Introduction

From cutting-edge technology such as aerospace control and semiconductor manufacture to most universal applications like household gas meters, flowmeters are closely linked with our life in many aspects. Flowmeters based on different principles have been developed to satisfy various application scenarios from the booming flow monitoring market. Distinguished from invasive approaches featuring pressure-loss of the medium to be measured such as the Coriolis force flowmeter and the electromagnetic flowmeter, ultrasonic flowmeters have gained significant attraction due to their non-invasive, ease of installation characteristics and adaptation to various pipe sizes and fluid types1,2,3,4. In the realm of ultrasonic flowmeters, the volume flow rate can be measured through either the Doppler shift of the ultrasonic signal or the difference in time-of-flight (ToF) of ultrasound signals propagating upstream and downstream. While Doppler shift flowmeters rely on the presence of particulates in the fluid, ultrasonic flowmeters based on ToF, which offer enhanced sensitivity and accuracy, are more commonly employed due to great flexibility and no purity or particle limitations5,6,7. Traditionally, in ToF flowmeters, two paired ultrasonic transducers are positioned oppositely on either side of the pipe and used as transmitter (TX) and receiver (RX) alternately to measure the propagation time of ultrasonic signals traveling upstream and downstream in stages, thereby obtaining the differential fluid information necessary for calculating the volume flow rate. However, this two-step flow monitoring scheme faces intrinsic frame rate limitations and presents a high demand for balancing the TX and RX performance of the two paired transducers, which restrain further optimization of the ultrasonic flow rate monitoring system.

Micro-scale MEMS ultrasonic transducers, featuring miniaturization and easily achievable array structures, have offered more flexibility in designing ultrasound transmitting beam patterns, facilitating novel flow rate monitoring mechanisms. Different from traditional bulk ultrasonic transducer operating in the thickness mode, micromachined ultrasonic transducer (MUT) operates in the flexural mode, which enables better acoustic coupling efficiency. Leveraging the comprehensive design principles inherent in array configurations and channel sequential control, MUTs have demonstrated considerable potential in intricate scenarios of ultrasonic transmission and reception, making them strong candidates for next-generation ultrasonic devices. MUT can be mainly categorized into capacitive MUT (CMUT) and piezoelectric MUT (PMUT). CMUTs are well-regarded for their high bandwidth and electromechanical coupling coefficients. However, a substantial DC bias voltage associated with a small gap thickness is typically inevitable in CMUTs to achieve the necessary vibration displacement for desirable output sound pressure8,9,10. In contrast, PMUTs do not face concerns regarding gap distance and are free from DC bias voltage11,12,13,14. This flexibility allows PMUTs to be applied in various scenarios advocating low power consumption and large-scale system integration, including range-finding15,16,17, fingerprint sensors18,19,20, imaging13,21,22,23,24,25, neural modulation9,26,27, ultrasonic flowmeters1,28,29,30, etc. While innovative piezoelectric materials like potassium sodium niobate (KNN) and lithium niobate (LN) are under investigation15,31,32, lead zirconate titanate (PZT) and aluminum nitride (AlN) continue to be the most widely used materials in PMUTs12,13,24,33,34. PZT, in particular, boasts an exceptional piezoelectric coefficient compared to AlN35. In this study, we employed PMUT phased array based on PZT thin films to enhance coupling efficiency and, consequently, transmitting performance.

Aiming to address the frame rate limitations in traditional ToF ultrasonic flowmeters, in this paper, we innovatively utilize the grating lobe generated by a five-channel PZT PMUT phased array to form a novel acoustic field pattern featuring symmetric bidirectional V-shaped beams, which enables synchronous upstream and downstream ToF read-out, and therefore one-step flow rate measurement. The proposed methodology breaks the λ/2 pitch design principle attributed to the negative stereotype of grating lobes and eliminates the usage of the T/R switch and any other signal-processing units associated with the two-step flow monitoring scheme1,13,36,37. Furthermore, in contrast to the previous methods requiring strong single-axis directivity of the identical paired transducers, our approach enables differentiated TX/RX transducer optimization, where the V-shaped bidirectional TX and omnidirectional RXs leading to flat installation are adopted. Benefitting from the one-step flow monitoring scheme, the installation geometry of the flowmeter can be further optimized. Taking advantage of the V-shaped joint of the zigzag pipe structure, the ultrasound propagation length—critical for determining ToF resolution—is no longer constrained by the pipe diameter as it is in conventional straight pipes, which facilitates high frame rate, high resolution, and high dynamic range flow rate monitoring, as shown in Fig. 1.

Fig. 1: The principle of the synchronous upstream and downstream ultrasonic flow monitoring enabled by PMUT phased array with a novel V-shaped beam pattern.
Fig. 1: The principle of the synchronous upstream and downstream ultrasonic flow monitoring enabled by PMUT phased array with a novel V-shaped beam pattern.
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An optimized zigzag-shaped installation is adopted to enhance the sensing range and resolution. The proposed one-step ultrasonic flow rate monitoring scheme presents significant potential in applications that demand extremely high response rates and operating ranges, such as gas trade, semiconductor foundry, and pharma industry

Materials and methods

Structure and fabrication

Compact circular PMUTs based on PZT thin film were utilized to achieve effective synchronous bidirectional ultrasound transmission and omnidirectional reception. The fabrication process of the 3.6 mm × 3.6 mm PMUT device is depicted in Fig. 2 a. The structure consists of a 0.1 µm top platinum layer, a 2 µm PZT layer, and a 0.12 µm bottom platinum layer, all patterned on a SOI substrate with 0.5 µm SiO2, 4 µm epitaxial polysilicon, and another layer of 1 µm SiO2. Additionally, a 0.7 µm patterned Al-Cu metal interconnection was established between individual PMUTs over 0.04 µm Al2O3 and 0.4 µm USG passivation layers to minimize parasitic effects. Patterned bottom electrodes and via-hole connections were incorporated to further reduce these parasitics. To enhance the device’s robustness, a 0.3 µm Si3N4 covering layer was deposited. Finally, the vibration membrane was defined using a backside DRIE (deep reactive-ion etching) process, which includes trench isolation through the polysilicon layer to mitigate mechanical crosstalk between PMUT elements38. An optical microscope photo of the manufactured PMUT is illustrated in Fig. 2b, where five adjacent channels constitute the TX phased array, with each of them consisting of three PMUT cells. A scanning electron microscope (SEM) image of the corresponding structure is shown in Fig. 2d, clearly revealing the detailed layer properties and backside etching hole. The measured thickness of the membrane (3.735 µm Si) demonstrates a slight deviation from the nominal value (4 µm Si), primarily due to the non-longitudinal section: the roughness of the naturally-formed membrane fracture surface could lead to fluctuation of the measured layer thickness.

Fig. 2: The structure of the PMUT device.
Fig. 2: The structure of the PMUT device.
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a The fabrication process of the PMUT. b The microscope photo of the PMUT. c The layer properties of the PMUT. d The scanning electron microscope (SEM) image of the PMUT. Five adjacent channels constitute the TX PMUT phased array, with each of them consisting of three PMUT cells. Multi-layer protection layer, vias connection, patterned bottom electrode and etching isolation were adopted to reduce mechanical and acoustic crosstalk

Analytical simulation

The equivalent circuit model (ECM) was developed to study the electrical and mechanical performance of the PMUTs preliminarily. An analytical Mason equivalent circuit model tailored for circular, clamped plate PMUT designs in the 31-mode with an arbitrary electrode configuration at any axisymmetric vibration mode, considering radiation acoustic impedance, was adopted. As an effective analytical simulation method, the ECM quantitatively reveals the operating principles of flexural-mode PMUTs, explaining the conversion of electrical excitation into mechanical deflection and, ultimately, acoustic sound pressure transmission, as shown in Fig. 3a–c.

Fig. 3: The analytical simulation results of the PMUT.
Fig. 3: The analytical simulation results of the PMUT.
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a The mechanical deflection of the 31-mode PMUT given by finite element model (FEM), side view. b The mechanical deflection of the 31-mode PMUT given by FEM, top view. c The equivalent circuit model (ECM) of the PMUT. d The vibration velocity simulation results given by both the ECM and FEM methods. e The electrical impedance simulation results of a single PMUT cell. f The electrical impedance simulation results of a PMUT channel

Given the stack properties of the PMUT shown in Table 1, the calculation method for the lumped parameters and the setup of the corresponding Kirchhoff voltage law (KVL) equations of the ECM are described as follows21,39,40,41. When operating in transmitting mode, the electrical excitation serves as the input of the model. The electrical shunt capacitance can be calculated using the following equation:

$${C}_{0}=\left(1-{k}_{31}^{2}\right)\frac{{\epsilon }_{33}^{\sigma }\pi \left({a}_{k}^{{\prime\prime} 2}-{a}_{k}^{{\prime} 2}\right)}{{h}_{p}}$$
(1)

where k31 is the electromechanical coupling coefficient, \({\epsilon }_{33}^{\sigma }\) is the dielectric constant measured at constant stress, hp is the thickness of the piezoelectric layer, \({a}_{k}^{{\prime\prime} }\) and \({a}_{k}^{{\prime} }\) are the outer and inner radius of the kth electrode, respectively. The conversion coefficient of the electrical and mechanical domain is defined by:

$$\eta ={N}_{n}{B}_{{nk}}$$
(2)

where the components Nn and Bnk are the electromechanical transformation ratio at axisymmetric vibration mode n and dimensionless coupling between electrode k and mode n, respectively. Both of them can be calculated through the geometric, mechanical, and piezoelectric coefficients of the PMUT40. The PMUT fabricated is designed to operate at the fundamental resonant mode ((0,1) mode), with the radius of the circular top electrode equal to ~70% of the diaphragm radius, a. The mode-shape function used for electrical-mechanical conversion at distance r from the center of the diaphragm is written as:

$${\Psi }_{01}\left(r\right)={J}_{0}\left(3.196\left(\frac{r}{a}\right)\right)-\frac{{J}_{0}\left(3.196\right)}{{I}_{0}\left(3.196\right)}{I}_{0}\left(3.196\left(\frac{r}{a}\right)\right)$$
(3)

where J0 and I0 are the zero-order and modified Bessel functions of the first kind, respectively.

Table 1 Layer properties used in the ECM calculation
Full size table

The mechanical domain impedance, consisting of the compliance and inductance at axisymmetric vibration mode n can be calculated using the following simplified form:

$${C}_{m,n}^{-1}={K}_{m,n}={b}_{n}\frac{{\lambda }_{0n}^{4}\pi D}{{a}^{2}}$$
(4)
$${L}_{m,n}={b}_{n}\pi {a}^{2}{\rho }_{0}$$
(5)

where λ0n is the vibration mode constant of mode n, D is the flexural rigidity, and ρ0 is the surface density (mass per unit area). The axisymmetric vibration mode n-dependent mechanical constant, bn, is expressed as:

$${b}_{n}=\frac{1}{2}{\left(\frac{{\lambda }_{0n}{J}_{0}\left({\lambda }_{0n}\right)}{2{J}_{1}\left({\lambda }_{0n}\right)}\right)}^{2}$$
(6)

in which J0 and J1 are the zero and first-order Bessel functions of the first kind.

The acoustic lumped parameters for PMUT comprise the self-radiation impedance, which characterizes how a PMUT cell interacts acoustically with the sound field it produces, and the mutual-radiation impedance, which characterizes the acoustic interaction between the cell and the sound field produced by its surrounding array elements. Both the self-radiation and mutual-radiation impedance are vital components in simulating PMUT behavior, where the crosstalk of cells in the array is taken into full consideration. Based on the Rayleigh integral and regarding the average velocity as the reference velocity, the formula for the self-radiation impedance of a PMUT cell, Zii, set in an infinite baffle, is described as:

$$\frac{{Z}_{{ii}}}{\rho {cA}}=6{\int }_{0}^{\frac{\pi }{2}+j{\infty }}{\left(48\frac{{J}_{3}\left(\frac{2\pi }{\lambda }a\sin \theta \right)}{{(\frac{2\pi }{\lambda }a\sin \theta )}^{3}}\right)}^{2}\sin \theta d\theta$$
(7)

where ρ and c are density and acoustic velocity of the medium, \(\lambda\) is the acoustic wavelength, J3 is the third-order Bessel function of the first kind, θ is the azimuthal angle of spherical coordinates used in determining far-field pressure of PMUT cells, and A is the effective surface area and also the conversion ratio between mechanical and acoustic domains, equal to one third of the whole circular membrane area. Moreover, the formula for the mutual-radiation impedance of any two cells in a uniform array, Zij, is written as follows39:

$$\begin{array}{c}\frac{{Z}_{{ij}}}{\rho {cA}}=\frac{3456}{{(\frac{2\pi a}{\lambda })}^{4}}\mathop{\sum }\limits_{m=0}^{{\infty }}\mathop{\sum }\limits_{n=0}^{{\infty }}\,\frac{\Gamma \left(m+n+0.5\right)}{\sqrt{\pi }m!n!}{\left(\frac{a}{d}\right)}^{m+n}\\ \times {J}_{m+3}\left(\frac{2\pi a}{\lambda }\right){J}_{n+3}\left(\frac{2\pi a}{\lambda }\right){\zeta }_{m+n}\left(\frac{2\pi d}{\lambda }\right)\end{array}$$
(8)

where d is center spacing of two PMUT cells, Γ is the Gamma function, J is the Bessel function, and ζm+n is the Riccati-Bessel function, defined by spherical Bessel functions Sm+n and Cm+n of m + n order:

$${\zeta }_{m+n}\left(\frac{2\pi d}{\lambda }\right)={S}_{m+n}\left(\frac{2\pi d}{\lambda }\right)+i{C}_{m+n}\left(\frac{2\pi d}{\lambda }\right)$$
(9)

The general acoustic impedance of a PMUT cell, Zi, is the combination of its self-radiation impedance and the mutual-radiation impedance introduced by any other cells in the array, which can be written as:

$${Z}_{i}={Z}_{{ii}}+\mathop{\sum }\limits_{j\ne i}^{{MN}}\frac{{u}_{j}}{{u}_{i}}{Z}_{{ij}}$$
(10)

where ui and uj are the average vibration velocities of the cell i and cell j, respectively. Then the acoustic impedance Za of an M × N rectangular array can be written as the following matrix:

$${Z}_{a}=\left[\begin{array}{ccc}\begin{array}{c}\begin{array}{cc}{Z}_{11} & {Z}_{12}\end{array}\\ \begin{array}{cc}{Z}_{21} & {Z}_{22}\end{array}\end{array} & \cdots & \begin{array}{c}{Z}_{1{MN}}\\ {Z}_{2{MN}}\end{array}\\ \vdots & \ddots & \vdots \\ \begin{array}{cc}{Z}_{{MN}1} & {Z}_{{MN}2}\end{array} & \cdots & {Z}_{{MN\; MN}}\end{array}\right]$$
(11)

By writing the mechanical impedance Zm similarly into the matrix form, the KVL equation of the equivalent circuit model can be eventually written as:

$$\begin{array}{c}\left[\begin{array}{c}\eta v\\ \eta v\\ \vdots \\ \eta v\end{array}\right]=\left[\begin{array}{cccc}{Z}_{11} & {Z}_{12} & & {Z}_{1{MN}}\\ {Z}_{21} & {Z}_{22} & & {Z}_{2{MN}}\\ \vdots & & \ddots & \vdots \\ {Z}_{{MN}1} & {Z}_{{MN}2} & \cdots & {Z}_{{MN\; MN}}\end{array}\right]\left[\begin{array}{c}{\bar{u}}_{1}\\ {\bar{u}}_{2}\\ \vdots \\ {\bar{u}}_{{MN}}\end{array}\right]\\ +\left[\begin{array}{cccc}{Z}_{m11} & & & \\ & \ddots {\,Z}_{m\,M1} & & \\ & & \ddots & \\ & & & {Z}_{m{MN}}\end{array}\right]\left[\begin{array}{c}{\bar{u}}_{1}\\ {\bar{u}}_{2}\\ \vdots \\ {\bar{u}}_{{MN}}\end{array}\right]\end{array}$$
(12)

And the solution of this vector equation is:

$$\left[\begin{array}{c}{\bar{u}}_{1}\\ {\bar{u}}_{2}\\ \vdots \\ {\bar{u}}_{{MN}}\end{array}\right]={\left({Z}_{a}+{Z}_{m}\right)}^{-1}{\left[\begin{array}{c}\eta v\\ \eta v\\ \vdots \\ \eta v\end{array}\right]}_{1\times {MN}}$$
(13)

The average vibration velocities of the cell diaphragm serve as the solutions to the equation, which is used for further calculation of electrical impedance. By simply exchanging the role of the electrical excitation voltage inputs and the average vibration velocity outputs, the receiving performance of the operating mode PMUT can be evaluated.

The finite element model (FEM) simulation was further employed to verify the ECM calculation results and provide more concise analytical simulation results, as shown in Fig. 3d–f. The ECM calculation results align well with the FEM simulation results, demonstrating a relatively slight difference in predicting the resonant frequency, vibration velocity, and electrical impedance. Given the relatively poor timeliness of the FEM method, the ECM method offers an approach to quickly derive the resonant frequency and other basic properties of a uniform PMUT array with proper approximation. In practical device design, the ECM can be utilized to calculate the rough, wide-range frequency response of the PMUT primarily, and then FEM can be used to satisfy precise and complex simulation scenarios, such as acoustic beam pattern simulation considering time delay.

Results and discussion

Impedance characterization

The resonant frequency of the PMUT was primarily characterized through electrical impedance analysis, as shown in Fig. 4a, indicating that the PMUT has a ~ 250 kHz mid-air resonant frequency, which demonstrates a slight deviation from the analytically simulated nominal result affected by the intrinsic stress. Relatively-higher frequencies were not adopted in mid-air ultrasonic applications due to the severe attenuation of ultrasound during propagation, while relatively-lower frequencies lead to longer pulses, larger transducer sizes, and therefore worse temporal and spatial utilization efficiency were neither considered in the PMUT frequency design. The impedance magnitude measurement results of the fabricated discrete five channels in a die are illustrated in Fig. 4b, demonstrating relatively good batch uniformity.

Fig. 4: The characterization of the PMUT.
Fig. 4: The characterization of the PMUT.
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a The electrical impedance of a single PMUT channel and five PMUT channels in parallel. b The electrical impedance of five discrete channels in a die. c The mechanical frequency response of the bilateral PMUT cells. d The mechanical frequency response of the centric PMUT cells. e The mechanical frequency response of a PMUT cell under various AC voltages. f The harmonic magnitude of the PMUT cell operating in the deep linear region, the turning point, and the non-linear region. g The mechanical frequency response of PMUT cells in a single channel that operate in linear region. h The mechanical frequency response of PMUT cells in a single channel that operate in non-linear region. i The displacement variation with AC voltages of PMUT cells in a single channel. j The resonant frequency variation with AC voltages of PMUT cells in a single channel. All of the vibration behaviors were excited through periodic chirp signals

Vibration characterization

The mechanical characterization of the PMUT diaphragm was performed using a laser Doppler vibrometer (LDV). Each of the five channels, consisting of three PMUT cells on the same die, was excited through a periodic chirp signal, and the corresponding displacement characterization results of a bilateral/centric cell are illustrated in Fig. 4c, d, respectively. The measured mechanical resonant frequency, reflecting the individual vibration behavior of the cells, demonstrated a slight difference from the impedance characterization results that represent the resonant performance of the whole channel. The frequency responses of the bilateral and centric cells demonstrate a slight difference as well, mainly due to the mutual acoustic radiation effect. To avoid frequency mismatch and consequent overall ultrasound transmitting efficiency loss, nonlinearity vibration that enables higher displacement and larger bandwidth was utilized through higher excitation voltages, and therefore, the frequency responses under various AC excitation voltages were further characterized to gain a thorough understanding of the device’s mechanical performance. With the applied AC voltage ranging from 0.01 V to 4.8 V, the center point displacement of the PMUT cell exhibits a linear variation initially, and then gradually transitions into a non-linear vibration region under the influence of both mechanical displacement saturation and periodically changing ferroelectric polarization23,31,42,43. The normalized electrical-mechanical sensitivity of the PMUT cell is illustrated in Fig. 4e, revealing a shift in resonant frequency, a drop in maximum sensitivity, and therefore the dissipation of vibration energy under relatively high AC excitation voltages. The harmonic magnitude characterization results of the PMUT cell operating in deep linear region (AC = 0.1 V), turning point (AC = 2.0 V), and the non-linear region (AC = 3.0 V) are illustrated in Fig. 4f, clearly demonstrating the enhancement of the relative intensity of the high-order harmonics in comparison with the fundamental vibration. Moreover, the enhancement of the mutual-radiation of PMUT cells under relatively large AC voltage was also observed. When larger AC excitation voltages are applied, the displacement and the resonant frequency deviation of the three cells inside the same channel become more distinct due to the more intense acoustic crosstalk, as shown in Fig. 4g–j.

V-shaped beam generation and characterization

The V-shaped beam generation can be simulated after establishing the PMUT resonant frequency. The grating lobe, which has the same intensity with the main lobe in the transducer’s acoustic directivity pattern, is utilized to form the bidirectional beam pattern. Theoretically, for a linear N-channel PMUT array, the directivity of the transducer, D(\(\theta\)), is described by the following equation1,12,29:

$$D\left(\theta \right)=\frac{{48J}_{3}\left(\frac{2\pi }{\lambda }a\sin \theta \right)}{{\left(\frac{2\pi }{\lambda }a\sin \theta \right)}^{3}}\times \frac{\sin \left[\frac{\pi {Nd}}{\lambda }\left(\sin \theta -{\sin \theta }_{0}\right)\right]}{N\sin \left[\frac{\pi d}{\lambda }\left(\sin \theta -{\sin \theta }_{0}\right)\right]}$$
(14)

where \(\theta\) is the angle of incidence, \(\theta\)0 is the initial steering angle of the acoustic beam generated by the phased array, \(\lambda\) is the acoustic wavelength, a is the radius of a PMUT cell, d is the pitch between adjacent cells in the linear array, and J3 is the third-order Bessel function of the first kind. Once the wavelength of the operating frequency, \(\lambda\), the radius of the cell, a, and the number of channels, N, are determined, the generation of the grating lobes and other side lobes is then primarily defined by the pitch of the array, d. The corresponding numerical calculation results are illustrated in Fig. 5a. When the pitch design fulfills the following condition:

$$\frac{d}{\lambda }\le \frac{N-1}{2N}$$
(15)

there will be no grating lobes, regardless of whether beam steering is adopted. Most of the previous MUT designs follow this case, and the pitch of the transducer array is typically set to half the wavelength of the operating frequency (\(\lambda /2\)) to maximize the energy of the main lobe.

Fig. 5: Analytical simulation and experimental verification of the synchronous bidirectional ultrasound transmitting PMUT.
Fig. 5: Analytical simulation and experimental verification of the synchronous bidirectional ultrasound transmitting PMUT.
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a The principle of generating the V-shaped bidirectional beam pattern through pitch design and sequential control, given by the numerical calculation. b The FEM simulation results of generating the V-shaped beam. c The experimental verification of the V-shaped beam generation. When the excitation pulse of the adjacent channels had an optimized interval time of ~2000 ns, a symmetric V-shaped beam pattern with bidirectional beams measured at 27° and 153° could be generated

Once the pitch value exceeds the above limitation, grating lobes can be generated during the beam-steering process. Under specific sequential control of the excitation signal, a symmetric bidirectional V-shaped beam pattern can be eventually formed. With the increasing pitch value, the flare angle of the V-shaped beam generated demonstrates a decreasing trend. It is also worth mentioning that when the pitch is large enough to fulfill the following condition:

$$\frac{d}{\lambda } > \frac{N-1}{N}$$
(16)

grating lobes will exist without an initial steering angle. Considering both the requirements of the V-shaped beam generation and the array fill-factor enhancement, we chose a moderate pitch value for an obtuse-angled V-shaped beam. The pitch of the 1D five-channel linear array was set to be 625 μm, larger than 2/5 of the wavelength (the operating frequency is 250 kHz, corresponding wavelength is about 1360 μm). The FEM results are shown in Fig. 5b, clearly revealing the spatial split of the acoustic beam.

The experimentally measured acoustic directivity beam pattern normalized sound pressure angular distribution of the five-channel PMUT array without sequential control is shown in Fig. 5c, i, where a single-directional beam pattern was observed. Then, beam-steering was carried out through time-delay control. When the excitation pulse of the adjacent channels had an optimized interval time of ~2000 ns, a symmetric V-shaped beam pattern with bidirectional beams measured at 27° and 153° could be generated, as shown in Fig. 5c ii. The width of each main lobe becomes narrower compared to the single-beam case, and the intensity of other side lobes has been enhanced, indicating the potential spatial dispersal of acoustic energy. With the developed synchronous bidirectional ultrasound transmitting PMUT, flow monitoring with a high frame rate can be achieved.

Synchronous upstream and downstream flow monitoring

We applied and evaluated our synchronous upstream and downstream flow rate measurement methodology in two different pipe geometries: the conventional straight pipe (Pipe A) and its optimization, the zigzag-shaped pipe (Pipe B). The principle of the proposed methodology is shown in Fig. 6 a, which enables one-step flow rate readout in less than 1 ms, and therefore up to 1000 times of repeat measurement in 1 s. The flow rate measurement intervals are needed to be much longer than the absolute ToF to ensure the generation and transmission of the bidirectional ultrasound signal with sufficient energy and SNR. On this basis, moderate 1 ms intervals were adopted to achieve flow rate monitoring of a high frame rate. Flow metering with reasonably good adjusted R-squares within 1–5 L·min–1 and 0.5–35 L·min–1 was achieved in Pipe A and Pipe B, respectively. The variation of the upstream and downstream RX waveforms with the flow rate is illustrated in Fig. 6b i and ii. With increasing volume flow rate, the ToF of the upstream and downstream ultrasound signals have an opposite shift tendency, revealing the therewith increasing \(\triangle \text{ToF}\). The variation of the received signals when applying different flow rates mainly originates from the shape change of the bidirectional beam pattern due to the change of the flow field. With the increase of flow rates, the flow components that are perpendicular to the ultrasound propagation direction could lead to the steering of the bidirectional beams, and eventually result in the variation of receiving intensity. The zero-flow condition measurement result is illustrated in Fig. 6b iii, where the absolute ToF of the upstream and downstream ultrasound signals demonstrates a slight difference due to the installation error. The zero-flow upstream and downstream signals were calibrated to the same starting line to facilitate the calculation of the \(\triangle \text{ToF}\), which could be obtained through the addition of the upstream and downstream ToF differences. The overall flow rate monitoring results, adopting the proposed synchronous upstream and downstream ultrasound transmitting methods and the optimized zigzag-shaped installation geometry, are shown in Fig. 6b iv, where a reasonably good adjusted R-square of 0.997 and a high resolution of 185 ns/(L·min–1) (corresponding to 2032 ns/(m·s–1)) were achieved.

Fig. 6: The flow rate measurement results through our synchronous bidirectional ultrasound transmitting methodology.
Fig. 6: The flow rate measurement results through our synchronous bidirectional ultrasound transmitting methodology.
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a The one-step synchronous upstream and downstream flow monitoring in the common straight pipe (pipe A). b The synchronous flow results in the optimized zigzag-shaped pipe (pipe B). The proposed flow measurement method enables remarkable-frame rate (1000 times of upstream and downstream ToF measurements in 1 s), large-range (0.5–35 L·min–1 or 0.045–3.177 m·s–1, airflow), and high-resolution (185 ns/(L·min–1) or 2032 ns/(m·s–1)) flow metering with significant linearity (0.997)

Flow rate measurement system and discussion

The overall flow rate measurement system is shown in Fig. 7. Driven by an air pump with a reducing valve, a mass flow controller, Alicat-MFC-0.5-to-50SLPM with a \(\pm\)0.8% reading error range and a \(\pm\)0.2% full scale error range, was used to generate steady airflow ranging from 0.1 L·min–1 to 35 L·min–1. Conventional and novel pipe installation geometries were both adopted and evaluated. The ToF resolution in ultrasonic flowmeters based on transit time is proportional to the ultrasound propagation length, which is strongly limited by the pipe diameter in traditional straight pipe layouts (Pipe A). Moreover, the directional acoustic beam can be ‘blown away’ in large flow rate conditions, resulting in severe performance loss in large range flow monitoring. Given these limitations, the zigzag-shaped pipe installation geometry (Pipe B) was eventually adopted. Utilizing the joint structure in complex flow monitoring scenarios, the zigzag-shaped pipe exhibits significant flexibility, and effectively complements our one-step sensing scheme enabled by the bidirectional ultrasound beam. The ultrasound travels along the fluid direction in the proposed zigzag-shaped pipe, enabling robust large-range sensing stability, sufficient ultrasound propagation length, and therefore, significant ToF resolution. Installed at the joint of the zigzag-shaped pipe, the five-channel TX PMUT phased array, driven by the TX7332EVM board, could synchronously couple the bidirectional acoustic beams into the dual arms of the pipe. The upstream and downstream RX signals were captured through a trans-impedance amplifier (TIA), finally contributing to the \(\Delta\)ToF readout.

Fig. 7: The overall flow rate measurement system and the pipe installation geometry optimization.
Fig. 7: The overall flow rate measurement system and the pipe installation geometry optimization.
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Installation geometry optimization was proposed to enhance the ToF resolution and adaptation to various pipe circumstances of our method. The flow rate measurements in conventional straight pipe (pipe A) and optimized zigzag-shaped pipe with 150 mm sufficient ultrasound propagation length (pipe B) were both taken and evaluated

Conclusion

This article presents synchronous bidirectional ultrasound transmitting PMUT empowered one-step ultrasonic flow rate measurement with an optimized zigzag-shaped pipe installation geometry, featuring a remarkable frame rate (1000 times of measurement in 1 s), a large monitoring range (0.5–35 L·min–1 or 0.045–3.177 m·s–1, airflow), a high resolution (185 ns/(L·min–1) or 2032 ns/(m·s–1)), and a significant linearity (0.997). A ~ 250 kHz five-channel PMUT phased array based on PZT thin film tailored for the generation of bidirectional V-shaped beam pattern was designed and optimized, taking advantage of the timeliness of the ECM method and the precision of the FEM method. The electrical, mechanical, and acoustic performance of the fabricated PMUT, with enhanced mechanical robustness and reduced crosstalk, was then thoroughly studied through impedance analysis, vibration characterization, and experimental verification of the V-shaped beam generation, respectively. Leveraging the flexibility and reliability of the novel PMUT array with bidirectional beams measured at 27° and 153°, ultrasonic flow rate monitoring using the proposed methodology was successfully demonstrated, thereby releasing the potential of compact and powerful MEMS ultrasonic transducers in application scenarios that demand extremely high response rates and operating ranges.