Efficient Sensing of the von K\'arm\'an Vortices Using Compressive Sensing

TL;DR

This paper demonstrates that compressive sensing can efficiently measure and analyze von Kármán vortices in flow fields around different shapes, reducing sampling requirements compared to traditional methods.

Contribution

The study introduces the application of compressive sensing to vortex flow analysis, showing its effectiveness and advantages over Shannon sampling in fluid dynamics measurements.

Findings

Compressive sensing accurately reconstructs vortex flow signals with fewer samples.

Effective analysis of von Kármán vortices using compressive sampling in different flow scenarios.

Potential applications in structural vibration monitoring and aerodynamic analysis.

Abstract

In this paper, we discuss the usage and implementation of the compressive sensing (CS) for the efficient measurement and analysis of the von K\'arm\'an vortices. We consider two different flow fields, the flow fields around a circle and an ellipse. We solve the governing $k-\epsilon$ transport equations numerically in order to model the flow fields around these bodies. Using the time series of the drag, $C_D$, and the lift, $C_L$, coefficients, and their Fourier spectra, we show that compressive sampling can be effectively used to measure and analyze Von K\'arm\'an vortices. We discuss the effects of the number of samples on reconstruction and the benefits of using compressive sampling over the classical Shannon sampling in the flow measurement and analysis where Von K\'arm\'an vortices are present. We comment on our findings and indicate their possible usage areas and extensions. Our results can find many important applications including but are not limited to measure, control, and analyze vibrations around coastal and offshore structures, bridges, aerodynamics, and Bose-Einstein condensation, just to name a few.