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ME 475/675 Introduction to Combustion

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ME 475/675 Introduction to Combustion

Lecture 21

- 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

- Four simple reactor systems, p 184
- Constant pressure and fixed Mass
- Time dependent, well mixed

- Constant-volume fixed-mass
- Time dependent, well mixed

- Well-stirred reactor
- Steady, different inlet and exit conditions

- Plug-Flow
- Steady, dependent on location

- Constant pressure and fixed Mass
- Coupled Energy, species production, and state constraints
- For plug flow also need momentum since speeds and pressure vary with location

- 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

- Temperature
- Assume we know “production rates” per unit volume
- Rate depends on current molar concentration (per volume) of each constituent, and temperature
- From chemical Kinetics

- Only boundary work:
- Where enthalpy , For a mixture
- Production rate ;
- ; ;

- First order differential equation, Initial conditions (IC):
- At each time step, to find the change in
- Need , and

- *
- Species production andvolume 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, ,

- Initial Conditions, at t = 0
- , , and

- Assume we also know
- Use the first order differentials to find and at time
- ;

- System Volume

- Constant V and m
- Find versus time
- 1st Law
- ;
- ;
- ,

- , divide by

- Need to evaluate (true but not useful)
- However, tables only have
- , so use
- , so use

- However, tables only have
- (true and useful)
- Initial Condition: at

- Species Production

- Ideal Gas Law
- Divide by (constant)
- Pressure Rate of change (affects detonation)

- 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

- 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.

- 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