IV C Cycles - IV C AIR STANDARD CYCLES Model 1 for working...

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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 rC-l rcy-l ) (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 Vl-V2 rc_1 But —— a ————— = (12) m V1 re (2* = (WM (2an ( ) (13) 1'c For a typical stoichometric case of C8H18: rc-l Q* = 2920 ( ) kJ/kg air (l4)( rc .r‘\\ Q* I'C-l . 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 (7-1)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 afiV-l 1 flf,i = 1 ‘ —-*—————~——-— I (18) rev-l L a7(fi'l) + a'1 J IMEP Q* [ rc 1 (19) — = 17 ' P1 CVT1(1-l) L rc-l 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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