1 MAE 5310: COMBUSTION FUNDAMENTALS Introduction to Chemical Kinetics September 24, 2012 Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk

2 CHEMICAL KINETICS OVERVIEW In many combustion processes, chemical reaction rates control rate of combustion Chemical reaction rates determine pollutant formation and destruction Ignition and flame extinction are dependent on rate processes Overall reaction of a mole of fuel, F, with a moles of oxidizer, O, to form b moles of products, P, can be expressed by a global reaction mechanism as: From experimental measurements, rate at which the fuel is consumed expressed as: [  i ] is molar concentration of i th species in mixture Equation states that rate of disappearance of fuel is proportional to each of reactants raised to a power Constant of proportionality, k global, is called global rate coefficient, which is a strong function of temperature and minus sign indicates that fuel concentration decreases with time Exponents n and m relate to reaction order –Reaction is n th order with respect to fuel –Reaction is m th order with respect to oxidizer –Reaction is (n+m) th order overall

3 EXAMPLE OF INTERMEDIATE SPECIES Consider global reaction of conversion of hydrogen and oxygen to water The following elementary reactions are important: First reaction produces hydroperoxy, HO 2 and a hydrogen atom, H –HO 2 and H are called radicals –Radicals, or free radicals, are reactive molecules, or atoms, that have unpaired electrons To have a complete picture of hydrogen and oxygen combustion over 20 elementary reactions are necessary Collection of elementary reactions necessary to describe an overall reaction is called a mechanism

4 MOLECULAR KINETIC AND COLLISION THEORY OVERVIEW: BIMOLECULAR REACTIONS Molecular collision theory an be used to provide insight into form of bimolecular reaction rates and to suggest the temperature dependence of the bimolecular rate coefficient Consider a single molecule of diameter  traveling at constant speed v and experiencing collisions with identical, but stationary, molecules –If distance between traveled between collisions (mean free path, ) is large then moving molecule sweeps out a cylindrical volume in which collisions are possible = v  2  t in a time interval  t. –At ambient conditions for gases: Time between collisions ~ O(10 -9 s) Duration of collisions ~ O( – s) –If stationary molecules distributed randomly and have a number density, n/V, the number of collisions experienced by the traveling molecule per unit time is: Z = collisions per unit time = (n/V)v  2 In actual gas all molecules are moving –Assuming a Maxwellian distribution for all molecules, the collision frequency, Z c, is given by:

5 MOLECULAR KINETIC AND COLLISION THEORY OVERVIEW: BIMOLECULAR REACTIONS So far theory applies to identical molecules –Extend analysis to collisions between unlike molecules have diameters  A and  B. Diameter of collision volume is then given as  AB =(  A +  B )/2 –This is an expression for the frequency of collision of a single A molecule with all B molecules Ultimately we want collision frequency associated with all A and B molecules –Total number of collisions per unit volume and per unit time is obtained by multiplying collision frequency of a single A molecule by the number of A molecules per unit volume and using the appropriate mean molecular speed (RMS) –Z AB /V = Number of collisions between all A and all B / Unit volume Unit time

6 MOLECULAR KINETIC AND COLLISION THEORY OVERVIEW: BIMOLECULAR REACTIONS N Avogadro = 6.022x10 23 molecules/mol or 6.022x10 26 molecules/kmol Probability, P, that a collision leads to reaction can be expressed as product of two terms 1.Energy factor, exp[-E A /RT] Expresses the fraction of collisions that occur with an energy above the threshold level necessary for reaction, E A, or activation energy 2.Geometrical or steric factor, p Takes into account the geometry of collisions between A and B More common curve fit A, n and E A are empirical parameters

7 EXAMPLE: H 2 OXIDATION AND NET PRODUCTION RATES System of 1 st order, ordinary differential equations Initial conditions for each participating species Global reaction Partial mechanism Find: d[O 2 ]/dt, d[H]/dt, etc.

8 GENERAL NOTATION

9 EXAMPLE Determine the collision-theory steric factor for the reaction O + H 2 → OH + H at T=2000 K give the sphere diameters,  O =3.050 and  H2 =2.827 Å using the data in Appendix 2 of Glassman Comments Pay attention to units: –k b =1.381x J/K = 1.381x g cm 2 /s 2 K