A Multi‐Path Ultrasonic Transit Time Flow Meter Using a Tomography Method for Gas Flow Velocity Profile Measurement

Abstract

A velocity profile is the distribution of velocities in the axial direction over a cross-section of circular pipe. In this study, a new ultrasonic flow meter with a modified multi-path configuration, namely, a tomographic ultrasonic flow meter is proposed for the measurement of the flow velocity profile. The flow meter consists of a set of transmitting transducers and a set of receiving transducers placed at different positions on the pipe surroundings. This configuration produces an ultrasonic path in various directions and positions for the flow detection. Transmitting transducers, in sequence, propagate the ultrasound wave to all receiving transducers, and the axial velocity in each ultrasonic path is measured. The average velocity is calculated by using the weighting method. Using the theoretical flow profiles, the tomographic ultrasonic flow meter is simulated in asymmetric flow and compared to both the diametrical and quadrature configurations. The filtered back projection method is employed to reconstruct a flow velocity profile. In the reconstruction process, the flow velocity obtained in each ultrasonic path is used as the projection data. An experiment is also performed in a circular pipe for measuring the air flow velocity profile, in order to validate the proposed flow meter.

Diagnostic flow metering using ultrasound tomography

“…When the measured data (7 paths × 19angles) are transformed without interpolation in Radon space, the reconstructed flow image suffers from insufficient resolution, as indicated in Fig. 3(b) [3,4]. The spatial resolution of reconstructed flow image becomes 25 mm, as shown in Table 1.…”

“…While most of the previous works have focused on the selfvalidation of flow metering in a metering station in applications with wireless sensor networks, some other works have suggested flow diagnostic parameters to investigate flow conditions by examining the mean flow velocity profile. Hydrodynamic factors, which are a ratio between the theoretical and the measured mean flow velocity, or orientation sensitivity factors, which are derived from the difference of the hydrodynamic factors, were suggested to emphasize the efficacy of tomographic flow metering compared with the conventional flow metering (diametrical or multi-path transit-time ultrasonic methods) [3]. However, there were no flow diagnostic parameters to look at the shapes of the mean flow velocity profiles with respect to statistical moments.…”

“…Ultrasound tomography is a means of reconstructing flow images from line-averaged velocity distribution by inverse Radon transform [2][3][4][5][6][7]. In the literature, ultrasound tomography has been implemented by using 16 ultrasonic transducers for flow image reconstruction purposes [3,4].…”

“…In the literature, ultrasound tomography has been implemented by using 16 ultrasonic transducers for flow image reconstruction purposes [3,4]. Eight ultrasonic transducers were installed on the upstream side, and the other eight ultrasonic transducers were installed on the downstream side of the flow metering section.…”

“…By rotation of the ultrasonic flow meter at small angular intervals, the line-averaged velocity distribution can be mapped into Radon space. The back-projection algorithm (inverse Radon transform) is then performed to reconstruct a flow image from the line-averaged velocity distribution [2][3][4].…”