Gas Power Cycles and IC Engines

Petrol engines, diesel engines and gas turbines use air (with fuel) as the working fluid. Their air-standard cycles give simple formulas for efficiency.

Otto cycle (petrol / SI engine)

Two isentropic and two constant-volume processes. With compression ratio r = V₁/V₂:

η_Otto = 1 − 1/r^(γ−1)

Efficiency depends only on r (and γ). It is limited by knock in SI engines.

Diesel cycle (CI engine)

Heat is added at constant pressure. With cut-off ratio ρ = V₃/V₂:

η_Diesel = 1 − (1/r^(γ−1)) × (ρ^γ − 1)/(γ(ρ − 1))

For the same compression ratio, η_Otto > η_dual > η_Diesel. For the same maximum pressure and temperature, Diesel > dual > Otto. Diesel engines reach higher efficiencies in practice because they run at much higher r.

Brayton cycle (gas turbine)

Two isentropic and two constant-pressure processes. With pressure ratio r_p:

η_Brayton = 1 − 1/r_p^((γ−1)/γ)

• Optimum pressure ratio for maximum net work: r_p = (T_max/T_min)^(γ/(2(γ−1))), where T₂ = √(T₁T₃).
• Back work ratio is large (40–80%), so compressor efficiency matters a lot.
• Regeneration (heat exchanger using exhaust), intercooling and reheating improve it.

Mean effective pressure

MEP = net work per cycle / swept volume. It compares engines of different sizes.

IC engine performance

• Indicated power IP = p_mi L A n k, where p_mi is the indicated mean effective pressure, L the stroke, A the piston area, k the number of cylinders and n the power strokes per second per cylinder: N/60 for a two-stroke and N/120 for a four-stroke engine (N in rpm).
• Brake power BP = 2πNT/60. Mechanical efficiency η_m = BP/IP. Friction power = IP − BP.
• Brake thermal efficiency = BP/(ṁ_f × CV).
• Volumetric efficiency = actual air inducted / swept volume at intake conditions.
• Specific fuel consumption = fuel used per kWh.

Worked example

An Otto cycle has r = 9 and γ = 1.4.

• η = 1 − 1/9^0.4 = 1 − 1/2.408 = 58.5%.

Practice