The
Rankine cycle is a
thermodynamicIn physics, thermodynamics is the study of the conversion of energy into work and heat and its relation to macroscopic variables such as temperature, volume and pressure...
cycle which converts heat into work. The heat is supplied externally to a closed loop, which usually uses water as the working fluid. This cycle generates about 80% of all electric power used throughout the world, including virtually all solar thermal,
biomassBiomass, a renewable energy source, is biological material derived from living, or recently living organisms, such as wood, waste, and alcohol fuels. Biomass is commonly plant matter grown to generate electricity or produce heat. For example, forest residues , yard clippings and wood chips may be...
, coal and nuclear power plants. It is named after
William John Macquorn RankineWilliam John Macquorn Rankine FRS was a Scottish engineer and physicist. He was a founding contributor, with Rudolf Clausius and William Thomson , to the science of thermodynamics. Rankine developed a complete theory of the steam engine and indeed of all heat engines...
, a Scottish
polymathA polymath is a person whose expertise fills a significant number of subject areas. In less formal terms, a polymath may simply refer to someone who is very knowledgeable...
.
A Rankine cycle describes a model of the operation of steam heat engines most commonly found in power generation plants.
The
Rankine cycle is a
thermodynamicIn physics, thermodynamics is the study of the conversion of energy into work and heat and its relation to macroscopic variables such as temperature, volume and pressure...
cycle which converts heat into work. The heat is supplied externally to a closed loop, which usually uses water as the working fluid. This cycle generates about 80% of all electric power used throughout the world, including virtually all solar thermal,
biomassBiomass, a renewable energy source, is biological material derived from living, or recently living organisms, such as wood, waste, and alcohol fuels. Biomass is commonly plant matter grown to generate electricity or produce heat. For example, forest residues , yard clippings and wood chips may be...
, coal and nuclear power plants. It is named after
William John Macquorn RankineWilliam John Macquorn Rankine FRS was a Scottish engineer and physicist. He was a founding contributor, with Rudolf Clausius and William Thomson , to the science of thermodynamics. Rankine developed a complete theory of the steam engine and indeed of all heat engines...
, a Scottish
polymathA polymath is a person whose expertise fills a significant number of subject areas. In less formal terms, a polymath may simply refer to someone who is very knowledgeable...
.
Description
A Rankine cycle describes a model of the operation of steam heat engines most commonly found in power generation plants. Common heat sources for power plants using the Rankine cycle are the combustion of
coalCoal is a readily combustible black or brownish-black sedimentary rock normally occurring in rock strata in layers or veins called coal beds. The harder forms, such as anthracite coal, can be regarded as metamorphic rock because of later exposure to elevated temperature and pressure...
,
natural gasNatural gas is a gas consisting primarily of methane. It is found associated with fossil fuels, in coal beds, as methane clathrates, and is created by methanogenic organisms in marshes, bogs, and landfills...
,
oilAn oil is any substance that is liquid at ambient temperatures and is hydrophobic but soluble in organic solvents. Oils have a high carbon and hydrogen content and are nonpolar substances. The general definition above includes compound classes with otherwise unrelated chemical structures,...
, and
nuclear fissionNuclear power is power produced from controlled nuclear reactions. Commercial plants in use to date use nuclear fission reactions....
.
The Rankine cycle is sometimes referred to as a practical
Carnot cycleEvery thermodynamic system exists in a particular state. When a system is taken through a series of different states and finally returned to its initial state, a thermodynamic cycle is said to have occurred. In the process of going through this cycle, the system may perform work on its...
as, when an efficient turbine is used, the TS diagram will begin to resemble the Carnot cycle. The main difference is that heat addition and rejection are isobaric in the Rankine cycle and isothermal in the theoretical Carnot cycle. A pump is used to pressurize liquid instead of gas. This requires about 1/100th (1%) as much energy than that compressing a gas in a compressor (as in the
Carnot cycleEvery thermodynamic system exists in a particular state. When a system is taken through a series of different states and finally returned to its initial state, a thermodynamic cycle is said to have occurred. In the process of going through this cycle, the system may perform work on its...
).
The efficiency of a Rankine cycle is usually limited by the working fluid. Without the pressure reaching
super criticalIn physical chemistry, thermodynamics, chemistry and condensed matter physics, a critical point, also called a critical state, specifies the conditions at which a phase boundary ceases to exist...
levels for the working fluid, the temperature range the cycle can operate over is quite small: turbine entry temperatures are typically 565°C (the
creepCreep is the tendency of a solid material to slowly move or deform permanently under the influence of stresses. It occurs as a result of long term exposure to levels of stress that are below the yield strength of the material....
limit of stainless steel) and condenser temperatures are around 30°C. This gives a theoretical Carnot efficiency of around 63% compared with an actual efficiency of 42% for a modern coal-fired power station. This low turbine entry temperature (compared with a
gas turbineA gas turbine, also called a combustion turbine, is a rotary engine that extracts energy from a flow of combustion gas. It has an upstream compressor coupled to a downstream turbine, and a combustion chamber in-between. Energy is added to the gas stream in the combustor, where air is mixed with...
) is why the Rankine cycle is often used as a bottoming cycle in
combined cycle gas turbineA combined cycle is characteristic of a power producing engine or plant that employs more than one thermodynamic cycle. Heat engines are only able to use a portion of the energy their fuel generates . The remaining heat from combustion is generally wasted...
power stations.
The working fluid in a Rankine cycle follows a closed loop and is re-used constantly. The water
vaporA vapor or vapour is a substance in the gas phase at a temperature lower than its critical temperature....
and entrained droplets often seen billowing from power stations is generated by the cooling systems (not from the closed loop Rankine power cycle) and represents the waste heat that could not be converted to useful work. Note that cooling towers operate using the latent heat of vaporization of the cooling fluid. The white billowing clouds that form in
cooling towerCooling towers are heat removal devices used to transfer process waste heat to the atmosphere. Cooling towers may either use the evaporation of water to remove process heat and cool the working fluid to near the wet-bulb air temperature or rely solely on air to cool the working fluid to near the ...
operation are the result of water droplets which are entrained in the cooling tower airflow; it is not, as commonly thought, steam. While many substances could be used in the Rankine cycle, water is usually the fluid of choice due to its favorable properties, such as nontoxic and unreactive chemistry, abundance, and low cost, as well as its thermodynamic properties.
One of the principal advantages it holds over other cycles is that during the compression stage relatively little work is required to drive the pump, due to the working fluid being in its liquid phase at this point. By condensing the fluid to liquid, the work required by the pump will only consume approximately 1% to 3% of the turbine power and so give a much higher efficiency for a real cycle. The benefit of this is lost somewhat due to the lower heat addition temperature.
Gas turbineA gas turbine, also called a combustion turbine, is a rotary engine that extracts energy from a flow of combustion gas. It has an upstream compressor coupled to a downstream turbine, and a combustion chamber in-between. Energy is added to the gas stream in the combustor, where air is mixed with...
s, for instance, have turbine entry temperatures approaching 1500°C. Nonetheless, the efficiencies of steam cycles and gas turbines are fairly well matched.
Processes of the Rankine cycle
There are four processes in the Rankine cycle, 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 vapor.
- Process 3-4: The dry saturated vapor expands through a turbine
A turbine is a rotary engine that extracts energy from a fluid or air flow and converts it into useful work.The simplest turbines have one moving part, a rotor assembly, which is a shaft or drum, with blades attached. Moving fluid acts on the blades, or the blades react to the flow, so that they...
, generating power. This decreases the temperature and pressure of the vapor, and some condensation may occur.
- Process 4-1: The wet vapor then enters a condenser where it is condensed at a constant pressure and temperature to become a saturated liquid
The boiling point of an element or a substance is the temperature at which the vapor pressure of the liquid equals the environmental pressure surrounding the liquid....
. The pressure and temperature of the condenser is fixed by the temperature of the cooling coils as the fluid is undergoing a phase-changeA phase transition is a natural physical process. It has the characteristic of taking a given medium with given properties and transforming some or all of that medium, into a new medium with new properties. Phase transitions occur frequently and are found everywhere in the natural world...
.
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 Ts diagram and more closely resemble that of the Carnot cycle. The Rankine cycle shown here prevents the vapor ending up in the superheat region after the expansion in the turbine, which reduces the energy removed by the condensers.
Variables
| Heat flow rate to or from the system (energy per unit time) |
| Mass flow rate Mass flow rate is the mass of substance which passes through a given surface per unit time. Its unit is mass divided by time, so kilogram per second in SI units, and slug per second or pound per second in US customary units...
(mass per unit time) |
| Mechanical powerIn physics, power is the rate at which work is performed or energy is converted. It is an energy per unit of time. As a rate of change of work done or the energy of a subsystem, power iswhere P is power, W is work and t is time....
consumed by or provided to the system (energy per unit time) |
| Thermodynamic efficiency of the process (net power output per heat input, dimensionless) |
| Isentropic efficiency of the compression (feed pump) and expansion (turbine) processes, dimensionless |
| The "specific enthalpiesIn thermodynamics and molecular chemistry, the enthalpy is a thermodynamic property of a thermodynamic system. It can be used to calculate the heat transfer during a quasistatic process taking place in a closed thermodynamic system under constant pressure...
" at indicated points on the T-S diagram |
| The final "specific enthalpyIn thermodynamics and molecular chemistry, the enthalpy is a thermodynamic property of a thermodynamic system. It can be used to calculate the heat transfer during a quasistatic process taking place in a closed thermodynamic system under constant pressure...
" of the fluid if the turbine were isentropic |
| The pressures before and after the compression process |
Equations
Each of the first four equations is easily derived from the
energyIn physics, energy is a scalar physical quantity that describes the amount of work that can be performed by a force, an attribute of objects and systems that is subject to a conservation law...
and
mass balanceA mass balance is an application of conservation of mass to the analysis of physical systems. By accounting for material entering and leaving a system, mass flows can be identified which might have been unknown, or difficult to measure without this technique...
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.
Real Rankine cycle (non-ideal)
In a real Rankine cycle, the compression by the
pumpA pump is a device used to move fluids, such as gases, liquids or slurries. A pump displaces a volume by physical or mechanical action. One common misconception about pumps is the thought that they create pressure. Pumps alone do not create pressure; they only displace fluid, causing a flow. ...
and the expansion in the
turbineA turbine is a rotary engine that extracts energy from a fluid or air flow and converts it into useful work.The simplest turbines have one moving part, a rotor assembly, which is a shaft or drum, with blades attached. Moving fluid acts on the blades, or the blades react to the flow, so that they...
are not isentropic. In other words, these processes are non-reversible and
entropyEntropy is a concept of information maintaining great importance in physics, chemistry, and information theory...
is increased during the two processes. This somewhat increases the
powerIn physics, power is the rate at which work is performed or energy is converted. It is an energy per unit of time. As a rate of change of work done or the energy of a subsystem, power iswhere P is power, W is work and t is time....
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 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
The overall thermodynamic efficiency (of almost any cycle) can be increased by raising the average
heatIn physics and thermodynamics, heat is the process of energy transfer from one body or system due to thermal contact, which in turn is defined as an energy transfer to a body in any other way than due to work performed on the body....
input
temperatureIn physics, temperature is a physical property of a system that underlies the common notions of hot and cold; something that feels hotter generally has the higher temperature. Temperature is one of the principal parameters of thermodynamics...
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 which are designed to raise the thermal efficiency of the cycle in this way; two of these are described below.
Rankine cycle with reheat
In this variation, two
turbineA turbine is a rotary engine that extracts energy from a fluid or air flow and converts it into useful work.The simplest turbines have one moving part, a rotor assembly, which is a shaft or drum, with blades attached. Moving fluid acts on the blades, or the blades react to the flow, so that they...
s work in series. The first accepts
vaporVaporization of an element or compound is a phase transition from the liquid phase to gas phase. There are two types of vaporization: evaporation and boiling....
from the
boilerA boiler is a closed vessel in which water or other fluid is heated. The heated or vaporized fluid exits the boiler for use in various processes or heating applications.-Overview:-Materials:...
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. Among other advantages, this prevents the vapor from
condensingCondensation is the change of the physical state of aggregation of matter from gaseous phase into liquid phase and the reverse of evaporation. When the transition happens from the gaseous phase into the solid phase directly, bypassing the liquid phase, the change is called deposition...
during its expansion which can seriously damage the turbine blades, and improves the efficiency of the cycle.
Regenerative Rankine cycle
The regenerative Rankine cycle is so named because after emerging from the condenser (possibly as a
subcooled liquidSubcooled liquid is a liquid at a temperature lower than the saturation temperature at a given pressure. Compressed liquid is a synonymous term, but it stresses that the pressure is greater than the saturation pressure for the given temperature. Both terms have the same meaning...
) the working fluid is heated by
steamSteam is vaporized water. It is a transparent gas . At standard temperature and pressure, pure steam occupies about 1,600 times the volume of an equal mass of liquid water...
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. The Regenerative Rankine cycle (with minor variants) is commonly used in real power stations.
Another variation is where 'bleed steam' from between turbine stages is sent to
feedwater heaterA feedwater heater is a power plant component used to pre-heat water delivered to a steam generating boiler. Preheating the feedwater reduces the irreversibilities involved in steam generation and therefore improves the thermodynamic efficiency of the system...
s to preheat the water on its way from the condenser to the boiler.
Organic Rankine Cycle
The organic Rankine cycle (ORC) uses an organic fluid such as
n-pentanePentane is any or one of the organic compounds with the formula C
5H
12. This alkane is a component of some fuels and is employed as a specialty solvent in the laboratory. Its properties are very similar to those of butane and hexane...
or
tolueneToluene, also known as methylbenzene, or Toluol, is a clear water-insoluble liquid with the typical smell of paint thinners, reminiscent of the related compound benzene. It is an aromatic hydrocarbon that is widely used as an industrial feedstock and as a solvent...
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. 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. Alternatively, fluids can be used that have boiling points above water, and this may have thermodynamic benefits.
The Rankine cycle does not restrict the working fluid in its definition, so the inclusion of an "organic" cycle is simply a marketing concept that should not be regarded as a separate thermodynamic cycle.
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