An eigenmode analysis and reduced-order models of the unsteady transonic aerodynamic flow around isolated airfoils are presented. The unsteady flow is modeled using the time-linearized frequency-domain unsteady transonic full potential equation. The full potential was discretized in space using a finite element method. The resulting equations are linear in the unknown velocity potential and quadratic in the reduced frequency of excitation. The dominant eigenfrequencies and corresponding mode shapes of the discretized potential model are computed, and the effect of different parameters that determine the steady and unsteady flowfield (e.g., the far-field Mach number, the angle of attack, and the airfoil shape) are investigated. A normal mode analysis and a static correction technique are then used to construct a low degree-of-freedom, reduced-order model of the unsteady flowfield. Depending on the range of frequencies of interest, a relatively small number of eigenmodes are required. An alternative reduced-order modeling technique based on Arnoldi-Ritz vectors is also presented. For the case where the structural excitations are known a priori, the latter method is more efficient. Using the aerodynamic reduced-order models, we construct aeroelastic reduced-order models and compute flutter boundaries for different airfoils at several different Mach numbers.
Transonic flow;Unsteady flow;Mathematical models;Eigenvalues and eigenfunctions;Frequency domain analysis;Modal analysis;Degrees of freedom (mechanics);Vectors;Flutter (aerodynamics);Potential flow;Finite element method;