ME 475/675 Introduction to
CombustionLecture 21
Announcements• HW 8, Numerical Solution to Example 6.1• Due Friday, Oct. 17, 2014 (?)
• College Distinguished Lecture• The future of drone technology• Saturday, October 18, 2014,
• 5 pm posters; • 6 pm Lecture• https://
www.unr.edu/nevada-today/news/2014/college-of-engineering-distinguished-lecture-series
Chapter 6 Coupling Chemical and Thermal Analysis of Reacting systems• Four simple reactor systems, p 184
1. Constant pressure and fixed Mass• Time dependent, well mixed
2. Constant-volume fixed-mass• Time dependent, well mixed
3. Well-stirred reactor• Steady, different inlet and exit conditions
4. Plug-Flow• Steady, dependent on location
• Coupled Energy, species production, and state constraints • For plug flow also need momentum
since speeds and pressure vary with location
Constant pressure and fixed Mass Reactor• Constituents • reactants and products, (book uses )• P and m constant
• Find as a function of time, t• Temperature
• To find use conservation of energy• Molar concentration (book calls this )
• use species generation/consumption rates from chemical kinetics•
• state, mixture• Highly coupled
• Assume we know “production rates” per unit volume
• Rate depends on current molar concentration (per volume) of each constituent, and temperature• From chemical Kinetics
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First Law (EnergyConservation)
• Only boundary work:
• • Where enthalpy , For a mixture
• Production rate ; • ; ;
• Divide by
• ; Solve for
• First order differential equation, Initial conditions (IC): • At each time step, to find the change in
• Need , and
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Change in Molar Concentrations• *• Species production and volume change affect molar concentration
• Find the volume V from ideal gas equation of state
• Take time derivative to see how volume changes with time
• Divide both sides by
• Plug into *
• Initial Conditions: at t = 0, ,
coupled System of 1st order differential equations• Initial Conditions, at t = 0
• , , and
• Assume we also know • Use the first order differentials to find and at time
• • ;
• System Volume
t T [1] [2] … [M] w1 w2 … wM V Q d[1]/dt d[2]/dt … d[M]/dt dT/dt
0 T0 [1]0 [2]0 … [M]0
Dt2Dt
Constant-Volume Fixed-Mass Reactor• Constant V and m • Find versus time • 1st Law
• ;
• ; • ,
• , divide by
• , solve for
Tabulated Data• Need to evaluate (true but not useful)• However, tables only have
• , so use
• , so use
• (true and useful)• Initial Condition: at
• Species Production
Reactor Pressure• Ideal Gas Law•
• Divide by (constant)
• Pressure Rate of change (affects detonation)
Example 6.1 (p. 189) This will be HW• In spark-ignition engines, knock occurs when the unburned fuel-air mixture ahead
of the flame reacts homogeneously, i.e., it auto-ignites. The rate-of-pressure rise is a key parameter in determining knock intensity and propensity for mechanical damage to the piston-crank assembly. Pressure-versus-time traces for normal and knocking combustion in a spark-ignition engine are illustrated in Fig. 6.2. Note the rapid pressure rise in the case of heavy knock. Figure 6.3 shows schleiren (index-of-refraction gradient) photographs of flame propagation for normal and knocking combustion
•
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*107j/kg
• The stoichiometric air-fuel ratio is 16.0 and restrict combustion to stoichiometric or lean conditions.
Global and Quasi-global mechanisms• Empirical•
• stoichiometric mixture with not air
• • Page 157, Table 5.1: , for different fuels
• These values are based on flame speed data fit (Ch 8)• In Table 5.1 units for • However, we often want in units of
Given in Table 5.1, p. 157
Sometimes Want These Units
•