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ME 475/675 Introduction to Combustion Lecture 4 Announcements • Extra Credit example due now • HW 1 Due Friday • Tutorials • Wednesday 1 pm PE 113 • Thursday 2 pm PE 113 • Please bring you textbook to class • Please turn in HW on white or engineering paper • Grading based on solution (not solely on answers) Example: • Last lecture (turned in today) • Problem 2.14, p 71: Consider a stoichiometric mixture of isooctane and air. Calculate the enthalpy of the mixture at the standard-state temperature (298.15 K) on a per-kmol-of-fuel basis (kJ/kmolfuel), on a per-kmol-of-mixture basis (kJ/kmolmix), and on a per-mass-of-mixture basis (kJ/kgmix). • Find enthalpy at 298.15 K of different bases • This time (turn in next lecture) • Problem 2.15: Repeat for T = 500 K Standard Enthalpy of Isooctane T [K] 298.15 theta 0.29815 h [kJ/Kmol] -224108.82 a1 a2 -0.55313 181.62 -0.16492 8.072412 a3 a4 a5 -97.787 20.402 -0.03095 -0.8639 0.040304 0.103807 a6 -60.751 -60.751 • Coefficients π1 to π8 from Page 702 π [πΎ] ; 1000 πΎ ππ½ π β = πππππ • π= • 4184(π1 π π2 + π2 2 π3 + π3 3 • Spreadsheet really helps this calculation + π4 π4 4 − π5 π + π6 ) a8 20.232 Enthalpy of Combustion (or reaction) Products Complete Combustion Cο CO2 Hο H2O 298.15 K, 1 atm Reactants 298.15 K, P = 1 atm Stoichiometric ππΌπ < 0 ππππ = 0 • How much energy is released from a reaction if the product and reactant temperatures and pressures are the same? • 1st Law, Steady Flow Reactor • ππΌπ − ππππ = π»π − π»π = π βπ − βπ • ππΌπ = βπ»π = π»π − π»π = π βπ − βπ = πββπ • βπ»π and ββπ Enthalpy of Reaction (< 0 for combustion) • Dependent on T and P of reaction • Heat of Combustion ββπΆ = −ββπ = βπ − βπ > 0 Stoichiometric Methane Combustion, CH4 • CH4 + __ (O2 + 3.76 N2) ο __ CO2 + __ H2O + ___ N2 • @ 25C and 1 kmol CH4 • βπ»π = π»π − π»π = Water Vapor 1 βππ + ββπ + 2 βππ + ββπ + 7.52 βππ + ββπ πΆπ2 − 1 π βπ + ββπ πΆπ»4 π»2 π + 2 π βπ + ββπ π π π = βπ,πΆπ + 2 β − 1 β = π,π» π π,πΆπ» 2 2 4 = ππ½ −393,546 ππππ p 688 = −802,405 +2 ππ½ πππππΉπ’ππ π2 + 7.52 π ππ βπ,π ππ½ −241,845 ππππ ππππ −1 π βπ − π2 + ββπ π2 π ππ βπ,π π ππππ‘ ππ½ −74,831 ππππ p 692 p 701 (Heat in to system for TR = TP) Other Bases • Per kg fuel • πππΆπ»4 = 16.043 • ββπ = − ππ ππππ ππ½ πππππΉπ’ππ ππ 16.043 ππππ 802,405 • Heat of Combustion • ββπ = −ββπ = 50,016 = −50,016 ππ½ πππΉπ’ππ ππ½ πππΉπ’ππ (Heat out for TR = TP) ππ½ • See page 701, LHV = Lower Heating Value = 50,016 πππΉπ’ππ • Corresponds to water vapor in the products π π π • βπ»π ,πΏππ€ππ = βπ,πΆπ + 2 β − 1 β π,π»2 π,π£ππππ π,πΆπ»4 2 • π βπ,π» 2 π,πΏπππ’ππ = π βπ,π» 2 π,π£ππππ − βπ»2π,ππ = ππ½ −241,845 ππππ p 692 π π π • βπ»π ,π»ππβππ = βπ,πΆπ + 2 β − 1 β π,π» π,πΏπππ’ππ π,πΆπ» 2 2 4 • = −393,546 + 2 −241,845 − 1 −74,831 = −890,425 ππ½ • ββπΆ = − −890,425ππππ ππ πΉπ’ππ 16.043ππππ = 55,502 ππ½ πππΉπ’ππ ππ½ πππΉπ’ππ • p. 701: Higher Heating Value = HHV = 55,528 − ππ½ 44,010 ππππ p 692 ππ½ πππΉπ’ππ (slightly larger due to dissociation?) = ππ½ −285,855 ππππ Per kg of reactant mixture • ππΉπ’ππ ππππ₯ • π΄ πΉ = = ππΉπ’ππ ππΉπ’ππ +ππ΄ππ ππ΄ππ πππ΄ππ ππΉπ’ππ πππΉπ’ππ = • LHV = ββπ,πΏππ€ππ = = 1 ππ΄ππ 1+π πΉπ’ππ = 1 π΄ 1+πΉ = 1 1+17.12 = 1 πππΉπ’ππ 18.12 πππππ₯ 2∗ 3.76+1 ∗28.85 πππ΄ππ = 17.12 1∗16.043 πππΉπ’ππ ππ½ 1 πππΉπ’ππ ππ½ 50,016 ∗ = 2760 πππΉπ’ππ 18.12 πππππ₯ πππππ₯ Adiabatic (π = 0) Flame Temperature Complete Combustion Products Cο CO2 Hο H2O PP = PR, T = TAd Stoichiometric Reactants TR PR ππΌπ = 0 ππππ = 0 • 1st Law, Steady Flow Reactor • ππΌπ − ππππ = 0 = π»π − π»π = π βπ − βπ • All chemical energy goes into heating the products • To find adiabatic flame temperature use • PP = PR and βπ = βπ Adiabatic Methane Combustion TR = 25°C • CH4 + 2 (O2 + 3.76 N2) ο 1 CO2 + 2 H2O + 7.52 N2 • π»π ππππ‘ = 1 βππ + ββπ πΆπ»4 • = π»ππππ = 1 βππ + ββπ + 2 βππ + ββπ πΆπ2 π = βπ,πΆπ» 4 π2 + 2 βππ + ββπ + 7.52 βππ + ββπ π»2 π π2 π ππππ‘ + 7.52 βππ + ββπ π π π • βπ,πΆπ» − 1 β − 2 β π,πΆπ2 π,π»2 π = 1ββπ ,πΆπ2 + 2ββπ ,π»2 π + 7.52ββπ ,π2 4 • ββπ ,π,ππ΄π = π π ππ ππ π,π π ππ ≈ ππ,π ππ΄π − ππ ππ π2 ππππ ππ΄π Example (Turn in next time for Extra Credit) • Find TAd for a 25°C Stoichiometric mixture of Acetylene and air
