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Abstract
It is necessary to develop a novel optical low velocity sensor for seawater. In this paper, a fiber optic seawater velocity sensor based on a target cantilever reflective polarization interferometer is presented theoretically and experimentally. Height: width of equal strength cantilever is determined by finite element method as 22:5, and the seawater velocity sensing experiment is carried out using this parameter. The sensitivity obtained by experiment is consistent with the theory, whose correlation coefficient is 0.96, and the mean relative error is 3.65%. The velocity measurement results of the sensor were also compared by Acoustic doppler velocimetry, the correlation coefficient and the mean relative error are 0.92 and 4.5% respectively, which realized the high precision measurement of water velocity. The maximum sensitivity of the sensor is 355.55 nm/(m·s−1) when the velocity is 0.09 m/s. In addition, when the thickness of the cantilever is 0.5 mm, the velocity measurement can be realized in the range of 0-0.22 m/s. Finally, the influence factors of sensor sensitivity are discussed, which shows that the sensitivity is related to wavelength, velocity and the size of the cantilever structure, and is independent on the length of the panda fiber. The fiber optic velocity sensor based on the target cantilever is expected to play an important role in the field of seawater measurement due to its advantages of small size, stable structure and high sensitivity.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Current is a common form of sea water movement, which is usually characterized by velocity and direction of flow. Direct and accurate monitoring of ocean surface flow field, mastering and predicting ocean current law are of great significance to global climate change monitoring, oceanographic research, atmosphere-ocean interaction and physical-biochemical interaction. The average velocity of seawater is 3 m/s, with most areas flowing at less than 1 m/s. Therefore, the design of velocity sensor is mainly aimed at the measurement of low velocity water flow. At present, acoustic doppler velocimetry (ADV) is the main electrical sensor used in seawater velocity measurement, but the electrical sensor is limited by electromagnetic interference, complex equipment, high cost, and face the risk of electric leakage. In recent years, optical measurement methods represented by optical fiber sensors provide a new idea for fluid velocity measurement.
The application of optical fiber sensor in the field of velocity measurement has been reported a lot [1,2], and according to the sensing principle can be divided into hot-wire type and strain type. Hot-wire optical fiber velocity sensor based on the principle of heat balance relies on the cooling effect of fluid to realize the velocity measurement. Cheng J (2015) proposed an optical fiber thermal gas flowmeter based on a core-offset fiber Bragg grating (FBG) and demonstrated for low-rate gas flow measurement, which through the misplacement welding of single-mode fiber and FBG to stimulate the cladding mode and the interaction with the gold film coated on the cladding to form a “hot wire" [3]. However, the thermal conversion coefficient of the gold film coating is low, and a stronger pumping laser is required to significantly raise the temperature of the sensing probe [4,5]. Therefore, Li H (2021) proposed and experimentally demonstrated an airflow velocity sensing method based on a 45° tilt fiber grating (TFG) that is combined with a single-walled carbon nanotube (SWCNT) coated fiber Bragg grating, which realized the flow measurement in the range of 0-1 m/s [6]. The use of SWCNT greatly reduces the power requirement of the sensor on the pump light, and the way of excited cladding mode of TFBG simplifies the sensor structure [7,8]. However, using FBG as a sensor to perceive temperature changes is often accompanied by low sensitivity. A hot-wire water flow sensor proposed by Guigen Liu (2016) based on laser-heated silicon Fabry-Pérot interferometer (FPI) greatly improves the measurement accuracy of the sensor, with an average velocity sensitivity of 52.4 nm/(m/s) and a flow velocity resolution of up to 1 µm/s [9]. But such structures can only measure small flows of water [10,11]. At present, many fiber optic velocity sensors based on the principle of heat balance have been reported successively [12,13], but hot-wire fiber velocity sensors are mainly used for microfluidic or wind speed measurement due to the mechanism problem. On account of the thermal conductivity and convective heat transfer coefficient of seawater are much greater than that of air, the heat of the sensor probe will be absorbed and dissipated immediately in the ocean, so the hot-wire fiber optic velocity sensor is difficult to be applied in the field of ocean velocity measurement.
The strain-type fiber optic velocity sensor can measure the velocity by monitoring the force of the fluid on the fiber sensing unit, and the sensor based on the coupling of the target cantilever and the fiber optic sensor is one of the more mature sensors. Yong Zhao (2017) adopted a hollow cylindrical cantilever for pipeline flow measurement, achieving 0-22.5m3/h flow measurement with a resolution of 0.81m3/h [14]. Ri-qing Lv (2018) symmetrically stuck a pair of FBGs on a capillary steel tube cantilever in a wind tunnel, and realized synchronous measurement of flow and temperature by measuring the strain of the cantilever [15]. In the same year, Qiang Zhao et al. proposed an optical fiber system that uses five FBGs to measure three parameters of pipeline flow, temperature and pressure [16]. However, the strain of each point on the cylindrical cantilever changes with the change of position, and the chirp effect of the FBG pasted on the cantilever will lead to the widening of the reflection spectrum due to the uneven force, thus reducing the measurement accuracy of the sensor [17]. Therefore, Manasa Perikala et al. (2021) used a triangular cantilever of equal strength instead of a cylindrical capillary steel tube cantilever, effectively solving the chirp effect caused by uneven stress of FBG, and realized the flow velocity measurement of 0.1 m/s-10 m/s [18]. The strain-type fiber optic velocity sensor does not require additional heating source [19], and compared with the hot-wire fiber optic velocity sensor, it is not limited by the measurement object and has greater potential in the field of water flow rate measurement.
To sum up, a great deal of research on optical fiber velocity sensors are mainly oriented to wind tunnel testing, pipeline flow or microfluidic fields [20,21], and there are no reports for seawater measurement. Moreover, the reported sensors, especially the target cantilever-type sensors, are mostly based on FBG, whose measurement accuracy cannot meet the requirements of marine scientific research. Aiming at the requirement of high accuracy and low velocity measurement of ocean current, a target cantilever seawater velocity sensor based on reflecting panda fiber polarization interferometer (PI) is proposed in this paper, which converts the impact force of fluid on the cantilever into the movement of spectrum, so as to realize the velocity measurement. Compared with the published results, panda fiber is more sensitive to strain than ordinary Bragg grating due to its unique birefringence effect, which can effectively improve the velocity sensitivity of the sensor. In addition, the selection of equal strength cantilever avoids the problem of measurement accuracy limitation caused by uneven force of optical fiber sensing unit. To the best of our knowledge, this is the first time that coupling a target cantilever with a panda fiber polarization interferometer has been proposed for the measurement of seawater velocity.
2. Sensor design and theoretical analysis
2.1 Structure design of target cantilever
The structure for seawater velocity measurement based on the target cantilever and panda fiber polarization interferometer coupling is shown in Fig. 1. The upper end of the cantilever is fixed, and the other end is connected with the circular target through the cylindrical force transfer rod. Optical fiber sensing unit is pasted on the central axis of the cantilever to measure the bending stress caused by the impact of water flow when the target is immersed in water, and the fluid velocity is measured according to the relationship between the cantilever strain and the velocity. In order to avoid the decrease of measurement accuracy caused by the uneven distribution of stress, the cantilever with equal strength is selected, that is, the stress of each point on the central axis of the isosceles triangle is equal.
The target immersed in water is subjected to three forces of water flow, which are the dynamic pressure caused by the fluid impacting the target, the static pressure difference caused by the separation of the flow beam behind the target, and the friction generated at the boundary of the target when the fluid passes through the target. The pressure and velocity in front of the target are defined as P0 and V0 respectively, the pressure and velocity when water flows through the target are P and V respectively, the fluid density is ρ, and the local drag coefficient is ξ. According to Bernoulli equation, the sum of pressure potential energy, kinetic energy and potential energy at any two points on the flow line remains unchanged in the flow where viscous loss is ignored:
Equation (1) multiply both sides by the cross-sectional area A of the target plate facing the fluid:
The first term of the above equation is static pressure, and the second term is dynamic pressure. Since the friction contact surface is small, the friction force is ignored. The relationship between fluid velocity V and the force of the fluid on the target F is simplified as follows:
The equal strength cantilever will undergo bending deformation due to the impact of fluid, and the bending normal stress strength conditions are as follows:
Where, ${\sigma _{max}}$ represents the maximum normal stress generated by bending of the cantilever, E and ɛ is the elastic modulus and strain of the cantilever respectively. ${M_{max}} = FL$ and WZ represent the bending moment and the bending section coefficient of the cantilever, respectively. ymax is the distance from the point on the cross section to the central axis, Iz is the moment of inertia of the cross section to the central axis. For the cantilever with a rectangular cross section, the bending section coefficient is ${W_z} = ({b{h^2}} )/6$, b is the length of the rectangular cross section, namely the length of the isosceles triangle base, h is the width of the rectangular cross section, namely the thickness of the triangular cantilever. The relation between fluid impact force and strain on the central axis of an equal-strength cantilever can be expressed as:Formula (5) represents the relationship between the structural parameters and the strain on the central axis of the cantilever, that is, as long as the triangular structural parameters are determined, the strain on the structure under different force can be determined. However, not all structures satisfying the isosceles triangle condition are cantilever of equal strength. In order to determine the structural parameter range of the cantilever and select the optimal solution, the finite element algorithm is used to solve the stress distribution of the cantilever of equal strength, and the results are shown in Fig. 2. Benefiting from the low elastic modulus and better recovery performance of Polyvinyl chloride (PVC) material, it can effectively improve the sensitivity of the sensor and perform better repeatability. PVC was selected as the cantilever material, the radius of the circular target was set at 2.5 cm, and combined with the environmental requirements of laboratory flume measurement, the triangular aspect ratio of the cantilever was finally determined to be 22:5. If the impact force on the circular target is arbitrarily set to 50N, the stress distribution of the cantilever can be obtained, as shown in Fig. 2(a), and the stress sizes of different positions on the central axis of the cantilever were extracted and plotted as shown in Fig. 2(b). It's worth noting that the rectangular region at the upper end of the structure is a fixed end designed for the convenience of fixing the cantilever during the experiment, and the simulation results show that the existence of the fixed end has no effect on the stress distribution and magnitude of the structure. The connection point between the rectangular fixed end and the cantilever is denoted as position 0, so there is a stress mutation at this position in the curve shown in Fig. 2(b). In addition, the stress anomaly occurs near the position of 20 cm from position 0, which is due to the cylindrical force transfer rod connecting the circular target with the cantilever for force transfer. Considering the influence of fixed ends and force transmission points in practical applications, the optical fiber sensing unit should be pasted within 5-15 cm of the central axis in the preparation of the sensor, so as to ensure that the stress of each point of the panda fiber is equal as far as possible. The stress on the central axis of the cantilever is about 1.45 × 1010N/m2 by finite element algorithm, and the theoretical stress of the cantilever is 1.46 × 1010N/m2 calculated by formula (5), which shows the simulation results are consistent with the theoretical calculation results.
Fig. 2. (a) Surface stress distribution of the equal strength cantilever with a height to width ratio of 22:5, a thickness of 0.3 mm and a circular target radius of 2.5 cm. (b) The stress curve at each point on the central axis of the cantilever when the force is 50N.
2.2 Sensing principle of reflective panda fiber polarization interferometer
In order to improve the stability of the sensor and facilitate the subsequent experimental operation, DC magnetron sputtering technology is used on the panda fiber tip end face gold-plated film as a mirror, and its transmission spectrum is equivalent to that of the traditional polarization interferometer [22]. Figure 3 shows the schematic diagram of the sensing principle of the reflective polarization interferometer, and the transmission process of the system is as follows: The signal light emitted from a wideband light source (NKT Photonics SuperK Compact, 450-2200 nm) is transmitted to the polarizer through an optical fiber circulator. Each device is connected through the single mode optical fiber (SMF). The fiber polarizer converts the unpolarized signal light into linearly polarized light and injects it into the panda polarizing-maintaining fiber (PMF). Due to the birefringence effect of the panda fiber, two beams of linearly polarized light with different effective refractive indexes will be generated on the fast and slow axes of the fiber, which will be reflected by the gold film on the end of the fiber, and interference occurs after passing through the polarizer again. And finally, the interference light is received by the spectrometer (Ando AQ6370C, 600-1700nm with resolution of 0.2 nm) after passing through the circulator. Stress birefringence in panda-type PMF is caused by photoelasticity effect: In the process of PMF preparation, due to the different linear thermal expansion coefficients of each part of the fiber, the cooling makes the fiber produce anisotropic stress. Then the photoelasticity effect makes the refractive index of the material show anisotropy, resulting in high birefringence, which shows excellent characteristics in the field of stress sensing.
The output power of the reflective polarization interferometer is approximately a periodic function of wavelength, expressed as:
The phase difference of panda fiber due to birefringence effect is expressed as:
Where, B is the birefringence index of the panda fiber, L0 is the length of the panda fiber, and λ is the input light wavelength. When the cantilever is bent as a result of the fluid impact on the target, the panda fiber pasted on the central axis of the cantilever is subjected to the bending stress, resulting in the fiber stretching or compression. At the same time, the optical fiber refractive index changes due to the photoelasticity effect, then the phase changes eventually:The first term represents the phase delay caused by the change of refractive index of the fiber core due to the photoelasticity effect. The second and third term represent the phase delay caused by the change of fiber length and the change of fiber core diameter due to the waveguide effect, respectively. However, the phase delay caused by the change of fiber diameter is small and can be generally ignored.
Integral against the above equation, and the change of phase difference is expressed as:
Strain is defined as:
Simultaneous formulas (9) and (10) obtain the relation of phase change caused by strain:
Free spectral range (FSR) of the polarization interferometer can be deduced as:
According to the relationship between phase change and wavelength shift $\Delta \lambda = FSR \cdot ({\Delta \varphi /2\pi } )$, Eqs. (11) and (12) are combined and simplified to obtain the relationship between wavelength drift and strain [23]:
Where, Pe is the constant of strain-induced birefringence change and is related to the fiber material [24]. As can be seen from Eq. (13), the wavelength shift has a linear relationship with strain, so wavelength at the position of interference cancellation caused by stress can be expressed as:Simultaneous equations (3), (5) and (14) can obtain the relationship between wavelength and velocity at the interference elimination position, and the velocity of the fluid can be obtained by monitoring the interference wavelength offset:
The velocity sensitivity of the sensor can be obtained by differentiating the velocity of the above equation:
According to the formula (16) derived from the theory, the velocity sensitivity of the sensor is affected by the detection wavelength λ, the velocity V and the structural parameters of the equal strength cantilever. The optimal solution of the aspect ratio of the cantilever has been determined as 22:5 by finite element analysis, and the relationship between the other influencing factors and the sensitivity of the sensor will be discussed by experimental methods.
3. Velocity sensing experiment and results
3.1 Velocity sensing experiment
The velocity measurement system as shown in Fig. 4 was built to simulate the change of seawater velocity, and the size of the glass tank is 130cm × 22cm × 30 cm, which can provide 0-0.4 m/s range of flow rate. Acoustic Doppler velocimetry (ADV) is used for flume velocity measurement and sensor calibration. The measurement accuracy of ADV (Nortek As, Vector) is ±0.5%±1 mm/s, and the measurement range is 0-4 m/s, fixed near the sensor so that the velocity around the sensor could be monitored in real time. The “H” bracket is designed as shown in the illustration for fixing the cantilever and adjusting the position of the sensor. The rectangular fixed end of the cantilever is pasted on the short arm in the middle of the H-bracket, which can be moved up and down and fixed to ensure that the target is just completely immersed in water during the experiment. The two arms extending outwards at both ends of the H-shaped bracket are placed on the water tank to fix the sensor, so as to ensure that the impact of high velocity water flow will not affect the measurement position of the sensor. According to the stress distribution on the surface of the cantilever as shown in Fig. 2(b), the optical fiber sensing unit is pasted with 502 glue at the position 5-15 cm on the central axis of the cantilever due to the influence of the fixed end and the force transmission rod. We designed sensors with different cantilever thicknesses, different radius of target and different fiber lengths, then carried out several seawater velocity sensing experiments with these sensors.
Seawater velocity measurement is related to the marine environment, due to the fiber-optic sensing unit in the proposed cantilever sensor is not directly in contact with seawater, so we have carried out the measurement experiment of the single parameter of seawater velocity. The experiment was conducted at room temperature(20°C). In order to avoid the unsteady flow rate of the water inlet at the left end and the water outlet at the right end affecting the measurement results, the H-shaped bracket fixing the sensor is placed in the middle of the water tank. Adjust the circulation flow tank to increase the water velocity, at the same time ADV recorded the current fluid velocity, and then the spectrometer recorded the reflection spectrum under different flow velocity after the flow is stable. With the increase of water velocity, the shape variable of the cantilever increases, and the optical fiber is subjected to bending stress, resulting in spectral redshift, as shown in Fig. 5(a). In order to characterize the velocity response of the sensor, dip near the wavelength of 1491 nm was used for fitting and merging to calculate its sensitivity, which shows in the red data and curve in Fig. 5(b), and the fitting degree is up to 0.98. The relationship between sensitivity and velocity was obtained by derivation of the fitting curve, as shown by the blue solid line, indicating that sensor velocity sensitivity increased with the increase of velocity, which was consistent with the results of theoretical derivation. The thickness of cantilever used in the experiment is 0.3 mm, the radius of the circular target is 2.5 cm, and the length of the panda fiber is 4.6 cm. For the above parameters, formula (16) was used to solve the relationship between theoretical sensitivity of the sensor and velocity, as shown in the black dotted line in the Fig. 5(b). The experimental results (solid blue line) agree well with the theoretical results (dashed black line), and the relative error is 3.4%.
Fig. 5. (a) The reflectance spectra of the sensor obtained at different seawater velocity when the aspect ratio of the cantilever is 22:5, the thickness is 0.3 mm and the radius of the circular target is 2.5 cm, (b) velocity - wavelength fitting curve and experimental and theoretical sensitivity curve at 1491 nm dip, (c) sensor sensitivity curve with velocity change at different wavelength, (d) the relationship between experimental and theoretical sensitivity with wavelength change at velocity of 0.09 m/s. See Data File 1, Data File 2 for underlying values.
All dips in Fig. 5(a) were fitted to solve the sensitivity, and the relationship between sensitivity and velocity at different wavelengths was obtained, as shown in Fig. 5(c), which illustrate that the velocity sensitivity increases with the increase of detection wavelength, the maximum sensitivity is 355.55 nm/(m·s−1) at wavelength 1626 nm when the flow velocity is 0.09 m/s, and the minimum sensitivity is 270.54 nm/(m·s−1) at wavelength 1249 nm. The black solid line in Fig. 5(d) represents the curve of theoretical sensitivity as a function of wavelength at 0.09 m/s, while the blue data points represented the sensitivity of different dip under the velocity of 0.09 m/s obtained from the experimental results in Fig. 5(c). The experimental data points fluctuate up and down around the theoretical curve, with a mean relative error of 1.68%, and the mean absolute error is 5.23 nm/(m·s−1), the experimental sensitivity is in good agreement with the theoretical sensitivity.
To sum up, ten groups of experiments were designed to carry out the measurement of seawater velocity. In order to verify the accuracy of sensor sensitivity obtained by experiments, formula (16) was used to calculate the theoretical sensitivity at different dips in each group of experiments, and the experimental results were compared with the theoretical results, as shown in Fig. 6(a). The correlation coefficient between experimental results and theoretical results is 0.96, and the root mean square error (RMSE) is 11.6 nm/m·s−1. Figure 6(b) shows that the average absolute error of the experimental results is 8.75 nm/m·s−1, and the average relative error is 3.65%, which indicated that the experimental sensitivity is in good agreement with the theoretical value, and the slight error in the experimental results is due to the vibration of the cantilever caused by water surface turbulence.
Fig. 6. (a) Comparison of experimental sensitivity and theoretical sensitivity values of the sensor with ten groups of experiments. (b) Absolute error of experimental sensitivity with ten groups of experiments.
3.2 Velocity measurement results
The proposed optical fiber velocity sensor with cantilever thickness of 0.4 mm, the target radius of 3 cm, and the panda fiber length of 2.2 cm is applied to the water velocity measurement of laboratory flume, and the measurement results of the proposed sensor are compared with that of ADV. When the velocity in the circulating tank was increased, the spectrum accepted by the spectrometer was redshifted, as shown in the illustration in Fig. 7(a), while ADV recorded the current velocity. The measurement results of dip A and dip B were calculated based on the sensitivity calibration of the sensor in the velocity sensing experiment above, and compared with the measurement results of ADV, as shown in Fig. 7(a). According to the results, the correlation coefficient between ADV and the proposed sensor was 0.92, and the root-mean-square error (RMSE) was 0.0065 m/s, which shows that the sensor measurement results are in good agreement with that of ADV, and the fiber optic velocity sensor has high reliability in the field of seawater velocity measurement. Figure 7(b) shows the absolute measurement error (MAE) and mean relative error (MRE) of the optical fiber sensor are 0.0059m·s−1 and 5.7% respectively at dip A, while the MAE and MRE are 0.0049m·s−1 and 4.5% respectively at dip B. Dip B has larger wavelength than dip A, it is more sensitive than dip A, so the error of dip B is smaller for the same velocity measurement. In addition, as the shape variable of the cantilever increases with the increase of the velocity, the target gradually approaches the surface, and the surface turbulence affects the stability of the sensor, resulting in the error increase with the increase of the velocity. But in general, the error of the fiber optic velocity sensor proposed in this paper is relatively small, which can meet the high precision requirements of seawater measurement.
Fig. 7. (a) Comparison of the fiber optic velocity sensor and ADV used for water velocity measurement and the illustration shows the interference spectrum of the sensor at different velocity. (b)Velocity measurement error of optical fiber velocity sensor.
In order to show the superiority of the sensors proposed in this paper, we compared the results of the cantilever velocity sensors in the last five years, as shown in Table 1. A great deal of research are mainly oriented to wind tunnel testing or pipeline flow, and the reported target cantilever-type sensors are mostly based on FBG, whose measurement accuracy cannot meet the requirements of marine scientific research. In addition, some studies use stiffer materials such as stainless steel to prepare cantilever, which may make it impossible to measure low water velocity. The choice of cylindrical cantilever may produce chirp effect, which leads to the reduction of measurement accuracy of the sensor.
Table 1. Comparison of target cantilever fiber optic sensor
4. Discussion
4.1 Discussion on the thickness of cantilever
Three groups of cantilever structures were designed with thickness of 0.3 mm, 0.4 mm and 0.5 mm, respectively, and coupled with three groups of panda fiber sensing probes with length of 4.6 cm to carry out velocity sensing experiments. The sensitivity curve of the sensor with different thickness of the cantilever varies with the velocity, as shown in Fig. 8(a), the three sets of experiments strictly adhered to the variable that only the thickness of the cantilever was different. Dips with similar wavelength were selected from the three experimental results for comparison, and the results follow the change rule that the sensitivity decreases with the increase of cantilever thickness, which is consistent with the theoretical derivation. It is worth noting that the thickness of the cantilever also affects the measurement range of the sensor: when the velocity increases gradually and the cantilever reaches its maximum shape variable, the spectrum will no longer shift with the increase in velocity, as shown in the illustration in Fig. 8(a). For the structure with a thickness of 0.3 mm, when the velocity is greater than 0.097 m/s, the spectrum does not move regularly with the increase of velocity, and the slight deviation of the spectrum at high velocity is due to the cantilever jitter caused by water surface turbulence. The experimental results reveal the law that the measuring range of the sensor increases with the increase of the cantilever thickness, and the maximum measurement range of the sensor with a thickness of 0.5 mm designed in the experiment is 0-0.218 m/s. Therefore, a larger range of seawater velocity can be measured by increasing the thickness of the cantilever. Figure 8(b) discusses whether the relationship between sensitivity and cantilever thickness under different dip in three experiments still satisfies the theoretical rule. According to formula (16), when the detection wavelength is 1485 nm, 1525 nm and 1612 nm, the sensor sensitivity varies with the thickness, as shown in the curve in the Fig. 8(b), and the three groups of data points in the figure are the experimental results, which shows the variation trend is consistent with the theoretical calculation. However, there is an error between the experimental results and the theoretical curve. This is because the three independent experiments cannot guarantee that the dip positions of each group are completely consistent, so only dips with similar wavelength can be selected when discussing the influence of thickness.
Fig. 8. (a) The experimental sensitivity of the sensor changes with the velocity when the thickness of the cantilever is 0.3 mm, 0.4 mm and 0.5 mm respectively. The illustration shows the interference spectrum of the sensor with a thickness of 0.3 mm at different velocity. (b) The sensitivity of the sensor varies with the thickness when the wavelength is 1485 nm, 1525 nm and 1612 nm respectively, the solid line is the theoretical result and the dot is the experimental result. See Data File 3 for underlying values.
4.2 Discussion on the target area
Three groups of sensor structures were designed for velocity sensing experiments, with the target radius of 2.5 cm, 3.0 cm and 3.5 cm respectively, and other structural parameters were consistent. Experimental results were obtained as shown in Fig. 9(a). Under the same velocity, sensitivity increases with the increase of target radius, and the variation trend is consistent with the theory. In addition, the target area also affects the measurement range of the sensor: the larger the target area is, the larger the shape variable of the cantilever at the same velocity, so it is easier to reach the maximum shape variable. The experimental results reveal the law that the measuring range of the sensor decreases with the increase of the target area, and when the radius of the circular target is 2.5 cm, the sensor can measure the water velocity in the range of 0-0.156 m/s. Therefore, in addition to increasing the thickness of the cantilever, the range of the sensor can be expanded by reducing the target area. However, it is worth noting that since the sensitivity decreases with the reduction of the target area, expanding the range by reducing the target area means sacrificing the sensitivity. According to formula (16), the relationship between the theoretical sensitivity and the radius of the target under different dip was calculated, as shown in the curve in Fig. 9(b), where the data points were the results of the experimental sensitivity changing with the target area under different dips. The variation trend of the three groups of experimental results is consistent with the theoretical calculation curve, and the error between the experimental results and the theoretical curve in Fig. 9(b) is due to the slight difference in the dip wavelength used for comparison among the three groups of experiments.
Fig. 9. (a) The experimental sensitivity of the sensor changes with the velocity when the target radius is 2.5 cm, 3.0 cm and 3.5 cm respectively. (b) Relationship of sensor sensitivity changing with the radius of target when the wavelength is 1400 nm, 1470 nm and 1565 nm, the solid line is the theoretical result and the dot is the experimental result. See Data File 4 for underlying values.
4.3 Discussion on the panda fiber length
Panda fiber is the main sensing unit of the velocity sensor, so whether its length affects the sensitivity of the sensor is a problem we are concerned about. Optical fiber length is not included in formula (16), that is, sensor sensitivity is not related to panda fiber length according to theoretical reasoning. Therefore, four groups of sensing structures with cantilever thickness of 0.4 mm, target radius of 2.5 cm and panda fiber length of 2.2 cm, 3.7 cm, 4.0 cm and 4.7 cm were designed for the velocity sensing experiments to verify the influence of panda fiber length on velocity sensitivity. Experimental results were obtained in Fig. 10(a), which shows the sensitivity curves of sensors with different fiber lengths almost coincide. The sensitivity of the sensor at 0.1 m/s was extracted and the relationship curve between sensitivity and fiber length was drawn as shown in Fig. 10(b), which illustrated the sensitivity was independent of the panda fiber length. However, the dip of different sensors used for comparison are not guaranteed to be identical, the experimental results are subject to error, as shown in the curve in Fig. 10(b), which is not completely a straight line. Theoretical and experimental results confirmed that the sensitivity of sensor is independent of the length of fiber, the fusion of short panda fiber in the process of sensor preparation is not only beneficial to the coupling of the optical fiber sensor unit with any cantilever structure, but also according to formula (12), the free spectral range increases with the decrease of the length of the panda fiber, and the increase of FSR is more conducive to sensor demodulation to improve sensor measurement accuracy.
Fig. 10. (a) Curve of sensor sensitivity with velocity when the cantilever thickness is 0.4 mm, the force target radius is 2.5 cm, and the panda fiber lengths are 2.2 cm, 3.7 cm, 4.0 cm and 4.7 cm respectively. (b) The sensor sensitivity changes with the panda fiber length when the velocity is 0.1 m/s. See Data File 5 for underlying values.
4.4 Repeatability
In order to further evaluate the reliability of the sensor, the repeatability of the fiber optic sensor was tested by increasing and decreasing the flow velocity several times. The experimental results are shown in Fig. 11. Since it is impossible to accurately control the velocity of the same size each time, we recorded the spectrum of each time at 0 m/s when the sensor measure the velocity from high drop to 0 m/s, and evaluated the recovery ability of the sensor after deformation by observing the wavelength fluctuation of the interference valley. Figure 11(a) shows the wavelength change of the velocity recorded by an interference valley of the sensor as it increases from 0 m/s to a certain flow velocity and then decreases to 0 m/s. Figure 11(b) shows the wavelength fluctuation of the interference valley when the velocity is 0 m/s. It can be seen that after multiple deformations of the sensor, the wavelength fluctuates in the range of 0.6 nm, which has good recovery and repeated measurement ability.
Fig. 11. (a) Sensor repeatability test, where the spectrum of the sensor under multiple increases and decreases in flow velocity is illustrated, (b) the interference valley fluctuation is 0.6 nm at 0 m/s.
5. Conclusion
In this paper, a fiber optic velocity sensor for seawater measurement is proposed and demonstrated by coupling a reflective panda fiber polarization interferometer with a target cantilever of equal strength. The sensor sensitivity obtained by experiment is consistent with the theory, which correlation coefficient is 0.96, and the MRE is 3.65%. ADV was used to calibrate the sensor, the correlation coefficient and the MRE are 0.92 and 4.5% respectively, which can meet the high precision requirements of seawater measurement. A high sensitivity measurement of seawater velocity is realized by converting the impact force of the fluid to the movement of the spectrum, the water velocity measurement can be realized in the range of 0-0.218 m/s when the cantilever thickness is 0.5 mm, and the maximum velocity sensitivity of the sensor is 355.55 nm/(m·s−1) when the velocity is 0.09 m/s. In addition, the factors influencing the velocity sensitivity of the proposed sensor are discussed theoretically and experimentally, which shows that under the condition of determining the cantilever aspect ratio and elastic modulus, the sensitivity of the sensor is related to wavelength, velocity and the size of the cantilever structure, and is independent of the length of the panda fiber. The range of the sensor is related to the cantilever thickness and the target area, the high velocity measurement can be achieved to meet the needs of seawater velocity measurement by increasing the thickness of the cantilever and reducing the target area. Compared with the published research results, the panda fiber used in the proposed structure is more sensitive to strain due to its birefringence efficiency, thus effectively improving the velocity sensitivity of the sensor. The coupling with the equal strength cantilever makes the fiber velocity sensor prominent advantages in the field of seawater measurement, and the advantage that the optical fiber sensing unit does not contact with the fluid directly avoids the influence of temperature cross sensitivity effect. The fiber optic velocity sensor based on the target cantilever is expected to play an important role in the field of seawater measurement due to its advantages of small size, stable structure and high sensitivity.
Funding
National Natural Science Foundation of China (61871353); Natural Science Foundation of Shandong Province (ZR2021MF123).
Acknowledgments
The authors thank Xu Chen and Jing Meng for useful help in the experiment.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are available in Data File 1, Data File 2, Data File 3, Data File 4, Data File 5.
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