|Thermodynamics and Propulsion
3.24(b), based on a compressor exit temperature of (922 K).
An initial view of the concept of adiabatic flame temperature is provided by examining two reacting gases, at a given pressure, and asking what the end temperature is. The process is shown schematically in Figure 15.3, where temperature is plotted versus the percentage completion of the reaction. The initial state is and the final state is , with the final state at a higher temperature than the initial state. The solid line in the figure shows a representation of the ``actual'' process.
To see how we would arrive at the final completion state the dashed lines break the state of reaction change into two parts. Process (1) is reaction at constant and . To carry out such a process, we would need to extract heat. Suppose the total amount of heat extracted per unit mass is . The relation between the enthalpy changes in Process (1) is
where is the ``heat of reaction.''
For Process (2), we put this amount back into the products to raise their temperature to the final level. For this process,
or, if we can approximate the specific heat as constant (using some appropriate average value)
For the overall process there is no work done and no heat exchanged so that the difference in enthalpy between initial and final states is zero:
The temperature change during this second process is therefore given by (approximately)
The value of the adiabatic flame temperature given in Equation (15.5) is for 100% completion of the reaction. In reality, as the temperature increases, the tendency is for the degree of reaction to be less than 100%. For example, for the combustion of hydrogen and oxygen, at high temperatures the combustion product (water) dissociates back into the simpler elemental reactants. The degree of reaction is thus itself a function of temperature that needs to be computed. We used this idea in discussing the stoichiometric ramjet, when we said that the maximum temperature was independent of flight Mach number and hence of inlet stagnation temperature. It is also to be emphasized that the idea of a constant (average) specific heat, , is for illustration and not inherently part of the definition of adiabatic flame temperature.
An example computation of adiabatic flame temperature is furnished by the combustion of liquid octane at with 400% theoretical air. The reaction is
For an adiabatic process
We can again think of the general process in steps:
In the present case Equation (15.6) is, explicitly:
We can examine the terms in the SFEE separately, starting with the heat of formation terms, and keeping track of units:
The exit state at the adiabatic flame temperature is specified by:
We find the adiabatic flame temperature in three ways:
15.2 we can use the values at 500 K as representative. These are:
and using the exit state calculated above, find that
Tables give the following evolutions of specific heats with temperature:
and the same equation as above, we obtain
Plugging in the numbers shows the answer is between these two conditions. Linearly interpolating gives a value of
Does ``adiabatic flame temperature'' assume 100% combustion? (MP 15.7)
What part of the computation for adiabatic flame temperature involves iteration? (MP 15.8)