The Ideal Air-Standard Cycle - EngineKnowHow

The phenomena which occurs within an internal combustion engines are very difficult to analyse, air is inducted into the cylinder, mixed with fuel either before or in the cylinder, compressed, combusted and exhausted from the cylinder.  During this time the air / fuel mixture under goes high pressure and temperature changes and undergoes a chemical reaction which converts the air / fuel into exhaust products.

 

Due to the complexities of the actual engine cycle several assumptions can be made to simplify the process. With these assumptions the engine cycles are known as Air-Standard Cycles and allow us to better understand an engine’s potential performance and efficiency.  The assumptions of the Air-Standard Cycles are:

 

  • The cylinder is only filled air. Fortunately the properties of air are a good approximation for the properties of exhaust products whilst less than 7% of the cylinder contents is fuel;
  • The air is considered ideal and the specific heat ratio remains constant.
  • It is a closed loop system, therefore the exhaust (assumed air) is fed back into the intake system. In reality it’s an open loop as the exhaust is exhausted to the atmosphere;
  • No heat is lost to the engine, the only heat transfer is to and from the working fluid, air;
  • The inlet and exhaust pressures are constant;
  • There is no friction; and,
  • All processes are reversible.

 

Using these assumptions it is possible to determine the ideal thermodynamic cycles for modern internal combustion engines.  These include:

 

 

Specific Heat Ratio

The specific heat ratio, γ is the ratio of the heat capacity at a constant pressure, Cp relative to the heat capacity at a constant volume, Cv for an ideal gas.

 

 

 

The heat capacity is the amount of energy which must be added to a system to result in a change in temperature.   So for example, for air in a cylinder at a constant volume, (consider a piston fixed in the cylinder) the heat capacity at a constant volume is how much energy must be delivered to the air to result in 1°C temperature change.  Therefore, for a system with a fixed volume:

 

 

 

In reality, the specific heat capacity will change with temperature, as at higher temperatures increasing amounts of energy must be added to the system to increase the temperature.   The table below shows the specific heat capacity for air over different temperatures:

Temperature cp cv γ
K °C kJ/kg.K kJ/kg.K
273 0 1.004 0.717 1.40
298 25 1.005 0.718 1.40
300 27 1.005 0.718 1.40
500 227 1.029 0.742 1.39
1000 727 1.140 0.853 1.34
1500 1227 1.210 0.923 1.31
2000 1727 1.249 0.962 1.30
2500 2227 1.274 0.987 1.29
3000 2727 1.291 1.004 1.29

 

In the Air-Standard Cycle the specific heat capacity is assumed to remain constant and therefore γ = 1.35 is a good compromise between the temperature of the air which enters the cylinder and the temperature of the air following the addition of heat (combustion)