How is efficiency calculated in the Rankine cycle?

Short Answer:

The efficiency of the Rankine cycle is calculated by comparing the net work output of the cycle to the heat input supplied to the boiler. It tells how effectively the cycle converts heat energy into useful mechanical work. The higher the efficiency, the better the performance of the power plant.

Mathematically, efficiency (η) is calculated using the formula:
η = (W_turbine – W_pump) / Q_boiler
This formula shows that the cycle’s efficiency depends on the amount of work produced by the turbine, the work consumed by the pump, and the heat added in the boiler.

Detailed Explanation:

Efficiency calculation in the Rankine cycle

The Rankine cycle is the standard thermodynamic cycle used in steam power plants to convert heat energy into mechanical energy and then into electricity. Like any energy system, it is important to know how much of the input energy is converted into useful work. This is measured by the thermal efficiency of the cycle.

In the Rankine cycle, heat is added in the boiler, and work is produced in the turbine. Some energy is lost during condensation and compression, and not all the heat can be converted into work due to thermodynamic limitations. The efficiency formula tells us what percentage of heat input is actually used to produce net work output.

Formula for Efficiency

The thermal efficiency of the Rankine cycle is:

η = (W_net) / Q_in

Where:

  • η = Thermal efficiency of the cycle
  • W_net = Net work output = W_turbine – W_pump
  • Q_in = Heat added in the boiler (Q_boiler)

So,
η = (W_turbine – W_pump) / Q_boiler

This is a simple ratio that gives the effectiveness of the cycle in using the input heat energy.

Work and Heat in the Cycle

Let us understand how each component contributes to the efficiency:

  1. Turbine Work (W_turbine)
    • Steam expands in the turbine from high pressure to low pressure.
    • This produces mechanical work.
    • The area under the curve on the T-s or h-s diagram represents this work.
  2. Pump Work (W_pump)
    • The feedwater pump increases the pressure of water before it enters the boiler.
    • This process consumes a small amount of work.
    • Subtracted from turbine work to get net work.
  3. Boiler Heat Input (Q_boiler)
    • Heat is added to water at high pressure to produce high-temperature steam.
    • This is the major input energy for the cycle.

Efficiency Based on Enthalpy

In practical problems, efficiency is calculated using enthalpy values (h) from steam tables or Mollier diagrams.

The formula becomes:

η = [(h₃ – h₄) – (h₂ – h₁)] / (h₃ – h₂)

Where:

  • h₁ = Enthalpy before pump
  • h₂ = Enthalpy after pump
  • h₃ = Enthalpy before turbine (high-pressure steam)
  • h₄ = Enthalpy after turbine (low-pressure steam)

This version helps engineers calculate efficiency accurately using data from actual steam conditions.

How to Improve Rankine Cycle Efficiency

  1. Increase Boiler Pressure and Temperature
    • Produces more high-quality steam and increases turbine output.
  2. Use Superheating
    • Increases the average temperature at which heat is added.
  3. Add Reheating
    • Reduces moisture content in the turbine and increases efficiency.
  4. Apply Regeneration
    • Preheats feedwater using steam extracted from the turbine, reducing heat needed in the boiler.
  5. Reduce Condenser Pressure
    • Makes more room for steam expansion, improving turbine work output.

All these methods aim to either increase net work or decrease heat input, thus boosting efficiency.

Importance of Efficiency Calculation

  • Performance Evaluation: Helps measure how good the cycle is in converting heat to work.
  • Fuel Saving: Higher efficiency means less fuel required for the same power.
  • Cost Reduction: Efficient cycles reduce operational costs and emissions.
  • Design Comparison: Allows engineers to compare different power plant designs.
Conclusion

Efficiency in the Rankine cycle is calculated by dividing the net work output by the heat input in the boiler. It reflects how well the cycle converts heat energy into useful work. By using enthalpy values from steam tables, we can determine the exact efficiency of any Rankine-based system. Improving this efficiency helps in saving energy, reducing costs, and making power plants more sustainable and effective.