## THERMAL SCIENCE

International Scientific Journal

### SIMULTANEOUS RECONSTRUCTION OF TEMPERATURE FIELD AND RADIATIVE PROPERTIES BY INVERSE RADIATION ANALYSIS USING STOCHASTIC PARTICLE SWARM OPTIMIZATION

**ABSTRACT**

Simultaneous reconstruction of temperature field and radiative properties including scattering albedo and extinction coefficient is presented in a two-dimensional (2-D) rectangular, absorbing, emitting and isotropically scattering gray medium from the knowledge of the exit radiative intensities received by charge-coupled device (CCD) cameras at boundary surfaces. The inverse problem is formulated as a non-linear optimization problem and solved by stochastic particle swarm optimization. The effects of particle swarm size, generation number, measurement errors, and optical thickness on the accuracy of the estimation, and computing time were investigated and the results show that the temperature field and radiative properties can be reconstructed well for the exact and noisy data, but radiative properties are harder to obtain than temperature field. Moreover, the extinction coefficient is more difficult to reconstruct than scattering albedo.

**KEYWORDS**

PAPER SUBMITTED: 2013-06-21

PAPER REVISED: 2014-03-09

PAPER ACCEPTED: 2014-04-01

PUBLISHED ONLINE: 2014-05-04

**THERMAL SCIENCE** YEAR

**2016**, VOLUME

**20**, ISSUE

**2**, PAGES [493 - 504]

- McCormick, N.J., Inverse radiative transfer problems: a review, Nuclear Science and Engineering, 112 (1992), pp. 185-198
- Li, H.Y., Özişik, M.N., Identification of the temperature profile in an absorbing, emitting, and isotropically scattering medium by inverse analysis, J. Heat Transfer, 114 (1992), pp. 1060-1063
- Siewert, C.E., An inverse source problem in radiation transfer, JQSRT, 50 (1993), pp. 603-609
- Siewert, C.E., A radiative-transfer inverse-source problem for a sphere, JQSRT, 52 (1994), pp. 157-160
- Li, H.Y., Estimation of the temperature profile in a cylindrical medium by inverse analysis, JQSRT, 52 (1994), pp. 755-764
- Li, H.Y., Inverse radiation problem in two-dimensional rectangular media. J. Thermophys. Heat Transfer, 11 (1997), 4, pp. 556-561
- Li, H.Y., A two-dimensional cylindrical inverse source problem in radiative transfer, JQSRT, 69 (2001), pp. 403-414
- Liu, L.H., Tan, H.P., Yu, Q.Z., Inverse radiation problem of temperature field in three-dimensional rectangular furnaces, Int. Comm. Heat Mass Transfer, 26 (1999), 2, pp. 239-248
- Liu, L.H., Tan, H.P., Inverse radiation problem in three-dimensional complicated geometric systems with opaque boundaries, JQSRT, 68 (2001), pp. 559-573
- Liu, L.H., Tan, H.P., Zhi, Z.H., Inverse radiation problem of source term in three-dimensional complicated geometric semitransparent media, Int. J. Therm. Sci., 40 (2001), pp. 528-538
- Zhou, H.C., Han, S.D., Sheng, F., Zheng, C.G., Visualization of three-dimensional temperature distributions in a large-scale furnace via regularized reconstruction from radiative energy images: numerical studies, JQSRT, 72 (2002), pp. 361-383
- Liu, D., Wang, F., Yan, J.H., Huang, Q.X., Chi, Y., Cen, K.F., Inverse radiation problem of temperature field in three-dimensional rectangular enclosure containing inhomogeneous, anisotropically scattering media, Int. J. Heat Mass Transfer, 51 (2008), pp. 3434-3441
- Liu, D., Wang, F., Cen, K.F., Yan, J.H., Huang, Q.X., Chi, Y., Noncontact temperature measurement by means of CCD cameras in a participating medium, Optics Letters, 33 (2008), pp. 422-424
- Wang, F., Liu, D., Cen, K.F., Yan, J.H., Huang, Q.X., Chi, Y., Efficient inverse radiation analysis of temperature distribution in participating medium based on backward Monte Carlo method, JQSRT, 109 (2008), pp. 2171-2181
- Liu, D., Wang, F., Huang, Q. X., Yan, J. H., Chi, Y., Cen, K. F., Simulation study on reconstruction model of three-dimensional temperature distribution within visible range in furnace, Chinese Physics B, 17 (2008), pp. 1312-1317
- Liu, D., Wang, F., Huang, Q. X., Yan, J. H., Chi, Y., Cen, K. F., Fast reconstruction of two-dimensional temperature distribution in participating medium, Acta Phys. Sin., 57 (2008), pp. 4812-4816
- Li, H.Y., Özişik, M.N., Inverse radiation problem for simultaneous estimation of temperature profile and surface reflectivity, J. Thermophys. Heat Transfer, 7 (1993), 1, pp. 88-93
- Liu, L.H., Tan, H.P., Yu, Q.Z., Simultaneous identification of temperature profile and wall emissivities in one-dimensional semitransparent medium by inverse radiation analysis, Numerical Heat Transfer, Part A, 36 (1999), pp. 511-525
- Liu, L.H., Tan, H.P., Yu, Q.Z., Inverse radiation problem of sources and emissivities in one-dimensional semitransparent media, Int. J. Heat Mass Transfer, 44 (2001), pp. 63-72
- Liu, L.H., Simultaneous identification of temperature profile and absorption coefficient in one-dimensional semitransparent medium by inverse radiation analysis. Int. Comm. Heat Mass Transfer, 27 (2000), 5, pp. 635-643
- Zhou, H.C., Hou, Y.B., Chen, D.L., Zheng, C.G., An inverse radiative transfer problem of simultaneously estimating profiles of temperature and radiative parameters from boundary intensity and temperature measurements, JQSRT, 74 (2002), pp. 605-620
- Snelling, D.R., Thomson, K.A., Smallwood, G.J., Gülder, Ö.L., Weckman, E.J., Fraser, R.A., Spectrally Resolved Measurement of Flame Radiation to Determine Soot Temperature and Concentration, AIAA JOURNAL, 40 (2002), 9, pp. 1789-1795
- Ayrancı, I., Vaillon, R., Selçuk, N., André, F., Escudié, D., Determination of soot temperature, volume fraction and refractive index from flame emission spectrometry, JQSRT, 104 (2007), pp. 266-276
- Zhou, H.C., Han, S.D., Simultaneous reconstruction of temperature distribution, absorptivity of wall surface and absorption coefficient of medium in a 2-D furnace system, Int. J. Heat Mass Transfer, 46 (2003), pp. 2645-2653
- Lou, C., Zhou, H.C., Yu, P.F., Jiang, Z.W., Measurements of the flame emissivity and radiative properties of particulate medium in pulverized-coal-fired boiler furnaces by image processing of visible radiation, Proceedings of the Combustion Institute, 31 (2007), pp. 2771-2778
- Liu, D., Yan, J.H., Wang, F., Huang, Q.X., Chi, Y., Cen, K.F., Inverse radiation analysis of simultaneous estimation of temperature field and radiative properties in a two-dimensional participating medium, Int. J. Heat Mass Transfer, 53 (2010), pp. 4474-4481
- Liu, D., Huang, Q.X., Wang, F., Chi, Y., Cen, K.F., Yan, J.H., Simultaneous measurement of three-dimensional soot temperature and volume fraction fields in axisymmetric or asymmetric small unconfined flames with CCD cameras, J. Heat Transfer, 132 (2010), pp. 061202 1-7.
- Liu, D., Yan, J. H., Wang, F., Huang, Q. X., Chi, Y. and Cen, K. F., Simultaneous experimental reconstruction of three-dimensional flame soot temperature and volume fraction distributions, Acta Phys. Sin., 6 (2011), pp. 060701 1-8
- Lou, C., Li, W.H., Zhou, H.C., Salinas, C.T., Experimental investigation on imultaneous measurement of temperature distributions and radiative properties in an oil-fired tunnel furnace by radiation analysis, Int. J. Heat Mass Transfer, 54 (2011), pp. 1-8
- Wang, F., Yan, J.H., Cen, K.F., Huang, Q.X., Liu, D., Chi, Y., Ni, M.J., Simultaneous measurements of two-dimensional temperature and particle concentration distribution from the image of the pulverized coal flame, Fuel, 89 (2010), pp. 202-211
- Liu, D., Yan, J.H., Cen, K.F., On the treatment of scattering for three-dimensional temperature distribution reconstruction accuracy in participating medium, Int. J. Heat Mass Transfer, 54 (2010), pp. 1684-1687
- Lou, C., Zhou, H.C., Assessment of regularized reconstruction of three-dimensional temperature distributions in large-scale furnaces, Numerical Heat Transfer, Part B, 53 (2008), pp. 555-567
- Li, H.Y., Yang, C.Y., A genetic algorithm for inverse radiation problems, Int. J. Heat Mass Transfer, 40 (1997), pp. 1545-1549
- Kim, K.W., Baek, S.W., Kim, M.Y., Ryou, H.S., Estimation of emissivities in a two-dimensional irregular geometry by inverse radiation analysis using hybrid genetic algorithm, JQSRT, 87 (2004), pp. 1-14
- Kim, K.W., Baek, S.W., Inverse surface radiation analysis in an axisymmetric cylindrical enclosure using a hybrid genetic algorithm, Numerical Heat Transfer, Part A, 46 (2004), pp. 367-381
- Kim, K.W., Baek, S.W., Efficient inverse radiation analysis in a cylindrical geometry using a combined method of hybrid genetic algorithm and finite-difference Newton method, JQSRT, 108 (2007), pp. 423-439
- Verma, S., Balaji, C., Multi-parameter estimation in combined conduction-radiation from a plane parallel participating medium using genetic algorithms, Int. J. Heat Mass Transfer, 50 (2007), pp. 1706-1714
- Das, R., Mishra, S.C., Ajith, M., Uppaluri, R., An inverse analysis of a transient 2-D conduction-radiation problem using the lattice Boltzmann method and the finite volume method coupled with the genetic algorithm, JQSRT, 109 (2008), pp. 2060-2077
- Qi, H., Ruan, L.M., Zhang, H.C., Wang, Y.M., Tan, H.P., Inverse radiation analysis of a one-dimensional participating slab by stochastic particle swarm optimizer algorithm, International Journal of Thermal Sciences, 46 (2007), pp. 649-661
- Qi, H., Ruan, L.M., Shi, M., An, W., Tan, H.P., Application of multi-phase particle swarm optimization technique to inverse radiation problem, JQSRT, 109 (2008), pp. 476-493
- Lee, K.H., Baek, S.W., Kim, K.W., Inverse radiation analysis using repulsive particle swarm optimization algorithm, Int. J. Heat Mass Transfer, 51 (2008), pp.2772-2783
- Sun, Y.P., Lou, C., Zhou, H.C., Estimating soot volume fraction and temperature in flames using stochastic particle swarm optimization algorithm, Int. J. Heat Mass Transfer, 54 (2011), pp. 217-224
- Modest, M.F., Radiative Heat Transfer, 2nd ed., Academic Press, 2003.
- Lockwood, F.C., Shah, N.G., A new radiation solution method for incorporation in general combustion prediction procedures, Proceedings, 18th Symposium (Int.) on Combustion, The combustion Institute, Pittsburgh, USA, 1981, pp. 1405-1414
- Magel, H.C., Schneider, R., Risio, B., Schnell, U., Hein, K.R.G., Numerical simulation of utility boilers with advanced combustion technologies, Proceedings, 8th International Symposium on Transport Phenomena in Combustion, San Francisco, USA, 1995, pp. 1-12
- Knaus, H., Schnell, U., Hein, K.R.G., Evaluation of the 3D-furnace simulation code AIOLOS by comparing CFD predictions of gas compositions with in-furnace measurements in a 210 MW coal-fired utility boiler, Progress in Computational Fluid Dynamics, 1 (2001), pp. 62-69