Engine Cycles

Air-Standard Cycle Assumptions:

The actual cycle is rather more complicated so we deduce it by considering following assumptions:

• The working fluid is air which continuously flow in a closed loop and act as ideal gas.
• All process are internally reversible.
• Combustion process is replaced by Heat addition process.
• Exhaust process is replaced by Heat rejection process.

Here we are discussing 4 main cycles, namely:

1. Otto Cycle or Constant Volume Heat Addition Cycle
2. Diesel Cycle or Constant Pressure Heat Addition Cycle 
3. Dual Cycle
4. Brayton Cycle

1. Otto Cycle or Constant Volume Heat Addition Cycle:

The information about the diagram is given by:

• 1 ➤ 2: Isentropic Compression 
• 2 ➤ 3: Constant Volume Heat Addition 
• 3 ➤ 4: Isentropic Expansion 
• 4 ➤ 1: Constant Volume Heat Rejection

A. Efficiency of Otto Cycle:

The efficiency of Otto Cycle is given by clicking the picture below:

B. Work Output of Otto Cycle:

The work output of Otto Cycle is given by:

C. Mean Effective Pressure:

The ratio of Work Output to the change in volume of the cylinder that means swept volume is called Mean Effective Pressure. MEP of Otto Cycle is given by:

2. Diesel Cycle or Constant Pressure Heat Addition Cycle:

The figure shows:

• 1 ➤ 2: Isentropic Compression 
• 2 ➤ 3: Constant Pressure Heat Addition 
• 3 ➤ 4: Isentropic Expansion 
• 4 ➤ 1: Constant Volume Heat Rejection

A. Efficiency of Diesel Cycle:

The efficiency of Otto Cycle is given by clicking the picture below:

B. Work Output of Diesel Cycle:

The work output is given by:

C. Mean Effective Pressure:

Mean Effective Pressure is the ratio of work output to the swept volume. The mean effective pressure is given by:

3. Dual Cycle or Mixed Cycle:

The figure shows:

• 1 ➤ 2: Isentropic Compression 
• 2 ➤ 3: Constant Volume Heat Addition
• 3 ➤ 4: Constant Pressure Heat Addition
• 4 ➤ 5: Isentropic Expansion
• 5 ➤ 1: Constant Volume Heat Rejection

A. Efficiency of Dual Cycle:

Efficiency is the ratio of work output and the heat input. Thermal efficiency of Dual Cycle is given by:

B. Work Output:

Work Output for Dual Cycle or Mixed Cycle is given by:

C. Mean Effective Pressure:

It is the ratio of work output to the change in volume that is swept volume. The mean effective pressure is given by:

Comparison Of Cycles (Otto, Diesel & Dual):

1. Same Compression Ratio & Heat Addition:

Since, Qout (4 → 1) in Otto Cycle is lesser than Qout (4' → 1) in diesel cycle, therefore

ηotto > ηdual > ηdiesel

2. Same Compression Ratio & Heat Rejection:

 Since, Qin (2 → 3) in Otto Cycle is greater than Qin (2 → 3') in diesel cycle, therefore

ηotto > ηdual > ηdiesel

3. Same Peak Pressure, Peak Temperature & Heat Rejection:

Since, Qin (2 → 3) in Otto Cycle is lesser than Qin (2 → 3') in diesel cycle, therefore

ηotto < ηdual < ηdiesel

4. Same Maximum Pressure & Heat Input:

Since, Qout (4 → 1) in Otto Cycle is greater than Qout (4' → 1) in diesel cycle, therefore

ηotto < ηdual < ηdiesel

5. Same Maximum Pressure & Work Output:

Since, Qout (4 → 1) in Otto Cycle is greater than Qout (4' → 1) in diesel cycle, therefore

ηotto < ηdual < ηdiesel

4. Brayton Cycle:

The figure shows:

• 1 ➤ 2: Isentropic Compression 
• 2 ➤ 3: Constant Pressure Heat Addition 
• 3 ➤ 4: Isentropic Expansion 
• 4 ➤ 1: Constant Pressure Heat Rejection

Brayton cycle is completely explained in the video given below:

Efficiency of Brayton Cycle:

Efficiency is the ratio of work output to the heat input. The efficiency of Brayton Cycle is given by:

Brayton Cycle with Regeneration:

The exhaust gas leaving the turbine (state 4) is higher than the temperature of the gas leaving the compressor.

Therefore heat can be transferred from the exhaust gases to the high pressure gas leaving the compressor using a Counter-Flow Heat Exchanger called Regenerator.  

The extent to which regenerator reaches an ideal regenerator is called the Effectiveness ϵ, which is given by:

When cold-air standard assumptions are utilized, it reduces to

References:

• University notes + my knowledge.
• Videos from YouTube.
• Images from Google Images.
• Book: IC Engines by V Ganesan (4th Edition).
• Class Lectures.