How to Calculate Thermal Efficiency of Rankine Cycle
Rankine Cycle:
Before calculating Thermal Efficiency of Rankine cycle, let’s understand about Rankine Cycle. Rankine cycle is a theoretical cycle in which heat energy converts into work. Rankine Cycle is developed by William John Macquorn Rankine in the 19th century. It has been widely used across all kinds of steam engines.
Roles
1–2: Work Done by Turbine
2–3: Heat Rejection in Cooling Tower
3–4: Pump
4–1: Heat Addition in Boiler
Working Fluid in Rankine Cycle is water. Water goes through the following process in the Cycle. C-D, D-F, F-G, G-C are the defining process in Rankine Cycle.
- C-D Process: This is an isentropic process, where water is pumped from low pressure to high pressure with a Centrifugal Pump. This is a process where there is no change in entropy and water remains in liquid phase only.
- D-F Process: It happens inside a boiler. Water changes its phase from liquid to steam.
- F-G Process: The process occurs in Steam Turbine. The steam from the boiler enters the turbine and undergoes an isentropic-expansion process. The energy stored in water vapor converts to kinetic energy in the turbine.
- G-C Process: It is an Isobaric Compression process and happens in a Condenser. The phase change of the working fluid happens here from steam to water.
Calculation of Thermal Efficiency of Rankine Cycle:
Thermal Efficiency of Rankine Cycle: The thermal efficiency of the Rankine cycle is the ratio between the work produced by the steam turbine that has been reduced by the pump work, with the incoming heat energy from the boiler.
The heat energy from the fuel is transferred to the working fluid i.e. water. The calorific value absorbed by water vapor can be calculated using the following formula:
Qin = m (hF — hD)
The superheated steam produced by the boiler then goes to the steam turbine. Heat energy from water vapor is then converted into kinetic energy, shown by the F-G line in the image above. The reduction of the enthalpy can be used to calculate the magnitude of the motion energy produced by the steam turbine using the following formula:
Wout = m (hF — hG)
The steam coming out from the steam turbine enters the condenser to be condensed back into liquid phase. Here the heat energy not converted into kinetic energy, because the energy is used to convert the water into steam (latent heat). The decreases of the enthalpy (G-C line) can be used to calculate the thermal energy of condensed water using the following formula:
Qout = m (hG — hC)
In the next process, the condensate water is pumped to the boiler to increase its pressure. Shown by the C-D line, water does not experience much increase in enthalpy. This means that the energy given to the air is not too significant. Incoming energy values can be calculated using the following formula:
Win = m (hD — hC)
So now we can calculate the thermal efficiency by using the formula below:
Thermal Efficiency = [(Work Output — Work input)/Heat entered into the system]
Rankine cycle efficiency formula
Thermal Efficiency = [(Work Output — Work input)/Heat entered into the system]
Rankine Cycle Efficiency
Rankine Cycle Efficiency = [m (hF — hG) — m (hD — hC) ] / [m (hF — hD)]
Lets solve a Rankine Cycle Efficiency Problem
1. Identify Key Parameters:
- Turbine Inlet Temperature (T1): The temperature of the steam entering the turbine.
- Condenser Temperature (T2): The temperature of the steam exiting the turbine and entering the condenser.
- Boiler Pressure (P1): The pressure of the steam generated in the boiler.
- Condenser Pressure (P2): The pressure of the steam after condensation.
2. Determine Enthalpy Values:
- Use a steam table or online calculator to find the enthalpy values (h1, h2, h3, and h4) corresponding to the given temperatures and pressures at each stage of the cycle:
- h1: Enthalpy of steam at turbine inlet (P1, T1)
- h2: Enthalpy of steam at turbine outlet (P2, T2)
- h3: Enthalpy of water at condenser outlet (P2)
- h4: Enthalpy of water at boiler inlet (P1)
3. Calculate Net Work Output:
- Net work output (W_net) is the difference between the work done by the turbine and the work required by the pump: W_net = (h1 — h2) — (h4 — h3)
4. Calculate Heat Input:
- Heat input (Q_in) is the energy added to the water in the boiler to generate steam: Q_in = h1 — h4
5. Calculate Efficiency:
- Rankine cycle efficiency (η_Rankine) is the ratio of net work output to heat input: η_Rankine = W_net / Q_in = (h1 — h2 — h4 + h3) / (h1 — h4)
6. Express as a Percentage:
- Multiply the result by 100 to express efficiency as a percentage.
Example:
Assuming T1 = 500°C, T2 = 30°C, P1 = 10 MPa, and P2 = 0.1 MPa, and using typical steam table values:
- h1 = 3375 kJ/kg
- h2 = 2510 kJ/kg
- h3 = 125 kJ/kg
- h4 = 125 kJ/kg
Efficiency = [(3375–2510–125 + 125) / (3375–125)] * 100 = 25.54%
Additional Notes:
- Actual efficiency values for real-world power plants are often lower due to irreversible losses and inefficiencies in components.
- Increasing the temperature and pressure at the turbine inlet, lowering the condenser pressure, or using superheated steam can all improve efficiency.
- The rankine cycle is the fundamental thermodynamic cycle for most steam power plants, including those used for electricity generation.
Originally published at Merrykit.
