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.

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In recent years, several fitting techniques have been presented to reconstruct the parameters of a plate from its Lamb wave dispersion curves. Published studies show that these techniques can yield high accuracy results and have the potential of reconstructing several parameters at once. The precision with which parameters can be reconstructed by inverting Lamb wave dispersion curves, however, remains an open question of fundamental importance to many applications. In this work, we introduce a method of analyzing dispersion curves that yields quantitative information on the precision with which the parameters can be extracted. In our method, rather than employing error minimization algorithms, we compare a target dispersion curve to a database of theoretical ones that covers a given parameter space. By calculating a measure of dissimilarity (error) for every point in the parameter space, we reconstruct the distribution of the error in that space, beside the location of its minimum. We then introduce dimensionless quantities that describe the distribution of this error, thus yielding information about the spread of similar curves in the parameter space. We demonstrate our approach by considering both idealized and realistic scenarios, analyzing the dispersion curves obtained numerically for a plate and experimentally for a pipe. Our results show that the precision with which each parameter is reconstructed depends on the mode used, as well as the frequency range in which it is considered.

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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@en

Common clamp-on ultrasonic flow meters consist of two single-element transducers placed on the pipe wall. Flow speed is measured noninvasively, i.e., without interrupting the flow and without perforating the pipe wall, which also minimizes safety risks and avoids pressure drops inside the pipe. However, before metering, the transducers have to be carefully positioned along the pipe axis to correctly align the acoustic beams and obtain a well-calibrated flowmeter. This process is done manually, is dependent on the properties of the pipe and the liquid, does not account for pipe imperfections, and becomes troublesome on pipelines with an intricate shape. Matrix transducer arrays are suitable to dynamically steer acoustic beams and realize self-alignment upon reception, without user input. In this work, the design of a broadband 37×17 matrix array (center frequency of 1 MHz) to perform clamp-on ultrasonic flow measurements over a wide range of liquids (c=1000-2000m/s, α≤1 dB/MHz · cm) and pipe sizes is presented. Three critical aspects were assessed: efficiency, electronic beam steering, and wave mode conversion in the pipe wall. A prototype of a proof-of-concept flowmeter consisting of two 36-element linear arrays (center frequency of 1.1 MHz) was fabricated and placed on a 1-mm-thick, 40-mm inner diameter stainless steel pipe in a custom-made flow loop filled with water. At resonance, simulated and measured efficiencies in water of the linear arrays compared well: 0.88 and 0.81 kPa/V, respectively. Mean flow measurements were achieved by electronic beam steering of the acoustic beams and using both compressional and shear waves generated in the pipe wall. Correlation coefficients of R2>0.99 between measured and reference flow speeds were obtained, thus showing the operational concept of an array-based clamp-on ultrasonic flowmeter.

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Coatings with dynamic surface structures are appealing to many applications like haptics and soft robotics. Restrictively, the speed of the surface dynamics in these coatings is often limited to frequencies below 1 kHz, which makes them unsuitable for applications like acoustics and communication optics. This work describes a method to create high-frequency surface dynamics controlled by alternating electric fields on a substrate-contact-modulated coating that consists of an elastic poly(dimethyl siloxane) network supported by SU-8 microstructures. The principle is based on the global application of Maxwell stress that is locally resisted by the supporting SU-8 microstructures. In-between the microstructures the elastic material is stretched, causing a large deformation of the surface topography, which is supported by the authors’ finite element method models. By applying a high-frequency alternating field, they discovered resonance effects at frequencies up to 230 kHz, where the surface of the coating vibrates at high speeds and large amplitudes. At these high frequencies, the coatings can produce and detect ultrasound waves underwater, indicating their potential for ultrasound transducers in the future.

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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.

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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.

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Ultrasonic flow meters are widely applied to measure flow in a variety of applications. The vast majority of ultrasonic flow meters are based on the measurement of the transit time of an acoustic pulse through the fluid. This can either be done in-line, by inserting a spool piece with ultrasonic transducers into the pipe carrying the fluid, or by clamping the transducers on an existing pipe. Clamp-on meters are attractive as they can be installed without cutting the pipe or shutting down the flow, but their stability is limited, and they are unable to measure flow profiles (in contrast with expensive multi-path in-line meters), which limits their linearity at low flow speeds. Moreover, their installation requires complex manual alignment of the transducers and input of a variety of setup parameters (e.g. pipe dimensions and material properties, speed of sound in the fluid) by the user. In this thesis, clamp-on meters based on matrix ultrasonic transducers are developed to address these drawbacks. These matrix transducers consist of a two-dimensional array of 100+ elements that enables beam steering in two directions by programming the timing of the electrical pulses applied to the elements. This allows to develop three innovative measurement techniques: (1) automatic beam alignment by adjusting the steering angles so as to optimize the signal-to-noise ratio and the path of the received pulse, thus simplifying installation and improving stability; (2) multi-path measurement by steering the beam at different angles, realizing the measurement of multiple paths through the fluid with a single pair of matrix transducers, and thus providing information about the flow profile; (3) self-calibration by using pulse-echo measurements between the elements of the matrix transducer to characterize the pipe wall and fluid, thus reducing the dependence on a-priori knowledge of their properties. The most significant steps to realize these kind of sensors were taken in this thesis. The mentioned measurement techniques were elaborated, and the relevant wave-propagation phenomena, beamforming schemes and transducer design were performed. Based on this, a prototype sensor was fabricated and successfully tested. Moreover, application-specific integrated circuits (ASICs) were developed with dedicated transmit and receive electronics to realize a cost-effective and accurate implementation of the beam forming and transit-time measurement. @en

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.@en

Design, fabrication and acoustic characterization of a transducer array for ultrasonic clamp-on flow measurements. @en

Transit-time ultrasonic flow meters are widely used in industry to measure fluid flow. In practice ultrasonic flow meters either show a zero-flow error or suffer from a significant random error due to a limited signal-to-noise ratio, requiring a significant amount of averaging to achieve good precision. This work presents a method that minimizes the zero-flow error whilst keeping the random error low, independent of the hardware used. The proposed algorithm can adjust to changing zero-flow errors while a flow is present. The technique combines the benefits of two common methods of determining the transit-time difference between the upstream and downstream ultrasonic waves: cross-correlation and zero-crossing detection. The algorithm is verified experimentally using a flow-loop. It is shown that the zero-flow error can be greatly reduced without compromising the random error or increasing circuit complexity.@en

Current ultrasonic clamp-on flow meters are manually calibrated. This process is based on manual placement of two single-element transducers along a pipe wall. Due to the usually unknown pipe properties and inhomogeneities in the pipe geometry, the axial distance of the transducers needs to be manually calibrated to align the location of the emitted beam on the receiver. In this work it is presented an automatic calibration procedure, based on matrix transducer arrays, to provide calibration information that would normally be entered into the instrument manually prior to ultrasonic clamp-on flow measurements. The calibration consists of two steps: First, along the axial direction of the pipe, Lamb waves are excited and recorded. Then, the measured time signals are combined with the Rayleigh-Lamb dispersion equation to extract pipe wall thickness and bulk wave sound speeds. Second, along the circumferential direction of the pipe, a specific Lamb wave mode is excited and recorded, from which the pipe diameter is estimated. The potential of both calibration procedures is shown, and the necessity of a matrix transducer array (i.e. small elements) is highlighted@en

Clamp-on flow meters need a-priori knowledge of pipe geometry and material properties for their operation. Estimation of these properties may limit the accuracy of flow measurements. We are currently investigating the use of clamp-on flow meters based on matrix transducer arrays. Besides the benefits for flow measurement, these can be used for a-priori measurement of the required pipe properties. In the axial direction, average longitudinal wave speed and thickness of the pipe can be obtained from the dispersion curves of the Lamb waves in the pipe wall. In the circumferential direction, the arrival time of the fastest Lamb wave mode can be used to measure the pipe diameter. In our presentation, this method is discussed and proof of principle is provided through FEM simulations and measurements. The setup consisted of two pipes (outer diameters 64.5 mm and 93 mm), with two transducers (1 MHz) on top. The arrival time of the fastest Lamb wave mode was measured. For the outer diameter, the error between simulation and measurement was below 1% (small diameter) and below 3% (large diameter). The results suggest that further exploration of the unique possibilities of matrix transducers to accurately measure pipe parameters is opportune.@en

Current ultrasonic clamp-on flow meters are based on single-element transducers that require manual calibration by aligning these to a fixed acoustic path. Moreover, the size and operational frequency of the transducers cannot be adapted to the parameters of the pipe and the liquid, which are in practice not precisely known a priory. A set of two transducer arrays could be used to solve these issues. With an array, properties of the pipe and the liquid can be estimated before measuring flow. Furthermore, electronic beam steering can be used for auto-alignment of the acoustic beam, reducing the need for manual calibration. Moreover, an array allows for the use of signal processing to suppress the effects of spurious Lamb waves propagating in the pipe wall. This research work describes the acoustic design process of a transducer array for ultrasonic clamp-on flow measurements for a wide range of conditions. First, performance requirements are defined. Then, the design models are presented, and a step by step process of the acoustic stack design of the transducer array is described. At each design step, material dimensions are optimized to achieve a thickness resonance mode at 1 MHz within a bandwidth of interest between 0.2 MHz and 2 MHz. Finally, the expected performance of the designed array is reported, based on simulation results.

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Transit-time ultrasonic flow meters are based on the fundamental idea that the flow is the only non-reciprocal effect between an upstream and downstream measurement. Non-identical transducers can be used in a reciprocal manner if the circuit is made reciprocal. In this paper we analyze the effect of driver- and readout electronics on the zero-flow error in transit-time ultrasonic flow meters by simulation and measurement. Using the frequency characteristic of two nonidentical transducers, the cause of the zero-flow error in nonreciprocal circuits is evaluated. Both simulation and measurement results show that the lowest zero-flow error can be obtained by using circuits that have an impedance significantly higher or lower than the impedance of the transducers.@en

Typically, ultrasonic flow meters assume linear wave propagation. Nevertheless, if the transducers of an ultrasonic flow sensor excite a pressure wave with a high amplitude, nonlinear wave propagation effects become significant. The appearance of higher harmonics increases the bandwidth of the received signal, which may potentially lead to a more precise flow measurement. However, the question arises whether the increased bandwidth can be used in practice, since the intensity of the 2nd harmonic can be 25 dB below the fundamental. One exploit of the increased bandwidth is to filter the received signals and to obtain two components: the fundamental and the 2nd harmonic. Differences between the upstream and downstream transit times are directly related to the flow speed, and these can be computed for each component of the received signals. This paper shows that averaging the transit time differences of the fundamental signals and the 2nd harmonic signals results in a lower standard deviation compared to the standard deviation of the transit time differences of the fundamental or the 2nd harmonic signal alone. This demonstrates the feasibility of using non-linear wave propagation to improve the precision of flow measurements using ultrasound.@en