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Abstract
This paper presents a dielectric, all-optical thermal time-of-flight fluid flow velocity sensor. The proposed sensor utilizes a sequence of three short sections of optical fibers, which are positioned in a direction perpendicular to the measured fluid flow. One of these three fiber sections is highly doped with vanadium and acts as an optically controlled heater, while the other two fiber sections contain fiber Bragg gratings (FBG) that act as dynamic temperature sensors. The vanadium-doped fiber is heated periodically by a laser source, while observing temperature variations within the fluid flow downstream by the two fiber sections with inscribed Bragg gratings. The time delay in temperature variations recorded at both FBG sensors correlates directly with the flow rate of the fluid. When the sensor was placed within the glass capillary with inner diameter of 650 µm, it enabled a flow rate measurement range between 1 ml/h and 1200 ml/h. The sensor thus provides a broad flow-rate dynamic range and is insensitive to changes in losses in the lead optical fibers or optical heating source power fluctuations. Furthermore, the thermal properties of the measured liquid, for example, the liquid’s thermal conductivity and heat capacity, have mostly limited effects on the measurement results, which allows for thermal-principle-based flow velocity measurements in cases of liquids with variable or poorly defined compositions.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Flow rate is an essential physical parameter that needs to be measured in many different applications, ranging from the process industry to applications in biomedical systems. A variety of different principles are employed to meet the specific needs of a given metering application. Conventional mechanical principles, differential pressure flow rate devices, vortex flow sensors, and other similar flow rate measurement techniques are well proven, and find applications in macroscale applications; however they possess limited potential for miniaturization, and work well in restricted ranges of fluids’ rheological parameters. Conventional thermal flow rate measurement principles, such as calorimetric and anemometric principles, on the other hand, provide good miniaturization potential and straightforward technical realization, and are, thus, encountered commonly in micro-fluidic flow measurements` solutions. Conventional thermal principle microfluidic flow sensors usually depend on electrical heating (actuation) and electrical temperature detection, and have, therefore, limited potential for use at elevated temperatures, in chemically aggressive environments, electromagnetically polluted areas and explosive environments. Recently, many researchers have proposed the use of optical fiber sensor technology for applications in thermal flow metering, using several different operating principles [1–9]. In many studies fiber Bragg gratings (FGBs) and high attenuation fibers doped with cobalt or vanadium [2,4,6,8] were used to design calorimetric or anemometric fiber-optic arrangements. Other studies [3,9] used optically absorbing coatings, established onto the fibers, to generate heat for anemometric or calorimetric flow measurement. These approaches are based on King’s law, and depend on a fluid’s properties, like heat capacity, specific heat, viscosity, and others, which restricts the use of these approaches to liquids with a well-defined composition. Another important shortage of fiber-optic thermal sensors based on King’s law is their dependence on the changes in the heating optical power, as the delivered heating optical power affects the measurement result directly. It is well known from other sensor applications that maintaining precise and constant optical power, especially at the end of a remotely located fiber, is a difficult task, and with a limited achievable stability (this is one of the main reasons for the limited use of intensity based optical fiber sensors in most practical applications). Fluctuations in optical power at the heated end of the sensor thus, inevitably, lead to a reduction of the achievable measurement uncertainty. Recently, progress has been made in measuring flow rate with optical fiber sensors, and new approaches have been utilized. Oraie et al. [10] are using optofluidic waveguides to measure flow rate. Microbubble resonators in a Bernoullie effect configuration have been used by Chen et al. [11]. Lee et al. [12] have employed an NIR laser focused beam to heat the flowing water and measure the temperature change, to determine flow in a rather impractical setup. Liu et al. [13] used multiple FBGs and a heating fiber positioned in the end of a seven bore tubing to enable measurement of the flow vector in water.
One of the possible approaches that might mitigate the above mentioned limitations is to use measurement of the thermal time-of-flight (TTOF) among two points of interest within the fluid flow, while relying on the local modulation of the fluid’s temperature. In this approach, a time varying heat source is placed within the fluid flow, which creates local temperature variations within the same fluid flow. These temperature variations are detected downstream by suitable (dynamic) temperature sensor(s). The time delay between temperature variations at two spatially allocated points along the flow stream thus correlates directly with the velocity of the fluid in the observed flow stream. The TTOF approach can be implemented straightforwardly, especially in systems with smaller dimensions. It is also independent of fluid composition, and is not sensitive to variation of the heat source power. The first electrical TTOF flow sensors were demonstrated by Bauer [14]. Bauer used a very short electrical pulse to heat a thin wire (47 µs and 2.54µm, respectively) submerged in a fluid flow. The propagation of heated fluid was then detected through observation of a change in the resistance of a similar wire positioned downstream of the heated wire. The time measured between the heating pulse and temperature rise on the sensor wire was correlated inversely-proportionally to the velocity of the surrounding fluid. Ćerimovič et al. [15] proposed a combined micromachined TTOF and calorimetric approach with a heater in the middle and two temperature sensors positioned upstream and downstream from the heater. Ashauer et al. [16] have also employed TTOF and calorimetric principles, and have achieved good results for a measuring range from 0.1 to 150 mm/s. Ecin et al. [17] employed TTOF on a macro scale, utilizing thermocouples and a heating wire. The heating wire and thermocouples were positioned in the middle of the flow, which provided improved results, because the heat transport avoids the boundary layers at the wall of the flow channel/pipe. Crescini et al. [18] used a micro machined thick film device with a heater and two temperature sensors upstream and downstream to measure TTOF in the middle of the flow channel. Berthet et al. [19] positioned a micro machined heater and sensors in the middle of the flow channel, and used the TTOF regime with pseudo-stochastic heating pulses, and demonstrated a measurement range of 0.6–60 ml/h. All the above mentioned TTOF sensors, however, rely on electrical heating and electrical temperature detection, which limits their use to fluids and environments that allow the presence of miniature electrical systems.
In this paper we present an all-silica, all-optical, all-dielectric, microfluidic TTOF based fluid flow sensor. To our knowledge, this is the first successful attempt of TTOF utilization with optical fiber technology which yields a broad dynamic range and high resolution. The proposed sensor is highly insensitive to the variations or the changes of the heating power, which is rarely the case with other thermal flow rate sensors. Adequate utilization of the TTOF principle offers the ability to measure fluid flow of fluids with various thermal and rheological parameters, while requiring only limited composition related calibration adjustments.
2. Sensor design and operation
The proposed sensor utilizes three thinned optical fibers, placed perpendicular to the flow direction in a microfluidic channel. Heating power is delivered optically to the measured fluid through a short section of the first vanadium doped fiber (VDF). This fiber exhibits high optical absorption, and acts as an optically controlled heater that is modulated continuously sinusoidally over time by application of a properly modulated laser source. VDF thus generates periodically modulated temperature variation with the flow stream, which is further detected by a pair of spatially dislocated fiber Bragg grating (FBG) temperature sensors inscribed in the second and the third fibers, located further down the flow stream, as shown schematically in Fig. 1.
The proposed flow sensor was built within a glass capillary with an inner and an outer diameter of 650 µm and 1000 µm, respectively. The heating fiber consisted of a 150 µm long vanadium doped single-mode fiber (VDF), which was “sandwiched” between two sections of single-mode fibers. This configuration allowed for concentrated delivery of the heat into the geometrical center of the capillary. The used VDF was custom made. The production process and fiber properties are described in detail in [20] (the fiber used in this investigation was the fiber designated as fiber 3 in Table 2 of [20]). The VDF was initially drawn to 125 µm diameter with a core diameter of about 9 µm. The VDF had high optical absorption (1.2dB/mm @980nm), and was heated optically by a high power laser diode (HPLD). The optical properties and the other applications of VDFs have been described in detail in several publications [20–24]. Fibers with inscribed short FBGs (the FBGs were only 250 µm long), acted as short time response temperature sensors, and were located further down the flow stream. The distances between the heating and both sensing fibers corresponded to 500 µm, thus yielding a total sensor length of about 1 mm. The diameters of all three fiber sections (the fiber section containing the heater and two fiber sections containing FBGs) were reduced to about 35 µm, to shorten their response times. The joints between the capillary and fibers were further sealed by an epoxy glue. The experimentally produced sensor is shown in Fig. 2 under an optical microscope.
The manufacturing process of the proposed sensing structure is depicted in Fig. 3. The optical heater was made by a sequence of fiber cleaves and splices: An arbitrary long section of lead-in single-mode fiber (HI1060) was firstly cleaved, and then fusion-spliced to the cleaved end of the VDF, as shown in Fig. 4(a). This structure was then precision-cleaved under an optical microscope in such a way that the remaining VDF section was about 150 µm long. Another section of the single-mode fiber was then cleaved and spliced to the fiber structure containing the VDF [Fig. 4(b)]. The remaining spliced single-mode section was trimmed further in its length to about 1 cm. The fiber sensing sections containing Bragg gratings were inscribed in two standard SMFs (SMF-28e) using a femtosecond laser FBG inscription system. The high-index contrast achieved by femtosecond FBG inscription provides the possibility of creating short FBGs, as required by this application. The lengths of both inscribed FBGs were, thus, only 250 µm, with a resonance reflection of about 10%. Both fibers containing FBGs were further cleaved, around 1 cm from the ends of FBGs at one of their sides. All fiber tips (containing FBGs and VDF) were then etched in 40% HF, to reduce their diameters controllably to 35 µm, as depicted in Fig. 4(c). Fiber diameter reduction shortens the thermal time constant for the FBGs` sensor and, consequently, allows sensor operation and higher modulation frequency, which extends the operation range. The reflected spectrum of both FBG’s is visible in Fig. 3. Despite the low diameter of the etched fibers, we did not encounter any issues with the mechanical stability of the fibers or production issues. Three pairs of opposite-facing holes with a diameter of about 40 µm were created by a femtosecond laser micromachining system at the capillary walls, as depicted in Fig. 4(d). Hole pairs were spaced 500 µm apart. The etched fiber tips where then pushed through the pairs of capillary holes [Fig. 4(e)]. This was done manually under an optical microscope, and with the help of linear translation stages. Care was taken to position the FBGs and VDF in the center of the capillary. The holes were sealed with two component epoxy glue with high initial viscosity, to prevent penetration of the glue within the capillary. A fully assembled sensor is depicted in Fig. 2.
The sensor’s interrogation setup consists of two subsystems: A heating power delivery subsystem and a dynamic temperature measurement system with signal processing. The complete setup is depicted in Fig. 5. The heating subsystem consisted of the heating element with VDF, which was connected to the HPLD with an operating wavelength of 980 nm. The HPLD was connected to a current driver, which was further connected to a programmable signal generator. The HPLD was modulated continuously in time using sinusoidal amplitude modulation. The HPLD provided periodic delivery of the optical power to the heater, with a maximum peak output power of about 50 mW. The Programable Function generator allowed control over the frequency, shape and amplitude of the HPLD output power. The dynamic temperature measurement system consisted of temperature sensing FBGs, which were connected to a high-speed (1k samples/s) FBG interrogator (FAZ I4E). Bragg wavelength data were transferred in real time to a personal computer (PC) running LabVIEW code for further signal processing.
Sinusoidal modulation of optical power delivered to the VDF causes sinusoidal temperature modulation within the flow stream, which is detected by the FBG temperature sensor pair. Due to the spatial dislocation of both FBG temperature sensors, the flow velocity can be calculated as:
where d is the distance between the FBG sensors, and $\; \varDelta t$ is the time delay between the temperature signals detected by both spatially dislocated sensors. Since the sinusoidal modulation of the heating power was used, the recovery of time delay between the temperature sensors was obtained by measuring the phase difference between the detected temperatures (Bragg wavelengths) of both sensors. Time delay can, thus, be calculated from the phase delay as: where $\varDelta \varphi $ is the measured phase difference between the sinusoidal temperature signals recorded by both temperature sensors, and f is the HPLD modulation frequency. The phase difference between the temperatures at both sensors can, thus, be related to the measured flow velocity as:For our measurement setup it was ensured with the flow rate that the $\varDelta \varphi $ never exceeded 2π, because that would lead to measurement uncertainties. Volumetric flow Q is related to the measured flow velocity vf by the cross-section area A of the flow channel and the calibration flow constant αf, which depends on the flow profile, and shall, in general, be determined within a proper calibration procedure:
3. Experimental results
The proposed and experimentally produced sensor was configured and tested in two different liquid-flow control systems. The first system used a calibrated syringe pump [ Fig. 6(a)], which provided the possibility to set absolute flow rates over a broad range of flow rate values. The fluid that flew out of the sensor was further discarded into an open glass beaker. Connections between the syringe, sensor and waste beaker were made with silicon tubing with an inner diameter of 1mm. The second setup, shown in Fig. 6(b), used siphoning, while changing the height of the liquid in a siphoning glass beaker to control the flow rate. This approach was necessary to eliminate the noise in the flow rate created by the syringe pump operation (we also tested other pumps, but most of them created fluctuations in the flow rate that were in the range of, or above, the proposed sensor resolution). Siphoning provided a pulsation free and smooth flow, while allowing for small changes in the flow rate by changing the height of the liquid level in the siphoning beaker. Siphoning also allows for faster changes in fluid flow compared to the syringe pump system. The flow rate in the siphoning system was calibrated prior to conducting any tests by measuring the mass of the liquid that flew through the system in a known time.
In the first set of experiments, we demonstrated the proposed sensor operation by establishing a flow of Isopropyl Alcohol (IPA) with the flow rate of 60 ml/h and 120 ml/h through the sensor. Figure 7 shows the temperature variations measured at both sensors` FBGs, when the modulation frequency of the heating laser diode was set to 10 Hz, and when the heating peak-to-peak power amplitude corresponded to 50 mW. The phase difference among both signals corresponded to 39.7 degrees, which corresponds to a time delay of 11 ms for the flow rate 60 ml/h, and 23.4 degrees, corresponding to 6.5 ms for the flow rate 120 ml/h. To establish a continuous flow rate measurement through the sensor, the phase difference between both FBGs’ temperature signals was measured continuously over time. This was accomplished by performing a fast Fourier transformation (FFT) continuously on both FBGs` temperature versus time signals acquired within 1 s long time intervals. The phase difference between both temperature signals was then obtained simply by subtracting the phases of the components in the FFT that correspond to modulation frequency.
This provided a robust and noise-tolerant calculation of phase difference between both FBGs` temperature signals. The phase difference between both FBGs’ temperature signals was converted to a time delay, and, consequently, flow velocity, using Eq. (2) and Eq. (3), respectively. An example of measured time delay versus flow rate, using IPA and the above-mentioned modulation parameters, is shown in Fig. 8 for the flow rate between 0 and 200 ml/h.
The flow velocity and measured time delay are in inverse proportionality, as predicted by Eqs. (2) and (3). Figure 9 shows flow velocity calculated using Eq. (3) and the data in Fig. 8. Nearly linear correlation can be observed between the measured fluid flow velocity and induced flow rate. Potential reasons for the appearance of nonlinearity are discussed further below in the Discussion Section.
Another set of experiments was devoted to a demonstration of a sensor’s performance when operated over a broad dynamic range of flow rates, and when measuring flows of fluids with different thermal and rheological properties. The sensor was tested using isopropyl alcohol (IPA), ethanol, and water. The basic properties of the measured liquids are presented in Table 1.
Table 1. Properties of measured liquids.
To accommodate a wide flow range at good signal to noise ratio, we used three different thermal modulation frequencies. The thermal modulation frequency must be adapted to the flow rate, as the phase difference can become either very small or too large, leading to poor signal to noise ratio or unambiguous response when operating a sensor over a wide flow range. For example, when the phase difference between the temperature signals approaches zero, noise intensifies because the measured flow velocity has inverse proportionality to the measured phase difference. Therefore, the correct choice of modulation frequency is vital for the optimal acquisition of measurement results. Measured flow velocities versus experimentally set flow rates for operation of the same sensor at very different flow rates are shown in Figs. 10, 11, and 12. Flow velocity in a range of 1–10 ml/h was measured using 1 Hz modulation frequency, flow velocity in a range of 10–200 ml/h was measured using 10 Hz modulation frequency, and flow velocity in a range of 50–1200 ml/h was measured using 100 Hz modulation frequency. Well defined responses with nearly coinciding curves for all three used liquids were obtained for all selected measurement ranges. The left scale in Figs. 10–12 represents the measured flow velocity calculated using Eq. (3), while the right scale represents the measured flow rate calculated using Eq. (4), with α1 = 1.05, α10 = 1.53 and α100 = 3.15, respectively. α were determined experimentally using linear regression over the flow range. Potential reasons for frequency dependence of flow constants are discussed further below in the Discussion Section.
Figure 13 summarizes all the above measurements in a single logarithmic graph. Discontinuities in the measured results among curves can be observed when switching among modulation frequencies. These discontinuities can likely be attributed to the unavoidable partial conduction of heat through the wall of the sensor’s capillary, which introduces small, but non-negligible offsets in the measured results. The latter depend on the modulation frequency and ratio among the thermal conductivities of the capillary and measured liquid, and can, therefore, be eliminated from the measurement result by proper initial calibration. In general, Fig. 13 demonstrates clearly the ability of a sensor to provide consistent results over a very broad span of flow rates, and for fluids with substantially different properties, which can rarely be found in the flow rate, especially in thermal effect-based flow rate sensors. However, initial calibration is still required with respect to extraction frequency, and at least in part in respect to the fluid composition.
Fig. 13. Measured flow velocities for three different liquids at three different modulation frequencies (both scales are logarithmic).
Most thermo-optic fiber-based flow sensors reported in the literature [2,3,5,6,8,10–13] assume that the delivered heating optical power is known and constant. Deviation from this assumption usually translates directly into increased measurement uncertainty. The proposed sensor is, however, due to the application of the TTOF principle, highly tolerant to the variation in delivered heating power, as demonstrated by Fig. 14. Figure 14 shows the experiment where the flow rate was measured at three substantially different amplitudes of sinusoidal modulation optical power. The results in Fig. 14 demonstrate that there is no correlation between total delivered optical power to the vanadium doped fiber and the measured flow velocity. However, it should also be stressed that, at lower flow velocities, the delivered power shall be limited to prevent reaching the fluid’s boiling point, as this disturbs the flow and affects measurement. On the other hand, very low optical powers lead to the degradation of signal amplitude, and, thus, to reduced signal to noise ratio, which is reflected further in degradation of the measurement resolution.
The last set of experiments performed was devoted to experimental investigation of the proposed sensor’s measurement resolution. The sensor’s resolution was demonstrated at different flow rates using the siphoning setup shown in Fig. 6(b) (as already explained, siphoning was used to obtain a pulsation free and smooth fluid flow). For substantial changes in the flow rates through the sensor, we changed the height of the first (siphoning) beaker. For small changes in flow rate, we added a predetermined amount of liquid to the beaker, which changed the liquid level in the beaker, and, thus, increased the flow rate in small increments/steps accordingly. Predetermined amounts of liquid were added to the top beaker at about 20–25 s intervals to step-increase the liquid’s flow rate controllably over time to demonstrate the sensor’s response to small step changes in the flow rate. An example of the sensor`s resolution demonstration is, thus, presented in Figs. 15, 16, and 17 at initial flow rates of around 3, 21 and 225 ml/h, respectively. Modulation frequencies of 1, 10 and 100 Hz were used at these substantially different flow rates.
By comparing the sensor’s output change with the measurement noise levels in Figs. 15–17, we concluded that the sensor’s resolution was about 0.08 ml/h for modulation frequency 1 Hz, 0.07 ml/h for modulation frequency 10 Hz, and 0.2 ml/h for 100 Hz modulation at typical flow rates` ranges for the given modulation frequencies. Altogether, we can conclude that the proposed senor’s overall resolution was better than 0.2 ml/h in the flow range from 1 to 1200 ml/h, which corresponded to about 0.016% of the full-scale resolution.
4. Discussion
While the relationship between the flow rate and the measured time delay shall be linear in the TTOF method, experimental results indicate limited deviation from this predicted linear relationship. This nonlinearity in the sensor’s static characteristics depends both on modulation frequency and fluid composition. It should, however, be stressed that, once the modulation frequency is selected, relatively significant fluid composition change will have limited effect on the measurement result, usually at the edges of the measurement range. Also, the above results show sensor behavior when the modulation frequency was varied significantly, i.e., by a factor of 100. While we did not investigate in detail all the possible effects that lead to this non-linear behavior, several possible causes might be responsible for its appearance. The authors believe that in the current experimental setup and at low modulation frequency, a notable portion of the heat transport is accomplished through the capillary wall. Another phenomenon that may increase the nonlinearity in response, is heat transfer within the measured liquid. Furthermore, at high flow rates and high modulation frequency, the authors believe that dispersion of the traveling heat profile occurs. Both phenomena are modulation frequency and fluid/capillary composition dependent, and can affect the time delay between both temperature sensors. Heating power reduction also leads to reduction of temperature amplitude measured by both FBG sensors, and, consequently, the reduction of power reduces the signal to noise ratio. In Fig. 7 it is also evident that the second FBG receives substantially reduced thermal excitation when compared to the first FBG; we believe that the heat dispersion influences this effect considerably. Therefore, care must be taken that the fluid flow is not too low for the chosen frequency, as the system would not be able to calculate the phase component from the 2nd FBG`s signal. While in most practical cases frequency can be set in a way that phase difference never exceeds 2π during measurements, in a high dynamic flow-rate measurement, a dynamic frequency adjustment might however easily be implemented to prevent ambiguity of phase measurement, i.e., measurements could always start with low frequency excitation, which would be then increased to improve SNR at the target flow rate.
5. Conclusions
An all-fiber, all-silica microfluidic thermal time-of-flight flow sensor was presented in this paper. The sensor was based on a short section of vanadium doped fiber, which was heated optically and periodically in time by a medium power laser diode, while two FBG temperature sensors, placed downstream the fluid flow, acted as dynamic temperature sensors. The time delay in temperatures measured at both FBG sensors was used to determine the flow velocity at the sensor. The sensor was packaged in a capillary with a diameter of 650 µm, and tested for different flow rates using fluids with different thermal and rheological properties.
The proposed sensor shows three distinctive attributes. Firstly, the sensor is insensitive to fluctuations and even larger changes in amplitude of the modulation power, which usually affects calorimetric and anemometric setups adversely, and is of special concern in fiber-optic systems, where full stabilization of the optical power at the measurement site is often difficult to achieve. Secondly, the sensor can be operated over a very broad dynamic measuring range with high resolution, especially when dynamic adaptation of the modulation frequency is applied. The experimental version of the sensor was, for example, demonstrated for flow rate measurements between 1 ml/h and 1200 ml/h, with resolution exceeding 0.016% of the full measurement span. Finally, the sensor`s performance was also demonstrated using three quite different liquids: water, isopropyl alcohol, and ethanol, with very limited offset in the measurement results, requiring only limited correction of measurement results. This contrasts with most calorimetric and anemometric setups, which require significant calibration of the sensor`s operating parameters to a particular measured fluid, and limits their use in liquids with variable composition. The proposed sensor also possesses all the advantages associated with fiber-optic sensors, such as, for example, dielectric and chemically inert design, electrical passivity, immunity to electromagnetic interference, small size and biocompatibility. The proposed sensor can measure the flow velocities of aggressive fluids, and enabled use of long lead-in fibers to measure flow in remote locations, separated from the opto-electronic interrogation unit. The presented sensor is based on a capillary with an inner diameter of 650 µm. We believe that upscaling and downscaling of the proposed sensor is possible. Even a free-flow setup should be possible with the sensor freely submerged in the flowing liquid. While other flow sensing solutions may offer even better dynamic range and/or sensitivity [15], none of the existing solutions offer the above described advantages delivered by optical fiber sensing principles.
Funding
Javna Agencija za Raziskovalno Dejavnost RS (P2-0368); (J2-8192).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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