buletinul institutului politehnic din iaşi - Universitatea Tehnică ...

Bul. Inst. Polit. Iaşi, t. LVIII (LXII), f. 4, 2012 133
The fuel vapor availability consists of two parts. The first part, usually
termed “thermal” or “thermo-mechanical” part, is equal to
a = h −T s −g
. (9)
fv,termomechanical fv 0 fv
0
fv
This is the amount of availability introduced by the injected gas. A
second part, usually termed “thermo-chemical” availability, is due to the ability
of fuel to react and produce reactants of lower availability. For the calculation
of the thermo-chemical availability, we consider the reaction of complete
oxidation of the fuel in atmospheric air.
It is shown (Bejan, 1988), that the thermo-chemical availability is equal
to the difference in Gibbs free energy between reactants and products at
temperature T0 and pressure P0. It follows that
β ⎛ β γ⎞
a g αg g α g
2 ⎝ 4 2⎠
0 0 0 0
fv,termochemical = fv − CO −
2 H2O+ ⎜ + − ⎟ O2
−
β /2
⎡ α ⎛ β ⎞ ⎤ ε
⎢ α ⎜ ⎟ ε ⎥
2
− RT ln ln ⎢ ⎝ ⎠ ⎥,
α+ β/4 −γ/2
⎢⎛ β γ⎞
⎥
ζ
⎢⎜α+ − ⎟ ζ ⎥
⎣⎝ 4 2⎠
⎦
(10)
where the last term of the sum accounts for the difference in entropy of mixing
between products and reactants, and ε and ζ are defined as follows
β γ
ε= α+ − ,
4 2
β
ζ = 0.79ε+
α+
.
2
(11)
Adding Eqs. (9) and (10) we get for the total fuel availability
β ⎛ β γ⎞
a = h −T s −αg − g + α + − g
2 ⎝ 4 2⎠
0 0 0
fv fv 0 fv CO2 H2O⎜ ⎟ O2
β/2
⎡ α⎛ β ⎞ ⎤ ε
⎢ α ⎜
2
⎟ ε ⎥
− RT ln ⎢ ⎝ ⎠ ⎥.
α+ β/4 −γ/2
⎢⎛ β γ⎞
⎥
ζ
⎢⎜α+ − ⎟ ζ ⎥
⎣⎝ 4 2⎠
⎦
−
.
(12)
If we substitute Eqs. (4) and (8) in Eq. (5) and subtract Eq. (2) multiplied
by T0/T, we get