ME 475/675 Introduction to

CombustionLecture 23

Example 6.1 Excel programing, Effect of equivalence ratio

Announcements• HW 8, Numerical Solution to Example 6.1• Due Monday, Oct. 19, 2015

• Course Project• Construct a homemade camp stove fueled with absolute alcohol• See, for example:

• http://www.backpacking.net/makegear/stove/• https

://www.google.com/search?q=homemade+backpacking+stove&biw=1461&bih=708&tbm=isch&tbo=u&source=univ&sa=X&sqi=2&ved=0CBwQsARqFQoTCN_ctrCmx8gCFck0iAodLokG7g

• To bring 0.5 liters of room-temperature water to a boil, determine • How much time is required • How much fuel is consumed• Is soot deposited on the water container?

• Work in groups of two with our teaching assistant• Hasibul Alam hasibul.alam.bd@gmail.com

• Due date and group assignments soon

Example 6.1• Create a simple constant-volume model of the autoignition process and determine the

temperature and the fuel and product concentration histories. Also determine the dP/dt as a function of time. Assume initial conditions corresponding to compression of a fuel-air mixture from 300 K and 1 atm to top-dead-center for a compression ratio of 10:1. The initial volume before compression is 3.68*10-4 m3, which corresponds to an engine with both a bore and a stroke of 75 mm. Use ethane as fuel. Assume:• One-step global kinetics using the rate parameters for ethane C2H6 (Table 5.1)• Fuel, air, and products all have equal molecular weights: MWF= MWOx= MWP= 29• The specific heats of the fuel, air and products are constants and equal:

• cp,F = cp,Ox = cp,Pr = 1200 J/kgK

• The enthalpy of formation of the air and products are zero, and that of the fuel is • 4*107 J/kg

• The stoichiometric air-fuel ratio is 16.0 and restrict combustion to stoichiometric or lean conditions, .

• Constant Pressure, or constant Volume?

Last Lecture found Numerical values• Species Production

• Assuming (only true initially since is not consumed)

• 1st Law

• Pressure Rate of change (affects detonation)• ;

• Initial Conditions at t = 0•

Numerical Solution (Excel)

• Starting point• http://wolfweb.unr.edu/homepage/greiner/teaching/MECH.475.675.Combustion/Ex6.1.start.xlsx• Make sure [Fu] and [Ox] are ≥ 0 (use MAX(0,value) function in Excel)

• Results, , • Low temperature, slow start • Temperature and pressure spike and rapid reaction at t = 0.00307 sec = 3.07 ms• Extinction when both fuel and oxidizer are consumed

• Realistic results, but not realistic reaction model, which should be multi-stepped

dt [sec] phi t [sec] [Fuel] [Oxidizer] [Products] T P [kPa] d[F]/dt d[Ox]/dt d[Pr]/dt dT/dt [K/s] dP/dT1.00E-07 1 0 0.023888 0.382206 0 753.5659 2544.541 -0.13195 -2.11122 2.243168 14231.31 48054.4

1.00E-07 2.39E-02 3.82E-01 2.24E-07 7.54E+02 2.54E+03 -0.13196 -2.11129 2.243251 14231.84 48056.172.00E-07 2.39E-02 3.82E-01 4.49E-07 7.54E+02 2.54E+03 -0.13196 -2.11137 2.243333 14232.36 48057.94

Dependence on

• As before the reaction is “delayed” • Initial [Fuel] is decreases• Due to excess air, the mixture takes longer to heat up, and reaches lower temperatures and pressures• Lower temperatures delay reaction to 3.12 and 3.53 ms (3.07 ms for )

Φ=0.1

Φ=0.5

•