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130 Adrian Sabău et al.
The energy balance for a closed system of variable volume:
11 11
∑ ∑ .
dQ+ d N ( h −h ) − pdV = udN + dT N c −dN
h
pr fl fv i i i vi pr fv
i= 1 i=
1
The first two terms on the left-hand side are the heat influx. The third
term is the work output of the system. The first two terms on the right hand side
are the change in internal energy of the working medium due to the change of
its composition and temperature respectively. The third term is the enthalpy
influx to the working medium due to fuel vaporization. The volume is
calculated analytically as a function of the crank angle. The thermodynamic
properties are computed as a function of T by polynomial fittings to the data of
JANAF Thermo-chemical Tables. Heat transfer through the system boundary is
calculated as a function of T, the thermodynamic properties of the working
medium and the wall temperature using Annand’s formula, as described in Ref.
(Sabau et al., 2001).
The molar quantities Ni are calculated using a chemical equilibrium
assumption. Specifically, we assume that the following six reactions among the
above 10 species were in equilibrium
H2↔2H, O2↔2O, H2 + O2 ↔2OH,
N + O ↔2NO,
(3)
2 2
2H + O ↔2HO,
2 2 2
2CO + O ↔2CO
.
2 2
At each crank angle, equilibrium equations for these six reactions as well
as atom number conservation equations for the atoms of C, H, O and N,
constitute a 10x10 system of equations which can be solved for Ni. This is a
generalization of the procedure described in Refs. (Rakopoulos et al.,1993) and
(Sabau et al., 2001) for diesel fuel, where the validity of the chemical
equilibrium assumption is discussed. In general, the chemical equilibrium
assumption is not valid for the formation of pollutants. Given the fact that the
quantities of pollutants are small, the main conclusions of work are not affected.
4. Second-law Analysis
Availability of a system is defined as the maximum work that can be
produced from the system through interaction with its surroundings during a
reversible transition to a state of thermal, mechanical, and chemical equilibrium
with its environment, and while heat is exchanged during the transition only
(2)