Eigenmode Analysis and Reduced-Order Modeling of Unsteady Transonic Potential Flow Around Airfoils

Abstract

An eigenmode analysis and reduced-order models of the unsteady transonic aerodynamic e ow around isolated airfoilsarepresented.Theunsteadye owismodeledusingthetime-linearizedfrequency-domainunsteadytransonic full potential equation. The full potential was discretized in space using a e nite 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 theeffect ofdifferent parametersthat determinethesteady and unsteady e owe eld (e.g.,thefar-e eld Mach number, theangleofattack,and theairfoilshape )areinvestigated.Anormalmodeanalysisanda staticcorrectiontechnique are then used to construct a low degree-of-freedom, reduced-order model of the unsteady e owe eld. Depending on the range of frequencies of interest, a relatively small number of eigenmodes are required. An alternative reducedorder 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 efe cient. Using the aerodynamic reduced-order models, we construct aeroelastic reduced-order models and compute e utter boundaries for different airfoils at several different Mach numbers.