AE 558 Central Heating Systems
Homework #2
Combustion Fundamentals
1. The following equation can be utilized to describe the combustion process
of methane. If α = 1.0 in equation below the combustion stoichiometric.
The equivalence ratio, [=(fuel/air) actual / (fuel/air) stoichiometric)], for this
stoichiometric condition would equal 1. For fuel rich combustion (α< 1
and > 1) and for fuel lean combustion (α> 1.0,< 1 ). Methane is our
surrogate for natural gas:
CH4 + 2α(O2 + 3.76 N2) = CO2 + 2H2O + 2(α - 1)O2 + (2α)3.76N2
The flammability limit of methane is approximately 5% by volume (or mole
composition) at standard T & P air conditions. Natural gas, because of the
other hydrocarbons present in its composition, which makes its ignition
easier, has a lower flammability limit, ~ 4.5% by volume. Give the α values
shown in the table below, fill in the values for the columns labeled (fuel/air) by
mass, Ф and %CH4 by volume (Because PV = nRT, at standard conditions %
volume = % mole) in the table below.
Now use the first worksheet (CH4, C3H8 T-flame) to estimate the adiabatic
flame temperatures for each of the conditions noted in the table. In the
Adiabatic Flame Temperature Calculations Sections you guess the T f (F)
adiabatic flame temperature until the calculated total enthalpy value (h value
of the combustion gas products) ~ equals the lower heating value of methane
(3.439x105 BTU/lbm-mole). Case 1, the stoichiometric case,  = 1 in the
equation above, is done already and the gas products temperature dependent
heat capacity flame temperature comes out to be 3508 o F. In the lower
section, when using the when using the mean, average heat capacities for the
product gases the flame temperature comes out to be 3614 F.
The flame temperature calculation part of the worksheet also has 17cases of
methane combustion for both the temperature dependent heat capacity
calculation method as well as the mean heat capacity calculation method.
Two cases of propane combustion are given, but we are ignoring this fuel for
now.
One simply enters a guessed flame temperature in column H in the
appropriate case row and continues “guessing” until the h enthalpy total in
the adjacent I column matches the LHV of the methane in column F. You can
get the flame temperatures for the conditions noted in the above table by
simply using the appropriate combustion condition row in the top section as
matched with the flame temperature rows in the two bottom sections of the
spreadsheet. Determine the adiabatic flame temperatures for each  and
place in the appropriate space in the Table for both temperature dependent
product gas heat capacities and mean heat capacities for product gases.
T Dependent Cp's
Case
1
2
2a
3
4
5
6
7
8
9
10*
11***
12
13*
14**
15**
16
17

1.00
1.10
1.10
1.15
1.20
1.25
1.30
1.35
1.50
1.60
2.00
1.00
1.50
2.00
2.25
2.50
1.50
1.75
(fuel/air)
by mass
0.05827
0.05297
0.05107
0.05066
0.04855
0.04661
0.04482
0.04316
0.03884
0.03641
0.029
0.250
0.039
0.029
0.026
0.023
0.039
0.033

1
0.909
0.909
0.870
0.833
0.800
0.769
0.741
0.667
0.625
0.500
1.000
0.667
0.500
0.445
0.400
0.667
0.572
CH4 by
volume
5.51
5.03
5.03
4.82
4.63
4.82
4.29
4.14
3.74
3.51
2.83
5.51
3.74
2.83
2.52
2.28
3.74
3.22
Flame Temp (F)
3508
3300
3300
3205
3115
3030
2950
2875
2670
2550
2165
1307
2670
2165
1980
1825
418
378
Mean Cp's
Flame
Temp (F)
3685
3470
3480
3373
3255
3150
3045
2950
2700
2555
2110
1105
340
2110
260
243
339
306
*** = pure oxygen combustion conditions
* = lower limit of methane stability (not necessarily natural gas)
** = Unstable (if pure methane) and will need pilot flame assist of some sort
2. Plot the two sets of flame temperatures on the same graph using 3800 F
as the upper temperature value for the graph, 1600 F for the lower value
and 0.30 for the lower PHI with 1.10 as the upper PHI.
3. Comment on the results in terms of relative accuracy of the two
approaches.
The two approaches provide relatively similar values, however the mean
Cp values tend to be slightly higher than the time dependent Cps.
4. Why are the pure combustion flame temperatures so different in estimate?
A pure combustion reaction is when there is no nitrogen in the reaction, and
there is only oxygen in the reaction. The pure combustion flame temperatures
are very different because there is no nitrogen for the enthalpy to spread out in
the products. The nitrogen part of the air is not heated, so fuel consumption goes
down, and this results in a higher flame temperature.
5. Why is adiabatic flame temperature such an important factor in
determining leading to comparative engine or heat exchange
performance?
6. Show by a diagram the meaning of an adiabatic flame temperature
calculation for methane (See Lecture 2 notes). Next to the diagram show
the general form of the equation that is used to calculate the adiabatic
flame by:
a.) use of temperature dependent heat capacities for each the product
gases;
b.) Use of mean temperature dependent heat capacities for the
product gases.
7. What do you think the plot of NOx vs flame temperature would look like?
(See Lecture 2 notes) for the flame conditions noted above. Sketch an
expected plot of relative NOx concentrations vs adiabatic flame
temperature for the PHI range calculated above.
8. Explain qualitatively and using a physical combustion mechanism process
why it is more difficult to control NOx in an oil furnace or boiler than a
natural gas or propane gas fired furnace or boiler. (See oil drop
combustion diagram in Lecture 2 notes.)