Flow measurement is crucial in many fields, such as chemical manufacturing, the oil and gas industry, and water transportation. A conventional method for measuring flow fields is based on hot-wire anemometry [1]. The rate of heat removal from the electrically heated wires or films to the surrounding flow is a measure of the incoming flow velocity. Several flow measurements have been developed for time-of-flight flow sensing [2–6], differential pressure methods [7–10], and heat-transfer enhancement [11–18]. With the development of fiber-optic sensor technology, an increasing number of flowmeters have been proposed that combine traditional flowmeter concepts and various fiber-optic technologies [19–24]. Fiber-optical sensors have some potential safety in situations with strong radiation or flammable and combustible materials, and have some merits of intrinsic safety, high sensitivity, long lifetime, and antielectromagnetic properties. Another advantage is that measurements of changes in temperature or mechanical strain are determined by a shift in the initial Bragg wavelength. Fiber Bragg grating (FBG)-based flow sensors have also been reported, using several different design methods [25–30]. An FBG is an optical element placed within an optical fiber by creating a set of gratings at specific grating periods. The choice of wavelength-shift-detection method in the FBG flow sensor depends on the intended application. Therefore, the noise level and measurement bandwidth of the detection system should be considered in the detection method. In our previous work, a constant-temperature-difference flow sensor based on FBG sensing and hot-wire anemometry was reported and demonstrated [30]. The FBG flow sensor was affected by the ambient temperature fluctuations.

In this study, we propose an improved gas-flow fiber sensor with two FBG sensing regions in an optical-fiber sensor. To ensure robustness against ambient and transient temperature fluctuations, the proposed sensor consists of two FBGs used as the upper and lower sensors on the optical fiber. A Ni-Cr coil heater is used to operate the resonance-wavelength shift in the FBG sensor. The coil heater is wound around the FBG region of the fiber, and a constant current source is supplied to the coil for heating. Because the heating power in the FBG region induces a change in the refractive index, the Bragg wavelength can be shifted. The sensor can detect the amount of fluid by measuring the change in the Bragg wavelength of the FBG, as the temperature of the FBG sensor surrounded by the coil could change based on the fluid flow in the gas pipe. We evaluate the feasibility of the proposed sensor, which exploits the difference in the Bragg wavelengths of the FBGs.

2.1. Sensor Structure and Working Principle

This study presents an optical-fiber sensor for gas flow that works by measuring the temperature difference between two sensing parts. An optical-fiber grating is a type of distributed Bragg reflector fabricated in a short fragment of optical fiber, and the FBG is based on the characteristic that when temperature variation occurs in the FBG, the period and refractive index of the fiber grating change accordingly, such that the Bragg wavelength is shifted. Figure 1 shows a schematic of the proposed flow sensor, which is composed of two FBG-based temperature-sensing units surrounded by a Ni-Cr coil heater. The two FBGs are fabricated using single-mode (SM) fiber. The length of the two uniform FBGs in one optical fiber is 27 mm, and each FBG has a different center wavelength (1,534.27 nm and 1,530.16 nm respectively). The distance between the two FBGs is 125 mm. The coil heaters have a diameter of 210 μm and resistance of 30 Ω. The coil has a length of 30 mm, surrounding the entire FBG. Note that the refractive index of a single FBG written on a commercial SM fiber can be partially changed by local heating of the FBG region.

Figure 1. Schematic of the multiple-FBG flow sensor surrounded by a Ni-Cr coil heater. Insert: the coiled heater, with FBG.

The Bragg wavelength is defined by

(1)$${\lambda }_B=2n_{eff}\Lambda$$

where neff and Λ are the effective refractive index and grating period of the FBG respectively. The Bragg-wavelength changes with the effective refractive index and grating period. When the grating is affected by strain and ambient temperature, the Bragg-wavelength shift (ΔλB) is expressed as follows [31]:

(2)$$\Delta {\lambda }_B\approx 2\left(\Lambda \frac{d{n}_{\text{eff}}}{dL}+n_{\text{eff}}\frac{d\Lambda }{dL}\right)\Delta L+2\left(\Lambda \frac{d{n}_{\text{eff}}}{dT}+n_{\text{eff}}\frac{d\Lambda }{dT}\right)\Delta T$$

where L is the grating length, ∆L is the change in grating length, T is the temperature, and ∆T is the change in temperature. The first and second terms on the right-hand side of Eq. (2) are related to strain and temperature respectively. In our study the axial strain of the FBG in this system can be ignored, because the measurements of the flow sensor depend mainly on the temperature change of the FBGs. The Bragg-wavelength shift (ΔλB) can be expressed as [31]:

(3)$$\Delta {\lambda }_B\approx 2\left(\Lambda \frac{d{n}_{\text{eff}}}{dT}+n_{\text{eff}}\frac{d\Lambda }{dT}\right)\Delta T$$

where the first term in Eq. (3) is related to the thermo-optic effect, which results in a change in the refractive index, whereas the second term of the above equation is related to thermal expansion, which causes a change in the grating period.

The factors affecting the Bragg-wavelength change include temperature, strain, and pressure. However, in this study we assume that the most influential factors on the FBG are the heat generated by the coil heater and the heat reduction due to the gas flow.

The working principle for all known variations of the thermal FBG flow sensor is schematically explained in Fig. 2. The air flows through a small tube. Thermal FBG sensors are placed at S1 and S2, downstream (FBG1) and upstream (FBG2) respectively. The resulting temperature profile in the tube is plotted while constant electrical power is supplied to the coil heater. The temperature profiles of the two sensors are symmetrical at zero flow (flow = 0) because the temperature at the location of the coil increases momentarily. When the flow is turned on (flow > 0), the temperature profile is asymmetric because the temperature distribution is distorted by heat diffusion.

Figure 2. Working principle of the flow sensor with FBGs and heaters.

With any forced gas flow, the thermal flow resulting from FBG2 can add a small amount of heat to the flow in the FBG1 region, and thus the heat loss of FBG1 is slightly smaller than that of FBG2. The resulting temperature difference between FBG1 and FBG2 is a measure of the air flow, because the Bragg wavelength is shifted by the refractive-index change in the fiber and fiber elongation. With increasing flow, Δλ_B2 (the shift in the Bragg wavelength of the FBG2 sensor) is slightly greater than Δλ_B1 (of the FBG1 sensor), because the heat loss of FBG2 placed upstream is slightly larger than that of FBG1 downstream.

2.2. Measurement of FBG Flow Sensor

The experimental setup shown in Fig. 3 is utilized to characterize the FBG gas-flow sensor. The sensor is composed of two sensing FBGs wound by a heating coil, two current sources, a wide-spectral-range light source, a fiber coupler, an optical-spectrum analyzer (AQ6317B; Ando Electric Co., Kanagawa, Japan), a nitrogen gas chamber, a standard ball flow meter, and Teflon-PFA tubing. Two sensing FBGs and heating coils are integrated into the measured flow line, with an inner diameter of 10 mm. The spectral data are obtained in the wavelength range 1,528–1,537 nm with a high-wavelength-resolution mode of the optical-spectrum analyzer. Pure nitrogen from the gas chamber continuously flows in the test-flow tube and the full range of gas-flow rate is set to 25 ℓ/min, which is regulated by the calibrated flow meter with a resolution of 1 ℓ/min. In the case of the internal flow in the pipe, the flow rate is affected by the structure of the sensor. It is assumed that the size and shape of the gas pipe used in the experiment are constant, and that the flow rate at the inlet and outlet of the gas pipe is steady.

Figure 3. Schematic of the experimental setup used for sensor characterization.

The anemometry principle is applied to these measurements. In our previous experiment, an FBG sensor kept downstream of a heating element placed in the flow path was used to measure the temperature variations. The measured temperature was proportional to the gas-flow rate, which provided higher heat dissipation at higher flow rates. However, that method is characterized by heat consumption in the gas stream, which is undesirable in the case of temporary ambient temperature drift by the air stream. To improve the previous design, we propose a different approach that uses two FBGs in one fiber sensor. This provides more stable and accurate results when measuring the temperature difference between the two FBGs.

When the coil is heated by the setup current from the current source and nitrogen gas flows into the channel, the coil heater cools down depending on the flow speed of the gas. Thus a single Bragg wavelength of the FBG is shifted, owing to the high dissipation of heat by convection at high flow rates in the heating unit. As the gas flows through the pipe it begins to dissipate heat from the coil heater, which leads to a reduction in the temperature around the sensor, finally reaching a thermal equilibrium state. Therefore, the temperature difference between FBG1 and FBG2 in the sensor reaches a stable value. By measuring that temperature difference, the flow rate of the gas in the tube can be estimated. In the thermal equilibrium state, the shift in the reflected wavelength of the FBG is stabilized, and the flow rate can be measured using the proposed sensor. This indicates that the response time of the sensor is related to the thermal equilibrium state. Assuming that the size of the pipe in which the sensor is installed is constant and the flow rate stable, the response time of the sensor is also related to the measurement sample, flow rate, and thermal diffusion time [32]. Although various factors are related to the flow rate and temperature diffusion, only the thermal equilibrium state for the flow rate and temperature diffusion is considered in confirming the feasibility of the proposed sensor. Particularly because the optical fiber sensor is made of glass [thermal conductivity: 0.8 W/(m K)], it can be considered that it is less sensitive to ambient heat than metal [aluminum thermal conductivity: 205 W/(m K), copper thermal conductivity: 385 W/(m K)] [33].

The feasibility of the proposed sensor, which uses the difference in the Bragg wavelengths of the FBGs, is evaluated through experiments. The first experiment measures the change in the Bragg wavelength of the sensor at applied currents ranging from 40 mA to 120 mA, in 20-mA steps. The second experiment is conducted at six flow rates at an applied current of 120 mA. The Teflon-PFA tube can undergo thermal deformation or thermal damage when a high current is applied; a current of 120 mA is reasonable, to prevent thermal deformation of the tube.

Figure 4 shows the wavelength spectra of the two FBGs in terms of the change in applied current. A current source is used to generate the electrical power of the coil heater. When currents of 40, 60, 80, 100, and 120 mA are supplied to the coil heater, the temperature of the FBGs is raised by resistance heating. Device operation is based on the thermally induced refractive-index variation of the FBG optical fiber using a coil heater. The Bragg wavelength shifts to a larger value because the volume of the FBG sensor increases according to its thermo-optical coefficient, and the width of the resonant-wavelength peak slightly widens as the current increases. In this experiment, the unheated Bragg-wavelength peaks of the two FBGs appeared at 1,534.27 nm (FBG1) and 1,530.16 nm (FBG2). Figure 5 shows a plot of the Bragg-wavelength shifts of the FBG sensors as a function of applied current. From these plots the sensitivities of the measured FBG1 and FBG2 sensors are 15.0 pm/mA and 14.0 pm/mA respectively, and the linear relationships are experimentally confirmed during repeated tests. This result shows that the sensor can be used in temperature-sensing applications.

Figure 4. Wavelength spectral responses according to the change in applied current, under no gas flow: (a) FBG1 sensor, and (b) FBG2 sensor.

Figure 5. Shift in resonant wavelength as a function of applied current, when there is no gas flow: (a) FBG1 sensor, and (b) FBG2 sensor.

For the flow measurement, the FBG-sensor head in Fig. 1 is installed in a test tube with a diameter of 10 mm, as shown in the experimental setup of Fig. 3. The flow rate is controlled by a rotameter. We measure the wavelength shift based on gas-flow rates ranging from 0 to 25 ℓ/min, at an applied current of 120 mA; the results are shown in Figs. 6 and 7. Although slightly nonuniform thermal profiles appear in the FBG reflection spectra, the well-defined wavelength peaks of the FBG spectra can be effectively used to determine the flow sensing of the proposed sensor. The operation of the heated FBG sensor is similar to that of metal-based hot-wire-anemometry flow sensors. The flow sensitivities of the proposed sensor were 11.7 pm/(ℓ/min) (at FBG1) and 10.9 pm/(ℓ/min) (at FBG2) within a linear region, and a reasonably linear relationship is found in repeated tests.

Figure 6. Wavelength spectral response according to gas-flow rate, at a current of 120 mA: (a) FBG1 sensor, and (b) FBG2 sensor.

Figure 7. Bragg-wavelength shift according to gas-flow rate, at a current of 120 mA: (a) FBG1 sensor, and (b) FBG2 sensor.

When the gas flows into the tube, the heat energy from the coil heater around the FBG sensor is transferred to the gas flow, which reduces the temperature of the FBG sensor and shifts its Bragg wavelength. Figure 7 shows the Bragg-wavelength shift with respect to the gas-flow rate. The Bragg-wavelength shifts of sensors FBG1 and FBG2 exhibit linear relationships for N₂ gas-flow rates in 5 ℓ/min steps. To obtain improved results, the difference in the Bragg wavelengths of the two FBGs at each flow rate is acquired. Figure 8 shows the difference in the Bragg wavelengths of the two FBGs at gas-flow rates ranging from 0 to 25 ℓ/min, at a current of 120 mA. The experimental results show that the proposed FBG sensor has excellent linearity within our measurement precision. The measured sensitivity of the sensor is 3.2 pm/(ℓ/min) at the coil current of 120 mA within the linear region.

Figure 8. Sensor response obtained from the Bragg-wavelength difference of the two FBGs for flow rates of 5 ℓ/min and higher, at a current of 120 mA.

As previously mentioned, a flow sensor with a single FBG can suffer a transient ambient temperature drift in the flow channel, which leads to measurement error in the Bragg-wavelength-shift curve of a single-FBG sensor. However, the wavelength-difference curves of the two FBGs here are independent of temperature fluctuation caused by flow fluctuation in the flow channel, as indicated in Fig. 8. Consequently, the proposed sensor using the wavelength-difference method is resistant to temperature fluctuations.

The proposed flow-rate sensor is notably effective when the temperature of the coil is sufficiently high. Therefore, it has the limitation that it can only be used for nonreactive gases, due to concerns about explosiveness at high temperatures. Additionally, if the lengths of the two FBGs are different due to the manufacturing process, the temperature change owing to the flow rate is different. Therefore, to optimize the sensor for field applications, it is necessary to perform additional analyses of e.g. structural changes (the length between the two FBGs, the coil heater, and the location of the sensor in the tube) and long-term measurements.

Although this sensor shows good performance only with nitrogen gas, it is clear that the proposed FBG sensor could be applied to measure flow rates of other types of gas, and other physical variables (pressure, strain, etc.) in future research . It is also possible to enhance the accuracy and stability of the sensor and increase its operation range by changing the sensor configuration and employing different flow-packaging and heating techniques.

In this study, two FBGs in a SM fiber wound by coil heaters to measure gas-flow rate were presented. The gas-flow rate was obtained by monitoring the difference in the Bragg-wavelength shifts of the two FBGs, which demonstrated features that exclude the effect of temperature fluctuations. The obtained results showed that the sensor had accurate linear characteristics at flow rates from 0 to 25 ℓ/min. The measured sensitivity of the sensor was 3.2 pm/(ℓ/min) at a coil current of 120 mA. The proposed sensor with two FBGs exhibited excellent linearity within our measurement precision because of the independent characteristics of temperature fluctuations. A sensor with a single FBG can lose linearity in its response, owing to environmental changes. However, the proposed sensor with two FBGs was independent of physical variables such as temperature. Because the sensing properties of the two FBGs can simultaneously change according to the physical variables, the response obtained from the difference in the Bragg wavelengths of the two FBGs was independent of the physical variables. The merits of this FBG sensor and its excellent performance make it a potential candidate for flow monitoring in the gas industry.

The authors declare no conflicts of interest.

Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.

The FBG materials used in this study were provided by Dr. Nam-Kwon Lee of the Convergence of IT Devices Institute of Busan.

Korean Institute of Marine Science and Technology Promotion (KIMST) (Grant Number 20170263).