Combined with the light-field imaging technique, the Landweber method is applied to the reconstruction of three-dimensional (3D) temperature distribution in absorbing media theoretically and experimentally. In the theoretical research, simulated exit radiation intensities on the boundary of absorbing media according to the computing model of light field are employed as inputs for inverse analysis. Compared with the commonly used iterative methods, i.e., the least-square QR decomposition method and algebraic reconstruction technique (ART), the Landweber method can produce reconstruction results with better quality and less computational time. Based on the numerical study, an experimental investigation is conducted to validate the suitability of the proposed method. The temperature distribution of the ethylene diffusion flame is reconstructed by using the Landweber method from the flame image captured by a light-field camera. Good agreement was found between the reconstructed temperature distribution and the measured temperature data obtained by a thermocouple. All the experimental results demonstrate that the temperature distribution of ethylene flame can be reconstructed reasonably by using the Landweber method combined with the light-field imaging technique, which is proven to have potential for the use in noncontract measurement of temperature distribution in practical engineering applications.
Issue Section:
Radiative Heat Transfer
References
1.
Liu
, D.
, Wang
, F.
, Yan
, J. H.
, Huang
, Q. X.
, Chi
, Y.
, and Cen
, K. F.
, 2008
, “Inverse Radiation Problem of Temperature Field in Three-Dimensional Rectangular Enclosure Containing Inhomogeneous Anisotropically Scattering Media
,” Int. J. Heat Mass Transfer
, 51
(13–14
), pp. 3434
–3441
.2.
Cai
, J.
, Marquez
, R.
, and Modest
, M. F.
, 2014
, “Comparisons of Radiative Heat Transfer Calculations in a Jet Diffusion Flame Using Spherical Harmonics and k-Distributions
,” ASME J. Heat Transfer
, 136
(11
), p. 112702
.3.
Cheng
, Q.
, Zhang
, X. Y.
, Wang
, Z. C.
, Zhou
, H. C.
, and Shao
, S.
, 2014
, “Simultaneous Measurement of Three-Dimensional Temperature Distributions and Radiative Properties Based on Radiation Image Processing Technology in a Gas-Fired Pilot Tubular Furnace
,” Heat Transfer Eng.
, 35
(6–8
), pp. 770
–779
.4.
Wang
, F.
, Yan
, J. H.
, Cen
, K. F.
, Huang
, Q. X.
, Liu
, D.
, Chi
, Y.
, and Ni
, M. J.
, 2010
, “Simultaneous Measurements of Two-Dimensional Temperature and Particle Concentration Distribution From the Image of the Pulverized Coal Flame
,” Fuel
, 89
(1
), pp. 202
–211
.5.
Wei
, Z. H.
, Li
, Y.
, Li
, Z. H.
, Song
, S. B.
, and Li
, B. Y.
, 2016
, “3-D Reconstruction Algorithm of Flame Based on Inversion Calculation of Thermal Radiation
,” IEEE Trans. Instrum. Meas.
, 65
(12
), pp. 2808
–2815
.6.
Rankin
, B. A.
, Blunck
, D. L.
, and Gore
, J. P.
, 2012
, “Infrared Imaging and Spatiotemporal Radiation Properties of a Turbulent Nonpremixed Jet Flame and Plume
,” ASME J. Heat Transfer
, 135
(2
), p. 021201
.7.
Cai
, W. W.
, Li
, X. S.
, Li
, F.
, and Ma
, L.
, 2013
, “Numerical and Experimental Validation of a Three-Dimensional Combustion Diagnostic Based on Tomographic Chemiluminescence
,” Opt. Express
, 21
(6
), pp. 7050
–7064
.8.
Cai
, W. W.
, and Kaminski
, C. F.
, 2015
, “A Numerical Investigation of High-Resolution Multispectral Absorption Tomography for Flow Thermometry
,” Appl. Phys. B
, 119
(1
), pp. 29
–35
.9.
Zhang
, B.
, Xu
, C. L.
, and Wang
, S. M.
, 2017
, “Generalized Source Finite Volume Method for Radiative Transfer Equation in Participating Media
,” J. Quant. Spectrosc. Radiat. Transfer
, 189
, pp. 189
–197
.10.
Qi
, C. B.
, Zheng
, S.
, and Zhou
, H. C.
, 2017
, “Experimental Investigation on Gas-Phase Temperature of Axisymmetric Ethylene Flames by Large Lateral Shearing Interferometry
,” Int. J. Therm. Sci.
, 115
, pp. 104
–111
.11.
Hossain
, M. M.
, Lu
, G.
, and Yan
, Y.
, 2012
, “Optical Fiber Imaging Based Tomographic Reconstruction of Burner Flames
,” IEEE Trans. Instrum. Meas.
, 61
(5
), pp. 1417
–1425
.12.
Hossain
, M. M.
, Lu
, G.
, Sun
, D.
, and Yan
, Y.
, 2013
, “Three-Dimensional Reconstruction of Flame Temperature and Emissivity Distribution Using Optical Tomographic and Two-Colour Pyrometric Techniques
,” Meas. Sci. Technol.
, 24
(7
), p. 074010
.13.
Wang
, F.
, Ma
, Z. Y.
, Yan
, J. H.
, Chi
, Y.
, Ni
, M. J.
, and Cen
, K. F.
, 2003
, “Experimental Study of Temperature and Concentration Distribution Measurement Based on Flame Image
,” Power Eng.
, 23
(3), pp. 2404
–2408
.14.
Wang
, F.
, Wang
, X. J.
, Ma
, Z. Y.
, Yan
, J. H.
, Chi
, Y.
, Wei
, C. Y.
, Ni
, M. J.
, and Cen
, K. F.
, 2002
, “The Research on the Estimation for the NOx Emissive Concentration of the Pulverized Coal Boiler by the Flame Image Processing Technique
,” Fuel
, 81
(16
), pp. 2113
–2120
.15.
Wang
, F.
, Cen
, K. F.
, Li
, N.
, Jeffries
, J. B.
, Huang
, Q. X.
, Yan
, J. H.
, and Chi
, Y.
, 2010
, “Two-Dimensional Tomography for Gas Concentration and Temperature Distributions Based on Tunable Diode Laser Absorption Spectroscopy
,” Meas. Sci. Technol.
, 21
(4
), p. 045301
.16.
Huang
, Q. X.
, Wang
, F.
, Liu
, D.
, Ma
, Z. Y.
, Yan
, J. H.
, Chi
, Y.
, and Cen
, K. F.
, 2009
, “Reconstruction of Soot Temperature and Volume Fraction Profiles of an Asymmetric Flame Using Stereoscopic Tomography
,” Combust. Flame
, 156
(3
), pp. 565
–573
.17.
Luo
, Z. X.
, and Zhou
, H. C.
, 2007
, “A Combustion-Monitoring System With 3-D Temperature Reconstruction Based on Flame-Image Processing Technique
,” IEEE Trans. Instrum. Meas.
, 56
(5
), pp. 1877
–1882
.18.
Wang
, H. J.
, Huang
, Z. F.
, Wang
, D. D.
, Luo
, Z. X.
, Sun
, Y. P.
, Fang
, Q. Y.
, Lou
, C.
, and Zhou
, H. C.
, 2009
, “Measurements on Flame Temperature and Its 3D Distribution in a 660 MWe Arch-Fired Coal Combustion Furnace by Visible Image Processing and Verification by Using an Infrared Pyrometer
,” Meas. Sci. Technol.
, 20
(11
), p. 114006
.19.
Sheng
, F.
, Zhou
, H. C.
, Han
, S. D.
, Li
, J.
, and Zheng
, C. G.
, 1999
, “Reconstruction of Temperature Profiles in Two-Dimensional Furnaces From Radiation Image by Solving Inverse Radiative Heat Transfer Problem
,” Proc. CSEE
, 19
(10), pp. 2
–6
.20.
Zhou
, H. C.
, Lou
, C.
, Cheng
, Q.
, Jiang
, Z. W.
, He
, J.
, Huang
, B. Y.
, Pei
, Z. L.
, and Lu
, C. X.
, 2005
, “Experimental Investigations on Visualization of Three-Dimensional Temperature Distributions in a Large-Scale Pulverized-Coal-Fired Boiler Furnace
,” Proc. Combust. Inst.
, 30
(1
), pp. 1699
–1706
.21.
Wang
, S. M.
, Zhao
, Y. J.
, and Wang
, F. L.
, 2002
, “Theoretical and Experimental Investigation on 3-Dimensional Temperature Reconstruction in Flame by Optical Sectioning Tomography
,” J. Eng. Thermophys.
, 23
(1
), pp. 233
–236
.22.
Zhou
, B.
, Wang
, S. M.
, Xu
, C. L.
, and Zhang
, J. Y.
, 2009
, “3-D Flame Temperature Reconstruction in Optical Sectioning Tomography
,” IEEE International Workshop on Imaging Systems and Techniques
(IST
), Shenzhen, China, May 11–12, pp. 313
–318
.23.
Cheng
, Z. H.
, Cai
, X. S.
, and Mao
, W. P.
, 2004
, “Investigate Into the Characteristic Emission Line of Flame
,” J. Eng. Thermophys.
, 25
(3
), pp. 519
–522
.24.
Yan
, Y.
, Qiu
, T.
, Lu
, G.
, Hossain
, M. M.
, Gilabert
, G.
, and Liu
, S.
, 2012
, “Recent Advances in Flame Tomography
,” Chin. J. Chem. Eng.
, 20
(2
), pp. 389
–399
.25.
Ren
, N.
, Marc
, L.
, Mathieu
, B.
, Gene
, D.
, Mark
, H.
, and Pat
, H.
, 2005
, “Light Field Photography With a Hand-Held Plenoptic Camera
,” Stanford University, Palo Alto, CA, Stanford Technical Report No. CTSR 2005-02
.http://graphics.stanford.edu/papers/lfcamera/26.
Jeong
, Y.
, Kim
, J.
, Yeom
, J.
, Lee
, C. K.
, and Lee
, B.
, 2015
, “Real-Time Depth Controllable Integral Imaging Pickup and Reconstruction Method With a Light Field Camera
,” Appl. Opt.
, 54
(35
), pp. 10333
–10341
.27.
Fischer
, A.
, Kupsch
, C.
, Gurtler
, J.
, and Czarske
, J.
, 2015
, “High-Speed Light Field Camera and Frequency Division Multiplexing for Fast Multi-Plane Velocity Measurements
,” Opt. Express
, 23
(19
), pp. 24910
–24922
.28.
Sun
, J.
, Xu
, C. L.
, Zhang
, B.
, Hossain
, M. M.
, Wang
, S. M.
, Qi
, H.
, and Tan
, H. P.
, 2016
, “Three-Dimensional Temperature Field Measurement of Flame Using a Single Light Field Camera
,” Opt. Express
, 24
(2
), pp. 1118
–1132
.29.
Zhou
, H. C.
, Han
, S. D.
, Sheng
, F.
, and Zheng
, C. G.
, 2002
, “Visualization of Three-Dimensional Temperature Distributions in a Large-Scale Furnace Via Regularized Reconstruction From Radiative Energy Images: Numerical Studies
,” J. Quant. Spectrosc. Radiat. Transfer
, 72
(4
), pp. 361
–383
.30.
Zhang
, X. Y.
, Zheng
, S.
, Zhou
, H. C.
, Zhang
, B.
, Wang
, H. J.
, and Xu
, H. J.
, 2016
, “Simultaneously Reconstruction of Inhomogeneous Temperature and Radiative Properties by Radiation Image Processing
,” Int. J. Therm. Sci.
, 107
, pp. 121
–130
.31.
Liu
, D.
, Yan
, J. H.
, Wang
, F.
, Huang
, Q. X.
, Chi
, Y.
, and Cen
, K. F.
, 2010
, “Inverse Radiation Analysis of Simultaneous Estimation of Temperature Field and Radiative Properties in a Two-Dimensional Participating Medium
,” Int. J. Heat Mass Transfer
, 53
(21–22
), pp. 4474
–4481
.32.
Liu
, D.
, Yan
, J. H.
, and Cen
, K. F.
, 2012
, “On the Treatment of Non-Optimal Regularization Parameter Influence on Temperature Distribution Reconstruction Accuracy in Participating Medium
,” Int. J. Heat Mass Transfer
, 55
(5–6
), pp. 1553
–1560
.33.
Xia
, H. H.
, Kan
, R. F.
, Liu
, J. G.
, Xu
, Z. Y.
, and He
, Y. B.
, 2016
, “Analysis of Algebraic Reconstruction Technique for Accurate Imaging of Gas Temperature and Concentration Based on Tunable Diode Laser Absorption Spectroscopy
,” Chin. Phys. B
, 25
(6
), p. 064205
.34.
Liu
, C. L.
, Xu
, L. J.
, Chen
, J. L.
, Cao
, Z.
, Lin
, Y. Z.
, and Cai
, W. W.
, 2015
, “Development of a Fan-Beam TDLAS-Based Tomographic Sensor for Rapid Imaging of Temperature and Gas Concentration
,” Opt. Express
, 23
(17
), pp. 22494
–22511
.35.
Felske
, J. D.
, and Tien
, C. L.
, 1973
, “Calculation of the Emissivity of Luminous Flames
,” Combust. Sci. Technol.
, 7
(1
), pp. 25
–31
.36.
Landweber
, L.
, 1951
, “An Iteration Formula for Fredholm Integral Equations of the First Kind
,” Am. J. Math.
, 73
(3
), pp. 615
–624
.37.
Zong
, Z. X.
, and Gao
, F.
, 2008
, “Acceleration of Landweber Method of Iterated Regularization
,” J. Wuhan Univ. Technol.
, 30
(10
), pp. 178
–180
.38.
Yan
, W. J.
, Zheng
, S.
, and Zhou
, H. C.
, 2017
, “Experiments Investigation on 2D Distribution of Soot Temperature and Volume Fraction by Image Processing of Visible Radiation
,” Appl. Therm. Eng.
, 124
, pp. 1014
–1022
.39.
Liu
, H. W.
, Zheng
, S.
, and Zhou
, H. C.
, 2017
, “Measurement of Soot Temperature and Volume Fraction of Axisymmetric Ethylene Laminar Flames Using Hyper-Spectral Tomography
,” IEEE Trans. Instrum. Meas.
, 66
(2
), pp. 315
–324
.40.
Turns
, S. R.
, 1996
, An Introduction to Combustion
, McGraw-Hill
, New York
.Copyright © 2018 by ASME
You do not currently have access to this content.
