How to Calculate 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. Before further discussing the thermal efficiency of the rankine cycle, it is easier to understand by discuss the processes first.
The rankine cycle is one form of energy conservation laws. The source of energy that exists on earth is converted into another beneficial form of energy to humans. Heat energy is used as the energy source of the rankine cycle process. This energy can be taken from the burning of fossil fuels, geothermal usage, or from nuclear reactions.
The heat energy from the above sources is transferred to the working fluid, such as water. When the fuel used is coal then this process occurs in the boiler. Through the diagram above D-E-A-F, the D-E line, water is still in liquid form, on the E-A line boiling process occurs and the water phase is liquid and steam mixture, while on the A-F line the water working fluid has water-vapor phase and got further heating process to obtain superheated point. 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 motion 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 we can see there is amount of heat energy not converted into motion 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)
The next process is pumping the condensate water to increase its pressure before entering the boiler. 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:
What is Rankine Cycle? Rankine cycle is a theoritical cycle which converts heat energy into work. Developed by William John Macquorn Rankine in the 19th century, it has been widely used to steam engines. Currently, the rankine cycle is used in power plants and produces 90% of the world’s electricity.
Water becomes the closed-loop rankine cycle’s working fluid. It means that water at the end of the cycle process, back to use into the first step of the cycle. In the rankine cycle, this water undergoes four processes according to the image above:
C-D Process: The working fluid is pumped from low to high pressure, and in this process the working fluid is still at liquid phase. This process is called isentropic-compression because when pumped, ideally there is no entropy change.
D-F Process: High pressure water from C-D process, pumped into the boiler. Water is isobaric heated (constant pressure) at the boiler. Boiler use various heat sources from outside such as coal, diesel, or nuclear reactions. In the boiler, water undergoes a phase change from the liquid, a mixture of liquid and steam (saturated steam), and 100% dry vapor (superheated steam).
F-G Process: This process occurs in a steam turbine. The steam from the boiler enters the turbine and undergoes an isentropic-expansion process. The energy stored in water vapor is converted to motion energy in the turbine.
G-C Process: The steam coming out from the steam turbine enters the condenser to condensed at isobaric pressure. The steam changed its phase back to a liquid so it can be reused in the cycle process.
The cycle described through the T-S diagram above is the most basic and simple Rankine Cycle. In its practical use, there are several process modifications to obtain higher thermal efficiency. Such as the use of preheated water prior to entering the boiler, as well as the use of reheated steam from the first turbine (so called high-pressure turbine) so that it can be used again to enter the second steam turbine (intermediate pressure turbine).
In the illustration above, the condensate water pumped by the condensate extraction pump from the condenser, through the low pressure preheater system, before flowing to the deaerator/feedwater tank. As well as the water pumped by feedwater pump from the feedwater tank, also passing the high pressure preheater system before going to the boiler. The heat source used by the preheater is derived from the steam extraction taken from the steam turbine at certain stages.
Another difference with the conventional rankine cycle is the reheating of steam coming out from the high-pressure turbine by the reheater boiler to re-gain the superheater phase. The reheated steam than use as the energy source of the intermediate-pressure turbine.
There is also a bypass system, so steam not to be passed to the steam turbine. The superheater steam from the boiler does not enter the turbine and bypasses back into the reheater boiler. The steam coming out of the reheater boiler is bypassed for direct entry to the condenser. The function of this bypass system is as a protection system of the rankine cycle so that it can avoid severe damage. And also used at the beginning of the start-up process of the cycle system and even the process of turning it off.