Assessment of added mass effects on flutter boundaries using the Leishman–Beddoes dynamic stall model

Example of a non-smooth Hopf bifurcation in an aero-elastic system

“…We have chosen the structural model to be linear so as to ensure that the non-linear behaviour is exclusively due to the aerodynamics loading represented by the LB model. The present papers differs from others on a similar topic [21][22][23][24][25] because it is mainly concerned with the effects of the interaction between the discontinuous definition of an aero-elastic system and its main Hopf bifurcation. The paper is organised as follows.…”

“…The symbol (′) denotes differentiation with respect to the non-dimensional time S = tU/b. The offset angle θ 0 is defined as the angle wherein the spring restoring moment equals zero and C M0 denotes the static moment coefficient at zero incidence [23][24][25]. We highlight the coefficient C M0 is used to break the mathematical symmetry of a symmetric dynamical system (e.g.…”

“…The main advantage of using the state-space form is that it can be appended to the structural model to construct a system of ODEs representing a dynamical system including both structural and aerodynamic states. Only the most relevant features of the model will be presented here, more details can be found in references [23,24,25,28]. The dynamic stall model is represented by a set of ODEs of the form…”

“…At the same time the dynamic stall model will provide the aerodynamic forces required by the mechanics of the airfoil. Using the quasi-steady approach [28], the effective angle of incidence is given by [24,28] ( , , ) e e α α α α ξ ʹ′ ʹ′ = .…”

Stall Flutter Suppression for Absolutely Divergent Motions of Wind Turbine Blade Base on H-Infinity Mixed-Sensitivity Synthesis Method

“…S. Sarkar investigates the effect of system parametric uncertainty on the stall flutter bifurcation behavior of a pitching airfoil, with the aerodynamic moment on the two-dimensional rigid airfoil being computed using the ONERA dynamic stall model [3]. J. Peiró investigates the dynamics of a typical airfoil section and demonstrates the importance of the added mass terms, with structural behavior being modeled by linear springs and the aerodynamic loading being exerted by Beddoes-Leishman (B-L) model [4]. Zhiwei adopts a nonlinear time-domain aeroservoelastic model and designs flutter suppression control systems, with a novel state-space model being descripted for control design [5].…”