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Unformatted text preview: sections, the methodology used to calculate the maximum temperature, or adiabatic
ﬂame temperature, will be presented. 2.4.1 ConstantPressure Combustion Processes An adiabatic constantpressure analysis is used here to calculate the adiabatic ﬂame
temperature. Under this idealized condition, conservation of energy is:
HP ðTP Þ ¼ HR ðTR Þ; (2.37) where
HP ðTP Þ ¼ X ^
Ni;P hi;P ¼ i X ^
^
Ni;P ½Dho;P þ hsi;P ðTP Þ
i i and
HR ðTR Þ ¼ X
i ^
Ni;R hi;R ¼ X ^
^
Ni;R ½Dho;R þ hsi;R ðTR Þ:
i i Figure 2.3 is a graphic explanation of how the adiabatic ﬂame temperature is
determined. At the initial reactant temperature, the enthalpy of the product mixture 32 2 Thermodynamics of Combustion HR (T)
HR (TR) = Hp (TP) Enthalpy HR (TR)
Ο x Energy
Release Ο HP(T) HP (TR) Reactant
Temperature Adiabatic Flame
Temperature
Temperature, T Fig. 2.3 Graphical interpretation of adiabatic ﬂame temperature is lower than that of the reactant mixture. The energy released from combustion
is used to heat up the products such that the condition HP ðTP Þ ¼ HR ðTR Þ is met.
The task is ﬁnding the product temperature given the enthalpy of reactants.
Three different methods can be used to obtain TP:
1. Using an average cp value,
2. An iterative enthalpy balance,
3. Finding the equilibrium state using computer software (such as Cantera).
The ﬁrst two methods can be performed manually if complete combustion is
considered and provide only quick estimates. An equilibrium state solver takes into
account dissociation of products at high temperature, making it more accurate than
the ﬁrst two methods.
Method 1: Constant, average cp
From conservation of energy, Hp ðTp Þ ¼ HR ðTR Þ, which can be expressed as
X ^
^
Ni;P ½Dho;P þ hsi;P ðTP Þ ¼
i X i ^
^
Ni;R ½Dho;R þ hsi;R ðTR Þ
i i Rearranging yields
X (
^
Ni;P hsi;P ðTP Þ ¼ À i X ^
Ni;P Dho;P À
i i ¼ ÀQ0 ;p
rxn þ X
i X )
^
Ni;R Dho;R
i i ^
Ni;R hsi;R ðTR Þ þ X ^
Ni;R hsi;R ðTR Þ i (2.38) 2.4 Adiabatic Flame Temperature 33 with
À Q0 ;p ¼
rxn X ^
Ni;R Dho;R À
i i X ^
Ni;P Dho;P :
i (2.39) i Note that water in the products is likely in gas phase due to the high combustion
temperature; therefore À Q0 ;p ¼ LHVÁNfuelÁMfuel ¼ LHVÁmf when the fuel is
rxn
P
^
completely consumed. The second term,
Ni;R hsi;R ðTR Þ,...
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This document was uploaded on 01/20/2014.
 Winter '14
 Physics, Energy, Heat

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