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A calibration-free scanned wavelength modulation spectroscopy scheme requiring minimal laser characterization is presented. Species concentration and temperature are retrieved simultaneously from a single fit to a group of 2f/1f-WMS lineshapes acquired in one laser scan. The fitting algorithm includes a novel method to obtain the phase shift between laser intensity and wavelength modulation, and allows for a wavelength-dependent modulation amplitude. The scheme is demonstrated by detection of H2O concentration and temperature in atmospheric, premixed CH4/air flat flames using a sensor operating near 1.4 µm. The detection sensitivity for H2O at 2000 K was 4 × 10−5 cm−1 Hz-1/2, and temperature was determined with a precision of 10 K and absolute accuracy of ~50 K. A parametric study of the dependence of H2O and temperature on distance to the burner and total fuel mass flow rate shows good agreement with 1D simulations.
© 2015 Optical Society of America
1. Introduction
The growing interest in biomass as renewable energy source has propelled the development of suitable combustion and gasification technologies. However, biofuels typically contain high amounts of chlorine, sulfur and alkali metals, which evokes ash-formation followed by slagging, agglomeration, corrosion and potentially harmful emissions [1]. While the secondary ash-forming reactions and final combustion products are well known, little is understood about the primary reactions close to the fuel particles, directly after volatile release [2]. A better understanding and improved theoretical models of the ash-chemistry in and near flames are needed to mitigate the operational problems. Thus, researchers are interested in conducting in situ measurements of ash-forming compounds and key combustion parameters, such as H2O and process gas temperature, during thermochemical conversion of biomass in facilities ranging from flat flame burners [3] and laboratory furnaces [4] to pilot-scale reactors [5]. For this purpose, versatile, fast, and preferably calibration-free, analytical techniques are required that are able to asses both species concentration and temperature in a wide dynamic range and in harsh environments with limited optical access.
Optical techniques based on absorption or dispersion spectroscopy with tunable lasers are frequently used in science and industry for sensitive and accurate gas analysis with high time resolution [5–11]. One of the most established tunable diode laser spectroscopy (TDLS) technique for in situ measurements in harsh, high-temperature environments is wavelength modulation spectroscopy (WMS), as it offers high sensitivity and stability with robust, compact and affordable instrumentation [5]. Two-line thermometry can be used to retrieve gas temperature, which is not only an important combustion parameter, but also essential for species quantification due to the temperature dependence of the absorption linestrengths. In contrast to scanned direct absorption spectroscopy (DAS), which allows retrieval of absolute number densities, WMS traditionally requires calibration for the mutually dependent concentration and temperature [6,8]. This constitutes a major drawback in many applications, for example, when large and unexpected changes in temperature and concentration may occur.
Strategies to realize calibration-free WMS (CF-WMS) involve 1f-normalization [12–16], multi-parameter fitting of advanced Fourier series models to WMS lineshapes [17], the recovery of DAS lineshapes [18] or quasi-simultaneous DAS detection [10]. A practical, scanned CF-WMS scheme with 2f/1f-WMS spectral fitting was recently introduced by Sun et al. [13] and Goldenstein et al. [15] that is not limited to optically thin conditions or small modulation amplitude (MA) and does not rely on a theoretical description of WMS signals based on Taylor or Fourier series. Moreover, the measured background signal is incorporated in the simulated absorption to account for unwanted frequency dependent losses without separate background subtraction. However, the existing two-color implementations of this CF-WMS approach need good initial values of temperature and concentration and/or iterative procedures to achieve accurate results [15,16]. In addition, the MA is assumed constant throughout the laser wavelength scan, and both MA and the phase shift (PS) between laser intensity and wavelength modulation have to be estimated or determined by measuring the laser frequency response to the modulation.
The aim of this work was to develop a scanned, spectral fitting CF-WMS methodology that requires minimal laser characterization and allows for accurate single-laser two-line thermometry in flames. We show that only the laser frequency response to the scan, the background and the analytical signal have to be measured to obtain PS, relative MA change during the scan and analyte information. Species concentration and temperature are determined simultaneously, independently of initial values and without iterative procedures, from a least-squares fit to a group of 2f/1f-WMS lineshapes. If the temperature dependence of the lineshape is known, the relative MA can be included as fitting parameter. This scheme was recently used by our group in the temperature range 670-1600 K to investigate biomass combustion in a single pellet reactor [19]. Here, the novel features of the algorithm are described in more detail and the sensor is applied to H2O quantification and temperature measurements up to 2100 K in a burner-stabilized flat flame, which is a well-defined model system for high-temperature reacting flows. In-depth flame characterization will provide valuable insights regarding the performance of line-of-sight techniques in this context, and facilitate future biomass combustion studies.
2. Two-line thermometry with WMS
In WMS two-line thermometry, the gas temperature is usually inferred by comparing the measured peak ratio of two absorption lines (or groups of lines) with different temperature dependence to calculated values [6,8]. Calibration is needed because instrumentation factors and the laser intensity variation during the scan are not known or cannot be modeled accurately. However, the WMS peak ratio depends not only on temperature, but also on concentration. Figure 1(a) shows the WMS peak ratio as a function of temperature for a range of H2O concentrations for the transitions employed in this work (two distinct WMS peaks). The line parameters are listed in Table 1.
Fig. 1 (a) WMS peak ratio versus temperature for different H2O concentrations for the transitions listed in Table 1, (b) laser frequency (up) and normalized MA (below) for a typical scan with the laser employed in this work.
Table 1. Spectroscopic data for the selected H2O lines taken from the HITRAN 2012 database [20].
Large errors are introduced if the actual H2O concentration in the sample differs from the one used at the time of temperature calibration. For example, if 5% H2O was used for calibration, but 10% is present in the sample, the temperature obtained for a peak ratio of 0.75 will be incorrect by more than 200 K, which, in turn, will lead to an incorrect concentration assessment. In existing CF-WMS methods, calibration is circumvented by extensive laser characterization, but if the results deviate from the initial parameters, iterative procedures are required to approach the true values [12,15]. This drawback is overcome in the current CF-WMS scheme by retrieving temperature and concentration simultaneously from a fit to 2f/1f-WMS lineshapes.
3. Calibration-free scanned wavelength modulation spectroscopy
In scanned WMS, the frequency of the light, ν(t), varies due to a slow scan, νs(t), and a fast sinusoidal modulation with amplitude am(t) and frequency fm according to
where θ denotes the PS. Using Beer-Lambert’s law, the laser intensity transmitted through an absorbing medium of temperature T and pressure P can be written as [19]where IBG(t) is the laser intensity in the absence of the analyte (background) and α(ν) is the absorption, which depends on the relative concentration of the analyte c, the absorption path length L, and the transition linestrength S(νj,T) of the j-th transition at frequency νj with associated lineshape function χj(ν,c,P,T). A lock-in amplifier extracts nf-WMS signals as [13]where LPF indicates a low-pass filter. Using a software-based digital lock-in, any nf-WMS component within the bandwidth of the data acquisition system can be demodulated. The varying laser intensity and setup-dependent instrumentation factors are accounted for by normalizing 2f-WMS with 1f-WMS signals. Simulated 2f/1f-WMS spectra are calculated from Eqs. (2) and (3) using the measured background signal, and subsequently least-squares fitted to the measured 2f/1f-WMS signals.The amplitude and shape of the 2f/1f-WMS signals depend heavily on MA and PS. Therefore, these parameters need to be accurately known to achieve a good spectral fit and accurate results. While PS is constant during a scan for a given modulation frequency, the MA usually varies because of the wavelength-dependent response of a diode laser to modulation via the injection current. In Fig. 1(b), the laser frequency (upper plot) and normalized MA (lower plot) are displayed for the specific laser and scan range used in this work. A relative MA change of almost 20% is observed, which corresponds to a reduction of the absolute MA from 0.1410 cm−1 to 0.1193 cm−1. The fact that MA is wavelength-dependent for most diode lasers is especially significant at high pressure and when scanning across several absorption lines. Due to the small amplitude and high frequency of the modulation, a long etalon with small free-spectral-range and a fast data acquisition system are needed to experimentally determine MA and PS [13]. Thus, often, only the first term in Eq. (1) is measured, while MA and PS are estimated [15].
In the present CF-WMS scheme, the relative MA change is derived from the slope of the laser frequency response to the scan, and then used as open parameter in the 2f/1f-WMS fitting routine to find the absolute MA values. To determine PS, we make use of the fact that, following Eq. (2), the shape of the transmitted laser intensity is a function of PS in the vicinity of an absorption feature. Thus, PS can be determined by least-squares fitting the simulated transmitted laser intensity to the measured intensity. Figure 2(a) shows the transmitted laser intensity (black markers) in the presence of the analyte, together with the fitted simulated intensity (red line). A section of the plot around one of the absorption features is depicted in Fig. 2(b), where measured raw data (black line) and best fit (red circular markers) are displayed together with two slightly out-of-phase simulations (square and triangular markers). The curves are shifted along the y-axis for clarity. The dependence of the shape of the transmitted laser intensity on PS can clearly be observed.
Fig. 2 (a) Measured (black markers) and fitted simulated (red solid line) laser intensity, (b) fine structure of the laser intensity around an absorption line; measured (solid black), best fit (round red markers) and two slightly out-of-phase simulations (square and triangular markers).
A flow-chart of the novel CF-WMS methodology is presented in Fig. 3(a). Three signals need to be measured: the frequency scale, νs(t), the background signal, IBG(t), and the transmitted laser intensity in the presence of the analyte, I(t). In the first step of the algorithm, the loop to the left (red dashed arrows) determines PS by (i) simulating ν(t) using νs(t) and an initial θ value, (ii) simulating an absorption spectrum assuming an (arbitrary) initial concentration and temperature, (iii) calculating the simulated laser intensity according to Eq. (2), by adding the simulated absorption spectrum to IBG(t), and (iv) fitting the simulated to the measured laser intensity to extract PS. In the second step, the loop to the right (blue solid arrows) recalculates the simulated intensity using the obtained PS, extracts the 1f- and 2f-WMS signals from the measured and simulated laser intensities, and performs a fit of the simulated to the measured 2f/1f-WMS signal to determine temperature, concentration and absolute MA. If the temperature dependence of the lineshape is not known, the absolute MA can be estimated and the collisional width be used as fitting parameter.
Fig. 3 (a) CF-WMS flow chart with PS (red) and 2f/1f-WMS (blue) fitting routine, (b) measured 1f-, 2f- (blue solid lines) and 2f/1f-WMS (round markers) signals at 1952 K and 17.6% H2O, together with best fit (red line), fit residual (black solid line) and background signal (green diamond markers). The two WMS peaks consist of five H2O transitions (Table 1).
Typical 1f-, 2f- (blue solid lines) and 2f/1f-WMS signals (round black markers) from H2O in the flat flame, are shown in Fig. 3(b) together with the best 2f/1f-WMS fit (red solid line) using a Voigt function. The fact that the measured background signal (green diamond markers) with all unwanted wavelength dependent losses is included in the simulated 2f/1f-WMS signal, provides the possibility to recover information from the target region even in the presence of etalon effects or absorption due to ambient water vapor [13,19].
4. Experimental setup
A schematic drawing of the CF-WMS setup is shown in Fig. 4(a). A fiber-coupled distributed feedback (DFB) laser (Nanoplus GmbH) emitting around 1398 nm (7153 cm−1) is scanned with a 40 Hz triangular and modulated with 5 kHz sinusoidal waveform. The MA is optimized for 2f-WMS detection of the peak at 7154.35 cm−1. The laser frequency response to the scan is obtained prior to a measurement series by recording the transmission through an uncoated fused silica etalon (SLS Optics) with a free-spectral range of 0.05 cm−1. Single-mode fibers deliver the light (1 mm beam diameter) to etalon and burner. The transmitted intensity (ten averages) is recorded by photodetector PD1 (Thorlabs, PDA20CS). Stray light and background radiation from the flame are minimized using a narrowband optical filter (Thorlabs, FB1400-12). Synchronized board cards (National Instruments, PXI-5402 and PXIe-6356) provide the scan and modulation waveforms and acquire (1.25 MS/s) the photodetector signal, respectively. A software lock-in (MATLAB) is used to extract the nf-WMS signals. The minimum detectable absorption for H2O at 2000 K was 4 × 10−5 cm−1 Hz-1/2, corresponding to about 400 ppm∙m for the peak at 7154.35 cm−1.
Fig. 4 (a) Schematic experimental setup, FGen-function generator card, DAQ-data acquisition card, PD-photodetector, (b) flat flame burner with optics and PD1, (c) photograph of the flat flame at φ = 1 and TFR of 10 L/min. The white frame indicates the investigated flame area.
The flat flame burner, shown in Fig. 4(b), is based on the design suggested in [21], Hartung et al. Methane and air were premixed at room temperature with the help of mass flow controllers (MKS, GM50A) to yield an equivalence ratio of φ = 1, and supplied to the burner center ring (38 mm diameter). Without using a co-flow, a stable, laminar and homogeneous flat flame, as in Fig. 4(c), was obtained in the total flow rate (TFR) range 3-24 L/min (corresponding to mass fluxes of 0.0045-0.0398 g/cm2s). The burner was water cooled (0.5 L/min) and mounted on micrometer stages to enable precise control of the height above burner (HAB) and radial position with respect to the laser beam.
5. Burner-stabilized flat flame measurements
Figure 5 presents measured axial temperature (a) and H2O concentration (b) profiles (markers) as a function of HAB for three TFRs, together with 1D simulations (lines) performed with CANTERA [22]. A typical experimental 2f/1f-WMS signal is shown in Fig. 3(b). The residual of the fit is probably caused by a slightly inhomogeneous flame and non-identical on/off flame background signals. The repeatability of a temperature measurement was within 10 K, whereas the absolute accuracy was estimated to 50 K, mostly attributed to uncertainties in the absorption line parameters. The accuracy of a concentration measurement was better than 1% H2O. For all TFRs, the measured temperatures exceed the simulation results (and reach their maximum) near the reaction zone, while they decrease below the model prediction in the post-flame region. This is in accordance with results obtained by other groups [21,23]. The measured H2O concentrations deviate significantly from the simulation at low TFR, but agree well up to a HAB of 8 mm for a TFR of 18 L/min.
Fig. 5 Measured axial temperature (a) and H2O concentration (b) profiles (markers) for φ = 1 and TFRs of 4, 10 and 18 L/min (corresponding to mass fluxes of 0.0066, 0.0166 and 0.0299 g/cm2s) compared to CANTERA simulations (lines). In panel (a), the marker size indicates the absolute accuracy of the temperature measurement.
As evident from the measured radial temperature profiles shown in Fig. 6(a), the temperature was rather homogeneously distributed along the line-of-sight and decreased volumetrically with increasing HAB. This suggests that the disagreement between experiment and simulation observed at high HAB in Fig. 5(a) is due to radiative heat loss, which was not included in the model. The reason for the deviation close to the reaction zone could be that the modeling of the heat loss to the surface of the specific burner was not accurate enough. The cone-shaped flame structure apparent in Figs. 4(c) and 6(a) indicates that diffusion of the burnt gases and mixing with the surrounding air are significant factors. The higher above the burner and the lower the flow rate, the more cold air will get entrained into the flame/air boundary region, thus reducing the temperature at the flame edge.
Fig. 6 (a) Measured radial temperature profiles at φ = 1 and TFR = 10 L/min for 4 HABs, (b) maximum measured temperature (markers) versus TFR, and CANTERA simulation (line).
Diffusion and mixing are the main reasons for the discrepancy between the measured and simulated water vapor concentrations plotted in Fig. 5(b). In the analysis of the CF-WMS spectra, an absorption path length of 38 mm (diameter of burner center ring) was assumed for all HABs, while the actual path length decreased with increasing HAB, as indicated by the cone-shaped flame. Theory and experiment coincide only at high TFR close to the burner, where diffusion and mixing have little influence and the path length is unaffected. To further substantiate the reliability of technique and model, Fig. 6(b) presents the maximum measured flame temperature as a function of TFR. Here, the agreement with the corresponding simulation is excellent within the accuracy of the measurement. Radiative heat loss and mixing may be the reasons why the predicted maximum flame temperatures are not reached at low TFR [23].
Since the interaction of the post-flame combustion products with the surrounding air, radiative heat losses and the specific burner geometry are not taken into account in the 1D model, the simulations cannot fully represent the actual flame. At the same time, path-averaged TDLS measurements cannot resolve potential inhomogeneities, and species quantification relies on accurate knowledge of the absorption path length. Better agreement between theory and experiment could be achieved by comparison to 2D axisymmetric simulations of the flame or by using tomographic techniques.
6. Conclusion
We present a scanned CF-WMS scheme for two-line thermometry with a single diode laser and with laser characterization procedures comparable to those used in DAS. High accuracy of the 2f/1f-WMS spectral fitting is ensured by inclusion of a wavelength-dependent modulation amplitude. The phase shift between laser intensity and wavelength modulation is obtained from a fit of the simulated to the measured laser intensity in the presence of the analyte. The sensor is applied to detection of H2O vapor and temperature in atmospheric, burner-stabilized CH4/air flat flames. Within the limitations of technique and 1D simulations, good agreement is achieved without calibration and iterative procedures. The technique opens up for sensitive and accurate simultaneous measurement of temperature and species concentration in applications where parameters vary rapidly and in a wide dynamic range.
Acknowledgments
This work was supported by the Swedish Energy Agency (36160-1), the Kempe Foundations (JCK-1316) and the Swedish strategic research program Bio4Energy. The authors thank Dr. Alexei Sepman for valuable discussions regarding flat flame simulations.
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