Decomposition Analysis of an Automotive Powertrain Design ...

Engine Model
The engine model is based on the model of Kuzak et al. (1984) but accounts for manifold
tuning effects slightly differently. We use the friction model of Patton et al. (1989), include a
simple NOx model, and account for effects of combustion stability degradation with burn duration.
The expression for torque is developed in terms of mean effective pressure, which is
torque normalized against swept displacement volume. The expression for engine torque is
T e = 7.955 x 10 -6 P bmep b 2 s π /4 n c (40)
where P bmep has units of bars. The brake mean effective pressure, P bmep , is the difference
between indicated mean effective pressure and friction mean effective pressure
P bmep = P imep - P fmep (41)
The indicated mean effective pressure is the amount of fuel energy converted to indicated work
normalized against displacement volume. It is given by the product of the mass of fuel, the lower
heating value of the fuel, Q, the thermal efficiency of the engine cycle, η t , and the air-to-fuel
ratio, R af ,
P imep = 3.479 x10 -2 η t ( p it / T m ) Q/ R af . (42)
The thermal efficiency is expressed as
η t = 0.9 ( 1 - c r (-0.33 - .01 Regr/30) )f c - S v (1500/N e ) 0.5 (4.137/P imep ) 0.2 (43)
where
f c = (1.18 - 0.18 φ /0.8) φ ≤ 1
= (1.655 - 0.7 φ) φ > 1 (44)
S v = 0.83 (12s + (c r - 1)( 6b + 4s) ) / (b s (2 + c r )). (45)
The 0.9 multiplier accounts for losses due to finite combustion times and is considered valid for
displacements of 400 - 600 cc/cylinder and bore to stroke ratios of 0.8 - 1.2. The air-fuel
correction factor, f c , is based on the well-known effects of air-fuel ratio on idealized Otto cycles
(Taylor, 1985). Heat transfer is strongly dependent upon surface-to-volume ratio. The S v term is