9781441979421-c1

# 23 graphical interpretation of adiabatic ame

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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 Constant-Pressure Combustion Processes An adiabatic constant-pressure 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.

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