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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 correspon<strong>din</strong>g curve should appear.
Bul. Inst. Polit. Iaşi, t. LVIII (LXII), f. 4, 2012 135 Fig. 3 – Availability balance for operation with diesel fuel. Fig. 4. – Availability balance for operation with methane. During fuel injection and preparation, there is a gradual fuel availability influx. It can be noted that there is a significant loss of working medium availability during the fuel preparation. This is due to working medium cooling because of fuel vaporization. The production of irreversibility due to irreversible heat transfer during compression is negligible compared to the combustion irreversibility. In fact, significant production of irreversibility takes place only after ignition. This may be due to insufficient modelling of heat transfer within the framework of a single-zone. No Fig. experiments 5 – Availability were balance conducted for wi operation with methanol. Diesel Metan Metanol Fig. 6 – Injected fuel availability.
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BULETINUL INSTITUTULUI POLITEHNIC D
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