Page 232 - Advanced thermodynamics for engineers

10.5 COMBUSTION PROCESSES 219

10.4.3.1 Higher and lower calorific values
The enthalpy of reaction of CH 4 derived above ( 50,178 kJ/kg) is the negative of the lower calorific
value (LCV) because it is based on gaseous water (H 2 O(g)) in the products. If the water in the products
(exhaust) was condensed to a liquid then extra energy could be released by the process. In this case the
enthalpy of reaction would be

Q p ¼ðDH f Þ þ 2ðDH f Þ ðDH f Þ
25 CO 2 H 2 OðlÞ CH 4
¼ 890225 kJ=kmol
This gives an enthalpy of reaction per kilogram of CH 4 of 55,639 kJ/kg. This is the negative of
the higher calorific value.
Normally the LCV, or lower internal energy or enthalpy of reaction, is used in engine calculations
because the water in the exhaust system is usually in the vapour phase.

10.5 COMBUSTION PROCESSES
10.5.1 ADIABATIC COMBUSTION
The heats of reaction of fuels have been described in terms of isothermal processes i.e. the temperature
of the products is made equal to the temperature of the reactants. However, it is common experience
that combustion is definitely not isothermal; in fact, its major characteristic is to raise the temperature
of a system. How can this be depicted on the enthalpy–temperature diagram?
Consider a constant pressure combustion process, as might occur in a gas turbine, in which there is
no heat or work transfer (Fig. 10.5(a)).
Applying the steady flow energy equation, Eqn (10.11), to the combustion chamber shown in
Fig. 10.5(a) gives
H P ¼ H R : (10.21)

Hence adiabatic combustion is a process which occurs at constant enthalpy (or internal energy, in
the case of combustion at constant volume), and the criterion for equilibrium is that the enthalpies at
the beginning and end of the process are equal. This process can be shown on an H–T diagram
(Fig. 10.5(b)) and it is possible to develop from this an equation suitable for evaluating the product
temperature. The sequences of reactions defining combustion are denoted by the ‘cycle ABCD’. Going
clockwise around the cycle, from A, gives

¼ 0 (10.22)
Q p þ H R T R H R T s H P T P H P T s
s
The term [H R (T R ) H R (T s )] is the difference between the enthalpy of the reactants at the tem-
perature at the start of combustion (T R ) and the standardised temperature (T s ). The term [H P (T P )
H P (T s )] is a similar one for the products. These terms can be written as
n n n
X X X

h ðT s Þ¼
h ðT R Þ
H R T R H R T s ¼ n R i R i n R i R i n R i h R i ðT R Þ h R i ðT s Þ (10.23)
i¼1 i¼1 i¼1
where i is the particular component in the reactants and n is the number of components over which the
summation is made.