Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Distributed temperature profile in hydrogen flame measured by telecom fiber and its durability under flame by OFDR

Open Access Open Access

Abstract

The distributed temperature profile of hydrogen flame based on optical frequency-domain reflectometry (OFDR) was experimentally demonstrated for the first time. Spatial temperature field at different flow rate of H2 flame was monitored by OFDR via a telecom fiber (Corning SMF-28, CPC6) inside the flame over seconds, and the highest temperature is on the sides of center flame separated by ∼1.4mm with difference of 140∼190°C over the flame dimension of 2.5 mm above 900°C. Uniformity level of temperature is studied by varying the distance between fiber and tube entrance, and the largest uniform region over 1-millimeter length of fiber is obtained. Rayleigh scatters correlation coefficient decreases with temperature to 90% around 400°C, further reduces to 70% about 800°C, and 50% roughly at 1000°C. It indicates that a nonlinear thermal sensitivity of SMF is expected for temperature higher than 400°C with OFDR measurement. The durability of single-mode fiber under H2 flame is studied via decorrelation time at various temperature. It maintains 20s at 880°C with correlation coefficient around 68% and drops to 50% decorrelation at 1000°C over 20s. This information is important for high temperature measurement using telecom fiber over 800°C based on OFDR. A maximum temperature of 1100°C was measured by OFDR, and it is possible for higher temperature measurement beyond of 1100°C with quicker system response time (<1s).

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1 Introduction

Optical frequency-domain reflectometry provides both the high sensitivity and spatial resolution necessary by measuring the localized Rayleigh scatter pattern. Owing to its wide tunable range and interferometric configuration, it offers great spatial resolution on strain and temperature measurement. The basic working principle is based on the assumption that amplitude and phase pattern of local Rayleigh spectra have a static random property over the fiber length, which can be modeled as a long, weak fiber Bragg grating (FBG) with a random period. The small density fluctuations are introduced locally during the fiber fabrication by the presence of nonuniform strain. Engendered by these random inhomogeneities, each scatter could be viewed as a collection of local scattered electric-dipoles when encountering a traveling electromagnetic field. As laser frequency is tuned continuously, scattering amplitude and phase are recorded subsequently along the entire fiber. Due to the confinement of fiber waveguide design, Rayleigh backscattering profiles is generated as a function of time. And this profile can be resolved along the fiber location and it varies with temperature and applied strain. Compared with reference profile, spectral shifts were accordingly reconstructed with respect to the time and fiber location by cross-correlation method [1].

A high temperature environment built with radiation, conduction, or convection could be involved with natural and industrial process. Distributed high temperature measurement based on OFDR has been a challenge in those extreme conditions. The modified FBG (Type II fs-IR) by femtosecond laser can endure over 1130$^{\circ }$C with a relative 2000 GHz frequency shift ($\sim$16 nm wavelength shift) and single mode fiber of 950$^{\circ }$C has also been measured in a furnace with 1600 GHz frequency shift ($\sim$12.8 nm wavelength shift) [2]. It is noted that single mode fiber subjected to the plasma radiation of electric arc can be measured with maximum spectral shift of 21 nm during the short arc excitation time of few seconds [3]. The thermal sensitivity of SMF and silica-based FBG have been studied at different range from room temperature to 1000$^{\circ }$C [46], respectively. It is also found that silica-based fiber sensors show different thermal sensitivity with various packaging and coating materials [7, 8]. Improvements of temperature range on telcom fiber have also been achieved by adaptive algorithm [2]. However, it is still unclear that how long does the commonly used temperature and wavelength shift relation, i.e., 10 pm/$^{\circ }$C the silica fiber maintain under high temperature, especially when it is close to the glass softening range, at which gradual rearrangement of glass network occurs. The sustained linearity of SMF under high temperature could be critical for the reliable measurement.

Different from conduction or convection heating, radiant heat released from plasma or $\gamma$-ray can be faster and storing higher density of energy. It is important to investigate fiber durability under this type of heating for sensing application, such as micro-combustion system, mining and nuclear industry. Converse to the nitrogen irons emission induced by high-voltage splicing arc [3] and $\gamma$-ray dose [9] arising from the radioactive decay of atomic nuclei, hydrogen flame exhibits broad black-body spectrum from UV to IR, which enables the sufficient energy exchange with vitreous silica fiber under test. The resulting temperature rises up from 1500 to 2100$^{\circ }$C [10, 11] and significant thermal gradient appears from inner core to outer shell. Design of micro power system as stable energy source with decent combustion efficiency has received considerable attention [12] and giving a general characterization of thermal distribution becomes essential for further optimization. In terms of microfiber fabrication, establishing a uniform flame zone is key to tapering with small core diameter [13]. The characterization of temperature gradient surrounding the fiber in situ could make the fabrication repeatable and reliable. Conventionally, flame temperature is measured with CARS (Coherent Anti-Stokes Raman) technique [14] or computed tomography with CCD camera [10], while estimation of the temperature distribution with optical lens, especially for inner flame core, could inevitably introduce large uncertainty due to image distortions. Long exposure time and lower spatial resolution may also lead to compromise on detailed dynamic features.

In this study, we proposed a novel method to measure the distributed temperature of hydrogen flame by using telecom fiber based on OFDR, which is capable of making spatially distributed measurement within micrometers to meters. Spatial temperature profiles are obtained in combustion with varied ${\rm H_2}$ gas flow rate. The temperature gradient over the flame is monitored by telecom fiber, and its durability time under high temperature is studied by Rayleigh spectrum correlation method. 16 nm spectral shift up to a few seconds with equivalent 1100$^{\circ }$C is measured after numerical calibration. The soften condition essentially determines the upper limit of exposure time that placing telecom fiber under extreme high temperature for sensing, which permanently change the silicate structure and eventually the spectral shape of Rayleigh scatter pattern. This allows us to estimate fiber durability time (fiber operation time) under radiation heating of hydrogen flame via a decorrelation time through spectral shift measurement in OFDR system at different decorrelation level, quantitatively, when the correlation coefficient drops to a certain percentage. To our best knowledge, above 1050$^{\circ }$C a dropping time to 50% correlation could take a few seconds, which demonstrates the capability based on Rayleigh scattering of telecom fiber for high temperature measurement.

2 Principle and experimental setup

The OFDR setup designed for distributed high-temperature measurement with hydrogen flame combustion is shown in Fig. 1. Initially, a tunable laser source (TLS, New-Focus-Venturi-TLB-6600, Newport Corporation, Irvine, CA, USA) is coupled into fiber and further split into two parallel branches of Mach-Zehnder interferometer configuration. One of which functions as auxiliary interferometer (AUI), circled by a dashed square. The output of AUI played as an external clock for data acquisition, known as frequency-sampling method and widely adopted for its accuracy and convenience in coping with the nonlinearity of laser tuning [15]. Another branch named as main interferometer (MI), splitting light into reference and probe arms, is used for the interrogation of fiber under test. Light propagating in the probe arm is further guided by a circulator and routed back into a coupler. Interfered with local reference, it generates detectable beat patterns, eventually collected by photodetector and digitized for post data processing. Considering a wavelength tuned linearly by the laser, light propagating in the reference arm arrives at the photodetector prior to that in the probe arm, which leads to a time delay between two arms and hence the delay corresponds to the frequency of generated beat signal. Essentially, for a certain wavelength, traveling time of light in a single mode fiber (SMF) depends on the product of local refractive index n and its physical length l. Assuming dispersion within small region of SMF is negligible, local refractive index of SMF can be replaced by an effective value. The corresponding spatial resolution $\Delta$z in Rayleigh scattering measurement is determined by the spectral bandwidth of tuning range and given by:

$$\Delta z = \frac{\lambda_i\lambda_f}{ 2n_g\Delta\lambda},$$
where $n_g$ is the group index of the silica fiber assumed as constant value 1.47, $\lambda _i$ and $\lambda _f$ are initial and final wavelengths, $\Delta \lambda$ is the total scanned wavelength range for the measurement. In this setup, the laser scanned from 1520 to 1620 nm, which corresponds to a spatial resolution $\Delta$z approximate to 7.6 $\mu$m.

 figure: Fig. 1.

Fig. 1. Schematic of optical frequency-domain reflectometry system for hydrogen flame measurement. TLS: tunable light source; FRM: Faraday rotating mirror; PD: photodetector; BPD: balanced photodetector. Circled by a dashed square, an Auxiliary Michelson interferometer was configured as a clock generator for digital acquisition, armed with a 25-meter length of delay fiber and two Faraday rotating mirrors. An inset at top right showed a front view of solid tube located closely underneath a tested fiber, which were indicated respectively in a white arrow. Combustion diagram at bottom left showed a basic layout with a telecom fiber placed in the flame core for temperature measurement along the x axis. Capital L represents the vertical distance between fiber and nozzle along the z axis.

Download Full Size | PDF

Inset of Fig. 1 partially shows the combustion layout: a cylindrical stainless tube with an inner diameter of $\sim$8.7 mm was standing vertically as a gas channel, which was directly underneath a bare optical fiber with its coating mechanically stripped. Non-premixed hydrogen fuel was generated continuously by a commercial water electrolysis device (QL-300, Hydrogen Generator), and under control of a gas mass flow controller (FMA5506, OMEGA). The combustion setup was built in a semi-closed chamber using plastic partition. The flame of given gas in quiescent air was considered as a typical laminar flow without magnificent turbulence occurring, and the presence of fiber is negligible for the temperature distribution of flame.

For the temperature distribution measurement, the tuning rate of the light source was set to 100 nm/s, hence the auxiliary interferometer armed with a 25.0 m length of delay fiber generated a sampling rate of 3.2 MHz for Digital Acquisition (DAQ). Each trace took up 1.13 second in a complete scan and being detected by a photodetector (Thorlabs-PDB130C). Eventually, a 3.4 mega-sample of raw data was collected by digital acquisition card (NI-PCI6115) for post process. The flow rate was controlled from 2.0 to 7.5 mL/min by steps of 0.5 mL/min separately for each measurement. As the fuel was sparked by a butane lighter, fiber was then heated up for seconds before starting measurement. Considering glass transition occurs once temperature goes above certain threshold, the gas fuel supply was immediately terminated after measurement. And minutes of the time was reserved for equilibrium condition so that combustion system and heated fiber could be cooling down to the room temperature prior to requiring new reference. It avoids introducing artificial errors as maintaining the same referential condition is required for relative measurement by OFDR. Similar procedure was implemented as well for the temperature profile when fiber position relative to flame core varied with vertical distance from 0 to 200 $\mu$m by steps of 25 $\mu$m through a high precision stage while flow rate maintained constant at 4.5 mL/min.

For small range of temperature measurement by OFDR, spectral shift has approximately shown linear dependence on a change in temperature for telcom fiber, so good estimation can be safely made from linear correspondence. However, it turns to be nonlinear at transition temperature, which gave rise to a large deviation from the linear estimation shown in Fig. 2. Therefore, temperature conversion was implemented by evaluating spectral shift with a numerical method. As the real temperature is unknown due to the limited technique for calibration, assumption has been made by referring to the thermal sensitivity of a Type II fs-IR FBG, which was experimentally tested in a furnace [6]. Cubic fit was applied to this conversion by using a least squares method with three slope rates separately at 50, 500, 1000$^{\circ }$C and the known room temperature ($\sim$22$^{\circ }$C). The relationship between wavelength shift and estimated temperature was constructively characterized by the three-order polynomial, and hence the temperature can be estimated by solving the following cubic equation:

$$\Delta S = \left( 6.0819\times10^{{-}10}\right) T^3+\left(2.8827\times10^{{-}6} \right) T^2+\left(1.0872\times10^{{-}2}\right) T - 0.2406$$
where the $\Delta S$ is the wavelength shift in unit of nm compared to the Rayleigh spectrum at 22$^{\circ }$C, and $T$ is the temperature $^{\circ }$C for the flame. The resolved relationship in between is then shown in Fig. 2, where a black, solid-dot line was the calibrated temperature converted by the measured spectral shift while a black dashed line determined a temperature value at higher spectral shift. It was found that this relation also fits reasonably from room temperature to 1000$^{\circ }$C [4, 5]. The associated thermal sensitivity of silica fiber varying at different wavelength shift is estimated in red, solid dot line, which starts from $\sim$11 pm/$^{\circ }$C at room temperature, increases linearly to $\sim$14 pm/$^{\circ }$C at 500$^{\circ }$C, and rise over $\sim$18 pm/$^{\circ }$C at 1000$^{\circ }$C. The red dashed dot line gives a tendency of thermal sensitivity for higher temperature associated wavelength shift, which shows a $\sim$22 pm/$^{\circ }$C of thermal sensitivity at 1300$^{\circ }$C.

 figure: Fig. 2.

Fig. 2. Evaluation of temperature and thermal sensitivity in terms of the given spectral shift in ignorance of the coating or packaging effect on the interrogated fiber. The wavelength shift was initially obtained by cross-correlation method and the conversion relationship was constructed by the three-order polynomial. (i) The black, solid-dot line gives a general estimation that was adopted for the rest temperature conversion. The black dashed line forecasts the temperature changes associated wavelength shift; (ii) the red, sold line is the thermal sensitivity associated with converted temperature for wavelength shift, and the red dashed line is the estimative thermal sensitivity intended for higher wavelength shift.

Download Full Size | PDF

Grating inscribed by femtosecond laser represents the refractive index modulation introduced delay time. While hydrogen flame induced black body radiation, which heats the optical fiber by extended fiber length in addition to the refractive index change. Wavelength shift is directly related to phase shift and temperature should have linear relation due to thermal heating in which case the induced length change is dominating, and refractive index change plays minor role. As to the case that both of the refractive index and length are changed due to high temperature, the wavelength shifts and temperature will start showing nonlinear relation, as show in red curve with some bending at 500-600$^{\circ }$C. Since the process is asymmetric, likely in the third-order expansion term.

3 Experimental results and data analysis in discussion

The interference pattern of signal, including amplitude and phase information, was digitized for post data processing, which involved three main steps to retrieve the signal of interest. In the first step, fast Fourier transform (FFT) was performed to convert both measurement $i_m(\nu )$and reference $i_r(\nu )$ traces into time domain. Rayleigh scattering intensities as a function of fiber location was initially reconstructed by $\tilde {I}_m(\tau )$ and $\tilde {I}_r(\tau )$. Next, a certain length of window was selected to filter out the region of interest labeled as and its local spectrum was recovered via inverse fast Fourier transform (IFFT). It is noted that there is a trade-off between spatial sensing resolution and required sensitivity over the window length. In our data analysis, a spatial sensing resolution of 346 $\mu$m was applied to the distributed measurement and corresponding temperature resolution is $\pm$2$^{\circ }$C, and the step between two consecutive windows is 7.6 $\mu$m for the following data processing. Spectral shift was finally determined with zero-mean normalized cross-correlation (ZNCC) method, which is commonly used to correlate two Rayleigh spectra of interest between measurement $\tilde {\tilde {I}}_m(\nu )$ and reference $\tilde {\tilde {I}}_r(\nu )$ [2, 3]. Hence correlation coefficient become one of useful criteria to evaluate the quality and reliability of measurement, which is given by:

$$Q = max\left\lbrace \Delta I_m(\nu)\otimes\Delta I_r(\nu)\right\rbrace,$$
where $\Delta I_m(\nu ) = \tilde {\tilde {I}}_m(\nu ) - \bar {I}_m(\nu )$ and $\Delta I_r(\nu ) = \tilde {\tilde {I}}_r(\nu ) - \bar {I}_r(\nu )$ represent sub-spectrum that removed an averaged intensity $\bar {I}_m(\nu )$ or $\bar {I}_r(\nu )$ separately from the initial one, namely zero-mean operation. Symbol $\otimes$ is a normalized cross-correlation operator. Compared to NCC, ZNCC largely eliminates the false maximum identification due to intrinsic weak Rayleigh scattering. After obtained the specific spectral shift, the corresponding temperature can be directly converted by the relation given in Fig. 2.

The assumption we made that total change of group refractive index and thermal expansion is negligible for current system spatial sensing resolution is need to be justified over a wide temperature range. To simplify this question, we calculated the extra retardation of Rayleigh scattering over the heated section by temporally correlating the amplitude of Rayleigh scattering $\left |\tilde {I}_m(\tau )\right |$ and $\left | \tilde {I}_r(\tau )\right |$ in time domain between reference (room temperature) and heated section. As shown in Fig. 3, extra retardation induced by radiation heat varies from 0.15 to 0.4 picosecond by increasing flow rate from 2.0 mL/min to 7.5 mL/min over duration of $\sim$80 picoseconds Rayleigh scattering, which is almost 200 times of the extra retardation (0.4ps). It means the accumulated change of refractive index or thermal expansion over heating section should be minor effect compared to the spatial sensing resolution as 346 $\mu$m.

 figure: Fig. 3.

Fig. 3. Extra retardation (subtraction to room temperature delay) versus time delay of light traveling in fiber over radiation heating at different flow rate from 2.0 mL/min to 7.5 mL/min. The thermal induced extra retardation amounts to 0.15 ps at 2.0 mL/min and 0.4 ps at 7.5 mL/min. Note that color bar on right gives the reliability of OFDR on retardation measurement by associated correlation coefficient.

Download Full Size | PDF

3.1 Distributed high-temperature property of flame structure

Characteristic of a combustion on hydrogen gas were investigated in detail with respect to fuel flow velocity (F parameter) and vertical distance (L parameter) of interrogated fiber relative to the tube top. 2D temperature distributions are shown in Fig. 4 (i) and (ii) respectively. Basically, the temperature due to radiation heat near the tube lip grew with fuel velocity. The core temperature stayed constantly at around 900$^{\circ }$C as flow rate raised above 3.5 mL/min. The highest temperature of flame at 7.5 mL/min is on the sides of center separated by 1.4 mm with difference of 140-190$^{\circ }$C over a dimension of 2.5 mm above 900$^{\circ }$C. It can be referred that the flame reaction zone was lifted off from tube as increasing flow rate and inner temperature appeared to be cooler than outer due to indirect contact with oxygen (oxygen-deficient region), in which chemical reaction came to a dynamic balancing. The temperature distribution was essentially affected by the shape of micro flame, which also determined the details of thermal interactions between flame and solid tube [16, 17]. One of the reason for asymmetrical flame shape would be an unbalanced thermal interaction between flame and solid tube walls due to the imperfectly flattened nozzle. It should be noted that repeated thermal reaction also gave rise to the uneven growth of oxidates on the tube surface. A more detailed study on the tube design will benefit the heat exchange between fuel gases and tube walls, and the stability of micro-jet flame associated thermal uniformity. Additionally, temperature distribution was measured by adjusting the vertical position of tube entrance relative to the fiber, and make sure the spacing in between was equally incremented from 0 to 200 $\mu$m by steps of 25 $\mu$m. It is noted that temperature field at flame center grew significantly with the enlarged spacing while expanded slightly on both sides. The maximum temperature measured by telecom fiber is up to 1100$^{\circ }$C for both scenarios (hottest region), which is comparable to Type II fs-IR FBG. Note that the fiber survived with repeated thermal annealing treatments, and no additional loss appeared in Rayleigh scattering.

 figure: Fig. 4.

Fig. 4. (i) Distributed temperature profile of hydrogen flame at different flow rate (F parameter) in units of mL/min. With fixed spacing L = 0 $\mu$m between tube and fiber, a 2D flame structure was obtained below 1100$^{\circ }$C with slight asymmetrical shape at high flow rate. It showed a characteristic combustion of micro-jet flame that thermal radiation grows higher and broader on increasing fed fuel while cooler temperature was kept stationary in core when above certain flow rate. Peak A, B and Valley in arrow are the extreme points at both sides and center of temperature field. $\Delta$T represents gradient between Peak (A or B) and valley, while $\Delta$S is a spatial separation between Peak A and B growing with the increasing flow rate; (ii) With incremented spacing (L parameter), growth on temperature was observed by adjusting the scale of displacement while keeping the flow rate constant at F = 4.5 mL/min. Note that color bar on right side of each figure gives the reliability on distributed temperature measurement, dots in red shows high correlation coefficient and inversely in blue.

Download Full Size | PDF

Temperature uniformity is essential for making small diameters of tapered fiber with minimum loss since leaky modes from local defects on the surface limits the taper diameter to several micrometers due to nonuniform internal strain released inside during the heating and pulling process. Here, we characterize the uniformity of hydrogen flame with respect to distance L between fiber and tube entrance by referring to its full-width at 90% maximum of temperature field, which is denoted as length W. The definition of uniformity coefficient $\sigma$ is given by: in a repeatable and reliable manner

$$\sigma = \frac{\int_{0}^{W} [T(x) - T_{90\%max}]dx}{(T_{max}-T_{90\%max}) \times W}.$$
It equals to 1 for a complete uniform temperature distribution. Generally, the full width at 90% maximum of temperature field decreases slowly as the distance increases from $\sim$1650 $\mu$m at initial position to $\sim$1400 $\mu$m at L = 200 $\mu$m and the position at L = 100 $\mu$m shows the largest uniformity level as shown in Fig. 5 (i). The shape of the temperature field changes significantly with distance as shown in Fig. 5 (ii), the temperature gradient $\Delta$T experiences a fast fall as fiber moving towards L = 100 $\mu$m and raises again above L = 125 $\mu$m. And it shows a similar behavior that Peak separation $\Delta$S decreases and rises back. Transformation on the uniformity of field can also be observed in Fig. 4 (ii) with progressively varying distance between fiber and nozzle, in which temperature profile in red dots at L = 100 $\mu$m shows up a flat top at 1000$^{\circ }$C.

 figure: Fig. 5.

Fig. 5. Characterization of hydrogen flame at flow rate of 4.5 mL/min on (i) uniformity level with full-width at 90% maximum of temperature and (ii) local thermal gradient varied with distance L between fiber and tube entrance.

Download Full Size | PDF

Hydrogen flame with respect to the flow rate F and distance L is critical to create a uniform temperature.The spatial temperature distribution of hydrogen flame can characterize the uniformity of temperature at different flow rate and distance, which provide guideline to design reliable tapering process with the same diameter and taper length. It is know that glass transition plays major role and can be further inferred from the temperature dependent correlation shown in Fig. 6, which will be discussed in the following section.

 figure: Fig. 6.

Fig. 6. Temperature dependent correlation between Rayleigh spectra from measurement and reference. Statistically, dots represent result with various flow rate in different color, which give a general tendency of the correlation varying with increasing thermal level. It decreases slowly to 90|% as temperature goes up to 400$^{\circ }$C. The correlation starts to spread out as it comes to the range from 400 to 800$^{\circ }$C, for which a nonlinear thermal coefficients is expected for temperature higher than 400$^{\circ }$C with OFDR measurement. A significant drop down is shown here when the temperature goes over 900$^{\circ }$C, which could be related to the rearrangement process of glass structure. It shows a correlation of 50% around 1100$^{\circ }$C as maximum temperature limited by fast glass transition.

Download Full Size | PDF

3.2 Temperature dependent deformation of fiber

The occurrence of deformation limits fiber being applicable for higher and long-term temperature measurements. While the boundary between durability is unknown since glass transition involves a series of softening and melting process in fused silica, and the glass network is mixed randomly with ${\rm GeO_2}$ and ${\rm SiO_2}$ species. The knowledge of it is expected to help improve a quantitative and reliable measurement in most scenarios. The hydrogen flame radiates a broad spectrum along the fiber, which involves a significant energy release and diffusion. Along different fiber positions, it naturally formed a temperature field decreasing from the inner core to outer flame. In this section, fiber deformation will be closely related to temperature of hydrogen flame at different flow rate of ${\rm H_2}$ gas. The statistical result is exhibited in Fig. 6 among various flow rates. The correlation between two spectra of reference (room temperature) and measurement (heated status) shows a decay above 900$^{\circ }$C and drops quickly far above the annealing temperature 1000$^{\circ }$C, which is consistent with behavior that located at frequency shift of 1500 GHz ($\sim$12 nm wavelength shift) measured inside a furnace by using SMF [2]. It may relate to the structure rearrangement that mixed rings of ${\rm SiO_2}$-${\rm GeO_2}$ broke up and rebuilt in glass network of core [18] and along with relaxation of glass densification or strong compressed stress. Furthermore, correlation at 1100$^{\circ }$C corresponds to a 16nm spectral shift with 50% correlation. While higher temperature measurement is limited by fast glass transition (melting point for ${\rm GeO_2}$ is 1115$^{\circ }$C), during which silica fiber received sufficient energy and rearrangement of structures become more active. Without evident optical loss on Rayleigh scattering in the measurement, fiber cladding largely acts as a barrier to the OH bond invading into core [19] and enhances the sustainability for high temperature measurement.

3.3 Durability of telecom fiber in combustion reaction

A time dependent durability of fiber in a continuous combustion reaction is studied to understand limits that single-mode fiber for high temperature measurement. A fiber was placed in an enclosure of radiant heat below melting point, we ran system continuously with combustion at constant flow rate. The traces taken by OFDR were in order with a series of measurement preceding with one renewed reference after interrogated fiber was naturally cooling down to the room temperature. Separation time was made to make sure heat dissipation completed undisturbedly in an open equilibrium system. A timestamp was automatically built in trace through a data channel with DAQ function. The interval time between two traces was about 7.32 seconds on average, including 1.13 seconds for measurement as system response time, and for restart. Since reference was updated after finishing measurement, all timestamps can be viewed as one temporally reversed relative to the ending time of measurement. Noted that glass transition was undergoing inside core and cladding as fiber being burnt, which means the later measured time, the smaller change that fiber experienced compared with renewed reference. The fuel supply was immediately terminated after completed measurement. A complete array was composed of 20 traces in total, and the whole process takes up to 140 seconds.

As shown in Fig. 7 (i) to (iv), time-varying distributed temperature profiles with its associated correlation coefficient at flow rate 4.0 to 7.0 mL/min are demonstrated for the durability of single-mode fiber in experiment. As silica fiber continuously received the amount of radiant heat transferred from hydrogen flame, the resolved temperature reduced especially close to the hottest region of flame. The fiber is progressively deformed as indicated by the degradation of correlation coefficient due to the thermal expansion of fiber along with processes of soften and deformation of glass structure. Converse to the nitrogen irons emission in UV band, black-body radiation of hydrogen flame played major role. A permanent irreversible change occurred to the structure due to a plenty of energy absorption by glass lattice (${\rm SiO_2}$-${\rm GeO_2}$) in IR band, which affects the Rayleigh pattern, and hence the local spectrum. It gives rise to the degradation of spectral shift and restricts the measurable temperature range for OFDR system. It can be inferred that time evolution of the Hydrogen flame under thermal dynamic equilibrium is slower than OFDR response time, which makes hydrogen flame spatial distribution measurement to be meaningful. It is possible for higher temperature beyond of 1100$^{\circ }$C with quicker system response time (<1s).

 figure: Fig. 7.

Fig. 7. Time-varying distributed temperature obtained from flow rate (i) 4.0, (ii) 5.0, (iii) 6.0, and (iv) 7.0 mL/min. The associated correlation coefficient in temperature profile, as indicated by the color bar on right side of figure is progressively degrading over time, mainly at top region where temperature reached the highest. It shows different degrading rate in terms of flow rate. With 140 seconds’ free burns of hydrogen flame, the resolved temperature in the innermost zone of the flame degrades down to 900$^{\circ }$C in the end.

Download Full Size | PDF

In order to characterize the durability of single-mode fiber for high temperature measurement, a quantitative analysis of the decorrelation time is performed in Fig. 8 based on the degradation of spectral shift that accumulated over time. F = 10 mL/min was selected as it created a great temperature gradient ranging from room temperature to beyond of 1100$^{\circ }$C, which enabled us to characterize the durability above 1000$^{\circ }$C. 12 arrays were collected for averaging purpose. It was initially operated by poly-fitting to the time dependent correlation coefficient that degraded at different temperature range and then get the specific root of time at which coefficient drops down to a certain level. We inspect it separately when correlation fell at 50%, 55%, 60%, 65% and found 67.9% was the maximum threshold that we were able to measure the degradation. A situation has been taken into account when temperature close to the softening point, the correlation becomes highly fluctuated. Area in gray color presents 95% confidence intervals related to an uncertainty of the calculated decorrelation time and applied temperature within a small, selected region, which includes 5 spatial points for evaluations, and corresponds to an interaction length of 40 $\mu$m. It shows that The decorrelation time is associated with the spatial sensing resolution used in data processing since the selected size of silica fiber essentially determined the received amount of radiation energy from hydrogen flame and hence the softening or deformation degree of the fiber.

 figure: Fig. 8.

Fig. 8. Decorrelation time evaluated at certain range of the temperature when coefficient separately dropping to 50%(blue hexagram), 55%(red pentagram), 60%(yellow square), 65%(purple triangle) and 67.9%(green circle) of correlation. The area in gray color for each marked line gives 95% confidence intervals. It drops to 50% decorrelation at 1000$^{\circ }$C around 20s and same time for 55% at 990$^{\circ }$C, 60% at 960$^{\circ }$C, 65% at 920$^{\circ }$C, and only 68% at 880$^{\circ }$C. It indicates rapidly changed thermal coefficients in small temperature range above 880$^{\circ }$C.

Download Full Size | PDF

The decorrelation time reasonably explained the upper limits for high temperature measurement in a furnace by telecom fiber since a long heating and thermal equilibrium process usually required by heat exchanger during the measurement, where the correlation would progressively be thermally erased due to glass structural change. Comparatively, hydrogen flame radiation has faster heat release and diffusion rate, which enable us to demonstrate the high temperature limits for single mode fiber. It also implies a feasibility that used for fast combustion process, where the thermal energy received by silica fiber might be high density but time limited and potentially used for the micro power system design. Fiber is reusable based on the multiple annealing times over which repeated trace tracking has been done by OFDR provided that applied temperature is below the glass transition point such that no significant deformation or bending loss occur inside fiber core. A trade-off between sustainable time and upper limit of temperature should be considered in practical scenarios, which is an importance factor for reliable measurement.

4 Conclusion

In conclusion, we demonstrate a novel method on distributed temperature measurement of hydrogen flame by using a telecom fiber based on OFDR. A numerical method is initially adopted for converting a given spectral shift to a temperature value, which shows a good agreement with previous measured result. The characteristic of hydrogen combustion on radiation scope and flame structure have been demonstrated with respect to different flow rate F and vertical distance L to tube entrance. Uniformity level of temperature is studied by varying the distance between fiber and nozzle to determine a thermal uniform region for sub-micrometer fiber tapering. OFDR potentially offers a better solution for characterization of certain combustion region in detail, especially for the flame core within a durable temperature range. The OFDR measurement time is 1.13 seconds for 7.6 $\mu$m readout resolution, which is limited by the tuning speed and range of the tunable laser. An upper operational temperature limit of 1100$^{\circ }$C is determined for the distributed measurement technique based on Rayleigh backscattering. Exposure time to high energy radiation of hydrogen flame essentially determined the distortion level of spectral shift. The decorrelation time shows that a single mode fiber withstanding high temperature for measurement can last a few seconds with 50% correlation remaining. Long-time and higher temperature measurement require metal coating.

Funding

NSERC CRDPJ (479630-2015); Canada Research Chairs (950-231352); NSERC Discovery Grant (RGPIN-2020-06302).

Acknowledgments

Thank Dr. Chams Baker for discussion on temperature measurement of hydrogen flame. Congratulations and wish him all the success in his new role!

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.

References

1. M. Froggatt and J. Moore, “High-spatial-resolution distributed strain measurement in optical fiber with rayleigh scatter,” Appl. Opt. 37(10), 1735–1740 (1998). [CrossRef]  

2. D. C. Sweeney, D. M. Sweeney, and C. M. Petrie, “Graphical optimization of spectral shift reconstructions for optical backscatter reflectometry,” Sensors 21(18), 6154 (2021). [CrossRef]  

3. C. Chen, S. Gao, L. Chen, and X. Bao, “Distributed high temperature monitoring of smf under electrical arc discharges based on ofdr,” Sensors 20(22), 6407 (2020). [CrossRef]  

4. J. T. Jones, D. C. Sweeney, A. Birri, C. M. Petrie, and T. E. Blue, “Calibration of distributed temperature sensors using commercially available SMF-28 optical fiber from 22°C to 1000°C,” IEEE Sens. J. 22(5), 4144–4151 (2022). [CrossRef]  

5. T. W. Wood, B. Blake, T. E. Blue, C. M. Petrie, and D. Hawn, “Evaluation of the performance of distributed temperature measurements with single-mode fiber using Rayleigh backscatter up to 1000°C,” IEEE Sens. J. 14(1), 124–128 (2014). [CrossRef]  

6. B. Xu, J. He, B. Du, X. Xiao, X. Xu, C. Fu, J. He, C. Liao, and Y. Wang, “Femtosecond laser point-by-point inscription of an ultra-weak fiber bragg grating array for distributed high-temperature sensing,” Opt. Express 29(20), 32615–32626 (2021). [CrossRef]  

7. D. Barrera, V. Finazzi, J. Villatoro, S. Sales, and V. Pruneri, “Packaged optical sensors based on regenerated fiber bragg gratings for high temperature applications,” IEEE Sens. J. 12(1), 107–112 (2012). [CrossRef]  

8. M. Wang, K. Zhao, J. Wu, Y. Li, Y. Yang, S. Huang, J. Zhao, T. Tweedle, D. Carpenter, G. Zheng, Q. Yu, and K. P. Chen, “Femtosecond laser fabrication of nanograting-based distributed fiber sensors for extreme environmental applications,” Int. J. Extreme Manuf. 3(2), 025401 (2021). [CrossRef]  

9. S. Rizzolo, A. Boukenter, E. Marin, M. Cannas, J. Perisse, S. Bauer, J.-R. Mace, Y. Ouerdane, and S. Girard, “Vulnerability of ofdr-based distributed sensors to high γ-ray doses,” Opt. Express 23(15), 18997–19009 (2015). [CrossRef]  

10. J. Zhang, X. Li, H. Yang, L. Jiang, X. Wang, and D. Zhao, “Study on the combustion characteristics of non-premixed hydrogen micro-jet flame and the thermal interaction with solid micro tube,” Int. J. Hydrogen Energy 42(6), 3853–3862 (2017). [CrossRef]  

11. L. Li, Z. Yuan, Y. Xiang, and A. Fan, “Numerical investigation on mixing performance and diffusion combustion characteristics of h2 and air in planar micro-combustor,” Int. J. Hydrogen Energy 43(27), 12491–12498 (2018). [CrossRef]  

12. J. E J. Ding, J. Chen, G. Liao, F. Zhang, and B. Luo, “Process in micro-combustion and energy conversion of micro power system: A review,” Energy Convers. Manage. 246, 114664 (2021). [CrossRef]  

13. X. Wang, W. Li, L. Chen, and X. Bao, “Thermal and mechanical properties of tapered single mode fiber measured by ofdr and its application for high-sensitivity force measurement,” Opt. Express 20(14), 14779–14788 (2012). [CrossRef]  

14. J. E. Retter, G. S. Elliott, and S. P. Kearney, “Dielectric-barrier-discharge plasma-assisted hydrogen diffusion flame. part 1: Temperature, oxygen, and fuel measurements by one-dimensional fs/ps rotational cars imaging,” Combust. Flame 191, 527–540 (2018). [CrossRef]  

15. U. Glombitza and E. Brinkmeyer, “Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides,” J. Lightwave Technol. 11(8), 1377–1384 (1993). [CrossRef]  

16. K. Fujiwara and Y. Nakamura, “Experimental study on the unique stability mechanism via miniaturization of jet diffusion flames (microflame) by utilizing preheated air system,” Combust. Flame 160(8), 1373–1380 (2013). [CrossRef]  

17. A. Hossain and Y. Nakamura, “Thermal and chemical structures formed in the micro burner of miniaturized hydrogen-air jet flames,” Proc. Combust. Inst. 35(3), 3413–3420 (2015). [CrossRef]  

18. G. S. Henderson, D. R. Neuville, B. Cochain, and L. Cormier, “The structure of geo2–sio2 glasses and melts: A raman spectroscopy study,” J. Non-Cryst. Solids 355(8), 468–474 (2009). [CrossRef]  

19. T. Li, Optical fiber communications: fiber fabrication (Elsevier, 2012).

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.

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1.
Fig. 1. Schematic of optical frequency-domain reflectometry system for hydrogen flame measurement. TLS: tunable light source; FRM: Faraday rotating mirror; PD: photodetector; BPD: balanced photodetector. Circled by a dashed square, an Auxiliary Michelson interferometer was configured as a clock generator for digital acquisition, armed with a 25-meter length of delay fiber and two Faraday rotating mirrors. An inset at top right showed a front view of solid tube located closely underneath a tested fiber, which were indicated respectively in a white arrow. Combustion diagram at bottom left showed a basic layout with a telecom fiber placed in the flame core for temperature measurement along the x axis. Capital L represents the vertical distance between fiber and nozzle along the z axis.
Fig. 2.
Fig. 2. Evaluation of temperature and thermal sensitivity in terms of the given spectral shift in ignorance of the coating or packaging effect on the interrogated fiber. The wavelength shift was initially obtained by cross-correlation method and the conversion relationship was constructed by the three-order polynomial. (i) The black, solid-dot line gives a general estimation that was adopted for the rest temperature conversion. The black dashed line forecasts the temperature changes associated wavelength shift; (ii) the red, sold line is the thermal sensitivity associated with converted temperature for wavelength shift, and the red dashed line is the estimative thermal sensitivity intended for higher wavelength shift.
Fig. 3.
Fig. 3. Extra retardation (subtraction to room temperature delay) versus time delay of light traveling in fiber over radiation heating at different flow rate from 2.0 mL/min to 7.5 mL/min. The thermal induced extra retardation amounts to 0.15 ps at 2.0 mL/min and 0.4 ps at 7.5 mL/min. Note that color bar on right gives the reliability of OFDR on retardation measurement by associated correlation coefficient.
Fig. 4.
Fig. 4. (i) Distributed temperature profile of hydrogen flame at different flow rate (F parameter) in units of mL/min. With fixed spacing L = 0 $\mu$m between tube and fiber, a 2D flame structure was obtained below 1100$^{\circ }$C with slight asymmetrical shape at high flow rate. It showed a characteristic combustion of micro-jet flame that thermal radiation grows higher and broader on increasing fed fuel while cooler temperature was kept stationary in core when above certain flow rate. Peak A, B and Valley in arrow are the extreme points at both sides and center of temperature field. $\Delta$T represents gradient between Peak (A or B) and valley, while $\Delta$S is a spatial separation between Peak A and B growing with the increasing flow rate; (ii) With incremented spacing (L parameter), growth on temperature was observed by adjusting the scale of displacement while keeping the flow rate constant at F = 4.5 mL/min. Note that color bar on right side of each figure gives the reliability on distributed temperature measurement, dots in red shows high correlation coefficient and inversely in blue.
Fig. 5.
Fig. 5. Characterization of hydrogen flame at flow rate of 4.5 mL/min on (i) uniformity level with full-width at 90% maximum of temperature and (ii) local thermal gradient varied with distance L between fiber and tube entrance.
Fig. 6.
Fig. 6. Temperature dependent correlation between Rayleigh spectra from measurement and reference. Statistically, dots represent result with various flow rate in different color, which give a general tendency of the correlation varying with increasing thermal level. It decreases slowly to 90|% as temperature goes up to 400$^{\circ }$C. The correlation starts to spread out as it comes to the range from 400 to 800$^{\circ }$C, for which a nonlinear thermal coefficients is expected for temperature higher than 400$^{\circ }$C with OFDR measurement. A significant drop down is shown here when the temperature goes over 900$^{\circ }$C, which could be related to the rearrangement process of glass structure. It shows a correlation of 50% around 1100$^{\circ }$C as maximum temperature limited by fast glass transition.
Fig. 7.
Fig. 7. Time-varying distributed temperature obtained from flow rate (i) 4.0, (ii) 5.0, (iii) 6.0, and (iv) 7.0 mL/min. The associated correlation coefficient in temperature profile, as indicated by the color bar on right side of figure is progressively degrading over time, mainly at top region where temperature reached the highest. It shows different degrading rate in terms of flow rate. With 140 seconds’ free burns of hydrogen flame, the resolved temperature in the innermost zone of the flame degrades down to 900$^{\circ }$C in the end.
Fig. 8.
Fig. 8. Decorrelation time evaluated at certain range of the temperature when coefficient separately dropping to 50%(blue hexagram), 55%(red pentagram), 60%(yellow square), 65%(purple triangle) and 67.9%(green circle) of correlation. The area in gray color for each marked line gives 95% confidence intervals. It drops to 50% decorrelation at 1000$^{\circ }$C around 20s and same time for 55% at 990$^{\circ }$C, 60% at 960$^{\circ }$C, 65% at 920$^{\circ }$C, and only 68% at 880$^{\circ }$C. It indicates rapidly changed thermal coefficients in small temperature range above 880$^{\circ }$C.

Equations (4)

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

Δ z = λ i λ f 2 n g Δ λ ,
Δ S = ( 6.0819 × 10 10 ) T 3 + ( 2.8827 × 10 6 ) T 2 + ( 1.0872 × 10 2 ) T 0.2406
Q = m a x { Δ I m ( ν ) Δ I r ( ν ) } ,
σ = 0 W [ T ( x ) T 90 % m a x ] d x ( T m a x T 90 % m a x ) × W .
Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.