Application of the modified reduced-order aerodynamics modelling approach to aeroelastic analysis

Abstract

This study presents the application of the Proposed Modified Reduced-Order Aerodynamics Modelling approach for aeroelastic analysis based on the boundary element method (BEM) as a novel approach. The used BEM has the capability to capture the thickness effect and geometric complexity of a general three-dimensional model. In this approach the reduced-order aerodynamic model is defined through the eigenvalue problem of unsteady flow based on the unknown wake singularities. Based on the used aerodynamic model an explicit algebraic form of the aeroelastic equations is derived that reduces computational efforts and complexity. This special feature enables us to determine the aeroelastic instability directly via eigenanalysis of the aeroelastic problem. The eigenanalysis and reduced-order modelling of unsteady flow over a NACA 0012 airfoil are performed as an example and the results are compared with those obtained from conventional reduced-order modelling (CROM) method. The obtained results demonstrate the accuracy and superior efficiency of the present method over the CROM method. The method was then applied to the aeroelastic analyses of a typical section, in order to show the procedure of driving the explicit algebraic form. Furthermore, to illustrate the capability of the method in the handling of the three-dimensional problems, aeroelastic results for a wing are presented and compared with the results of the Theodorsen's aerodynamic theory.

Aeroelastic numerical approach of a wing based on the finite element and boundary element methods

“…Finding a solution to equation ( 11) is the main objective in unsteady aerodynamics, where A is the influence coefficient matrix of doublet singular elements and B the coefficient matrix relating the strength of the wake elements in different time steps using Kelvin's theorem (for more details, see the study of Shahverdi et al 10 ).…”

“…Hence, application of BEM based on the potential flow has recently implemented as an efficient and popular tool in many studies. [3][4][5][6][8][9][10][11] An advantage of the BEM is that the method reduces the problem dimensionality by one.…”

“…In this method, aerodynamic reduced-order models are constructed by the related flow eigenmodes similar to the structural modal analysis. The advantage of a modal approach is that the field quantity is approximated by just a few of the system eigenmodes and results in decreasing the system degrees of freedom in orders of magnitude not only in aerospace applications focusing on airfoils, wings, and airplane bodies, [7][8][9][10][11] but also in dealing with circular cylinders. 12,13 Esfahanian and Behbahani-Nejad 8 utilized ROM based on the BEM along with the potential flow to simulate subsonic unsteady flows around complex geometries and showed that if the static correction technique is employed, conventional ROM (CROM) will give accurate results.…”

“…Also, the presented method was employed by them to investigate flutter instability of fixed and rotary wings. 10,11 Other aerodynamic solvers based on the high-fidelity ENS formulations have been applied to the aeroelastic models. [14][15][16] However, the BEM has been known as a rapid and efficient numerical tool in applied engineering sciences.…”