Analysis of the dynamic modes of the transonic flow around a cylinder

The present work investigates the transonic flow past a 2D circular cylinder using the dynamic mode decomposition (DMD) method. The DMD is a data-driven tool for the analysis and characterisation of dynamic systems that identifies coherent structures (or modes) in the data with corresponding frequencies and rates of growth. Numerical simulations using the Euler equations for compressible flows are done considering Mach numbers 0.5 and 0.75. In the first case, the flow is periodic and acoustic oscillations are synchronised with the vortex shedding, while in the second case it presents more complex structures with shock waves. The DMD revealed that the cylinder emits noise similarly to an acoustic dipole, and captured the fundamental Strouhal number for the flow in both cases. Additionally, the DMD modes were used to reconstruct the data set. The reconstruction was able to describe well the time series for a Mach number of 0.5, but there was a significant error for Mach 0.75. The Sound Pressure Level field was also reconstructed, and the maximum error for Mach 0.5 was around 1 dB, while for Mach 0.75 was 18 dB.