Lesson 7.5: Vapor & Gas Power Cycles (Rankine, Brayton, Otto, Diesel, Dual)

Understanding vapor and gas power cycles is critical for mechanical engineering exams. GATE and PSU often test cycle analysis, efficiency, work output, and thermal efficiency formulas.

🔹 1. Introduction

• Definition: A thermodynamic cycle in which working fluid undergoes a series of processes and returns to its initial state

• Applications: Steam power plants, gas turbines, IC engines, combined cycle power plants

• Key Concepts: Work output, heat input, thermal efficiency, ideal vs real cycles

🔹 2. Rankine Cycle (Vapor Power Cycle)

• Used in: Steam power plants

• Components: Boiler, Turbine, Condenser, Pump

• Process:

  1. Pump (liquid compressed)

  2. Boiler (heat added, vaporization)

  3. Turbine (expansion, work output)

  4. Condenser (condensation, heat rejection)

• Thermal Efficiency:

ηth=WnetQin=Wturbine−WpumpQin\eta_\text{th} = \frac{W_\text{net}}{Q_\text{in}} = \frac{W_\text{turbine} – W_\text{pump}}{Q_\text{in}}ηth​=Qin​Wnet​​=Qin​Wturbine​−Wpump​​

🔹 3. Brayton Cycle (Gas Turbine Cycle)

• Used in: Jet engines, gas turbines

• Components: Compressor, Combustion chamber, Turbine

• Process:

  1. Isentropic compression

  2. Constant pressure heat addition

  3. Isentropic expansion

  4. Constant pressure heat rejection

• Thermal Efficiency:

ηth=1−1rpγ−1\eta_\text{th} = 1 – \frac{1}{r_p^{\gamma-1}}ηth​=1−rpγ−1​1​

Where rₚ = pressure ratio, γ = Cp/Cv

🔹 4. Otto Cycle (Spark Ignition Engine)

• Used in: Petrol engines

• Process: Adiabatic compression, constant volume heat addition, adiabatic expansion, constant volume heat rejection

• Thermal Efficiency:

ηth=1−1rγ−1\eta_\text{th} = 1 – \frac{1}{r^{\gamma-1}}ηth​=1−rγ−11​

Where r = compression ratio

🔹 5. Diesel Cycle (Compression Ignition Engine)

• Used in: Diesel engines

• Process: Adiabatic compression, constant pressure heat addition, adiabatic expansion, constant volume heat rejection

• Thermal Efficiency:

ηth=1−1rγ−1⋅ργ−1γ(ρ−1)\eta_\text{th} = 1 – \frac{1}{r^{\gamma-1}} \cdot \frac{\rho^\gamma – 1}{\gamma (\rho-1)}ηth​=1−rγ−11​⋅γ(ρ−1)ργ−1​

Where ρ = cutoff ratio

🔹 6. Dual Cycle (Combined SI & CI Engine)

• Used in: Engine design with part constant volume and part constant pressure heat addition

• Thermal Efficiency: Combination of Otto & Diesel formulas

• Applications: Advanced IC engine analysis

🔹 7. Solved Examples (PYQ Style)

1. Calculate work output and efficiency of Rankine cycle using boiler and condenser data

2. Determine thermal efficiency of Brayton cycle for given pressure ratio and temperatures

3. Compute Otto and Diesel cycle efficiencies for engines with given compression ratios

4. Analyze Dual cycle performance and mean effective pressure

🔹 8. Practice Exercises

1. Solve Rankine cycle problems for net work and heat rejection

2. Calculate Brayton cycle efficiency for varying pressure ratios

3. Determine engine efficiency for Otto and Diesel cycles

4. Compare thermal efficiencies of Otto, Diesel, and Dual cycles

5. Draw PV and TS diagrams for all cycles

🔹 9. Summary

• Rankine: Steam power plants, work = turbine – pump

• Brayton: Gas turbines, efficiency depends on pressure ratio

• Otto: Spark ignition engines, constant volume heat addition

• Diesel: Compression ignition engines, constant pressure heat addition

• Dual: Mixed SI & CI, used in advanced IC engines

• Exam Tip: Always draw PV & TS diagrams and use standard formulas for efficiency