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Research on simultaneous reconstruction of the temperature distribution of a 3D participating medium and its boundary

Feng Yu-Xiao Huang Qun-Xing Liang Jun-Hui Wang Fei Yan Jian-Hua Chi Yong

Research on simultaneous reconstruction of the temperature distribution of a 3D participating medium and its boundary

Feng Yu-Xiao, Huang Qun-Xing, Liang Jun-Hui, Wang Fei, Yan Jian-Hua, Chi Yong
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  • In-situ and nonintrusive 3D temperature measurement is very important for combustion diagnosis and controlling of pollutants. The temperature reconstruction technique based on radiation inverse analysis has received intensive attention. In order to reduce the computation cost and take boundary temperature into consideration, a discrete method is presented for 3D temperature distribution determination for an absorbing, emitting and scattering combustion medium and its boundary by using the emission image measured by four CCD cameras. First the radiative source term is retrieved through the discrete transfer method. Then, the temperature is inferred from the blackbody intensity obtained by subtracting the media scattering and boundary reflecting contribution from the source term by the discrete ordinate approximation. The least squares minimum residual algorithm is improved to solve the ill-posed reconstruction equations. The performance of the proposed method is examined by numerical test. The effects of measurement noise and radiative properties on the reconstruction accuracy are investigated. The results show that the method proposed in this paper is capable of reproducing the temperature of the medium and its boundary accurately, even with noise. The reconstruction time cost is reduced significantly compared with those of other methods.
    • Funds: Project supported by the National Basic Research Program of China (Grant Nos. 2009CB219802 and 2011CB201500), the Sewage Sludge Incineration Projects (Grant Nos. 2009ZX07317-003, A2009R50049).
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    Li H Y, Yang C Y 1997 Int. J. Heat Mass Transfer 40 1545

    [4]

    Ozisik M N, Orlande H R B 2000 Inverse heat transfer: fundamentals and applications (New York: Taylor Francis) pp253-288

    [5]
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    Modest M F 2003 Radiative Heat Transfer (2nd ed) (New York: Academic) pp729-739

    [8]
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    Kohse-Hinghaus K, Barlow R S 2005 Proc. Combust. Inst. 30 89

    [10]

    Sielschott H 1997 Flow Meas. Instrum. 8 191

    [11]
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    Docquier N, Candel S 2002 Prog. Energy Combust. Sci. 28 107

    [14]
    [15]

    Ballester J, Garcia-Armingol T 2010 Prog. Energy Combust. Sci. 36 375

    [16]

    Li H Y, Ozisik M N 1992 ASME J. Heat Transfer 114 1060

    [17]
    [18]

    Li H Y, Ozisik M N 1992 JQSRT. 48 237

    [19]
    [20]
    [21]

    Li H Y 2001 JQSRT. 69 403

    [22]

    Liu L H, Tan H P, Yu Q Z 1999 Int. Commun. Heat Mass Transfer 26 239

    [23]
    [24]

    Liu L H, Tan H P, Yu Q Z 2001 Int. J. Heat Mass Transfer 44 63

    [25]
    [26]
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    Liu L H, Tan H P 2001 JQSRT. 68 559

    [28]

    Park H M, Yoo D H 2001 Int. J. Heat Mass Transfer 44 2949

    [29]
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    Namjoo A, HosseiniSarvari S M, Behzadmehr A, Mansouri S H 2009 JQSRT. 110 491

    [32]

    Correia D P, Ferrao P, Caldeira-Pires A 2000 Proc. Combust. Inst. 28 431

    [33]
    [34]
    [35]

    Wang F, Yan J H, Cen K F, Huang Q X, Liu D, Chi Y, Ni M J 2010 Fuel 89 202

    [36]
    [37]

    Zhou H C, Han S D, Sheng F, Zheng C G 2002 JQSRT. 72 361

    [38]

    Zhou H C, Lou C, Cheng Q, Jian Z W 2005 Proc. Combust. Inst. 30 1699

    [39]
    [40]
    [41]

    Lou C, Li W H, Zhou H C, Salinas C T 2011 Int. J. Heat Mass Transfer 54 1

    [42]

    Huang Z F, Cheng Q, Zhou H C 2009 JQSRT. 110 1072

    [43]
    [44]

    Liu D, Wang F, Yan J H, Huang Q X, Chi Y, Cen K F 2008 Int. J. Heat Mass Transfer 51 3434

    [45]
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    Liu D, Wang F, Huang Q X, Yan J H, Chi Y, Cen K F 2008 Acta Phys. Sin. 57 4812(in Chinese) [刘 冬, 王飞, 黄群星, 严建华, 池 涌, 岑可法 2008 物理学报 57 4812]

    [48]

    Liu D, Wang F, Cen K F, Yan J H, Huang Q X, Chi Y 2008 Opt. Lett. 33 422

    [49]
    [50]

    Liu D, Yan J H, Cen K F 2011 Int. J. Heat Mass Transfer 54 1684

    [51]
    [52]
    [53]

    Lockwood F C, Shah N G 1981 Symposium (International) on Combustion 18 1405

    [54]

    Coelho P J, Carvalho M G 1997 ASME J. Heat Transfer 119 118

    [55]
    [56]

    Ayranci I, Vaillon R, Selcuk N 2007 JQSRT. 104 266

    [57]
    [58]

    Snelling D R, Thomson K A , Smallwood G J, Gulder O L, Weckman E J, Fraser R A 2002 AIAA Journal 40 1789

    [59]
    [60]

    Fiveland W A 1987 ASME J. Heat Transfer 109 809

    [61]
    [62]
    [63]

    Chang H, Charalampopoulos T T 1990 P. Roy. Soc. A-Math. Phy. 430 577

    [64]
    [65]

    Lathrop K D, Carlson B G 1965 Discrete-Ordinates Angular Quadrature of the Neutron Transport Equation (Los Alamos Scientific Laboratory of the University of California: California)

    [66]
    [67]

    Hansen P C 2007 Numer. Algorithms 46 189

    [68]
    [69]

    Fong D C L, Saunders M A 2011 arXiv: 1006.0758v2 [cs.MS]

    [70]

    Paige C C, Saunders M A 1982 AMC Trans. Math. Softw. 8 195

    [71]
    [72]

    Huang Q X, Liu D, Wang F, Yan J H, Chi Y, Cen K F 2008 Acta Phys. Sin. 57 7928(in Chinese) [黄群星, 刘冬, 王 飞, 严建华, 池 涌, 岑可法 2008 物理学报 57 7928]

    [73]
    [74]

    Liu D, Wang F, Huang Q X, Yan J H, Chi Y, Cen K F 2008 Chin. Phys. B 17 1312

    [75]
    [76]
    [77]

    Groetsch C W 1984 The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind (Botson: Pitman)

    [78]

    Huang Q X, Liu D, Wang F, Yan J H, Chi Y, Cen K F 2007 Acta Phys. Sin. 56 6742(in Chinese) [黄群星, 刘 冬, 王 飞, 严建华, 池涌, 岑可法 2007 物理学报 56 6742]

    [79]
  • [1]

    Siewert C E 1993 JQSRT. 50 603

    [2]
    [3]

    Li H Y, Yang C Y 1997 Int. J. Heat Mass Transfer 40 1545

    [4]

    Ozisik M N, Orlande H R B 2000 Inverse heat transfer: fundamentals and applications (New York: Taylor Francis) pp253-288

    [5]
    [6]
    [7]

    Modest M F 2003 Radiative Heat Transfer (2nd ed) (New York: Academic) pp729-739

    [8]
    [9]

    Kohse-Hinghaus K, Barlow R S 2005 Proc. Combust. Inst. 30 89

    [10]

    Sielschott H 1997 Flow Meas. Instrum. 8 191

    [11]
    [12]
    [13]

    Docquier N, Candel S 2002 Prog. Energy Combust. Sci. 28 107

    [14]
    [15]

    Ballester J, Garcia-Armingol T 2010 Prog. Energy Combust. Sci. 36 375

    [16]

    Li H Y, Ozisik M N 1992 ASME J. Heat Transfer 114 1060

    [17]
    [18]

    Li H Y, Ozisik M N 1992 JQSRT. 48 237

    [19]
    [20]
    [21]

    Li H Y 2001 JQSRT. 69 403

    [22]

    Liu L H, Tan H P, Yu Q Z 1999 Int. Commun. Heat Mass Transfer 26 239

    [23]
    [24]

    Liu L H, Tan H P, Yu Q Z 2001 Int. J. Heat Mass Transfer 44 63

    [25]
    [26]
    [27]

    Liu L H, Tan H P 2001 JQSRT. 68 559

    [28]

    Park H M, Yoo D H 2001 Int. J. Heat Mass Transfer 44 2949

    [29]
    [30]
    [31]

    Namjoo A, HosseiniSarvari S M, Behzadmehr A, Mansouri S H 2009 JQSRT. 110 491

    [32]

    Correia D P, Ferrao P, Caldeira-Pires A 2000 Proc. Combust. Inst. 28 431

    [33]
    [34]
    [35]

    Wang F, Yan J H, Cen K F, Huang Q X, Liu D, Chi Y, Ni M J 2010 Fuel 89 202

    [36]
    [37]

    Zhou H C, Han S D, Sheng F, Zheng C G 2002 JQSRT. 72 361

    [38]

    Zhou H C, Lou C, Cheng Q, Jian Z W 2005 Proc. Combust. Inst. 30 1699

    [39]
    [40]
    [41]

    Lou C, Li W H, Zhou H C, Salinas C T 2011 Int. J. Heat Mass Transfer 54 1

    [42]

    Huang Z F, Cheng Q, Zhou H C 2009 JQSRT. 110 1072

    [43]
    [44]

    Liu D, Wang F, Yan J H, Huang Q X, Chi Y, Cen K F 2008 Int. J. Heat Mass Transfer 51 3434

    [45]
    [46]
    [47]

    Liu D, Wang F, Huang Q X, Yan J H, Chi Y, Cen K F 2008 Acta Phys. Sin. 57 4812(in Chinese) [刘 冬, 王飞, 黄群星, 严建华, 池 涌, 岑可法 2008 物理学报 57 4812]

    [48]

    Liu D, Wang F, Cen K F, Yan J H, Huang Q X, Chi Y 2008 Opt. Lett. 33 422

    [49]
    [50]

    Liu D, Yan J H, Cen K F 2011 Int. J. Heat Mass Transfer 54 1684

    [51]
    [52]
    [53]

    Lockwood F C, Shah N G 1981 Symposium (International) on Combustion 18 1405

    [54]

    Coelho P J, Carvalho M G 1997 ASME J. Heat Transfer 119 118

    [55]
    [56]

    Ayranci I, Vaillon R, Selcuk N 2007 JQSRT. 104 266

    [57]
    [58]

    Snelling D R, Thomson K A , Smallwood G J, Gulder O L, Weckman E J, Fraser R A 2002 AIAA Journal 40 1789

    [59]
    [60]

    Fiveland W A 1987 ASME J. Heat Transfer 109 809

    [61]
    [62]
    [63]

    Chang H, Charalampopoulos T T 1990 P. Roy. Soc. A-Math. Phy. 430 577

    [64]
    [65]

    Lathrop K D, Carlson B G 1965 Discrete-Ordinates Angular Quadrature of the Neutron Transport Equation (Los Alamos Scientific Laboratory of the University of California: California)

    [66]
    [67]

    Hansen P C 2007 Numer. Algorithms 46 189

    [68]
    [69]

    Fong D C L, Saunders M A 2011 arXiv: 1006.0758v2 [cs.MS]

    [70]

    Paige C C, Saunders M A 1982 AMC Trans. Math. Softw. 8 195

    [71]
    [72]

    Huang Q X, Liu D, Wang F, Yan J H, Chi Y, Cen K F 2008 Acta Phys. Sin. 57 7928(in Chinese) [黄群星, 刘冬, 王 飞, 严建华, 池 涌, 岑可法 2008 物理学报 57 7928]

    [73]
    [74]

    Liu D, Wang F, Huang Q X, Yan J H, Chi Y, Cen K F 2008 Chin. Phys. B 17 1312

    [75]
    [76]
    [77]

    Groetsch C W 1984 The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind (Botson: Pitman)

    [78]

    Huang Q X, Liu D, Wang F, Yan J H, Chi Y, Cen K F 2007 Acta Phys. Sin. 56 6742(in Chinese) [黄群星, 刘 冬, 王 飞, 严建华, 池涌, 岑可法 2007 物理学报 56 6742]

    [79]
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Publishing process
  • Received Date:  23 October 2011
  • Accepted Date:  23 November 2011
  • Published Online:  05 July 2012

Research on simultaneous reconstruction of the temperature distribution of a 3D participating medium and its boundary

  • 1. State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China
Fund Project:  Project supported by the National Basic Research Program of China (Grant Nos. 2009CB219802 and 2011CB201500), the Sewage Sludge Incineration Projects (Grant Nos. 2009ZX07317-003, A2009R50049).

Abstract: In-situ and nonintrusive 3D temperature measurement is very important for combustion diagnosis and controlling of pollutants. The temperature reconstruction technique based on radiation inverse analysis has received intensive attention. In order to reduce the computation cost and take boundary temperature into consideration, a discrete method is presented for 3D temperature distribution determination for an absorbing, emitting and scattering combustion medium and its boundary by using the emission image measured by four CCD cameras. First the radiative source term is retrieved through the discrete transfer method. Then, the temperature is inferred from the blackbody intensity obtained by subtracting the media scattering and boundary reflecting contribution from the source term by the discrete ordinate approximation. The least squares minimum residual algorithm is improved to solve the ill-posed reconstruction equations. The performance of the proposed method is examined by numerical test. The effects of measurement noise and radiative properties on the reconstruction accuracy are investigated. The results show that the method proposed in this paper is capable of reproducing the temperature of the medium and its boundary accurately, even with noise. The reconstruction time cost is reduced significantly compared with those of other methods.

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