ME 525: Combustion Lecture 15: Laminar Premixed Flame

1. ME 525: CombustionLecture 15: Laminar Premixed Flame • Comments on approximations, notation, HW hints. • Heat Transfer from Flames and Combustors: Boundaries, • Boundary Conditions and Source/Sink Term Heat Transfer. • Laminar Premixed Flame

2. A few comments homework and associated reading • Observe symbols and notation carefully and deliberately • to avoid confusion. For example: what is “h?” Particularly • in the context of Home work 6 and in the context of the • Energy Conservation equation. • Textbook sections not explicitly covered in class (yet) may • be good reference material for doing the homework. • For example: pp. 94-101, 374-402 nicely connect to HW 6.

3. Structure of Premixed Hydrocarbon/Air Flames Recombination Reaction Preheat T Reactants q H2O2 Fuel Intermediates T HO2 7/30

4. Structure of Premixed Hydrocarbon Flames • Flame consists of three zones: Preheat zone, Reaction zone, Recombination zone • Reaction zone can be further divided into a pyrolysis zone where hydrocarbon fragments are formed, and a zone in which intermediates like CO and H2 are consumed. • Flame structure is determined by advection flow of unburned gases towards and diffusion of heat and radical species away from the reaction zone. • Diffusion dominated by the H atom. • Considerable HO2 formed by H + O2 + M → HO2 + M in preheat zone. 8/30

5. Structure of Premixed Hydrocarbon Flames • HO2 then forms H2O2 which is advected towards high T reaction zone and then breaks down to form OH. • OH plays very important role in H-atom abstraction from HCs in the pyrolysis zone and then in oxidation of CO and H2. • Heat release curve peaks in latter part of the reaction zone because of the reactions that convert CO to CO2, including the CO + OH → CO2 + H reaction. • Recombination zone: temperature rises slowly because of exothermic radical recombination reactions like H + OH + M → H2O + M. 9/30

6. Analysis of Premixed Hydrocarbon Flames • Assumptions • Steady state • 1-D, constant area flame • No radiation heat transfer • No shaft work or viscous dissipation • Potential energy changes are negligible • Kinetic energy changes are negligible • Diffusion of heat and mass follows Fourier and Fick’s laws, no thermal diffusion • Diffusion coefficient is the same for each species • Le = 1 11/30

7. Structure of Premixed Hydrocarbon Flames Mass conservation equation 12/30

8. Analysis of Premixed Hydrocarbon Flames • Species Conservation: Dassumed same for all species.

9. Analysis of Premixed Hydrocarbon Flames • Conservation of Energy

10. Analysis of Premixed Hydrocarbon Flames • Using the assumption of Le =1: Second order equation, four boundary conditions→ Eigen value problem with as the Eigen value.

11. Solution with Assumed Temperature Boundaries • Integrate from x=- to x=+:

12. Solution with Assumed Temperature Profile

13. Integral of the volumetric reaction rate of the fuel

14. Approximate Solution with Reaction Rate Profile • Now integrate from x = - to x = d/2 to obtain another relation between the mass flux and flame thickness. From our discussion of the structure of premixed flames, it is reasonable to assume that in this region the volumetric chemical reaction rate for the fuel is negligible:

15. Burning Rate and Flame Speed Eigen Values • Substitute and rearrange: • The laminar flame speed:

16. Rewriting the expressions for the laminar flame speed and laminar flame thickness