Application of a POD-Galerkin based method to time resolved and time unresolved data for the determination of the Convective Velocity of Large-Scale Coherent Structures in High Speed Flows

Motivated by the aero-acoustic feedback loop phenomenon in high speed free jets and impinging jets, a thorough examination of a POD (Proper Orthogonal Decomposition)-Galerkin method to determine the average convection velocity of coherent structures in the shear layer is presented in this paper. The technique is shown to be applicable to both time resolved as well as time unresolved data, if the data set meets certain requirements. Using a detailed sensitivity analysis on a synthetic data set, a quantitative estimate on the required time resolution for the technique has been found, which can be useful for both experimental, as well as numerical studies investigating the aero-acoustic feedback loop in high speed flows. Moreover, some innovative ways to apply the technique are also demonstrated using a simulated data set, showing the effectiveness of the technique to any general problem in supersonic jets, heat transfer, combustion or other areas in fluid mechanics, where an advection process can be identified.