Tomography system for measurement of gas properties in combustion flow field

Junling SONG,Ynji HONG,Mingyun XIN,Gungyu WANG,Zhorn LIU

aState Key Laboratory of Laser Propulsion&Application,Space Engineering University,Beijing 101416,China

bScience and Technology on Scramjet Laboratory,Hypervelocity Aerodynamics Institute,CARDC,Mianyang 621000,China

Tomography system for measurement of gas properties in combustion flow field

Junling SONGa,b,*,Yanji HONGa,Mingyuan XINa,Guangyu WANGa,Zhaoran LIUa

aState Key Laboratory of Laser Propulsion&Application,Space Engineering University,Beijing 101416,China

bScience and Technology on Scramjet Laboratory,Hypervelocity Aerodynamics Institute,CARDC,Mianyang 621000,China

This paper describes a self-designed fiber-coupled tomography system and its application in combustion diagnostics.The tomographic technique,which combines tunable diode laser spectroscopy and algebraic reconstruction technique,enables the simultaneous reconstruction of temperature and gas concentration with both spatial and temporal resolutions.The system measures a maximum diameter of 35 cm in a circular area with a minimum spatial resolution of 1 mm×1 mm and temporal response of up to 1 kHz.Simulations validate the effects of the beam arrangement and discrete grid on reconstruction accuracy,and give the optimal beam arrangements.Experiments are made to demonstrate the tomography method,and systems are constructed in laboratory and on engineering test benches.

1.Introduction

To measure the properties in high-speed and enthalpy flows,Tunable Diode Laser Absorption Spectroscopy(TDLAS)is a valuable optical tool.Compared with traditional implementations,using TDLAS sensor has many advantages,such as high sensitivity,fast time response and non-intrusion.1–3Multiple parameters such as temperature,concentration,velocity and pressure,which are used to evaluate combustor performance,can be obtained simultaneously.4–6The measurement ability of TDLAS system has been demonstrated in many ground and flight tests.Moreover,TDLAS sensors have been applied in energy conversion,which resolve mole fractions insitu syngas for long-term measurement.7,8

In a practical combustor,it is hard to install many optical sensors due to limited space.To optimize performance or minimize sensors in combustion systems,designers are pushing operating points toward the optimal sensor distribution in tomographic reconstruction.A parallel,9–11a fan12–14or an irregular and sparse beam arrangement15–17is chosen by laser absorption tomography.Thefan-beam arrangement saves the cost of emitters,but causes distortion in the corner of the reconstruction image at the same time.11The irregular beam arrangement uses the optimization strategy to reduce the number of beams and find optimal beam locations.However,this beam arrangement usually needs a complex optical system.Compared with the above two beam arrangements,the parallel-beam arrangement with a simple structure and easy operation is chosen in this paper to be applied in combustion diagnostics.

Beam arrangement is different for different reconstructed methods.A large number of projected beams and a uniform distribution over 180°or 360°are required to obtain accurate reconstruction for the transform-based methods.13,18By contrast,Algebraic Reconstruction Technique(ART)completes the reconstruction in irregular beam distribution and requires a small beam number.A new reconstructed method,named hyperspectral tomography technique,9,10utilizes only perpendicular and parallel projections,which simplifies the optical design.However,the post processing usually costs several hours,because the problem translates into a solution of a nonlinear minimization problem.Recently,an approach based on Computed Tomography of Chemiluminescence(CTC)is developed and demonstrated to obtain three-dimensional(3D)spatial distribution of reactive flows.Multiple cameras from different angles resolve continuous 3D flame structures at more than one kHz rates.19–21

For cost and spatial constraints,ART seems attractive and prominent in practical combustion.The efficiency and accuracy of ART and the modification algorithm used for twodimensional(2D)reconstruction have been extensively analyzed.Hansen and Saxild-Hansen22provided strategies for choosing the relaxation parameter and the stopping rulefor ART.Li and Weng23developed a Modified Adaptive Reconstruction Technique(MART)with an auto-adjustment relaxation parameter to improve the calculation efficiency.In order to decrease the utilization number of the projected beams,a virtual ray method was proposed by Song et al.11to reconstruct the temperature distribution.Twynstra and Daun17analyzed the influence of the optical components based on mathematical matrices in the ory.Tsekenis et al.24considered the imaging system as ‘black box” to quantify the spatial resolution of a tomography system.Guha and Schoegl25illuminated the impact of tomographic artifacts on the reconstruction quality,and found that the small errors were magnified in low-signal regions.In this paper,the effects of the beam arrangement and the discrete grids on the reconstruction performance are analyzed,and the reconstruction accuracy limits are obtained for different discrete grid numbers.

The experimental and numerical laser absorption tomography widely adopts the parallel-beam arrangement.Moreover,a self-designed tomography system with fiber-coupled structure is developed to reconstruct temperature and concentration distributions.Measurement data based on a tomography system are collected at a flat flame and at a direct-connected supersonic combustion exit to demonstrate the tomographic method.

This paper is organized as follows.A short review about the foundation of the tomographic reconstruction is presented in Section 2.Section 3 establishes parallel-beam projection models.The effects of the beam arrangement and the number of discrete grid in the reconstruction are presented by simulation.Section 4 describes the tomography system in detail,including hardware and data processing.Experimental validation of the number of projected angles is performed in the laboratory.The tomography system with small modifications is applied in an engineering test.The experimental results are discussed in Section 5.Conclusions are given in Section 6.

2.Theoretical background

2.1.Laser-based spectroscopy for gas parameter measurement

Wavelength-scanned Direct Absorption Spectroscopy(DAS)and Wavelength Modulation Spectroscopy(WMS)are two major techniques applied in combustion diagnostics.The DAS technique is widely used for detecting object with low temperatures and pressures.The WMS technique followed by a lock-in based detection can suppress the noises of engine vibration,light scattering and so on,which has a high Signal to Noise Ratio(SNR).However,the WMS has a complex expression compared with DAS.The integrated area cannot be obtained by WMS,which,however,is a necessary parameter in tomographic reconstruction based on ART technique.When the absorption spectroscopy is combined with the tomography which is usually an ill-posed problem,the 2D flow field reconstruction is complex.26Therefore,DAS technique is used in this paper.

The principle of DAS measurement is based upon the attenuation of the incident intensity passing through the area of interest,described by the Beer-Lambert law:

where I0is the incident intensity,Itthe transmitted laser intensity,and kυthe absorption coefficient.

where p is the gas pressure,Χ the mole fraction of the absorbing species,S(T)the line strength at temperature T,and φυthe line shape function approximated by Voigt line shape function in this paper.

The temperature dependent line strength can be calculated by the following scaling relation:

where S(T0)is the line strength at reference temperature T0(T0=296 K),Q(T)is the partition function of the absorbing molecule,which can be written by polynomial expression of temperature27;υ0the line center frequency of the transition;E′the low-state energy of the transition;h Planck’s constant;c the speed of light;k Boltzmann’s constant.

Table 1 Spectroscopic data for H2O line.

The temperature is calculated by the ratio of the integrated areas of two absorption lines,each with different low-state energies,and can be expressed by Eqs.(4)and(5).

where the subscript 1 and 2 represent the number of the transitions,A is the integrated area,L is the path length.When the gas temperature is known,species concentration can be determined from the integrated area of one transition:

H2O is selected as the target species because it is a major product of the combustion of hydrocarbons.Based on the selection criteria for optimal line pair,28–30two transitions of H2O,7185.597 cm-1and 7454.445 cm-1are selected for the measurement.The parameters of the absorbance spectra are based on HITRAN 2012 database,31as listed in Table 1.

2.2.Fundamental of tomographic reconstruction

A tomographic measurement system is separated into four basic parts:optical measurement subsystem,data acquisition subsystem,reconstruction algorithm subsystem and postprocessing subsystem for image presentation.The optical measurement system determines information collection from the area of interest.In practical tomography,spatial averaging and dense rays are impossible due to physical obstructions,which brings challenges for using reconstruction algorithm to obtain acceptable reconstruction image.The iteration method,which uses a small number of beams and a few projected angles to complete the reconstruction,seems to be an optimal method.

In order to obtain the 2D temperature and concentration,the area of interest f is discretized to N=n×n square grid points firstly.The gas parameters such as temperature,pressure and species concentration are assumed to be steady.When the laser beam passes through the nonuniform flow field,the general Eq.(1)can be written in discretized matrix form:

where N is the number of grid point,M the number of beams for projection,f the gas property of the test area fj=(pS(T)Χ)j,L the projection coefficient matrix and Lijthe length of beam i that spans grid point j.Lijremains constant once the number of rays and the projection angle arefixed.The process can be mathematically described in ART as follows32:

where the superscript k represents the iteration index in ART,α the relaxation parameter,and Li=[Li1,Li2,...,LiN].Using the MART technique mentioned in Ref.11,an automatically changing relaxation parameter is added in iterative equation to accelerate convergence.Eq.(8)can be rewritten as follows:

where β is a constant value of 0.25.Moreover,the nonnegative constraint as prior information is added to the iterative process.A smoothness regulation is used to reduce the discrepancy among the nearest cells,and the details can befound in Refs.33,34.

3.Numerical validation

A numerical phantom with feature of a Gaussian peak has been designed to test the method as shown in Fig.1.To study the influence of beam arrangement,the phantom is discretized to 30×30 grid points,in which the temperature is assumed in a range of 300–1300 K.

Fig.1 Phantom for numerical validation.

3.1.Effect of beam arrangement on reconstruction

Some numerical simulations are examined to validate the reconstruction method of the laser infrared absorption tomography.To evaluate the reconstruction accuracy,the reconstruction error eTis defined as

where DE=N,superscripts ‘cal” and ‘orig” denote the calculated and original values,respectively.The subscripts ‘d”and ‘e” represent the grid point number.

In this paper,parallel-beam projection is adopted in all cases.The laser emitter and detector comprise the beam pair.The beam arrangement contains the number of the projected angles and the number of the beams for each projected angle.The goal of this section is to study the effect of the beam arrangement,and find the optimization projected angel corresponding to beam numbers.Different number of projected angles NPA of 2,3,4 and 6 are used,which are in accordance with the rotation angle θ of 90°,60°,45°and 30°respectively.For each condition,different beam numbers of 10–40 are utilized.Fig.2 shows the relationship between the number of beams and the reconstruction error values eTfor different projected angles.For a fixed projected angle,eTdecreases when the number of beams increases.However,the trend tends to be smooth when the number exceeds 20.

Fig.2 Reconstruction error and number of projected beams for different rotation angles.

Fig.3 Effect of the number of projected angles on the reconstruction.

When the number of beams per projected angle is fixed to 30,for different projected angles the value of eTis listed in Table 2.The maximum eTis 0.0905 when the re are only two projected angles.A significant improvement in reconstruction with the increased number of projected angle is observed.When the projected number exceeds 4,eTdrops to less than 0.02.

The effect of the number of projected angles on the reconstruction,when the total number of projected beams is fixed to 120,is shown in Fig.3.Poor reconstruction appears on the corner of the reconstruction area because of limited projected angles.As the number of projected angles increases,eTis the smallest for an optimal projected angle of 5.However,when the number of projected angles increases to 12,eTincreases because the number of beams per projected angle is too sparse to reconstruct the area.

3.2.Effect of number of discrete grids

In tomographic reconstruction,the area of interest is divided into square grids in which the value of the reconstruction is assumed to be constant.Therefore,the size of the grid point determines the spatial resolution of the measurement.To improve the efficiency of the projected beams,the optimal number of beams needs to befound for a fixed discrete grid point.The area of interest is separated into 10×10,20×20,30×30 and 40×40 grids.For each condition,the number of beams is from 10 to 65 with a 5-beam interval.Five kinds of number of projected angles are used in the simulation.

Table 2 Relationship among reconstruction error,number of projected angle and rotation angle.

Table 3 Effect of number of grids and projected beams on reconstruction error.

Fig.4 Reconstruction error eTvs relationship between grid size and number of beams η at four grid numbers.

The simulation results are listed in Table 3.When eTvariation is less than 1%,the optimal number for the corresponding projected angle is obtained.eTfor the optimal number of beams for each grid is in the bracket.For the same number of projected angle,the number of 40×40 grids has better reconstruction performance than the other three kinds of grid points.When only three projected angles are present,all four simulations have higher reconstruction error than the other projected angle conditions.The sparse projected angle is the major factor affecting the reconstruction accuracy.

An optimal number of beams and a reconstruction accuracy limit are obtained for each grid when the projected angle is greater than 4.Therefore,improving accuracy by increasing the number of projected angles or the number of beams is not helpful.The number of discrete grid determines the reconstruction accuracy the most.

To examine the relationship between grid size and the number of beams,variable η is quantified as follows11:

where Δdbeamis the interval between the two projected beams,and Δdgridthe length of the grid point.The relationship between eTand η for different grid numbers is shown in Fig.4.As η is greater than 1,eTsharply increases because a small number of beams results in a few even no beam crossing through some grids.Therefore,an optimal beam-grid distribution of η is less than 1.

4.Flat flame test

4.1.Experimental setup

Fig.5 Overview of experimental setup with an 8-beam fiber-coupled sensor.

An overview of the experimental setup is shown in Fig.5.Two Distributed-FeedBack(DFB)lasers were controlled by the laser current/temperature controllers and synchronized by Data AcQuisition(DAQ)for time division multiplexing.Thefiber-coupled lasers operating near 1341 nm and 1398 nm were multiplexed into a single-mode fiber.The light was split into another eight beams by the fiber splitter,delivered to the tomography frame by the single mode fibers,and transmitted through the area of interest.Four beams were aligned in the x direction and four in the y direction.In opposite directions,eight coupling lens were used to focus the light onto multimodefibers.The light was delivered to the detector matrix.The DAQ card acquired and digitized voltage signals from the detectors.Before the test,the etalon transfer function was used to convert the laser signal from time domain to frequency domain,and the signal after conversion was recorded in the computer.To generate dense projected beams,the tomography frame was mounted to two linear stages with a maximum range of 100 mm.Moreover,a rotary stage which was mounted above the linear stage rotated 360°incrementally around the area of interest.

Fig.6 presents a photograph of the tomography frame.Eight beams were installed on a self-designed aluminum frame,which was used both to hold the probe beams in the measurement area and to expediently move the frame as the projected beams and angles increase.The inner area of the frame was 25 cm×25 cm,with spacing of 3 cm between two probe beams.Eight probe beams were installed on each side of the frame as an initialized design.However,due to the hardware limit and intensity of the output laser,only four probe beams for each side were used in the test.Each of the eight beams adopted a module-design consisting of emitter and detectormodules.The emitter contained a built-in-wall part,a medium part,and a collimating lens.A wedged widow was fixed in the built-in-wall to eliminate etalons and isolate the test gas.Through the medium part,a collimating lens(Thorlabs F240APC-C)with a diameter of 8 mm was used to collect light into the test area.By releasing and tightening the screws on the medium part,the precise placement of the laser spot is focused onto the detector center.In the opposite position,the detectormodule was similar to the emitter-module.A large collimator(Oz Optics HPUCO-25-1300-M-10BQ)was used to focus the free-space beam onto a 400 μm-diameter multimode fiber(Thorlabs FT400EMT-CUSTOM)with a numerical aperture of 0.4 and length of 4 m.

In the test,the area of interest was a circular region with a diameter of 22 cm and height of 0.5 cm above the furnace.Thirty-one projected beams and six kinds of projected angles of 2,3,4,5,6 and 10 were used.The distance between the first and the last beams was 15 cm,and the interval between the two beams was 0.5 cm.

Fig.6 Photograph of tomography frame.

Fig.7 Temperature of the rmocouple readings.

Sixteen the rmocouples(Omega,type-K)with equally spaced intervals of 1 cm compose a line the rmocouple matrix.The the rmocouple matrix was mounted on a linear stage by a stainless steel bracket.Through moving the the rmocouple matrix with a 5 mm step,the temperature of the rectangle area was measured.Fig.7 shows the temperatures measured by the rmocouple.

4.2.Effect of number of projected angles

The beam arrangement has a pronounced effect on the accuracy of the tomography reconstruction as discussed in Section 4.1.A set of temperature reconstruction in beam arrangement tests is shown in Fig.8.The left image of each group shows the arrangement of the projected beams.Six projected angles,2,3,4,5,6 and 10 are used.The right image of each group represents the reconstruction of the area of interest.The combustion area was reconstructed roughly at two projected angles.As the projected angles increased,a clear profile of the combusted area was obtained.Noise appeared on the corner of the area of interest because of sparse beams projected in the area.Information on the corner of the area could not be included in the iterative equations.As a result,when the number of projected angles was less than five,the reconstruction was greatly in fluenced by the projected angles.

The tomography reconstructed temperatures were compared with the the rmocouple readings in Fig.9.The subscript 2,3,4,5,6 and 10 indicate the number of projected angles in Fig.9.Great differences between the reconstruction and measurement appeared in the noncombusted circular area with a diameter of 3 cm.The smoothness regulation was applied in the iteration,which was used to reduce the discrepancy among the nearest grids.At the same time,nonuniformity was trailed off.The results indicate that tomography reconstruction has a spatial resolution.If the detail of the flow field is characterized,dense grids and projected beams are required.

Fig.8 Reconstruction for different projected angles.

Fig.9 Comparison between tomography reconstruction and the rmocouple-measured temperatures(along x axis,y=11 cm).

5.Combustor exit in a direct-connected scramjet test

The tomography system was applied to a direct-connected scramjet to measure the 2 D temperature and concentration distribution.The system was the same as the one used in the flat flame test but was redesigned in size to match the combustor exit,as shown in Fig.10.Five horizontal and three vertical beams were employed across the combustor exit,forming a square mesh of 15 grid points with a size of 3 cm×3 cm.Laser generation and data analysis were conducted in the control room.The laser beams were delivered to the measurement location by single-mode fibers(approximately 5 m in length)and transmitted back to the detectors by multimode fibers(approximately 5 m in length).

Successful measurement of H2O temperature and concentration distributions were performed throughout the approximately 8 s measurement campaign,including five significant conditions.Fig.11 illustrates the photograph and details of the beam arrangement.The desired temperature and pressure were obtained by hydrogen combustion in the heater.The operation parameters of the scramjet facility were Mach number(Ma)of 2.5,total temperature of 1250 K,total pressure of 1.8 MPa,and flow rate of 2.68 kg/s,which were used to simulate the Ma=5 flight condition.

The five conditions include pre-ignition,ignition assisted by hydrogen flame,oxygen-enriched combustion,oil-enriched combustion,and after-burner operation.The time sequence of the measurement and the fuel injection in TDLAS system is shown in Fig.12(a).Line-of-sight temperature and concentration measurement for different beams is shown in Fig.12(b)and(c).Two beams were chosen to represent ‘hot” and‘cold” beams.Beams 8 and 6 are denoted by a red and yellow line respectively in Fig.12.As beam 8 was located on the downstream side of the cavity,the average temperatures were higher than those of the other seven beams at about 1734 K and 1850 K.

Fig.10 Experimental setup for measurement at combustor exit of direct-connected scramjet.

Fig.11 Beam arrangement.

Fig.12 TDLAS measurements for different beams.

Fig.13 Temperature and concentration distributions at the combustion exit.

Fig.13 shows a set of sample results of the temperature distributions measured under five significant conditions at the combustion exit.The measurement was taken at 1 kHz,and the time-division multiplexing strategy was used.To improve the reconstruction accuracy,10 times of measurement were conducted to obtain the average value of the integrated area.Each panel in Fig.13 shows one frame chosen from the measurement frames corresponding to dashed lines in Fig.12.In the first condition,the temperature and concentration have uniform condition.When the hydrogen ignites,the temperature and concentration in the top region increase.In the third condition,the kerosene is injected upstream in the cavity on the top of the combustor wall.As shown in Fig.13(c)and(d),the temperature and concentration are high near the top wall.With the fuel injection for the second time,high temperature area is widened.The high static temperature is more than 2200 K.Beam 8 crosses the ‘hot” region,and gives the average values of temperature and concentration,which are about 1830 K and 0.25 respectively.In the fifth condition,the fuel stops injecting,and the 2 D temperature and concentration distribute nearly uniformly at low level.

6.Conclusions

This paper develops a tomography system based on laser absorption spectroscopy and ART algorithm to reconstruct 2D distributions of temperature and H2O concentration.The self-designed tomography system has a fiber-coupled structure and a translated/rotated function.Eight probe beams were installed on each side of the frame with a spacing of 3 cm between two probe beams.The system can measure a maximum diameter of 35 cm in a circular area with a minimum spatial resolution of 1 mm×1 mm.The numerical results indicate that the reconstruction error decreases when the number of projected beams increases,but the trend becomes smooth under fixed projected angles.Moreover,the reconstruction error decreases as the area of interest is separated into more grid points.For fixed grid points,an optimal number of beams and limited reconstruction accuracy are obtained when the projected angle is greater than 4.Experiments were performed in the laboratory and on engineering test benches to validate and demonstrate the tomography method and system.The tomography system provides measurement with a temporal resolution of 1 kHz at 15 spatial grid points.Temperature and concentration images were simultaneously obtained under different engine operation conditions throughout the 8 s measurement campaign.

Acknowledgements

This study was supported by the National Natural Science Foundation of China(No.61505263).The authors thank Dr.Wei RAO and Dr.Dongsheng QU for their assistance with tomographic experiments.

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30 September 2016;revised 16 January 2017;accepted 5 March 2017

Available online 22 August 2017

Absorption;

Combustion diagnostics;

Spectroscopy;

Temperature;

Tomographic image

*Corresponding author.

E-mail address:songjl@mail.ustc.edu.cn(J.SONG).

Peer review under responsibility of Editorial Committee of CJA.

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?2017 Production and hosting by Elsevier Ltd.on behalf of Chinese Society of Aeronautics and Astronautics.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).