Numerical investigation of hyperspectral tomography for simultaneous temperature and concentration imaging

Simultaneous Reconstruction of Gas Concentration and Temperature Using Acoustic Tomography

Acoustic tomography utilizes sensor arrays to collect sound wave signals, enabling non-contact measurement of physical parameters within an area of interest. Compared to optical technologies, acoustic tomography offers the advantages of low cost, low maintenance, and easy installation. Current research in acoustic tomography mainly focuses on reconstruction algorithms for temperature fields, while monitoring the composition and concentration of gases is significant for ensuring safety and improving efficiency, such as in scenarios like boiler furnaces and aviation engine nozzles. In excitable gases, the speed of sound exhibits an S-shaped curve that changes with frequency, a characteristic that could be potentially useful for acoustic tomography. Therefore, this study primarily discusses the quantitative calculation of gas concentration and temperature based on the dispersion of the speed of sound. By employing graphic processing and pattern matching methods, a coupled relationship of the dispersion of the speed of sound with gas concentration and temperature is established. The projection intersection method is used to calculate the concentration and temperature of binary and ternary gas mixtures. Combined with the inversion method, a joint reconstruction method for gas concentration fields and temperature fields based on the dispersion of the speed of sound is developed. The feasibility of the proposed simultaneous reconstruction method for temperature and concentration fields is validated using numerical simulations. Additionally, an acoustic tomography experimental system was set up to conduct reconstruction experiments for binary gas concentration fields and temperature fields, confirming the effectiveness of the proposed method.

Integral absorbance measurement for a non-uniform flow field using wavelength modulation absorption spectroscopy

Combined with computed tomography (CT), the laser absorption spectroscopy technique is used to measure the two-dimensional distribution information of the flow field. The CT method needs an "integral parameter" as a known quantity. The integrated absorbance satisfies the criterion in the laser absorption spectral measurement. The direct absorption spectroscopy method directly measures the integrated absorbance. However, fitting the absorbance curve is difficult due to the distorted baseline in harsh environments. By contrast, the wavelength modulation spectroscopy (WMS) method has satisfactory noise rejection capability. The difficulty that introduces WMS method to measure the non-uniform flow distribution is the integrated absorbance cannot be written in a mathematical expression. Previous efforts focused on solving the average temperature, concentration, and pressure and recalculating the integrated absorbance. This paper aims to develop an integrated absorbance measurement based on the calibration-free WMS method for non-uniform flow, which is called the calibration-free WMS-A method. First, the relationship between the transmissivity and integrated absorbance was established. Then, integrated absorbance was written into the WMS harmonic signals and solved by comparing the measured and simulated signals. The systematic comparison between the WMS-A and the previous WMS method showed the effectivity of the WMS-A method for non-uniform flow measurement. The reliable integrated absorbance can considerably improve the two-dimensional reconstruction quality.

Deep neural network inversion for 3D laser absorption imaging of methane in reacting flows

Mid-infrared laser absorption imaging of methane in flames is performed with a learning-based approach to the limited view-angle inversion problem. A deep neural network is trained with superimposed Gaussian field distributions of spectral absorption coefficients, and the prediction capability is compared to linear tomography methods at a varying number of view angles for simulated fields representative of a flame pair. Experimental 3D imaging is demonstrated on a methane-oxygen laminar flame doublet (${\lt}\text{cm}$<cm) backlit with tunable radiation from an interband cascade laser near 3.16 µm. Spectrally resolved data at each pixel provide for species-specific projected absorbance. 2D images were collected at six projection angles on a high-speed infrared camera, yielding an aggregate of 27,648 unique lines of sight capturing the scene with a pixel resolution of $\sim 70$∼70 µm. Mole fraction measurements are inferred from the predicted absorption coefficient images using an estimated temperature field, showing consistency with expected values from reactant flow rates. To the authors' knowledge, this work represents the first 3D imaging of methane in a reacting flow.

Two-Dimensional Temperature Measurement in a High-Temperature and High-Pressure Combustor Using Computed Tomography Tunable Diode Laser Absorption Spectroscopy (CT-TDLAS) with a Wide-Scanning Laser at 1335-1375 nm

Tunable diode laser absorption spectroscopy (TDLAS) technology is a developing method for temperature and species concentration measurements with the features of non-contact, high precision, high sensitivity, etc. The difficulty of two-dimensional (2D) temperature measurement in actual combustors has not yet been solved because of pressure broadening of absorption spectra, optical accessibility, etc. In this study, the combination of computed tomography (CT) and TDLAS with a wide scanning laser at 1335-1375 nm has been applied to a combustor for 2D temperature measurement in high temperature of 300-2000 K and high pressure of 0.1-2.5 MPa condition. An external cavity type laser diode with wide wavelength range scanning at 1335-1375 nm was used to evaluate the broadened H₂O absorption spectra due to the high-temperature and high-pressure effect. The spectroscopic database in high temperature of 300-2000 K and high pressure of 0.1-5.0 MPa condition has been revised to improve the accuracy for temperature quantitative analysis. CT reconstruction accuracy was also evaluated in different cases, which presented the consistent temperature distribution between CT reconstruction and assumed distributions. The spatial and temporal distributions of temperature in the high-temperature and high-pressure combustor were measured successfully by CT-TDLAS using the revised spectroscopic database.

Measurement Enhancement on Two-Dimensional Temperature Distribution of Methane-Air Premixed Flame Using SMART Algorithm in CT-TDLAS

In this study, the temperature distribution of the Methane-Air premixed flame was measured. In order to enhance the measurement accuracy of the CT-TDLAS (Computed tomography-tunable diode laser absorption spectroscopy), the SMART (simultaneous multiplicative algebraic reconstruction technique) algorithm has been adopted. Further, the SLOS (summation of line of sight) and the CSLOS (corrective summation of line of sight) methods have been adopted to increase measurement accuracies. It has been verified that the relative error for the temperatures measured by the thermocouples and calculated by the CT-TDLAS was about 10%.

3D tomography reconstruction improved by integrating view registration

Tomographic measurements involve two steps: view registration (VR) to determine the orientation of the projections and the subsequent tomography reconstruction. Therefore, the practical error in both steps impacts the overall accuracy of the final tomographic measurements. Past work treated these two steps separately. This work shows that the overall tomography accuracy can be enhanced substantially if these two steps are considered holistically because there is an opportunity for each step to leverage the information in the other step to improve the overall accuracy if they are considered holistically. Based on this recognition, this work has developed a new method called the reconstruction integration view registration (RIVR) method to implement such a holistic scheme. The key of this implementation involved the use of the Metropolis criterion to adjust the initial orientation provided by the traditional VR process dynamically. Both controlled experiments and accompanying numerical analyses were conducted to validate the RIVR method. Two sets of controlled experiments were conducted and analyzed, including a static uniform dye solution and turbulent flows, where the RIVR technique was demonstrated to significantly reduce the overall reconstruction error (by ∼37% and ∼35%, respectively) compared to past methods that treated VR and tomography separately.

Rapid tomographic reconstruction based on machine learning for time-resolved combustion diagnostics

Optical tomography has attracted surged research efforts recently due to the progress in both the imaging concepts and the sensor and laser technologies. The high spatial and temporal resolutions achievable by these methods provide unprecedented opportunity for diagnosis of complicated turbulent combustion. However, due to the high data throughput and the inefficiency of the prevailing iterative methods, the tomographic reconstructions which are typically conducted off-line are computationally formidable. In this work, we propose an efficient inversion method based on a machine learning algorithm, which can extract useful information from the previous reconstructions and build efficient neural networks to serve as a surrogate model to rapidly predict the reconstructions. Extreme learning machine is cited here as an example for demonstrative purpose simply due to its ease of implementation, fast learning speed, and good generalization performance. Extensive numerical studies were performed, and the results show that the new method can dramatically reduce the computational time compared with the classical iterative methods. This technique is expected to be an alternative to existing methods when sufficient training data are available. Although this work is discussed under the context of tomographic absorption spectroscopy, we expect it to be useful also to other high speed tomographic modalities such as volumetric laser-induced fluorescence and tomographic laser-induced incandescence which have been demonstrated for combustion diagnostics.

Development and validation of a reconstruction algorithm for three-dimensional nonlinear tomography problems

This work reports the development and experimental validation of a reconstruction algorithm for three-dimensional (3D) nonlinear tomography problems. Many optical tomography problems encountered in practice are nonlinear, for example, due to significant absorption, multiple-scattering, or radiation trapping. Past research efforts have predominately focused on reconstruction algorithms for linear problems, and these algorithms are not readily extendable to nonlinear problems due to several challenges. These challenges include the computational cost caused by the nonlinearity (which was compounded by the large scale of the problems when they are 3D), the limited view angles available in many practical applications, and the measurement uncertainty. A new algorithm was therefore developed to overcome these challenges. The algorithm was validated both numerically and experimentally, and was demonstrated to be able to solve a range of nonlinear tomography problems with significantly enhanced efficiency and accuracy compared to existing algorithms.

High-resolution bispectral imager at 1000 frames per second

We describe a bispectral, 1000-frames per second imaging instrument working simultaneously in two spectral bands. These bands may be selected for a specific application; however, we implement a pair centered at 4.3 μm and 4.66 μm. Synchronization is accomplished by employing a single focal plane array. To demonstrate the performance of the bispectral imager, we apply it to the methane flame of a Bunsen burner in a near conjugate configuration with flame image length subtending at about 200 pixels. The instrument detects bispectral puffing at 2 Hz, pulsations, and bispectral radiation oscillations, first reported here in two spectral intervals. The period of oscillatory spectral components in two bands is the same, about 3 Hz for this flame, with delay of a quarter period between them, first reported here. With 1-ms integration time, we detect significant formation of turbulence and vortices, especially pronounced in the region where the flame transitions into a plume. We display bispectral ratioed images of flames in near-real time with either the laboratory or the field device.

Tomographic laser absorption spectroscopy using Tikhonov regularization

The application of tunable diode laser absorption spectroscopy (TDLAS) to flames with nonhomogeneous temperature and concentration fields is an area where only few studies exist. Experimental work explores the performance of tomographic reconstructions of species concentration and temperature profiles from wavelength-modulated TDLAS measurements within the plume of an axisymmetric McKenna burner. Water vapor transitions at 1391.67 and 1442.67 nm are probed using calibration-free wavelength modulation spectroscopy with second harmonic detection (WMS-2f). A single collimated laser beam is swept parallel to the burner surface, where scans yield pairs of line-of-sight (LOS) data at multiple radial locations. Radial profiles of absorption data are reconstructed using Tikhonov regularized Abel inversion, which suppresses the amplification of experimental noise that is typically observed for reconstructions with high spatial resolution. Based on spectral data reconstructions, temperatures and mole fractions are calculated point-by-point. Here, a least-squares approach addresses difficulties due to modulation depths that cannot be universally optimized due to a nonuniform domain. Experimental results show successful reconstructions of temperature and mole fraction profiles based on two-transition, nonoptimally modulated WMS-2f and Tikhonov regularized Abel inversion, and thus validate the technique as a viable diagnostic tool for flame measurements.

Characterization of linearity and uniformity of fiber-based endoscopes for 3D combustion measurements

This work reports the application of fiber-based endoscopes (FBEs) for instantaneous three-dimensional (3D) flow and combustion measurements, with an emphasis on characterizing the linearity and uniformity of the FBEs and exploring their potential for obtaining quantitative measurements. Controlled experiments were performed using a uniform illuminator to characterize the linearity and uniformity of the FBEs. Based on such characterization, 3D instantaneous measurements of flames were demonstrated by a combined use of FBEs and tomography. To obtain 3D flame measurement, 3D tomographic reconstructions were made from multiple projections of the target flames collected from various orientations by the FBEs. The results illustrate the potential of FBEs to obtain quantitative 3D flow and combustion measurements and also the advantages FBEs offer, including overcoming optical access restrictions and equipment cost.

Numerical and experimental validation of a three-dimensional combustion diagnostic based on tomographic chemiluminescence

Three-dimensional (3D) measurements are highly desirable both for fundamental combustion research and practical monitoring and control of combustion systems. This work discusses a 3D diagnostic based on tomographic chemiluminescence (TC) to address this measurement need. The major contributions of this work are threefold. First, a hybrid algorithm is developed to solve the 3D TC problem. The algorithm was demonstrated in extensive tests, both numerical and experimental, to yield 3D reconstruction with high fidelity. Second, an experimental approach was designed to enable quantifiable metrics for examining key aspects of the 3D TC technique, including its spatial resolution and reconstruction accuracy. Third, based on the reconstruction algorithm and experimental results, we investigated the effects of the view orientations. The results suggested that for an unknown flame, it is better to use projections measured from random orientations than restricted orientations (e.g., coplanar orientations). These findings are expected to provide insights to the fundamental capabilities of the TC technique, and also to facilitate its practical application.

50-kHz-rate 2D imaging of temperature and H2O concentration at the exhaust plane of a J85 engine using hyperspectral tomography

This paper describes a novel laser diagnostic and its demonstration in a practical aero-propulsion engine (General Electric J85). The diagnostic technique, named hyperspectral tomography (HT), enables simultaneous 2-dimensional (2D) imaging of temperature and water-vapor concentration at 225 spatial grid points with a temporal response up to 50 kHz. To our knowledge, this is the first time that such sensing capabilities have been reported. This paper introduces the principles of the HT techniques, reports its operation and application in a J85 engine, and discusses its perspective for the study of high-speed reactive flows.

Validation of temperature imaging by H2O absorption spectroscopy using hyperspectral tomography in controlled experiments

This paper describes a preliminary demonstration and validation of temperature imaging using hyperspectral H2O absorption tomography in controlled experiments. Fifteen wavelengths are monitored on each of 30 laser beams to reconstruct the temperature image in a 381 mm × 381 mm square room-temperature plane that contains a 102 mm × 102 mm square zone of lower or higher temperature. The hyperspectral tomography technique attempts to leverage multispectral information to enhance measurement fidelity. The experimental temperature images exhibit average accuracies of 2.3% or better, with pixel-by-pixel standard deviations of less than 1%. In addition, even when the internal zone is only 4 K cooler than the surroundings, its presence is still detectable; statistical analysis of the associated experimental image reveals a 98% confidence that the internal zone is in fact cooler than the surroundings.

Selection of multiple optimal absorption transitions for nonuniform temperature sensing

A crucial aspect in the design of sensors based on absorption spectroscopy involves selecting the optimal transitions. Therefore, the goal of this paper is to develop a method of selecting multiple optimal transitions for the measurement of nonuniform temperature distributions based on absorption spectroscopy. Previously developed methods are largely restricted to the relatively simple case of selecting two transitions for uniform distributions. Our new method addresses the restrictions of previous methods and is applicable to more general cases. The method was validated using both numerical tests and experimental results and is expected to be useful in the design of sensors based on multispectral absorption spectroscopy.

Application of time-division-multiplexed lasers for measurements of gas temperature and CH4 and H2O concentrations at 30 kHz in a high-pressure combustor

Two time-division-multiplexed (TDM) sources based on fiber Bragg gratings were applied to monitor gas temperature, H(2)O mole fraction, and CH(4) mole fraction using line-of-sight absorption spectroscopy in a practical high-pressure gas turbine combustor test article. Collectively, the two sources cycle through 14 wavelengths in the 1329-1667 nm range every 33 μs. Although it is based on absorption spectroscopy, this sensing technology is fundamentally different from typical diode-laser-based absorption sensors and has many advantages. Specifically, the TDM lasers allow efficient, flexible acquisition of discrete-wavelength information over a wide spectral range at very high speeds (typically 30 kHz) and thereby provide a multiplicity of precise data at high speeds. For the present gas turbine application, the TDM source wavelengths were chosen using simulated temperature-difference spectra. This approach is used to select TDM wavelengths that are near the optimum values for precise temperature and species-concentration measurements. The application of TDM lasers for other measurements in high-pressure, turbulent reacting flows and for two-dimensional tomographic reconstruction of the temperature and species-concentration fields is also forecast.

Hyperspectral tomography based on proper orthogonal decomposition as motivated by imaging diagnostics of unsteady reactive flows

A series of previous studies, both numerical and experimental, have demonstrated the advantages of hyperspectral tomography (HT) as a promising technique to measure the two-dimensional distributions of temperature and species concentration in reacting flows. This paper intends to prepare the mathematical groundwork for extended use of the HT technique for three-dimensional and/or time-correlated measurements. Direct application of the methods developed previously encounters both experimental and computational difficulties. Numerical studies reported in this paper suggest that the use of proper orthogonal decomposition (POD) is effective to overcome these difficulties. The use of POD in HT significantly reduces the computational cost, enhances the fidelity of the tomographic reconstructions, and improves the stability of the reconstruction in the presence of measurement noise. Implications of these results for practical applications are also discussed.

Tomographic imaging of temperature and chemical species based on hyperspectral absorption spectroscopy

A novel technique has been developed to obtain simultaneous tomographic images of temperature and species concentration based on hyperspectral absorption spectroscopy. The hyperspectral information enables several key advantages when compared to traditional tomography techniques based on limited spectral information. These advantages include a significant reduction in the number of required projection measurements, and an enhanced insensitivity to measurements/inversion uncertainties. These advantages greatly facilitate the practical implementation and application of the tomography technique. This paper reports the development of the technique, and the experimental demonstration of a prototype sensor in a near-adiabatic, atmospheric-pressure laboratory Hencken burner. The spatial and temporal resolution enabled by this new sensing technique is expected to resolve several key issues in practical combustion devices.

Assessment of a novel flow visualization technique using photodissociation spectroscopy

The study of complicated flows continuously calls for new nonintrusive flow diagnostics. A novel flow visualization technique based on photodissociation spectroscopy (PDS) is described, demonstrated, and assessed in this paper. This technique is centered around the creative use of photodissociation (PD). A PD precursor is seeded in the flow of interest, either passive or reactive. A laser pulse is then generated to completely and rapidly photodissociate both the precursor and the products formed from the precursor (if it reacts) into photofragments. A target photofragment is then imaged to obtain multidimensional information about the flow. An analytical methodology was developed to assess the feasibility of the PDS-based technique. This analytical method was applied to the case where molecular iodine was used as an example PD precursor, and the results were validated by experimental data. Both the analytical and experimental findings provided a promising outlook for this new technique as a practical flow visualization technique. With a properly chosen PD precursor, the PDS-based technique provides an attractive alternative for imaging several critical flow properties, including the mixture fraction and temperature field. This technique shares some key advantages with established techniques, e.g., a high spatial and temporal resolution comparable to the planar laser-induced fluorescence (PLIF) technique. Meanwhile, this technique offers several unique advantages to overcome the limitations of existing techniques, including enhancing the signal level and simplifying the interpretation of the signal.

Determination of the optimal regularization parameters in hyperspectral tomography

In a previous paper, we described a novel technique to exploit hyperspectral absorption spectroscopy to retrieve tomographic imaging of temperature and species concentration simultaneously. This technique casts the tomographic inversion into a nonlinear minimization problem with regularizations. Here a simple and effective method is developed to determine the optimal regularization parameters in the nonlinear optimization problem. This method, combined with the minimization method described previously, provides a robust algorithm for hyperspectral tomography. This method takes advantage of an inherent feature of absorption and is therefore expected to be useful for other sensing techniques based on absorption spectroscopy.