5310 Combustion Introduction Lecture 11

5310 Combustion Introduction Lecture 11 - MAE 5310:...

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Unformatted text preview: MAE 5310: COMBUSTION FUNDAMENTALS Chemical Time Scales and Examples September 27, 2011 Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk CHAIN AND CHAIN-BRANCHING REACTIONS • Chain reactions involve production of a radical species that subsequently reacts to produce another radical. This radical in turn, reacts to produce yet another radical • Sequence of events, called chain reaction, continues until a reaction involving the formation of a stable species from two radicals breaks the chain • Consider a hypothetical reaction, represented by a global mechanism: M AB M B A A AB A B B AB B A M A A M A AB B A k k k k + → + + + → + + → + + + → + → + 4 3 2 1 2 2 2 2 2 2 Chain-initiation reaction Chain-propagating reactions Chain-terminating reaction Global model CHAIN AND CHAIN-BRANCHING REACTIONS: EXAMPLE [ ] [ ][ ] [ ][ ] [ ] [ ][ ] [ ] [ ][ ] [ ][ ] [ ][ ][ ] [ ][ ] [ ][ ] [ ][ ] [ ][ ][ ] [ ][ ] [ ][ ] [ ][ ][ ] [ ] [ ][ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ][ ] [ ] [ ] [ ][ ] 2 1 4 3 2 1 2 1 2 2 2 1 2 2 4 1 3 2 2 1 2 2 1 4 2 3 1 2 1 2 2 2 1 2 2 4 1 3 2 2 2 2 1 4 2 3 2 2 4 2 3 2 2 2 1 4 2 3 2 2 2 2 2 2 3 2 1 2 4 1 1 2 4 1 1 2 2 - ≈ + +- = ≈ + + = =-- =- +- + + =- =-- = k k k k B A M B k k k k A M k dt B d k k k k B A M B k k k k B A M k k A M B A k A B k B A k M B A k A B k B A k M A k M B A k A B k B A k dt AB d A B k dt B d B A k M A k dt A d Steady-state approximation for radical concentration In the early stages of reaction, the concentration of the product AB is small, as are the concentrations of A and B throughout the course of the reaction therefore, reverse reactions may be neglected at this reaction stage CONCLUSIONS • Term in brackets [ ] >> 1 because the rate coefficients for the radical concentrations, k 2 and k 3 are much larger than k 1 and k 4 • Can write approximate expressions for [A] and d[B...
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This note was uploaded on 02/11/2012 for the course MAE 5310 taught by Professor Danielkirk during the Fall '09 term at FIT.

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5310 Combustion Introduction Lecture 11 - MAE 5310:...

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