The Otto cycle is the backbone of spark-ignition engines, powering most cars on the road today. It's a four-stroke process that turns fuel and air into mechanical energy, using intake, compression, combustion, and exhaust strokes.

Understanding the Otto cycle is key to grasping how gas power cycles work in real-world applications. It showcases how thermodynamic principles are applied in engines, demonstrating the conversion of heat energy into useful work through a series of processes.

Otto cycle principles

Basic components and operation

• The Otto cycle is a four-stroke thermodynamic cycle used in spark-ignition internal combustion engines (gasoline engines in automobiles)
• The four strokes of the Otto cycle are intake, compression, combustion (power), and exhaust which correspond to the four stages of the thermodynamic cycle
• The Otto cycle operates on an air-fuel mixture that is ignited by a spark plug at the end of the compression stroke
• The main components of an Otto cycle engine include the cylinder, piston, connecting rod, crankshaft, valves (intake and exhaust), and spark plug

Ideal gas assumptions

• The Otto cycle assumes an ideal gas with constant specific heats
• The cycle assumes instantaneous combustion
• The cycle assumes no heat transfer to the surroundings during the cycle

Thermodynamic processes in the Otto cycle

Intake and compression strokes

• The intake stroke (process 0-1) involves the piston moving downward, drawing in the air-fuel mixture at constant pressure
• The compression stroke (process 1-2) is an isentropic compression of the air-fuel mixture as the piston moves upward and compresses the mixture
• During the compression stroke, the temperature and pressure of the air-fuel mixture increase significantly (up to 400-500°C and 10-20 bar)

Combustion and power strokes

• The combustion stage (process 2-3) is a constant-volume heat addition process where the air-fuel mixture is ignited by the spark plug causing a rapid increase in pressure and temperature
• The power stroke (process 3-4) is an isentropic expansion of the hot, high-pressure gases pushing the piston downward and producing work
• During the power stroke, the expanding gases can reach temperatures over 2000°C and pressures around 50-60 bar

Exhaust stroke and cycle repetition

• The exhaust stroke (process 4-1) is a constant-volume heat rejection process as the piston moves upward, expelling the burnt gases from the cylinder
• The exhaust gases are typically at a temperature of 600-800°C and a pressure slightly above atmospheric pressure
• The cycle then repeats, starting with the intake stroke

Efficiency and work output of the Otto cycle

Thermal efficiency calculation

• Thermal efficiency is the ratio of the net work output to the heat input during the cycle
• The thermal efficiency of an Otto cycle depends on the compression ratio (r) and the specific heat ratio (γ) of the working fluid: $η = 1 - (1 / r^(γ-1))$
• A higher compression ratio leads to a higher thermal efficiency as it allows for more work to be extracted from the heat input
• Typical compression ratios for Otto cycle engines range from 8:1 to 12:1, resulting in thermal efficiencies of 50-60%

Work output determination

• The net work output of the Otto cycle is the difference between the work done during the power stroke and the work done during the compression stroke
• The work output can be calculated using the first law of thermodynamics and the ideal gas law, considering the changes in temperature and volume during the isentropic processes
• The heat input during the combustion stage is determined by the change in internal energy of the system and the mass of the air-fuel mixture
• The specific work output (work per unit mass of air) can be expressed as: $w_net = c_v (T_3 - T_2 - T_4 + T_1)$

Factors affecting Otto cycle performance

Engine design parameters

• Compression ratio: A higher compression ratio improves thermal efficiency but can lead to engine knocking if the ratio is too high
• Valve timing: Proper valve timing is essential for efficient gas exchange and can affect volumetric efficiency and engine performance
• Engine geometry (bore, stroke, connecting rod length) influences the compression ratio, engine speed, and heat transfer characteristics

Fuel and combustion factors

• Air-fuel ratio: The stoichiometric air-fuel ratio provides the most complete combustion, but slightly lean mixtures can improve efficiency and reduce emissions
• Fuel octane rating: Higher octane fuels resist knocking and allow for higher compression ratios, improving efficiency
• Spark timing: Optimal spark timing ensures maximum work output and efficiency, while improper timing can lead to knocking or reduced performance

Operating conditions and losses

• Engine speed: The efficiency and power output of an Otto cycle engine vary with engine speed, with peak efficiency often occurring at lower speeds than peak power
• Heat losses: Heat transfer to the cylinder walls and exhaust gases reduces the available energy for work output, lowering efficiency
• Friction losses: Mechanical friction between moving parts (piston rings, bearings) consumes some of the work output, reducing the overall efficiency