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The unsteady-state energy conservation equation for a small spherical particle in LII modeling

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Abstract

This paper discusses the formalization of the energy variation rate of a small particle encountered in the modeling of an unsteady-state soot particle temperature and diameter during laser-induced incandescence. A derivation of the particle energy equation is presented based on the first law of thermodynamics applied to an open system. Problems associated with an incorrect particle internal energy variation rate used in the literature are discussed. Numerical calculations are presented to demonstrate the effects of several incorrect particle internal energy variation rates on the calculated particle temperature and diameter.

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References

  1. B. Quay, T.-W. Lee, T. Ni, R.J. Santoro, Combust. Flame 97, 384 (1994)

    Article  Google Scholar 

  2. R.L. Vander Wal, K.J. Weiland, Appl. Phys. B 59, 445 (1994)

    Article  ADS  Google Scholar 

  3. C.R. Shaddix, K.C. Smyth, Combust. Flame 107, 418 (1996)

    Article  Google Scholar 

  4. D.R. Snelling, G.J. Smallwood, I.G. Campbell, J.E. Medlock, Ö.L. Gülder, AGARD 90th Symp. of the Propulsion and Energetics Panel on Advanced Non-intrusive Instrumentation for Propulsion Engines, Brussels, Belgium, 1997

  5. S. Will, S. Schraml, A. Leipertz, Opt. Lett. 20, 2342 (1995)

    ADS  Google Scholar 

  6. P. Roth, A.V. Filippov, J. Aerosol Sci. 27, 95 (1996)

    Article  Google Scholar 

  7. S. Will, S. Schraml, A. Leipertz, Proc. Combust. Inst. 26, 2277 (1996)

    Google Scholar 

  8. B. Mewes, J.M. Seitzman, Appl. Opt. 36, 709 (1997)

    ADS  Google Scholar 

  9. R.L. Vander Wal, T.M. Ticich, A.B. Stephens, Combust. Flame 116, 291 (1999)

    Article  Google Scholar 

  10. B. Axelsson, P.E. Bengtsson, Appl. Phys. B 72, 361 (2001)

    ADS  Google Scholar 

  11. T. Lehre, B. Jungfleisch, R. Suntz, H. Bockhorn, Appl. Opt. 42, 2021 (2003)

    Article  ADS  Google Scholar 

  12. S. Dankers, A. Leipertz, Appl. Opt. 43, 3726 (2004)

    Article  ADS  Google Scholar 

  13. F. Liu, B.J. Stagg, D.R. Snelling, G.J. Smallwood, Int. J. Heat Mass Transf. 49, 777 (2006)

    Article  Google Scholar 

  14. B.F. Kock, C. Kayan, J. Knipping, H.R. Orthner, P. Roth, Proc. Combust. Inst. 30, 1689 (2005)

    Article  Google Scholar 

  15. T. Lehre, R. Suntz, H. Bockhorn, Proc. Combust. Inst. 30, 2585 (2005)

    Article  Google Scholar 

  16. H.A. Michelsen, F. Liu, B.F. Kock, H. Bladh, A. Boiarciuc, M. Charwath, T. Dreier, R. Hadef, M. Hofmann, J. Reimann, S. Will, P.-E. Bengtsson, H. Bockhorn, F. Foucher, K.-P. Geigle, C. Mounaïm-Rousselle, C. Schultz, R. Stirn, B. Tribalet, R. Suntz, Appl. Phys. B 87, 503 (2007)

    Article  ADS  Google Scholar 

  17. H.A. Michelsen, J. Chem. Phys. 118, 7012 (2003)

    Article  ADS  Google Scholar 

  18. M. Hofmann, B.F. Kock, C. Schulz, A Web-Based Interface for Modeling Laser-Induced Incandescence (LIISim), in: Proc. 2nd. Intl. Discussion Meeting and Workshop on Laser-Induced Incandescence: Quantitative Interpretation, Modelling, Applications, ed. by R. Suntz, H. Bockhorn, Bad Herrenalb, CEUR Workshop Proc., ISSN 1613-0073, Vol. 211 (http://ceur-ws.org/Vol-211) 2006

  19. D.R. Snelling, F. Liu, G.J. Smallwood, Ö.L. Gülder, Combust. Flame 136, 180 (2004)

    Article  Google Scholar 

  20. R. Hiers, Rarefaction J. Thermophys. Heat Transf. 11, 232 (1997)

    Article  Google Scholar 

  21. R.S. Hiers III, J. Thermophys. Heat Transf. 14, 53 (2000)

    Article  Google Scholar 

  22. C.-P. Mao, G.A. Szekely Jr., G.M. Faeth, J. Energy 4, 78 (1980)

    Google Scholar 

  23. M.Y. Ha, S. Yavuzkurt, Combust. Flame 86, 33 (1991)

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute for Chemical Process and Environmental Technology, National Research Council Canada, Building M-9, 1200 Montreal Road, Ottawa, Ontario, K1A 0R6, Canada

    F. Liu & D.R. Snelling

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  1. F. Liu
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  2. D.R. Snelling
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Correspondence to F. Liu.

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PACS

44.05.+e; 61.46.Df

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Liu, F., Snelling, D. The unsteady-state energy conservation equation for a small spherical particle in LII modeling. Appl. Phys. B 89, 115–121 (2007). https://doi.org/10.1007/s00340-007-2761-0

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  • DOI: https://doi.org/10.1007/s00340-007-2761-0

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