Algorithm to Correct Measurement Offsets Introduced by Inactive Elements of Transducer Arrays in Ultrasonic Flow Metering

Ultrasonic flow meters (UFMs) based on transducer arrays offer several advantages. With electronic beam steering, it is possible to tune the steering angle of the beam for optimal signal-tonoise ratio (SNR) upon reception. Moreover, multiple beams can be generated to propagate through different travel paths, covering a wider section of the flow profile. Furthermore, in a clamp-on configuration, UFMs based on transducer arrays can perform self-calibration. In this manner, userinput is minimized and measurement repeatability is increased. In practice, transducer array elements may break down. This could happen due to aging, exposure to rough environments, and/or rough mechanical contact. As a consequence of inactive array elements, the measured transit time difference contains two offsets. One offset originates from non-uniform spatial sampling of the generated wavefield. Another offset originates from the ill-defined beam propagating through a travel path different from the intended one. In this paper, an algorithm is proposed that corrects for both of these offsets. The algorithm also performs a filtering operation in the frequency-wavenumber domain of all spurious (i.e., flow-insensitive) wave modes. The advantage of implementing the proposed algorithm is demonstrated on simulations and measurements, showing improved accuracy and precision of the transit time differences compared to the values obtained when the algorithm is not applied. The proposed algorithm can be implemented in both in-line and clamp-on configuration of UFMs based on transducer arrays.

Measurement of Pipe and Liquid Parameters Using the Beam Steering Capabilities of Array-Based Clamp-On Ultrasonic Flow Meters

Clamp-on ultrasonic flow meters (UFMs) are installed on the outside of the pipe wall. Typically, they consist of two single-element transducers mounted on angled wedges, which are acoustically coupled to the pipe wall. Before flow metering, the transducers are placed at the correct axial position by manually moving one transducer along the pipe wall until the maximum amplitude of the relevant acoustic pulse is obtained. This process is time-consuming and operator-dependent. Next to this, at least five parameters of the pipe and the liquid need to be provided manually to compute the flow speed. In this work, a method is proposed to obtain the five parameters of the pipe and the liquid required to compute the flow speed. The method consists of obtaining the optimal angles for different wave travel paths by varying the steering angle of the emitted acoustic beam systematically. Based on these optimal angles, a system of equations is built and solved to extract the desired parameters. The proposed method was tested experimentally with a custom-made clamp-on UFM consisting of two linear arrays placed on a water-filled stainless steel pipe. The obtained parameters of the pipe and the liquid correspond very well with the expected (nominal) values. Furthermore, the performed experiment also demonstrates that a clamp-on UFM based on transducer arrays can achieve self-alignment without the need to manually move the transducers.

Measurement of Pipe and Fluid Properties With a Matrix Array-Based Ultrasonic Clamp-On Flow Meter

Current ultrasonic clamp-on flow meters consist of a pair of single-element transducers that are carefully positioned before use. This positioning process consists of manually finding the distance between the transducer elements, along the pipe axis, for which maximum signal-to-noise ratio (SNR) is achieved. This distance depends on the sound speed, thickness, and diameter of the pipe and on the sound speed of the liquid. However, these parameters are either known with low accuracy or completely unknown during positioning, making it a manual and troublesome process. Furthermore, even when sensor positioning is done properly, uncertainty about the mentioned parameters, and therefore on the path of the acoustic beams, limits the final accuracy of flow measurements. In this research, we address these issues using an ultrasonic clamp-on flow meter consisting of two matrix arrays, which enables the measurement of pipe and liquid parameters by the flow meter itself. Automatic parameter extraction, combined with the beam-steering capabilities of transducer arrays, yields a sensor capable of compensating for pipe imperfections. Three parameter extraction procedures are presented. In contrast to similar literature, the procedures proposed here do not require that the medium be submerged nor do they require a priori information about it. First, axial Lamb waves are excited along the pipe wall and recorded with one of the arrays. A dispersion curve-fitting algorithm is used to extract bulk sound speeds and wall thickness of the pipe from the measured dispersion curves. Second, circumferential Lamb waves are excited, measured, and corrected for dispersion to extract the pipe diameter. Third, pulse-echo measurements provide the sound speed of the liquid. The effectiveness of the first two procedures has been evaluated using simulated and measured data of stainless steel and aluminum pipes, and the feasibility of the third procedure has been evaluated using simulated data.

Exploiting nonlinear wave propagation to improve the precision of ultrasonic flow meters

Acoustic wave propagation in ultrasonic flow measurements is typically assumed to be linear and reciprocal. However, if the transmitting transducer generates a sufficiently high pressure, nonlinear wave propagation effects become significant. In flow measurements, this would translate into more information to estimate the flow and therefore a higher precision relative to the linear case. In this work, we investigate how the generated harmonics can be used to measure flow. Measurements in a custom-made flow loop and simulations using the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation will show that the second harmonic component provides similar transit time differences to those obtained from the fundamental component, their linear combination results in more precise flow measurements compared to the estimations with the fundamental component alone.

Suppression of Lamb wave excitation via aperture control of a transducer array for ultrasonic clamp-on flow metering

During ultrasonic clamp-on flow metering, Lamb waves propagating in the pipe wall may limit the measurement accuracy by introducing absolute errors in the flow estimates. Upon reception, these waves can interfere with the up and downstream waves refracting from the liquid, and disturb the measurement of the transit time difference that is used to obtain the flow speed. Thus, suppression of the generation of Lamb waves might directly increase the accuracy of a clamp-on flow meter. Existing techniques apply to flow meters with single element transducers. This paper considers the application of transducer arrays and presents a method to achieve a predefined amount of suppression of these spurious Lamb waves based on appropriate amplitude weightings of the transducer elements. Finite element simulations of an ultrasonic clamp-on flow measurement setting will be presented to show the effect of array aperture control on the suppression of the Lamb waves in a 1-mm-thick stainless steel pipe wall. Furthermore, a proof-of-principle experiment will be shown that demonstrates a good agreement with the simulations.