Review
The Rankine cycle is a thermodynamic cycle that is used in power plants to generate electricity. It is also used as a standard to rate the performance of steam power plants.
In thermal power plant, energy conversion takes place by employing various processes. All the processes are interconnected sequentially, thus forming a thermodynamic cycle.
The simplest of such cycles is shown in the schematic below.
Schematic flow diagram of a Power Plant Cycle
All power plants convert some form of easily and naturally available energy in to electrical energy. In thermal power plant, Water is the working fluid. The source of energy is Chemical Energy of fuel.
In thermal power plant, sequence of energy conversion is:
Following figure shows how a unit mass of working fluid, undergoes various external heat and work interactions in executing a power cycle. Since the fluid is undergoing cyclic process, there is no net change in its internal energy over the cycle. The net energy transferred to the fluid as heat in the cycle is equal to net energy transferred as work from fluid.
The following figure shows the cyclic heat engine operating on the vapour power cycle, where the working substance, water, follows Boiler – Turbine – Condenser – Pump path interacting externally as shown, and converting net heat input to net work output continuously.
By the first law,
Σ Q net = Σ W net
cycle cycle
Q1 – Q2 = WT – WP
Where Q1 – Heat transferred to working fluid, in Boiler
Q2 – Heat rejected by working fluid, in Condenser
WT – Work transferred from working fluid, in Turbine
WP – Work transferred to working fluid, in Pump.
The efficiency of the cycle = Wnet /Q1
= (Q1- Q2)/Q1
= 1- Q2 / Q1
The cycle described above is called Rankine Cycle. In every process of the cycle, energy conversion is taking place. After every conversion, state of Water ( i.e. of working fluid) change. These changes are analyzed graphically on different coordinate systems.
One such graphical analysis is called P- V plane, where P stands for Pressure and is plotted on Y-Axis
and V stands for Volume, which is plotted on X-Axis. Most widely used graphical analysis is called T- S plane, where T stands for temperature and is plotted on Y- Axis and S stands for Entropy, which is plotted on X-Axis. Through these plots, the work output, rejected energy etc. can be analyzed.
The cycle is demonstrated graphically below.
For unit mass of water :
In Boiler :
h4 + Q1= h1
Q1 = h1- h4, Increase in enthalpy of water from h4 to h1 due to heating.
In Turbine :
h1 = WT + h2
WT = h1- h2, Enthalpy drop from h1 to h2, difference converted to work
In Condenser :
h2= Q2 + h3
Q2= h2-h3, Rejection of Heat energy (condensation of steam to water)
In Pump :
h3+Wp= h4
Wp= h4- h3, Pump work added to raise water Pressure.
The efficiency of Rankine Cycle is then given by
η = (WT – Wp ) / Q1 = { (h1- h2) – (h4-h3) } / (h1-h4)
Steam rate = 3600 / (WT – Wp)
The efficiency of Rankine Cycle is represented on T-S diagram as shown in figure.
Q1 is proportional to area bounded by points 1,5,6,4.
Q2 is proportional to area bounded by points 2,5,6,3.
Net work is proportional to area bounded by points 1,2,3, 4.
