Download Module 5: Combustion Technology Lecture 35: Adiabatic flame

1 | P a g e Module 5: Combustion Technology
Lecture 35: Adiabatic flame temperature calculation
IIT Kharagpur NPTEL Phase – II Web CoursesHome 2 | P a g e Keywords: Constant pressure adiabatic flame temperature, constant volume adiabatic flame
temperature
5.4 Adiabatic flame temperature calculation
The temperature of the products in an adiabatic combustion of fuel without applying any shaft
work, is defined as the “Adiabatic Flame Temperature”. In a combustion process the heat
produced during the exothermic chemical reaction is released to their product and the
temperature of the products is raised. There is no possibility for dissipation of the heat to the
surrounding and the process will be adiabatic as there is no heat loss to the surrounding. As a
result, the temperature of the products suddenly increases and it produces a flame. This will heat
up the product gases in flame region and the temperature rise will be maximum. This highest
temperature is known as the adiabatic flame temperature. The temperature rise depends on the
amount of excess air used or the air-fuel ratio. The flame temperature has the highest value for
using pure oxygen gas and it decreases by using air. So, the exact stoichiometric air is to be
supplied for better result. With too large amount of excess air the flame temperature will be
reduced. When the heat lose to the environment or diluted by the inert gases and there is an
incomplete combustion. So, the temperature of the products will be less. The flame temperature
is determined from the energy balance of the reaction at equilibrium. There are two type of
adiabatic flame temperature: constant pressure adiabatic flame temperature and constant volume
adiabatic flame temperature.
IIT Kharagpur NPTEL Phase – II Web CoursesHome 3 | P a g e Constant pressure adiabatic flame temperature:
From the first law of thermodynamics at constant pressure process
∆
At constant pressure,
∆
Under adiabatic condition,
∆
∆
0,∆
∆
∆
∆
∆
0,
For equilibrium reaction,
Fig. 1 Combustion of fuel
,
,
,
IIT Kharagpur NPTEL Phase – II Web CoursesHome 4 | P a g e Where,
= latent heat of vaporization or condensation for phase change of the product
during the change of temperature of from
to T K.
Ti is the inlet temperature of fuel and air and TR is the reference temperature, 298 K.
Where,
is the heat capacities which is expressed as
Therefore,
,
∆
,
2
3
The flame temperature, T may be calculated from the above equations. It is assumed that
0. Also if the mean heat capacity data is used,
,
∆
,
,
Constant volume adiabatic flame temperature:
From the first law of thermodynamics,
∆ , and
In adiabatic process,
,
0
∆
∆
∆
,
0
Example 1 : Determine the constant pressure adiabatic flame temperature for the combustion of
methane with a stoichiometric air at 1 atm pressure. The reactant temperature at initial
condition, Ti=298 K. The reaction is CH4 + 2O2 + 7.52 N2 = CO2 + 2H2O + 7.524 N2 .Also,
determine the constant volume adiabatic flame temperature using the following Table 1.
(The problem may be solved by trial and error method if specific heats data are available as a
function of temperature. In the present problem, the specific heats of reactants are taken at an
average temperature between initial and final temperature which is (298+1850)/2 = 1074
K 1100 K. Where, the final temperature is assumed as the adiabatic flame temperature of 1850
K in air. )
IIT Kharagpur NPTEL Phase – II Web CoursesHome 5 | P a g e Table:1
___________________________________________________________________
Species
Standard Enthalpy of
Formation at 298 K
Average specific heat
_________________________________________________________________________ CH4
-72.1 kJ/mol
-75.328 kJ/kmolK
CO2
-394.0
55.396 kJ/kmolK
H2O
-244.5
42.44 kJ/kmolK
N2
0
33.0 kJ/kmolK
O2
0
---
___________________________________________________________________ Solution:
=298 K
Basis : 1 kmol of methane ,
At constant pressure process, we have
= -72100 + 2(0) + 7.524(0) = -72100 kJ/kmol
= ∑
∆
,
,
298
= [-394000 + 55.396(Tad -298)]
+[-244500 + 42.44(Tad -298)](2)
+[0.0 + 33.0(Tad -298)](7.52)
= -883000+388.436 (Tad -298) =
= -72100 kJ/kmol
Hence, Tad = 2385.6 K, So the adiabatic flame temperature is 2385.6 K.
At constant volume process,
products,
is to add with the final enthalpy of
. The constant volume adiabatic temperature will be larger than the constant
pressure adiabatic flame temperature.
IIT Kharagpur NPTEL Phase – II Web CoursesHome 6 | P a g e Then we can write,
∑
∆
,
,
298
10.52= constant
As in the above reaction,
8.314 10.52 298
. For specific heat data slight
higher temperature may be assumed. The problem is solved considering same Cp data.
= -883000+388.436 (Tad -298) + 8.314(10.52)(298- Tad ) = -72100 kJ/kmol
-810900 + (383.84 - 87.463)( Tad -298) =0 ,
Tad = adiabatic flame temperature at constant volume process = 2992.3 K
The constant volume adiabatic flame temperature is greater than the constant pressure value.
Determination of adiabatic flame temperature using heat of combustion of fuel
If the heat of combustion of the fuel is known and the heat capacity data of all products are
available, the adiabatic flame temperature can be calculated by using the following equation:
,
Where ,
∆
the heat of combustion of the gaseous fuel. The mean CP -values may be
used for the calculation. Average temperature may be used as, from the arithmetic mean of 298
and Tf .
Example 2: Determine the adiabatic flame temperature at constant pressure combustion of
propane gas using stoichiometric air. The heat of combustion of propane is 2220 kJ/mol.
IIT Kharagpur NPTEL Phase – II Web CoursesHome 7 | P a g e Mean Cp data at 1200 K is available as
CO2 : 0.05632 kJ/mol-K; H2O : 0.04365 kJ/mol-K; N2 : 0.03371 kJ/mol-K
Solution:
Basis: 1 mol of propane burning with soichiometric air
Reaction Soichiometry: C3H8 (g) + 5O2 (g) = 3 CO2(g) + 4H2O (g) + 18.81 N2
298
,
∑
,
298 =
3
0.05632
4
0.04365
0.9777
0.9777
298
2220,
18.81
0.03371
298
298
2570
The adiabatic temperature is 2570 K with soichiometric air.
IIT Kharagpur NPTEL Phase – II Web CoursesHome 8 | P a g e References
1. Chemical Process principles, Part-I, Materials and Energy Balances, O. A. Hougen, K.
M. Watson and R. A. Ragatz, 1st Edn, (Reprint), Asia Publishing House, Calcutta, 1976.
2. Physical Chemistry, P. C. Rakshit, 6th Edition, Sarat Book Distributers,India, 2001
IIT Kharagpur NPTEL Phase – II Web CoursesHome