Modal analysis of the transonic shock process over a griffith-type, laminar-flow airfoil

Proper orthogonal decomposition (POD) is applied to schlieren data of a Griffith-type transonic, laminar-flow airfoil across a range of angles of attack to analyze the influence boundary layer suction had on the shock oscillatory process. This particular class of airfoils utilizes active boundary-layer suction to assist an aggressive pressure recovery process near the trailing edge of the airfoil. In the absence of active suction, the boundary layer separates, producing a highly unsteady compressible flow. For the no-suction cases it was observed that the leading mode displayed unsteady perturbations applied about a coherent shock structure and its frequency associated with the time dependent amplitude agreed with the oscillatory peak frequency of 22.38 Hz identified in a previous study. Higher order modes were characterized by bidirectional fluctuations in the density gradient fields having shorter wavelengths and covering a spatial amplitude symmetric about the average shock location, effectively capturing the shock travel area. The shock structure under suction conditions appeared to have a lambda foot that originated from the same chordwise location as that produced from the no-suction case, but extended further downstream. The application of boundary-layer suction was observed to decrease the unsteadiness associated with the shock travel, relative to the no-suction cases. Lastly, a reduced order model (ROM) of the oscillatory process was produced based on the spectral characteristics of the first 10 modes whose amplitudes were assumed to follow a sinusoidal profile. The reconstruction was successful in identifying the relevant physics and spatial characteristics of the dynamical process without the associated unsteadiness present in the data.