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Abstract
The wavelength modulation spectroscopy (WMS) technique has been demonstrated as a powerful and indispensable tool for quantitative and real-time measurements on the combustion process of various industrial devices. However, the varying pressure occurred in the aero-engine combustor significantly affects the accuracy and efficiency of the WMS technique. To address this issue, this work reports a novel method named WMS pressure correction model, which can enable fast signal processing in the measurements at varying pressure. The method was first validated in a heated optical cell, and then applied to the pressure and temperature measurements in an aero-engine combustor. The results show that the new method can efficiently and accurately measure the pressure and temperature at the varying pressure conditions.
© 2017 Optical Society of America
1. Introduction
Quantitative and real-time temperature measurements on the engine combustion have been long desired for both monitoring and controlling purpose of the engine operation. Tunable diode laser absorption spectroscopy (TDLAS) technique represents a well-established technique to provide in situ measurements of flame temperature, composition, and velocity. Wavelength Modulation Spectroscopy (WMS), as an extension of the TDLAS technique, is well-known for its ability to significantly improve the signal-to-noise ratio (SNR) and has been widely used in the measurements of temperature and species in engines. A detailed review of the WMS in practical measurements is referred to [1–3].
Though WMS technique offers many benefits, quantitative WMS measurements are challenging due to the following reasons. The WMS signal depends both on the laser intensity and the line-shape, which are all affected by the complicated mechanisms in the combustion process. First, the laser intensity is strongly disturbed by the beam steering, mechanical misalignments, scattering particles and windows fouling in engine combustion measurements. Second, the line-shape for specific line transitions is varying at different engine conditions since the line-shape depends on temperature (Doppler broadening) and pressure (Collision broadening). And the temperature and pressure are always high and change sharply in many practical engine systems (i.e., temperature changes from 500K to 3000K, pressure from 1atm to 30atm in the new aero-engine combustor). Third, the line-shape is Voigt profile in the engine combustion environment. And there is no closed analytical form expression for the Voigt profile, neither for the absorption nor for the WMS signal. Therefore, the influence of the temperature, pressure and concentration on the WMS signal is complicated and remains a key issue for the measurement accuracy.
Past work have been performed to address the above issues. For the vibrations of laser intensity, G.B. Rieker et al. [4] developed a normalization method to normalize the WMS-2f signal with WMS-1f signal magnitude to remove the need for correcting laser intensity fluctuations and instrument factors, and this effective method has been widely used in the harsh environment. As for the varying of line-shape, the influence of the temperature on line-shape can be minimized by using the optimal modulation index as described in [5, 6]. The effect of the varying pressure on the line-shape is much more complicated because the collision broadening is predominant in engine combustion. To solve this problem, J. Chen et al. [7] developed a nonlinear curve fitting method by assuming a Lorentzian-based gas absorption line profile for the measurement of concentration and pressure in the exhaust of a gas furnace. G. Stewart et al. [8–12] presented two approaches, namely the residual amplitude modulation approach and the phasor decomposition method, to recover the absolute gas absorption line-shapes by using WMS signals. These methods have the potential of simultaneous measurement for concentration, pressure, and temperature, and are further validated and improved by Z. Peng and associates [13, 14]. Recently, K. Sun et al. [15] and C. S. Goldenstein et al. [16, 17] have developed a strategy for the analysis of wavelength-scanned WMS with tunable diode lasers. The new analysis scheme allows for the fitting of the wavelength-scanned WMS signal waveform to an absorption spectrum similar to wavelength scanned Direct Absorption Spectroscopy (DAS). The method was applied to measure CO, CO2, CH4 and H2O in a high-pressure engineering-scale transport-reactor coal gasifies [18]. Based on the above methods, Z. Qu [19, 20] optimized the WMS spectral fitting procedures by simulating the measured laser intensity to obtain the phase shift between the laser intensity and wavelength modulation, so that a calibration-free of WMS spectral fitting scheme requiring minimal laser characteristics is realized.
The strategies and methods mentioned above provide a calibration-free WMS technique for the measurements in the harsh environment. However, the characteristic of calibration-free is only one of the evaluation factors for the TDLAS technique. Other key factors include the measurement accuracy, simple operability, compact structure, fast signal processing and real-time data readout. Considering all these factors, the main drawback of the aforementioned methods is the complicated inverse calculations, which consumes considerable calculating time and prevents its application to the application of the real-time data readout. For example, the WMS signal fitting strategy [16–18] needs to calculate the WMS signal and iterative procedures to achieve accurate results, and may have the problem of convergence and uniqueness in the fitting process when the pressure, temperature and gas compositions are all setting as variables. In addition, the uncertainty from the determination of the laser characteristics, absorption path length, and spectroscopic parameters results in errors between the numerical and experimental values, which essentially affects the measurement error. Similarly, the line-shape recovery scheme needs more than fifth order harmonic signals [14] to acquire acceptable accuracy and the computation process is also complicated.
Based on the above understanding, this work presents a new method to simultaneously measure the temperature and pressure at the varying pressure condition based on WMS signal. This method features fast signal processing, which is suitable for developing real-time TDLAS sensors in the applications of monitoring and controlling the non-steady engine combustion. The basic idea to solve the effect of pressure on WMS-2f measurements is to use the width of WMS-2f signal to calculate the pressure, and then use the calculated pressure to correct the magnitude of WMS-2f signal. The computation steps are relatively efficient and accurate since the inverse formulas are pre-acquired before their applications in the following steps. In the rest of this paper, the proposed method was first validated in a heated optical cell, the transitions of H2O at 6873.674 cm−1 and 7450.932 cm−1 are selected in the validation experiments. Then the method was applied to continuously monitor the pressure and temperature in an aero-engine combustor.
2. Mathematic formulation and pressure correction model description
2.1 Mathematic formulation of WMS
A detailed description of the basic principle of WMS can be either found in [5] and [6]. Here, a brief introduction is described to facilitate the following explanation of the pressure correction model. As can be seen in Fig. 1, in scanned-wavelength WMS strategy, a higher-frequency modulation sine wave (typically hundreds of kHz) is added to a slower-frequency laser tuning ramp wave (typically several kHz). When the laser wavelength tunes to near the center of absorption line, nonlinear modulation in the absorbed laser intensity is introduced due to the nonlinear transmission (similar to the line-shape), which accounts for the existence of harmonic signals in the absorbed laser intensity. Therefore, the harmonics signals (usually detected with a lock-in amplifier) of modulated laser intensity are dependent on the absorption term, from which gas properties can be inferred.
Fig. 1 Basic principles of the WMS-2f processes, the red waveform denotes the varying of laser wavelength versus time, the pink waveform denotes the varying of absorbed laser intensity versus time. Owing to the nonlinear transmission (similar to the line-shape), the absorbed laser intensity is nonlinear modulated when the laser wavelength tunes to near the center of absorption line.
When the absorption is small (the absorbance less than about 0.1) [21], the height of second harmonic signal (WMS-2f) and their ratio of two absorption lines shown in Fig. 1 can be expressed as [21]:
Where G is the electro-optical gain of the measurement system (including the detector setting, signal amplification and lock-in setting etc.), P (atm) is the total pressure, X is the mole fraction of absorbing species, L (cm) is the absorption path length, I(ν) is the laser intensity at the absorption line center ν (cm−1), S(T) (cm−2atm−1) is the temperature-dependent line strength, ϕ(ν) (cm) is the line-shape, a (cm−1) is the wavelength modulation amplitude, K is the second harmonic Fourier component, subscript i represent absorption line i.For two-line thermometry, the temperature is obtained by comparing the line strength S(T) of two different absorption lines which have different temperature dependence. Utilizing the expression of S(T) [1, 21], the temperature can be formulated as:
Where Q(T) is the partition function, Tref (K) is the reference temperature for the line strength, E″ (cm−1) is the lower state energy of absorption line, h is Planck’s constant, c is the speed of light, k is Boltzmann’s constant, hc/k has a numerical value of 1.438 (cm·K). Apparently, the value of laser intensity I(ν) and the second Fourier component K are needed to calculate the temperature T from Eq. (5). I(ν) can be evaluated by monitoring the laser intensity or using the 1f signal normalization method [4]. The determination of the second Fourier component K is much more difficult since the line-shape ϕ(ν) depends on the temperature (Doppler broadening), the pressure (Collision broadening) and the gas compositions (air-broadening and self-broadening coefficient), which are all varying in engine combustion. In order to evaluate the effects of these parameters on K, this work simulates the K for two water lines 6873.674 cm−1 and 7450.932 cm−1 by using Voigt line-shape function [21] and line parameters found in spectral database HITEMP2010 [22] (the high-temperature extended database for HITRAN, which lists more bands and transitions than HITRAN for the absorbers H2O).The Δν (Full Width at Half Maximum of the line-shapes, FWHM) are 0.0866 cm−1 and 0.1156 cm−1 for Line 6873.674 cm−1 and Line 7450.932 cm−1 at T = 1500 K, P = 1 atm and water mole fraction X = 0.1, respectively. Owing to the maximum WMS-2f signal occurs near a modulation index m (m = 2a/Δν) of 2.2 [4, 5]. Thus, the wavelength modulation amplitude a we utilized in simulation are 0.095 cm−1 and 0.125 cm−1, respectively, in order to optimize the amplitude of K profile expressed as Eq. (3).
Figure 2 shows the influence of the temperature on the line-shape, K profile, and the ratio of K height for two selected water lines at the conditions of P = 1 atm, X = 0.1. Since the collision broadening is predominant at atmospheric environment, the changing of line-shape is very small in the different temperatures as shown in Fig. 2(a). Thus, the temperature has a trivial influence on the varying of K profile shown in Fig. 2(b). Figure 2(c) presents the K height for two selected lines from 500 K to 3000 K. The magnitude of Line 6873.674 cm−1 is greater than Line 7450.932 cm−1 due to its smaller Δν. There are two broadening mechanisms of the temperature. The first one is the Doppler broadening in which a higher temperature corresponds to a bigger the Doppler width. The second one is the temperature dependent collisional broadening coefficients (γself and γair), in which a higher temperature correspond to a smaller γself and γair. As can be seen in Fig. 2(c), the relationship of the K height and the temperature is not a monotone function due to the competition of the two temperature broadening mechanisms. The maximal difference of the ratio for two lines shown in Fig. 2(c) is less than 4% from 500 K to 3000 K. Therefore, the effects of temperature can be neglected when using the optimal modulation amplitude [5, 6] or calibrating in laboratory.
Fig. 2 Panel (a): the calculated line-shape in different temperatures. Panel (b): the calculated K profile in different temperatures. Panel (c): the height of K profile and the ratio of the two water lines as a function of temperature.
The broadening mechanisms of gas compositions are related to the collisional broadening coefficient γj of specific component. Due to the limitation of the HITEMP2010 [22], this work only considers the γself and γair in the simulation. Figure 3 shows the simulated line-shape, K profile and the height at different water fractions. Apparently, the line-shape is broadening and decreasing as the increase of the water fraction as shown in Fig. 3(a), leading to the decrease of the height of K profile in Fig. 3(b). This is because the value of γself is much higher than (about one order of magnitude) γair found in HITEMP2010 [22]. Thus, the height of K profile is decreasing monotonously as a function of water fraction shown in Fig. 3(c), which is mainly attributed to the reduction of line-shape and modulation index m (m = 2a/Δν) when the Δν is increasing with water mole fraction (i.e. m changes from 2.37 to 1.74 for Line 6873.674 cm−1 and from 2.24 to 1.95 for Line 7450.932 cm−1). The maximal discrepancy of the ratio for two lines shown in Fig. 3(c) is ~25% from X = 0.05 to 0.25. Hence, a large change of gas compositions in engine combustion will lead to a considerable temperature measurement error by using the WMS technique.
Fig. 3 Panel (a): the calculated line-shape in different water concentrations. Panel (b): the calculated K profile in different water concentrations. Panel (c): the K height and the ratio of two water lines as a function of water fraction. a = 0.095 cm−1 for Line 6873.674 cm−1 and 0.125 cm−1 for Line 7450.932 cm−1.
The effect of pressure on line-shape is mainly due to the Collision broadening, leading to a proportional relationship between the collisional width (FWHM) Δνc and the pressure. Therefore, the pressure has a strong effect on the line-shape and K profile as shown in Figs. 4(a) and 4(b), and the height of K profile decreases sharply with the increase of the pressure as shown in Fig. 4(c). Moreover, the ratio of the two water lines also varies apparently at different pressure; the maximal discrepancy shown in Fig. 4(c) is ~35% in the pressure range from 1 atm to 15 atm. The reasons of the decrease of the K profile with pressures are as follows: Frist, the modulation index m reduces when using the fixed modulation amplitude, as shown in Fig. 5(a). Second, the magnitude of K profile has a positive correlation with the derivative of line-shape [21], resulting in the decrease of the height of K profile with the broadening of the line-shape at elevated pressure, even though the modulation index is optimized (i.e. m = 2.2), as shown in Fig. 5(b).
Fig. 4 Panel (a): the calculated line-shape in different pressures. Panel (b): the calculated K profile in different pressures. Panel (c): the K height and the ratio of two water lines as a function of pressure. T = 1500 K, X = 0.1, a = 0.095 cm−1 for Line 6873.674 cm−1 and 0.125 cm−1 for Line 7450.932 cm−1.
Fig. 5 Panel (a): the varying of modulation index m for two water lines in different pressures. Panel (b): the varying of K height under optimal modulation index 2.2 in different pressures.
2.2 Description of the pressure correction model
Based on the above understanding, the main challenging of the temperature measurement using WMS-2f technique is the determination of the line-shape ϕ(ν) and the second Fourier component K. And the pressure plays a key role to determine these two terms. This section describes the pressure correction model developed to solve this problem with enhanced accuracy and efficiency compared to the existing methods.
Similar to the line-shape, the width of K profile is also dependent on the pressure as shown in Fig. 6(a), which becomes wider as the pressure increases. However, the width of K profile is also varying with the modulation index [21]. Thus, it is necessary to identify the conditions at which the FWHM of WMS-2f signal is single-valued with pressure. Figure 6(b) illustrates the full width at half maximum (FWHM) of K profile (solid lines) and relevant modulation index m (dashed lines) varying with pressure at four different modulation amplitudes. The FWHM is single-valued with pressure at the condition of m<2.2 (i.e. the FWHM is a monotonous function with pressure for a = 0.125 cm−1 in the range of P > 1 atm). This result indicates that it is possible to measure the combustion pressure though the width of WMS-2f signal if it has a weak correlation with temperature and gas compositions.
Fig. 6 Panel (a): the K profile for water line 7450.932 cm−1 in different pressures. Panel (b): the FWHM of K profile and modulation index m as a function of pressure in different modulation amplitudes. Panel (c): the enlarged view of the dashed border in panel (b).
Figure 7 shows the FWHM of K profile in different temperatures (Fig. 7(a)) and water mole fractions (Fig. 7(b)) as a function of pressure. The maximal discrepancy of the FWHM of K profile is less than 5% both for temperature varying from 800 K to 2500 K and water mole fraction varying from 0.05 to 0.15 in the pressure range of 1 atm to 15 atm, indicating that the width of K profile has a weak correlation with temperature and gas compositions. The effects of other gas compositions are similar to the water, which depend on the collisional broadening coefficient γj of specific component. Generally, the value of γself is much higher (about one order) than γair found in HITEMP database [22]. Thus, the effects of other gas compositions on the FWHM of K profile are much lower than water itself and can then be neglected. The discrepancies of the FWHM in different temperatures and water mole fractions become higher as the pressure increases. This is because that the modulation index m become more deviate from optimal value (i.e. m = 2.2) with modulation amplitude of 0.125 cm−1. Fortunately, the discrepancies are very small (less than 2%) in the pressures range of 1 atm to 5 atm in which the height of K profile decreases sharply (shown in Fig. 4(c)). Therefore, the more discrepancies of the width of K profile due to the changing of temperature and water mole fraction in higher pressure (above 5 atm) has smaller influence on the pressure correction model presented below, because the varied pressure above 5 atm has smaller influence on the K height ratio, as shown in Fig. 4(c).
Fig. 7 Panel (a): the FWHM of K profile as a function of pressure at different temperatures. Panel (b): the FWHM of K profile as a function of pressure at different water mole fractions. Water Line 7450.932 cm−1.
Hence, the basic idea to solve the effect of pressure on WMS-2f measurements is to use the width of WMS-2f signal to calculate the pressure, and then use the calculated pressure to correct the magnitude of WMS-2f signal. Figure 8 shows the flow chart of the pressure correction model for the measurements of pressure, temperature and concentration based on the WMS-2f signal. The pressure correction algorithm consists of three steps: (1) calculating combustion pressure based on the width of WMS signal; (2) introducing pressure correction factor to eliminate the influence of pressure on the magnitude of WMS signal; (3) calculating the temperature and gas concentration based on traditional two-line thermometry by using the pressure correcting magnitude of WMS signal.
Fig. 8 Flow chart of pressure correction model for the measurements of pressure, temperature and concentration based on WMS-2f technique at varying pressure conditions.
The first step is to use the width of WMS-2f signal to calculate the pressure using the following equation:
where, w denotes the width of WMS-2f signal which can be either the FWHM or the width between two minimal points shown in Fig. 6(a). Reminding that, it is difficult to determine the minimal points of WMS-2f signal in high pressure environment (P > 5 atm). Here, the FWHM was used in the following simulation and experimental demonstration. f(w) is the function of pressure versus w, which is the curve shown in Fig. 7. It can be calibrated in laboratory or calculated with specific laser modulation and line parameters.The second step is to introduce the pressure correction factor, so that we can compensate the influence of the pressure on the height of WMS-2f signal. According to Eq. (5), the calculation of temperature T requires the value of the item ln(K2/K1), and this item varying with pressure significantly based on our simulations. Thus, the pressure correction factor is actually the item ln(K2/K1) in Eq. (5). In order to be measurable in laboratory, we combined the item ln(K2/K1) together with the ln[S2(Tref)/S1(Tref)] in Eq. (5), and the formula of pressure correction factor is expressed as:
where P is the pressure obtained from the first step, H(P, Tref) is the height of WMS-2f signal as a function of pressure at the reference temperature Tref, Ic(ν) is the laser intensity for the measurement of H(P,Tref), subscript 1 and 2 represent absorption line 1 and line 2. C is pressure correction coefficient which can be calibrated in laboratory or calculated with specific laser modulation and line parameters.The third step is to use the traditional Two-line method [21] to calculate the temperature T and concentration X:
where H is the measured height of WMS-2f signal in applications, C is the pressure correction coefficient acquired in the second step, and L is the absorption path length, Gc, Lc and Xc are the electro-optical gain, absorption path length and concentration for the measurement of H(P,Tref) in the second step.Consequently, the pressure, temperature and concentration can be simultaneously measured in a non-steady combustion flow through Eqs. (6)-(9) using the pressure correction model. Note that, the computation steps from Eqs. (6)-(9) are relatively less time consuming since the calibration or the calculation curve are pre-acquired before the model. This model is suitable for developing the real-time TDLAS sensors in the applications of monitoring and controlling the non-steady engine combustion. Furthermore, the pressure correction method presented in this paper has the potential to be established as a calibration-free method, the main terms f(w) and pressure correction coefficient C expressed in Eqs. (6) and (7) can be calculated with the laser characteristics and line parameters pre-determined.
3. Experimental results
3.1 Validation in a heated optical cell
The pressure correction model is first validated and evaluated in a heated optical cell. Two water absorption lines 6873.674 cm−1 and 7450.932 cm−1 are selected based on their strong absorption strength over 500 K to 3000 K. These two lines were chosen also because of their sharp peaks compared to their neighbor lines. The diagram of the experimental setup is shown in Fig. 9. The heated optical cell is reconstructed from a three zone tube furnace (OTF-1200X), which is designed to withstand pressure up to 35 atm and temperature up to 1373 K. The stainless steel tube is 120 cm long, of which the middle 20 cm is occupied by the cell path length in order to achieve temperature uniformity (<3 K). The two quartz rods provide optical access and are essential to match the cell path length with the central 20 cm region.
Two DFB diode lasers emit the light beam with the wavelength near to 1342.11 nm (NLK1B5EAAA) and 1454.83 nm (NLK1E5EAAA). The lasers are separated by Time Division Multiplexing (TDM) scheme (detailed structure shown below). The selection of TDM for the two lasers separation is due to its flexibility and relative simple setup, i.e., using only one detector and Lock-in channel with the same electro-optical gain. The injection current of the lasers was driven by a 500 Hz sawtooth ramp to tune the wavelength. A 150 kHz sine wave was combined to the lasers for wavelength modulation. The tune and modulation waveforms are generated by Labview codes running on a National Instruments data acquisition card (USB-6366). The magnitudes of the sine waves are adjusted so that the amplitude of WMS-2f signal for line 6873.674 cm−1 and line 7450.932 cm−1are maximized at the atmospheric pressure, respectively(i.e., the optimal modulation index at 1 atm). The output laser was collimated (F240-APC) and passed through the heated optical cell, and then was filtered and detected by a narrow band filter (Spectogon) to prevent the thermal radiation from the furnace and a photodetector (DET50B). The collimator and detector were placed closely to the stainless steel tube in order to reduce the absorption from room air. A lock-in amplifier (HF2LI) was used to measure the WMS-2f signal of the transmitted laser signal. Both the WMS-2f signal and the transmitted laser signal were recorded and analyzed by the DAQ computer. Figure 10 shows the synchronous measured laser intensity and WMS-2f signal during one sawtooth ramp cycle. The modulated laser intensity is smoothed by a Zero Phase Filter based on Labview coding. And the smoothed laser intensity corresponding to the peaks of the measured WMS-2f signal refer to the term I(ν1) and I(ν2) shown in Eqs. (7)-(9).
Fig. 10 The synchronous measured laser intensity and WMS-2f signal. Panel (a): the measured laser intensity in one cycle. Panel (b): the measured WMS-2f signal in one cycle.
Figure 11 presents the measured WMS-2f spectra for two selected water lines at different pressure. Obviously, the WMS-2f spectra decrease and broaden at high pressures, as shown in Figs. 11(a) and 11(b). The height of measured WMS-2f spectra as a function of pressure H(P) is normalized by H(P = 1atm) and pressure P, so that we can eliminate the line strength S(T) and compare the measured data with the calculated value (shown in Fig. 4(c), but normalized by the value at P = 1 atm). In consistent with our theory analysis, the discrepancies of normalized WMS-2f height between different temperatures are very small because the line-shape has a weak correlation with temperature, shown in Figs. 11(c) and 11(d). The overall changing trend of measured data along with pressure is in agreement with the calculated value. The differences are mainly resulted from the following reasons: First, the neighbor lines of two selected water lines are not considered in the simulation. Second, the laser modulation characteristics such as nonlinear modulation both for intensity and wavelength are not introduced in the simulation. Third, the line parameters, especially the broaden parameters, is calibrated with certain uncertainty in HITEMP2010 [22]. Thus, we utilize the measured data to establish the pressure correction model presented in section 2.2.
Fig. 11 Measured WMS-2f signal for two selected water lines at different pressures. Panel (a): measured WMS-2f signal for Line 6873.674 cm−1. Panel (b): measured WMS-2f signal for Line 7450.932 cm−1. Panel (c): normalized WMS-2f height versus pressure for Line 6873.674 cm−1. Panel (d): normalized WMS-2f height versus pressure for Line 7450.932 cm−1. The measured height of WMS-2f signal for the two lines is normalized by H(P = 1atm) and pressure P. The calculation value for the two lines is normalized by their value at P = 1 atm, respectively.
Figure 12 illustrates the measured curve expressed as Eqs. (6) and (7), which are the key parameters used in the pressure correction model. In Fig. 12(a), the pressure is single-valued function of the FWHM of WMS-2f signal (expressed as DAQ sample points), and the discrepancies between different temperature are less than 1%. For the sake of application in high temperature, we used the two order polynomial fitting curve of measured data at 1173K as Eq. (6) to minimize the system error of pressure inverse calculation. Figure 12(b) is the measured pressure correction factor C and exponential decay fitting at three different reference temperatures.
Fig. 12 Measured data of Eqs. (6) and (7) in the pressure correction model. Panel (a): the measured FWHM of WMS-2f signal versus pressure. Panel (b): the measured pressure correction factor C versus pressure at three different reference temperatures.
The TDLAS WMS-2f sensor is calibrated from 573 K to 1373 K at atmospheric pressure, and the maximal temperature deviation is less than 2.5% as shown in Fig. 13(a). Figures 13(b)-13(d) display the temperature measurement errors over 1 atm to 12 atm for 773 K, 973 K and 1173 K, respectively. Obviously, the temperatures measured by traditional two-line method without pressure correction differ from real temperature when the pressure is rising, and the maximal difference reaches up to 31% in Fig. 13(c). In comparison, the temperatures measured by pressure correction model are much reliable over 1 atm to 12 atm, and the maximal difference among three different reference temperature 1173 K, 973 K, and 773 K are 5.3%, 4.1%, and 4.2% in term of Fig. 13(c), respectively. The discrepancies between different reference temperatures utilized in Eq. (7) are not apparent in our experiment. However, the same changing trends versus pressure for different reference temperature shown in Figs. 13(b)-13(d) indicate that they have the same system errors in the experiment, probably due to the pressure control errors of the heated optical cell.
Fig. 13 The temperature measurement errors of established TDLAS WMS-2f sensor. Panel (a): the measured errors versus temperature at atmospheric pressure. Panel (b): the measured errors over 1 atm to 12 atm for 773 K. Panel (c): the measured errors over 1 atm to 12 atm for 973 K. Panel (d): the measured errors over 1 atm to 12 atm for 1173 K.
3.2 Demonstration in the Aero-engine combustor
After the validation, the TDLAS WMS-2f sensor was applied on a single-headed and kerosene fueled model combustor of aero-engine. The pressure in the combustor is up to several atmospheric pressures, and the temperature in the combustor is around 2000 K [23]. Figure 14 shows the experimental setup for the measurements in the aero-engine combustor based on Time Division Multiplexing (TDM) scheme. An example of measured pressure and temperature based on pressure correction model is illustrated in Fig. 15. As shown in Fig. 15(a), the trend of pressure measured by the WMS-2f signal is consistent with the data acquired from pressure gauge. Comparing with the wall pressure measured by pressure gauge, the data measured by the WMS-2f signal is the internal flow field pressure, which has a better time response. Figure 15(b) shows the measured temperatures as a function of time. Apparently, the temperatures measured from pressure correction model are steady and around 2000 K, while the temperatures measured from traditional two-line method are lower and decreasing with time (i.e., decreasing with pressure). Compared to the theoretical predictions [23], the pressure correction results are more likely to be true than the lower temperatures measured by the traditional method.
Fig. 14 Experimental setup for the measurements of aero-engine combustor based on time division multiplexing scheme.
Fig. 15 The measured pressure and temperature based on the established WMS-2f sensor. Panel (a): the comparison of measured pressure between the pressure gauge and the WMS-2f sensor. Panel (b): the comparison of measured temperature between the traditional Two-line Method and the Pressure Correction Method.
4. Conclusions and future work
The combustion in the new generation engines features high temperature, high pressure and non-steady. The WMS technique based on TDLAS is a useful tool to study the combustion process in the new generation engines. However, the varying pressure has a strong effect on the WMS-2f signals, which complicates the quantitative measurement. As a solution, we proposed a novel method named pressure correction model which has the advantage of fast signal processing, it is suitable for developing real-time TDLAS sensors for monitoring and controlling the non-steady engine combustion. To validate this method, two transitions lines of H2O at 6873.674 cm−1 and 7450.932 cm−1 were selected, and the validation experiment was performed in a heated optical cell. The experimental result was consistence with the simulation, and the maximal discrepancy of temperature between the measured data and real data over 1 atm to 12 atm was within 4.1%. After the validation, this method was then applied to monitor pressure and temperature continuously in an aero-engine combustor. The results show that the pressure correction model can efficiently and accurately measure the pressure and temperature at the varying pressure conditions.
It should be noted that the simulation in this paper is under the weak absorption and not consider the laser characteristics. Moreover, the neighbored lines of two selected water lines are not included in our simulation. Thus, as presented in Section 3.1, we utilize the measured data of Eqs. (6) and (7) to establish the pressure correction model, which contains the influence of non-ideal laser behavior and the neighboring lines. The pressure correction model can be further improved by combining the WMS-1f signal normalization method developed by G. B. Rieker et al [4] and the method presented by K. Sun et al [15] to solve the problem of the influence of neighboring lines and the non-linear modulation in the lasers. Based on this, a calibration-free method for the pressure correction model can be established, which will be described in a separate paper.
However, based on our analysis, quantitative measurements of non-steady combustion at high pressure still have several problems. First, the varying of gas compositions will lead to the measurement error of the ratio of two selected absorption lines. According to our simulation, the error could reach up to 25% when the water mole fraction changes from 0.05 to 0.25. This is a significant point that deserves more efforts considering that the mechanism of gas composition on the line-shape is always too complicated to be quantified separately, even if utilizing the WMS-2f fitting method proposed by the previous researchers. Second, the magnitude of WMS signal is decreasing with pressures. Thus, the WMS signal may be too weak to be detected at high pressures. For example, the absorption lines utilized in this paper is difficult to be used when the pressure is above 12 atm. For higher pressures, there is a need to distinguish two other absorption lines with stronger absorption strength
Acknowledgments
This work was supported by the National Natural Science Foundation of China under Grant No.51176159, NO.91541203 and NO.91441201.
References and links
1. M. A. Bolshov, Y. A. Kuritsyn, and Y. V. Romanovskii, “Tunable diode laser spectroscopy as a technique for combustion diagnostics,” Spectrochim. Acta B At. Spectrosc. 106, 45–66 (2015). [CrossRef]
2. R. K. Hanson and D. F. Davidson, “Recent advances in laser absorption and shock tube methods for studies of combustion chemistry,” Prog. Energ. Combust. 44, 103–114 (2014). [CrossRef]
3. R. K. Hanson, “Applications of quantitative laser sensors to kinetics propulsion and practical energy systems,” Proc. Combust. Inst. 33(1), 1–40 (2011). [CrossRef]
4. G. B. Rieker, J. B. Jeffries, and R. K. Hanson, “Calibration-free wavelength-modulation spectroscopy for measurements of gas temperature and concentration in harsh environments,” Appl. Opt. 48(29), 5546–5560 (2009). [CrossRef] [PubMed]
5. J. T. C. Liu, J. B. Jeffries, and R. K. Hanson, “Wavelength modulation absorption spectroscopy with 2f detection using multiplexed diode lasers for rapid temperature measurements in gaseous flows,” Appl. Phys. B 78(3-4), 503–511 (2004). [CrossRef]
6. H. Li, A. Farooq, J. B. Jeffries, and R. K. Hanson, “Near-infrared diode laser absorption sensor for rapid measurements of temperature and water vapor in a shock tube,” Appl. Phys. B 87(2-3), 407–416 (2007). [CrossRef]
7. J. Chen, A. Hangauer, R. Strzoda, and M. C. Amann, “Laser spectroscopic oxygen sensor using diffuse reflector based optical cell and advanced signal processing,” Appl. Phys. B 100(2), 417–425 (2010). [CrossRef]
8. K. Duffin, A. J. McGettrick, W. Johnstone, G. Stewart, and D. G. Moodie, “Tunable Diode-Laser Spectroscopy With Wavelength Modulation: A Calibration-Free Approach to the Recovery of Absolute Gas Absorption Line-shapes,” J. Lightwave Technol. 25(10), 3114–3125 (2007). [CrossRef]
9. W. Johnstone, A. J. McGettrick, K. Duffin, A. Cheung, and G. Stewart, “Tunable diode laser spectroscopy for industrial process applications: system characterization in conventional and new approaches,” IEEE Sens. J. 8(7), 1079–1088 (2008). [CrossRef]
10. A. J. McGettrick, W. Johnstone, R. Cunningham, and J. D. Black, “Tunable diode laser spectroscopy with wavelength modulation: calibration-free measurement of gas compositions at elevated temperatures and varying pressure,” J. Lightwave Technol. 27(15), 3150–3161 (2009). [CrossRef]
11. G. Stewart, W. Johnstone, J. R. P. Bain, K. Ruxton, and K. Duffin, “Recovery of absolute gas absorption line-shapes using tunable diode laser spectroscopy with wavelength modulation—part I: theoretical analysis,” J. Lightwave Technol. 29(6), 811–821 (2011).
12. J. R. P. Bain, W. Johnstone, K. Ruxton, G. Stewart, M. Lengden, and K. Duffin, “Recovery of absolute gas absorption line-shapes using tunable diode laser spectroscopy with wavelength modulation—part 2: experimental investigation,” J. Lightwave Technol. 29(7), 987–996 (2011). [CrossRef]
13. P. Zhimin, D. Yanjun, C. Lu, L. Xiaohang, and Z. Kangjie, “Calibration-free wavelength modulated TDLAS under high absorbance conditions,” Opt. Express 19(23), 23104–23110 (2011). [CrossRef] [PubMed]
14. P. Zhimin, D. Yanjun, C. Lu, and Y. Qiansuo, “Odd harmonics with wavelength modulation spectroscopy for recovering gas absorbance shape,” Opt. Express 20(11), 11976–11985 (2012). [CrossRef] [PubMed]
15. K. Sun, X. Chao, R. Sur, J. B. Jeffries, and R. K. Hanson, “Wavelength modulation diode laser absorption spectroscopy for high-pressure gas sensing,” Appl. Phys. B 110(4), 497–508 (2013). [CrossRef]
16. C. S. Goldenstein, C. L. Strand, I. A. Schultz, K. Sun, J. B. Jeffries, and R. K. Hanson, “Fitting of calibration-free scanned-wavelength-modulation spectroscopy spectra for determination of gas properties and absorption lineshapes,” Appl. Opt. 53(3), 356–367 (2014). [CrossRef] [PubMed]
17. C. S. Goldenstein, R. M. Spearrin, J. B. Jeffries, and R. K. Hanson, “Wavelength-modulation spectroscopy near 2.5 μm for H2O and temperature in high-pressure and -temperature gases,” Appl. Phys. B 116(3), 705–716 (2014). [CrossRef]
18. R. Sur, K. Sun, J. B. Jeffries, J. G. Socha, and R. K. Hanson, “Scanned-wavelength-modulation-spectroscopy sensor for CO, CO2, CH4and H2O in a high-pressure engineering-scale transport-reactor coal gasifies,” Fuel 150, 102–111 (2015). [CrossRef]
19. Z. Qu, R. Ghorbani, D. Valiev, and F. M. Schmidt, “Calibration-free scanned wavelength modulation spectroscopy-application to H2O and temperature sensing in flames,” Opt. Express 23(12), 16492–16499 (2015). [CrossRef] [PubMed]
20. Z. C. Qu and F. M. Schmidt, “In situ H2O and temperature detection close to burning biomass pellets using calibration-free wavelength modulation spectroscopy,” Appl. Phys. B 119(1), 45–53 (2015). [CrossRef]
21. X. Zhou, Diode-laser Absorption Sensors for Combustion Control (Academic, 2005), Chap. 2.
22. L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transf. 111(15), 2139–2150 (2011). [CrossRef]
23. H. Z. Feng, Z. Ma, Y. G. Yang, Y. Liang, M. Li, and J. Q. Suo, “Study on combustion characteristics of an aeroengine combustion chamber with kerosene into diesel,” Advan. Aeronauti. Sci. Engi. 8(1), 29–37 (2017).
