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134 Adrian Sabău et al.
11 T ⎛
0
N ⎞
i
dI = d Nprafv − [dQ+ d Npr( hfl − hfv )] + t0∑dNi⎜si−Rln ⎟−
T ⎜
i= 1
N ⎟
⎝ ∑ i ⎠
T T
− − + +
11 4
0 0
0
dNprhfv VdP∑dNicpidT∑d Nig0i. T T i= 1 i=
1
.
(13)
The energy balance for the system can be reformulated in enthalpy terms as
dQ+ d N ( h − h ) + VdP= hdN +
pr fl fv i i
fv
10 ⎛
⎜∑ i=
1
i pi fv
i=
1
⎞
pfv ⎟d
d prhfv + h + N c + N c T − N
⎝ ⎠
10
∑
(14)
Eq. (14) is the expression of the same energy balance as Eq. (2)
reformulated in terms of enthalpy. If Eq. (14) is multiplied by T0/T and
subtracted from Eq. (13), keeping in mind that the expression for gi is:
it is shown that
Ni
gi = hi − Tsi + RTln
∑ Ni
, (15)
T 11
4
0
dI = − ∑ dNi
gi
+ ∑ dNi
g0i
+ dN pr fv fv
T
[ a − h 1 T / T ]
0 ( − 0
i=
1 i=
1
. (16)
This proves that the differential availability destruction is only a function
of the differential change in mixture composition. It is interesting to note that
one of the main mechanisms of irreversibility production, namely heat transfer,
affects the final result only indirectly since dI is not an explicit function of dQ.
Irreversibility production due to fluid viscosity, as discussed in (Dunbar &
Lior, 1994), cannot be calculated within the framework of the current singlezone
analysis.
5. Results and Analysis
The “availability balance” during the engine cycle is presented for the
diesel fuel injection case in Fig. 3. Only the “closed” part of the engine cycle is
presented. This is a balance between five terms: working medium availability,
availability transfer through work, availability transfer through heat, input of
availability with the injected fuel, and destruction of availability (production of
irreversibility). All five terms are calculated independently as described earlier
use a computer code writes in Matlab. The “deficit” in the balance caused by
the employed numerical scheme is of the order of 1% of the availability of the
injected fuel. Since the availability input with the injected fuel starts and ends
abruptly with the start and end of injection, respectively, it is expected that
discontinuities in the derivative of the corresponding curve should appear.