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    └[Introduction to turbomachinery]

11. Turbomachine

Author: Jiří Škorpík, skorpik@fme.vutbr.cz : updated 2014-02 RSS twitter google-plus facebook

Turbomachines are wide group of machines (for example steam turbines, gas turbines, turbocompressors, centrifugal pumps/rotodynamic pumps, water turbines and etc.). Their characteristic feature is a rotor with blades on its circumference, which is usually called impeller or runner. These blades form passages (so called blade-to-blade passage shortly blade passage), a working fluid flows through these passages. Energy is transformed through a force between the working fluid and the blades.

Nomenclature and principle of operation

A rotation of the rotor is caused by the force on blades. If energy is transmitted from the working fluid on the rotor, then this machine is called a turbine (an action force from the flow of the working fluid and a reaction force from the blades). Rotodynamic pumps, turbocompressors, fans work opposite, the working fluid consumes the energy from the rotor (the action force from the blades and the reaction force from the flow of the working fluid).

For the turbomachines is typical some pressure difference (pressure gradient) between the inlet and the exit of the blade passage such as for case a Kaplan turbine (Figure 1.). This type water turbine doe's not contain only the rotor but it contains so called guide blades which are located in front of the rotor. The stationary blades are aranged on periphery of the rotor and they are called stator blades*. In the stator blades is transformed a part of pressure energy of water column over the turbine to kinetic energy. This water flow is guided to the impeller.

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A Kaplan turbine as an example transformation of potential energy of water to work (hydraulic turbomachine).
Figure 1. A Kaplan turbine as an example transformation of potential energy of water to work (a hydraulic machine).
a level in top tank; b level in low tank; c guide vanes (stator); d reinforcement of spiral casing. H [m] height difference between top and low level; ØD [m] impeller diameter (external diameter of rotor); ω [rad·s-1] angular velocity.
The guide blades or stator blades
These blades contain most types of turbomachines. Their purpose is guiding stream of the working fluid under required angle and velocity to the impeller.

A turbocharger of internal combustion engine (ICE) for personal car is an example small and simple machine. It contains two impellers on one a shaft, one turbine impeller and compressor impeller. Purpose of the turbocharger is to increase pressure of sucked air to the engine through a flow of an exhaust gas.

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The cross-sectional view of a turbocharger as an example a heat turbomachine.
The cross-sectional view of a turbocharger as an example a heat turbomachine.
a turbine impeller; b compressor rotor; c double spiral casing (volute); d exhaust; e inlet to compressor; f vaneless diffuser.In this case in front of the turbine impeller is a spiral passage, which has the same function as the guide blades of the Kaplan turbine. The flow of the exhaust gas is guided to the impeller on a spiral track. Inside compressor impeller is air compressed and simultaneously accelerated (increasing pressure and kinetic energy of air). On the exit of compressor impeller is also the spiral passage for uniform flow of air from the impeller and decreasing of velocity this flow (transformation kinetic energy to pressure energy).

The most large of the turbomachine in relation to the diameter of the rotors are wind turbines. In the wind turbines is transformed kinetic energy of wind to work. The wind turbine is not inside any casing, therefore wind flow behind the turbine is influenced by the parallel flow with higher kinetic energy.

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An axial wind turbine.
Figure 3. An axial wind turbine.
c [m·s-1] wind velocity far upstream of turbine.

Choice method of calculation of the turbomachine is more influence by the working fluid properties accurately its compressibility. From this point of view is advantageous classified turbomachines on hydraulic and heat machines. Inside hydraulic turbomachines is not any change density of the working fluid during energy transformation (ρ≈const.). Inside heat turbomachines is changed density of the working fluid during energy transformation. According this classification are the water turbines and the wind turbines a hydraulic machine and the turbochargers a heat machine.

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General classification and application of turbomachines

There are many types and ways use of the turbomachines, therefore this subchapter shows only their base applications.

Rotodynamic pumps are machines for transmission and increasing pressure of the working liquids. The rotodynamic pumps can be subdivided to classes by work conditions on circulation pumps, pumps for pumping of a condensate and feed pumps. The Circulating pumps are used for circulating of the working liquid in loops, they compensate a pressure drop inside a pipe. An increase of working liquid energy inside the circulation pump is probably 100 J·kg-1. A power of circulation pumps can be up a few MW (main circulating pump of a nuclear power plant). On Figure 4. is shown an example small circulating close-coupled pump, with centrifugal impeller and its function in a technological unit. The liquid flows through the impeller from the center to its perimeter under the centrifugal forces. The working liquid exits from the impeller to the spiral casing and to the exit of the pump.

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A circulation pump and an example its application.
Figure 4. A circulation pump and an example its application.
a heat exchanger; b consumer of heat; c circulation pump.

The Condensate pumps are used for pumping of the working liquid near its saturating (for example a condensate). The transferred energy to working liquid inside these pumps is higher than in case of the circulation pumps, because the condensate usually is pumped to higher pressure (500 J·kg-1 for the case of water).

For the feed pumps is typical pumping of the working liquid to high pressure. The transferred energy to the working liquid inside the feed pumps is approximately several tens of kJ·kg-1.

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A simplified section view through a multi-stage feedwater centrifugal pump.Figure 5. A simplified section view through a multi-stage feedwater centrifugal pump.
In order to transfer to working liquid so much energy is needed several impellers behind (multi-stage turbomachine). Photo from [2].

Water wheels are machines able to convert potential and kinetic energy of water on work. Base type of the water wheels are overshot, breastshot and undershot water wheels. The overshot water wheels exploits water potential gradient (this gradient is function of wheel diameter) and kinetic energy of water stream in a head race. Undershot water wheel exploits of kinetic energy of water stream only. This kinetic energy is very low (3 to 5 J·kg-1), therefore for higher power is necessary bigger mass flow rate of water.

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An overshot, a breastshot and an undershot water wheel.
Figure 6. An overshot, a breastshot and an undershot water wheel.
c1 [m·s-1] velocity of water stream in front of wheel; c2 [m·s-1] velocity of water stream behind wheel. The overshot water wheel cannot be considered purely the turbomachine. [3, 4].

For processing of more potential gradient of water than the water wheels are used water turbines. The most used are three types of water turbines: a Pelton turbine, a Francis turbine and a Kaplan turbine. The water turbine need at least small water potential gradient for its function (an exception is the turbine for tidal power plant).

In case of the Pelton turbine is first transformed potential energy of water on kinetic energy through a nozzle. The water stream drives the impeller during touch with its blades, where is transformed the kinetic energy of the water stream to work.

The Francis and the Kaplan turbine are similar between themselves. In front of the guide vanes is pressure of water function of water potential gradient. Inside the guide is increase of water velocity (through decrease of flow area of blade passage) and decrease of pressure of water. Water flows to the blade passages of the rotating runner. The guide blades are swivel, this function enables a regulating of power output. The rotor blades of

the Kaplan turbines are swivel also (unlike the Francis turbines). The water turbines are almost the most powerful turbomachines with power output to 1 000 MW.
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A rotor of the Kaplan turbine.
Figure 7. A rotor of the Kaplan turbine.
The blade passages are very well visible.
The rotor of the Kaplan turbine from the Orlík Dam (Czech republic), made in ČKD Blansko.

A typical feature of heat turbines is expansion of the working gas and a decrease its temperature. The most used types of the heat turbines are steam and gas turbines. On Figure 8. is a section view through one-stage steam turbine (a Laval turbine) for purpose of the description of the heat turbine function.

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A section view through the Laval turbine.
Figure 8. A section view through the Laval turbine.
a nozzle (guide vanes disk usually has several nozzles for higher mass flow rate and power); b rotor; c exit flange; d gearbox; e generator; f direction of rotating. 0 inlet of steam; 1 gap between guide vanes and rotor; 2 exit of steam from rotor; 3 exhaust. p [Pa] pressure. The steam expands from the state 0 to the state 1 through the Laval nozzle (stator). In this Laval nozzle is enthalpy transformed to kinetic energy (the velocity of steam is c1). This steam stream enters to the blade-to-blade passages of the rotor, where kinetic energy of steam is transformed to work. Kinetic energy of the steam is less behind the rotor than in front of the rotor (the velocity of steam is c2), the difference of kinetic energy is work of steam.

The working fluid in the steam turbines is steam (water steam most often). The steam turbines have a very wide use: the steam power plants (in coal or nuclear power plants), industry etc.

For higher power output are made multi-stage steam turbines. One stage of the turbomachine contents: one row of the stator blades fixed to the casing, which forms nozzle row (the nozzle need not be only one, but the blades of stator may forms a few nozzles sorted on periphery of the rotor) and one row of the rotor blades.

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A simplified longitudinal section view through a multi-stage steam turbine.
Figure 9. A simplified longitudinal section view through a multi-stage steam turbine.
S stator blade row; R rotor blade row. The steam turbine: 6 MW, 9 980 min-1, the admission steam 36,6 bar, 437°C, the exhaust steam 6,2 bar (for next used). Made in Alstom (factory PBS–CZ). Information source: [7].

The steam turbines with high power output are composed of several smaller turbines, which are arranged on shared shaft (together shaft may not for all cases) connected by couplings. These turbines are called multi–casing turbines.

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A multi-casing steam turbine (Temelin nuclear power plant cz).
Figure 10. A multi-casing steam turbine (Temelin nuclear power plant cz).
4x casing (1x high-pressure casing, 3x low-pressure casing). The last casing of turbine is closed. The length of turboset is 63 m, it means the leght including generator, the length of the turbine rotor is 59,035 m and its weighs 326,4 t (2000 t is total weight of turboset). Made in Škoda (cz). Photo from [8].

The working fluid of Gas turbines is a gas or a combustion products. The gas turbines are most often used with combustion chambers (therefore are called also combustion turbines). The combustion turbine contents a turbine section, a turbocompressor section and the combustion chamber. For the combustion turbine is typical simplicity, because the fuel is combusted inside the machine.

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An combustion turbine for industrial use.
Figure 11. An combustion turbine for industrial use.
a air inlet; b compressor; c combustion chambers; d turbine; e exhaust. Made in GE; 9F series; power output 300 MW. Inside of the compressor is compressed intake air. The fuel and air are burned inside the combustion chamber. During combustion are being created hot combustion products, which feed of the turbine section. The power output of the turbine section is consumed by the compressor section and by the electric generator or other device. Figure from [9], edited by author.

The combustion turbines are used for drive of jet engines. In this case is the power output of the turbine section equal to the power input of the compressor and surplus of enthalpy gradient inside the combustion products is used for expansion in the nozzle and it does a thrust of the jet engine. The gas turbines are used for drive a blower of the ICEs (the set of the gas turbine-blower is called the turbocharger). In this case the hot combustion products from the exhaust of the ICE feeds the turbocharger, which compresses air for the ICE see flow chart of set of ICE and turbocharger.

Turbocompressors are the turbomachines for compression of gases and steams. The Blade passages inside the turbocompressor forms diffusers, in which is transformed kinetic energy to enthalpy. For higher compress are used multi-stage turbocompressors.

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A simplified longitudinal section view through an multi-stage axial compressor.Figure 12. A simplified longitudinal section view through an multi-stage axial compressor.
Photo: GE multi-stage axial compressor [10].

Other information about heat turbines and turbocompressors are in the article Heat turbine and turbocompressor[25].

Fans are used for the transport of the gases (most often air) and smaller increasing of pressure (change of density is negligible). Increasing the pressure inside the fans is from 0 to 1 kPa (low pressure), to 3 kPa (middle pressure), to 6 kPa and higher (high pressure). The fans have wide use in industry and in households.

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A simplified section views through a radial–flow fan with forward curved vanes.Figure 13. A simplified section views through a radial–flow fan with forward curved vanes.
b [m] width of impeller; h [m] width of spiral casing. Inside this impeller is only increased the velocity of the working gas, pressure can be increased in a diffuser passage behind of the exhaust of the spiral casing. Photo: Ebmpapst radial–flow fan [11], the casing of cast aluminium alloy.

Wind turbines are the turbomachines without housing such as airplane propellers or marine screw propellers. The change of specific energy of wind during flow of the wind turbine is about 100 J·kg-1. Other information about the wind turbines are in the article Use of wind energy.

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The wind turbine.Figure 14. The wind turbine.
R [m] rotor radius.
Vestas wind turbine V90, hub height 105 m; rotor diameter 90 m, nominal output 2 MW, locality Drahany (cz).

Difference between piston engine and turbomachine

The working fluid flows through the turbomachine continuously, but in a piston machine it is closed inside volume of the machine (a working volume). The working volume is formed by walls of machine parts (piston, cylinder, head..) where at least one wall is moveable (the piston). In case working fluid generates work, then the working volume is increased. In case working fluid consumes work, then the working volume is decreased. Work of the piston machine is transported through a movement of the piston (a piston engine; a piston compressor; a piston pump, a Wankel engine, a gear pump...).

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The piston engine versus the turbomachine.Figure 15. The piston engine versus the turbomachine.
This figure shows difference between principle of a steam piston engine and the Laval turbine.
a working fluid (steam). c [m·s-1] velocity of steam; F [N] force. Subscript ok denotes surroundings.

There are a wide number of criteria for select between the turbomachine and the piston machine. The most significant can be power, weight, consumption (efficiency), reliability, frequency of maintenance, vibration, emission..., there are others criteria out technical criteria as machine availability on the market, price and rate of return on investment etc. As significant technical criterion can be considered the efficiency of machine. For the piston machines is characteristic higher efficiency at small power in several tens and hundreds kilowatts opposite the turbomachines.

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A comparison of the efficiencies of the piston machines and the turbomachines.
Figure 16. A comparison of the efficiencies of the piston machines and the turbomachines.
P [W] power output of machine; Q [W] heat flow at fuel; η [-] efficiency of machine; X [W] point of start higher efficiency of turbomachine than efficiency of piston machine. Indexes O-piston machine, L-turbomachine. For example at 100..500 kW of the power output can have steam turbines higher efficiency than the steam piston engines. For case the ICEs and the combustion turbines is located this balance of the efficiency about 1 MW of the power outputs.
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Classification of turbomachines by stream direction

Classification of the turbomachines by a stream direction in relation to the axis of the shaft (meridional direction) informs about design of the machine.

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Classification of the turbomachines by the stream direction in relation to the axis of the shaft.
Figure 17. Classification of the turbomachines by the stream direction in relation to the axis of the shaft.
a to d are pumps, compressors or fans; e to j are turbines.
a axial–flow; b radial–with axial inlet; c mixed–flow; d radial–flow (centrifugal); e axial–flow; f radial–with axial exit; g mixed–flow; h radial–flow (in case with alternate rotors rotating opposite); i radial–flow (centripetal); j tangential– (Pelton turbine).

From last Figure is evident four basic directions: axial, radial, mixed–flow and tangential direction. Type of the turbomachine according to stream direction is usually chosen through an assumption its specific speed and working conditions.

Construction features of turbomachines

Parts of turbomachines are different by type of the turbomachine. Nevertheless can be identified common construction features of the turbomachines. The most of the turbomachines contain an inlet section-inlet branch (the working fluid enters to the machine); an exit section–exit branche (working fluid exits from the machine); blades/vanes (rotor blades, stator blades); the shaft; the turbomachine casing; shaft bearings. The turbomachines usually contains a regulate of quality and quantity of working fluid; an oil system, etc.

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Main construction features of the turbomachines.
Figure 18. Main construction features of the turbomachines.
The Kaplan turbine: 1 inlet of water to turbine through spiral casing; 2 stator blades–are swivelable for regulation of mass flow rate; 3 rotor blades–are swivelable–for regulation of efficiency; 4 suction pipe–exit section; 5 radial bearing–absorbs of forces which are perpendicular to axis of rotation; 6 axial bearing–absorbs of forces which are parallel to axis of rotation.

Blade, blade passage and blade row

The blades are usually made separately. The blades are fixed into the stator and the rotor through a blade root or by other ways and they forms the blade passages (blade row) with a required size. Some turbomachines contain the swivel blades (these blades enable a change the size of the flow area of the passages or close of the flow) for example the Kaplan turbines. The blade passage is bordered by the shroud on the tip of the blades or the cylindrical surface of the casing and by the rotor on the hub of the blades. The blade passage of radial machines is bordered by a disk of the rotor or the stator (F. 13.).

The flow area of the blade passage is function the radius of the cylindrical sectional view. In case F. 19 the blades are short in relation to the radius of the rotor then the variation size of the area flow is not significant, this type of the blade is called a straight blade. For higher efficiency are used so-called twisted blades (the variations size and the shape with radius, for example F. 7; F. 12., 14.). The straight blades are usually used as the stator blades for the hydraulic machines (F. 18.) or at heat turbomachines with short blades (F. 19.).

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The blade and the blade row (the Laval turbine).
Figure 19. The blade and the blade row (the Laval turbine).
a blade; b blade passages are formed by blades; c turbine rotor with blades; d cylindrical sectional view through blade passages at radius R (blade row or blade cascade); e shroud (may not always be); z.l. blade root. u [m·s-1] circumference velocity at radius R; s [m] pitch of blade row; ØD [m] mean diameter of blade length.
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The basic terminology of the blade.
Figure 20. The basic terminology of the blade.
NH leading edge; OH trailing edge; SS suction side; PS pressure side (this term is derived from variation of pressure on blade profile).

Power output/input of turbomachine

The significant parameter of the turbomachine is its internal power output/input. The internal power output is power of the working fluid flowing through the turbomachine:

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The power output/input of a turbomachine.
Equation 1. The power output/input of the turbomachine.
Pi [W] power output/input is transfered power between working fluid and rotor inside turbomachine; ai [J·kg-1] specific internal work of turbomachine (transfered energy between working fluid and rotor); m [kg·s-1] mass flow rate through turbomachine. If working fluid consumes work, then ai and Pi inside turbomachine be negative, but this sign "negative" is not usually used and is used term "input".

Enthalpy, kinetic energy and potential energy of the working fluid can change during flow through the turbomachine. The working fluid temperature inside of the turbomachine can change (heat can be transmitted with working fluid through a border of the control volume-walls of the turbomachine; or heat produced inside the control volume, for example chemical reaction in the volume of the working fluid). For calculation of the specific internal work is used the equation of the First law of thermodynamics for open system. This equation take into account all these forms of energy.

The equation for First law of thermodynamics for open system can be simplified with species of the working fluids and the type of the turbomachine. For example: for a case ideal liquid (hydraulic machine) can be derived this equation:

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Specific work of the working fluid inside the hydraulic turbomachine (ρ=constant; working fluid is liquid) and a change of specific total energy of the working fluid.
Equation 3. Specific work of the working fluid inside the hydraulic turbomachine (ρ=constant; working fluid is liquid) and a change of specific total energy of the working fluid.
ρ [kg·m-3] density of liquid; g [m·s-2] gravitational acceleration; Yi, e [J·kg-1] specific total energy of liquid at inlet and at exit; ΔY [J·kg-1] change of specific total energy of working liquid between inlet and exit; ΔYz [J·kg-1] specific losses of total energy of working liquid at flowing between inlet and exit; q [J·kg-1] specific heat of working fluid transmitted with surroundings; H [m] level of inlet / exit flange. The index i denotes the inlet, index e denotes the exit.
Remark
For description energy equations of the hydraulic machines is usual marking of specific energy by letter Y.

The equation First law of thermodynamics for open hydraulic system is called Bernoulli equation for incompressible flow. The change of internal heat energy of the working liquid is considered to be the loss for the hydraulic turbomachinery (it be reducing work of the working liquid). The change of internal heat energy of the working liquid arise during the flowing (the usable energy is transformed to the heat, which can not use in the hydraulic turbomachine). External heat transfer inside the hydraulic turbomachine only increases the internal energy of liquid and does not affected to work machine.

In case of the heat machines can be simplify of the equation for First law of thermodynamics for open system to next form:

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The specific internal work of the heat turbomachine (the working fluid is the gas).
Equation 4. The specific internal work of the heat turbomachine (the working fluid is the gas).
Assumptions solution of this equation is: negligible influence of potential energy of working gas.
More information about energy balance of of heat turbomachines are shown for cases adiabatic processes (q=0) in chapters Energy balance of heat turbine[13] and Energy balance of turbocompressor[13] and for cases polytropic processes (q≠0) in chapters Expansion inside of turbomachine at heat transfer with surroundings[14] and Compression inside of turbomachine at heat transfer with surroundings[14].

The Equations 3. and the Equations 4. can be use for a simple calculation of basic parameters of the turbomachine:

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20 t·h-1 of water is pumped from a lower tank to a higher tank through the rotodynamic pump. Pressure is 1 bar in the lower tank, the pressure is 40 bar in the higher tank. The height difference between levels in tanks is 7 m. What is approximate power input of this pump?
Problem 1.
ai  [J·kg-1] -3968,67
Pi  [W]       22048,2
Results of Problem 1.
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Steam enters to the steam turbine at 36,6 bar and 437 °C. The exit pressure is 6,2 bar. Find the specific internal work of this steam turbine.
Problem 2.
ii  [kJ·kg-1]  3306,04
ie  [kJ·kg-1]  2845,51
ai  [kJ·kg-1]   460,53
Results of Problem 2.

Turbomachine stage

The turbomachine stage contains the stator (stator blade row) and the rotor (rotor blade row):

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The definition of the turbomachine stage (for example reversible Francis turbine).
Figure 21. The definition of the turbomachine stage (for example reversible Francis turbine).
Total energy of the working fluid can be transformed in work only inside the rotor, therefore for states of working fluid are used subscript 1 in front of the rotor blade row and subscript 2 behind the rotor blade row. For case the turbines is used subscript 0 in front of the stator blade row. For case the pumps, the compressors etc. is used subscript 3 behind the stator blade row (the stator blade row is behind the rotor blade row):
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The denote of working fluid state of multi-stage turbomachine (longitudinal section view).
Figure 22. The denote of working fluid state of multi-stage turbomachine (longitudinal section view).
a turbine stage; b compressor stage.

In case of adiabatic process, a change of sum of energy of the working fluid is being done in blade passage of the rotor only (input/output work). The sum of energy of the working fluid is constant in blade passage of the stator.

In case of the hydraulic machines, the energy equilibrium can be derived from the Equation 3. for the stator (individual types of energy can be transformed between themselves, but their sum is constant and reduced about the losses):

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The energy balance equation of the stator blade row of the hydraulic turbomachine stator (derived from the Equation 3. for a<sub>i</sub>=0).
Equation 5. The energy balance equation of the stator blade row of the hydraulic turbomachine stator (derived from the Equation 3. for ai=0).
ΔYz,S [J·kg-1] specific losses arise during flowing of liquid through blade passages of the stator; 0 state of working liquid in front of the stator row; 1 state of working liquid behind stator row.

In case of the heat machines, the equilibrium of stagnation enthalpy can be derived from the Equation 4.:

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The energy balance equation of the stator blade row of the heat turbomachine.
Equation 6. The energy balance equation of the stator blade row of the heat turbomachine.
q1-2 [J·kg-1] heat transffered to working gas in stator. Derived from Equation 4.

The sum of energy of the working fluid is changed inside the rotor blade row and ai≠0. In case of turbines, energy is extracted from working fluid (sum of energy at the exit is lesser than at the inlet of the rotor blade row). In case pump/compressor, energy is consumed by the working fluid (sum of energy at the inlet is lesser than at the exit of the rotor blade row).

Velocity triangle

The rotor of the turbomachine is a rotating mechanism. The blade passages of the rotor rotates around the axis of the rotor. The working fluid flows with the velocity c1 to these passages and with the velocity c2 from these passages.

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The absolute velocity and its components.
Figure 23. The absolute velocity and its components.
c absolute velocity of flow; a axial direction; u tangential direction; r radial direction.

The velocity of the working fluid c is called absolute and it has three spatial components. The component of the absolute velocity in direction of the axis is called an axial component and it is denoted by index a. The component of the absolute velocity in direction of the rotating is called a circumference/tangential component and it is denoted by index u. The component of the absolute velocity in direction of a perpendicular on the axis is called radial component and it is denoted by index r.

The absolute velocity of the working fluid c is a vector summation of a relative velocity w and a circumference velocity u (the blade velocity). The relative velocity w is velocity of flow, which is measured with respect to the rotating system (the move of the observer is with the rotating system). The relative velocity has three spatial components as absolute velocity:

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The explanation of the relative velocity.
Figure 24. The explanation of the relative velocity.
A cyclist; B stationary observer. c [m·s-1] absolute velocity of wind; v velocity of cyclist; w [m·s-1] velocity of wind respect to cyclist, this velocity is called relative velocity of wind.

The circumference velocity is function of the rotating radius r and the angular velocity ω. It has not any components in axial and radial direction as the absolute velocity. The circumference velocity lies in the plane which is perpendicular on the axial direction:

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The circumference velocity of rotor.
Equation 7. The circumference velocity of the rotor.

A scheme, which shows of the absolute, relative and circumference velocity of working fluid is called the velocity triangle:

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The velocity triangle of the Laval turbine.
Figure 25. The velocity triangle of the Laval turbine.
The working gas (steam) flows with the velocity c1 to the rotor blade passages and flowing from rotor blade passages with the velocity c2.

The velocity triangle is being usually portrayed separately from the picture of blade row (for better a overview and need of the calculations).

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The dimensioning of the angles of the velocity triangle (for a case the axial stage).
Figure 26. The dimensioning of the angles of the velocity triangle (for a case the axial stage).
α [deg] angle of absolute velocity; β [deg] angle of relative velocity. The inlet and the exit velocity triangle is portrayed in a meridian plane. The positive direction any components of the velocities is at the direction of the circumference velocity. The angle between the absolute velocity and the circumference velocity is denoted by α. The angle between the relative velocity and the circumference velocity is denoted by β. The angles are dimensioned counterclockwise (so there is no need to examine to the positive direction of the velocity), there are others ways of the angle dimensioning for example [1, p. 26].

For design of the turbomachine stage is first the velocity triangle is computed, which is the base for the design of the blades. There are three possible procedures for a calculation of the turbomachine stage:

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(1) 1D calculation of main streamline only (the mean diameter of the stage).
(2) 2D calculation of several streamlines (several diameters along          
    length of the blade).                                                   
(3) 3D calculation whole volume of stage (Finite element methods; CFD).     
List 1. Basic calculation methods of the turbomachine stage.
1D calculation of the turbomachine stage
In this case is used many simplifications to simplify of the calculation. This method of calculation is used for the turbomachine stages with negligible influence of spatial character of the stream (the change of the velocity triangle along the length of the blade is negligible) or for an approximate calculation. The mean diameter or a quadratic diameter (flow area of the stage is the same over the diameter and under the diameter) is used as the reference diameter. The Figure 17. shows reference streamlines on the reference diameters. This type of calculation is described in the article Design of turbomachine stage with negligible influence of spatial character of stream[20].
2D calculation of the turbomachine stage
This method is the same as previous method with the difference, that the calculation of the velocity triangle is being performed on several diameters along the length of the blade. This method is used for calculations of turbomachine stages with a big influence on spatial character of flow inside stage (twist blades). This calculation is described in the article Design of turbomachine stage with taking into account spatial character of flow[21].
3D calculation of the turbomachine stage
The completely numerically calculation of the turbomachine stage using advanced CFD software. This method usually taking into account changes of the velocity triangle near blade profiles (influences of boundary layer). Before use the 3D calculation is known approximate geometry of the turbomachine stage from the 1D or the 2D calculation.
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Turbomachine Losses

Inside of the turbomachine occurs losses, which influence its power output. There is an friction inside the stream of the working fluid and on the surface of the parts machine. The working fluid can flow from working volumes through seals and others gaps and etc. Others losses are in mechanical parts of the turbomachine (mechanical losses). The Losses are usually increased during no-nominal state of the turbomachine*. The turbomachine losses is possible subdivided to the classes, which are influenced between them:

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(1) Mechanical losses (friction between mechanical parts of machine).  
(2) Aerodynamic losses (change of forces on blade profiles during      
    flowing fluid).                                                    
(3) Energy losses (example decreasing of enthalpy due transfer heat to 
    surroundings etc.).                                                
(4) Losses is caused by change properties of working fluid (for example
    condensation during steam expansion).                              
(5) Losses is caused by leakages (there is internal /leakage between   
    stages/ and external /escape working fluid outside machine/)       
List 2. A classification of the turbomachine losses.
*Remark
The nominal state is a state of the working fluid (pressure, gradient, temperature, density...), for which the turbomachine designed to operate as efficiently as possible.

At the calculation start of the turbomachine or its parts the losses usually need estimate (because the geometry of the machine is not know). At the calculation end, these estimates are checked by control calculations. If the results of the control calculations are not same as the estimates (they are outside required interval), then new calculation an estimate of losses is necessary.

Questions for study

(1)  Describe methods of calculation of turbomachine stages (3 methods).

(2)  Base classification of turbomachine losses.                        

References

  1. KADRNOŽKA, Jaroslav. Lopatkové stroje, 2003. 1. vydání, upravené. Brno: Akademické nakladatelství CERM, s.r.o., ISBN 80–7204-297-1.
  2. Odstředivá horizontální článková hydrodynamická čerpadla H-V-D, [2009]. Katolog společnosti Sigma Hranice. Dostupné z http://www.sigmahra.cz.
  3. ŠTĚPÁN, Luděk, KŘIVANOVÁ, Magda. Dílo a život mlynářů a sekerníků v Čechách, 2000. 1. vydání. Praha: Argo, ISBN 80-7203-254-2.
  4. HLOUŠEK, Jiří. Termomechanika, 1992. 1. vydání. Brno: Vysoké učení technické v Brně, ISBN 80-214-0387-X.
  5. KALČÍK, Josef, SÝKORA, Karel. Technická termomechanika, 1973. 1. vydání, Praha: Academia.
  6. Alstom–referenční list 2006.
  7. HLAVATÝ, Ivo, KREJČÍ, Lucie. Welding the components of nuclear power plants, All for power, 2007. Praha: AF POWER agency, a.s., ISSN–1802–8535, 2007. Dostupné z http://www.allforpower.com/clanek/380-welding-the-components-of-nuclear-power-plants.
  8. All for power, 2011. Katalog General Electric Company. Dostupné z http://www.ge.com.
  9. Centrifugal & Axial Compressors, 2009. Katalog General Electric Company. Dostupné z http://www.ge.com.
  10. Centrifugal fans and blowers, 2009. Version 07. Katalog společnosti ebmpapst. Dostupné z http://www.ebmpapst.com.

Citation this article

This document is English version of the original in Czech language: ŠKORPÍK, Jiří. Lopatkový stroj, Transformační technologie, 2009-08, [last updated 2014-02]. Brno: Jiří Škorpík, [online] pokračující zdroj, ISSN 1804-8293. Dostupné z http://www.transformacni-technologie.cz/lopatkovy-stroj.html. English version: Turbomachine. Web: http://www.transformacni-technologie.cz/en_lopatkovy-stroj.html.

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