Thermodynamic Cycles for CI engines • In early CI engines the fuel was injected when the piston reached TC and thus combustion lasted well into the expansion stroke.

• In modern engines the fuel is injected before TC (about 20o)

Fuel injection starts Fuel injection starts

Early CI engine Modern CI engine

• The combustion process in the early CI engines is best approximated by a constant pressure heat addition process → Diesel Cycle

• The combustion process in the modern CI engines is best approximated by a combination of constant volume & constant pressure → Dual Cycle Early CI Engine Cycle vs Diesel Cycle

FUEL Fuel injected A at TC I R

Fuel/Air Mixture Combustion Actual Products Cycle

Intake Compression Power Exhaust Stroke Stroke Stroke Stroke

Qin Qout

Air Diesel TC Cycle BC

Compression Const pressure Expansion Const volume Process heat addition Process heat rejection Process Process Air-Standard Diesel Cycle

Process 1→ 2 Isentropic compression Process 2 → 3 Constant pressure heat addition Process 3 → 4 Isentropic expansion Process 4 → 1 Constant volume heat rejection

Cut-off ratio: Qin v3 rc = v2

Qout

v v 2 1 BC TC BC TC First Law Analysis of Diesel Cycle

Equations for processes 1→2, 4→1 are the same as those presented for the Otto cycle

2→3 Constant Pressure Heat Addition AIR Qin Q P (V −V ) (u − u ) = (+ in ) − 2 3 2 3 2 m m Q in = (u + P v ) − (u + P v ) m 3 3 3 2 2 2 RT RT T v Qin P = 2 = 3 → 3 = 3 = r = (h3 − h2 ) c m v2 v3 T2 v2 3 → 4 Isentropic Expansion

Q Wout (u4 − u3 ) = − (+ ) m m AIR W out = (u − u ) m 3 4 v v r4 v v4 v4 v2 v1 v2 r r v r = 4 note v =v so =  =  = → 4 = 4 = v v 4 1 v v v v v r v v r r3 3 3 2 3 2 3 c r3 3 c

P v P v P T r 4 4 = 3 3 → 4 = 4  T4 T3 P3 T3 rc Thermal Efficiency

Qout m u4 − u1 Diesel =1− =1− cycle Qin m h3 − h2

For cold air-standard the above reduces to:

k 1 1 (rc −1) 1 Diesel =1−    recall, Otto =1− k−1 k rk−1 const cV r  (rc −1)

Note the term in the square bracket is always larger than one so for the same compression ratio, r, the Diesel cycle has a lower thermal efficiency than the Otto cycle

When rc (=v3/v2)→1 the Diesel cycle efficiency approaches the efficiency of the Otto cycle Thermal Efficiency

Modern CI Engines 12 < r < 23

The cut-off ratio is not a natural choice for the independent variable A more suitable parameter is the heat input, the two are related by:

k −1 Qin  1 r =1−   as Qin→ 0, rc→1 and  →Otto c   k−1 k  P1V1  r