Proper Orthogonal Decomposition Technique for Transonic Unsteady Aerodynamic Flows

TLDR

The study introduces a new method for constructing reduced‑order models of unsteady small‑disturbance flows. The approach derives POD basis vectors from an ensemble of efficient time‑linearized frequency‑domain small‑disturbance solutions and employs these ROMs to predict the unsteady aerodynamics and aeroelastic behavior of a transonic airfoil and a two‑dimensional cascade. The resulting ROMs, built with only a few POD modes, deliver highly accurate predictions over a wide range of frequencies.

Abstract

A new method for constructing reduced-order models (ROM) of unsteady small-disturbance e ows is presented. The reduced-order models are constructed using basis vectors determined from the proper orthogonal decomposition (POD) of an ensemble of small-disturbance frequency-domain solutions. Each of the individual frequencydomain solutions is computed using an efe cient time-linearized e ow solver. We show that reduced-order models can be constructed using just a handful of POD basis vectors, producing low-order but highly accurate models of the unsteady e ow over a wide range of frequencies. We apply the POD/ROM technique to compute the unsteady aerodynamic and aeroelastic behavior of an isolated transonic airfoil and to a two-dimensional cascade of airfoils.