Turbomachines are wide group of machines (e.g. 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 an impeller or a 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.
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 (so called working machines) 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 pice of pressure energy of a water column over the turbine to kinetic energy. This water flow is guided 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 the exhaust gas.
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.
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 classification of turbomachines on hydraulic and heat machines. Inside hydraulic turbomachines is not any change density of the working fluid during energy transformation. Inside heat turbomachines is changed density of the working fluid during energy transformation. The water turbines and the wind turbines are hydraulic machines and the turbochargers are heat machines according this classification.
There are many types and ways use of the turbomachines. Sets of machines with turbomachines are called turbosets. Basic applications of the turbomachines are shown next chapter:
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. The liquid flows through the impeller from the center to its perimeter under the centrifugal forces. The working liquid flows from the impeller to the spiral casing and to the exit of the pump.
The Condensate pumps are used for pumping of the working liquid near its saturating (e.g. 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.
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.
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.
|7.295 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.
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.
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, Figure 10.
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, Figure 11.
|10.297 A multi-casing steam turbine (Temelin nuclear power plant in Czech republic).|
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 weight 326,4 t (2000 t is total weight of turboset). Made in Škoda (cz). Photo from .
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 internal combustion engines (ICE) (the set of the gas turbine-blower is called the turbocharger). In this case the turbocharger is connected with the exhaust and the suction of the ICE. Hot combustion products from the exhaust of the ICE feeds the turbocharger, which compresses air for the ICE.
Turbocompressors are the turbomachines for compression of gases and vapors, it means the pressure energy and internal energy (under increasing temperature) is increased inside them. The Blade passages inside the turbocompressor forms diffusers, in which is transformed kinetic energy to enthalpy. For higher compress are used multi-stage turbocompressors.
Other information about heat turbines and turbocompressors are in the article 23. Heat turbines and turbocompressors.
Fans are used for the transport of the gases and smaller increasing of pressure (change of density is negligible). Increasing the pressure through the fans is from 0 to 1 kPa (low pressure), to 3 kPa (middle pressure), to 6 kPa and higher (high pressure).
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 4. Use of wind energy.
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, the Wankel engine, the Stirling engine, a gear pump, ...).
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, regulation characteristics..., 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.
|16.928 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.
Classification of the turbomachines by a stream direction in relation to the axis of the shaft (meridional direction) informs about design of the machine.
From last Figure is evident four basic directions: axial, radial, mixed–flow and tangential direction. Stream direction of turbomachine is usually chosen through an assumption its specific speed and working conditions.
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.
|18.189 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.
The blades are usually made separately. The blades are fixed into the stator and the rotor through a root of blade 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) e.g. 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.
The flow area of the blade passage is function the radius of the cylindrical sectional view. In case Figure 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, e.g. Figures 7, F. 12., 14). The straight blades are usually used as the stator blades for the hydraulic machines or at heat turbomachines with short blades.
|20.195 The basic terminology of the blade.|
NH leading edge; OH trailing edge; SS suction side; PS pressure side.
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:
The working fluid at flow through the turbomachine can produced/consumed to work, it can by heating or cooling (heat can be transmitted through walls of the turbomachine or heat produced inside the working fluid, for ex. a chemical reaction). It means that enthalpy, kinetic energy and potential energy of the working fluid can be change, beacause the equation of the First law of thermodynamics for open system is used for calculation ai. 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:
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 liquid is considered to be the loss for the hy. turbomachinery (reduced work of the liquid). The change of internal heat energy of the liquid arise during the flowing (the usable energy is transformed to the heat, which cannot use in the hy. turbomachine). External heat transfer inside the hy. 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:
The Equations 22 and the Equations 23 can be use for a simple calculation of basic parameters of the turbomachine:
ai [J·kg-1] -3968,67 Pi [W] 22048,2
|Results of Problem 1.|
ii [kJ·kg-1] 3306,04 ie [kJ·kg-1] 2845,51 ai [kJ·kg-1] 460,53
|Results of Problem 2.|
The turbomachine stage contains the stator (stator blade row) and the rotor (rotor blade row):
Change of sum of energy of the working fluid is being done in blade passage of the rotor only in case of adiabatic process. 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 inside the stator can be derived from the Equation 22 (individual types of energy can be transformed between themselves, but their sum is constant and reduced about the losses):
|26.190 The energy balance of the stator blade row of the hydraulic turbomachine.|
0 state of working liquid in front of the stator row; 1 state of working liquid behind stator row. Derived from the Equation 22 for ai=0. Use indexes 2 and 3 at the working machine.
In case of the heat machines, the equilibrium of stagnation enthalpy inside the stator can be derived from the Equation 23:
|27.547 The energy balance equation of the stator blade row of the heat turbomachine.|
q0-1 [J·kg-1] heat transffered to working gas in stator. Use indexes 2 and 3 at the working machine.
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 the working fluid (sum of energy at the exit is lesser than at the inlet). Energy is consumed by the working fluid (sum of energy at the inlet is lesser than at the exit) in case working machine.
The velocity of the working fluid c is called absolute and it has three spatial components. The component in direction of the axis is called an axial a. The component in direction of the rotating is called a tangential component u. The component in direction of a perpendicular on the axis is called radial component r.
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.
The absolute velocity c is vector summation of the relative velocity w and the tangential velocity u. 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:
|29.257 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 tangential velocity is function of the rotating radius r and the angular velocity ω. It has not any components in axial and radial direction. The tangential velocity lies in the plane which is perpendicular on the axial direction:
|30.548 The tangential velocity of the rotor.|
n [s-1] shaft speed.
A scheme, which shows of the absolute, relative and tangential velocity of working fluid is called the velocity triangle:
The velocity triangle is being usually portrayed separately from the picture of blade row (for better a overview and need of the calculations).
u1 [m·s-1] 248,19 c1a [m·s-1] 185,78 w2 [m·s-1] 310,02 u2 [m·s-1] 248,19 w1a [m·s-1] 185,78 α1 [°] 20,52 w2u [m·s-1] -248,19 c2 [m·s-1] 185,78 β1 [°] 36,82 c1u [m·s-1] 496,37 w2a [m·s-1] 185,78 β2 [°] 143,18 w1u [m·s-1] 248,19 w1 [m·s-1] 310,02Problem 3: results.
u1 [m·s-1] 188,50 c1r [m·s-1] 91,94 w2 [m·s-1] 142,38 u2 [m·s-1] 96,34 w1 [m·s-1] 91,94 α2 [°] 99,59 c1u [m·s-1] 188,50 w1r [m·s-1] 91,94 β2 [°] 141,45 w2u [m·s-1] -111,34 c2a [m·s-1] 88,74 c1 [m·s-1] 209,72 w2a [m·s-1] 88,74
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:
(1) 1D calculation of one streamline only on reference radius of blade. (2) 2D calculation of several streamlines (several diameters along length of blade). (3) 3D calculation whole volume of stage (Finite element methods; CFD).
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 losses are possible subdivided to the classes, which are influenced between them:
(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 to transfer heat to surroundings etc.). (4) Losses is caused by change properties of working fluid (e.g. condensation during steam expansion). (5) Losses is caused by leakages (there is internal /leakage between stages/ and external /escape working fluid outside machine/)
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.
This document is English version of the original in Czech language: ŠKORPÍK, Jiří. Lopatkový stroj, Transformační technologie, 2009-08, [last updated 2017-01-29]. Brno: Jiří Škorpík, [on-line] pokračující zdroj, ISSN 1804-8293. Dostupné z http://www.transformacni-technologie.cz/11.html. English version: Turbomachine. Web: http://www.transformacni-technologie.cz/en_11.html.