Measured unsteady surface pressures, which are a function of both space and time, of a harmonically pitching airfoil are expressed in terms of a parametric proper orthogonal decomposition (PPOD) in order to obtain an optimum (in the mean-square sense) modal representation. This decomposition is formulated in such a way that the resulting spatial modes act optimally over the entirety of a parameter space defined by the airfoil pitching motion characteristics, i.e. for attached flow pitching, light stall, and deep stall. This method provides a systematic and quantitative framework by which to elucidate common and disparate features of the light and deep dynamic stall processes and provides a bridge to the development of low-order models for the prediction of unsteady airloads, such as the normal force and quarter-chord pitching moment.
This work primarily focuses on the development of two low-order models, distinguished by frame of reference, used for the reconstruction of unsteady aerodynamic loads. The first model decomposes the unsteady pressure field where the steady inviscid pressure field, provided by a Smith-Hess panel method, is removed. Conversely, the second model decomposes the unsteady pressure field with the fully viscous, steady pressure field removed. In each model, the parameter-independent modal shapes are determined from unsteady surface pressures of an arbitrarily chosen reference airfoil geometry operating over a large range of pitching trajectories. It is shown that the aerodynamic loads of the reference geometry are reconstructed with as few as 5 PPOD modes. For the first model, the airloads of a candidate airfoil, one where the unsteady surface pressure field is desired for a given pitching trajectory, are shown to be reconstructed using the same 5 reference PPOD modes plus an additional spatial mode calculated from the candidate airfoil?s steady pressure field. Likewise, the second model is capable of reconstructing the candidate airfoil?s unsteady surface pressure with only the 5 reference PPOD modes. A subtle result realized by comparing the two models is that the nature of the dynamic stall process is a general feature acting as a perturbation to the steady behavior of a given airfoil geometry.