MAE 5310: COMBUSTION FUNDAMENTALS

1. MAE 5310: COMBUSTION FUNDAMENTALS Coupled Thermodynamic and Chemical Systems: Constant Pressure and Constant Volume Reactors October 22, 2012 Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk

2. MOTIVATION • Calculation of flame temperature given only initial and final states as determined by equilibrium, but no requirements on chemical rates (Chapter 1) • Development of chemical rate equations and chemical time scales (Chapter 2) • Couple chemical kinetics with fundamental conservation principles (mass and momentum) for 4 archetypal thermodynamic systems • Constant-pressure, fixed mass reactor • Constant-volume, fixed-reactor • Well-Stirred reactor • Plug-flow reactor • Coupling allows description of detailed evolution of a reacting system from its initial reactant state to final product state • System may or may not be in chemical equilibrium • Goal: Calculate the system temperature and various species concentrations as functions of time as system proceeds from reactants to products

3. 4 USEFUL REACTOR MODELS 1 2 4 3

4. SUMMARY OF USEFUL RELATIONS ci: mole fraction Yi: mass fraction [Xi]: molar concentration Mole / mass fraction relation Mass fraction / molar concentration Mole fraction / molar concentration Mass concentration MWmix defined in terms of mass fractions MWmix defined in terms of mole fractions MWmix defined in terms of molar concentrations

5. 1. CONSTANT PRESSURE, FIXED MASS REACTOR 1st Law Differentiation of enthalpy Note that enthalpy’s are on per mole basis Calorically perfect gas short hand notation for net production rate for complete mechanism Substitution into 1st Law Volume expression Expression for rate of change of molar concentrations

6. 2. CONSTANT VOLUME, FIXED MASS REACTOR 1st Law Substitution into 1st Law In terms of molar enthalpy’s (instead of internal energy) Expression for time rate of change of pressure Very useful for explosion calculations

7. EXAMPLE: ENGINE KNOCK (LECTURE 1) • In internal combustion engines, compressed gasoline-air mixtures have a tendency to ignite prematurely rather than burning smoothly • This creates engine knock, a characteristic rattling or pinging sound in one or more cylinders • Octane number of gasoline is a measure of its resistance to knock (or its ability to wait for a spark to initiate a flame). • Octane number is determined by comparing the characteristics of a gasoline to isooctane (2,2,4-trimethylpentane) and heptane. • Isooctane is assigned an octane number of 100. It is a highly branched compound that burns smoothly, with little knock. • Heptane is given an octane rating of zero. It is an unbranched compound and knocks badly. Flame Mode Non-Flame Mode

8. EXAMPLE: ENGINE KNOCK • In spark ignition engines, knock occurs when unburned fuel-air mixture ahead of flame reacts homogeneously, i.e., it autoignites • Rate of pressure rise is a key parameter in determining knock intensity and propensity for mechanical damage to piston-crank engine assembly • Pressure vs. time traces for normal and knocking combustion in a spark-ignition engine shown below • Note very rapid pressure rise in case of heavy knock. Piston exposed to long terms effects of knock http://www-cms.llnl.gov/s-t/int_combustion_eng.html

9. EXAMPLE: ENGINE KNOCK • Create a simple constant volume model of autoignition process and determine temperature, pressure and fuel and product concentrations as a function of time • Assume that initial conditions corresponding to compression of a fuel-air mixture from 300 K and 1 atm to TDC for a compression ratio of 10:1. Initial volume before compression is 3.68x10-4 m3 which corresponds to an engine with both bore and a stroke of 75 mm. Use ethane, C2H6, as fuel. • Other assumptions: • One-step global kinetics using rate parameters for ethane • Fuel, air and products all have equal molecular weights, MW=29 • Specific heats for the fuel, air, and products are constant and equal, cp=1,200 J/kg K • Enthalpy of formation of air and products is zero and enthalpy of formation of fuel is 4x107 J/kg • Stoichiometric air-fuel ratio is 16, and combustion is restricted to stoichiometric or lean cases

10. SOLUTION: MATLAB SIMULATION, CONSTANT VOLUME Products Oxidizer Fuel

11. SOLUTION: EXPANDED SCALE ON TOP PLOT Oxidizer Products Fuel Large temperature increase in ~ 0.1 ms

12. EXAMPLE RESULTS AND COMMENTS • Equations are integrated numerically using MATLAB • Coupled ODE’s are stiff • Temperature increases only about 200 K in first 3 ms, then T rises extremely rapidly to adiabatic flame temperature, Tad ~ 3300 K, in less than 0.1 ms • This rapid temperature rise and rapid consumption of fuel is characteristic of a thermal explosion, where the energy released and temperature rise from reaction feeds back to produce ever-increasing reaction rates because of the (-Ea/RT) temperature dependence of the reaction rate. • It can also be shown that huge pressure derivatives are associated with exploding stage of reaction, with peak values of dP/dt ~ 1.9x1013 Pa/s !!! • Although this model predicted explosive combustion of mixture after an initial period of slow combustion, as is observed in real knocking combustion, single-step kinetics mechanism does not model true behavior of autoigniting mixtures • In reality, induction period, or ignition delay, is controlled by formation of intermediate species (radicals) • To accurately model knock, a more detailed mechanism would be required

13. HOMEWORK #3: PART 1 • Explicitly derive all relevant equations and initial conditions shown in class for the constant volume engine knock simulation • Calculate the actual value of the specific heat ratio, g(T), for ethane C2H6 • Use an program to solve the set of coupled differential equations • If possible make your code ‘intelligent’ using a variable time step based on some convergence criteria related to temperature gradient • Generate plots of fuel, oxidizer and product molar concentrations versus time • Generate a plot of temperature versus time • Generate a plot of dP/dt versus time • Repeat for f = 0.7 and comment on results • Repeat with methane fuel, CH4 with f=1.0 and f=0.7 and comment on results • Discuss the following issues in detail: • How would you modify your code to account for variable molecular weights and specific heats, i.e. which governing ODE’s change and how? • How would you update your code to utilize the 4-step quasi-global mechanism on page 156?