Application of statistical techniques of principal component analysis in the study of turbulence phenomena applying active control by sound pressure waves

The focus of this work is the application of a multivariate statistical method, principal component analysis (PCA), to experimental data on the active control of a fluid using acoustic pressure waves, measured with thermistors. This study investigates the active control of flow past a circular cylinder at two distinct low Reynolds numbers (33.63 cm/s and 51.32 cm/s). Active control was applied via an acoustic actuator at 80 dB with forcing frequencies of 1 Hz, 2 Hz, and 3 Hz. A key novelty of this work is the use of Principal Component Analysis (PCA) as a rigorous post-processing tool for analyzing high-dimensional velocity fluctuation data. The objectives were to evaluate the efficacy of low-frequency acoustic forcing for wake stabilization and to validate PCA as a method for quantifying this efficacy by identifying dominant flow modes. Results show that control effectiveness is highly dependent on the Reynolds number. For the flow at Reynolds number approximately 490, applying acoustic control at 3 Hz, near the natural vortex shedding frequency, quantitatively suppressed velocity fluctuations by 87.4%. Conversely, for the flow at Reynolds number approximately 747, the 3 Hz control was less effective, providing only a 17.9% reduction. PCA successfully reduced the dimensionality of the data, capturing substantial flow variance, thus demonstrating PCA's utility in validating active control strategies.