Rankine cycle

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The Rankine cycle is an idealized
thermodynamic cycle A thermodynamic cycle consists of a linked sequence of thermodynamic processes that involve transfer of heat and work into and out of the system, while varying pressure, temperature, and other state variables within the system, and that eventual ...
describing the process by which certain
heat engine In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, radiation, and physical properties of matter. The behavior of these quantities is gove ...

s, such as
steam turbine A steam turbine is a device that extracts thermal energy from pressurized steam and uses it to do Work (physics), mechanical work on a rotating output shaft. Its modern manifestation was invented by Charles Algernon Parsons, Charles Parsons in 188 ...
s or reciprocating steam engines, allow mechanical work to be extracted from a fluid as it moves between a heat source and
heat sink File:Laptop Heatsink.jpg, 330px, Typical heatsink-fan combination found on a consumer laptop. The heatpipes which contain a working fluid make direct contact with the CPU and GPU, conducting heat away from the component and transferring it to the f ...

. The Rankine cycle is named after
William John Macquorn Rankine William John Macquorn Rankine (; 5 July 1820 – 24 December 1872) was a Scottish mechanical engineer who also contributed to civil engineering Civil engineering is a Regulation and licensure in engineering, professional engineering disciplin ...
, a Scottish
polymath A polymath ( el, πολυμαθής, ', "having learned much"; Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rom ...

professor at
Glasgow University , image_name = University_of_Glasgow_Coat_of_Arms.jpg , image_size = 150px , latin_name = Universitas Glasguensis , motto = la, Via, Veritas, Vita ''Via et veritas et vita'' (, ) is a Latin language, Latin phrase meaning "the way and the t ...
. Heat energy is supplied to the system via a
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where the
working fluid For fluid power, a working fluid is a gas or liquid A liquid is a nearly incompressible fluid In physics, a fluid is a substance that continually Deformation (mechanics), deforms (flows) under an applied shear stress, or external force ...
(typically water) is converted to a high pressure gaseous state (steam) in order to turn a
turbine A turbine ( or ) (from the Greek , ''tyrbē'', or Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Lat ...

. After passing over the turbine the fluid is allowed to condense back into a liquid state as waste heat energy is rejected before being returned to boiler, completing the cycle. Friction losses throughout the system are often neglected for the purpose of simplifying calculations as such losses are usually much less significant than thermodynamic losses, especially in larger systems.

# Description

The Rankine cycle closely describes the process by which steam engines commonly found in thermal harness the thermal energy of a fuel or other heat source to generate electricity. Possible heat sources include combustion of fossil fuels such as
coal Coal is a combustible black or brownish-black sedimentary rock, formed as rock strata (Argentina Argentina (), officially the Argentine Republic ( es, link=no, República Argentina), is a country located mostly in the southern half o ...

,
natural gas Natural gas (also called fossil gas; sometimes just gas) is a naturally occurring hydrocarbon gas mixture consisting of methane and commonly including varying amounts of other higher alkanes, and sometimes a small percentage of carbon dioxide ...

, or
oil An oil is any nonpolar chemical substance A chemical substance is a form of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can b ...
, renewable fuels like
biomass Biomass is plant or animal material used as fuel to produce electricity or heat. Examples are wood, energy crops and waste from forests, yards, or farms. Since biomass technically can be used as a fuel directly (e.g. wood logs), some people use t ...
or
ethanol Ethanol (also called ethyl alcohol, grain alcohol, drinking alcohol, or simply alcohol) is an organic Organic may refer to: * Organic, of or relating to an organism, a living entity * Organic, of or relating to an anatomical organ (anatomy), o ...

,
nuclear fission Nuclear fission is a reaction Reaction may refer to a response (disambiguation), response to an action, event, or exposure. Examples: *Adverse drug reaction *Allergy, Allergic reaction *Chemical reaction *Chain reaction (disambiguation) *Comment ...

, and
concentrated solar power Concentrated solar power (CSP, also known as concentrating solar power, concentrated solar thermal) systems generate solar power Solar power is the energy transformation, conversion of energy from sunlight into electricity, either direct ...
. Common heat sinks include ambient air above or around a facility and bodies of water such as rivers, ponds, and oceans. The ability of a Rankine engine to harness energy depends on the relative temperature difference between the heat source and heat sink. The greater the differential, the more mechanical power can be efficiently extracted out of heat energy, as per Carnot's theorem. The efficiency of the Rankine cycle is limited by the high heat of vaporization of the working fluid. Unless the pressure and temperature reach super critical levels in the boiler, the temperature range that the cycle can operate over is quite small: Steam turbine entry temperatures are typically around 565 °C and condenser temperatures are around 30 °C. This gives a theoretical maximum
Carnot efficiency Carnot's theorem, developed in 1824 by Nicolas Léonard Sadi Carnot, also called Carnot's rule, is a principle that specifies limits on the maximum efficiency any heat engine can obtain. The efficiency of a Carnot engine depends solely on the tempe ...

for the turbine alone of about 63.8% compared with an actual overall thermal efficiency of less than 50% for typical power stations. This low steam turbine entry temperature (compared to a
gas turbine A gas turbine, also called a combustion turbine, is a type of Internal combustion engine#Continuous combustion, continuous and internal combustion engine. The main elements common to all gas turbine engines are: * an upstream rotating gas compress ...
) is why the Rankine (steam) cycle is often used as a bottoming cycle to recover otherwise rejected heat in combined-cycle gas turbine power stations. Rankine engines generally operate in a closed loop where the working fluid is reused. The water
vapor In physics, a vapor (American English American English (AmE, AE, AmEng, USEng, en-US), sometimes called United States English or U.S. English, is the set of varieties of the English language native to the United States. Currently, America ...
with condensed droplets often seen billowing from power stations is created by the cooling systems (not directly from the closed-loop Rankine power cycle). This 'exhaust' heat is represented by the "Qout" flowing out of the lower side of the cycle shown in the T–s diagram below.
Cooling tower A cooling tower is a heat rejection device that rejects waste heat Waste heat is heat that is produced by a machine, or other process that uses energy, as a byproduct of doing Work (thermodynamics), work. All such processes give off some wa ...
s operate as large heat exchangers by absorbing the latent
heat of vaporization The enthalpy of vaporization (symbol ), also known as the (latent) heat of vaporization or heat of evaporation, is the amount of energy (enthalpy) that must be added to a liquid substance to transform a quantity of that substance into a gas. Th ...
of the working fluid and simultaneously evaporating cooling water to the atmosphere. While many substances can be used as the working fluid, water is usually chosen for its simple chemistry, relative abundance, low cost, and
thermodynamic propertiesIn thermodynamics, a physical property is any property that is measurable, and whose value describes a state of a physical system. Thermodynamic properties are defined as characteristic features of a system, capable of specifying the system's state. ...
. By condensing the working steam vapor to a liquid the pressure at the turbine outlet is lowered and the energy required by the feed pump consumes only 1% to 3% of the turbine output power and these factors contribute to a higher efficiency for the cycle. The benefit of this is offset by the low temperatures of steam admitted to the turbine(s).
Gas turbine A gas turbine, also called a combustion turbine, is a type of continuous Continuity or continuous may refer to: Mathematics * Continuity (mathematics), the opposing concept to discreteness; common examples include ** Continuous probability dis ...
s, for instance, have turbine entry temperatures approaching 1500 °C. However, the thermal efficiency of actual large steam power stations and large modern gas turbine stations are similar.

# The four processes in the Rankine cycle

There are four processes in the Rankine cycle. The states are identified by numbers (in brown) in the T–s diagram. *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 1-2 is isentropic compression. *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. 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. Process 2-3 is constant pressure heat addition in boiler. *Process 3–4: The dry saturated vapour expands through a
turbine A turbine ( or ) (from the Greek , ''tyrbē'', or Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Lat ...

, 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. Process 3-4 is isentropic expansion. *Process 4–1: The wet vapour then enters a Surface condenser, condenser, where it is condensed at a constant pressure to become a Boiling point, saturated liquid. Process 4-1 is constant pressure heat rejection in condenser. In an ideal Rankine cycle the pump and turbine would be isentropic, i.e., the pump and turbine would generate no entropy and hence maximize the net work output. Processes 1–2 and 3–4 would be represented by vertical lines on the T–s diagram and more closely resemble that of the Carnot cycle. The Rankine cycle shown here prevents the state of the working fluid from ending up in the superheated vapor region after the expansion in the turbine, which reduces the energy removed by the condensers. The actual vapor power cycle differs from the ideal Rankine cycle because of irreversibilities in the inherent components caused by fluid friction and heat loss to the surroundings; fluid friction causes pressure drops in the boiler, the condenser, and the piping between the components, and as a result the steam leaves the boiler at a lower pressure; heat loss reduces the net work output, thus heat addition to the steam in the boiler is required to maintain the same level of net work output.

# Equations

In general, the efficiency of a simple rankine cycle can be written as : $\eta_\text = \frac \approx \frac.$ Each of the next four equations is derived from the energy and mass balance for a control volume. $\eta_\text$ 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, it can be simplified. : $\frac = h_3 - h_2,$ : $\frac = h_4 - h_1,$ : $\frac = h_2 - h_1,$ : $\frac = h_3 - h_4.$ When dealing with the efficiencies of the turbines and pumps, an adjustment to the work terms must be made: :$\frac = h_2 - h_1 \approx \frac = \frac,$ :$\frac = h_3-h_4 \approx \left(h_3 - h_4\right) \eta_\text.$

# Real Rankine cycle (non-ideal)

In a real power-plant cycle (the name "Rankine" cycle is used only for the ideal cycle), the compression by the pump and the expansion in the
turbine A turbine ( or ) (from the Greek , ''tyrbē'', or Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Lat ...

are not isentropic. In other words, these processes are non-reversible, and entropy is increased during the two processes. This somewhat increases the power (physics), power required by the pump and decreases the power generated by the turbine. 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 life of turbine blades and efficiency of the turbine. The easiest way to overcome this problem is by superheating the steam. On the T–s diagram above, state 3 is at a border of the 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 (and up) in the diagram and hence produce a drier steam after expansion.

# Variations of the basic Rankine cycle

The overall thermodynamic efficiency can be increased by raising the average heat input temperature :$\bar_\text = \frac$ of that cycle. Increasing the temperature of the steam into the superheat region is a simple way of doing this. There are also variations of the basic Rankine cycle designed to raise the thermal efficiency of the cycle in this way; two of these are described below.

## Rankine cycle with reheat

The purpose of a reheating cycle is to remove the moisture carried by the steam at the final stages of the expansion process. In this variation, two
turbine A turbine ( or ) (from the Greek , ''tyrbē'', or Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Lat ...

s work in series. The first accepts vaporization, vapor from the
boiler Poland Poland ( pl, Polska ), officially the Republic of Poland ( pl, Rzeczpospolita Polska, links=no ), is a country located in Central Europe. It is divided into 16 Voivodeships of Poland, administrative provinces, covering an area of , ...
at high pressure. After the vapor has passed through the first turbine, it re-enters the boiler and is reheated before passing through a second, lower-pressure, turbine. The reheat temperatures are very close or equal to the inlet temperatures, whereas the optimal reheat pressure needed is only one fourth of the original boiler pressure. Among other advantages, this prevents the vapor from condensation, condensing during its expansion and thereby reducing the damage in the turbine blades, and improves the efficiency of the cycle, because more of the heat flow into the cycle occurs at higher temperature. The reheat cycle was first introduced in the 1920s, but was not operational for long due to technical difficulties. In the 1940s, it was reintroduced with the increasing manufacture of high-pressure
boiler Poland Poland ( pl, Polska ), officially the Republic of Poland ( pl, Rzeczpospolita Polska, links=no ), is a country located in Central Europe. It is divided into 16 Voivodeships of Poland, administrative provinces, covering an area of , ...
s, and eventually double reheating was introduced in the 1950s. The idea behind double reheating is to increase the average temperature. It was observed that more than two stages of reheating are generally unnecessary, since the next stage increases the cycle efficiency only half as much as the preceding stage. Today, double reheating is commonly used in power plants that operate under supercritical pressure.

## 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. On the diagram shown, the fluid at 2 is mixed with the fluid at 4 (both at the same pressure) to end up with the saturated liquid at 7. This is called "direct-contact heating". The Regenerative Rankine cycle (with minor variants) is commonly used in real power stations. Another variation sends ''bleed steam'' from between turbine stages to feedwater heaters to preheat the water on its way from the condenser to the boiler. These heaters do not mix the input steam and condensate, function as an ordinary tubular heat exchanger, and are named "closed feedwater heaters". Regeneration increases the cycle heat input temperature by eliminating the addition of heat from the boiler/fuel source at the relatively low feedwater temperatures that would exist without regenerative feedwater heating. This improves the efficiency of the cycle, as more of the heat flow into the cycle occurs at higher temperature.

# Organic Rankine cycle

The organic Rankine cycle (ORC) uses an organic fluid such as pentane, n-pentane or toluene in place of water and steam. This allows use of lower-temperature heat sources, such as solar ponds, which typically operate at around 70–90 °C.Nielsen et al., 2005, Proc. Int. Solar Energy Soc. The Thermodynamic efficiency, 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. Alternatively, fluids can be used that have boiling points above water, and this may have thermodynamic benefits (See, for example, mercury vapour turbine). The working fluids, properties of the actual working fluid have great influence on the quality of steam (vapour) after the expansion step, influencing the design of the whole cycle. The Rankine cycle does not restrict the working fluid in its definition, so the name "organic cycle" is simply a marketing concept and the cycle should not be regarded as a separate thermodynamic cycle.

# Supercritical Rankine cycle

The Rankine cycle applied using a supercritical fluid combines the concepts of heat regeneration and supercritical Rankine cycle into a unified process called the regenerative supercritical cycle (RGSC). It is optimised for temperature sources 125–450 °C.