Modern Engineering Thermodynamics

15.8 Adiabatic Flame Temperature 613
Table 15.4 Explosion Limits and Ignition Temperatures for Common Fuel–Air Mixtures
Substance LEL (%) UEL (%) Ignition Temp. (°F)
Carbon monoxide (CO) 12.5 74.0 1128
Hydrogen (H 2 ) 4.00 75.0 968
Methane (CH 4 ) 5.00 15.0 1301
Acetylene (C 2 H 2 ) 2.50 81.0 763–824
Ethylene (C 2 H 4 ) 2.75 28.6 914
Ethane (C 2 H 6 ) 3.00 12.5 968–1166
Propylene (C 3 H 6 ) 2.00 11.1 856
Propane (C 3 H 8 ) 2.10 10.1 871
n-Butane (C 4 H 10 ) 1.86 8.4 761
Gasoline 1.12 6.75 495
15.8 ADIABATIC FLAME TEMPERATURE
The maximum possible combustion temperature occurs when combustion takes place inside an adiabatic (i.e.,
insulated) system. This temperature is called the adiabatic combustion temperature or the adiabatic flame temperature.
In practice, though, the combustion temperature can never reach this temperature, because
1. No system can be made truly adiabatic.
2. The combustion reaction is always somewhat incomplete.
3. The combustion products ionize at high temperatures and thus lower the reaction temperature.
Nonetheless, the adiabatic flame temperature provides a useful upper bound on combustion temperatures and
can be used to estimate the thermal effects of combustion on material physical properties and exhaust gas states.
There are actually two types of adiabatic flame temperature, depending on whether the combustion process is
carried out under constant volume or constant pressure. The constant volume adiabatic flame temperature is the
temperature resulting from a complete combustion process that occurs inside of a closed, rigid vessel with no
work, heat transfer, or changes in kinetic or potential energy. The constant pressure adiabatic flame temperature is
the temperature that results from a complete combustion process that occurs at a constant pressure (like an
open flame) with no heat transfer or change in kinetic or potential energy. The constant pressure adiabatic
flame temperature is lower than the constant volume adiabatic flame temperature, because some of the combustion
energy is used to change the volume of the reactants and thus generates work.
For an open, constant pressure, adiabatic system, q r = 0 and Eq. (15.9) reduces to h R = h P , then,
∑
R
ðn i /n fuel Þ½h°+hðTÞ f − hðT°ÞŠ i
= ∑ ðn i /n fuel Þ½h°+hðT f A Þ − hðT°ÞŠ i
where T A is the adiabatic flame temperature and T is the temperature of the reactants. If the reactants are all at
the standard reference state and the products can all be treated as ideal gases with constant specific heats over
the temperature range from T° to T A , then the previous equation reduces to
∑
R
ðn i /n fuel Þ h° f i = ∑ P
P
ðn i /n fuel Þ h°+c f p ðT A − T° Þ i
Now, let us suppose that all of the reactants except the fuel are elements; then, their h f ° values are all zero. This
equation can now be solved for T A as
Open system, constant pressure, adiabatic, flame temperature when the reactants are at the SRS:
T A
= T°+
open
system
h f ° fuel −∑ P
∑
P
ðn i /n fuel Þ h° f i
ðn i /n fuel Þ c pi
avg
(15.17)
Equation (15.17) represents the only method for calculating the adiabatic flame temperature directly. It requires
ideal gas behavior, which is usually reasonable, and it requires constant specific heats over the range T° =25.0°C