MAE 5360: Hypersonic Airbreathing Engines

1. MAE 5360: Hypersonic Airbreathing Engines Combustion Kinetics Overview 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: • [ci] is molar concentration of ith species in mixture • Equation states that rate of disappearance of fuel is proportional to each of reactants raised to a power • Constant of proportionality, kglobal, 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 nth order with respect to fuel • Reaction is mth 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, HO2 and a hydrogen atom, H • HO2 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 s traveling at constant speed v and experiencing collisions with identical, but stationary, molecules • If distance between traveled between collisions (mean free path, l) is large then moving molecule sweeps out a cylindrical volume in which collisions are possible = vps2Dt in a time interval Dt. • At ambient conditions for gases: • Time between collisions ~ O(10-9 s) • Duration of collisions ~ O(10-12 – 10-13 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)vps2 • In actual gas all molecules are moving • Assuming a Maxwellian distribution for all molecules, the collision frequency, Zc, 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 sA and sB. Diameter of collision volume is then given as sAB=(sA+ sB)/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) • ZAB/V = Number of collisions between all A and all B / Unit volume Unit time

6. MOLECULAR KINETIC AND COLLISION THEORY OVERVIEW:BIMOLECULAR REACTIONS • NAvogadro = 6.022x1023 molecules/mol or 6.022x1026 molecules/kmol • Probability, P, that a collision leads to reaction can be expressed as product of two terms • Energy factor, exp[-EA/RT] • Expresses the fraction of collisions that occur with an energy above the threshold level necessary for reaction, EA, or activation energy • Geometrical or steric factor, p • Takes into account the geometry of collisions between A and B More common curve fit A, n and EA are empirical parameters

7. EXAMPLE: H2 OXIDATION AND NET PRODUCTION RATES Global reaction Partial mechanism Find: d[O2]/dt, d[H]/dt, etc. System of 1st order, ordinary differential equations Initial conditions for each participating species

8. GENERAL (SHORTHAND) NOTATION

9. RELATION BETWEEN RATE COEFFICIENTS AND EQUILIBRIUM CONSTANTS Equilibrium condition d[A]dt→0 Relationship between concentration and partial pressure [M] ↑ when P ↑ at constant cM and T True for all reactions True for all bimolecular reactions

10. STEADY-STATE APPROXIMATION • What are we talking about: • In many chemical combustion systems, many highly reactive intermediate species (radicals) are formed • Physical explanation: • Rapid initial build-up of radical concentration • Then radicals are destroyed as quickly as they are being created • Implies that rate of radical formation = rate of radical destruction • Situation typically occurs when the reaction forming the radicals is slow and the reaction destroying the radicals is fast • This implies that the concentration of radicals is small in comparison with those of the reactants and products • Radical species can thus be assumed to be at steady-state

11. MECHANISM FOR UNIMOLECULAR REACTIONS

12. 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: Global model Chain-initiation reaction Chain-propagating reactions Chain-terminating reaction

13. CHAIN AND CHAIN-BRANCHING REACTIONS: EXAMPLE In early stages of reaction, concentration of product AB is small, as are concentrations of A and B throughout course of the reaction therefore, reverse reactions may be neglected at this reaction stage Steady-state approximation for radical concentration

14. CONCLUSIONS • Term in brackets [ ] >> 1 because rate coefficients for radical concentrations, k2 and k3 are much larger than k1 and k4 • Can write approximate expressions for [A] and d[B2]/dt • Radical concentration depends on the square root ratio of k1 to k4 • The greater the initiation rate, the greater the radical concentration • The greater the termination rate, the lesser the radical concentration • Rate coefficients of chain-propagating steps are likely to have little effect upon radical concentration because k2 and k3 appear as a ratio, and their influence on the radical concentration would be small for rate coefficients of similar magnitude. • Increasing k2 and k3 results in an increased disappearance of [B2] • Note that these scalings break down at pressure sufficiently high to cause 4k2k3[B2]/(k1k4[M]2) >> 1

15. COMMENTS ON CHAIN-BRANCHING • Chain branching reactions involve formation of two radical species from a reaction that consumes only one radical • Example: O + H2O → OH + OH • Existence of a chain-branching step in a chain reaction mechanism can have an explosive effect • Example: Explosions in H2 and O2 mixtures, that we will examine in our study of detailed mechanisms, are a direct result of chain-branching steps • Example: Chain-branching reactions are responsible for a flame being self-propagating • In systems with chain branching, it is possible for the concentration of a radical species to build up geometrically, causing the rapid formation of products • Unlike previous hypothetical example, rate of chain-initiation step does not control overall reaction rate • With chain-branching, the rates of radical reactions dominate

16. EXAMPLE: ZELDOVICH MECHANISM FOR NO • A famous mechanism for the formation of nitric oxide from atmospheric nitrogen is called the Zeldovich (thermal) mechanism, given by: • Because the second reaction is much fast than the first, the steady-state approximation can be used to evaluate the N-atom concentration. Furthermore, in high-temperature systems, the NO formation reaction is typically much slower than other reactions involving O2 and O. This, the O2 and O can be assumed to be in equilibrium, i.e., O2↔ 2O. • Construct a global mechanism: • Determine kglobal, m, and n using the elementary rate coefficients, etc., from the detailed mechanism • Using these results and the heating of air to 2500 K and 3 atmospheres, determine: • The initial NO formation rate in ppm/s • The amount of NO formed (in ppm) in the 0.25 ms • The rate coefficient, k1f, is k1f=1.82x1014exp(-38,370/T)

17. Insight gained from knowledge of chemical time scale, tchem What is approximate magnitude of time scale? Characteristic time is defined as time required for concentration of A to fall from its initial value to a value equal to 1/e times the initial value [A](t=tchem)/[A]0=1/e RC circuit analog CHEMICAL TIME SCALES Unimolecular reactions Bimolecular reactions Bimolecular reactions case where [B]0 >> [A]0 Termolecular reactions Termolecular reactions case where [B]0 >> [A]0

18. EXAMPLE: CHEMICAL TIME SCALE CALCULATIONS 1 • Reaction 1 is an important step in oxidation of CH4 • Reaction 2 is key step in CO oxidation • Reaction 3 is a rate-limiting step in prompt-NO mechanism • Reaction 4 is a typical radical recombination reaction • Estimate tchem associated with least abundant reactant in each reaction for following 2 conditions • Assume that each of 4 reactions is uncoupled from all others and that third-body collision partner concentration is the sum of the N2 and H2O concentrations) k=1.0x108T1.6exp(-1570/T) k=4.76x107T1.23exp(-35.2/T) k=2.86x108T1.1exp(-10,267/T) k=2.2x1022T-2.0 2 3 4 Condition II: High Temperature T=2199 K, P=1 atm cCH4=3.773x10-6 cN2=0.7077 cCO=1.106x10-2 cOH=3.678x10-3 cH=6.634x10-4 cCH=9.148x10-9 cH2O=0.1815 Condition I: Low Temperature T=1344 K, P=1 atm cCH4=2.012x10-4 cN2=0.7125 cCO=4.083x10-3 cOH=1.818x10-4 cH=1.418x10-4 cCH=2.082x10-9 cH2O=0.1864

19. EXAMPLE SOLUTION • Increasing T shortens chemical time scales for all species, but most dramatically for CH4 + OH and CH + N2 reactions • For the CH4 + OH reaction, the dominant factor is the decrease in the given CH4 concentration • For the CH + N2 reaction, the large increase in the rate coefficient dominates • Characteristic times at either condition vary widely among the various reactions • Notice long characteristic times associated with recombination reaction H + OH + M → H2O + M, compared with the bimolecular reactions. • That recombination reactions are relatively slow plays a key role in using partial equilibrium assumptions to simplify complex chemical mechanisms (see next slide) • Note that tchem=1/[B]0kbimolec could have been used with good accuracy for reaction 3 at both low and high temperature conditions, as well as reaction 1 at high temperature because in these cases one of reactants was much more abundant than other

20. PARTIAL EQUILIBRIUM • Many combustion process simultaneously involve both fast and slow reactions such that the fast reactions are rapid in both the forward and reverse directions • These fast reactions are usually chain-propagating or chain-branching steps • The slow reactions are usually the termolecular recombination reactions • Treating fast reactions as if they were equilibrated simplifies chemical kinetics by eliminating need to write rate equations for radical species involved, which is called the partial-equilibrium approximation • Consider the following hypothetical mechanism:

21. PARTIAL EQUILIBRIUM VS. STEADY-STATE • Net result of invoking either partial equilibrium assumption or steady-state approximation is the same: • A radical concentration is determined by an algebraic equation rather than through the integration of an ordinary differential equation • Keep in mind that physically the two approximations are quite different: • Partial equilibrium approximationforcing a reaction, or sets of reactions, to be essentially equilibrated • Steady-state approximationforces the individual net production rate of one or more species to be essentially zero • Many examples in combustion literature where partial equilibrium approximation is invoked to simplify a problem • Examples: • Calculation of CO concentrations during the expansion stroke of a spark-ignition engine • Calculation of NO emissions in turbulent jet flames • In both examples, slow recombination reactions cause radical concentrations to build up to levels in excess of their values for full equilibrium

22. INTRODUCTION TO IMPORTANT CHEMICAL MECHANISMS • Purpose • Outline elementary steps involved in a number of chemical mechanisms of significant importance to combustion and combustion generated air pollution • Fundamental ideas developed in chemical kinetics directly applicable to understanding complex real systems • Precautionary note • Complex mechanisms are evolutionary products of chemists’ thoughts and experiments, and may change with time as new insights are developed • Therefore when we discuss a particular mechanism, we are not referring to the mechanism in the same sense that we might refer to the first law of thermodynamics

23. H2-O2 SYSTEM • Hydrogen-oxygen system is important in rocket propulsion and also important subsystem in oxidation of hydrocarbons and carbon monoxide • Depending on temperature, pressure, and extent of reaction, reverse reactions may be possible • In modeling H2-O2 system as many as 40 reactions can be taken into account involving 8 species: H2, O2, H2O, OH, O, H, HO2, and H2O2 • Consider detailed mechanism shown on next slide • Consider explosive behavior of H2-O2 system • Comments • Understanding of detailed chemistry of a system is very useful in understanding experimental observations • Such an understanding is essential to development of predictive models of combustion phenomena when chemical effects are important

24. THE H2-O2 SYSTEM

25. H2-O2 EXPLOSION CHARACTERISTICS: f=1.0

26. H2-O2 EXPLOSION CHARACTERISTICS • Follow a vertical line at, say 500 C • 1 – 1.5 mm Hg there is no explosion • Lack of explosion is a result of the free radicals produced in the chain initiation step (H.2) and chain sequence (H.3-H.6) being destroyed by reactions on the wall of the vessel • Wall reactions break the chain, preventing build-up of radicals that lead to explosion • Note that the wall reactions are not explicitly included in the mechanism since they are not strictly gas phase reactions. Symbolically: • 1.5 – 50 mm Hg there is an explosion • Direct result of gas-phase chain sequence H.3-H.6 prevailing over radical destruction at wall • Remember that increasing the pressure increases the radical concentration linearly, while increasing the reaction rate geometrically • 50 – 3,000 mm Hg there is no explosion • The cessation of explosive behavior can be explained by the competition for H atoms between the chain branching reactions, H.3, and what is effectively a chain-terminating step at low temperatures, reaction H.11. • Reaction H.11 is chain terminating because the hydroperoxy radical, HO2, is relatively unreactive at these conditions, and because of this, it can diffuse to wall where it is destroyed • Above 3,000 mm Hg there is an explosion • At these conditions reaction H.16 adds a chain-branching step with opens up the H2O2 chain sequence

27. CARBON MONOXIDE OXIDATION • Hydrocarbon combustion can be characterized as a two-step process: • Breakdown of the fuel to carbon monoxide • Oxidation of carbon monoxide to carbon dioxide • CO is slow to oxidize unless there is some hydrogen containing species present • Small quantities of H2O (often called moist CO) or H2 can have a tremendous effect on the oxidation rate • This is because the CO oxidation step involving the hydroxyl radical is much faster than the steps involving O2 and O • Assuming that water is primary hydrogen containing species, following steps describe oxidation of CO • First reaction is slow and does not contribute significantly to formation of CO2, but rather serves as the initiator of the chain sequence • The 3rd reaction is the actual CO oxidation step (chain propagating step), producing H atoms to react with O2 to form OH and O (in reaction 4) • These radicals, in turn, feed back into the oxidation step (reaction 3) and the first chain branching step (reaction 2). The CO + OH → CO2 + H (reaction 3) is the key reaction in the overall scheme

28. OXIDATION OF HIGHER PARAFFINS • Paraffins or alkanes, are saturated, straight-chain or branched chain, single bonded hydrocarbons with the general molecular formula CnH2n+2. We will consider cases where n > 2 • No attempt is made to explore or list many elementary reactions involved • Strategy instead will be to: • Present an overview of oxidation process • Indicate key reactions steps • Discuss multi-step global mechanisms approaches that have had some success • For further discussion of paraffins, olefins, etc., see Chapter 3, Section E • Oxidation of paraffins can be characterized by three sequential processes: • Fuel molecule attacked by O and H atoms and breaks down, mostly forming olefins (double carbon bonds, CnH2n) and H2. H2 oxidizes to water, based on available oxygen • Unsaturated olefins further oxidize to CO and H2. Essentially, all of H2 is converted to water • The CO burns out via reaction CO + OH → CO2 + H. Nearly all of heat release associated with the overall combustion process occurs in this step

29. ILLUSTRATION OF PROCESS WITH PROPANE • Step 1: A single carbon-carbon (C-C) bond is broken in the original fuel molecule. The C-C bonds are preferentially broken over hydrogen-carbon bonds because the C-C bonds are weaker • Example: C3H8 + M → C2H5 + CH3 + M • Step 2: The two resulting hydrocarbon radicals break down further, creating olefins (hydrocarbons with double carbon bonds, CnH2n) and hydrogen atoms. The removal of an H atom from the hydrocarbon is termed H-atom abstraction. In the example for this step, ethylene and methylene are produced. • C2H5 + M → C2H4 + H + M • CH3 + M → CH2 + H + M • Step 3: The creation of H atoms from Step 2 starts development of a radical pool • Example: H + O2 → O + OH • Step 4: With new radicals, new fuel-molecule attack pathways open up • Examples: • C3H8 + OH → C3H7 + H2O • C3H8 + H → C3H7 + H2 • C3H8 + O → C3H7 + OH

30. ILLUSTRATION OF PROCESS WITH PROPANE • Step 5: As in Step 2, the hydrocarbon radicals again decay into olefins and H atoms via H-atom abstraction • Example: C3H7 + M → C3H6 + H + M • And following the b-scission rule • Rule states that the C-C or C-H bond broken will be the one that is one place removed from the radical site (the site of the unpaired electron) • The unpaired electron at the radical site strengthens the adjacent bonds at the expense of those one placed removed from the site • For the C3H7 radical created in Step 4, two paths are possible • C3H7 + M → C3H6 + H + M • C3H7 + M → C2H4 + CH3 + M • Step 6: The oxidation of the olefins created in Steps 2 and 5 is initiated by O-atom attack, which produces formyl radicals (HCO) and formaldehyde (H2CO) • Examples: • C3H6 + O → C2H5 + HCO • C3H6 + O → C2H4 + H2CO • Step 7: • a: Methyl radicals (CH3) oxidize • b: Formaldehyde (H2CO) oxidizes • c: Methylene (CH2) oxidizes • Each of these steps produces carbon monoxide, the oxidation of which is Step 8 • Step 8: Carbon monoxide oxidizes following the moist CO mechanism discussed above

31. GLOBAL AND QUASI-GLOBAL MECHANISMS One step mechanism See parameters: A, Ea/R, m and n on next page Chosen to provide best fit agreement between Experimental and predicted flame temperatures, as well as flammability limits Four step mechanism See parameters: x, Ea/R, a, b, c on next page This particular mechanism assumes that ethylene (C2H4) is the intermediate hydrocarbon

32. GLOBAL AND QUASI-GLOBAL MECHANISMS

33. GRI MECH: METHANE COMBUSTION (1-46)

34. GRI MECH: METHANE COMBUSTION (47-92)

35. GRI MECH: METHANE COMBUSTION (93-137)

36. GRI MECH: METHANE COMBUSTION (138-177)

37. GRI MECH: METHANE COMBUSTION (178-219)

38. GRI MECH: METHANE COMBUSTION (220-262)

39. GRI MECH: METHANE COMBUSTION (263-279)

40. CH4 MOLECULAR STRUCTURE DIAGRAM: HIGH T • Consider the following molecular structure diagram which shows a linear progression of CH4 to CO2 with several side loops originating from the methyl (CH3) radical • Direct Pathways: Linear Progression, called the backbone • The linear progression starts with an attack on the CH4 molecule by OH, O and H radicals to produce the methyl radical • The methyl radical then combines with an oxygen atom to form formaldehyde (CH2O) • CH3 + O → CH2O + H • The formaldehyde is attacked by OH, H, and O radicals to produce the formyl radical (HCO) • The formal radical is converted to CO by a trio of reactions: • HCO + H2O • HCO + M • HCO + OH • Finally CO is converted to CO2, primarily by reaction with OH • Indirect Pathways: • CH3 radicals also react to form CH2 radicals in two possible electronic configurations, which are shown in the left side pathway: • The singlet electronic state of CH2 is designated as CH2(S) (does not stand for solid) • On the right side-loop, CH3 is first converted to CH2OH, which in turn is converted to CH2O • Other less important pathways complete the mechanism, which have reaction rates of less than 1x10-7 mol/cm3 s, and are not shown in the structure diagram

41. CH4 MOLECULAR STRUCTURE DIAGRAM: HIGH T

42. CH4 MOLECULAR STRUCTURE DIAGRAM: LOW T • At lower temperatures (say less than 1500 K) pathways that were unimportant at higher temperatures now become prominent • Consider the following diagram, which is at a temperature of T=1345 K • The black arrows show the new pathways that now complement all of the high-temperature pathways, and there are several interesting features: • There is a strong recombination of CH3 back to CH4 • An alternate route from CH3 to CH2O appears through the intermediate production of methanol (CH3OH) • CH3 radicals combine to form ethane (C2H6), a higher hydrocarbon than the original reactant, which was methane (CH4) • The C2H6 is ultimately converted to CO (and CH2) through C2H4 (ethene) and C2H2 (acetylene) • See steps 5-7 on slide 5 • The appearance of hydrocarbons higher than the initial reactant hydrocarbon is a common feature of low-temperature oxidation processes.

43. CH4 MOLECULAR STRUCTURE DIAGRAM: LOW T

44. OXIDES OF NITROGEN (NOx) FORMATION • Nitric oxide is an important minor species in combustion because of its contribution to air pollution • In combustion of fuels that contain no nitrogen, NO is formed by three chemical mechanisms that involve nitrogen from the air: • Zeldovich mechanism (also called the thermal mechanism) • Dominates at high temperatures over wide range of f • Usually unimportant for T < 1800 K • Fenimore (also called the prompt mechanism) • Important in fuel rich combustion • N2O-intermediate mechanism • Important in lean (f < 0.8), low temperature combustion • Mechanism is important in NO control strategies that involve lean premixed combustion • Currently being explored by gas-turbine manufacturers

45. EXTENDED ZELDOVICH MECHANISM • This 3 reaction set is referred to as the extended Zeldovich mechanism • Mechanism is coupled to the fuel chemistry through the O2, O, and OH species • In process where the fuel combustion is complete before NO formation becomes significant, the two processes can be uncoupled • If relevant time scales are sufficiently long can assume that the N2, O2, O, and OH concentrations are at their equilibrium values and the N atoms are in steady-state • May also assume that the NO concentrations are much less than their equilibrium values, the reverse reactions can be neglected • With these two assumptions (which greatly simplify the problem of calculating the NO formation), a simple rate expression results • Note that within flame zones and in short time scale post-flame processes, the equilibrium assumption is not valid • Compared with time scales of fuel oxidation process, NO is formed rather slowly by the thermal mechanism, thus thermal NO is generally considered to be formed in post-flame gases

46. FENIMORE (PROMPT) MECHANISM • Linked closely to combustion chemistry of hydrocarbons • Some NO rapidly produced in the flame zone of laminar premixed flames long before there would be time to form NO by the thermal mechanism • The general scheme of the Fenimore mechanism is that hydrocarbon radicals react with molecular nitrogen to form amines or cyano compounds, and the amines or cyano compounds are then converted to intermediate compounds that ultimately form NO • The mechanism can be written as (ignoring the processes that form the CH radicals to initiate the mechanism) • CH + N2↔ HCN + N • C + N2 ↔ CN + N • For f < 1.2 • HCN + O ↔ NCO + H • NCO + H ↔ NH + CO • NH + H ↔ N + H2 • N + OH ↔ NO + H • For f > 1.2, other routes open up and the chemistry becomes much more complex