Objective The measurement of key parameters of combustion flow field can effectively evaluate combustion efficiency, control pollution emission, and improve energy efficiency. Because of its obvious superior features such as high precision, noncontact measurement, and low cost, tunable diode laser absorption spectroscopy (TDLAS) is an effective way to measure temperature, concentration, velocity, and pressure in combustion flow field. Combined with computerized tomography (CT), TDLAS can achieve two-dimensional(2D) or three-dimensional (3D) tomography. In the 1980s, Emmerman et al. used the direct absorption spectroscopy (DAS) for combustion diagnosis in reactive flows, which verified the feasibility of the method to realize 2D combustion diagnosis. With the development of the laser and reconstruction algorithms, the DAS-based 2D reconstruction technology has begun to be applied to engineering practice. This technology has been successfully used in the Hypersonic International Flight Research Experiment (HIFiRE) conducted by the US Air Force Laboratory and NASA. Although the DAS exhibits many advantages, it is difficult to apply this method under low signal-to-noise ratio (SNR) conditions. The wavelength modulation spectroscopy developed on the basis of the DAS can significantly improve the SNR under weak absorption conditions, thus improving the detection accuracy and detection limit of the absorption spectroscopy. In line-of-sight measurement, the wavelength modulation spectroscopy (WMS) shows good noise resistance and is therefore suitable for the flow field measurement under weak absorption or high-pressure conditions. Calibration-free WMS (CF-WMS) proposed by Hanson's group from Stanford University is one of the widely used WMS methods. As far as we know, the literature mainly focused on numerical simulation analysis for the difference in 2D reconstruction between the DAS and WMS. It is necessary to verify the difference between the two methods by experiment.

Methods Combined with the algebraic reconstruction technique (ART), we introduced the principle of two-dimensional temperature reconstruction based on WMS, and analyzed the difference between DAS and WMS in the two-dimensional reconstruction under the influence of various noises through numerical simulation. Next, the combustion flow field generated by the McKenna flat flame furnace was used as the measurement object. The two-dimensional temperature measurement experimental system was built around the flat flame furnace. DAS- and WMS-based two-dimensional temperature reconstructions of methane-air premixed flame with an equivalent ratio of 1 were carried out, and the reconstruction results were analyzed.

Results and Discussions In numerical simulation, the temperature reconstruction results of the simulated flow field with two reconstruction methods under various noise intensities are provided (Table 2). The maximum deviation and mean square relative error of WMS are 0.0186 and 40.3 K, respectively, and those of DAS reconstruction are 0.0192 and 42.5 K, respectively. Under the condition of no noise, these values are relatively consistent. With the increase in noise intensity, the reconstruction error based on DAS gradually increases, while that of WMS does not change significantly. The maximum deviation and mean square relative error of WMS based reconstruction are 0.0206 and 49.8 K, respectively, and those of DAS based reconstruction are 0.0795 and 353.6 K, respectively (Fig. 3). Under the condition of noise intensity I_RIN=-140 dB/Hz, these values are greatly different. This result shows that the reconstruction accuracy of the WMS based method is higher than that of the DAS based method in the presence of measurement noise, and the suppression effect of the WMS based method on noise is still effective in a two-dimensional reconstruction. Under the condition of a weak-absorption flow field, the two-dimensional reconstruction method based on the WMS can effectively suppress the influence of noise in measurement with higher measurement accuracy.

In experimental verification, the maximum deviation between the reconstructed temperature field obtained by the DAS-based method and the thermocouple measurement result appeared in the range of 50 mm in diameter is about 56.6 K (8.5%), and the relative error of the mean square of the reconstructed temperature field is 0.0469 (Fig. 9). Although the reconstruction results based on DAS reflect the temperature distribution characteristics of the combustion flow field, the overall error is relatively large. This error mainly comes from the baseline fitting error and the Voigt fitting error caused by noise, while the influence of the baseline fitting error is more serious in a weak absorption environment. For a 2D reconstruction, the Voigt fitting error will affect the accuracy of ART 2D reconstruction, and it will eventually show up as a temperature reconstruction error. Selecting absorption spectral lines with stronger absorption will help reduce the error of the DAS based method in a two-dimensional reconstruction. The maximum deviation of the reconstructed temperature field obtained by the WMS-based method is 39.2 K (5.9%), which also occurred in the range of 50 mm in diameter (Fig. 9). The relative error of mean square is 0.0268. In general, the reconstruction result based on WMS is consistent with the thermocouple measurement result, and the measurement error is smaller than that of the DAS-based method. In one-dimensional TDLAS, WMS is not affected by the baseline and has significant inhibition effect on the noise at absorption peak, which is also reflected in 2D reconstruction. As the 2f/1f signal has a better suppression effect on the environmental noise, the signal of each ray has a higher SNR, which is helpful to a more accurate 2D reconstruction.

Conclusions In this paper, WMS combined with ART is applied to the two-dimensional reconstruction of the combustion flow field. The reconstruction speed is large, and the number of spectral lines required is small, which has great advantages in practical applications. From the numerical simulation and experimental verification, the difference between DAS- and WMS-based 2D reconstruction is analyzed. It is proved that WMS has a better suppression effect on noise than DAS in a 2D TDLAS. In a numerical simulation, the difference in the reconstruction result between the two methods under different noise levels is analyzed. The result shows that with the increase in the noise level, a WMS-based 2D reconstruction has better robustness while a DAS-based 2D reconstruction varies significantly. In the case of a high noise level, a DAS-based 2D reconstruction cannot accurately reflect the characteristics of a simulated flow field environment. In an experimental verification, by comparing with the result measured by the thermocouple, we find that the maximum deviations of the DAS-based 2D reconstruction and WMS-based 2D reconstruction are 8.5% and 5.9%, respectively, and the mean square relative errors are 0.0469 and 0.0268, respectively. The results show that the WMS-based 2D reconstruction has higher anti-noise capability than DAS-based 2D reconstruction and the accuracy of a WMS-based 2D reconstruction is higher than that of the DAS-based 2D reconstruction under weak absorption. It is advised that a WMS-based two-dimensional reconstruction method is suitable for engineering applications where noise has a great impact, such as 2D reconstruction of flow field in a scramjet combustion chamber and the wind tunnel flow field quality assessment.