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Fluid Dynamics of Combustion Determining the equilibrium products of combustion is a formidable task, and is often done with the help of computers. However, in this assignment, you are asked to determine the adiabatic flame temperature at constant pressure of 1 atm and initial reactants at 298 K and corresponding equilibrium products for rich methane-air combustion. You are asked to determine the equilibrium considering CO2, H2O, H2, CO and N2 in the products. The equilibrium composition and the adiabatic flame temperatures must be solved simultaneously. Please review the appendix to answer the questions below: 1. Using the discussion in the appendix, start with Eq. (4) and demonstrate Eq. (5). You will need to express the species partial pressures in terms of mole fractions (note that the actual pressure, p. in general may be different from the reference pressure, p°). 2. Writing the reaction balance for a rich mixture (o> 1) as follows: b CO2 +c H2O+ d H2 +e CO+7.52N2, express C. d and e in terms of b and busing the atom balance. b.d 3. Using the equilibrium condition for the water-gas shift reaction: CO2- H2 K, (T) , e.c rewrite this expression as a quadratic equation in b and a Therefore, this quadratic equation may have two possible roots of which only one root is valid (the one that yields positive coefficients in the balance equation). 4. Solve for the products temperature and the products mole fractions based on the reactants' conditions provided (the outcome of this work are the final adiabatic flame temperature and equilibrium composition, b, C, d and e, for an equivalence ratio of 1.1. You also need to discuss your procedure for determining these adiabatic equilibrium conditions. To solve for the adiabatic flame temperature and equilibrium composition simultaneously, you need to guess temperature values, determine the composition, and substitute into the energy balance: to verify if the equality stands. Typical combustion temperatures for hydrocarbon fuels at the prescribed conditions may fall in the range of 2200 K and 2400K. 5. Using the Engineering Colostate Education- Dandy Code determine the adiabatic flame temperature and the equilibrium composition based on CO2, H2O, CO, H2 and N2 in the products. How different your adiabatic flame temperature and products composition are from the value determine online? Note that the products' composition is provided as mole fractions. You will need to prescribe the following: The starting temperature and pressure is 298 K and 1 atm. The estimated equilibrium temperature and pressure is 2200 K and 1 atm (they are needed to start the calculation). The calculation constraint is "Constant pressure and enthalpy" The elements are C. H, O and N. 1 The reactants are (in moles) 1.1 mole of CH4, 2 moles of O2 and 7.52 moles of N2. Additional species include CO2, H2O, H2 and CO. The questions above are designed to allow you to discuss your results and not just briefly state whether the results are identical or different. Appendix: Equilibrium Major Products of Hydrocarbon Combustion The products of hydrocarbon combustion in air can be classified under major and minor species. For lean hydrocarbon combustion, the excess O2 is reasonably chemically stable. An account for major species is generally sufficient to determine the adiabatic flame temperature as they have major contribution to the products total enthalpy or internal energy; while, we sometimes need to determine minor species whose mole fractions can be significantly below 1% and in the parts-per-million (ppm) range, such as NO2. In lean hydrocarbon combustion in air, the major products of combustion are CO2, H2O, O2 and N2, as O2 and N2 are considered relatively chemically stable to survive the combustion process. Major Products Balance for Lean Hydrocarbon Combustion (Q 0) SC,H, am 6002 + d O2 + e N2 (1) The atom balance in this case is sufficient to determine the products composition of major species, b, c. d and e. However, if minor species are to be computed (e.g. H2, CO, OH, O, NO, ), equilibrium conditions must be invoked. For example, if we want to determine the amount of NO produced in methane lean combustion, we may also want to consider the equilibrium reaction: O2 N2 <> 2NN or a multiple of this reaction (like the formation of NO, which corresponds to multiplying the above reaction by 1/2). Note here that the choice of the equilibrium reaction is determined by the need to address all the unknowns in the reaction balance (i.e. do not include new species when choosing an equilibrium reaction). In near-stoichiometric and rich hydrocarbon combustion in air, two additional major products must be considered, H2 and CO. These products account for the fact that the primary hydrocarbon fuel is not chemically stable to survive the combustion process. Major Products Balance for Rich Hydrocarbon Combustion (stoichiometric and $>0) +am (02+3.73N2 CO2 C H2O + d H2 + e (2) Note that you will need an additional equilibrium reaction since the atom balance is not sufficient to determine all the major species. The most convenient form of an equilibrium reaction that takes into account H2 and CO is the so-called water-gas shift reaction: CO+H,O<> CO, H2 Again, this equilibrium reaction is convenient because it accounts for all the unknowns in the reaction balance. The stoichiometric coefficients for the equilibrium conditions are based on this reaction. The equilibrium constant for this reaction may be expressed in terms of the equilibrium constant for the formation of all species involved. Kp./co, (3) The equilibrium condition for the water-gas shift reaction is as follows: (4) (Pco/p°((Pro/p) This expression may be simplified to yield: b.d K,(T)= (5) e.c where the coefficients b, C, d and are the same as the ones listed in Eq. (2) above. 2

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