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The 'Rankine cycle' is a thermodynamic cycle. Like other thermodynamic cycles, the maximum efficiency of the Rankine cycle is given by calculating the efficiency of the Carnot cycle. It is named after William John Macquorn Rankine, a Scottish polymath.
This article will deal with the Rankine cycle from an engineering point of view.

Contents

Processes of the Rankine cycle

Description

Variables

Equations

Real Rankine cycle (non-ideal)

Variations of the basic Rankine cycle

Rankine cycle with reheat

Regenerative Rankine cycle

Reverse Rankine cycle

References

External links

Processes of the Rankine cycle

There are four processes in the Rankine cycle, each changing the state of the working fluid. These states are identified by number in the diagram to the right.

★ 'Process 1-2': 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.

★ 'Process 2-3': 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. Common heat sources for power plant systems are coal, natural gas, or nuclear power.

★ 'Process 3-4': The dry saturated vapour expands through a turbine generating power output usually orders of magnitude greater than the power required by the pump. This decreases the temperature and pressure of the vapour and some condensation may occur.

★ 'Process 4-1': The wet vapour then enters a condenser where it is cooled at a constant low pressure to become a saturated liquid. It is fully condensed to a liquid to minimise the work required by the pump.
In an ideal Rankine cycle the pump and turbine would be isentropic, i.e. the pump and turbine would generate no entropy and hence maximise the net work output. Processes 1-2 and 3-4 would be represented by vertical lines on the Ts diagram and more closely resemble the Ts diagram of the Carnot cycle.
The exposed Rankine cycle can also prevent vapour overheating , which reduces the amount of liquid condensed after the expansion in the turbine.

Description

Rankine cycles describe the operation of steam heat engines most commonly found in power generation plants. By taking advantage of the phase change of water (Mercury, ammonia and many other substances have also been used) the cycle can almost achieve iso-thermal heat addition and rejection. The cycle is sometimes referred to as a practical Carnot cycle as, when an efficient turbine is used, the Ts diagram will begin to closely resemble the Carnot cycle.
In gas turbines a significant fraction of the work generated by the turbine will go to driving the compressor and so limits net work output and efficiency. The Rankine cycle on the other hand does not face this problem. By condensing the steam to water, the work required by the pump will only consume approximately 1% of the turbine power and so give a much higher efficiency. As liquids are far less compressible they require only a fraction of the energy needed to compress a gas to the same pressure.
The efficiency of a Rankine cycle is usually limited by the working fluid. Without the pressure going super critical the temperature range the cycle can operate over is quite small, giving a maximum possible efficiency (Carnot efficiency) of around 50%. For this reason the Rankine cycle is often used as a bottoming cycle in combined cycle gas turbine power stations.
The working fluid in a Rankine cycle follows a closed loop and is re-used constantly. Water vapour seen billowing from power plants is evaporating cooling water, not working fluid. (Note that steam is invisible until it comes in contact with cool, saturated air, at which point it condenses and forms the white billowy clouds seen leaving cooling towers).

Variables

$dot\{Q\}$	Heat flow rate to/from the system(energy per unit time)
$dot\{m\}$	Mass flow rate (mass per unit time)
$dot\{W\}$	Mechanical power consumed/provided to the system (energy per unit time)
$eta$	Thermodynamic efficiency of the process (net power output per heat input, dimensionless)
$h\_1,\; h\_2,\; h\_3,\; h\_4$	The "specific enthalpies" at indicated points on the T-S diagram

Equations

Each of the first four equations are easily derived from the energy and mass balance for a control volume. The fifth equation defines the thermodynamic efficiency of the cycle as the ratio of net power output to heat input. As the work required by the pump is often around 1% of the turbine work output equation 5 can be simplified.
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Real Rankine cycle (non-ideal)

In a real Rankine cycle, the compression by the pump and the expansion in the turbine are not isentropic. In other words, these processes are non-reversible and entropy is increased during the two processes. This somewhat increases the power required by the pump and decreases the power generated by the turbine. It also makes calculations more involved and difficult.
In particular the efficiency of the steam turbine will be limited by water droplet formation. As the water condenses, water droplets hit the turbine blades at high speed causing pitting and erosion, gradually decreasing the efficiency of the turbine. The easiest way to overcome this problem is by superheating the steam. On the Ts diagram above, state 3 is above a two phase region of steam and water so after expansion the steam will be very wet. By superheating, state 3 will move to the right of the diagram and hence produce a dryer steam after expansion.

Variations of the basic Rankine cycle

Two main variations of the basic Rankine cycle are used in modern practice.

Rankine cycle with reheat

In this variation, two turbines work in series. The first accepts vapor from the boiler at high pressure. After the vapour has passed through the first turbine, it re-enters the boiler and is reheated before passing through a second, lower pressure turbine. Among other advantages, this prevents the vapour from condensing during its expansion which can seriously damage the turbine blades, and improves the efficiency of the cycle.
Another variation is where 'bleed steam' from between turbine stages is sent to feedwater heaters to preheat the water on its way from the condenser to the boiler.

Regenerative Rankine cycle

The regenerative Rankine cycle is so named because after emerging from the condenser (possibly as a subcooled liquid) the working fluid is heated by steam tapped from the hot portion of the cycle. This increases the average temperature of heat addition which in turn increases the thermodynamic efficiency of the cycle.
==Organic Rankine Cycle==
The Organic Rankine Cycle (ORC) uses organic fluids (such as pentane^[1] or butane^[2]) in place of water and steam. For example, this allows use of lower temperature heat sources such as solar ponds, which typically operated at around 70-90 °C^[3]. The efficiency of the cycle is much lower as a result of the lower temperature range, but this can be worthwhile, because of the lower cost involved in gathering heat at this lower temperature.

Reverse Rankine cycle

A Rankine cycle that is driven in reverse, via net work input, is the vapor-compression refrigeration cycle. Its purpose is to move heat, rather than produce work.

References

1. http://www.solar2006.org/presentations/tech_sessions/t38-A007.pdf
2. http://www.eere.energy.gov/troughnet/pdfs/batton_orc.pdf
3. Nielsen et al, 2005, Proc. Int. Solar Energy Soc.


★ '^'Van Wyllen 'Fundamentals of thermodynamics' (ISBN 85-212-0327-6)

★ Moran & Shapiro 'Fundamentals of Engineering Thermodynamics' (ISBN 0-471-27471-2)

★ Wikibooks Engineering Thermodynamics

External links

★ Rankine cycle on the Mathcad Application Server

★ Organic Rankine Cycle for electric power generation