Numerical Study of Coupled Non-Gray Radiation and Separation Convection Flow in a Duct using FSK Method

ADMT Journal

مقاله 4، دوره 9، شماره 4، اسفند 2016، صفحه 23-38   

نوع مقاله: Original Article

نویسندگان

Meysam Atashafrooz^{* 1}؛ Seyyed Abdolreza Gandjalikhan Nassab²؛ Khosro Lari³

¹Department of Mechanical Engineering, Sirjan University of Technology, Sirjan, Iran

²Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

³Department of Mechanical Engineering, Graduate University of Advanced Technology, Kerman, Iran

چکیده

In this research, the coupling between non-gray radiation and separation convection flow in a duct is investigated numerically. Distributions of absorption coefficients across the spectrum  are obtained from the HITRAN2008 database. The full-spectrum k-distribution method is used to deal with the non-gray part of the problem, while the gray radiation calculations are performed using the Planck mean absorption coefficient. To find the divergence of radiative heat flux distribution, the radiative transfer equation (RTE) is solved by the discrete ordinates method (DOM). The effects of radiation-conduction parameter, scattering coefficient and wall emissivity on thermal behaviors are investigated for both gray and non-gray mediums. In addition, the results of gray medium are compared with non-gray results as a real case. The results show that in many cases, use of gray simulations is not acceptable and leads to significant errors, especially in non-scattering medium with high values of radiation-conduction parameter and wall emissivity.

کلیدواژه‌ها

Backward facing step؛ Combined convection-radiation؛ DOM؛ FSK method؛ Non-gray medium؛ Separation flow

مراجع

[1]     Armaly, B. F., Durst, F., Pereira JCF, and Chonung, B., “Experimental and Theoretical Investigation of Backward-Facing Step Flow”, Journal of Fluid Mechanics, Vol. 127, 1983, pp. 473-496.

[2]     Iwai, H., Nakabe, K., and Suzuki, K., “Flow and Heat Transfer Characteristics of Backward-Facing Step Laminar Flow in a Rectangular Duct”, International Journal of Heat and Mass Transfer, Vol. 43, 2000, pp. 457-471.

[3]     Tylli, N., Kaiktsis L., and Ineichen, B., “Side Wall Effects in Flow Over Backward-Facing Step: Experiments and Numerical Solutions”, Physics Fluids, Vol. 14, No. 11, 2002, pp. 3835-3845.

[4]     Abu-Mulaweh, H. I., “A Review of Research on Laminar Mixed Convection Flow Over Backward- and Forward-Facing Steps”, International Journal of Thermal Sciences, Vol. 42, 2003, pp. 897-909.

[5]     Erturk, E., “Numerical Solutions of 2-D Steady Incompressible Flow Over a Backward-Facing Step, Part I: High Reynolds Number Solutions”, Computers & Fluids, Vol. 37, 2008, pp. 633–655.

[6]     Atashafrooz, M., Gandjalikhan Nassab, S. A. and Ansari, A. B., “Numerical Analysis of Laminar Forced Convection Flow Over Backward and Forward Facing Steps in a Duct Under Bleeding Condition”, International Review of Mechanical Engineering, Vol. 5, No. 3, 2011, pp. 513-518.

[7]     Nie, J.H., Chen Y.T., and Hsieh, H.T., “Effects of a Baffle on Separated Convection Flow Adjacent to Backward-Facing Step”, International Journal of Thermal Sciences, Vol. 48, 2009, pp. 618–625.

[8]     Tsay, Y. L., Chang T. S., and Cheng, J. C., “Heat Transfer Enhancement of Backward-Facing Step Flow in a Channel by Using Baffle Installation on Channel Wall”, ACTA Mechanica, Vol. 174, 2005, pp. 63–76.

[9]     Chen, Y. T., Nie, J. H., Hsieh, H. T., and Sun, L.J., “Three-Dimensional Convection Flow Adjacent to Inclined Backward-Facing Step”, International Journal of Heat and Mass Transfer, Vol. 49, 2006, pp. 4795-4803.

[10]  Abu-Nada, E., “Investigation of Entropy Generation Over a Backward Facing Step Under Bleeding Conditions”, Energy Conversion and Management, Vol. 49, 2008, pp. 3237-3242.

[11]  Atashafrooz, M., Gandjalikhan Nassab, S. A., and Ansari, A. B., “Numerical Study of Entropy Generation in Laminar Forced Convection Flow Over Inclined Backward and Forward Facing Steps in a Duct”, International Review of Mechanical Engineering, Vol. 5, No. 5, 2011, pp. 898-907.

[12]  Atashafrooz, M., Gandjalikhan Nassab S. A., and Ansari, A. B., “Numerical Investigation of Entropy Generation in Laminar Forced Convection Flow Over Inclined Backward and Forward Facing Steps in a Duct Under Bleeding Condition”, Thermal Science, Vol. 18, No. 2, 2014, pp. 479-492.

[13]  Selimefendigil, F., and Oztop, H. F., “Numerical Analysis of Laminar Pulsating Flow at a Backward Facing Step with an Upper Wall Mounted Adiabatic Thin Fin”, Computers & Fluids, Vol. 88, 2013, pp. 93–107.

[14]   Selimefendigil, F., Oztop, H. F., “Effect of a Rotating Cylinder in Forced Convection of Ferrofluid Over a Backward Facing Step”, International Journal of Heat and Mass Transfer, Vol. 71, 2014, pp. 142-148.

[15]  Yan W. M., Li, H.Y., “Radiation Effects on Mixed Convection Heat Transfer in a Vertical Square Duct”, International Journal of Heat and Mass Transfer, Vol. 44, 2001, pp. 1401-1410.

[16]  Chiu, H. C., Jang, J. H., and Yan, W. M., “Mixed Convection Heat Transfer in Horizontal Rectangular Ducts with Radiation Effects”, International Journal of Heat and Mass Transfer, Vol. 50, 2007, pp. 2874-2882.

[17]  Chiu, H. C., Yan, W. M., “Mixed Convection Heat Transfer in Inclined Rectangular Ducts with Radiation Effects”, International Journal of Heat and Mass Transfer, Vol. 51, 2008, pp. 1085-1094.

[18]  Nouanegue, H., Muftuoglu A., and Bilgen, E., “Conjugate Heat Transfer by Natural Convection, Conduction and Radiation in Open Cavities”, International Journal of Heat and Mass Transfer, Vol. 51, 2008, pp. 6054-6062.

[19]  Ko M., Anand, N. K., “Three-Dimensional Combined Convective-Radiative Heat Transfer Over a Horizontal Backward-Facing Step—A Finite-Volume Method”, Numerical Heat Transfer, Part A, Vol. 54, 2008, pp. 109-129.

[20]  Ansari, A. B., Gandjalikhan Nassab, S. A., “Forced Convection of Radiating Gas Over an Inclined Backward Facing Step Using the Blocked-Off Method”, Thermal Science, Vol. 17, No. 3, 2013, pp. 773-786.

[21]  Atashafrooz, M., Gandjalikhan Nassab, S. A., “Simulation of Three-Dimensional Laminar Forced Convection Flow of a Radiating Gas Over an Inclined Backward-Facing Step in a Duct Under Bleeding Condition”, Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science, Vol. 227, No. 2, 2012, pp. 332-345.

[22]  Atashafrooz, M., Gandjalikhan Nassab, S. A., “Three Dimensional Laminar Convection Flow of Radiating Gas Over a Backward Facing Step in a Duct”, International Journal of Engineering-Transactions A: Basics, Vol. 25, No. 4, 2012, pp. 399-410.

[23]  Atashafrooz M., Gandjalikhan Nassab, S. A., “Simulation of Laminar Mixed Convection Recess Flow Combined with Radiation Heat Transfer”, Iranian Journal of Science and Technology, Vol. 37, No. M1, 2013, pp 71-75.

[24]  Atashafrooz, M., Gandjalikhan Nassab, S. A., “Combined Heat Transfer of Radiation and Forced Convection Flow of Participating Gases in a Three-Dimensional Recess”, Journal of Mechanical Science and Technology, Vol. 26, No. 10, 2012, pp. 3357-3368.

[25]  Farias, T. L., Carvalho, M. G., “Radiative Heat Transfer in Soot-Containing Combustion Systems with Aggregation”, International Journal of Heat and Mass Transfer, Vol. 41, 1998, pp. 2581-2587.

[26]  Solovjov, V. P., Webb, B. W., “The Cumulative Wavenumber Method for Modeling Radiative Transfer in Gas Mixtures with Soot”, Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 93, 2005, pp. 273-287.

[27]  Ludwig, C. B., Malkmus, W., Reardon, J. E., and Thomson, J. A. L., “Handbook of Infrared Radiation from Combustion Gases”, Technical Report SP-3080, NASA, 1973.

[28]  Edwards, D. K., Balakrishnan, A., “Thermal Radiation by Combustion Gases”, International Journal of Heat and Mass Transfer, Vol. 16, No. 1, 1973, pp. 25–40.

[29]  Edwards, D. K., “Molecular Gas Band Radiation,” Advances in Heat Transfer, Vol. 12, 1976, pp. 115-193.

[30]  Liu, F., Smallwood, G. J., “An Efficient Approach for the Implementation of the SNB Based Correlated-k Method and Its Evaluation”, Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 84, No. 4, 2004, pp. 465-75.

[31]  Modest, M. F., “Narrow Band and Full Spectrum k-Distributions for Radiative Heat Transfer-Correlated-k vs., Scaling Approximation”, Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 76, No. 1, 2003, pp. 69–83.

[32]  Denison M. K., Webb, B. W., “A Spectral Line Based Weighted Sum of Gray Gases Model for Arbitrary RTE Solvers”, ASME, Journal of Heat Transfer, Vol. 115, No. 4, 1993, pp.1004-1012.

[33]  Solovjov, V. P., Webb, B. W., “SLW Modeling of Radiative Transfer in Multi Component Gas Mixtures”, Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 65, 2000, pp. 655–672.

[34]  Modest, M. F., “Radiative Heat Transfer”, 2nd Edition, McGraw-Hill, New York, 2003.

[35]  Pierrot, L., Soufiani, A., and Taine, J., “Accuracy of Narrow-Band and Global Models for Radiative Transfer in H₂O, CO₂, and H₂O–CO₂ Mixtures at High Temperature”, Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 62, 1999, pp. 523-548.

[36]  Colomer, G., Consul, R., and Oliva, A., “Coupled Radiation and Natural Convection: Different Approaches of the SLW Model for a Non-Gray Gas Mixture”, Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 107, 2007, pp. 30-46.

[37]  Ibrahim, A., Lemonnier, D., “Numerical Study of Coupled Double-Diffusive Natural Convection and Radiation in a Square Cavity Filled with A N₂-CO₂ Mixture”, International Communications in Heat and Mass Transfer, Vol. 36, 2009, pp. 197-202.

[38]  Modest, M. F., Zhang, H., “The Full-Spectrum Correlated-k Distribution for Thermal Radiation from Molecular Gas-Particulate Mixtures”, ASME, Journal of Heat Transfer, Vol. 124, No. 1, 2002, pp. 30–38.

[39]  Tencer, J., Howell, J. R., “A Multi-Source Full Spectrum k-Distribution Method for 1-D Inhomogeneous Media”, Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 129, 2013, pp. 308–315.

[40]  Proter, R., Liu, F., Pourkashanian, M., Williams A., and Smith, D., “Evaluation of Solution Method for Radiative Heat Transfer in Gaseous Oxy-Fuel Combustion Environments”, Journal of Quantitative Spectroscopy & Radiative Transfer, Vol. 111, 2010, pp. 2084-2094.

[41]  Lari, K., Baneshi, M., Gandjalikhan Nassab, S. A., Komiya, A., and Maruyama, S., “Numerical Study of Non-Gray Radiation and Natural Convection Using the Full-Spectrum k-Distribution Method”, Numerical Heat Transfer, Part A, Vol. 61, 2012, pp. 61-84.

[42]  Atashafrooz M., Gandjalikhan Nassab, S. A., “Numerical Analysis of Laminar Forced Convection Recess Flow with Two Inclined Steps Considering Gas Radiation Effect”, Computers & Fluids, Vol. 66, 2012, pp. 167-176.

[43]  Patankar, S. V., Spalding, D. B., “A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows”, International Journal of Heat and Mass Transfer, Vol. 15, No. 10, 1972, pp. 1787–1806.

[44]  Rothman, L. S, et al., “The HITRAN 2008 Molecular Spectroscopic Database”, Journal of Quantitative Spectroscopy & Radiative Transfer, Vol. 110, 2009, pp. 533–572.

[45]  Patankar, S. V., “Numerical Heat Transfer and Fluid Flow”, Taylor & Francis, Philadelphia, PA, 1981, Chaps. 7.

[46] Atashafrooz, M., Gandjalikhan Nassab, S. A., and Sadat Behineh, E., “Effects of Baffle on Separated Convection Step Flow of Radiating Gas in a Duct”, International Journal of Advanced Design and Manufacturing Technology, Vol. 8, No. 3, 2015, pp. 33-47.