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[[File:Dampfturbine Laeufer01.jpg|thumb|350px|A rotor of a modern steam turbine, used in a [[power plant]]]]
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.
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|Sir Charles Parsons]] in 1884.<ref>{{cite web|author=Encyclopædia Britannica |url=http://www.britannica.com/EBchecked/topic/444719/Sir-Charles-Algernon-Parsons |title=Sir Charles Algernon Parsons (British engineer) - Britannica Online Encyclopedia |publisher=Britannica.com |date=1931-02-11 |accessdate=2010-09-12}}</ref>


Because the turbine generates [[rotational motion|rotary motion]], it is particularly suited to be used to drive an [[Electric generator|electrical generator]]&nbsp;– about 90% of all electricity generation in the United States (1996) is by use of steam turbines.<ref Name="Wiser">{{cite book |title=Energy resources: occurrence, production, conversion, use|last= Wiser |first= Wendell H. |authorlink=  |year= 2000 |publisher= Birkhäuser |isbn= 978-0-387-98744-6 |page= 190 |url= http://books.google.com/books?id=UmMx9ixu90kC&pg=PA190&dq=electrical+power+generators+steam+percent&hl=en&ei=JppoTpVexNmBB4C72MkM&sa=X&oi=book_result&ct=result&resnum=2&ved=0CDgQ6AEwATgK#v=onepage&q=steam&f=false}}</ref>  The steam turbine is a form of [[heat engine]] that derives much of its improvement in [[thermodynamic efficiency]] through the use of multiple stages in the expansion of the steam, which results in a closer approach to the ideal [[Reversible process (thermodynamics)|reversible process]].
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==History==
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[[File:Curtis Steam Turbine.JPG|thumb|right|2000&nbsp;KW Curtis steam turbine circa 1905.]]The first device that may be classified as a reaction steam turbine was little more than a toy, the classic [[Aeolipile]], described in the 1st century by [[Greek mathematics|Greek]] mathematician [[Hero of Alexandria]] in [[Roman Egypt]].<ref>turbine. Encyclopædia Britannica Online</ref><ref name="New look" >A new look at Heron's 'steam engine'" (1992-06-25). Archive for History of Exact Sciences 44 (2): 107-124.</ref><ref name="O'Connor, Heron" >O'Connor, J. J.; E. E. Roberston (1999). Heron of Alexandria. MacTutor</ref>  In 1551, [[Taqi al-Din Muhammad ibn Ma'ruf|Taqi al-Din]] in [[Ottoman Egypt]] described a steam turbine with the practical application of rotating a [[Spit (cooking aide)|spit]].  Steam turbines were also described by the Italian [[Giovanni Branca]] (1629)<ref>"''[http://books.google.com/books?id=Cv9LH4ckuEwC&pg=PA432&dq&hl=en#v=onepage&q=&f=false Power plant engineering]''". P. K. Nag (2002). [[Tata McGraw-Hill]]. p.432. ISBN 978-0-07-043599-5</ref> and [[John Wilkins]] in England (1648).<ref>[http://www.history-science-technology.com/Notes/Notes%201.htm Taqi al-Din and the First Steam Turbine, 1551 A.D.], web page, accessed on line October 23, 2009; this web page refers to [[Ahmad Y Hassan]] (1976), ''Taqi al-Din and Arabic Mechanical Engineering'', pp. 34-5, Institute for the History of Arabic Science, [[University of Aleppo]].</ref> The devices described by al-Din and Wilkins are today known as [[steam jack]]s.
[[File:Wirnik turbiny parowej ORP Wicher.jpg|thumb|left|250px|Parsons turbine from the Polish destroyer [[ORP Wicher (1958)|ORP ''Wicher'']].]]


The modern steam turbine was invented in 1884 by [[Charles Algernon Parsons|Sir Charles Parsons]], whose first model was connected to a [[dynamo]] that generated 7.5&nbsp;kW (10&nbsp;hp) of electricity.<ref name="birrcastle.com">[http://www.birrcastle.com/steamTurbineAndElectricity.asp ]{{dead link|date=September 2010}}</ref> The invention of Parson's steam turbine made cheap and plentiful electricity possible and revolutionised marine transport and naval warfare.<ref>[http://www.universityscience.ie/pages/scientists/sci_charles_parsons.php ]{{dead link|date=September 2010}}</ref> His patent was licensed and the turbine scaled-up shortly after by an American, [[George Westinghouse]]. The Parsons turbine also turned out to be easy to scale up. Parsons had the satisfaction of seeing his invention adopted for all major world power stations, and the size of generators had increased from his first 7.5&nbsp;kW set up to units of 50,000&nbsp;kW capacity. Within Parson's lifetime the generating capacity of a unit was scaled up by about 10,000 times,<ref name="Parsons, Steam Turbine" >{{cite web
'''MathML'''
|title=The Steam Turbine
:<math forcemathmode="mathml">E=mc^2</math>
|url=http://www.history.rochester.edu/steam/parsons/part1.html
|last=Parsons  |first=Sir Charles A.  |authorlink=Charles A. Parsons
}}</ref> and the total output from turbo-generators constructed by his firm [[C. A. Parsons and Company]] and by their licensees, for land purposes alone, had exceeded thirty million horse-power.<ref name="birrcastle.com"/>


A number of other variations of turbines have been developed that work effectively with steam. The ''de Laval turbine'' (invented by [[Gustaf de Laval]]) accelerated the steam to full speed before running it against a turbine blade. Hence the (impulse) turbine is simpler, less expensive and does not need to be pressure-proof. It can operate with any pressure of steam, but is considerably less efficient.
<!--'''PNG''' (currently default in production)
[[File:AEG marine steam turbine (Rankin Kennedy, Modern Engines, Vol VI).jpg|thumb|left|250px|Cut away of an AEG marine steam turbine circa 1905]]
:<math forcemathmode="png">E=mc^2</math>
One of the founders of the modern theory of steam and gas turbines was also [[Aurel Stodola]], a Slovak physicist and engineer and professor at Swiss Polytechnical Institute (now [[ETH]]) in Zurich. His mature work was ''Die Dampfturbinen und ihre Aussichten als Wärmekraftmaschinen'' (English: The Steam Turbine and its perspective as a Heat Energy Machine) which was published in Berlin in 1903. In 1922, in Berlin, was published another important book ''Dampf und Gas-Turbinen'' (English: Steam and Gas Turbines).


The ''Brown-Curtis turbine'' which had been originally developed and patented by the U.S. company International Curtis Marine Turbine Company was developed in the 1900s in conjunction with [[John Brown & Company]]. It was used in John Brown's merchant ships and warships, including liners and Royal Navy warships.
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


==Types==
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].
[[File:Turbine generator systems1.png|thumb|right|400px|Schematic operation of a steam turbine generator system]]
Steam turbines are made in a variety of sizes ranging from small <0.75&nbsp;kW (1<&nbsp;hp) units (rare) used as mechanical drives for pumps, compressors and other shaft driven equipment, to 1,500,000&nbsp;kW (2,000,000&nbsp;hp) turbines used to generate electricity. There are several classifications for modern steam turbines.


===Steam supply and exhaust conditions===
==Demos==
These types include condensing, non-condensing, reheat, extraction and induction.


Condensing turbines are most commonly found in electrical power plants. These turbines exhaust steam in a partially condensed state, typically of a [[steam quality|quality]] near 90%, at a pressure well below atmospheric to a condenser.
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


Non-condensing or back pressure turbines are most widely used for process steam applications. The exhaust pressure is controlled by a regulating valve to suit the needs of the process steam pressure. These are commonly found at refineries, district heating units, pulp and paper plants, and [[desalination]] facilities where large amounts of low pressure process steam are available.


Reheat turbines are also used almost exclusively in electrical power plants. In a reheat turbine, steam flow exits from a high pressure section of the turbine and is returned to the boiler where additional superheat is added. The steam then goes back into an intermediate pressure section of the turbine and continues its expansion.
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Extracting type turbines are common in all applications. In an extracting type turbine, steam is released from various stages of the turbine, and used for industrial process needs or sent to boiler [[feedwater heater]]s to improve overall cycle efficiency.  Extraction flows may be controlled with a valve, or left uncontrolled.
==Test pages ==


Induction turbines introduce low pressure steam at an intermediate stage to produce additional power.
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
[[File:Dampfturbine Montage01.jpg|thumb|left|250px|Mounting of a steam turbine produced by [[Siemens]]]]
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===Casing or shaft arrangements===
*[[Inputtypes|Inputtypes (private Wikis only)]]
These arrangements include single casing, tandem compound and cross compound turbines. Single casing units are the most basic style where a single casing and shaft are coupled to a generator. Tandem compound are used where two or more casings are directly coupled together to drive a single generator. A cross compound turbine arrangement features two or more shafts not in line driving two or more generators that often operate at different speeds. A cross compound turbine is typically used for many large applications.
*[[Url2Image|Url2Image (private Wikis only)]]
 
==Bug reporting==
===Two-flow rotors===
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
[[File:Turbine power-plant hg.jpg|thumb|A two-flow turbine rotor. The steam enters in the middle of the shaft, and exits at each end, balancing the axial force.]]
The moving steam imparts both a tangential and axial thrust on the turbine shaft, but the axial thrust in a simple turbine is unopposed. To maintain the correct rotor position and balancing, this force must be counteracted by an opposing force. Either [[thrust bearings]] can be used for the shaft bearings, or the rotor can be designed so that the steam enters in the middle of the shaft and exits at both ends. The blades in each half face opposite ways, so that the axial forces negate each other but the tangential forces act together. This design of rotor is called '''two-flow''' or '''double-exhaust'''. This arrangement is common in low-pressure casings of a compound turbine.<ref name="phdengineer">{{cite web
| title = Steam Turbines (Course No. M-3006)
| url  = http://www.pdhengineer.com/Course%20Files/Completed%20Course%20PDF%20Files/Mechanical/Steam%20Turbines.pdf
| accessdate = 2011-09-22
| publisher = PhD Engineer
}}</ref>
 
==Principle of operation and design==
An ideal steam turbine is considered to be an [[isentropic process]], or constant entropy process, in which the entropy of the steam entering the turbine is equal to the entropy of the steam leaving the turbine. No steam turbine is truly isentropic, however, with typical isentropic efficiencies ranging from 20–90% based on the application of the turbine. The interior of a turbine comprises several sets of blades, or ''buckets'' as they are more commonly referred to. One set of stationary blades is connected to the casing and one set of rotating blades is connected to the shaft. The sets intermesh with certain minimum clearances, with the size and configuration of sets varying to efficiently exploit the expansion of steam at each stage.
 
=== Turbine efficiency ===
[[File:Turbines impulse v reaction.png|thumb|right|250px|Schematic diagram outlining the difference between an impulse and a 50% reaction turbine]]
To maximize turbine efficiency the steam is expanded, doing work, in a number of stages. These stages are characterized by how the energy is extracted from them and are known as either impulse or reaction turbines. Most steam turbines use a mixture of the reaction and impulse designs: each stage behaves as either one or the other, but the overall turbine uses both. Typically, higher pressure sections are impulse type and lower pressure stages are reaction type.
 
==== Impulse turbines ====
 
An impulse turbine has fixed nozzles that orient the steam flow into high speed jets. These jets contain significant kinetic energy,  which is converted into shaft rotation by the bucket-like shaped rotor blades, as the steam jet changes direction. A pressure drop occurs across only the stationary blades, with a net increase in steam velocity across the stage.
As the steam flows through the nozzle its pressure falls from inlet pressure to the exit pressure (atmospheric pressure, or more usually, the condenser vacuum). Due to this high ratio of expansion of steam, the steam leaves the nozzle with a very high velocity. The steam leaving the moving blades has a large portion of the maximum velocity of the steam when leaving the nozzle. The loss of energy due to this higher exit velocity is commonly called the carry over velocity or leaving loss.
 
[[File:TurbineBlades.jpg|border|thumb|left|A selection of turbine blades]]
 
 
The law of [[angular momentum|moment of momentum]] states that the sum of the moments of external forces acting on a fluid which is temporarily occupying the [[control volume]] is equal to the net time change of angular momentum flux through the control volume.
 
The swirling fluid enters the control volume at radius <math>r_1\,</math> with tangential velocity <math>V_{w1}\,</math> and leaves at radius <math>r_2\,</math> with tangential velocity <math>V_{w2}\,</math>.
 
[[File:Edited blade design 1.png |border|alt=Velocity triangles at the inlet and outlet on the blades of a turbo-machine.|thumb|Velocity triangle]]
 
 
 
 
 
 
 
 
A [[velocity triangle]] paves the way for a better understanding of the relationship between the various velocities. In the adjacent figure we have:
:<math>V_1\,</math> and <math>V_2\,</math> are the absolute velocities at the inlet and outlet respectively.
:<math>V_{f1}\,</math> and <math>V_{f2}\,</math> are the flow velocities at the inlet and outlet respectively.
:<math>V_{w1}\,</math> and <math>V_{w2}\,</math> are the swirl velocities at the inlet and outlet respectively.
:<math>V_{r1}\,</math> and <math>V_{r2}\,</math> are the relative velocities at the inlet and outlet respectively.
:<math>U_1\,</math> and <math>U_2\,</math> are the velocities of the blade at the inlet and outlet respectively.
<math>\alpha </math> is the guide vane angle and <math>\beta </math> is the blade angle.
 
Then by the law of moment of momentum, the torque on the fluid is given by:
 
:<math>
T = \dot{m} ( r_2 V_{w2} - r_1 V_{w1} ) \,
</math>
 
For an impulse steam turbine: <math> r_2 = r_1 = r</math>.
 
Therefore, the tangential force on the blades is <math> F_u = \dot{m}(V_{w1}-V_{w2}) \,</math>.
 
Work done per unit time or power developed: <math>{W} = {T*\omega}\,</math>
When ω is the angular velocity of the turbine, then the blade speed is <math>{U} = {\omega*r}\,</math>.
 
Work done per unit time or power developed <math>{W}\,</math> = <math>{\dot{m}U({\Delta }V_w)}\,</math>.
 
 
'''Blade efficiency'''
 
''Blade efficiency'' (<math>{\eta_b}\,</math>) can be defined as the ratio of the work done on the blades to kinetic energy supplied to the fluid, and is given by
 
<math>{\eta_b}\,</math> = <math>\frac{Work~Done}{Kinetic~Energy~Supplied}\,</math> = <math>\frac{2UV_w}{V_1^2}\,</math>
 
 
 
'''Stage efficiency'''
 
A stage of an impulse turbine consists of a nozzle set and a moving wheel. The stage efficiency defines a relationship between enthalpy drop in the nozzle and work done in the stage.
 
<math>{\eta_{stage}}= \frac{Work~done~on~blade}{Energy~supplied~per~stage}\,</math> = <math>\frac{U\Delta V_w}{\Delta h}\,</math>
 
[[File:Edited cdn.png|thumb|right|300px|Convergent-divergent nozzle]]
 
Where <math>{\Delta h}\,</math> =  <math> h_2-h_1 </math>  is the specific enthalpy drop of steam in the nozzle
 
By the [[first law of thermodynamics]]:
<math>{h_1}\,</math> + <math>\frac{V_1^2}{2}\,</math> = <math>{h_2}\,</math> + <math>\frac{V_2^2}{2}\,</math>
 
Assuming that <math>V_1\,</math> is appreciably less than <math>V_2\,</math>
 
We get <math>{\Delta h}\,</math> ≈ <math>\frac{V_2^2}{2}\,</math>
 
Furthermore, stage efficiency is the [[Product (mathematics)|product]] of blade efficiency and nozzle efficiency, or
 
<math>{\eta_{stage}}= {\eta_b}*{\eta_N}\,</math>
 
Nozzle efficiency is given by
<math>{\eta_N}\,</math>= <math>\frac{V_2^2}{2(h_1-h_2)}\,</math>
 
where the enthalpy (in J/Kg) of steam at the entrance of the nozzle is <math> h_1 </math> and the enthalpy of steam at the exit of the nozzle is <math> h_2 </math>.
 
<math>{\Delta V_w}=V_{w1}-(-V_{w2})\,</math>
 
<math>{\Delta V_w}=V_{w1}+V_{w2}\,</math>
 
<math>{\Delta V_w}\,</math> = <math>{V_{r1}\cos \beta_1+V_{r2}\cos \beta_2}\,</math>
 
<math>{\Delta V_w}\,</math>=<math>{V_{r1}\cos \beta_1}(1+\frac{V_{r2}\cos \beta_2}{V_{r1}\cos \beta_1})\,</math>
 
The ratio of the cosines of the blade angles at the outlet and inlet can be taken and denoted <math>{c}\,</math> = <math>\frac{\cos \beta_2}{\cos \beta_1}\,</math>.
The ratio of steam velocities relative to the rotor speed at the outlet to the inlet of the blade is defined by the friction coefficient <math>{k}\,</math> = <math>\frac{V_{r2}}{V_{r1}}\,</math>.
 
<math>{k < 1}\,</math> and depicts the loss in the relative velocity due to friction as the steam flows around the blades.
 
<math>{k = 1}\,</math> for smooth blades. 
 
 
<math>{\eta_b}\,</math> = <math>\frac{2 U \Delta V_w}{V_1^2}\,</math> = <math>\frac{2 U(\cos \alpha_1-U/V_1)(1+kc)}{V_1}\,</math>
 
The ratio of the blade speed to the absolute steam velocity at the inlet is termed the blade speed ratio <math>{\rho}\,</math> =  <math>\frac{U}{V_1}\,</math>
 
<math>{\eta_b}\,</math> is maximum when <math>{d\eta_b\over d\rho}\, = 0 </math>
 
or, <math>\frac{d}{d\rho}(2{\cos \alpha_1-\rho^2 }(1+kc))\, = 0 </math>
 
That implies <math>{\rho}= \frac{\cos \alpha_1}{2}\,</math>
 
and herefore <math>\frac{U}{V_1}\,</math> = <math>\frac{\cos \alpha_1}{2}\,</math>.
 
Now <math>{\rho_{opt}}= \frac{U}{V_1} = \frac{\cos \alpha_1}{2}\,</math> (for a single stage impulse turbine)
 
[[File:Edited efficiency impulse.png|thumb|right|400px|Graph depicting efficiency of Impulse turbine]]
 
Therefore the maximum value of stage efficiency is obtained by putting the value of <math>\frac{U}{V_1}\,</math> = <math>\frac{\cos \alpha_1}{2}\,</math> in the expression of <math>{\eta_b}\,</math>
 
We get:
 
<math>{(\eta_b)_{max}} = 2(\rho\cos\alpha_1-\rho^2)(1+kc)\,</math>
 
<math>{(\eta_b)_{max}} = \frac{\cos^2\alpha_1 (1+kc)}{2}\,</math>
 
For equiangular blades <math>\beta_1 </math> = <math>\beta_2 </math>, therefore <math>{c}\, = 1 </math>
 
Putting <math>{c}\, = 1 </math> we get <math>{(\eta_b)_{max}} = \frac{cos^2\alpha_1(1+k)}{2}\,</math>
 
If the friction due to the blade surface is neglected then <math>{k}\, = 1 </math>
 
And <math>{(\eta_b)_{max}} = {\cos^2\alpha_1}\,</math>
 
 
'''Conclusions on maximum efficiency'''
 
<math>{(\eta_b)_{max}} = {\cos^2\alpha_1}\,</math>
 
1. For a given steam velocity work done per kg of steam would be maximum when <math>{\cos^2\alpha_1}\,= 1 </math> or <math>\alpha_1 = 0 </math>.
 
2. As <math>\alpha_1 </math> increases, the work done on the blades reduces, but at the same time surface area of the blade reduces, therefore there are less frictional losses.
 
==== Reaction turbines ====
 
In the ''reaction turbine'', the [[Rotor (turbine)|rotor]] blades themselves are arranged to form convergent [[nozzle]]s. This type of turbine makes use of the reaction force produced as the steam accelerates through the nozzles formed by the rotor. Steam is directed onto the rotor by the fixed vanes of the [[stator]]. It leaves the stator as a jet that fills the entire circumference of the rotor. The steam then changes direction and increases its speed relative to the speed of the blades. A pressure drop occurs across both the stator and the rotor, with steam accelerating through the stator and decelerating through the rotor, with no net change in steam velocity across the stage but with a decrease in both pressure and temperature, reflecting the work performed in the driving of the rotor.
 
 
'''Blade efficiency'''
 
Energy input to the blades in a stage:
 
<math>E = {\Delta h}\,</math> is equal to the kinetic energy supplied to the fixed blades (f) + the kinetic energy supplied to the moving blades (m).
 
Or, <math>{E}\,</math> = enthalpy drop over the fixed blades, <math>{\Delta h_f}\,</math> + enthalpy drop over the moving blades, <math>{\Delta h_m}\,</math>.
 
The effect of expansion of steam over the moving blades is to increase the relative velocity at the exit. Therefore the relative velocity at the exit <math>V_{r2}\,</math> is always greater than the relative velocity at the inlet <math>V_{r1}\,</math>.
 
In terms of velocities, the enthalpy drop over the moving blades is given by:
 
<math>{\Delta h_m}\,</math> = <math>\frac{V_{r2}^2 - V_{r1}^2}{2}\,</math> 
(it contributes to a change in static pressure)
 
The enthalpy drop in the fixed blades, with the assumption that the velocity of steam entering the fixed blades is equal to the velocity of steam leaving the previously moving blades is given by:
 
[[File:Edited blade design.png|thumb|right|450px|Velocity diagram]]
 
<math>{\Delta h_f}\,</math> =  <math>\frac{V_1^2 - V_0^2}{2}\,</math>  where V<sub>0</sub> is the inlet velocity of steam in the nozzle
 
<math>V_{0}\,</math> is very small and hence can be neglected
 
Therefore, <math>{\Delta h_f}\,</math> = <math>\frac{V_1^2}{2}\,</math> 
 
<math>E = {\Delta h_f+\Delta h_m}\,</math>
 
<math>E =\frac{V_1^2}{2}\,</math> + <math>\frac{V_{r2}^2 - V_{r1}^2}{2}\,</math>
 
A very widely used design has half degree of reaction or 50% reaction and this is known as '''Parson’s turbine'''. This consists of symmetrical rotor and stator blades.
For this turbine the velocity triangle is similar and we have:
 
<math>\alpha_1 </math> = <math>\beta_2 </math>  ,  <math>\beta_1 </math> = <math>\alpha_2 </math>
 
<math>V_1\,</math> = <math>V_{r2}\,</math>  ,  <math>V_{r1}\,</math> = <math>V_2\,</math>
 
Assuming ''Parson’s turbine'' and obtaining all the expressions we get
 
<math>{E} = {V_1^2}-\frac{V_{r1}^2}{2}\,</math>
 
From the inlet velocity triangle we have <math>{V_{r1}^2} = {V_1^2-U^2-2UV_1\cos\alpha_1}\,</math>
 
<math>{E}\,</math> = <math>{V_1^2-\frac{V_1^2}{2}-\frac{U^2}{2}+\frac{2UV_1\cos\alpha_1}{2}}\,</math>
 
<math>{E}\,</math> = <math>\frac{V_1^2-U^2+2UV_1\cos\alpha_1}{2}\,</math>
 
Work done (for unit mass flow per second): <math>{W}\,</math> = <math>{U * \Delta V_w}\,</math> = <math>{U*(2*V_1\cos\alpha_1-U)}\,</math>
 
Therefore the '''blade efficiency''' is given by
 
<math>{\eta_b}\,</math> = <math>\frac{2U(2V_1\cos\alpha_1-U)}{V_1^2-U^2+2V_1U\cos\alpha_1}\,</math>
 
 
'''Condition of maximum blade efficiency'''
 
[[File:Edited comparing efficiencies.png|thumb|right|400px| Comparing Efficiencies of Impulse and Reaction turbines]]
 
If <math>{\rho}\,</math>=<math>\frac{U}{V_1}\,</math>, then
 
<math>{(\eta_b)_{max}}\,</math> = <math>\frac{2\rho(\cos\alpha_1-\rho)}{V_1^2-U^2+2UV_1\cos\alpha_1}\,</math>
 
For maximum efficiency  <math>{d\eta_b\over d\rho}\, = 0</math>, we get
 
<math>{(1-\rho^2+2\rho\cos \alpha_1)(4\cos \alpha_1-4\rho) -2\rho(2\cos \alpha_1- \rho)(-2\rho+2\cos \alpha_1) = 0}\,</math>
 
and this finally gives <math>{\rho_{opt}}= \frac{U}{V_1} = {\cos \alpha_1}\,</math>
 
Therefore <math>{(\eta_b)_{max}}\,</math> is found by putting the value of <math>{\rho}\,</math> = <math> {\cos \alpha_1}\,</math> in the expression of blade efficiency
 
<math>{(\eta_b)_{reaction}}\,</math> = <math>\frac{2\cos^2\alpha_1}{1+\cos^2\alpha_1}\,</math>
 
<math>{(\eta_b)_{impulse}}\,</math> = <math>{\cos^2\alpha_1}\,</math>
 
===Operation and maintenance===
When warming up a steam turbine for use, the main steam stop valves (after the boiler) have a bypass line to allow superheated steam to slowly bypass the valve and proceed to heat up the lines in the system along with the steam turbine.  Also, a [[turning gear]] is engaged when there is no steam to the turbine to slowly rotate the turbine to ensure even heating to prevent uneven expansion.  After first rotating the turbine by the turning gear, allowing time for the rotor to assume a straight plane (no bowing), then the turning gear is disengaged and  steam is admitted to the turbine, first to the astern blades then to the ahead blades slowly rotating the turbine at 10–15&nbsp;RPM (0.17–0.25&nbsp;Hz) to slowly warm the turbine.
 
[[File:Modern Steam Turbine Generator.jpg|thumb|left|250px|A modern steam turbine generator installation]]
Any imbalance of the rotor can lead to vibration, which in extreme cases can lead to a blade breaking away from the rotor at high velocity and being ejected directly through the casing.  To minimize risk it is essential that the turbine be very well balanced and turned with dry steam - that is, superheated steam with a minimal liquid water content.  If water gets into the steam and is blasted onto the blades (moisture carry over), rapid impingement and erosion of the blades can occur leading to imbalance and catastrophic failure.  Also, water entering the blades will result in the destruction of the thrust bearing for the turbine shaft.  To prevent this, along with controls and baffles in the boilers to ensure high quality steam, condensate drains are installed in the steam piping leading to the turbine. Modern designs are sufficiently refined that problems with turbines are rare and maintenance requirements are relatively small.
 
===Speed regulation===
The control of a turbine with a governor is essential, as turbines need to be run up slowly, to prevent damage while some applications (such as the generation of alternating current electricity) require precise speed control.<ref>{{cite book|last=Whitaker|first=Jerry C. |title=AC power systems handbook|publisher=Taylor and Francis|location=Boca Raton, FL|year=2006|page=35|isbn=978-0-8493-4034-5}}</ref> Uncontrolled acceleration of the turbine rotor can lead to an overspeed trip, which causes the nozzle valves that control the flow of steam to the turbine to close. If this fails then the turbine may continue accelerating until it breaks apart, often spectacularly. Turbines are expensive to make, requiring precision manufacture and special quality materials.
 
During normal operation in synchronization with the electricity network, power plants are governed with a five percent [[droop speed control]]. This  means the full load speed is 100% and the no-load speed is 105%. This is required for the stable operation of the network without hunting and drop-outs of power plants. Normally the changes in speed are  minor. Adjustments in power output are made by slowly raising the droop curve by increasing the spring pressure on a [[centrifugal governor]]. Generally this is a  basic system requirement for all power plants because  the older and newer plants have to be compatible in response to the instantaneous changes in frequency without depending on outside communication.<ref>Speed Droop and Power Generation. Application Note 01302. 2. Woodward. Speed</ref>
 
===Thermodynamics of steam turbines===
[[File:Rankine cycle with superheat.jpg|thumbnail|300px|Rankine cycle with superheat<br />
Process 1-2: The working fluid is pumped from low to high pressure.<br />
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.<br />
Process 3-3': The vapour is superheated.<br />
Process 3-4 and 3'-4': The dry saturated vapor expands through a turbine, generating power. This decreases the temperature and pressure of the vapor, and some condensation may occur.<br />
Process 4-1: The wet vapor then enters a condenser where it is condensed at a constant pressure to become a saturated liquid.
]]
The steam turbine operates on basic principles of [[thermodynamics]] using the part of the [[Rankine cycle]]. [[Superheated]] vapor (or dry saturated vapor, depending on application) enters the turbine, after it having exited the boiler, at high temperature and high pressure. The high heat/pressure steam is converted into kinetic energy using a nozzle (a fixed nozzle in an impulse type turbine or the fixed blades in a reaction type turbine). Once the steam has exited the nozzle it is moving at high velocity and is sent to the blades of the turbine. A force is created on the blades due to the pressure of the vapor on the blades causing them to move. A generator or other such device can be placed on the shaft, and the energy that was in the vapor can now be stored and used. The gas exits the turbine as a saturated vapor (or liquid-vapor mix depending on application) at a lower temperature and pressure than it entered with and is sent to the condenser to be cooled.<ref>Roymech, http://www.roymech.co.uk/Related/Thermos/Thermos_Steam_Turbine.html</ref> If we look at the first law we can find an equation comparing the rate at which work is developed per unit mass. Assuming there is no heat transfer to the surrounding environment and that the change in kinetic and potential energy is negligible when compared to the change in specific [[enthalpy]] we come up with the following equation
: <math> \frac {\dot{W}}{\dot{m}}=h_1-h_2 </math>
 
where
* '''Ẇ''' is the rate at which work is developed per unit time
* '''ṁ''' is the rate of mass flow through the turbine
 
====Isentropic turbine efficiency====
To measure how well a turbine is performing we can look at its [[isentropic]] efficiency. This compares the actual performance of the turbine with the performance that would be achieved by an ideal, isentropic, turbine.<ref name="ReferenceA">"Fundamentals of Engineering Thermodynamics" Moran and Shapiro, Published by Wiley</ref>  When calculating this efficiency, heat lost to the surroundings is assumed to be zero. The starting pressure and temperature is the same for both the actual and the ideal turbines, but at turbine exit the energy content ('specific enthalpy') for the actual turbine is greater than that for the ideal turbine because of irreversibility in the actual turbine. The specific enthalpy is evaluated at the same pressure for the actual and ideal turbines in order to give a good comparison between the two.
 
The isentropic efficiency is found by dividing the actual work by the ideal work.<ref name="ReferenceA"/>
: <math>\eta_t = \frac {h_1-h_2}{h_1-h_{2s}} </math>
 
where
* '''''h<sub>1</sub>''''' is the specific enthalpy at state one
* '''''h<sub>2</sub>''''' is the specific enthalpy at state two for the actual turbine
* '''''h<sub>2s</sub>''''' is the specific enthalpy at state two for the isentropic turbine
 
==Direct drive==
[[File:TMW 773 - Steam turbine generator set.jpg|thumb|300px|A small industrial steam turbine (right) directly linked to a generator (left). This turbine generator set of 1910 produced 250&nbsp;kW of electrical power.]]
[[electricity generation|Electrical power stations]] use large steam turbines driving [[electric generator]]s to produce most (about 80%) of the world's electricity. The advent of large steam turbines made central-station electricity generation practical, since reciprocating steam engines of large rating became very bulky, and operated at slow speeds.  Most central stations are [[fossil fuel power plant]]s and [[nuclear power plant]]s; some installations use [[geothermal]] steam, or use [[concentrated solar power]] (CSP) to create the steam.  Steam turbines can also be used directly to drive large [[centrifugal pump]]s, such as [[feedwater pump]]s at a [[thermal power plant]].
 
The turbines used for electric power generation are most often directly coupled to their generators.  As the generators must rotate at constant synchronous speeds according to the frequency of the electric power system, the most common speeds are 3,000&nbsp;RPM for 50&nbsp;Hz systems, and 3,600&nbsp;RPM for 60&nbsp;Hz systems.  Since nuclear reactors have lower temperature limits than fossil-fired plants, with lower steam [[Vapor quality|quality]], the turbine generator sets may be arranged to operate at half these speeds, but with four-pole generators, to reduce erosion of turbine blades.<ref>
{{cite book
| last = Leyzerovich
| first = Alexander
| authorlink =
| coauthors =
| title = Wet-steam Turbines for Nuclear Power Plants
| publisher = PennWell Books
| year = 2005
| location = Tulsa OK
| page = 111
| url =
| doi =
| id =
| isbn = 978-1-59370-032-4
}}</ref>
 
==Marine propulsion==
[[File:Turbinia At Speed.jpg|thumb|right|250px|The ''[[Turbinia]]'', 1894, the first steam turbine-powered ship]]
In ships, compelling advantages of steam turbines over reciprocating engines are smaller size, lower maintenance, lighter weight, and lower vibration. A steam turbine is only efficient when operating in the thousands of RPM, while the most effective propeller designs are for speeds less than 100 RPM; consequently, precise (thus expensive) reduction gears are usually required, although several ships, such as ''[[Turbinia]]'', had direct drive from the steam turbine to the propeller shafts. Another alternative is [[turbo-electric]] drive, where an electrical generator run by the high-speed turbine is used to run one or more slow-speed electric motors connected to the propeller shafts; precision gear cutting may be a production bottleneck during wartime.  The purchase cost is offset by much lower fuel and maintenance requirements and the small size of a turbine when compared to a reciprocating engine having an equivalent power. However, diesel engines are capable of higher efficiencies: propulsion steam turbine cycle efficiencies have yet to break 50%, yet diesel engines routinely exceed 50%, especially in marine applications.<ref>{{cite web|url=http://ansys.com/assets/testimonials/siemens.pdf |title=MCC CFXUpdate23 LO A/W.qxd |format=PDF |date= |accessdate=2010-09-12}}</ref><ref>{{cite web|url=http://pepei.pennnet.com/display_article/152601/6/ARTCL/none/none/1/New-Benchmarks-for-Steam-Turbine-Efficiency/ |title=New Benchmarks for Steam Turbine Efficiency - Power Engineering |publisher=Pepei.pennnet.com |date= |accessdate=2010-09-12|archiveurl = http://www.webcitation.org/5uL1DFU6x |archivedate = 2010-11-18|deadurl=no}}</ref><ref>https://www.mhi.co.jp/technology/review/pdf/e451/e451021.pdf</ref>
 
[[Nuclear marine propulsion|Nuclear-powered ships and submarines]] use a nuclear reactor to create steam.  Nuclear power is often chosen where diesel power would be impractical (as in [[submarine]] applications) or the logistics of refuelling pose significant problems (for example, [[icebreaker]]s). It has been estimated that the reactor fuel for the [[Royal Navy]]'s [[Vanguard class submarine]] is sufficient to last 40 circumnavigations of the globe – potentially sufficient for the vessel's entire service life. Nuclear propulsion has only been applied to a very few commercial vessels due to the expense of maintenance and the regulatory controls required on nuclear fuel cycles.
 
==Locomotives==
{{Main|Steam turbine locomotive}}
A steam turbine locomotive engine is a [[steam locomotive]] driven by a steam turbine.
 
The main advantages of a steam turbine locomotive are better rotational balance and reduced [[hammer blow]] on the track. However, a disadvantage is less flexible power output power so that turbine locomotives were best suited for long-haul operations at a constant output power.<ref name=Streeter>Streeter, Tony: 'Testing the Limit' (''Steam Railway Magazine'': 2007, 336), pp. 85</ref>
 
The first steam turbine rail locomotive was built in 1908 for the Officine Meccaniche Miani Silvestri Grodona Comi, Milan, Italy. In 1924 [[Krupp]] built the steam turbine locomotive T18 001, operational in 1929, for [[Deutsche Reichsbahn]].
 
==Testing==
British, German, other national and international test codes are used to standardize the procedures and definitions used to test steam turbines. Selection of the test code to be used is an agreement between the purchaser and the manufacturer, and has some significance to the design of the turbine and associated systems. In the United States, [[ASME]] has produced several performance test codes on steam turbines. These include ASME PTC 6-2004, Steam Turbines, ASME PTC 6.2-2011, Steam Turbines in Combined Cycles, PTC 6S-1988, Procedures for Routine Performance Test of Steam Turbines. These ASME performance test codes have gained international recognition and acceptance for testing steam turbines.<ref>William P. Sanders (ed), ''Turbine Steam Path Mechanical Design and Manufacture, Volume Iiia''
(PennWell Books, 2004) ISBN 1-59370-009-1 page 292 </ref>
 
==See also==
* [[Balancing machine]]
* [[Mercury vapour turbine ]]
* [[Tesla turbine]]
 
==References==
{{reflist}}
 
==Further reading==
* {{cite book
|title=Evaluating and Improving Steam Turbine Performance
|last=Cotton  |first=K.C.
|year=1998
|ref=Cotton
}}
* {{cite book
|title=[[s:The Steam Turbine|The Steam Turbine]]
|last=Parsons | first=Charles A.
|authorlink=Charles Algernon Parsons
|publisher=University Press, Cambridge
|year=1911}}
* {{cite book
|title=Thermische Turbomaschinen
|last=Traupel  |first=W.
|year=1977
|language=German
|ref=Traupel, Thermische Turbomaschinen
}}
* {{cite book
|title=A History of the Growth of the Steam Engine''
|last=Thurston  |first=R. H.
|publisher=D. Appleton and Co.
|year=1878
|ref=Thurston
}}
 
==External links==
{{Commons category|Steam turbines}}
* [[gutenberg:27687|''Steam Turbines: A Book of Instruction for the Adjustment and Operation of the Principal Types of this Class of Prime Movers'']] by Hubert E. Collins
* [http://www.spiraxsarco.com/resources/steam-engineering-tutorials/steam-engineering-principles-and-heat-transfer/superheated-steam.asp Tutorial: "Superheated Steam" ]
* [http://www.softinway.com/news/articles/Steam-turbine-disk-stator-cavities-1.asp Flow Phenomenon in Steam Turbine Disk-Stator Cavities Channeled by Balance Holes]
* [http://www.aqpl43.dsl.pipex.com/MUSEUM/LOCOLOCO/locoloco.htm Extreme Steam- Unusual Variations on The Steam Locomotive]
* [http://www.powerplant.vissim.com Interactive Simulation] of 350MW Steam Turbine with Boiler developed by [[The University of Queensland]], in Brisbane Australia
* [http://books.google.com/books?id=79oDAAAAMBAJ&pg=PA236&dq=Popular+Science+1933+plane+%22Popular+Mechanics%22&hl=en&ei=RasMTuyGFYifsQLC3sGzCg&sa=X&oi=book_result&ct=result&resnum=2&ved=0CC0Q6AEwATgK#v=onepage&q&f=true "Super-Steam...An Amazing Story of Achievement"] ''Popular Mechanics'', August 1937
 
{{Heat engines}}
 
{{DEFAULTSORT:Steam Turbine}}
[[Category:Turbines]]
[[Category:Steam engines|Turbine]]
[[Category:English inventions]]
[[Category:History of the steam engine|Turbine]]
[[Category:Steam turbines]]
[[Category:1884 introductions]]
 
[[ar:عنفة بخارية]]
[[bn:বাষ্পীয় টার্বাইন]]
[[bg:Парна турбина]]
[[ca:Turbina de vapor]]
[[cs:Parní turbína]]
[[da:Dampturbine]]
[[de:Dampfturbine]]
[[et:Auruturbiin]]
[[es:Turbina de vapor]]
[[fa:توربین بخار]]
[[fy:Stoomturbine]]
[[gl:Turbina de vapor]]
[[hr:Parna turbina]]
[[it:Turbina a vapore]]
[[he:טורבינת קיטור]]
[[lt:Garo turbina]]
[[li:Sjtoumturbine]]
[[hu:Gőzturbina]]
[[nl:Stoomturbine]]
[[ja:蒸気タービン]]
[[ce:Іаьнаран турбина]]
[[no:Dampturbin]]
[[nn:Dampturbin]]
[[pl:Turbina parowa]]
[[pt:Turbina a vapor]]
[[ro:Turbină cu abur]]
[[ru:Паровая турбина]]
[[si:වාෂ්ප ටර්බයිනය]]
[[sk:Parná turbína]]
[[sr:Parna turbina]]
[[sh:Parne turbine]]
[[fi:Höyryturbiini]]
[[sv:Ångturbin]]
[[ta:நீராவிச்சுழலி]]
[[th:กังหันไอน้ำ]]
[[tr:Buhar türbini]]
[[uk:Парова турбіна]]
[[vi:Tuốc bin hơi nước]]
[[zh:蒸汽渦輪發動機]]

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