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Stagnation-point spray flame ignition by an isothermal surface

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Abstract

We present a theory of stagnation-point spray flame ignition by an isothermal hot surface. A mixture of fuel droplets and air flowing against an isothermal hot surface (such as a hot ignition probe) is considered. The spray of droplets is modelled using the sectional approach, and a mono-sectional case is adopted for simplicity. A single global chemical reaction is assumed for the case when ignition occurs. The mathematical analysis makes use of a small parameter that is exploited for an asymptotic approach. The analysis produces a criterion for ignition that includes effects of the flow field, the reactants and the fuel spray-related parameters. Numerical computations reveal the way in which the spray impacts on whether ignition will occur or not.

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References

  1. Neophytou A (2010) Spark ignition and flame propagation. PhD dissertation, University of Cambridge

  2. Aggarwal SK (2014) Single droplet ignition: theoretical analyses and experimental findings. Prog Energy Combust Sci 45:79–107

    Article  Google Scholar 

  3. Kikby LL, Schmitz RA (1966) An analytical study of the stability of a laminar diffusion flame. Combust Flame 10:205–219

    Article  Google Scholar 

  4. Linan A (1974) The asymptotic structure of counterflow diffusion flames for large activation energies. Acta Astronaut 1:1007–1039

    Article  Google Scholar 

  5. Matalon M, Ludford GSS (1979) Chambered diffusion flames for different supply temperatures. Acta Astronaut 6:1377–1386

    Article  MATH  Google Scholar 

  6. Aggarwal SK, Sirignano WA (1984) Modeling of chemical and mixing effects on methane autoignition under direct-injection, stratified charged conditions. Proc Combust Inst 20:1773–1780

    Article  Google Scholar 

  7. Aggarwal SK, Sirignano WA (1986) Ignition of poly-disperse sprays: importance of D20. Combust Sci Technol 46(3–6):289–300

    Article  Google Scholar 

  8. Aggarwal SK (1988) Ignition and flame propagation in dilute polydipserse sprays: importance of \(d_{32}\) and \(d_{20}\). AIAA J Propuls 4(1):14–21

  9. Neophytou A, Mastorakos E, Cant RS (2011) Complex chemistry simulations of spark ignition in turbulent sprays. Proc Combust Inst 33:2135–2142

    Article  Google Scholar 

  10. Law CK (1978) On the stagnation-point ignition of a premixed combustible. Int J Heat Mass Transf 21:1363–1368

    Article  Google Scholar 

  11. Chen ZH, Lin TH, Sohrab SH (1988) Combustion of liquid fuel sprays in stagnation-point flow. Combust Sci Technol 60(1–3):63–77

    Article  Google Scholar 

  12. Hsu A-K, Lin TH (2003) A stagnation-point gasoline-spray premixed flame. Combust Sci Technol 175(12):2141–2159

    Article  Google Scholar 

  13. Matkowsky BJ, Sivashinsky GI (1979) An asymptotic derivation of two models in flame theory associated with the constant density approximation. SIAM J Appl Math 37(3):686–699

    Article  MathSciNet  MATH  Google Scholar 

  14. Buckmaster JD, Ludford GSS (1982) Theory of laminar flames. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  15. Law CK (2006) Combustion physics. Cambridge University Press, New York

    Book  Google Scholar 

  16. Silverman I, Greenberg JB, Tambour Y (1993) Stoichiometric and polydisperse effects in premixed spray flames. Combust Flame 93:97–118

  17. Chung PM (1965) Chemically reacting non-equilibrium boundary layers. Academic Press, New York, Advances in heat transfer

    Google Scholar 

  18. Greenberg JB, Silverman I, Tambour Y (1993) On the origins of spray sectional conservation equations. Combust Flame 93:90–96

    Article  Google Scholar 

  19. Williams FA (1985) Combustion theory. The Benjamin/Cummings Publishing Company Inc, Menlo Park

    Google Scholar 

  20. Dvorjetski A, Greenberg JB (2002) Steady state and extinction analyses of counter-flow spray diffusion flames with arbitrary finite evaporation rate. Combust Sci Technol 174(8):143–164

    Article  Google Scholar 

  21. Labowsky M (1980) Calculation of the burning rates of interacting fuel droplets. Combust Sci Technol 22:217–226

    Article  Google Scholar 

  22. Imaoka R, Sirignano WA (2004) Vaporization and combustion in three-dimensional droplet arrays. Proc Combust Inst 30:1981–1989

    Article  Google Scholar 

  23. Imaoka R, Sirignano WA (2005) A generalized analysis for liquid-fuel vaporization and burning. Int J Heat Mass Transf 48:4342–4353

    Article  MATH  Google Scholar 

  24. Imaoka R, Sirignano WA (2005) Transient vaporization and burning in dense droplet sprays. Int J Heat Mass Transf 48:4354–4366

    Article  MATH  Google Scholar 

  25. Chiang CH, Sirignano WA (1986) Interacting, convecting, vaporizing fuel droplets with variable properties. Int J Heat Mass Transf 36(4):875–886

    Article  Google Scholar 

  26. Chiang CH, Sirignano WA (1993) Axisymmetric calculations of three-droplet interactions. Atom Sprays 3(1):91–107

    Article  Google Scholar 

  27. Wu G, Sirignano WA (2011) Transient convective burning of a periodic fuel-droplet array. Proc Combust Inst 33:2109–16

    Article  Google Scholar 

  28. Wu G, Sirignano WA (2011) Transient convective burning of interactive fuel droplets in single-layer arrays. Combust Theor Model 15:227–243

    Article  MATH  Google Scholar 

  29. Wu G, Sirignano WA (2011) Transient convective burning of interactive fuel droplets in double-layer arrays. Combust Flame 158:2395–2407

    Article  MATH  Google Scholar 

  30. Silverman I, Sirignano WA (1994) Multi-droplet interaction effects in dense sprays. Int J Multiph Flow 20(1):99–116

    Article  MATH  Google Scholar 

  31. Abramzon B, Sirignano WA (1989) Droplet vaporization model for spray combustion calculations. Int J Heat Mass Transf 32(9):1605–1618

    Article  Google Scholar 

  32. Sirignano WA (1999) Fluid dynamics and transport of droplets and sprays. Cambridge University Press, Cambridge

    Book  Google Scholar 

  33. Linan A (1985) Theory of droplet vaporization and combustion. In: Borghi R, Clain P, Linan A, Pelce P, Sivashinsky GI (eds) Modelisation des Phenomenes de Combustion. CEA-EDF INRIA 59. Editions Eyrolles, Paris, pp 73–103

  34. Sanchez AL, Urzay J, Linan A (2015) The role of separation of scales in the description of spray combustion. Proc Combust Inst 35:1549–1577

    Article  Google Scholar 

  35. Sharma OP, Sirignano WA (1969) Ignition of stagnation point flow by a hot body. Combust Sci Technol 1(2):95–104

    Article  Google Scholar 

  36. Stull DR, Prophet H (1971) JANAF thermochemcial tables. NSRDS-NBS-37, 2nd edn. National Bureau of Standards, Washington, DC

  37. Vargaftik NB (1975) Tables on the thermophysical properties of liquids and gases, 2nd edn. Wiley, New York

    Google Scholar 

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Acknowledgements

JBG thanks the Lady Davis Chair in Aerospace Engineering for partial support of this research.

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Authors and Affiliations

  1. Aerospace Engineering, Technion, Israel Institute of Technology, Haifa, Israel

    G. Kats & J. B. Greenberg

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  1. G. Kats
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  2. J. B. Greenberg
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Correspondence to J. B. Greenberg.

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Kats, G., Greenberg, J.B. Stagnation-point spray flame ignition by an isothermal surface. J Eng Math 110, 181–194 (2018). https://doi.org/10.1007/s10665-017-9947-1

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