Engine Cycle Simulator: Otto & Diesel Thermodynamic Efficiency

simulator intermediate ~12 min
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η = 60.2% — ideal Otto cycle at r = 10

The ideal Otto cycle at compression ratio 10 with γ = 1.4 achieves 60.2% thermal efficiency. Real spark-ignition engines achieve about 35–40% due to friction, heat transfer, and incomplete combustion.

Formula

η_Otto = 1 − 1/r^(γ−1)
η_Diesel = 1 − (r_c^γ − 1) / [γ·r^(γ−1)·(r_c − 1)]
MEP = W_net / V_displacement

Ideal Thermodynamic Cycles

The Otto and Diesel cycles are idealized models of the processes inside reciprocating internal combustion engines. By treating the working fluid as an ideal gas undergoing reversible processes, we derive elegant efficiency expressions that capture the essential physics: higher compression means higher efficiency. These air-standard cycles serve as the theoretical ceiling against which real engine performance is benchmarked.

The P-V Diagram

The pressure-volume diagram is the fundamental visualization tool for engine cycles. The area enclosed by the cycle represents net work output per cycle. In the Otto cycle, the tall, narrow shape of constant-volume heat addition creates high peak pressures. In the Diesel cycle, the constant-pressure heat addition produces a wider loop with lower peak pressure but potentially more total work at high loads.

Compression Ratio: The Master Variable

Compression ratio is the single most important design parameter for engine efficiency. Increasing r from 8 to 12 boosts Otto cycle efficiency from 56% to 63%. But real engines face knock limits (Otto) or peak pressure limits (Diesel) that constrain maximum r. Modern gasoline engines use direct injection, cooled EGR, and variable compression to push these boundaries, achieving real efficiencies approaching 40%.

From Theory to Practice

The gap between ideal and real efficiency — typically a factor of 1.5–2× — arises from irreversibilities: heat loss through cylinder walls, friction in bearings and piston rings, incomplete combustion, pumping work to move air through the engine, and exhaust energy that escapes unrecovered. This simulation shows the ideal cycle while highlighting where real-world losses erode performance, helping engineers identify the most impactful areas for improvement.

FAQ

What is the Otto cycle?

The Otto cycle is the ideal thermodynamic cycle for spark-ignition internal combustion engines. It consists of four processes: isentropic compression, constant-volume heat addition (representing combustion), isentropic expansion, and constant-volume heat rejection. Its thermal efficiency depends only on compression ratio and specific heat ratio: η = 1 − 1/r^(γ−1).

How does the Diesel cycle differ?

The Diesel cycle models compression-ignition engines, where fuel is injected into highly compressed hot air. Heat addition occurs at approximately constant pressure rather than constant volume. This allows higher compression ratios (r = 15–22) without knock, but the constant-pressure process is inherently less efficient than constant-volume at the same compression ratio.

Why does higher compression ratio improve efficiency?

Higher compression ratio means the gas expands through a larger volume ratio during the power stroke, extracting more work per unit of heat input. Thermodynamically, the cycle approaches the Carnot efficiency as compression ratio increases, since the mean temperature of heat rejection decreases relative to heat addition.

What limits real engine efficiency?

Real engines achieve 35–45% of fuel energy as shaft work. Losses include: friction (5–10%), heat transfer to cylinder walls (10–15%), incomplete combustion (2–5%), pumping losses (5–10%), and exhaust enthalpy. Turbocharging, variable valve timing, and Miller cycling help close the gap to the ideal cycle.

Sources

Embed

<iframe src="https://homo-deus.com/lab/combustion/engine-cycle/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub