Thermal Efficiency of the Rankine Cycle (η thermal) is the ratio between the work produced by the Steam Turbine which has been reduced by the pump work (W out – W in), and the heat energy that enters from the boiler (Q in). Before further discussing the Thermal Efficiency of the Rankine Cycle, it is easier for us to understand by discussing the processes that occur in it.
The Rankine Cycle is a form of energy engineering to take advantage of the Law of Conservation of Energy. The abundant energy sources on earth are used to be converted into other forms of energy that are more beneficial to humans. The energy used early in the Rankine Cycle process is heat energy. This heat energy can be taken from the combustion of fossil fuels, the use of geothermal energy, or from nuclear reactions.
The heat energy from the above sources is transferred to the working fluid, such as water for example. If the fuel used is coal, this process occurs in the boiler. Through the T-S diagram above this process takes place on the D-E-A-F line. The D-E line of water is still liquid, on the E-A line the water undergoes a boiling process and has a mixed phase of water and steam, while on the A-F line the water working fluid has a water vapor phase and undergoes a further heating process to reach the Superheated point.
And the heating value absorbed by water vapor can be calculated using the following formula:
Q in = m. (HF – hD)
Superheated water vapor from the Boiler then enters the Steam Turbine to undergo the conversion of heat energy into motion energy. Water vapor has decreased Enthalpy during the conversion process of heat energy into motion energy, shown by the F-G line in the image above. The reduction in Enthalpy (h) can be used to calculate the amount of energy generated by the turbine using the following formula:
W out = m. (HF – hG)
The water vapor that comes out of the Steam Turbine enters the Condenser to be converted back into liquid phase. Here we can see that there is heat energy which is not completely converted into motion energy in the Steam Turbine, because this energy is used to change the phase of water into water vapor (latent heat). The condensed water vapor has an Enthalpy drop (G-C line) and the decrease can be used to calculate the heat energy released using the following formula:
Q out = m. (HG – hC)
The next process is the water from the condensation is pumped to increase its pressure before it enters the boiler. In the process indicated by the C-D line, the water did not experience much increase in the Enthalpy value. This means that the energy given to water is not very significant. The energy value entered can be calculated using the following formula:
W in = m. (HD – hC)
So the elaboration of the Rankine Cycle Thermal Efficiency formula is:
η thermal = (W out – W in) / Q in
To make it easier to calculate, the mass variable (m) can be omitted in each equation, because in the final calculation the Thermal Efficiency these variables share.