Rankine cycle

The Rankine cycle is an idealized thermodynamic cycle that explains how certain heat engines, like steam turbines or steam engines, can produce mechanical work. It shows how a fluid, usually water, moves between a source of heat and a cooler area, known as a heat sink. This cycle is named after William John Macquorn Rankine, a Scottish polymath who was a professor at Glasgow University.

Physical layout of the Rankine cycle1. Pump, 2. Boiler, 3. Turbine, 4. Condenser

In this cycle, heat energy is added to the system in a boiler. Here, the water turns into high-pressure steam. This steam then flows over a turbine, making it spin and creating mechanical work. After passing through the turbine, the steam cools and condenses back into liquid water. The water then returns to the boiler to start the cycle again.

When studying the Rankine cycle, scientists often ignore small losses caused by friction. This makes calculations simpler because, in large systems, these losses are usually much smaller than the main energy losses from the thermodynamics of the cycle itself.

Description

The Rankine cycle is a way that steam engines in power plants turn heat from fuels or other sources into electricity. Heat sources can be burning fuels like coal, natural gas, and oil, using nuclear fission, or even using sunlight or heat from the Earth. The engine works best when there is a big difference between the hot source and the cooler place where the heat is released.

Water is usually used in these engines because it is easy to find and works well. The engine uses the same water over and over again in a closed loop. The steam you sometimes see coming from power plants is from the cooling system, not the main engine itself. This cycle helps turn heat into useful power in an efficient way.

The four processes in the Rankine cycle

T–s diagram of a typical Rankine cycle operating between pressures of 0.06 bar and 50 bar. Left from the bell-shaped curve is liquid, right from it is gas, and under it is saturated liquid–vapour equilibrium.

There are four steps in the Rankine cycle. These steps show how a heat engine, like a steam turbine, uses heat to create movement. You can see these steps on a special diagram called a T–s diagram.

In an ideal version of the Rankine cycle, everything works perfectly without losing any energy. Real machines are not perfect because of things like friction and heat loss, which make the process less efficient.

Successive processes of the Rankine cycle
Process	Summary	Explanation
1–2	Isentropic compression	The working fluid is pumped from low to high pressure. As the fluid is a liquid at this stage, the pump requires little input energy.
2–3	Constant pressure heat addition in boiler	The high-pressure liquid enters a boiler, where it is heated at constant pressure by an external heat source to become a dry saturated vapour. The input energy required can be easily calculated graphically, using an enthalpy–entropy chart (h–s chart, or Mollier diagram), or numerically, using steam tables or software.
3–4	Isentropic expansion	The dry saturated vapour expands through a turbine, generating power. This decreases the temperature and pressure of the vapour, and some condensation may occur. The output in this process can be easily calculated using the chart or tables noted above.
4–1	Constant pressure heat rejection in condenser	The wet vapour then enters a condenser, where it is condensed at a constant pressure to become a saturated liquid.

Variables

Q ˙ {\displaystyle {\dot {Q}}}	Heat flow rate to or from the system (energy per unit time)
m ˙ {\displaystyle {\dot {m}}}	Mass flow rate (mass per unit time)
W ˙ {\displaystyle {\dot {W}}}	Mechanical power consumed by or provided to the system (energy per unit time)
η therm {\displaystyle \eta _{\text{therm}}}	Thermodynamic efficiency of the process (net power output per heat input, dimensionless)
η pump , η turb {\displaystyle \eta _{\text{pump}},\eta _{\text{turb}}}	Isentropic efficiency of the compression (feed pump) and expansion (turbine) processes, dimensionless
h 1 , h 2 , h 3 , h 4 {\displaystyle h_{1},h_{2},h_{3},h_{4}}	The "specific enthalpies" at indicated points on the T–s diagram
h 4 s {\displaystyle h_{4s}}	The final "specific enthalpy" of the fluid if the turbine were isentropic
p 1 , p 2 {\displaystyle p_{1},p_{2}}	The pressures before and after the compression process

Equations

The thermodynamic efficiency of the Rankine cycle is how much work we get compared to the heat energy we put in. Because the pump needs only a little work—about 1% of what the turbine makes—it is easier to figure out.

The efficiency depends on the work from the turbine and the heat added. The equations show how heat and work change the fluid’s energy and mass as it moves through the system. They also change a little bit depending on how well the turbines and pumps work.

Real Rankine cycle (non-ideal)

Rankine cycle with superheat

In real power plants, the pump and the turbine do not work perfectly. This means the pump needs a little more power, and the turbine makes a little less power.

When the steam cools down, tiny bits of water can form and hit the turbine blades. This can hurt the blades over time. One way to help this is to heat the steam extra, called superheating, so there is less water when the steam spins the turbine.

Variations of the basic Rankine cycle

The efficiency of a heat engine can be improved by increasing the temperature at which heat is added. One way to do this is by heating the steam to a higher temperature, called superheating.

Rankine cycle with reheat

There are special versions of the basic Rankine cycle that help improve efficiency. In one version, called the Rankine cycle with reheat, two turbines are used. The first turbine uses high-pressure steam from the boiler. After this, the steam is heated again before entering a second turbine that works at a lower pressure. This helps prevent damage to the turbine and makes the cycle more efficient.

Another version is the Regenerative Rankine cycle. In this cycle, some steam from the hot part of the process is used to heat the water before it reaches the boiler. This preheating improves efficiency. This method is widely used in real power plants.

Organic Rankine cycle

Main article: Organic Rankine cycle

The organic Rankine cycle uses special liquids like n-pentane or toluene instead of water and steam. This helps it work with warmer heat sources, such as solar ponds, which are usually around 70 – 90 °C. These heat sources are warmer but not as hot, so the cycle is not as efficient. But it can be useful because it costs less to collect heat at these warmer temperatures. Some fluids used in this cycle can boil at higher temperatures than water, which can be helpful. The type of liquid used changes how well the cycle works and its design.

The Rankine cycle can use different liquids, so calling it an “organic cycle” is more of a name than a new kind of thermodynamic cycle.

Supercritical Rankine cycle

The Rankine cycle can use a supercritical fluid. This special version combines ideas of saving heat and using supercritical fluids in one process called the regenerative supercritical cycle (RGSC). It works best when the heat source is between 125–450 °C.