What is efficiency of an air-standard cycle

Short Answer:

The efficiency of an air-standard cycle is the ratio of the useful work output produced by the engine cycle to the total heat energy supplied during the process. It represents how effectively the air-standard cycle converts heat energy into mechanical work. In simple words, it shows how much of the input heat energy is converted into useful work while the rest is lost as waste heat.

The efficiency mainly depends on factors such as the compression ratio and the type of thermodynamic cycle (Otto, Diesel, or Dual cycle). Higher compression ratios generally lead to higher efficiency in air-standard cycles.

Detailed Explanation:

Efficiency of an Air-Standard Cycle

The efficiency of an air-standard cycle is a measure of how well a heat engine converts the supplied heat energy into useful mechanical work. In the air-standard assumption, air is used as the working medium, and it behaves as an ideal gas that undergoes various thermodynamic processes such as compression, heat addition, expansion, and heat rejection.

The efficiency is calculated as the ratio between the work output and the heat supplied, which can be written as:

This expression indicates that higher efficiency can be achieved by minimizing the heat rejected and maximizing the useful work extracted from the cycle.

Concept of Air-Standard Cycle

An air-standard cycle is a simplified model used to analyze internal combustion engines. It assumes that:

  1. The working substance is pure air.
  2. The air behaves as an ideal gas and follows the laws of thermodynamics.
  3. The cycle is completed using reversible processes.
  4. Combustion and exhaust processes are replaced by external heat addition and rejection.

This simplification allows engineers to study the theoretical efficiency of different engine cycles such as the Otto cycle, Diesel cycle, and Dual cycle without considering complex chemical reactions.

Efficiency of Otto Cycle

The Otto cycle represents the working of a petrol engine. It consists of two adiabatic (isentropic) and two constant volume processes. The efficiency of the Otto cycle depends only on the compression ratio (r) and the specific heat ratio (γ) of air.

The efficiency is given by the formula:

Where,

  • r = Compression ratio (V₁/V₂)
  • γ = Ratio of specific heats (Cp/Cv), usually 1.4 for air.

From the formula, it is clear that efficiency increases with the increase in compression ratio. However, in practical engines, the compression ratio is limited by knocking in petrol engines.

Efficiency of Diesel Cycle

The Diesel cycle represents the working of a diesel engine. It includes two adiabatic, one constant pressure, and one constant volume process. The efficiency of the Diesel cycle depends on both the compression ratio (r) and the cut-off ratio (β), which is the ratio of volumes at the end and start of the combustion process.

The efficiency of a Diesel cycle is given by:

A higher cut-off ratio reduces the efficiency because it increases heat loss during the constant pressure process.

Efficiency of Dual Cycle

The Dual cycle combines features of both Otto and Diesel cycles. It includes both constant volume and constant pressure heat addition. The efficiency of the dual cycle lies between that of the Otto and Diesel cycles.

The formula for efficiency is:

Where,

  • α = Pressure ratio during constant volume heat addition
  • β = Cut-off ratio during constant pressure heat addition

This cycle is considered more practical because it closely represents real engine conditions.

Factors Affecting Efficiency of Air-Standard Cycle

  1. Compression Ratio:
    Higher compression ratios increase the pressure and temperature of air before combustion, leading to higher thermal efficiency.
  2. Specific Heat Ratio (γ):
    Higher γ values (Cp/Cv) lead to higher efficiency. For air, γ is approximately 1.4.
  3. Cut-off Ratio (for Diesel and Dual Cycles):
    Larger cut-off ratios decrease efficiency because more heat is rejected.
  4. Type of Cycle:
    For the same compression ratio, the Otto cycle is the most efficient, followed by the Dual cycle and then the Diesel cycle.

Comparison of Efficiencies

At the same compression ratio:

This is because, in the Otto cycle, all the heat is added at constant volume, producing higher temperatures and greater work output for the same amount of heat supplied.

Importance of Air-Standard Efficiency

  • It helps in evaluating theoretical limits of engine performance.
  • Provides a basis for comparing different types of engine cycles.
  • Useful for designing and optimizing engines for better thermal performance.
  • Helps engineers understand how factors like compression ratio and heat addition affect power and fuel consumption.
Conclusion

The efficiency of an air-standard cycle defines how effectively the cycle converts heat energy into mechanical work. It depends mainly on the compression ratio, type of cycle, and specific heat ratio. The Otto cycle provides the highest theoretical efficiency for the same compression ratio, while Diesel and Dual cycles follow. Understanding air-standard cycle efficiency helps engineers in designing engines that deliver higher power output with better fuel economy and reduced energy losses.