Technique Of Laser Calibration For Wavelengthmodulation Spectroscopy With Application To Proton Exchange Membrane Fuel Cell Measurements

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Technique of laser calibration for wavelengthmodulation spectroscopy with application to proton exchange membrane fuel cell measurements Ritobrata Sur, Thomas J. Boucher, Michael W. Renfro,* and Baki M. Cetegen Department of Mechanical Engineering, 191 Auditorium Road, Unit-3139, University of Connecticut, Storrs, Connecticut 06269, USA *Corresponding author: [email protected] Received 30 September 2009; revised 25 November 2009; accepted 25 November 2009; posted 30 November 2009 (Doc. ID 117797); published 21 December 2009 A diode laser sensor was developed for partial pressure and temperature measurements using a single water vapor transition. The Lorentzian half-width and line intensity of the transition were calibrated for conditions relevant to proton exchange membrane (PEM) fuel cell operation. Comparison of measured and simulated harmonics from wavelength-modulation spectroscopy is shown to yield accuracy of
2:5% in water vapor partial pressure and
3 °C in temperature despite the use of a single transition over a narrow range of temperatures. Collisional half-widths in air or hydrogen are measured so that calibrations can be applied to both anode and cathode channels of a PEM fuel cell. An in situ calibration of the nonlinear impact of modulation on laser wavelength is presented and used to improve the accuracy of the numerical simulation of the signal. © 2009 Optical Society of America OCIS codes: 300.1030, 280.4788. 1. Introduction Tunable diode laser based sensors provide an excellent tool for in situ measurement of physical parameters, such as partial pressure of species and temperature, in challenging environments such as combusting flow fields and fuel cell flow channels. In a typical experiment, a laser is passed through an absorbing medium and the laser wavelength is scanned over an absorption transition. The transmission of the laser is measured to determine absorption by the gas medium, which is then related to gas concentration or temperature when multiple transitions are measured. When the light absorption by the gas is large, a simple ratio of the laser power before and after absorption can be utilized. However, in many cases additional modulation of the laser is used to either reject noise or discriminate from background transmis0003-6935/10/010061-10$15.00/0 © 2010 Optical Society of America sion variations, thus enhancing the sensitivity of the absorption measurements. Modulation spectroscopy methods have been used widely in various applications, ranging from atmospheric pressure monitoring of trace gases [1] to simultaneous measurement of temperature, pressure, and velocity in shock heated oxygen flows [2] and hydrocarbon combustion [3–5], and also have long been recognized as an important tool in the study of electronic and molecular structure [6]. The theory of tunable diode laser absorption spectroscopy and the objective of this study are first presented in the following sections. A. Absorption Spectroscopy Light transmission through an absorbing medium follows the Beer–Lambert law [7] as I ¼ expð− I0 ZL α½νðtÞdlÞ; ð1Þ 0 1 January 2010 / Vol. 49, No. 1 / APPLIED OPTICS 61 where I 0 is the beam intensity before transmission, I is the beam intensity with absorption, αðatm−1 cm−1 Þ is the absorption coefficient that is dependent on instantaneous frequency νðtÞ, partial pressure Ps , and temperature T. The integration is taken over the total optical path length L of the absorbing gas medium. The absorption coefficient of the absorbing species can be expressed as [8] rffiffiffiffiffiffiffiffiffiffiffiffiffi ffi  α ¼ Ps × SðT; ν0 Þ × lnð2Þ π × VðX; YÞ; ΔνD =2 ð2Þ where the Voigt line shape function, V, is a convolution between Gaussian and Lorentzian line shapes governed by a Gaussian (Doppler) broadening term, pffiffiffiffiffiffiffiffi 0Þ X ¼ 2ðν−ν ln 2, and p a ffiffiffiffiffiffiffiffi Lorentzian (collisional) broadΔνD ΔνL ening term, Y ¼ Δν ln 2. SðTÞ is the temperature D dependent line intensity,ΔνD is the Doppler FWHM, ΔνL is the Lorentzian FWHM, and ν0 is the line center frequency. The Voigt line shape function can be written as the real part of the complex probability function [9]    ZZ  2  2i 2 −Z VðZÞ ¼ Ree 1 þ pffiffiffi et dt ; π ð3Þ 0 where Z ¼ X þ iY. The line intensity is given by [8]   ν0 1 − exp −hc kT QðT 0 Þ  SðTÞ ¼ SðT 0 Þ   QðTÞ ν0 1 − exp −hc kT 0    hcE00 1 1 ; − × exp k T0 T  ð4Þ where T 0 is the reference temperature (296 K), Q is the partition function of the absorbing gas, and E00 is the energy of the lower state of the transition (listed in the HITRAN 2008 database [10]). The Doppler broadening half-width can be easily expressed as a function of temperature and molecular weight, M, of the absorbing species by assuming a Maxwell– Boltzmann distribution, which can be written as [8]  0:5 T ΔνD ¼ 7:162 × 10 ν0 ; M 7 ð5Þ where T is in K. The Lorentzian half-width can be expressed as a function of the self-collision HWHM (γ self ), foreign gas collision HWHM (γ foreign ), partial pressure of the absorbing species (Ps ), and total pressure of the sample (P) as 62 APPLIED OPTICS / Vol. 49, No. 1 / 1 January 2010  n  n   T0 f T0 f ΔνL ¼ 2 Ps γ self ; þ ðP − Ps Þγ foreign T T ð6Þ where nf is the exponent of temperature dependence. Combining Eqs. (1)–(6), the absorption of a laser of any given wavelength can be computed as a function of temperature, pressure, and chemical composition for a path length L. The laser can be slowly tuned so that the absorption, I=I 0 , is measured at each frequency, ν, to resolve the absorption line shape and the partial pressure of the gas can be determined. Alternatively, modulation of the laser frequency can be used such that the measured absorption signals are a convolution of the absorption line shape and the laser modulation function. B. Modulation Spectroscopy Laser current modulation methods are classified as being either wavelength-modulation spectroscopy (WMS) or frequency-modulation spectroscopy (FMS). In both cases, a modulation is provided to the laser current controller, which modulates both the laser intensity (intensity modulation, IM) and the wavelength (frequency modulation, FM). Wavelengthmodulation techniques are reported to have a detection limit of 10−4 to 10−5 fractional absorption [11,12]. Several new methods of FM spectroscopy, such as two-tone [12–16] techniques, have extended the detection sensitivities to 10−7 –10−8 [17]. The distinction between the WMS and the FMS techniques is that the modulation depth frequency for WMS is much lower than the half-width of the absorption profile, while for FMS it is much greater than the absorption half-width. The method of WMS was demonstrated for trivalent Nd using an electro-optically tuned, wavelength-modulated CW dye laser experimentally by Tang and Telle [18]. FM spectroscopy was developed by Bjorklund [19] with a singleaxial-mode dye laser. The collected signal is filtered at the modulation frequency or at harmonics such that the absorption at individual wavelengths is not resolved, but instead a convolution of the laser modulation and absorption signal is measured. There has been significant research involving the theoretical prediction of harmonics of the absorption profiles [17,20–28]. Reid and Labrie [20] performed a series of experiments and demonstrated close agreement at low modulation depths with the theoretical expressions for harmonics of Lorentzian and Gaussian line shapes derived by Wahlquist [21], Arndt [22] and Wilson [23]. Cassidy and Reid [11] discussed several factors influencing the detection sensitivities and identified the important role of residual amplitude modulation (RAM). Theoretical expressions for harmonic line shapes including the effects of amplitude modulation and varying modulation depths were obtained by Philippe and Hanson [24]. Supplee et al. [25] put forward a general theory for frequency and WMS techniques and also for limiting cases of modulation indices in terms of Bessel series expansions. Schilt et al. [26] presented a simple theoretical model of WMS on a Lorentzian absorption line for a combined intensity and FM with an allowable arbitrary phase shift between them, characteristic of DFB diode lasers. Using Fourier analysis, Kluczynski et al. [27,28] developed and implemented a theoretical description of WMS that includes the nonlinear IM, IM-FM phase shift, the nonlinear IM associated with the sinusoidal current modulation and wavelength dependent transmission in harsh conditions. Li et al. [17] extended the formulation to large modulation depths for measurements in high pressure gases. In all these studies, an attempt has been made to semianalytically describe the problem. In the current study, a full-scale numerical simulation is performed for the convolution of modulation and absorption and this simulation is fitted directly to the obtained experimental profiles by a Levenberg–Marquardt nonlinear optimization routine. A correction for laser intensity variation by normalization of the WMS signal using harmonics of the same was first presented by Fernholz et al. [29]. This method was used by Li et al. [17] and Rieker et al. [30] to develop a sensitive high temperature and pressure sensor for temperature and water vapor concentration. The current study also implements a similar normalization scheme to correct for laser intensity baseline variations. This technique ensures that the absorption signature obtained is invariant of laser alignment and photodetector gain. The theoretical approach to address signal variations due to these effects can be complicated, as discussed in previous work [17,29,30]. An alternative approach to the data analysis is presented in this article. Our approach involves fitting a numerically simulated WMS signature versus sample domain to the raw data without making substantial efforts to numerically correct for the nonlinearity in the laser amplitude modulation and the baseline. This approach is applied to measurements of water broadening in air and hydrogen for application to single line measurements of water concentration and temperature in proton exchange membrane (PEM) fuel cells. C. Specific Goals The main objective of the experiments presented here is to obtain quantitative distributions of water vapor partial pressure and temperature in a typical PEM fuel cell at the cathode and anode side gas channels in the presence of air and hydrogen, respectively, for a typical temperature range of 65 °C–85 °C. Basu et al. have previously demonstrated measurements of water concentration and temperature on the cathode side of a PEM fuel cell using direct absorption spectroscopy [31]. This previous attempt assumed zero absorption at the laser scan extremities, i.e., the laser ramp peak, which was found to produce substantial error. Thus the absorption at the ramp peak needs to be considered, which is made possible through the current WMS technique. In the present study, measurements are made in both the cathode and anode sides with consideration of the effect of air and hydrogen on collisional broadening using the WMS technique with a modified analysis. The water vapor spectral transition line at 1469:637 nm was selected using the HITRAN [10] database in the experiments, keeping in view the high sensitivity of this line to both partial pressure and relatively good sensitivity to temperature. In this method, the diode laser is excited by a sinusoidal current modulation with linearly varying DC offset. The generated laser beam passes through the sample absorbing media (whose constituents are to be measured) where the intensity is attenuated and an absorption signature is obtained by a photodetector. A LabVIEW-based software lock-in amplifier is designed to extract the second (2f ) and first (1f ) harmonics of the absorption profile simultaneously corresponding to the reference frequency (modulation frequency in this case). A ratio of the 2f and 1f signals is taken to eliminate the resultant profile change due to beam alignment and beam steering effects. The profile thus obtained is the raw data that can be analyzed to obtain the measurement quantities of partial pressure and temperature. In the current study, a full numerical simulation of the modulation spectroscopy signal is generated and fitted to the experimental results. A technique to account for the nonlinear modulation of the laser at high frequencies is described. The resulting technique can be applied to measurements on both the anode and cathode sides of a PEM fuel cell with accuracies of
2:5% in water vapor partial pressure and
3 °C in temperature. 2. Experimental Setup An NEL distributed feedback (DFB) diode laser (NEL NLK1S5G1AA, center wavelength ¼ 1470 nm) was used for the experiments. It was controlled by a Thorlabs thermoelectric cooler (TEC2000) and a Thorlabs laser diode controller (LDC500), as shown in Fig. 1. In these experiments, the laser radiation is directed through the absorbing medium using a fiber-coupled collimator, and the transmitted beam is subsequently intercepted by a photodiode. The laser diode current is modulated by a voltage from the laser control and data acquisition computer. The IM produced as a result of injection current modulation in the diode laser is nonlinear as described previously by Kluczynski et al. [27,28] and Li et al. [17]. The IM was considered as a composite of a linearly increasing part and two IM harmonics in these studies. The IM features can be directly measured along with all the nonlinearities in an actual diode laser by using data with no absorption. The background intensity plot of such a curve is shown in Fig. 2 and can be expressed as I 0 ¼ gðtÞ. In the previous analyses by both Kluczynski et al. [27,28] and Li et al. [17], the FM was assumed to be a pure sinusoidal modulation around a mean unmodulated frequency as 1 January 2010 / Vol. 49, No. 1 / APPLIED OPTICS 63 Fig. 1. (Color online) Schematic for the calibration experiments. νðtÞ ¼ ν0 þ a cosðωt þ ψÞ; ð7Þ where a is the modulation depth and ψ is the IM-FM phase shift [17,26–28]. In the current study, a voltage signal is sent to the laser current controller that consists of a ramp with slope κ and a sinusoidal modulation of amplitude vm as V LDC ¼ κt þ vm sinðωtÞ; ð8Þ where κ is the slope of the linear DC offset, vm is the voltage amplitude corresponding to the modulation depth (m), and ω is the modulation frequency. However, at higher frequencies required for temporal resolution in the fuel cell experiments, the laser wavelength does not respond linearly and the amplitude of the sinusoidal variation is decreased such that the laser wavelength is found to follow Fig. 2. Modulated ramp for WMS. Measured intensity includes no absorption. 64 APPLIED OPTICS / Vol. 49, No. 1 / 1 January 2010 νðtÞ ¼ Cðκt þ εvm sinðωt þ ψÞÞ; ð9Þ where C is the calibration function relating the voltage to the laser frequency and ε is a factor that indicates the degree to which the laser wavelength cannot follow the modulation command. For slow modulation, ε approaches unity and for fast modulation it approaches zero. The calibration function, C, is determined from steady state calibration of the laser wavelength as discussed in the next section, and the modulation factor, ε, is determined experimentally during calibration absorption experiments as shown in Fig. 3 and described subsequently. During experiments with absorption, Eq. (9) is used along with Eqs. (1)–(6) to compute a simulated absorption signal using a Voigt profile generation routine with the Humlicek algorithm [9]. From this Fig. 3. (Color online) Calibration of diode laser: instantaneous light frequency—frequency at ramp peak (gigahertz) versus voltage sent to the laser diode controller. simulated absorption signal, a software lock-in amplifier program in LabVIEW, described later is used to predict 2f =1f WMS curves. This same routine was used to process the experimental measurements and parameters of the simulation were varied while fitting the simulated 2f =1f signal to the experimental results. A. Diode Laser Wavelength Calibration The wavelength calibration of the diode laser was performed by a fiber optic etalon device along with a fiber-coupled spectrum analyzer while supplying a linearly increasing unmodulated voltage signal to the diode laser current controller [vm ¼ 0 in Eq. (9)]. The etalon device consists of a 2 × 2 fiber optic coupler in which one arm on one side of the coupler is connected to one arm on the other side. The laser enters this setup from the free arm at the one side and the output beam with interference patterns is obtained from the opposite free end. The free spectral range of this device is 4:27 × 10−4 nm. The fine wavelength spacing was obtained from the fringe spacing of the interference peaks. The light frequency distribution has a nonlinear variation with the voltage sent to the laser diode controller as shown in Fig. 3. In choosing modulation depths for experiments, vm was selected such that the modulation was around 2.2 times the HWHM of the water absorption profile as suggested by Reid and Labrie [20] to maximize the signal. With an equal Doppler and collision HWHM (γ D ¼ γ L ¼ 1 GHz), a modulation depth of 3:5 GHz is optimum. From Fig. 3, this depth corresponds to vm ≈ 0:17 V sent to the LDC. Note that since the actual modulation, ε, is less than vm , the applied voltage modulation was increased to 0:2 V after experimental determination of ε. B. Software Lock-in Amplifier A software lock-in amplifier was used for signal processing instead of a hardware lock-in amplifier as also successfully implemented by previous researchers [17,30]. The measured (or simulated) signal from the photodiode in this case is multiplied by a sine wave of the same or double the frequency of the modulation applied to the laser. A fifth-order lowpass Bessel filter is used to remove higher harmonics of the signal. In order to compute the 1f profile (or 2f profile), the signal is multiplied by a sine function with the same frequency (or twice the frequency) and phase-locked with the laser modulation. The 1f and 2f versions of the lock-in amplifier were implemented on the same signal. The 2f calculation was normalized by that from the 1f calculation to determine the 2f =1f signal used in resulting data processing. C. Experiments in Calibration Cell A schematic of the experimental arrangement for the calibration cell is shown in Fig. 1. Gases flowing at controlled flow rates were set at a particular hu- midity by bubbling through a temperature-controlled humidifier (Fig. 1, 13). The flow lines leading to the calibration cell were heated to exceed the saturation temperature by at least 20 °C to prevent any condensation. The flow lines were also connected with a tube to feed dry gases to the calibration cell, thus bypassing the humidifier through a series of valves (Fig. 1, 7, 8, 12). The experimental setup was mounted rigidly on an optical bench to maintain good optical alignment. The flow valves were selected so that they produced as little disturbance as possible during switching. The calibration cell (Fig. 1, 1) was a copper tube of length 24:3 cm with an 8° angled antireflective glass wedge (Fig. 1, 16) at the end for allowing the beam to reach the photodiode (Fig. 1, 17) active element. The calibration cell experiments are broken into two parts: (1) direct absorption measurements, and (2) wavelength-modulation measurements. 1. Direct Absorption Measurements The gases were first fed into the calibration cell through the humidifier at a controlled temperature. The gas stream was assumed to achieve saturation corresponding to the liquid water temperature after it leaves the liquid water bath and enters into the pipeline. This assumption was verified by condensing the liquid water right after the humidifier exit over an extended period of time and determining the amount of condensate that closely matched with the expected amount of liquid water for each flow rate. The flow lines connecting the humidified gases were kept well above saturation to prevent condensation. The temperatures were measured along the length of the calibration cell with thermocouples and the maximum temperature difference across the cell was about 1 °C. The laser was sent a linear voltage ramp with zero modulation, and a scan of the transmitted beam intensities [denoted by I in Eq. (1)] was taken. The measurements were then taken for a background ramp by passing dry nitrogen through the calibration cell [which corresponds to I 0 in Eq. (1)]. The changes were performed carefully so as not to disturb the laser alignment. 2. Wavelength-Modulation Measurements In these experiments, sinusoidal modulations were added to the linear DC ramp voltage signal [Eq. (9)] that was sent to the laser diode current controller. The same conditions as those in the direct absorption measurements were repeated for these sets of experiments along with the background ramp measurements by activating the bypass dry gas line. The ratio I 0 =I measured during the modulated ramp is shown in Fig. 4. The maximum and minimum points in the oscillating transmission (the envelope of the modulation) reflect the shape of the underlying absorption feature. These maximum and minimum points are shown in Fig. 4 as the curves with symbols. With no modulation, a single direct absorption 1 January 2010 / Vol. 49, No. 1 / APPLIED OPTICS 65 Fig. 4. (Color online) I0 =I measured with modulated ramp showing modulation extreme points. feature is observed as the laser is scanned across the absorption feature, and with modulation, two identical absorption profiles form the modulation envelope with a separation equal to the modulation depth. The two absorption profiles in the modulation envelope are designated as λu and λl . Simulations were completed of this modulated absorption signal using the obtained line shape parameters from direct absorption measurements with a wavelength variation corresponding to Eq. (9). Since the transition parameters were fixed from direct absorption, only the laser nonlinearity factor, ε, was unknown in the simulations. The envelope features, λu (Fig. 5, pluses) and λl (Fig. 5, circles), were extracted from the simulations. The profiles from the WMS measurements matched very closely with those predicted using these direct absorption measured pa- Fig. 5. (Color online) Comparison of the experimental modulation extrema from Fig. 4 with those predicted using the direct absorption technique along with laser modulation from Eq. (9). The parameter, ε, describing laser modulation nonlinearities was directly fit in the simulations. 66 APPLIED OPTICS / Vol. 49, No. 1 / 1 January 2010 rameters, but the separation between the two profiles had to be matched with the actual diode laser by fitting the factor ε to account for the laser transients in Eq. (9). Figure 5 shows just the extrema from Fig. 4 along with absorption profiles simulated using Eq. (9) and Eqs. (1)–(6). The modulation factor ε in Eq. (9) was fitted to give the best agreement, and as seen in Fig. 5, this modification was sufficient to describe the laser wavelength; thus, the nonlinearities of the laser modulation can be empirically determined from a direct absorption measurement during a wavelength-modulation experiment. The IM-FM phase shift was adjusted in this method by keeping the experimentally measured IM via the parameter ε and shifting the FM modulation by a constant phase shift. Experimental and simulated profiles are compared to determine the FM shift once the wavelength modulation is obtained for a single value of ε. This FM phase shift was assumed to be constant throughout the rest of the measurements at the same modulation frequency as the laser transients were found to be repeatable. As the software lock-in amplifier used in experimentation employs a LabVIEW-based digital fifth-order Bessel low-pass filter, there are also phase delays associated with the filter. These delays were automatically taken into account in the numerical simulation as it uses a filter identical to the one used in the experiments to produce an identical effect in the simulated profile. The modulated ramp with absorption features was then fed to the software lock-in amplifier, which outputs the ratio of the second to the first harmonic of the absorption profile corresponding to the modulation frequency. The simulated profiles for 2f =1f profiles using the direct absorption parameters were in close agreement with the experimentally obtained Fig. 6. Experimental and simulated 2f =1f absorption profiles under varying water partial pressure conditions showing accuracy of the numerical simulation. Simulated 2f =1f absorption profiles use parameters fit from calibration experiments such that the model is completely predictive. profiles as shown in Fig. 6, indicating that the model for the laser modulation has been implemented accurately. The calibration cell was used to determine the Lorentzian half-widths and line intensities of the absorption lines at different water vapor partial pressures and temperatures in the presence of air and hydrogen. The calibration data obtained at 1 atm total pressure could be used at higher pressures by extending them in the following manner. A simplified form of Eq. (5) can be written as ΔνL ¼ lPs þ mP; ð10Þ where l and m are functions of temperature and collision half-widths. Ps is the water vapor partial pressure and P is the total pressure. The straight lines in the obtained plots for ΔνL and Ps at a particular value of total pressure P can be extrapolated to Ps ¼ 0, which then reveals the intercept value mP. For other values of total pressure P at the same temperature and water vapor partial pressure, the Lorentzian half-width of the absorbing species would then have the effect of translating this relationship with different intercept values. Hence, if the calibration was performed at 1 atm total pressure, a family of calibration curves corresponding to different total pressures can be obtained as shown in Fig. 7. D. Experiments in a Proton Exchange Membrane Fuel Cell The developed sensor was used in an operating PEM fuel cell. The experiments in the PEM fuel cell were carried out in an apparatus similar to the calibration set up with the calibration cell replaced by a prototypical PEM fuel cell as shown in Fig. 8(a). The collimator coupled to the DFB laser was fed directly into the optically accessible PEM fuel cell. The bipolar plates of this fuel cell had a counterflow serpentine channel geometry comprised of 15 straight segments of which the second and fourteenth channels from the air and hydrogen inlets at the cathode and anode sides were milled out to the end of the bipolar plate so that the diode laser beam can be transmitted along the channel length as shown in Fig. 8(b). Each flow channel is 7 cm long with cross-sectional dimensions of 1:5 mm × 2:0 mm. For making measurements simultaneously in the two anode and two cathode channels, the fiber-coupled output of the laser was divided into four fiber outputs via three 2 × 2 bifurcated optical fibers connected to four collimators fixed at one end of each optically accessible channel. Each laser beam, after crossing the flow channels, emerged out of the antireflective infraredtransparent wedged glass windows fixed at opposite ends of the fuel cell channels and collected by four different photodiodes (PD 1, 2, 3, 4). The fuel cell was controlled by a Scribner Associates 890C fuel cell load control box with the aid of a controller computer. The load current was changed, and water vapor partial pressure and gas temperature in each channel were measured at different current settings at steady state. The ramp modulation described by the first term in Eqs. (8) and (9) was actually a triangular wave that was configured to have uneven rising and falling sides so that more data points were collected during the rising edge of the ramp. For the steady state measurements, the rising edge contained 75,000 sample points, whereas the falling edge had 25,000 sample points. Thus, a total number of 100,000 sample points were collected for each spectrum. The frequency of the ramp (including the rise and fall), and therefore the overall collection frequency for each measurement, was 1 Hz. The frequency of the modulation sine wave (ω) was 240 Hz. A faster ramp caused the factor ε to increase due to the dynamics of the diode laser. To ensure proper modeling, the wavelength-modulation fitting routine described previously was repeated when the overall frequency of the measurement was changed. 3. Results The Lorentzian half-widths determined from the calibration experiments are shown in Fig. 9 as a function of the partial pressure of water. The linear trends match with theoretical expectations. It is also noted that the values of the Lorentzian half-width for mixtures with hydrogen are lower than those with air. This can be explained by the fact that hydrogen molecules are lighter and the air–water collisions are much more effective in collisional broadening than hydrogen–water collisions. While the selfbroadening half-width remains the same for both, the foreign gas collision half-width is smaller for hydrogen than air. Combining Eqs. (6) and (10): γ self l ¼1þ : γ foreign m Fig. 7. (Color online) Prediction of ΔνL for 0.6, 0.8, 1.0, 1.2, and 1.4 total pressures. ð11Þ From the linear fits to the calibration curves, the following values are obtained: 1 January 2010 / Vol. 49, No. 1 / APPLIED OPTICS 67 Fig. 8. (Color online) (a) Experimental setup for measurements in a PEM fuel cell and (b) PEM fuel cell gas channels showing optical access. γ self ¼ 4:7 γ air and γ self ¼ 6:1; γ H2 hence; γ H2 ¼ 0:77: γ air ð12Þ The values of γ self and γ air are obtained as 0.477 and 0.095 from the HITRAN 2008 [10] database, which indicates a γ self =γ air ratio of 5.02, which is reasonably close to the obtained value of 4.7. The half-width of water-hydrogen collisions for this particular transition can be written as γ H2 ¼ 0:078. As obtained experimentally, the line intensity has unchanged values for both experiments with hydrogen–water and air–water mixtures as shown in Fig. 10. 4. Application in a Proton Exchange Membrane Fuel Cell In the experiments involving an unknown partial pressure and temperature, the 2f =1f profiles at experimental conditions of interest were obtained. Subsequently, numerically simulated 2f =1f profiles using interpolated values from the list of database created for the half-widths and line intensities from the calibration experiments were used to fit to those curves using the Levenberg–Marquardt curve fit algorithm. The partial pressure and temperature values that minimized the error between these two are considered to be the corresponding actual values from the experiments. Fig. 9. (Color online) Lorentzian half-width versus Ps for (a) air– water and (b) hydrogen–water mixtures. 68 APPLIED OPTICS / Vol. 49, No. 1 / 1 January 2010 Fig. 10. (Color online) Variation of line intensity SðTÞ with temperature. Sample measurements of water partial pressure and temperatures for four measurement channels at steady state are shown in Figs. 11 and 12. For the case shown in Fig. 11, the anode gas supply was fed with hydrogen at 80% relative humidity and the cathode was fed with air at 18% relative humidity. At zero current density (nonoperating fuel cell), the anode gas stream decreases in water content from inlet to outlet due to transfer of water to the cathode side via diffusion. Likewise, the cathode side water content increases from inlet to outlet. As the current density of the fuel cell is increased, additional water is produced within the cell. The change in water content on the anode side from inlet to outlet decreases, but the cathode side shows a substantial increase in outlet water concentration. This is a result of the water production being localized to the cathode side of the cell. The steady state measurements of water concentration in Fig. 11 indicate that there is a monotonic rise in the partial pressure of water corresponding to the electrochemical reaction at the cathode side. The rise is not linear, however, as there is some backdiffusion of water toward the anode. Figure 12 shows the measurements of temperature at the same locations. The polarization curves (voltage versus current density) in Figs. 11 and 12 reflect the performance of the fuel cell. The performance of the fuel cell was not optimal, which was believed to be due to the particular membraneelectrode assembly used and the ratio of active to support areas in the bipolar plate. An uncertainty of
2:5% in partial pressure and
3 °C in temperature is predicted from the calibration experiments. These uncertainties arise due to the optical noise that could not be completely modeled and the fluctuations in temperatures throughout the calibration experiment setup. The line intensities also have a little scatter (Fig. 10) and result in further inaccuracies in temperature. Especially at the higher humidity levels, the condensation of liquid water in the optical path causes optical noise, leading to poor data. Fig. 12. (Color online) Variation of PEMFC temperature with current density at four different locations. 5. Conclusions A sensor utilizing WMS spectroscopy and ratios of signal harmonics (2f =1f ) was developed for applications in PEM fuel cells. A new approach to the data analysis procedure was described, involving fullscale numerical simulation of the harmonic profiles and utilization of direct absorption measurements while modulating the laser to account for nonlinear laser dynamics. This approach was shown to provide good agreement between measured and simulated spectra. The Lorentzian half-widths and line intensities for water-air and water-hydrogen transitions at different water vapor partial pressures and temperatures were measured by both direct absorption and WMS techniques. A procedure is described to obtain the corrected Lorentzian half-width for different total pressures from data obtained at 1 atm. The half-widths for hydrogen–water vapor collisions were obtained. Finally the sensor was tested for measuring water vapor partial pressure and temperature inside an operational PEM fuel cell within an uncertainty of
2:5% in partial pressure and
3 °C in temperature as predicted from the calibration experiments. Appendix A: List of Abbreviations Abbreviation WMS IM FM RAM PEM LDC TEC PD TC Fig. 11. (Color online) Variation of PEM fuel cell water vapor partial pressure with current density at four different locations. Term Wavelength-modulation spectroscopy Intensity modulation Frequency modulation Residual amplitude modulation Proton exchange membrane Laser diode controller Thermoelectric cooler Photodiode Thermocouple This work was sponsored by Connecticut Innovations Incorporated and United Technologies under the Yankee Ingenuity Program. 1 January 2010 / Vol. 49, No. 1 / APPLIED OPTICS 69 References 1. D. T. Cassidy and J. Reid, “Atmospheric pressure monitoring of trace gases using tunable diode lasers,” Appl. Opt. 21, 1185– 1190 (1982). 2. L. C. Philippe and R. K. Hanson, “Laser diode wavelengthmodulation spectroscopy for simultaneous measurement of temperature, pressure, and velocity in shock-heated oxygen flows,” Appl. 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