Time resolution improvement of ultrasonic velocity profiler for flow over cylinder using EPOD method with optimally placed time-resolved sensors

Ultrasonic velocity profiler (UVP) can be used for opaque and multiphase flows where particle image velocimetry (PIV) cannot be applied. The time resolution of PIV has greatly improved over the last few decades with the development of high-speed cameras and has been further improved using data-driven approaches. On the other hand, there have been very few works to improve the time resolution of UVP, which is already much lower than that of PIV. This study presents a proof of concept for time resolution improvement of UVP measurement, using an extended proper orthogonal decomposition (EPOD) method with optimized sensors. In this study, the EPOD method is improved by combining it with the sensor selection method, which eliminates the three-sigma (sigma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma$$\end{document}) rule-based filtering introduced by Discetti et al. 2018 in the original work of Hosseini et al. 2015. In this study, sensor locations are optimized using sensor selection methods, and time-resolved flow fields are reconstructed using the EPOD method. The sensors' locations along the line are optimized using non-time-resolved UVP velocity data by two sensor selection methods: determinant greedy (DG) and Bayesian determinant-based greedy (BDG). The performance of DG and BDG-optimized sensors is compared in reconstructing time-resolved flow fields. The technique is demonstrated with two sets of experimental data of flow over a cylinder: first, PIV data, which are down-sampled in the time domain and sampled along a line to mimic the UVP data, and second, actual UVP experimental data conducted in the wake of cylinder. The EPOD method's time-resolved reconstruction capability was found to depend on the sensors' location, and both sensor selection methods yielded similar results.