into account equation (7) in equation (9) as well as equations (10) considered in conjunction with equations (11). [4,14]. The effect of the Mach number can be taken into account in the indicial description, and this has also been emphasized in reference [4].…”

“…[4,14]. The effect of the Mach number can be taken into account in the indicial description, and this has also been emphasized in reference [4]. Being a non-linear partial differential equation, the velocity potential equation for the compressible flowfield cannot be solved analytically, and usually the solution is obtained using finite difference numerical techniques.…”

“…In order to overcome the fact that the local moving grid (LMG) based on the spring analogy is not appropriate to describe the indicial pitching motion without angle-of-attack changes [3], a total moving grid (TMG) technique, which is a pure Lagrangian description, has been used [4].…”

“…However, as it was shown in reference [2], also the time-domain representation of aerodynamic loads can be applied for the same purpose. Unsteady compressible aerodynamic loads are obtained by using the compressible counterparts of Wagner and Theodorsen's incompressible indicial functions, respectively references [1], [3], and [4], while in the transonic flight speed regime, the unsteady lift and aerodynamic moment are derived in terms of the non-linear indicial functions. The indicial expressions can involve the arbitrary time variation of the angle-of-attack and/or inflow velocity, and are carried out using Duhamel's superposition principle.…”