DMD-based Superresolution Measurement of Time-resolved Large-scale Turbulent Structures of a Supersonic Jet based on Acoustic and Dual Planar PIV Data*

The present study proposes a framework of the superresolution measurement using total least square dynamic mode decomposition (TLS-DMD), Kalman filter (KF) and Rauch-Tung-Striebel (RTS) smoother applied to a Mach 1.2 nearly perfectly expanded supersonic jet. Dual planar particle image velocimetry (PIV) was utilized and paired velocity fields of the flow at a temporal resolution of 5,000Hz were obtained. High frequency acoustic data were simultaneously obtained at 200,000Hz. The reconstruction of the flow throughout the framework allows us to obtain dynamic modes that evolve along the reconstructed flow at the same temporal resolution as the acoustic data. Although some modes decay or diverge due to measurement noise, most of the resulting modes are stable and useful for reconstructing the large-scale turbulent structures that cause jet noise. The proposed method works well obtaining high temporal-resolution velocity fields of the main modes responsible for the characteristic acoustic spectrum of perfectly expanded supersonic flow.