Multiple-scale processes, premixed and non-premixed combustion

ME 525: CombustionLecture 5: Chemical Kinetics, Global and Elementary Reactions, Rates and Types of Reactions • Multiple-scale processes, premixed and non-premixed combustion • Global and elementary chemical reactions. • Bimolecular reactions – the Arrhenius rate expression. • Tri-molecular reactions. • Forward and reverse reactions and the equilibrium constant

Non-premixed Flames Non-premixed combustion: Oil (mixture of may hydrocarbons blowing out of a well head and mixing with surrounding air and reacting with the oxygen from that air. Oil Well Blowout Fires: After Iraq’s invasion and retreat in 1991, over 200 oil wells were set on fire. Some of these fires were 200 meters tall! Yet the reactions in these fires were between fuel molecules and radicals and the primary energy release was because of formation of CO, CO2 and H2O and at the molecular scale! The pipes from which the oil escaped were 8 inches or 203.2 mm or 0.2 meters or 1/1000th the length of the jet flame. The maximum width of the visible fire was 1.5 to 2 meters. Personnel could not approach within 2 km of the fire without getting skin burns. Yet the reactions were at the scale of the molecular diameter! Molecules of oil needed to be vaporized and then mixed with the oxygen from the surrounding air. Since they were not mixed before the reaction started, the type of combustion is called non-premixed. Photograph is of a laboratory flame studied at Purdue

Premixed Flames Fuel and air are mixed before ignition and flame stabilization • Introducing Gibbs Free Energy (Gibbs Function): • Introducing Helmholtz Free Energy (Helmholtz Function):

Laboratory Flame Configurations Schematics of laboratory flame configurations: (a) premixed flame (b) counter-flow diffusion flame(c) co-flow diffusion flame (d) inverse diffusion flame

Length Scales in Combustion One of the key challenges in combustion is the wide range of length scales. A simple hypothesis is that the chemistry and chemical constants of the rates of reactions occurring at molecular scale are scale invariant. 1000 m 100 m 10 m 1 m 1/10 m 1/100 m Oil well blowout fires - Herrick Zucrow Lab. Expt. - Gatewood Expt.- Armstrong Expt. Rockets – Power Plants - Furnaces - Engines – Flows – Heat Transfer - Rates Diffusion dFPremixed Shock thickness---Soot particles---Clusters--Molecules dF 1/1,000 m 1/10,000 m 1/100,000 m 1/106 1/109 --- Zucrow Lab. Expt. --- Gatewood Expt.--- Armstrong Expt. – Birck Nanotech Center

Global Reactions • When the objective involves design parameters with sufficient adjustability, tuning and calibration, global reaction expression for combustion of fuel and oxidizer are used in combustion modeling: • With global reaction rate approximations, the rate expression is:

Elementary Reactions • Global reactions often do not actually take place but only capture the engineering effect of the elementary reactions in a narrow range. • Elementary reactions connect to the molecular structure and ease of breaking and forming bonds that represent the reaction. • Consider 2H2+ O2 = 2H2O. • It is unlikely if not impossible that an O2 mole collides with two H2 moles • One mole colliding with one mole involves ~third Avogadro number • (6.022.1026 molecules/kmol) of three body collisions. • These are just are not as likely as binary collisions. • creating radicals or free radicals. Further if a collision results in a chemical • reaction depends on whether bonds can be broken and/or new bonds • can be made. The probabilities of these occurrences are complex. • Combustion chemistry focuses on reaction mechanisms and rates. • Examples of elementary reactions are equations 4.4-4.7

Rates of Bimolecular Reactions Consider a reaction between species A and B producing products C and D: Law of Mass Action states that the rate at which the Reactions occur per unit time is proportional to the product of molar concentrations of the reactants per unit volume. is defined as the reaction rate constant and determining its value is an important task for both experimental and quantum chemists.

Collision Rate Theory

Reaction Rate Expression Probability of reaction is given by two factors a steric factor p that relates to the orientation of the molecules a the time of collision multiplied by the probability that the collisions are between partners of sufficiently high energy. Self-study Example 4.1, pp. 113 to review all the definitions & the unit conversions

EA,f Energy Reactants -DHR EA,r Products Reaction Coordinate

Tri-molecular Elementary Reactions • A third body is needed to carry away energy associated with recombination: • Three-body recombination reactions are very important in hydrogen-oxygen chemistry, for example. They become more important relative to bimolecular reactions as the pressure increases.

Rates of Forward and Reverse Reactions • Consider the reaction: • At equilibrium:

Rates of Forward and Reverse Reactions • Or, for a more general reaction:

Rates of Forward and Reverse Reactions • Summarizing:

Fast and Slow Reaction Pairs • Consider reaction pairs: • Net rate of generation of N • Steady State Approximation:

Unimolecular Reactions • Unimolecular reactions of an otherwise stable molecule can occur by collision with a wall or an inert molecule. If unimolecular reaction occurs without an energetic collision with a wall or inert, then the molecule is not stable. Unimolecular reactions are pressure dependent • The reaction rate is given by

Unimolecular Reactions with Initiation Source • To evaluate [A*], we realize that it can exist in small steady state quantities if an initiation source exists. • The overall reaction rate is given by

High Pressure and Low Pressure Limits of Reaction Rates • At high pressure [M] is large in relation to 1. In this case, theoverall reaction rate is given by • At low pressure [M] is small in relation to 1. In fact,[M] is so small that the term in relation to 1. Therefore in the low pressure limit, the apparent rate constant is:

Chain and Chain Branching Reactions Law of mass action applied to write the rates

Rates of radicals A and B and of inert M Steady state concentrations of radical species

Chain Reactions

Chain Branching Reactions Radical pool doubles as a result of chain branching reactions

Multiple-scale processes, premixed and non-premixed combustion