This preview shows page 1. Sign up to view the full content.
Unformatted text preview: in Eq. 2.38 represents
i the difference of sensible enthalpy between TR and T0 (25 C) for the reactant
mixture. With the assumption that the sensible enthalpy can be approximated by
ˆ
ˆ
ˆ
hsi,P(TP) % cpi (TP À T0) with cpi % constant, we have
ðTP À T0 Þ X ^
^
Ni;P cpi cp ðTP À T0 Þ X i Ni;P ¼ ÀQ0 ;p þ
rxn X i ^
Ni;R hsi;R ðTR Þ (2.40) i Rearranging the equation one ﬁnds TP as
P
^
ÀQ0 ;p þ Ni;R hsi;R ðTR Þ
rxn
i
P
TP ¼ T0 þ
^
Ni;P cpi
i ÀQ0 ;p
rxn
% TR þ P
^
Ni;P cpi (2.41) i LHV Á Nfuel Á Mfuel
P
¼ TR þ
;
^
Ni;P cpi
i where the following approximation has been applied4
P
i ^
Ni;R hsi;R ðTR Þ
P
¼
^
Ni;P cpi P
i i ^
Ni;R cp i;R ðTR À T0 Þ
P
% TR À T0
^
Ni;P cpi
i When reactants enter the combustor at the standard conditions, the above
equation reduces to (as sensible enthalpies of reactants are zero at T0)
TP ¼ T0 þ LHV Á Nfuel Á Mfuel
P
:
^
Ni;P cpi
i 4 P
i ^
Ni;R cp i;R and P
i ^
Ni;p cpi are assumed to be approximately equal. (2.42) 34 2 Thermodynamics of Combustion The above procedure is general and can be applied to any mixture. Note that
the speciﬁc heat is a function of temperature, so the accuracy of this approach
ˆ
depends on the value selected for the speciﬁc heat cp.
If the heating value of a fuel is given, a massbased analysis for the same control
volume can be conducted. The initial mixture consists of fuel and air with mf and ma,
respectively. By mass conservation, the products have a total mass of mf + ma. The
sensible enthalpy of the products is approximated by Hs,P ¼ (ma + mf )Á cp;P Á (TP – T0),
where cp;P is an average value of speciﬁc heat evaluated at the average temperature of
the reactants and products, i.e., cp;P ¼ cp ðT Þ; where T ¼ ðTp þ TR Þ=2. Similarly, the
sensible enthalpy of the reactants is estimated by Hs,R ¼ (ma + mf )Á cp;R Á (TR – T0),
where cp;R is an average value of speciﬁc heat evaluated at the average temperature of
reactants and the standa...
View
Full
Document
This document was uploaded on 01/20/2014.
 Winter '14
 Physics, Energy, Heat

Click to edit the document details