Wire-Mesh Sensor Super-Resolution Based on Statistical Reconstruction

Abstract

A wire-mesh sensor (WMS) is a widely used instrument to visualize and estimate derived parameters of multiphase flows, e.g., gas void fraction or liquid hold-up. The spatial resolution of obtained flow images is associated with the number of crossing points formed by the transmitter and receiver wires of a given sensor. This may be a limitation for applications that require high spatial resolution since WMS is an intrusive device and the increase of electrodes may increase pressure drop and deform/fragment bubbles. In order to minimize such undesirable effects and maximize the sensor resolution, we employed a reconstruction algorithm based on the minimum mean-square error (MMSE) estimator to increase image resolution of WMS with fewer wires than commonly reported in the literature, i.e., here, we apply <inline-formula> <tex-math notation= LaTeX >$8\\times 8$ </tex-math></inline-formula>, <inline-formula> <tex-math notation= LaTeX >$6\\times 6$ </tex-math></inline-formula>, <inline-formula> <tex-math notation= LaTeX >$4\\times 4$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation= LaTeX >$2\\times 2$ </tex-math></inline-formula> sensors for 1-in pipe. Since standard regularization approaches may provide incorrect solutions for such configurations, a new methodology to obtain the prior model is presented. In our approach, the prior is assumed as a multivariate Gaussian model, which is extracted from experimental flow data of a <inline-formula> <tex-math notation= LaTeX >$16\\times 16$ </tex-math></inline-formula> WMS (the most common resolution for 1-in pipe). Finally, the sensitivity matrix obtained by electric field simulation and the experimental prior model is incorporated into the MMSE algorithm to restore experimental flow data of the low-resolution sensors. The experiments were performed in a flow loop operating at slug flow. The experimental results suggest that the MMSE estimator combined with the experimental prior model has a high potential not only to improve image resolution but also to correct the average void fraction estimation.