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ME 475/675 Introduction to Combustion

ME 475/675 Introduction to Combustion. Lecture 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

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ME 475/675 Introduction to Combustion

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  1. ME 475/675 Introduction to Combustion Lecture 21

  2. 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

  3. Chapter 6 Coupling Chemical and Thermal Analysis of Reacting systems • 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 • Coupled Energy, species production, and state constraints • For plug flow also need momentum since speeds and pressure vary with location

  4. 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

  5. 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

  6. Change in Molar Concentrations • * • 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, ,

  7. 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

  8. Constant-Volume Fixed-Mass Reactor • Constant V and m • Find versus time • 1st Law • ; • ; • , • , divide by • , solve for

  9. 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

  10. Reactor Pressure • Ideal Gas Law • Divide by (constant) • Pressure Rate of change (affects detonation)

  11. 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

  12. 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.

  13. 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

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