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ME 525: Combustion Lecture 12: Review of Ten Classes

ME 525: Combustion Lecture 12: Review of Ten Classes. C hemical symbols r eactions and balancing . Control mass, control volume mass, energy balance with c hemical reactions. Heat of formation, heat of combustion, h eating value. Example problems.

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ME 525: Combustion Lecture 12: Review of Ten Classes

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  1. ME 525: CombustionLecture 12: Review of Ten Classes • Chemical symbols reactions and balancing. • Control mass, control volume mass, energy balance with • chemical reactions. Heat of formation, heat of combustion, • heating value. Example problems. • Chemical equilibrium criteria, Gibbs free energy, equilibrium • Constant(s). • (4) Law of mass action, chain reactions, reaction rates • (5) Reduced mechanism with steady state intermediates • (6) Time scales of reactions • (7) Control mass and control volume reactor models • (8) Mass Transfer • (9) Species Conservation • (10) Multi-component versus binary diffusion

  2. Stoichiometric Chemical Reaction • Generic fuel: CxHyOz , Molecular weight = (12x+y+16z) g/mol or kg/kmol. eg. CH4 and CH3OH • Molecular weight of CH4= 12.011+4*(1.00794) = 12.011+4.03176=16.04876 kg/kmol • Saves a lot of time and effort to make engineering assumption like: MWCH4 = 16 kg/kmol • CxHyOz + S (O2+ 3.76 N2) = xCO2 + y/2H2O + 3.76SN2 • S = moles of O2 from air needed for complete combustion of CxHyOz. • S=x+y/4-z/2. So for CH4, S=2; for generic paraffin CnH2n+2, S=n+(n+1)/2=1.5n+0.5; and for a generic paraffin alcohol CnH2n+1OH, S=n+(n+1)/2-1/2=1.5n • For Propane: S = 5; Propanol: C3H7OH, S = 4.5

  3. Control Volume Energy Balance for “pure working substance” with Combustion • Conservation of energy statement for control volume with appropriate assumptions, the energy equation can be: • The number of mol of products in the reactor and the number of mol of reactants in the • reactor depend on the conservation of mass equations for each species which also involve • the rates of reaction. • For now, let us assume steady state and

  4. Example Problems (Try to solve ahead of class) • Coal approximated as Carbon (C) burns with pure oxygen (O2) to produce CO2. Write an equation for the reaction and find the mass in kg of the product gases per mol of oxygen consumed in the combustion process. • Repeat 1 for hydrogen and carbon monoxide considered as fuel gases. • Write a chemically balanced equation for combustion of a generic paraffin CnH2n+2 with air. • Find the mass of product gases if one mol of heptane is burned with stoichiometrically correct amount of air. • Find mass fractions and mole fractions in reactants and products. Check that the mass is conserved in the reaction. Are the mol conserved? What is the consequence of this in practical combustor designs? • Find stoichiometrically correct air to fuel mol and mass ratio for heptane combustion. • Find mass and mole fractions of reactant and product species for complete combustion of heptane with 50% excess air. Find the equivalence ratio. • Partial pressures of CH₄, C₂H₆, C₃H₈ and C4H₁₀ in a fuel mixture of these 4 paraffins are 0.5 atm, 0.3 atm, 0.15 atm and 0.05 atm. Find the stoichiometric Air/Fuel ratio, mass and mole fractions of products resulting from complete combustion, mole fractions of CO₂, N₂ in the products if the water vapor is completely condensed out, mole fraction of H₂O, CO₂ and N₂ in the products if exhaust gas temperature is reduced to 50˚C and the water condensation process reaches equilibrium.

  5. Example 1: Equilibrium Composition Consider combustion of methanol with air in stoichiometrically correct amount at standard pressure and temperature and estimate equilibrium composition assuming P=1 atm., T = 2151 K and T= 2194 K and P=2 atm., T=2194 K. Find the concentrations of CO2, H2O, N2, O2, H2, and CO in the product species. Example 2: Equilibrium Composition Consider combustion of methanol with air in stoichiometrically correct amount at standard pressure and temperature and estimate equilibrium composition assuming P=1 atm., T = 2151 K and T= 2194 K and P=2 atm., T=2194 K. Find the concentrations of CO2, H2O, N2, O2, H2, CO, H, O, OH, NO, and N in the product species.

  6. Examples 1 & 2: Solution Consider combustion of methanol with air in stoichiometrically correct amount at standard pressure and temperature and estimate equilibrium composition assuming P=1 atm., T = 2151 K and T= 2194 K and P=2 atm., T=2194 K. Find the concentrations of CO2, H2O, N2, O2, H2, CO, H, O, OH, NO, and N in the product species. (1) (2) (3) 4 atom (CHON) balances provide the solutions to (1): a1=1, b1=2, c1=3.76(1.5), d1=0 (2) has 2 additional unknowns e2, f2. Equilibrium reactions of formation for CO, CO2 & H2O provide 3 additional equations. Two unknowns, three additional equations automatically indicate the presence of at least one additional species. Ex. C atoms (3) has 4 additional species H, O, OH, and NO and these bring 4 equilibrium equations but still not C atoms. C atoms exist in both cases (2) and (3) but in very small amounts!

  7. Example 2: Equilibrium Composition Consider combustion of methanol with air in stoichiometrically correct amount at standard pressure and temperature and estimate equilibrium composition assuming P=1 atm., T = 2151 K and T= 2194 K and P=2 atm., T=2194 K. Find the concentrations of CO2, H2O, N2, O2, H2, CO, H, O, OH, NO, and N in the product species. (T, P given or else energy and mass equations would have to be solved) (1) (2) (3) (4) (5) (6) (7)

  8. Example 2: Equilibrium Composition Consider combustion of methanol with air in stoichiometrically correct amount at standard pressure and temperature and estimate equilibrium composition assuming P=1 atm., T = 2151 K and T= 2194 K and P=2 atm., T=2194 K. Find the concentrations of CO2, H2O, N2, O2, H2, CO, H, O, OH, NO, and N in the product species. (T, P given or else energy and mass equations would have to be solved) (8) (1) (2) (9) (3) (4) (10) (5) (11) (6) (12) (7)

  9. Example 2: Equilibrium Composition Consider combustion of methanol with air in stoichiometrically correct amount at standard pressure and temperature and estimate equilibrium composition assuming P=1 atm., T = 2151 K and T= 2194 K and P=2 atm., T=2194 K. Find the concentrations of CO2, H2O, N2, O2, H2, CO, H, O, OH, NO, and N in the product species. (T, P given or else energy and mass equations would have to be solved) • High temperature leads to decomposition. • High pressure leads to recombination. • O, H are much smaller than OH and NO. • CO, H2 and OH should be considered • first before considering O, H. • NO2, N and C concentrations can be • checked by adding three more equations • but are small.

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

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

  12. Chain Reactions

  13. Time Scale of Ter-molecular Reactions Consider a reaction between species A and B producing products C in the presence of inert M:

  14. Control Mass Reactor Model Summary • Energy (1), Species (N), Mass Conservation (1) and Constitutive (eg. P-v-T relationship) Energy Species Mass Text Book derives the reactor equations on a molar basis for constant volume and constant pressure and on a mass basis for the well stirred and plug flow reactors.

  15. Control Volume Reactor Model Summary • Equations describing the Control Volume include: • Energy (1), Species (N), Mass Conservation (1) and Constitutive • (eg. P-v-T relationship) Energy: (Note heat transfer is defined as energy exchanged by the CV with the surroundings as a result of temperature difference. Work transfer includes shaft work and other mechanical boundary work. (Steady state) Species Mass

  16. Mass Transfer Mass Transfer occurs in many applications in Chemical, Pharmaceutical and Biological engineering. Large applications of Mass Transfer in Mechanical Engineering involve: humidifiers, dryers, carburetors, fuel sprays, fire extinguishing sprinkler sprays, agricultural sprays, etc. A vaporizing drop in a spray or a carburetor which contains a liquid at whose surface the fuel vaporizes and mixes with air flowing in a direction parallel to the liquid surface Consider a Carburetor Gas B Gas B + Vapor A x=L x=0 Liquid A

  17. Species Conservation for Reacting Flows with Spatial Gradients Net Velocity & components Convection/Advection Velocity & components Diffusion Velocity & components Divide by the small volume and take limits as the small volume tends to 0

  18. Example Problem: One Dimensional Advection-Diffusion Consider a one dimensional steady flow of a fuel air mixture from a burner into a quiescent oxidizer that diffuses into the fuel in a one dimensional manner. The fuel mixes with the oxidizer but does not react. Write the species conservation equations for the fuel and oxidizer and seek solutions with appropriate assumptions and with the boundary conditions: YF=YFoand YO=YOo, x=0 and YF=0 and YO2=YO2L, x=L. Steady State No reaction Large velocity, small K Small velocity, large K

  19. Example problem for effective diffusion coefficient calculations • Example Problem Multi-component Diffusion • Lecture 9: ME 525 SP2013 Courtesy: Prof. Lucht •  The table below lists flame properties calculated using the CHEMKIN PREMIX code for a burner-stabilized H2-air flame. The flame temperature (K) and the mole fractions of H2, O2, H2O, and N2 are listed as a function of distance z (in cm) from the burner surface. The mole fractions of all other species in the flame gases total less than 1% and can be neglected in calculating MWmix. The pressure of 1 atm is uniform throughout the flowfield. Assume that the multi-component diffusion coefficient Di,mix for a species i in the mixture is approximately equal to the binary diffusion coefficient for species i and N2, Di,N2. Use the Chapman-Enskog formula and the Lennard-Jones parameters, both given in the equation sheets, to calculate the binary diffusion coefficients. The atomic hydrogen (H) mole fraction profile and the polynomial fit to the data are shown in the plot on the next page. •  (a) Calculate the diffusive velocity, the total species velocity, the diffusive mass flux, and the total species mass flux for atomic hydrogen (H) at the axial flame position z = 0.0094 cm. Assume that the molecular weight of the mixture is approximately constant as a function of axial position at z = 0.0094 cm.

  20. Complexities of multi-component Diffusion

  21. Calculations involved in multi-component Diffusion For atomic hydrogen at Calculation of diffusion coefficient of hydrogen atom See Turns Appendix D, equation D4 and Table D.2 page 709

  22. Orders of Magnitude in Combustion: Molecular Scales meet Combustor Scales

  23. Similar calculations needed for then finally

  24. Methane Reduced Combustion Write down expressions for rates of change with respect to time of all the species in the following methane mechanism: If CO and H2 are found to be in steady state, write the equivalent rates:

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