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Unformatted text preview: IV C. AIR STANDARD CYCLES
Model 1 for working fluid in Table 4.2
ASSUMPTIONS:  Cp and CV constant for both burned and unburned gases
 Specific heats are same for burned and unburned gases RESULTS: i) Constant Volume Cycle WC m(ul " 1.12) = mCV(T1 — T2) (1) WE IIICV(T3 — T4) (2) NOTE: m = mass in combustion chamber = mmixture + mr Combustion:
va(T3 ‘ T2) = mf QLHV (3)
WC + WE T4 — T1 Since process 1—2 and 3—4 are isentropic: T2 (Vl)7_1 7 1
_._. = — = r _ 5
T1 v2 C _ ( )
T3 V4 7‘1 1
T4 V3
T4' T3
__ = __ (6)
T1 Ta
1
= "f,1 = 1 — 7—1 (constant volume Combustion) (7)
r Fuel conversion efficiency increases with compression ratio. MEAN EFFECTIVE PRESSURE: ’lf,i mf QLHv
IMEP Vd (8) Can show with above and ideal gas law: IMEP 9* 1 re 1
)(——)( )(1 31 cvml 7—1 rCl rcyl ) (9) —=( f (energy input, r0, 7) where
Q* = energy input per unit mass of working fluid
mf
9* = —— QLHV (10)
m .
mf ma
= (—) QLHv () (11)
a
ma VlV2 rc_1
But —— a ————— = (12)
m V1 re
(2* = (WM (2an ( ) (13)
1'c
For a typical stoichometric case of C8H18:
rcl
Q* = 2920 ( ) kJ/kg air (l4)(
rc .r‘\\
Q* I'Cl .
a ( ) a 9.3 ( ) for T1 = 333K .  (15) also a ratio of IMEP to peak pressure: IMEP 1 re 1’1/rcy_l
) ——————————————~—* (16)
P3 (71)rc7 rc'l CVTl/Q* + 1/rc7'1 ————=—( NOTE: Want a high IMEP/P3 to get as much torque as possible without high
structural requirements. Notice that IMEP/P3 decreases with increasing
compression ratio. RESIDUAL GAS MASS FRACTION, Xr
1 (Fe/Pi) 1/7 xr(throttled) = —— —~————————————~——~— (17)
rc [1 + Q*/(CVTlr07_1)]l/7 NOTE: Residual mass fraction increases with decreasing rc , Q* and as inlet pressure
drops below exhaust pressure. ii) Constant Pressure and Limited Pressure cycle
1 r aﬁVl 1
ﬂf,i = 1 ‘ —*—————~——— I (18)
revl L a7(ﬁ'l) + a'1 J
IMEP Q* [ rc 1 (19)
— = 17 '
P1 CVT1(1l) L rcl J f'l ‘
IMEP 1 < * )< 1 )( re ) V (20)
———— = —" ”f 1
P3 arCV CVTl 7‘1 330'1 I
where
P3
a = —— = 1 for constant P cycle
P2
V3b V3
5 = ——— = —— for constant P cycle V3a V2 ...
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 Spring '11
 Drallmeier

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