A rotor of a modern
steam turbine, used in a
power plant
A steam turbine is a device that extracts thermal energy from pressurized steam and uses it to do mechanical work on a rotating output shaft. Its modern manifestation was invented by Sir Charles Parsons in 1884.[1]
Because the turbine generates rotary motion, it is particularly suited to be used to drive an electrical generator – about 90% of all electricity generation in the United States (1996) is by use of steam turbines.[2] 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.
2000 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 mathematician Hero of Alexandria in Roman Egypt.[3][4][5] In 1551, Taqi al-Din in Ottoman Egypt described a steam turbine with the practical application of rotating a spit. Steam turbines were also described by the Italian Giovanni Branca (1629)[6] and John Wilkins in England (1648).[7] The devices described by al-Din and Wilkins are today known as steam jacks.
Parsons turbine from the Polish destroyer
ORP Wicher.
The modern steam turbine was invented in 1884 by the Anglo-Irish engineer Sir Charles Parsons, whose first model was connected to a dynamo that generated 7.5 kW (10 hp) of electricity.[8] The invention of Parson's steam turbine made cheap and plentiful electricity possible and revolutionised marine transport and naval warfare.[9] 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 kW set up to units of 50,000 kW capacity. Within Parson's lifetime the generating capacity of a unit was scaled up by about 10,000 times,[10] 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.[8]
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.
Cut away of an AEG marine steam turbine circa 1905
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.
Schematic operation of a steam turbine generator system
Steam turbines are made in a variety of sizes ranging from small <0.75 kW (1< hp) units (rare) used as mechanical drives for pumps, compressors and other shaft driven equipment, to 1,500,000 kW (2,000,000 hp) turbines used to generate electricity. There are several classifications for modern steam turbines.
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 quality near 90%, at a pressure well below atmospheric to a condenser.
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.
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 heaters to improve overall cycle efficiency. Extraction flows may be controlled with a valve, or left uncontrolled.
Induction turbines introduce low pressure steam at an intermediate stage to produce additional power.
Mounting of a steam turbine produced by
Siemens
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.
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.[11]
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.
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.
An impulse turbine has fixed nozzles that orient the steam flow into high speed jets. These jets contain significant kinetic energy, which is convert 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.
A selection of Turbine Blades
Blade efficiency
The law of moment of momentum states that the sum of moments of external forces acting on a fluid which is temporarily occupying the control volume is equal to the net time rate of efflux of angular momentum from the control volume. If the swirling fluid enters the control volume at radius Failed to parse (Missing texvc executable; please see math/README to configure.): r_1\,
with tangential velocity Failed to parse (Missing texvc executable; please see math/README to configure.): V_{w1}\,
and leaves at radius Failed to parse (Missing texvc executable; please see math/README to configure.): r_2\,
with tangential velocity Failed to parse (Missing texvc executable; please see math/README to configure.): V_{w2}\,
,
A velocity triangle paves the way for a better understanding of the relationship between the various velocities. In the adjacent figure we have:
- Failed to parse (Missing texvc executable; please see math/README to configure.): V_1\,
and Failed to parse (Missing texvc executable; please see math/README to configure.): V_2\,
are the absolute velocities at the inlet and outlet respectively.
- Failed to parse (Missing texvc executable; please see math/README to configure.): V_{f1}\,
and Failed to parse (Missing texvc executable; please see math/README to configure.): V_{f2}\,
are the flow velocities at the inlet and outlet respectively.
- Failed to parse (Missing texvc executable; please see math/README to configure.): V_{w1}\,
and Failed to parse (Missing texvc executable; please see math/README to configure.): V_{w2}\,
are the swirl velocities at the inlet and outlet respectively.
- Failed to parse (Missing texvc executable; please see math/README to configure.): V_{r1}\,
and Failed to parse (Missing texvc executable; please see math/README to configure.): V_{r2}\,
are the relative velocities at the inlet and outlet respectively.
- Failed to parse (Missing texvc executable; please see math/README to configure.): U_1\,
and Failed to parse (Missing texvc executable; please see math/README to configure.): U_2\,
are the velocities of the blade at the inlet and outlet respectively.
Failed to parse (Missing texvc executable; please see math/README to configure.): \alpha
is the guide vane angle and Failed to parse (Missing texvc executable; please see math/README to configure.): \beta
is the blade angle.
then by law of moment of momentum torque on the fluid is given by :
- Failed to parse (Missing texvc executable; please see math/README to configure.): T = \dot{m} ( r_2 V_{w2} - r_1 V_{w1} ) \,
For impulse steam turbine : Failed to parse (Missing texvc executable; please see math/README to configure.): r_2 = r_1 = r
Therefore,Tangential force on the blades, Failed to parse (Missing texvc executable; please see math/README to configure.): F_u = \dot{m}(V_{w1}-V_{w2}) \,
Work done per unit time or Power developed, Failed to parse (Missing texvc executable; please see math/README to configure.): {W} = {T*\omega}\,
Where Ω is the angular velocity of the turbine and blade speed, Failed to parse (Missing texvc executable; please see math/README to configure.): {U} = {\omega*r}\,
Work done per unit time or Power developed Failed to parse (Missing texvc executable; please see math/README to configure.): {W}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): {\dot{m}U({\Delta }V_w)}\,
Blade efficiency can be defined as the ratio of the work done on the blades to kinetic energy supplied to the fluid .
Blade efficiency, Failed to parse (Missing texvc executable; please see math/README to configure.): {\eta_b}\,
is given by
Failed to parse (Missing texvc executable; please see math/README to configure.): {\eta_b}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{Work~Done}{Kinetic~Energy Supplied}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{2UV_w}{V_1^2}\,
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.
Failed to parse (Missing texvc executable; please see math/README to configure.): {\eta_{stage}}= \frac{Work~done~on~blade}{Energy~supplied~per~stage}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{U\Delta V_w}{\Delta h}\,
Convergent-Divergent Nozzle
Where Failed to parse (Missing texvc executable; please see math/README to configure.): {\Delta h}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): h_2-h_1
is the specific enthalpy drop of steam in the nozzle
By first law of Thermodynamics : Failed to parse (Missing texvc executable; please see math/README to configure.): {h_1}\,
+ Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{V_1^2}{2}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): {h_2}\,
+ Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{V_2^2}{2}\,
Assuming that Failed to parse (Missing texvc executable; please see math/README to configure.): V_1\,
is appreciably less than Failed to parse (Missing texvc executable; please see math/README to configure.): V_2\,
We get Failed to parse (Missing texvc executable; please see math/README to configure.): {\Delta h}\,
≈ Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{V_2^2}{2}\,
Further , Stage Efficiency = Blade Efficiency * Nozzle Efficiency
Failed to parse (Missing texvc executable; please see math/README to configure.): {\eta_{stage}}= {\eta_b}*{\eta_N}\,
Nozzle efficiency is given by Failed to parse (Missing texvc executable; please see math/README to configure.): {\eta_N}\, = Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{V_2^2}{2(h_1-h_2)}\,
where,Enthalpy of steam at the entrance of the nozzle, J/Kg, = Failed to parse (Missing texvc executable; please see math/README to configure.): h_1
and Enthalpy of steam at the exit of the nozzle, J/Kg = Failed to parse (Missing texvc executable; please see math/README to configure.): h_2
Failed to parse (Missing texvc executable; please see math/README to configure.): {\Delta V_w}=V_{w1}-(-V_{w2})\,
Failed to parse (Missing texvc executable; please see math/README to configure.): {\Delta V_w}=V_{w1}+V_{w2}\,
Failed to parse (Missing texvc executable; please see math/README to configure.): {\Delta V_w}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): {V_{r1}\cos \beta_1+V_{r2}\cos \beta_2}\,
Failed to parse (Missing texvc executable; please see math/README to configure.): {\Delta V_w}\, =Failed to parse (Missing texvc executable; please see math/README to configure.): {V_{r1}\cos \beta_1}(1+\frac{V_{r2}\cos \beta_2}{V_{r1}\cos \beta_1})\,
The ratio of cosine of the blade angles at the outlet to the inlet can be taken as, Failed to parse (Missing texvc executable; please see math/README to configure.): {c}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{\cos \beta_2}{\cos \beta_1}\,
The ratio of steam velocities relative to the Rotor speed at the outlet to the inlet of the blade is defined by, Friction coefficient, Failed to parse (Missing texvc executable; please see math/README to configure.): {k}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{V_{r2}}{V_{r1}}\,
Failed to parse (Missing texvc executable; please see math/README to configure.): {k < 1}\,
and depicts the loss in the relative velocity due to Friction as the steam flows around the blade.
Failed to parse (Missing texvc executable; please see math/README to configure.): {k = 1}\,
for Smooth Blades.
Failed to parse (Missing texvc executable; please see math/README to configure.): {\eta_b}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{2 U \Delta V_w}{V_1^2}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{2 U(\cos \alpha_1-U/V_1)(1+kc)}{V_1}\,
The ratio of the Blade speed to the absolute steam velocity at the inlet is termed as Blade speed ratio, Failed to parse (Missing texvc executable; please see math/README to configure.): {\rho}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{U}{V_1}\,
Failed to parse (Missing texvc executable; please see math/README to configure.): {\eta_b}\,
is maximum when Failed to parse (Missing texvc executable; please see math/README to configure.): {d\eta_b\over d\rho}\, = 0
or , Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{d}{d\rho}(2{\cos \alpha_1-\rho^2 }(1+kc))\, = 0
That implies , Failed to parse (Missing texvc executable; please see math/README to configure.): {\rho}= \frac{\cos \alpha_1}{2}\,
Therefore Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{U}{V_1}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{\cos \alpha_1}{2}\,
Now Failed to parse (Missing texvc executable; please see math/README to configure.): {\rho_{opt}}= \frac{U}{V_1} = \frac{\cos \alpha_1}{2}\,
(for single stage impulse turbine)
Graph depicting efficiency of Impulse turbine
Therefore the maximum value of stage efficiency is obtained by putting the value of Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{U}{V_1}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{\cos \alpha_1}{2}\,
in the expression of Failed to parse (Missing texvc executable; please see math/README to configure.): {\eta_b}\,
We get, Failed to parse (Missing texvc executable; please see math/README to configure.): {(\eta_b)_{max}} = 2(\rho\cos\alpha_1-\rho^2)(1+kc)\,
Failed to parse (Missing texvc executable; please see math/README to configure.): {(\eta_b)_{max}} = \frac{\cos^2\alpha_1 (1+kc)}{2}\,
For equiangular blades Failed to parse (Missing texvc executable; please see math/README to configure.): \beta_1
= Failed to parse (Missing texvc executable; please see math/README to configure.): \beta_2
Therefore Failed to parse (Missing texvc executable; please see math/README to configure.): {c}\, = 1
Putting Failed to parse (Missing texvc executable; please see math/README to configure.): {c}\, = 1
we get Failed to parse (Missing texvc executable; please see math/README to configure.): {(\eta_b)_{max}} = \frac{cos^2\alpha_1(1+k)}{2}\,
If the friction over blade surface is neglected then Failed to parse (Missing texvc executable; please see math/README to configure.): {k}\, = 1
And Failed to parse (Missing texvc executable; please see math/README to configure.): {(\eta_b)_{max}} = {\cos^2\alpha_1}\,
Conclusions on maximum efficiency
Failed to parse (Missing texvc executable; please see math/README to configure.): {(\eta_b)_{max}} = {\cos^2\alpha_1}\,
1. For a given steam velocity work done per kg of steam would be maximum when Failed to parse (Missing texvc executable; please see math/README to configure.): {\cos^2\alpha_1}\,= 1
or Failed to parse (Missing texvc executable; please see math/README to configure.): \alpha_1 = 0
.
2. As Failed to parse (Missing texvc executable; please see math/README to configure.): \alpha_1
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.
In the reaction turbine, the rotor blades themselves are arranged to form convergent nozzles. 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 blade in a stage,
E = Failed to parse (Missing texvc executable; please see math/README to configure.): {\Delta h}\,
= Kinetic energy supplied to the fixed blades (F)+ Kinetic energy supplied to the moving blades(M)
Or, Failed to parse (Missing texvc executable; please see math/README to configure.): {E}\,
= Enthalpy drop in fixed blades,Failed to parse (Missing texvc executable; please see math/README to configure.): {\Delta h_f}\,
+ Enthalpy drop in moving blade,Failed to parse (Missing texvc executable; please see math/README to configure.): {\Delta h_m}\,
The effect of expansion of steam on the moving blade is to increase the relative velocity at the exit. Therefore the relative velocity at the exit Failed to parse (Missing texvc executable; please see math/README to configure.): V_{r2}\,
is always greater than the relative velocity at the inlet Failed to parse (Missing texvc executable; please see math/README to configure.): V_{r1}\,
.
In terms of velocities, the Enthalpy drop in moving blades is given by:
Failed to parse (Missing texvc executable; please see math/README to configure.): {\Delta h_m}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{V_{r2}^2 - V_{r1}^2}{2}\,
(It contributes to the Static Pressure change)
The Enthalpy drop in the fixed blades, with the assumption the velocity of steam entering the fixed blades is equal to the velocity of steam leaving the previously moving blades is given by:
Failed to parse (Missing texvc executable; please see math/README to configure.): {\Delta h_f}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{V_1^2 - V_0^2}{2}\,
where V0 is the inlet velocity of steam in the nozzle
Failed to parse (Missing texvc executable; please see math/README to configure.): V_{0}\,
is very small and hence can be neglected
Therefore, Failed to parse (Missing texvc executable; please see math/README to configure.): {\Delta h_f}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{V_1^2}{2}\,
Failed to parse (Missing texvc executable; please see math/README to configure.): E = {\Delta h_f+\Delta h_m}\,
Failed to parse (Missing texvc executable; please see math/README to configure.): E =\frac{V_1^2}{2}\,
+ Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{V_{r2}^2 - V_{r1}^2}{2}\,
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 are similar and we have:
Failed to parse (Missing texvc executable; please see math/README to configure.): \alpha_1
= Failed to parse (Missing texvc executable; please see math/README to configure.): \beta_2
, Failed to parse (Missing texvc executable; please see math/README to configure.): \beta_1
= Failed to parse (Missing texvc executable; please see math/README to configure.): \alpha_2
Failed to parse (Missing texvc executable; please see math/README to configure.): V_1\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): V_{r2}\,
, Failed to parse (Missing texvc executable; please see math/README to configure.): V_{r1}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): V_2\,
Assuming Parson’s turbine and obtaining all the expressions we get
Failed to parse (Missing texvc executable; please see math/README to configure.): {E} = {V_1^2}-\frac{V_{r1}^2}{2}\,
From the inlet velocity triangle we have, Failed to parse (Missing texvc executable; please see math/README to configure.): {V_{r1}^2} = {V_1^2-U^2-2UV_1\cos\alpha_1}\,
Failed to parse (Missing texvc executable; please see math/README to configure.): {E}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): {V_1^2-\frac{V_1^2}{2}-\frac{U^2}{2}+\frac{2UV_1\cos\alpha_1}{2}}\,
Failed to parse (Missing texvc executable; please see math/README to configure.): {E}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{V_1^2-U^2+2UV_1\cos\alpha_1}{2}\,
Work done(for unit mass flow per second), Failed to parse (Missing texvc executable; please see math/README to configure.): {W}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): {U * \Delta V_w}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): {U*(2*V_1\cos\alpha_1-U)}\,
Therefore Blade Efficiency is given by
Failed to parse (Missing texvc executable; please see math/README to configure.): {\eta_b}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{2U(2V_1\cos\alpha_1-U)}{V_1^2-U^2+2V_1U\cos\alpha_1}\,
Condition of Maximum Blade Efficiency
Comparing Efficiencies of Impulse and Reaction turbines
Put Failed to parse (Missing texvc executable; please see math/README to configure.): {\rho}\, =Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{U}{V_1}\,
,then
Failed to parse (Missing texvc executable; please see math/README to configure.): {(\eta_b)_{max}}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{2\rho(\cos\alpha_1-\rho)}{V_1^2-U^2+2UV_1\cos\alpha_1}\,
For Maximum Efficiency Failed to parse (Missing texvc executable; please see math/README to configure.): {d\eta_b\over d\rho}\, =0 , we get
Failed to parse (Missing texvc executable; please see math/README to configure.): {(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}\,
and this finally gives Failed to parse (Missing texvc executable; please see math/README to configure.): {\rho_{opt}}= \frac{U}{V_1} = {\cos \alpha_1}\,
Therefore Failed to parse (Missing texvc executable; please see math/README to configure.): {(\eta_b)_{max}}\,
by putting the value of Failed to parse (Missing texvc executable; please see math/README to configure.): {\rho}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): {\cos \alpha_1}\,
in the expression of blade efficiency
Failed to parse (Missing texvc executable; please see math/README to configure.): {(\eta_b)_{reaction}}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{2\cos^2\alpha_1}{1+\cos^2\alpha_1}\,
Failed to parse (Missing texvc executable; please see math/README to configure.): {(\eta_b)_{impulse}}\,
= Failed to parse (Missing texvc executable; please see math/README to configure.): {\cos^2\alpha_1}\,
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 RPM (0.17–0.25 Hz) to slowly warm the turbine.
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.
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.[12] 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.[13]
Rankine cycle with superheat
Process 1-2: The working fluid is pumped from low to high pressure.
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 3-3': The vapour is superheated.
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.
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.[14] 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
- Failed to parse (Missing texvc executable; please see math/README to configure.): \frac {\dot{W}}{\dot{m}}=h_1-h_2
where
- Ẇ is the rate at which work is developed per unit time
- ṁ is the rate of mass flow through the turbine
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.[15] 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.[15]
- Failed to parse (Missing texvc executable; please see math/README to configure.): \eta_t = \frac {h_1-h_2}{h_1-h_{2s}}
where
- h1 is the specific enthalpy at state one
- h2 is the specific enthalpy at state two for the actual turbine
- h2s is the specific enthalpy at state two for the isentropic turbine
A small industrial steam turbine (right) directly linked to a generator (left). This turbine generator set of 1910 produced 250 kW of electrical power.
Electrical power stations use large steam turbines driving electric generators 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 plants and nuclear power plants; 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 pumps, such as feedwater pumps 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 RPM for 50 Hz systems, and 3,600 RPM for 60 Hz systems. Since nuclear reactors have lower temperature limits than fossil-fired plants, with lower steam 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.[16]
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.[17][18][19]
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, icebreakers). 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.
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.[20]
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.
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.[21]
- ^ Encyclopædia Britannica (1931-02-11). "Sir Charles Algernon Parsons (British engineer) - Britannica Online Encyclopedia". Britannica.com. http://www.britannica.com/EBchecked/topic/444719/Sir-Charles-Algernon-Parsons. Retrieved 2010-09-12.
- ^ Wiser, Wendell H. (2000). Energy resources: occurrence, production, conversion, use. Birkhäuser. p. 190. ISBN 978-0-387-98744-6. 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.
- ^ turbine. Encyclopædia Britannica Online
- ^ A new look at Heron's 'steam engine'" (1992-06-25). Archive for History of Exact Sciences 44 (2): 107-124.
- ^ O'Connor, J. J.; E. E. Roberston (1999). Heron of Alexandria. MacTutor
- ^ "Power plant engineering". P. K. Nag (2002). Tata McGraw-Hill. p.432. ISBN 978-0-07-043599-5
- ^ 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.
- ^ a b [1][dead link]
- ^ [2][dead link]
- ^ Parsons, Sir Charles A.. "The Steam Turbine". http://www.history.rochester.edu/steam/parsons/part1.html.
- ^ "Steam Turbines (Course No. M-3006)". PhD Engineer. http://www.pdhengineer.com/Course%20Files/Completed%20Course%20PDF%20Files/Mechanical/Steam%20Turbines.pdf. Retrieved 2011-09-22.
- ^ Whitaker, Jerry C. (2006). AC power systems handbook. Boca Raton, FL: Taylor and Francis. p. 35. ISBN 978-0-8493-4034-5.
- ^ Speed Droop and Power Generation. Application Note 01302. 2. Woodward. Speed
- ^ Roymech, http://www.roymech.co.uk/Related/Thermos/Thermos_Steam_Turbine.html
- ^ a b "Fundamentals of Engineering Thermodynamics" Moran and Shapiro, Published by Wiley
- ^ Leyzerovich, Alexander (2005). Wet-steam Turbines for Nuclear Power Plants. Tulsa OK: PennWell Books. p. 111. ISBN 978-1-59370-032-4.
- ^ "MCC CFXUpdate23 LO A/W.qxd" (PDF). http://ansys.com/assets/testimonials/siemens.pdf. Retrieved 2010-09-12.
- ^ "New Benchmarks for Steam Turbine Efficiency - Power Engineering". Pepei.pennnet.com. Archived from the original on 2010-11-18. http://pepei.pennnet.com/display_article/152601/6/ARTCL/none/none/1/New-Benchmarks-for-Steam-Turbine-Efficiency/. Retrieved 2010-09-12.
- ^ https://www.mhi.co.jp/technology/review/pdf/e451/e451021.pdf
- ^ Streeter, Tony: 'Testing the Limit' (Steam Railway Magazine: 2007, 336), pp. 85
- ^ William P. Sanders (ed), Turbine Steam Path Mechanical Design and Manufacture, Volume Iiia (PennWell Books, 2004) ISBN 1-59370-009-1 page 292
- Cotton, K.C. (1998). Evaluating and Improving Steam Turbine Performance.
- Parsons, Charles A. (1911). The Steam Turbine. University Press, Cambridge.
- Traupel, W. (1977) (in German). Thermische Turbomaschinen.
- Thurston, R. H. (1878). A History of the Growth of the Steam Engine. D. Appleton and Co..
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