Review

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Review Paper C.K. Law. Performed at the Fire Protection Engineering Department, University of Maryland

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Review

  1. 1. Structure and extinction of diffusion flames with flame radiation B. H. CHAO 1 , C. K. LAW 1 and J. S. T’IEN 2 1 Princeton University 2 Case Western Reserve University 23 rd Symposium on combustion / The Combustion Institute Review : by Vivien Lecoustre
  2. 2. Problem formulation Steady state droplet burning. <ul><li>Isobaric </li></ul><ul><li>Spherical symmetric </li></ul><ul><li>Second order Arrhenius kinetics </li></ul><ul><li>No surface emission and absorption </li></ul><ul><li>Radius of the droplet used as a </li></ul><ul><li>characteristic dimension </li></ul><ul><li>Assume reaction zone embedded </li></ul><ul><li>in radiation zone. </li></ul><ul><li>ε << δ << 1 </li></ul><ul><li>Based on Sohrab : </li></ul>
  3. 3. Start: governing equations Mass conservation (Mass evaporation rate) Energy conservation Species conservation i =F, O Which can be combined:
  4. 4. Non Dimensional quantities
  5. 5. Solution of the problem <ul><li>The problem is reduce to solving </li></ul><ul><li>Solve the problem using asymptotic analysis tools. </li></ul><ul><li>Results obtained for heptane droplet in standard atmosphere. </li></ul>
  6. 6. First results <ul><li>First we consider infinitely thin reaction zone. </li></ul>For a fixed r s , increasing radiative heat loss decreases flame temperature and mass burning rate. Since infinitely fast reaction: no extinction
  7. 7. Finite rate chemistry a represents the flame temperature reduction For a given droplet size, heat loss promotes kinetic extinction
  8. 8. Double turning points For a fixed Γ , increasing Da implies increasing rs . Two turning points. Two critical Damk ö hler numbers. Only the lower branch has a physical meaning. Existence of a maximum Γ for burning to occur
  9. 9. Extinction Damköhler numbers
  10. 10. Conclusion <ul><li>Results show : heat loss promotes flames extinction </li></ul><ul><li>Dual extinction turning point (flame extinguishes due to reactant leakage-kinetic limitation occur for small and large droplet as a result of excessive heat loss) </li></ul><ul><li>Predict that there exist diffusive reactive systems for which steady combustion is not possible for all the droplet size. </li></ul><ul><li>They give an estimate of the radiative extinction droplet size. </li></ul>

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