INTRODUCTION TO COMBUSTION

(FSC 416/ME 416)

Our objective in this class is to introduce the basic concepts of combustion science and engineering through the use of the tools of stoichiometry, thermodynamics, kinetics and transport phenomena. We shall place special emphasis on the ‘visualization’ of the relevant equations. Therefore, familiarity with rudimentary combustion applications of math software (e.g., Mathematica, Matlab) – as a stepping stone toward the use of comprehensive commercial codes such as ChemKin or Fluent – will be an important goal. In this sense, the class will focus on “problem-based learning” (PBL). We shall discuss each one of the key concepts -- some briefly, some less so -- and will therefore cover most of the topics presented in the following required textbook:

“An Introduction to Combustion: Concepts and Applications,” by Stephen R. Turns, McGraw-Hill (2000).

Additional recommended reading:

1. “Principles of Combustion,” by K.K. Kuo, Wiley, 2005.

2. “The Chemical History of a Candle,” by M. Faraday, Dover, 2002.

3. “Combustion,” by I. Glassman, Academic Press, 1996.

Spring 2006 syllabus

Here is the grade scale that we shall use:

A 94-100

A- 90-93

B+ 85-89

B 80-84

B- 75-79

C+ 70-74

C 60-69

D 50-59

F <50

Classroom change: 011 Life Sciences Bldg. (“technology classroom”!)

Our class will not meet until 1/13. Instead, you should take this time to prepare for the use of math software (e.g., Mathematica) by studying the solutions to the following two combustion-related problems:

ThermoNOx1.nb CombustionKinetics1.nb

Be sure to send me at least one e-mail with any questions about them, or to acknowledge that you have ‘digested’ these problems.

Let’s start with excerpts from Faraday’s 1860-1861 public lectures at the Royal Institution… As we make progress in the class, we shall find confirmation and provide quantitative illustrations for these (for the most part) remarkably insightful descriptions.

“There is not a law under which any part of this universe is governed which does not come into play and is touched upon in these [candle combustion] phenomena.”

“[T]here are clearly two different kinds of action – one the production of the vapor, and the other the combustion of it – both of which take place in particular parts of the candle… In the middle of the flame, where the wick is, there is this combustible vapor; on the outside of the flame is the air which we shall find necessary for the burning of the candle; between the two, intense chemical action takes place, whereby the air and the fuel act upon one another, and at the very same time that we obtain light the vapor inside is destroyed… [and] the heat of that flame… is not in the inside, [but] in a ring, exactly in the place where … the chemical action [is]… The heat is… where the air and the fuel come together.”

“We have now the case of imperfect combustion, and this is to us so interesting that I want you to understand it as thoroughly as you do the case of a candle burning in its best possible manner… Look at the soots that fly off from the flame; see what an imperfect combustion it is, because it can not get enough air… Suppose I take a candle [flame] and examine that part of it which appears brightest to our eyes. Why, I get these black particles! … You would hardly think that all those substances which fly about London, in the form of soots and blacks, are the very beauty and life of the flame…”

“[W]hen a candle burns badly it produces smoke; but if it is burning well, there is no smoke… [and] the brightness of the candle is due to this smoke, which becomes ignited.”

“... although we produce, by [mixing hydrogen and oxygen] far greater heat than you can obtain from the candle, yet there is very little light. If, however, I take a solid substance, and put that into it, we produce an intense light… The heat that is in the flame of a candle decomposes the vapor of the wax, and sets free the carbon particles; they rise up heated and glowing as this now glows, and then enter into the air. But the particles, when burnt, never pass off from a candle in the form of carbon. They go off into the air as a perfectly invisible substance… And if I blow upon a bright gas-flame, so as to consume all this carbon before it gets heated to the glowing point, it will also burn blue.”

“It is wonderful how, by means of oxygen, we get combustion accelerated [compared to air]… So [we can distinguish in air] the two things of which it is composed: oxygen, which burns our candles, our phosphorus, or any thing else, and this other substance – nitrogen – which will not burn them… This nitrogen in its ordinary state is an inactive element, no action short of the most intense electric force, and then in the most infinitely small degree, can cause the nitrogen to combine directly with the other element of the atmosphere…”

“A candle will burn some four, five, six, or seven hours. What, then, must be the daily amount of carbon going up into the air in the way of carbonic acid! What a quantity of carbon must go from each of us in respiration! … A man in twenty-four hours converts as much as seven ounces of carbon into carbonic acid.”

“It is curious to see how different substances wait [to burn] – how some will wait till the temperature is raised a little, and others till it is raised a good deal… In the lungs, as soon as the air enters, it unites with the carbon… Thus you see the analogy between respiration and combustion is rendered still more beautiful and striking. Indeed, all I can say to you at the end of these lectures… is to express a wish that you may, in your generation, be fit to compare to a candle; that you may, like it, shine as lights to those about you; that, in all your actions, you may justify the beauty of the taper by making your deeds honorable and effectual in the discharge of your duty to your fellow-men.”

Stoichiometry and (chemical) equilibrium of combustion reactions

KEY CONCEPTS (See, for example, Ch. 2 in textbook)

-mole fraction

-mass fraction

-ideal gas law (why very often valid?)

-stoichiometric vs. fuel-lean vs. fuel-rich mixture

-A/F ratio

-equivalence ratio

-elementary reaction

-reaction mechanism

-chain reactions

-heat (enthalpy) of formation

-heat capacity

-heat (enthalpy) of reaction (HHV vs. LHV)

-equilibrium constant and free energy of reaction

-adiabatic flame temperature

Let’s do some of the problems in Ch. 2 of the textbook: 2.3 (MW=13.25 kg/kmol; 90.6 mass% O₂), 2.5 (MW=31 kg/kmol; 45.1 mol N₂/m³), 2.7, 2.8 (is it true that as n increases in C_nH_2n+2, the stoichiometric A/F ratio decreases?), 2.12, 2.14 (-3700 kJ/kmol mix), 2.15 (-2953 kJ/kmol mix), 2.16 (-3817 kJ/kmol mix), 2.19 (41.48 mol air/mol fuel), 2.27.

Do your solutions agree with these ones? Be prepared to discuss them in class on Monday, 01/30!

Let’s verify some of the Cp vs. T relationships shown in the very important Fig. 2.2, e.g., for CO₂ and H₂: see webbook.nist.gov. Knowledge of the heat capacity of substances is the key to all the thermodynamic calculations… In fact, examination of the heat capacity of solids at low temperatures played an important role in the ‘discovery’ of quantum mechanics. It is ironic, though, that Einstein, who contributed so much to this discovery, never accepted one of its important consequences: the statistical nature of microscopic phenomena (as symbolized by the often cited Einstein quote that “God does not play dice”)…

ChemKin format for thermodynamic data… in preparation for use of ChemKin to solve most combustion thermo and kinetics problems.

e.g., CH4…

! Species: CH4 CAS Number: 74-82-8

! Name: Methane

! Source: ReactionDesign fit to 1986 JANAF tables, J145

! H0(298K) = -17.8900 (Kcal/mole), S0(298K) = 44.4900 (cal/mole-K)

CH4 J145 C 1H 4 G 200.000 6000.000 1100.00 1

2.26318504e+00 9.09613262e-03 -3.14773529e-06 4.93921024e-10 -2.89309675e-14 2

-1.02756826e+04 6.46314277e+00 4.61528142e+00 -8.69776916e-03 3.37177999e-05 3

-2.94858722e-08 8.52035038e-12 -1.02340740e+04 -2.56731474e+00 4

Here is a graph of Cp and enthalpy values from these data… And here we reproduce some of the numbers for heat capacity and enthalpy of NO (see p. 638 in the textbook).

Exercise 1.

(a) In the previous exercise -- see also handout “Enthalpy (heat content)” -- we showed that the enthalpy of NO at 1000 K is 112.5 kJ/mol.

(b) Another (and more convenient!) way to calculate standardized enthalpies is as follows:

So, from Table A.9, we have H(1000 K) = 90.297 + 22.241 = 112.5 kJ/mol. (In rigor, these are h values, i.e., specific enthalpies, per mole, although this is usually clear from the context of the discussion.)

Exercise 2. Calculate the enthalpy of (formation of) CH₄ from the experimental value of the enthalpy of its combustion, which is -890 kJ/mol (Verify… HHV vs. LHV). See also problem 2.23 in HW1.

From

DH^o_comb = H^o(CO₂,g) + 2H^o(H₂O,l) – H^o(CH₄,g),

we have

H^o(CH₄,g) = -393.546 + (2)(-241.845-44.01) – (-890) = -75.3 kJ/mol

If you use HHV of 55,528 kJ/kg, will you get -74.831 kJ/mol, as in Table B.1? Is the discrepancy significant?

Note that experimental values are often NOT more ‘accurate’ than +/- 1 kJ/mol… And thermodynamics is still, to a large extent, an experimental science, although much can be calculated these days using quantum mechanics (“statistical thermodynamics”).

Methane combustion (in O₂): standardized enthalpy vs. T, enthalpy of reaction, heat of combustion, and first approximation to the calculation of adiabatic flame temperature.

Homework 1:

-(40%): Do textbook problems 2.2 (106 ppm NO, etc.; 28.55 kg/kmol; 19.63% CO₂, etc.), 2.4 (11% CH₄, 8.0 mol/m³), 2.6 (3.62e7 J/kmol), 2.10 (28.6, 26.0, and 25.0 kg air/kg fuel), 2.13 (6.44 for methanol vs. 17.2 for methane!?), 2.17 (1 mol fuel/33 mol air; 41.67 mol air/mol fuel), 2.21 (0.80, 9.64% CO₂), 2.23 (-76980 kJ/kmol… Close enough?).

-(20%): Download Chemeq.bas and add appropriate information for O, OH, HO₂ and H radicals to the react.dta file.

-(20%): Use Chemeq.bas and/or ChemKin, as well as Webbook.nist.gov information to compare the C_p vs. T relationships for SO₂ in the T range 300-2300 K.

-(20%): Make a graph of the temperature dependence of ‘absolute’ (standardized) enthalpies of O₂, O, H₂ and H, analogous to that shown in Figure 2.6. Does this graph explain the fact that the mechanism of H₂ combustion (see initiation reactions on p. 149) does include H₂ dissociation but not O₂ dissociation?

Note: If in doubt about what to submit, use the following ‘rule’: submit everything that your instructor needs in order to be able to (easily) figure out WHAT you did and HOW you did it!

Let’s use this spreadsheet, in conjunction with Prof. Turns’s TPEQUIL code, to analyze the effect of temperature and equivalence ratio on the composition of the products of combustion of methane in air.

Here is a thermo database…

Now that we know how, and have the convenient tools, to quickly calculate the adiabatic flame temperature, we need to do the more important part: analyze the PARAMETRIC SENSITIVITY of such calculations! How does T_f,ad depend on the following key parameters:

-nature of fuel

-nature of oxidant

-equivalence ratio

-others?

Follow-up on the “PBL-T_f,ad” class handout…

Homework 2:

Below are some notes about solutions… (In some cases, the end result will depend on the assumptions made along the way, so be sure to state those assumptions explicitly and clearly.)

Be sure to provide comments where necessary, and to clearly indicate the answers to the questions posed as well as the units of the important parameters or variables.

2.29: Use iso-octane and note the following: (a) If you cannot figure out how to use the Majer and Svoboda correlation (see NIST web site) for DH_vap vs. T (and I haven’t done it yet either), you may want to use the following correlation (valid all the way to the critical point, at which the enthalpy of vaporization is of course zero): DH_vap(T) = DH_vap(T_b)*((1-T/T_c)/(1-T_b/T_c))^0.375, where T_b and T_c are the boiling and critical point. (b) The C_p vs. T correlation in Table B2 does differ from the values provided on the NIST web site, especially at the higher temperatures. So we need to explore the impact of this (minor?) discrepancy on our h vs. T graph; (c) In the schematic graph on p. 31, why are the G and L curves parallel to each other? What assumption is made here? It is of course convenient (why?), but is it also appropriate? (d) Does one of your graphs look like the one shown here?

A reminding note about the enthalpy of phase change (Hess’s ‘law’): It is often convenient to postulate a hypothetical path for a reaction, for which the enthalpy of the intermediate steps is well known. (The beauty of thermodynamics is that the result is independent of the path taken; it depends only on the initial and final state… Right? And thus we can avoid doing the unnecessary experiments.) For example, you can verify that the reaction (combustion) enthalpy for H₂(g) + 0.5O₂(g) = H₂O(g) at 298 K can be conveniently determined from knowledge of the heat capacities of liquid and gaseous H₂O and the (more readily available) reaction enthalpy for H₂(g) + 0.5O₂(g) = H₂O(l), which is -285.8 kJ/mol. The hypothetical path is as follows: (i) reaction of the gases to form liquid H₂O at 298 K, with DH₁; (ii) heating of H₂O(l) from 298 to 373 K, with DH₂ ; (iii) vaporization of H₂O(l) at 373 K, with DH₃; and (iv) cooling of H₂O(g) from 373 to 298 K, with DH₄. If these heat capacities are 75.3 and 33.6 J/mol/K and the enthalpy of H₂O vaporization is 40.9 kJ/mol, show that the all-gas-phase enthalpy of combustion is DH_c = DH₁ + DH₂ + DH₃ + DH₄ = -241.8 kJ/mol.

2.34: 2013 K

2.38: 2551 K

2.44: K = 0.327 atm^0.5

2.49: at 0.5 atm, x_H2O = 0.99

2.53: Do your T_f,ad results agree with the bar-graph shown here?

2.56: Using just stoichiometry, phi=1.048, xO2=0.0… Why would the process be “overall (fuel-)lean” if CO is produced (at equilibrium)? Doesn’t it make more sense that it be oxygen-lean? In reality, CO may indeed be produced under fuel-lean conditions, but that’s a (relatively complex) kinetics issue, and it cannot be resolved using just stoichiometry. You can attempt to resolve it, by trial and error, using thermochemistry (e.g., TPEQUIL or Eqns. 2.76). Using HPEQUIL, the best I can do is CO2/CO=8.3 for phi=0.999 using liquid i-octane feed at 298 K. In contrast, using eqns 2.76, do you get xCO2/xCO=6.0 for phi=1.06?

Greg Lilik is proposing an interesting stoichiometry-based solution. See here one version of it… Comments?

2.58: F: Verify that the equilibrium mole fractions, according to eqns 2.76, and assuming K=0.193 for the water-gas-shift equilibrium, are as follows: xCO2=0.072, xCO=0.064, xH2O=0.155, xH2=0.027, xN2=0.682.

2.59. B: ca. 2400, 2620 and 2770 K.

2.60:

2.61. A: ca. 1920, 2260 and 2150 for phi = 0.75, 1.0 and 1.25, respectively.

2.62:

Exam1

#1

#2

#3a-b: The equilibrium constant (most conveniently and quickly obtained using Chemeq) is typically very high even at combustion temperatures, and therefore the analysis of pressure effects on equilibrium is mathematically difficult… see, for example, this Mathematica file. (You can also calculate K from deltaH and deltaS for the combustion reaction, but that’s a waste of time… Right?) The equilibrium conversion is likely to be close to 100%, and therefore a simple stoichiometric analysis is a good first approximation, as shown in this Excel file. Use of TPEQUIL is therefore most convenient to analyze the effects of pressure and equivalence ratio.

#4: The quick and appropriate calculation is that of T_f,ad using HPFLAME… It should be LOWER than that calculated in #2a. Right? (Why?) You can also use TPEQUIL to calculate the enthalpy of the products (as a function of T!) based on the more accurate product composition, including dissociated products, and then determine T_f,ad in the same way as in #2a. After long and tedious calculations, you should arrive at the same result.

KINETICS OF COMBUSTION

From stoichiometry we can readily calculate the feed rate of a fuel into a combustion device, e.g., in kg fuel/second. Obviously, when we multiply this feed rate by the residence time in the combustor we get the size of the combustor… So here we need to learn how to calculate or estimate the reaction time. (For the desired degree of fuel conversion, often close to 100%, the residence time should be at least as long as this reaction time.) And the reaction time is obtained by integrating the differential equation that describes the reaction rate.

Here is the simplest such equation.

KEY CONCEPTS (see, for example, Chs. 4 and 5 in Turns)

-rate constant (Arrhenius equation)

-activation energy

-preexponential term (frequency factor)

-modified Arrhenius equation

-global reaction

-reaction order

-elementary reaction

-reaction molecularity

-unimolecular reactions: pressure dependence (Lindemann mechanism)

-steady-state approximation

-rate determining step (RDS)

-thermal decomposition vs. oxidation reactions

-collision frequency

-transition state (activated complex)

-homogeneous vs. heterogeneous reactions

Mathematica solutions to examples in Ch. 4: 4.1 4.2 4.4 4.5

Practice textbook problems: 4.6, 4.7, 4.10, 4.14, 4.16 (d: 37 ms; e: 3.2x10¹⁰ m³/kmol/s; g: 9.5 ppb), 4.18 (43 ms vs. 1.3 s) , 4.19, 5.8 (ca. 10^-4 mol C/cm³/s for CH₄ vs. ca. 10⁰ for C₃H₈ vs. 10^-2 for C₈H₁₈), 5.12, 5.13 (part A: 30% approach to equilibrium; part B: 89%; part C: additional 6.7 ppm; part D: additional 338 ppm. Check the MW values and comment!), 5.15.

How does one control in Mathematica the number of significant figures in the results, so that these are REALLY significant?

Homework 3

-Do textbook problems 4.14, 4.16, 4.18, 4.19, 5.8, 5.15.

-Go to the GRI-Mech web site and use the information provided there to construct the Arrhenius plot of reactions of O, H and OH radicals with CH₄ and C₂H₆. Summarize the trends observed.

-Analyze the KinVsTransport_FSC416.nb file on the class web site, calculate the chemical and mass transport rate coefficients at 900 and 1300 K, and explain why we can clearly identify the rate-determining step under each one of these conditions.

TRANSPORT PHENOMENA IN COMBUSTION

Here is an important practical application of the RDS concept.

‘In-lieu’ class activity for 03/13: Work through Example 3.2 in the textbook, perform the same calculations for n-octane and benzene, and comment on the similarities/differences/trends observed.

Homework 4

-Following up on Example 3.2, compare the droplet evaporation times for n-dodecane, n-octane and benzene in air. Soln1 Soln2

-Do textbook problems 8.3, 8.4, and 8.12.

-Use the Mallard-LeChatelier equation to calculate the laminar flame speeds for ethane, ethylene and acetylene, and compare them (in both relative and absolute terms) with those shown in Figure 8.17 or Table 8.2.

-Use ChemKin to confirm (a) the fuel dependence of the laminar flame speed (see Table 8.2 in Turns); and (b) the pressure dependence of the laminar flame speed for methane (see Figure 8.14 in Turns).

Extra credit 1: Use ChemKin to reproduce Figure 8.10c in Turns, using both the complete set of kinetic equations (GRI-Mech) and the one that excludes the NOx reactions (ChemKin tutorial, Section 2.2.4). Briefly discuss the discrepancies observed.

Extra credit 2: Compare eqns. 11 and 53 in Table 5.3 (Turns) with the corresponding equations in the simplified methane combustion mechanism used in ChemKin’s Tutorial #2.2.4 (samples\flame_speed\freely_propagating\chem.inp). Do the Arrhenius plots differ significantly? Comment also on their (dis)agreement with the kinetic equations posted on the GRI-Mech web site?

Fuel-oxidizer Mixing/ Fluid motion: e.g., in G/L systems have evaporation, in G/S systems the oxidant must reach the surface, and in G/G systems need mixing for ignition)

-premixed/laminar: e.g., flat flame, Bunsen flame (inner cone)

-example of evaporation rate analysis (Comfortable with BOTH mass and molar units?)

-Mallard-LeChatelier equation for flame speed (pp. 261-269, Turns) Propane laminar flame speed (Example 8.2, Turns)

-effects of T, P, equivalence ratio and fuel type (pp. 274-283)

-flammability limits (pp. 283-290, 294-298)

-ignition (pp. 291-294): see also class handouts

-nonpremixed/laminar: e.g., wood fire, candle

-laminar diffusion flames: Notes 1 Notes2

-analysis of ChemKin results for H2 flame

-example of ChemKin results for CH4 premixed flame

-example of ChemKin results for CH4 diffusion flame

-let’s together develop a spreadsheet that allows us to quickly calculate the diffusion coefficient for a fuel in air using the Chapman-Enskog equation. For this purpose, we’ll compare the various proposed ‘algorithms’ and adopt and merge the best and/or most convenient ones into a “master program”.

-Here is some additional information on the diffusion coefficient of gases.

ChemKin uses only forward reaction rate coefficients: how does it ‘know’ the reverse ones? Here is an example…

Exam 2: Here is one version of the solutions. Compare it with yours and let’s discuss it, if necessary.

#1: Be sure to clearly indicate the units of the rate parameters on the y-axis!! For the most meaningful comparison, should compare rates of the global reactions (assuming constant concentrations), not rate constants, because of their different reaction orders. Note that ethane (as well as C2+ alkanes) reacts much more readily than methane with both O₂ and the radicals O, H and OH. Note also that for both methane and ethane the isokinetic temperatures for reactions with these radicals is within the range of typical flame temperatures.

#2: Is it appropriate to assume that the kinetic parameters for iso-alkanes are the same as for n-alkanes?

#3a #3b

#4

-premixed/turbulent (e.g., spark-ignited gasoline engine)

-for overview of turbulent flow, read Chapter 11 in Turns.

-let’s together develop a spreadsheet that allows us to quickly calculate turbulence intensity from experimental results on velocity fluctuations with time. For this purpose, we’ll compare the various proposed ‘algorithms’ and adopt and merge the best and/or most convenient ones into a “master program”.

-here is a summary of key issues and concepts for turbulent flames.

-nonpremixed/turbulent: PCC, Diesel engine

Homework 5 (due 04/10, accepted until 04/12)

-Textbook problems:

-8.17: Part a Part b Part c

-8.18 Ref. 34

Note: For phi=2.0 and phi=3.0, you may need to increase the number of grid points from 6 (in the default “flame_speed_freely_propagating” project) to 12. Because the maximum shown in Fig.8 of Ref. 34 is at ca. phi=1.6, be sure to include this point on your graph.

-9.8 (e.g., 5.45 vs. 8.96 cm, for simple Burke-Schumann vs. Roper equation).

-Use ChemKin to analyze the structure of a counterflow H₂-air laminar diffusion flame and compare it (or contrast it!) with the structure of (a) the premixed H₂-air flame obtained in problems 8.17 and 8.18, and (b) the diffusion CH₄-air flame (see the relevant graphs in Ch. 9). Be sure to describe in some detail the main differences, as well as any similarities.

-Prepare a graph of diffusivity vs. temperature (in the range 300-2500 K) for the following species of interest in combustion: CH₄, H₂, i-octane, cetane, O₂, N₂, H₂O, CO₂, CO, NO. Use the Chapman-Enskog equation and make comparisons based on Lennard-Jones parameters available in the ChemKin transport database and in at least one other independent source.

Summary of key issues in combustion of solids (RDS, burning time)

When turbulence intensity is maximized, have a perfectly mixed (or well stirred) combustion chamber (see Ch. 6 in Turns):

-Example of a PSR ChemKin result

-Comparison with a PFR: Note the effect of mixing on CO production!

-PFR tutorial: how to reduce NOx emissions

-Analysis of a PaSR: “to assess the extent of turbulence-kinetics interaction in a gas-turbine combustor or to provide information on how turbulence intensity will affect the combustor” (p. 52, ChemKin 4.0.2 tutorial):

-effect of mixing time scale on temperature pdf

-effect of mixing time scale on temperature vs. time behavior

-does the flame-‘initializing’ reactor composition (see p. 52 of PaSR tutorial) correspond to equilibrium or steady-state PSR composition?

-first attempt to reproduce the ReactionDesign example

-more comparisons of PSR and PaSR behavior (effect of ‘unmixedness’)

Calculation of Damköhler number: Problem 12-7 (see also Examples 12.1 and 12.2, as well as Problem 12.4)

Analysis of chemical times for NOx formation (Zeldovich mechanism).

Kinetics of NOx formation Notes 1 Notes2

Review of chemical equilibrium of NOx formation

Classwork exercise (04/17):

In preparation for HW6-2, let’s try to reproduce Figures 6.7 and 6.8 in the textbook using ChemKin’s PSR module and GRI-Mech chemistry and thermodynamics.

-Let’s construct first the ethane conversion vs. initial reactor temperature graph, for flowrates of 0.04 and 0.1 kg/s. (Specification of the ‘initial’ reactor temperature for the adiabatic PSR in ChemKin is essentially a ‘simulation’ of the ignition process.)

- At 100 g/s, verify that the initial reactor temperature has to be brought to ca. 1290 K in order for the final temperature to stabilize at 1385 K, thus achieving 94.8% ethane conversion in 0.7 ms. (Surprising? Compare with PFR! Do you find that, under otherwise identical conditions, 99.99% of ethane is consumed in less than 0.4 ms? Makes sense?) If the initial temperature is raised to ca. 1450 K, the final temperature stabilizes at 1955 K and essentially complete ethane combustion is achieved. (Does this result agree with Figure 6.7? Repeat the ChemKin analysis at several other mass flow rates and compare the result with Figure 6.7.)

At 250 g/s, if the initial temperature is 1430 K, the ethane flame stabilizes at 1533 K, achieving ??% ethane conversion in ?? ms. Extinction (blowout) is produced only if the initial temperature is reduced to ???.

At 500 g/s, verify that blowout is produced even if the initial temperature is raised to 1500 K.

Note: The position of the blowout curve on the equivalence ration vs. mass flowrate graph (e.g., Figure 6.8) is dependent on how energy for ignition is supplied to the combustible mixture as it enters the combustion chamber (e.g., recirculation of hot products, spark, preheating).

Homework 6 (due 04/28, accepted until 05/01, 9 am):

(1) Compare the extents of formation of CO in a premixed laminar vs. diffusion CH₄ flame. Compare them at the same equivalence ratio, and also analyze the effect of equivalence ratio in each case. Under which conditions is the production of CO minimized?

-For the premixed flame, do you get a monotonic increase in CO formation with increasing F? (Makes sense?)

-Is this helpful?

-And for the diffusion flame? (Surprised?)

-How can we compare the amounts of CO formed in the premixed vs. nonpremixed (diffusion) flame (under otherwise ‘identical’ conditions)?

(2) Make an attempt to reproduce the results in Example 6.3. Document in detail your success or failure!

(3) Reproduce the trend shown in Table 15.2 for the dependence of NOx emissions on the equivalence ratio in a well-stirred reactor. Are NOx emissions different in a PFR under comparable conditions? Illustrate your answers with graphs.

-Should the combustors be isothermal? Or adiabatic?

-Can you complete this graph? (Do your results agree with the trends shown?)

-Are NO levels more sensitive to temperature or equivalence ration variations? Can you study these two effects independently?

(4) Solve problem 14.13 in Turns. (You should get 0.1-1.0 s for the burning time (depending on your assumptions)… How would you determine t_chem?)

(5) As stated in the ChemKin manual (v. 4.0.2, p. 148), the “PaSR is related to and bounded by other models commonly used in combustion. When the mixing time scale approaches zero… the PaSR becomes a PSR… In the other extreme limit (large mixing time)… the PaSR acts like a plug-flow reactor.” Let’s use then the mixing time scale as a parameter to span this entire spectrum of interaction between chemical reaction and momentum and mass transfer. Select first the truncated CH₄ combustion mechanism from the “pasr_ch4_air” tutorial and analyze the effect of mixing time variation on a key performance indicator of the PaSR combustor. Make the relevant graph and compare it with the results obtained using PSR and PFR models under the same conditions. Then select the GRI-Mech mechanism and construct the analogous graph. Discuss the differences and similarities among the PaSR, PSR and PFR results, as well as between the two combustion mechanisms. (Note: Be prepared to discuss in class the selection of the range of values for the mixing time scale, as well the selection of a “key performance indicator”.)

Exam 3

The grade average this semester was 81% (B) … Good luck, and have a wonderful and productive summer!

LRR3@psu.edu (updated 05/07/2006, 9 pm)