Abstract

A differential-pressure fiber-optic airflow (DPFA) sensor based on Fabry-Perot (FP) interferometry for wind tunnel testing is proposed and demonstrated. The DPFA sensor can be well coupled with a Pitot tube, similar to the operation of the differential diaphragm capsule in the airspeed indicator on the aircraft. For differential pressure sensing between total pressure and static pressure in the airflow, an FP cavity is formed between the sensing diaphragm and a fiber end-face, and a tubule is inserted into the FP cavity. According to the principle of differential pressure derived from Bernoulli’s equation, the airflow velocity can be determined by monitoring the change of the FP cavity length. The experimental results demonstrate that a DPFA sensor with 0∼11 kPa measurable range, 826.975 nm/kPa sensitivity, and 0.008% (0.89 Pa) resolution can be realized. Combined with a 100 Hz-sweep frequency self-developed white light interferometric (WLI) interrogator and a Pitot tube, the DPFA sensor can be used for measuring the airflow velocity of 2.0∼119.24 m/s with an accuracy of 0.61%. The system is applied to the analysis of the flat-plate boundary layer, a wind tunnel experimental model, where the results are consistent with those of the theoretical analysis and from the standard electronic pressure transducer. With the large measurable range, high sweep frequency, and high precision, the system has potential application value for wind tunnel experimental investigation and in-flight measurement of airspeed.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Velocity measurement and distribution analysis of the airflow field have great practical significance in the areas of atmospheric environmental monitoring, aerodynamic studies, turbines maintenance, and navigation control [14]. Recently, fiber-optic airflow sensors have been viewed as new potential alternatives to the traditional technologies, because they have many distinctive advantages, such as lightweight, high sensitivity, corrosion resistance, and geometrical flexibility, especially immunity to electromagnetic interference in the environment of wireless communication, navigation, and radar [47]. Some fiber-optic airflow sensors with different structures or mechanisms have been demonstrated. Fiber-optic hot wire anemometry (HWA) is a well-known technique, in which fiber Bragg grating (FBG) [8], long-period fiber grating [9], or tilted fiber Bragg grating [10] are usually employed and coated with a thin film which can enhance thermal conversion. Nevertheless, complicated manufacturing processes and indirect measurements, are also identified as the problems to be solved of this method, resulting in limited applications for the anemometers based on fiber gratings, and the uneven heating effect will induce chirping which degrades the performance as well [11].

Fiber-optic Fabry-Perot (FP) sensors have been widely used in physical, chemical, and biological sensing, such as the measurement of pressure, temperature, strain, and refractive index [1215]. Currently, some researchers focus on the hot wire-based flow sensing to expand the application fields of the fiber-optic FP sensors. Traditionally, the systems of fiber-optic FP-based HWAs are similar to those of fiber grating-based HWAs, which both require a heating source and a detection instrument [16,17], and resulting in complex construction and high-power consumption. To simplify the sensing system and acquire accurate flow velocity information directly, some FP-based differential pressure sensors have been proposed, which are intrinsically pressure sensitive. A. Cipullo et al. presented a fiber-optic airflow velocity sensor based on a cantilever that fabricated on a Duran borosilicate ferrule by picosecond laser, and realized the measurement of airflow velocity in the range of 0 to 8 m/s [18]. C. Wang et al. demonstrated dual FP sensors that fixed on a customized cubic holder with a streamlined upper surface for differential pressure measurement in the airflow field and verified a velocity measurement range of 7.9∼81 m/s [19]. The aforementioned differential-pressure sensors are both made by complex manufacturing processes, and it seems that their design avoids the perturbations of the sensor to the airflow field distribution. However, in practical aerodynamics, the regular shape (circular cylinder or cube) and the large size of the sensor cannot be ignored, it will give rise to the variation of the airflow field distribution, and produce the flow drag and vortex, resulting in the imprecise measurement of the differential pressure.

Generally, for the wind tunnel investigation or in-flight monitoring, the pressure transfer devices, such as Pitot tube, are often used to guide the total pressure and static pressure of the airflow to pressure transducers, and the pressure transfer device (Pitot tube) plays a key role in reducing the perturbations of the airflow field and is often employed as the airspeed tube on the aircraft. Due to its easy and convenient operation, conventional multi-channel electronic pressure transducer, coupled with a Pitot tube for differential pressure detection in airflow field, is also commonly used in wind tunnel testing. However, its application is severely limited by electromagnetic interference that cannot be ignored and even lead to malfunctions [5,2022]. Thus, benefitting from the immunity to electromagnetic interference of fiber-optic sensors, a fiber-optic airflow sensor coupled with a Pitot tube can be used to realize the measurement of differential pressure in the airflow field, it may be a desirable situation for wind tunnel testing and in-flight airspeed measurement in harsh electromagnetic interference environment.

In this paper, we propose a differential-pressure fiber-optic airflow (DPFA) sensor based on a classic diaphragm-based fiber-optic FP interferometry (DFPI), nonetheless, a specially-designed differential-pressure transducer is constituted by a coupled Pitot tube and a diaphragm-based FP cavity, and it can be used for wind tunnel testing. The DPFA sensor can acquire the static pressure and total pressure information simultaneously, and easily obtain the absolute differential pressure in the airflow field without additional calculation, then the absolute differential pressure can be converted into the velocity by Bernoulli’s equation. Real-time velocity measurement requires a high demodulation rate, its high-speed data acquisition is realized by our self-developed white light interferometric (WLI) interrogator. The whole system, composed of the DPFA sensor, a Pitot tube, and the WLI interrogator, has a wide velocity measurable range and high precision. Due to its high sensitivity and resolution, the system can be employed to analyze the flat-plate boundary layer, an experimental model in aerodynamics.

2. Design and principle

2.1 Sensor design and principle

The schematic diagram of the DPFA sensor is shown in Fig. 1. It consists of a standard single-mode fiber (SMF), fused-silica diaphragm-based FP interferometer, and a plastic tubule. To simplify the manufacturing process, we employ three standard fused-silica tubes and a fused-silica diaphragm to construct an FP cavity. Primarily, the diaphragm with a diameter of 5 mm and a thickness of 30 μm is attached to the end-face of the first fused-silica tube (inner diameter-ID: 3.4 mm, outer diameter-OD: 4.3 mm, length: 5 mm, ITECH) using UV adhesive (3311, Loctite). To ensure that the UV adhesive does not diffuse into the first tube or the sensing diaphragm and its surface is flat, a thin film of the UV adhesive is first spin-coated onto a glass substrate. Then the adhesive is transferred to the tube end-face by pressing the tube onto the adhesive film and lifting it up. The tube end-face with adhesive is adjusted and pressed onto the diaphragm, and the UV adhesive is cured by UV irradiation. The second side-polished D-shaped silica tube (ID: 1.81 mm, OD: 2.7 mm, length: 7 mm, ITECH) is embedded into the first silica tube. The third silica tube (ID: 126 μm, OD: 1.8 mm, length: 7 mm, ITECH) is embedded into the second silica tube to ensure that the inserted fiber end-face is aligned with the diaphragm. Finally, an SMF is inserted into the third silica tube and the plastic tubule (ID: 0.3 mm, OD: 0.6 mm, PEEK) is inserted into the space between the first and the second silica tube. The inner surface of the silica diaphragm and the inserted SMF end-face formed a low-finesse FP interferometer with a 100∼200 μm cavity.

 figure: Fig. 1.

Fig. 1. Configuration of the proposed DPFA sensor, (a) the structure of the sensor probe, (b) the picture of a typical sensor.

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All fixed positions of the sensor’s structure are bonded with UV adhesive, which ensures that the FP cavity is sealed. Through the insertion of the plastic tubule, the sensor can directly get the differential pressure in the airflow field. The total pressure will cause the silica diaphragm’s deformation from the outside, while the static pressure is guided along the plastic tubule into the FP cavity and also causes the deformation of the sensing diaphragm from the inside. Thus, the total deformation of the silica diaphragm is determined by the difference between total pressure and static pressure, its operation principle is similar to that of the differential diaphragm capsule in the airspeed indicator on the aircraft. Finally, the total deformation of the silica diaphragm can be transformed into the variations of the FP cavity length, which can represent the change of differential pressure.

In this proposed DPFA sensor, the light is injected into the FP cavity by the SMF, when it arrives at the fiber-air interface, it is partly reflected, and the rest of the incident light is injected into the FP cavity when it arrives at the inner face of the silica diaphragm, it is reflected back into the fiber core at the end of SMF. The interference between the two reflections can be estimated by a dual-beam interferometer model, and the interference spectrum can be expressed as

$$I = {I_\textrm{1}} + {I_\textrm{2}} + \textrm{2}\sqrt {{I_\textrm{1}}{I_\textrm{2}}} \cos \left( {\frac{{4\pi nL}}{\lambda } + \pi } \right)$$
where I is the intensity of the interference spectrum, I1 and I2 are intensities of the two reflections, n is the refractive index of the medium filled in the FP cavity, L is the length of the FP cavity, λ is the working wavelength, and π is the additional phase of the half-wave loss.

The sensing diaphragm of the DPFA sensor is made by the fused silica with Young’s modulus of 73 GPa and Poisson’s ratio of 0.17. When the DPFA sensor is exposed to external pressure ΔP, the central deformation of the sensing diaphragm ΔL (or FP cavity length variations) can be determined by [23]:

$$\Delta L = \frac{{3(1 - {\gamma ^2}){a^4}}}{{16E{h^3}}}\Delta P$$
where γ and E are Poisson’s ratio and Young’s modulus of fused silica, respectively. a is the effective radius, and h is the thickness of the silica diaphragm.

The DPFA sensor also has a linear differential-pressure measurable range, which is determined by the elastic deformation limit of the fused-silica diaphragm (generally not more than 30% of its thickness), which can be described as [23]:

$${P_{limit}} = \frac{{8E{h^4}}}{{5(1 - {\gamma ^2}){a^4}}}$$

Based on Eq. (2) and Eq. (3), the sensitivity and measurable range of the DPFA sensor only depends on the effective radius and thickness of the fused-silica diaphragm. When the effective radius of the diaphragm is 1.7 mm and the thickness is 30 µm, the theoretical sensitivity of the DPFA sensor is calculated to be 771.57 nm/kPa. And the differential pressure measurable range is calculated to be 0∼11.67 kPa, which can match the differential pressure range of the airflow in the wind tunnel testing (0∼8.6 kPa).

2.2 Velocity measurement based on a Pitot tube

Pitot tube is a tubular device, which is mainly employed to measure the airspeed of aircraft and the velocity or pressure of the fluid in industrial pipelines. It is comprised of two thin pipes, which can be used for guiding the total pressure and static pressure of the fluid to pressure transducers, respectively, and then the velocity can be calculated by the differential pressure between them. As shown in Fig. 2, when the opening of its one pipe (Total pressure hole) faces the incoming flow, the kinetic energy of the airflow will be converted into potential energy after turning 90°, which is corresponding to the total pressure. The opening of the other pipe (Static pressure hole) is perpendicular to the airflow to produce the static pressure. Assuming that the airflow is uniform and steady, and mechanical loss is ignored, the velocity can be deduced from the Pitot tube based on the ideal Bernoulli’s equation [24]:

$$u = \sqrt {\frac{{2({{P_0}\textrm{ - }{P_s}} )}}{\rho }} $$
where u is the airflow velocity, P0 is total pressure in the airflow, Ps is static pressure in the airflow, ρ is the density of airflow in the experimental environment (generally 1.20∼1.29 kg/m3), obeying ρ=P/(RT), P is the ambient pressure, T is the ambient temperature and R is the ideal gas constant (R = 287.058 J/(kg·K) for dry air).

 figure: Fig. 2.

Fig. 2. Schematic diagram of the DPFA sensor connected to a Pitot tube for differential pressure measurement.

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According to Eq. (4), the airflow velocity is correlated to the differential pressure between total pressure and static pressure. The DPFA sensor can be coupled with the Pitot tube through two rubber hoses to directly measure the differential pressure in the airflow field, wherein the sensor probe is connected to the total pressure hole, the tubule inserted in the FP cavity is connected to the static pressure hole, as shown in Fig. 2. And the FP cavity always responds to the differential pressure between the lead-in total pressure and static pressure. Thus, the differential pressure and the airflow velocity can be obtained by measuring the variations of the FP cavity length.

3. Experimental results and discussion

3.1 Velocity measurement in a wind tunnel

To verify the feasibility of the velocity measurement by using this DPFA sensor, the relationship between the FP cavity length and differential pressure should be determined. Figure 3 shows the experimental setup for differential pressure testing at room temperature (23.0 °C). The internal pressure inside the pressure chamber is provided by a pressure generator (113A, ConST). The DPFA sensor is sealed in the chamber, and the tubule inserted in the FP cavity is extended out of the chamber to create an environment for differential pressure measurement. The data acquisition is realized by our self-developed WLI interrogator. The WLI interrogator consists of a broadly tunable modulated grating Y-branch (MG-Y) laser with the wavelength tuning range of 1527∼1567 nm and a single photodetector (PD), where the full-spectrum wavelength scanning with an interval of 8 pm and synchronized data acquisition with a frequency of 100 Hz are implemented by a field-programmable gate array (FPGA) [2527]. The output interference spectrum is processed by the cross-correlation signal processing method [28,29] to demodulate the absolute length of the FP cavity which can be expressed as a function of differential pressure, and the initial cavity length is measured to be 174.739 μm.

 figure: Fig. 3.

Fig. 3. The experimental setup for the differential pressure tests.

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Figure 4(a) shows the differential pressure response of the DPFA sensor after an increase/decrease pressure cycle in the range of 0∼11 kPa (1 kPa per step) and the sensitivity is 826.975 nm/kPa. The experimental sensitivity of the DPFA sensor is a little higher than the theoretical sensitivity calculated by Eq. (2) (771.57 nm/kPa) which may be caused by the overestimation of diaphragm thickness. Since the differential pressure of most airflow velocity to be measured in the wind tunnel is generally 0∼2 kPa, in this range, the differential pressure response is measured at a smaller interval of 0.2 kPa/step to verify that the linearity is the same as that of 0∼11 kPa. The differential pressure resolution of the DPFA sensor can be calculated by measuring the standard deviation (SD) of the FP cavity length [13,30]. As shown in Fig. 4(b), the FP cavity length is recorded at 5 kPa differential pressure for 15 seconds, and the SD is approximately 0.37 nm. The resolution of the FP cavity length can be calculated as twice the SD (0.74 nm), and the differential pressure resolution of the DPFA sensor is about 0.89 Pa, which is 0.008% of the full scale (F.S., 0∼11 kPa). Then the temperature response of the DPFA sensor from room temperature (23 °C) to 60 °C is investigated in a temperature control box. The sensor has a linear response to temperature and its sensitivity is 9.76 nm/°C, leading to a temperature dependence of 11.8 Pa/°C. The temperature crosstalk is mainly caused by the thermal expansion coefficient of the material constituting the DPFA sensor. Such error can be neglected in applications with limited temperature variations, such as experimental investigations in the constant temperature wind tunnel. Otherwise, the effective temperature compensation mechanism, such as series connection with an FBG fiber-optic temperature sensor in our related work, is required to eliminate the crosstalk between temperature and differential pressure [3133]. Besides, some adhesive-free fabrication processes can also be considered for sensor assembly in the future work to reduce the impact of material mismatch [13,30,34].

 figure: Fig. 4.

Fig. 4. The differential pressure response of the DPFA sensor from 0 to 11 kPa, (a) the linear response of the DPFA sensor between FP cavity length and differential pressure, and (b) the changes of the FP cavity length when the differential pressure is 5 kPa within 15s.

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The experimental setup for airflow velocity measurement in a wind tunnel is illustrated in Fig. 5. An air blower controlled by a variable-frequency drive (VFD) is placed in the front of a 2 m long wind tunnel to blow the air, and a steady airflow will be generated in a 32 cm×32 cm×100 cm test chamber inside the wind tunnel. A Pitot tube coupled with the DPFA sensor is mounted on a computer-controlled three-axis translation stage outside the test chamber. At the same time, the total and static pressure hole of the Pitot tube is also connected to the two channels of a standard electronic pressure transducer (Pressure Scanner, DSA3217, Scanivalve, 0.05% F.S.) via tracheal tees. The two channels can respectively measure the total pressure and static pressure in the airflow and the velocity is calculated from the differential pressure, where the velocity measured by the standard electronic pressure transducer serves as the reference velocity. The total pressure hole of the Pitot tube is then adjusted by the translation stage and placed in the center of the test chamber, and it faces the incoming flow. The interference spectrum of the DPFA sensor will be processed by our self-developed WLI interrogator.

 figure: Fig. 5.

Fig. 5. The experimental setup for velocity measurement in a wind tunnel.

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The spectrum of the DPFA sensor is recorded while the varieties of velocity range from 2.0 to 119.24 m/s, as shown in Figs. 6(a) and 6(c). The blue shift of the interference spectrum in Fig. 6(a) shows that the FP cavity length decreases with the increasing velocity in the range of 2.0∼37.74 m/s due to the deformation of the sensing diaphragm, and the output spectrum is simultaneously demodulated by the cross-correlation signal processing method in Fig. 6(b). When the airflow field starts to build, the FP cavity length decreases dramatically, denoting that the airflow begins to contact the sensing diaphragm and causes deformation. After the airflow is gradually steady, the FP cavity length becomes stable. The differential pressure in the airflow field can be obtained by dividing the change value of the FP cavity length by the sensitivity of the DPFA sensor. When the atmospheric pressure in the experimental environment is 102.1 kPa and the temperature is 23.0 °C, the airflow density of 1.20 kg/m3 can be obtained. And the airflow velocity in this experimental environment can be calculated by Eq. (4) in real time, as shown by the red curve in Fig. 6(b). After the testing, the airflow field is terminated and the DPFA sensor can also be restored to the original state.

 figure: Fig. 6.

Fig. 6. The shift in the reflection interference spectrum of the DPFA sensor, FP cavity length variations and the real-time velocities [calculated by Eq. (4)] in the input airflow velocity range of 2.0 to 119.24 m/s, (a) the shift in reflection interference spectrum in the low-velocity range of 2.0∼37.74 m/s, (b) FP cavity length variations and the real-time velocities in the low-velocity range, (c) the shift in reflection interference spectrum in the high-velocity range of 59.29∼119.24 m/s, (d) FP cavity length variations and the real-time velocities in the high-velocity range.

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Then another wind tunnel with a structure similar to that shown in Fig. 5, which is specially designed for high-velocity testing, is employed to evaluate the response characteristics of the DPFA sensor in the velocity range of 59.29∼119.24 m/s. As shown in Fig. 6(c), the interference spectrum of the DPFA sensor is also recorded at each velocity when the airflow field is stable. The shift of the interference spectrum is larger at high velocity and exceeds one cycle, which leads to confusion in distinguishing the actual change through the relative position of the peaks from each other. In this case, the adopted cross-correlation signal processing method shows noticeable advantages in such a large-scale detection field because of the absolute measurement of the FP cavity length [28,29], which makes it possible to obtain the unambiguous differential pressure information directly through the FP cavity length variations in Fig. 6(d). Theoretically, the DPFA sensor can operate in an airflow field with higher velocity (135.40 m/s with 11 kPa differential pressure limit), but 120 m/s is the upper limit of the high-velocity wind tunnel.

The response time is considered to be composed of the time delay when the pressure in the test chamber inside the wind tunnel reaches equilibrium and the measurement time required by the system (consisting of the DPFA sensor, a Pitot tube, and the WLI interrogator). Figure 7 is an enlargement of the evolution of the FP cavity length in Figs. 6(b) and 6(d), where the higher the input airflow velocity, the longer the response time is required. In the high-velocity range of 59.29 m/s∼119.24 m/s, the fluctuation of the FP cavity length seems to be smaller due to the larger variations of the velocity. Results show that the response time of the DPFA sensor mainly depends on the required time to establish a steady airflow field in the wind tunnel. And the airflow field with higher velocity often takes more time to completely stabilize. The required time to stabilize is determined by the parameters of the air blower and the structure of the wind tunnel. In addition, the energy conversion (kinetic energy to potential energy) inside the Pitot tube and the transfer of pressure to the DPFA sensor through the rubber hoses also need some time, but the time is far less than the required time to establish the airflow field. Moreover, there is no obvious response time delay between the DPFA sensor and the standard electronic pressure transducer.

 figure: Fig. 7.

Fig. 7. The response time of the DPFA sensor in the low-velocity and high-velocity wind tunnel respectively within the input airflow velocity range of 2.0∼119.24 m/s.

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When the input airflow velocity is within the range of 2.0 to 119.24 m/s, the airflow velocities measured by the DPFA sensor are compared with the input airflow velocity measured by the standard pressure transducer (reference velocity), as shown in Fig. 8. The red line is the linear fit of the experimental velocity increased curve, and the blue guideline indicates that the velocity is identical to the reference velocity. The accuracy of the DPFA sensor for airflow velocity measurement is evaluated by the absolute error between the obtained average velocity and the reference value, yielding the maximal absolute error (MAE) of 0.73 m/s, about 0.61% F.S. The estimation of the velocity resolution is performed by considering the SD of one-minute repeated measurements for each point in the velocity increased cycle from 2.0 m/s to 119.24 m/s (presented as error bars [35]), yielding the maximal SD of 0.16 m/s, about 0.13% F.S. The average airflow velocity measured by the DPFA sensor of a velocity decreased cycle is also introduced in red scatter which are in agreement within the error bars, indicating no obvious hysteresis and good repeatability.

 figure: Fig. 8.

Fig. 8. Comparison between the measured airflow velocity by the DPFA sensor and the input airflow velocity obtained by the standard pressure transducer.

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3.2 Analysis of flat-plate boundary-layer thickness

Since Ludwig Prandtl created modern fluid mechanics out of ancient hydraulics by proposing the existence of the fluid boundary layer [36,37], the study of the boundary layer has always been an important topic in aerodynamics, which is of great significance for reducing the drag of aircraft in flight, maintaining the aerodynamic layout and designing thermal protection. Generally, when the air flows through the flat plate, the velocity of the airflow close to the plate surface approaches to zero due to the viscous effect, and the velocity of the airflow increases gradually with the increasing of the distance from measuring point to the plate surface, and finally, it reaches to that of the inviscid flow in the outer flow (or input airflow). Since the viscosity of the airflow is very small, the area where the velocity changes greatly is limited to the thin layer near the flat plate surface, and it is usually called the boundary layer. The boundary-layer thickness is defined artificially as the distance between the flat plate surface and the position where the velocity reaches 99% of the input airflow velocity along the normal direction of the flat plate [38]. Therefore, the boundary-layer thickness can be obtained by measuring the velocity profile at different vertical distances from the flat plate surface in the wind tunnel.

Before boundary-layer thickness analysis, the velocity of the input airflow should be determined. The Pitot tube is coupled with the DPFA sensor and the standard pressure transducer for measurement, which are respectively 16.92 m/s and 16.85 m/s. Then the velocity profile in the boundary layer is measured, as shown in Fig. 9. The Pitot tube attached to the flat plate is placed in the wind tunnel, and the total pressure hole is close to the plate surface, facing the incoming flow to record the initial airflow velocity. The total pressure hole of the Pitot tube is 300 mm from the leading edge of the flat plate. Then the Pitot tube rises vertically with an interval of 0.8 mm by the three-axis translation stage, and the measured velocity is recorded at each position. While the velocity no longer changes significantly with the rising position and approximate to the velocity of the input airflow, the airflow completely separates from the flat plate. The distance between this position and the plate surface is the required boundary-layer thickness.

 figure: Fig. 9.

Fig. 9. The test process for flat-plate boundary-layer thickness.

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As shown in Fig. 10 (blue curve), when the total pressure hole of the Pitot tube is close to the flat plate surface, the airflow field starts to establish and the decrease of the FP cavity length starts from 25 s to 31 s, then gradually becomes stable. However, the total pressure hole cannot infinitely approach to the flat plate surface due to the thickness of the Pitot tube wall (about 1.5 mm). Thus, the total pressure hole is located at z=1.5 mm which is the actual initial measurement position. We record the variations of the FP cavity length (at z = 1.5 mm) within one minute after the airflow field is stable and take them as the reference values. Subsequently, the Pitot tube rises vertically with an interval of 0.8 mm, and the FP cavity length of the DPFA sensor is recorded for about one minute at each vertical position. Until about 962 s, the FP cavity length tends to be stable, indicating that the airflow velocity is almost constant. According to Eq. (4), the airflow velocity can be calculated in real time for the entire testing, as shown in Fig. 10 (red curve). When the vertical position is z = 9.5 mm, the airflow velocity is equal to the velocity of the input airflow, which denotes that the Pitot tube begins to enter into the outer flow and the airflow is no longer under the influence of the flat plate.

 figure: Fig. 10.

Fig. 10. Variations of the FP cavity length and the real-time velocities (calculated by Eq. (4)) in the boundary layer and outer flow respectively.

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Figure 11 shows the comparison between the average velocity measured by the DPFA sensor and that measured by the standard pressure transducer. Experimental results show that the airflow velocity reaches the velocity in the outer flow at z=9.5 mm, which indicates that the boundary-layer thickness is about 9.5 mm. Besides that, because of the viscosity, the airflow near the boundary layer is almost stationary, and assuming that the Pitot tube is infinitely close to the plate surface (z = 0) and the measured velocity is close to zero [38], which is also marked as a reference value in Fig. 11.

 figure: Fig. 11.

Fig. 11. The longitudinal velocity profile in the turbulent boundary layer.

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To verify the feasibility of the boundary-layer thickness analysis, whether the boundary layer is laminar or turbulent must be primarily considered. The transition between laminar flow and turbulent flow mainly depends on the Reynolds number (Re) of the airflow which is related to the characteristic velocity, such as the free stream velocity in the outer flow U, kinematic viscosity ν (1.57×10−5 m2/s at about 20 °C for airflow) and the distance x from the leading edge of the flat plate. The Reynolds number can be expressed as [24]:

$$Re = \frac{{Ux}}{\nu }$$

For the flat-plate boundary layer, while the laminar flow transits to turbulent flow, the critical Reynolds number can be considered as 3×105 [38]. According to Eq. (5), in the outer flow, the Reynolds number of the airflow measured by the DPFA sensor can be calculated as 3.23×105, which agrees well with that achieved by the standard pressure transducer (Re=3.22×105). The measured Reynolds number reaches the critical Reynolds number, so the airflow in the boundary layer transits from laminar flow to turbulent flow. And the thickness of the turbulent boundary layer defined in theory can be determined by [38]:

$${\delta _T}\textrm{ = }\frac{{0.377x}}{{R{e^{1/5}}}}$$

According to Eq. (6), the theoretical boundary-layer thickness in the airflow is calculated to be 8.95 mm, which is approximately the experimental result (9.5 mm) in our testing. The guideline in Fig. 11 (blue curve) is obtained from the theoretical velocity profile of the turbulent boundary layer, which conforms to the 1/7th power-law relationship in turbulent flow proposed by J. Nikuradse [38,39]. And it demonstrates that the experimental velocity profile is in good agreement with the theoretical value.

4. Conclusion

The DPFA sensor designed for airflow velocity measurement is proposed and experimentally demonstrated. Based on the principle of differential pressure, the airflow velocity can be calculated by the change of the FP cavity length, which is similar to the operation of the differential diaphragm capsule in the airspeed indicator on the aircraft. The proposed sensor can achieve a sensitivity of 826.975 nm/kPa with a resolution of 0.008% (0.89 Pa) within a 0∼11 kPa differential pressure range. Combined with our self-developed WLI interrogator and a Pitot tube, it is proved that this proposed sensor can be used for measuring the airflow velocity. Besides, the proposed sensor is also used to analyze the thickness of the flat boundary layer, which is an experimental model for aerodynamic studies. The experimental results are in good agreement with those of the standard electronic pressure transducer and theoretical analysis. The system consisting of the DPFA sensor, a Pitot tube, and the WLI interrogator has great potential for the wind tunnel testing and in-flight measurement of airspeed. In addition, an all-silica DPFA sensor can be realized by adhesive-free methods in the future [13,30,34], which may have better structure and long-term stability.

Funding

Fundamental Research Funds for the Central Universities (DUT18ZD215); National Natural Science Foundation of China (61520106013, 61727816).

Acknowledgments

Thanks for the wind tunnel testing equipment provided by School of Energy and Power Engineering, Dalian University of Technology, and the expert contributions from Dr. Xinpu Zhang and Mr. Chao Zhang to this article.

Disclosures

The authors have no relevant financial interests in this article and no potential conflicts of interests to disclose.

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6. J. Kumar, O. Prakash, S. K. Agrawal, R. Mahakud, A. Mokhariwale, S. K. Dixit, and S. V. Nakhe, “Distributed fiber Bragg grating sensor for multipoint temperature monitoring up to 500°C in high-electromagnetic interference environment,” Opt. Eng. 55(9), 090502 (2016). [CrossRef]  

7. M. S. O’Sullivan, Optical fiber sensors: Principles and components (Artech Books, 1989).

8. X. Wang, X. Dong, Y. Zhou, Y. Li, J. Cheng, and Z. Chen, “Optical fiber anemometer using silver-coated fiber Bragg grating and bitaper,” Sens. Actuators, A 214, 230–233 (2014). [CrossRef]  

9. Z. Liu, F. Wang, Y. Zhang, Z. Jing, and W. Peng, “Low-power-consumption fiber-optic anemometer based on long-period grating with SWCNT coating,” IEEE Sens. J. 19(7), 2592–2597 (2019). [CrossRef]  

10. Y. Zhang, F. Wang, Z. Liu, Z. Duan, W. Cui, J. Han, Y. Gu, Z. Wu, Z. Jing, C. Sun, and W. Peng, “Fiber-optic anemometer based on single-walled carbon nanotube coated tilted fiber Bragg grating,” Opt. Express 25(20), 24521–24530 (2017). [CrossRef]  

11. Y. Zhao, H.-f. Hu, D.-j. Bi, and Y. Yang, “Research on the optical fiber gas flowmeters based on intermodal interference,” Opt. Lasers Eng. 82, 122–126 (2016). [CrossRef]  

12. T. Liu, J. Yin, J. Jiang, K. Liu, S. Wang, and S. Zou, “Differential-pressure-based fiber-optic temperature sensor using Fabry-Perot interferometry,” Opt. Lett. 40(6), 1049–1052 (2015). [CrossRef]  

13. Y. Liu, Z. Jing, R. Li, Y. Zhang, Q. Liu, A. Li, C. Zhang, and W. Peng, “Miniature fiber-optic tip pressure sensor assembled by hydroxide catalysis bonding technology,” Opt. Express 28(2), 948–958 (2020). [CrossRef]  

14. T. Paixão, F. Araújo, and P. Antunes, “Highly sensitive fiber optic temperature and strain sensor based on an intrinsic Fabry-Perot interferometer fabricated by a femtosecond laser,” Opt. Lett. 44(19), 4833–4836 (2019). [CrossRef]  

15. Y. Liu, Z. Jing, A. Li, Q. Liu, P. Song, R. Li, and W. Peng, “An open-cavity fiber Fabry-Perot interferometer fabricated by femtosecond laser micromachining for refractive index sensing,” Proc. SPIE 11209, 3 (2019). [CrossRef]  

16. C. Lee, K. Liu, S. Luo, M. Wu, and C. Ma, “A Hot-Polymer Fiber Fabry-Perot Interferometer Anemometer for Sensing Airflow,” Sensors 17(9), 2015 (2017). [CrossRef]  

17. G. Liu, W. Hou, W. Qiao, and M. Han, “Fast-response fiber-optic anemometer with temperature self-compensation,” Opt. Express 23(10), 13562–13570 (2015). [CrossRef]  

18. A. Cipullo, G. Gruca, K. Heeck, F. De Filippis, D. Iannuzzi, A. Minardo, and L. Zeni, “Numerical study of a ferrule-top cantilever optical fiber sensor for wind-tunnel applications and comparison with experimental results,” Sens. Actuators, A 178, 17–25 (2012). [CrossRef]  

19. C. Wang, X. Zhang, J. Jiang, K. Liu, S. Wang, R. Wang, Y. Li, and T. Liu, “Fiber optical temperature compensated anemometer based on dual Fabry-Perot sensors with sealed cavity,” Opt. Express 27(13), 18157–18168 (2019). [CrossRef]  

20. J. J. Ely, “Electromagnetic interference to flight navigation and communication systems: new strategies in the age of wireless,” in Proceedings of AIAA Guidance, Navigation, Control Conference and Exhibit8, 1–28 (2005).

21. X. Tong, Advanced Materials and Design for Electromagnetic Interference Shielding (CRC Press, 2009).

22. F. Boden, N. Lawson, H. W. Jentik, and J. Kompenhams, Advanced in-flight measurement techniques (Research Topics in Aerospace, 2013). [CrossRef]  

23. D. Giovanni, Flat and corrugated diaphragm design handbook (Marcel Dekker, 1982).

24. F. M. White, Fluid Mechanics (in SI Units) (Mcgraw Hill Higher Education, 2011).

25. Q. Liu, Z. Jing, Y. Liu, A. Li, Z. Xia, and W. Peng, “Multiplexing fiber-optic Fabry–Perot acoustic sensors using self-calibrating wavelength shifting interferometry,” Opt. Express 27(26), 38191–38203 (2019). [CrossRef]  

26. Q. Liu, Z. Jing, A. Li, Y. Liu, Z. Huang, Y. Zhang, and W. Peng, “Common-path dual-wavelength quadrature phase demodulation of EFPI sensors using a broadly tunable MG-Y laser,” Opt. Express 27(20), 27873–27881 (2019). [CrossRef]  

27. Q. Liu, Z. Jing, Y. Liu, A. Li, Y. Zhang, Z. Huang, M. Han, and W. Peng, “Quadrature phase-stabilized three-wavelength interrogation of a fiber-optic Fabry–Perot acoustic sensor,” Opt. Lett. 44(22), 5402–5405 (2019). [CrossRef]  

28. Z. Jing, “Study on White Light Extrinsic Fabry-Perot Interferometric Optical Fiber Sensor and its Application,” Doctoral dissertation, Dalian University of Technology (2006).

29. Z. Jing and Q. Yu, “White light optical fiber EFPI sensor based on cross-correlation signal processing method,” in Proceedings of 6th International Symposium on Test and Measurement (Academic, 2005), pp. 3509–3511.

30. W. Wang, W. Wu, S. Wu, Y. Li, C. Huang, X. Tian, X. Fei, and J. Huang, “Adhesive-free bonding homogenous fused-silica Fabry-Perot optical fiber low pressure sensor in harsh environments by CO2 laser welding,” Opt. Commun. 435, 97–101 (2019). [CrossRef]  

31. X. Zhou, Q. Yu, and W. Peng, “Fiber-optic Fabry-Perot pressure sensor for down-hole application,” Opt. Lasers Eng. 121, 289–299 (2019). [CrossRef]  

32. Z. Jing, Y. Liu, Y. Zhang, A. Li, P. Song, Z. Wu, Y. Zhang, and W. Peng, “Highly Sensitive FBG-FP sensor for Simultaneous Measurement of Humidity and Temperature,” in 26th International Conference on Optical Fiber Sensors, 2018 OSA Technical Digest Series (Optical Society of America, 2018), paper WF79.

33. W. Wang, X. Jiang, and Q. Yu, “Temperature self-compensation fiber-optic pressure sensor based on fiber Bragg grating and Fabry-Perot interference multiplexing,” Opt. Commun. 285(16), 3466–3470 (2012). [CrossRef]  

34. W. Wang, N. Wu, Y. Tian, C. Niezrecki, and X. Wang, “Miniature all-silica optical fiber pressure sensor with an ultrathin uniform diaphragm,” Opt. Express 18(9), 9006–9014 (2010). [CrossRef]  

35. AIAA, Assessment of Experimental Uncertainty With Application to Wind Tunnel Testing, American Institute of Aeronautics and Astronautics (AIAA S-071A-1999), (1999).

36. L. Prandtl, “Motion of fluids with very little viscosity,” Technical Report Archive & Image Library, 1–18 (1928).

37. S. Grossmann and D. Lohse, “Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection,” Phys. Rev. E 66(1), 016305 (2002). [CrossRef]  

38. H. Schlichting, Boundary-Layer Theory (McGraw-Hill Book Company, 1979).

39. L. J. De Chant, “The venerable 1/7th power law turbulent velocity profile: a classical nonlinear boundary value problem solution and its relationship to stochastic processes,” Appl. Math. Comput. 161(2), 463–474 (2005). [CrossRef]  

References

  • View by:

  1. C. K. Thomas, A. M. Kennedy, J. S. Selker, A. Moretti, M. H. Schroth, A. R. Smoot, N. B. Tufillaro, and M. J. Zeeman, “High-resolution fibre-optic temperature sensing: A new tool to study the two-dimensional structure of atmospheric surface-layer flow,” Bound-Lay Meteorol. 142(2), 177–192 (2012).
    [Crossref]
  2. M. J. Gander, W. N. MacPherson, J. S. Barton, R. L. Reuben, J. D. C. Jones, R. Stevens, K. S. Chana, S. J. Anderson, and T. V. Jones, “Embedded micromachined fiber-optic Fabry-Perot pressure sensors in aerodynamics applications,” IEEE Sens. J. 3(1), 102–107 (2003).
    [Crossref]
  3. S. C. C. Bailey, M. Hultmark, J. P. Monty, P. H. Alfredsson, M. S. Chong, R. D. Duncan, J. H. M. Fransson, N. Hutchins, I. Marusic, B. J. McKeon, H. M. Nagib, R. Örlü, A. Segalini, A. J. Smits, and R. Vinuesa, “Obtaining accurate mean velocity measurements in high Reynolds number turbulent boundary layers using Pitot tubes,” J. Fluid Mech. 715, 642–670 (2013).
    [Crossref]
  4. G. Ma, C. Li, J. Jiang, J. Liang, Y. Luo, and Y. Cheng, “A passive optical fiber anemometer for wind speed measurement on high-voltage overhead transmission lines,” IEEE Trans. Instrum. Meas. 61(2), 539–544 (2012).
    [Crossref]
  5. B. Gage, R. Greenwell, M. Summerlin, and B. Zetlen, “Fiber Optic Aircraft Systems Electromagnetic Pulse (Emp) Survivability,” Proc. SPIE 0506, 109–115 (1984).
    [Crossref]
  6. J. Kumar, O. Prakash, S. K. Agrawal, R. Mahakud, A. Mokhariwale, S. K. Dixit, and S. V. Nakhe, “Distributed fiber Bragg grating sensor for multipoint temperature monitoring up to 500°C in high-electromagnetic interference environment,” Opt. Eng. 55(9), 090502 (2016).
    [Crossref]
  7. M. S. O’Sullivan, Optical fiber sensors: Principles and components (Artech Books, 1989).
  8. X. Wang, X. Dong, Y. Zhou, Y. Li, J. Cheng, and Z. Chen, “Optical fiber anemometer using silver-coated fiber Bragg grating and bitaper,” Sens. Actuators, A 214, 230–233 (2014).
    [Crossref]
  9. Z. Liu, F. Wang, Y. Zhang, Z. Jing, and W. Peng, “Low-power-consumption fiber-optic anemometer based on long-period grating with SWCNT coating,” IEEE Sens. J. 19(7), 2592–2597 (2019).
    [Crossref]
  10. Y. Zhang, F. Wang, Z. Liu, Z. Duan, W. Cui, J. Han, Y. Gu, Z. Wu, Z. Jing, C. Sun, and W. Peng, “Fiber-optic anemometer based on single-walled carbon nanotube coated tilted fiber Bragg grating,” Opt. Express 25(20), 24521–24530 (2017).
    [Crossref]
  11. Y. Zhao, H.-f. Hu, D.-j. Bi, and Y. Yang, “Research on the optical fiber gas flowmeters based on intermodal interference,” Opt. Lasers Eng. 82, 122–126 (2016).
    [Crossref]
  12. T. Liu, J. Yin, J. Jiang, K. Liu, S. Wang, and S. Zou, “Differential-pressure-based fiber-optic temperature sensor using Fabry-Perot interferometry,” Opt. Lett. 40(6), 1049–1052 (2015).
    [Crossref]
  13. Y. Liu, Z. Jing, R. Li, Y. Zhang, Q. Liu, A. Li, C. Zhang, and W. Peng, “Miniature fiber-optic tip pressure sensor assembled by hydroxide catalysis bonding technology,” Opt. Express 28(2), 948–958 (2020).
    [Crossref]
  14. T. Paixão, F. Araújo, and P. Antunes, “Highly sensitive fiber optic temperature and strain sensor based on an intrinsic Fabry-Perot interferometer fabricated by a femtosecond laser,” Opt. Lett. 44(19), 4833–4836 (2019).
    [Crossref]
  15. Y. Liu, Z. Jing, A. Li, Q. Liu, P. Song, R. Li, and W. Peng, “An open-cavity fiber Fabry-Perot interferometer fabricated by femtosecond laser micromachining for refractive index sensing,” Proc. SPIE 11209, 3 (2019).
    [Crossref]
  16. C. Lee, K. Liu, S. Luo, M. Wu, and C. Ma, “A Hot-Polymer Fiber Fabry-Perot Interferometer Anemometer for Sensing Airflow,” Sensors 17(9), 2015 (2017).
    [Crossref]
  17. G. Liu, W. Hou, W. Qiao, and M. Han, “Fast-response fiber-optic anemometer with temperature self-compensation,” Opt. Express 23(10), 13562–13570 (2015).
    [Crossref]
  18. A. Cipullo, G. Gruca, K. Heeck, F. De Filippis, D. Iannuzzi, A. Minardo, and L. Zeni, “Numerical study of a ferrule-top cantilever optical fiber sensor for wind-tunnel applications and comparison with experimental results,” Sens. Actuators, A 178, 17–25 (2012).
    [Crossref]
  19. C. Wang, X. Zhang, J. Jiang, K. Liu, S. Wang, R. Wang, Y. Li, and T. Liu, “Fiber optical temperature compensated anemometer based on dual Fabry-Perot sensors with sealed cavity,” Opt. Express 27(13), 18157–18168 (2019).
    [Crossref]
  20. J. J. Ely, “Electromagnetic interference to flight navigation and communication systems: new strategies in the age of wireless,” in Proceedings of AIAA Guidance, Navigation, Control Conference and Exhibit8, 1–28 (2005).
  21. X. Tong, Advanced Materials and Design for Electromagnetic Interference Shielding (CRC Press, 2009).
  22. F. Boden, N. Lawson, H. W. Jentik, and J. Kompenhams, Advanced in-flight measurement techniques (Research Topics in Aerospace, 2013).
    [Crossref]
  23. D. Giovanni, Flat and corrugated diaphragm design handbook (Marcel Dekker, 1982).
  24. F. M. White, Fluid Mechanics (in SI Units) (Mcgraw Hill Higher Education, 2011).
  25. Q. Liu, Z. Jing, Y. Liu, A. Li, Z. Xia, and W. Peng, “Multiplexing fiber-optic Fabry–Perot acoustic sensors using self-calibrating wavelength shifting interferometry,” Opt. Express 27(26), 38191–38203 (2019).
    [Crossref]
  26. Q. Liu, Z. Jing, A. Li, Y. Liu, Z. Huang, Y. Zhang, and W. Peng, “Common-path dual-wavelength quadrature phase demodulation of EFPI sensors using a broadly tunable MG-Y laser,” Opt. Express 27(20), 27873–27881 (2019).
    [Crossref]
  27. Q. Liu, Z. Jing, Y. Liu, A. Li, Y. Zhang, Z. Huang, M. Han, and W. Peng, “Quadrature phase-stabilized three-wavelength interrogation of a fiber-optic Fabry–Perot acoustic sensor,” Opt. Lett. 44(22), 5402–5405 (2019).
    [Crossref]
  28. Z. Jing, “Study on White Light Extrinsic Fabry-Perot Interferometric Optical Fiber Sensor and its Application,” Doctoral dissertation, Dalian University of Technology (2006).
  29. Z. Jing and Q. Yu, “White light optical fiber EFPI sensor based on cross-correlation signal processing method,” in Proceedings of 6th International Symposium on Test and Measurement (Academic, 2005), pp. 3509–3511.
  30. W. Wang, W. Wu, S. Wu, Y. Li, C. Huang, X. Tian, X. Fei, and J. Huang, “Adhesive-free bonding homogenous fused-silica Fabry-Perot optical fiber low pressure sensor in harsh environments by CO2 laser welding,” Opt. Commun. 435, 97–101 (2019).
    [Crossref]
  31. X. Zhou, Q. Yu, and W. Peng, “Fiber-optic Fabry-Perot pressure sensor for down-hole application,” Opt. Lasers Eng. 121, 289–299 (2019).
    [Crossref]
  32. Z. Jing, Y. Liu, Y. Zhang, A. Li, P. Song, Z. Wu, Y. Zhang, and W. Peng, “Highly Sensitive FBG-FP sensor for Simultaneous Measurement of Humidity and Temperature,” in 26th International Conference on Optical Fiber Sensors, 2018 OSA Technical Digest Series (Optical Society of America, 2018), paper WF79.
  33. W. Wang, X. Jiang, and Q. Yu, “Temperature self-compensation fiber-optic pressure sensor based on fiber Bragg grating and Fabry-Perot interference multiplexing,” Opt. Commun. 285(16), 3466–3470 (2012).
    [Crossref]
  34. W. Wang, N. Wu, Y. Tian, C. Niezrecki, and X. Wang, “Miniature all-silica optical fiber pressure sensor with an ultrathin uniform diaphragm,” Opt. Express 18(9), 9006–9014 (2010).
    [Crossref]
  35. AIAA, Assessment of Experimental Uncertainty With Application to Wind Tunnel Testing, American Institute of Aeronautics and Astronautics (AIAA S-071A-1999), (1999).
  36. L. Prandtl, “Motion of fluids with very little viscosity,” Technical Report Archive & Image Library, 1–18 (1928).
  37. S. Grossmann and D. Lohse, “Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection,” Phys. Rev. E 66(1), 016305 (2002).
    [Crossref]
  38. H. Schlichting, Boundary-Layer Theory (McGraw-Hill Book Company, 1979).
  39. L. J. De Chant, “The venerable 1/7th power law turbulent velocity profile: a classical nonlinear boundary value problem solution and its relationship to stochastic processes,” Appl. Math. Comput. 161(2), 463–474 (2005).
    [Crossref]

2020 (1)

2019 (9)

T. Paixão, F. Araújo, and P. Antunes, “Highly sensitive fiber optic temperature and strain sensor based on an intrinsic Fabry-Perot interferometer fabricated by a femtosecond laser,” Opt. Lett. 44(19), 4833–4836 (2019).
[Crossref]

Y. Liu, Z. Jing, A. Li, Q. Liu, P. Song, R. Li, and W. Peng, “An open-cavity fiber Fabry-Perot interferometer fabricated by femtosecond laser micromachining for refractive index sensing,” Proc. SPIE 11209, 3 (2019).
[Crossref]

Z. Liu, F. Wang, Y. Zhang, Z. Jing, and W. Peng, “Low-power-consumption fiber-optic anemometer based on long-period grating with SWCNT coating,” IEEE Sens. J. 19(7), 2592–2597 (2019).
[Crossref]

C. Wang, X. Zhang, J. Jiang, K. Liu, S. Wang, R. Wang, Y. Li, and T. Liu, “Fiber optical temperature compensated anemometer based on dual Fabry-Perot sensors with sealed cavity,” Opt. Express 27(13), 18157–18168 (2019).
[Crossref]

Q. Liu, Z. Jing, Y. Liu, A. Li, Z. Xia, and W. Peng, “Multiplexing fiber-optic Fabry–Perot acoustic sensors using self-calibrating wavelength shifting interferometry,” Opt. Express 27(26), 38191–38203 (2019).
[Crossref]

Q. Liu, Z. Jing, A. Li, Y. Liu, Z. Huang, Y. Zhang, and W. Peng, “Common-path dual-wavelength quadrature phase demodulation of EFPI sensors using a broadly tunable MG-Y laser,” Opt. Express 27(20), 27873–27881 (2019).
[Crossref]

Q. Liu, Z. Jing, Y. Liu, A. Li, Y. Zhang, Z. Huang, M. Han, and W. Peng, “Quadrature phase-stabilized three-wavelength interrogation of a fiber-optic Fabry–Perot acoustic sensor,” Opt. Lett. 44(22), 5402–5405 (2019).
[Crossref]

W. Wang, W. Wu, S. Wu, Y. Li, C. Huang, X. Tian, X. Fei, and J. Huang, “Adhesive-free bonding homogenous fused-silica Fabry-Perot optical fiber low pressure sensor in harsh environments by CO2 laser welding,” Opt. Commun. 435, 97–101 (2019).
[Crossref]

X. Zhou, Q. Yu, and W. Peng, “Fiber-optic Fabry-Perot pressure sensor for down-hole application,” Opt. Lasers Eng. 121, 289–299 (2019).
[Crossref]

2017 (2)

2016 (2)

J. Kumar, O. Prakash, S. K. Agrawal, R. Mahakud, A. Mokhariwale, S. K. Dixit, and S. V. Nakhe, “Distributed fiber Bragg grating sensor for multipoint temperature monitoring up to 500°C in high-electromagnetic interference environment,” Opt. Eng. 55(9), 090502 (2016).
[Crossref]

Y. Zhao, H.-f. Hu, D.-j. Bi, and Y. Yang, “Research on the optical fiber gas flowmeters based on intermodal interference,” Opt. Lasers Eng. 82, 122–126 (2016).
[Crossref]

2015 (2)

2014 (1)

X. Wang, X. Dong, Y. Zhou, Y. Li, J. Cheng, and Z. Chen, “Optical fiber anemometer using silver-coated fiber Bragg grating and bitaper,” Sens. Actuators, A 214, 230–233 (2014).
[Crossref]

2013 (1)

S. C. C. Bailey, M. Hultmark, J. P. Monty, P. H. Alfredsson, M. S. Chong, R. D. Duncan, J. H. M. Fransson, N. Hutchins, I. Marusic, B. J. McKeon, H. M. Nagib, R. Örlü, A. Segalini, A. J. Smits, and R. Vinuesa, “Obtaining accurate mean velocity measurements in high Reynolds number turbulent boundary layers using Pitot tubes,” J. Fluid Mech. 715, 642–670 (2013).
[Crossref]

2012 (4)

G. Ma, C. Li, J. Jiang, J. Liang, Y. Luo, and Y. Cheng, “A passive optical fiber anemometer for wind speed measurement on high-voltage overhead transmission lines,” IEEE Trans. Instrum. Meas. 61(2), 539–544 (2012).
[Crossref]

C. K. Thomas, A. M. Kennedy, J. S. Selker, A. Moretti, M. H. Schroth, A. R. Smoot, N. B. Tufillaro, and M. J. Zeeman, “High-resolution fibre-optic temperature sensing: A new tool to study the two-dimensional structure of atmospheric surface-layer flow,” Bound-Lay Meteorol. 142(2), 177–192 (2012).
[Crossref]

W. Wang, X. Jiang, and Q. Yu, “Temperature self-compensation fiber-optic pressure sensor based on fiber Bragg grating and Fabry-Perot interference multiplexing,” Opt. Commun. 285(16), 3466–3470 (2012).
[Crossref]

A. Cipullo, G. Gruca, K. Heeck, F. De Filippis, D. Iannuzzi, A. Minardo, and L. Zeni, “Numerical study of a ferrule-top cantilever optical fiber sensor for wind-tunnel applications and comparison with experimental results,” Sens. Actuators, A 178, 17–25 (2012).
[Crossref]

2010 (1)

2005 (1)

L. J. De Chant, “The venerable 1/7th power law turbulent velocity profile: a classical nonlinear boundary value problem solution and its relationship to stochastic processes,” Appl. Math. Comput. 161(2), 463–474 (2005).
[Crossref]

2003 (1)

M. J. Gander, W. N. MacPherson, J. S. Barton, R. L. Reuben, J. D. C. Jones, R. Stevens, K. S. Chana, S. J. Anderson, and T. V. Jones, “Embedded micromachined fiber-optic Fabry-Perot pressure sensors in aerodynamics applications,” IEEE Sens. J. 3(1), 102–107 (2003).
[Crossref]

2002 (1)

S. Grossmann and D. Lohse, “Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection,” Phys. Rev. E 66(1), 016305 (2002).
[Crossref]

1984 (1)

B. Gage, R. Greenwell, M. Summerlin, and B. Zetlen, “Fiber Optic Aircraft Systems Electromagnetic Pulse (Emp) Survivability,” Proc. SPIE 0506, 109–115 (1984).
[Crossref]

Agrawal, S. K.

J. Kumar, O. Prakash, S. K. Agrawal, R. Mahakud, A. Mokhariwale, S. K. Dixit, and S. V. Nakhe, “Distributed fiber Bragg grating sensor for multipoint temperature monitoring up to 500°C in high-electromagnetic interference environment,” Opt. Eng. 55(9), 090502 (2016).
[Crossref]

Alfredsson, P. H.

S. C. C. Bailey, M. Hultmark, J. P. Monty, P. H. Alfredsson, M. S. Chong, R. D. Duncan, J. H. M. Fransson, N. Hutchins, I. Marusic, B. J. McKeon, H. M. Nagib, R. Örlü, A. Segalini, A. J. Smits, and R. Vinuesa, “Obtaining accurate mean velocity measurements in high Reynolds number turbulent boundary layers using Pitot tubes,” J. Fluid Mech. 715, 642–670 (2013).
[Crossref]

Anderson, S. J.

M. J. Gander, W. N. MacPherson, J. S. Barton, R. L. Reuben, J. D. C. Jones, R. Stevens, K. S. Chana, S. J. Anderson, and T. V. Jones, “Embedded micromachined fiber-optic Fabry-Perot pressure sensors in aerodynamics applications,” IEEE Sens. J. 3(1), 102–107 (2003).
[Crossref]

Antunes, P.

Araújo, F.

Bailey, S. C. C.

S. C. C. Bailey, M. Hultmark, J. P. Monty, P. H. Alfredsson, M. S. Chong, R. D. Duncan, J. H. M. Fransson, N. Hutchins, I. Marusic, B. J. McKeon, H. M. Nagib, R. Örlü, A. Segalini, A. J. Smits, and R. Vinuesa, “Obtaining accurate mean velocity measurements in high Reynolds number turbulent boundary layers using Pitot tubes,” J. Fluid Mech. 715, 642–670 (2013).
[Crossref]

Barton, J. S.

M. J. Gander, W. N. MacPherson, J. S. Barton, R. L. Reuben, J. D. C. Jones, R. Stevens, K. S. Chana, S. J. Anderson, and T. V. Jones, “Embedded micromachined fiber-optic Fabry-Perot pressure sensors in aerodynamics applications,” IEEE Sens. J. 3(1), 102–107 (2003).
[Crossref]

Bi, D.-j.

Y. Zhao, H.-f. Hu, D.-j. Bi, and Y. Yang, “Research on the optical fiber gas flowmeters based on intermodal interference,” Opt. Lasers Eng. 82, 122–126 (2016).
[Crossref]

Boden, F.

F. Boden, N. Lawson, H. W. Jentik, and J. Kompenhams, Advanced in-flight measurement techniques (Research Topics in Aerospace, 2013).
[Crossref]

Chana, K. S.

M. J. Gander, W. N. MacPherson, J. S. Barton, R. L. Reuben, J. D. C. Jones, R. Stevens, K. S. Chana, S. J. Anderson, and T. V. Jones, “Embedded micromachined fiber-optic Fabry-Perot pressure sensors in aerodynamics applications,” IEEE Sens. J. 3(1), 102–107 (2003).
[Crossref]

Chen, Z.

X. Wang, X. Dong, Y. Zhou, Y. Li, J. Cheng, and Z. Chen, “Optical fiber anemometer using silver-coated fiber Bragg grating and bitaper,” Sens. Actuators, A 214, 230–233 (2014).
[Crossref]

Cheng, J.

X. Wang, X. Dong, Y. Zhou, Y. Li, J. Cheng, and Z. Chen, “Optical fiber anemometer using silver-coated fiber Bragg grating and bitaper,” Sens. Actuators, A 214, 230–233 (2014).
[Crossref]

Cheng, Y.

G. Ma, C. Li, J. Jiang, J. Liang, Y. Luo, and Y. Cheng, “A passive optical fiber anemometer for wind speed measurement on high-voltage overhead transmission lines,” IEEE Trans. Instrum. Meas. 61(2), 539–544 (2012).
[Crossref]

Chong, M. S.

S. C. C. Bailey, M. Hultmark, J. P. Monty, P. H. Alfredsson, M. S. Chong, R. D. Duncan, J. H. M. Fransson, N. Hutchins, I. Marusic, B. J. McKeon, H. M. Nagib, R. Örlü, A. Segalini, A. J. Smits, and R. Vinuesa, “Obtaining accurate mean velocity measurements in high Reynolds number turbulent boundary layers using Pitot tubes,” J. Fluid Mech. 715, 642–670 (2013).
[Crossref]

Cipullo, A.

A. Cipullo, G. Gruca, K. Heeck, F. De Filippis, D. Iannuzzi, A. Minardo, and L. Zeni, “Numerical study of a ferrule-top cantilever optical fiber sensor for wind-tunnel applications and comparison with experimental results,” Sens. Actuators, A 178, 17–25 (2012).
[Crossref]

Cui, W.

De Chant, L. J.

L. J. De Chant, “The venerable 1/7th power law turbulent velocity profile: a classical nonlinear boundary value problem solution and its relationship to stochastic processes,” Appl. Math. Comput. 161(2), 463–474 (2005).
[Crossref]

De Filippis, F.

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Q. Liu, Z. Jing, A. Li, Y. Liu, Z. Huang, Y. Zhang, and W. Peng, “Common-path dual-wavelength quadrature phase demodulation of EFPI sensors using a broadly tunable MG-Y laser,” Opt. Express 27(20), 27873–27881 (2019).
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Z. Jing, Y. Liu, Y. Zhang, A. Li, P. Song, Z. Wu, Y. Zhang, and W. Peng, “Highly Sensitive FBG-FP sensor for Simultaneous Measurement of Humidity and Temperature,” in 26th International Conference on Optical Fiber Sensors, 2018 OSA Technical Digest Series (Optical Society of America, 2018), paper WF79.

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X. Wang, X. Dong, Y. Zhou, Y. Li, J. Cheng, and Z. Chen, “Optical fiber anemometer using silver-coated fiber Bragg grating and bitaper,” Sens. Actuators, A 214, 230–233 (2014).
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Figures (11)

Fig. 1.
Fig. 1. Configuration of the proposed DPFA sensor, (a) the structure of the sensor probe, (b) the picture of a typical sensor.
Fig. 2.
Fig. 2. Schematic diagram of the DPFA sensor connected to a Pitot tube for differential pressure measurement.
Fig. 3.
Fig. 3. The experimental setup for the differential pressure tests.
Fig. 4.
Fig. 4. The differential pressure response of the DPFA sensor from 0 to 11 kPa, (a) the linear response of the DPFA sensor between FP cavity length and differential pressure, and (b) the changes of the FP cavity length when the differential pressure is 5 kPa within 15s.
Fig. 5.
Fig. 5. The experimental setup for velocity measurement in a wind tunnel.
Fig. 6.
Fig. 6. The shift in the reflection interference spectrum of the DPFA sensor, FP cavity length variations and the real-time velocities [calculated by Eq. (4)] in the input airflow velocity range of 2.0 to 119.24 m/s, (a) the shift in reflection interference spectrum in the low-velocity range of 2.0∼37.74 m/s, (b) FP cavity length variations and the real-time velocities in the low-velocity range, (c) the shift in reflection interference spectrum in the high-velocity range of 59.29∼119.24 m/s, (d) FP cavity length variations and the real-time velocities in the high-velocity range.
Fig. 7.
Fig. 7. The response time of the DPFA sensor in the low-velocity and high-velocity wind tunnel respectively within the input airflow velocity range of 2.0∼119.24 m/s.
Fig. 8.
Fig. 8. Comparison between the measured airflow velocity by the DPFA sensor and the input airflow velocity obtained by the standard pressure transducer.
Fig. 9.
Fig. 9. The test process for flat-plate boundary-layer thickness.
Fig. 10.
Fig. 10. Variations of the FP cavity length and the real-time velocities (calculated by Eq. (4)) in the boundary layer and outer flow respectively.
Fig. 11.
Fig. 11. The longitudinal velocity profile in the turbulent boundary layer.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

I = I 1 + I 2 + 2 I 1 I 2 cos ( 4 π n L λ + π )
Δ L = 3 ( 1 γ 2 ) a 4 16 E h 3 Δ P
P l i m i t = 8 E h 4 5 ( 1 γ 2 ) a 4
u = 2 ( P 0  -  P s ) ρ
R e = U x ν
δ T  =  0.377 x R e 1 / 5

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