The aeroelastic behavior of high aspect ratio wings in an incompressible flow is investigated. The nonlinear nonplanar bending-bending-twisting motions of beam theory is used for the structural equations assuming large deformations with small strains, small Poisson effects, inextensional beam theory, and linear elastic material characteristics by neglecting warping and shear deformation. An Unsteady nonlinear aerodynamic static stall model based on the Wagner function is introduced and then is used for determination of aerodynamic loading of the wing. In this aerodynamic model, the static lift curve vs. angle of attack is approximated by a piece-wise curve and for each linear part of this curve a corrected Wagner theory is used. Combining these two types of formulation yields fully nonlinear integro-differentials aeroelastic equations of motion. The governing equations will be solved to predict the nonlinear aeroelastic response of a wing in the stall and post stall regions using Galerkin's method and a numerical method without the need of adding any aerodynamic state-space variables and their corresponding equations. The obtained equations are solved for some test cases and the obtained results are compared with the results given in the literature. Also a study is done to show effects of nonlinear aerodynamic static stall model on the limit cycle oscillations.

The aeroelastic behavior of high aspect ratio wings in an incompressible flow is investigated. The nonlinear nonplanar bending-bending-twisting motions of beam theory is used for the structural equations assuming large deformations with small strains, small Poisson effects, inextensional beam theory, and linear elastic material characteristics by neglecting warping and shear deformation. An Unsteady nonlinear aerodynamic static stall model based on the Wagner function is introduced and then is used for determination of aerodynamic loading of the wing. In this aerodynamic model, the static lift curve vs. angle of attack is approximated by a piece-wise curve and for each linear part of this curve a corrected Wagner theory is used. Combining these two types of formulation yields fully nonlinear integro-differentials aeroelastic equations of motion. The governing equations will be solved to predict the nonlinear aeroelastic response of a wing in the stall and post stall regions using Galerkin's method and a numerical method without the need of adding any aerodynamic state-space variables and their corresponding equations. The obtained equations are solved for some test cases and the obtained results are compared with the results given in the literature. Also a study is done to show effects of nonlinear aerodynamic static stall model on the limit cycle oscillations.

A new semiempirical dynamic stall model is presented to predict the aerodynamic coefficients of an airfoil in unsteady conditions. The model is mainly based on two modifications on the airfoil angle of attack which introduce an equivalent angle of attack to implement in the proposed aerodynamic coefficients. The first modification includes unsteady wake effects of the airfoil in the proposed model which are not considered in most of the semiempirical models. Hence, an effective angle of attack is introduced based on an unsteady aerodynamic theory using the Wagner function for pitching and plunging oscillations of the airfoil. The second modification takes into account time delay effects and dynamic effects due to the flow separation on the airfoil. These effects are included in the model by developing a semiempirical relationship between static and dynamic angle of attack published in the literature. Finally, the modifications form the equivalent angle of attack to implement in a set of equations based on Kirchhoff flow theory. The proposed approach dynamically approximates trailing edge separation point on the airfoil by a completely new way and contributes its effects in the aerodynamic coefficients. Moreover, apparent mass effects and the airfoil leading edge vortex contributions are sufficiently included in the model. The presented method effectively predicts unsteady lift and pitching moment coefficients of the airfoil undergoing stall conditions. Consequently, the proposed model is verified against experimental data under various test cases where obtained numerical results are in good agreement with the test data. Furthermore, the performance of the proposed model is compared with various dynamic stall models including Leishman-Beddoes model, ONERA model and Boeing-Vertol model. The comparison shows that the proposed model minimizes the number of the semiempirical parameters determined from an experiment in dynamic stall modeling compared with Leishman-Beddoes model and ONERA model. It also demonstrates that the presented model performs as well as other well-known models using the various approaches.

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