Pressure spectra from single-snapshot tomographic PIV

Abstract

The power spectral density and coherence of temporal pressure fluctuations are obtained from low-repetition-rate tomographic PIV measurements. This is achieved by extension of recent single-snapshot pressure evaluation techniques based upon the Taylor’s hypothesis (TH) of frozen turbulence and vortex-in-cell (VIC) simulation. Finite time marching of the measured instantaneous velocity fields is performed using TH and VIC. Pressure is calculated from the resulting velocity time series. Because of the theoretical limitations, the finite time marching can be performed until the measured flow structures are convected out of the measurement volume. This provides a lower limit of resolvable frequency range. An upper limit is given by the spatial resolution of the measurements. Finite time-marching approaches are applied to low-repetition-rate tomographic PIV data of the flow past a straight trailing edge at 10 m/s. Reference results of the power spectral density and coherence are obtained from surface pressure transducers. In addition, the results are compared to state-of-the-art experimental data obtained from time-resolved tomographic PIV performed at 10 kHz. The time-resolved approach suffers from low spatial resolution and limited maximum acquisition frequency because of hardware limitations. Additionally, these approaches strongly depend upon the time kernel length chosen for pressure evaluation. On the other hand, the finite time-marching approaches make use of low-repetition-rate tomographic PIV measurements that offer higher spatial resolution. Consequently, increased accuracy of the power spectral density and coherence of pressure fluctuations are obtained in the high-frequency range, in comparison to the time-resolved measurements. The approaches based on TH and VIC are found to perform similarly in the high-frequency range. At lower frequencies, TH is found to underestimate coherence and intensity of the pressure fluctuations in comparison to time-resolved PIV and the microphone reference data. The VIC-based approach, on the other hand, returns results on the order of the reference.