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. These blades forms passages (so called blade-to-blade passage shortly blade passage), through these passages flows a working fluid. Energy is transformed through a force between working fluid and the blades.
A rotation of the rotor is caused by the force on blades. If energy is transmitted working fluid on the rotor, then this machine is called a turbine (an action force from flow of working fluid and a reaction force from the blades). Rotodynamic pumps, turbocompressors, fans work opposite, working fluid consumes the energy from the rotor (the action force from the blades and the reaction force from flow of working fluid).
For the turbomachines is typical some pressure difference between the input and the output (pressure gradient) or a velocity difference or their combination as is for example typical for water a Kaplan turbine (Figure 1.). This type water turbine is not only formed by 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 to kinetic energy. This water flow is guided to the impeller.
Other example is much small and simple machine , a turbocharger of internal combustion engine (ICE) for personal car. It is formed two impeller on one a shaft, one turbine impeller and compressor impeller. Purpose of the turbocharger is to increase pressure sucked air to the engine by flow of an exhaust gas.
The most large of the turbomachine in relation to diamter 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 affected 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 classified turbomachines on hydraulic and heat machines. Inside hydraulic turbomachines is not any change density of a working fluid during energy transformation (ρ≈const.). Inside heat turbomachines is changed density of working fluid during energy transformation. According this classification is the water turbine and the wind turbine a hydraulic machine and the turbocharger a heat machine.
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 increase pressure of 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 pump with integrated motor, 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.
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.
Water wheels are machines able to convert potential and kinetic energy of water. Base type of the water wheels are overshot, breastshot and undershot water wheels on work. 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
A typical feature of heat turbines is expansion of 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 (the 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.
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.
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.
Other information about heat turbines and turbocompressors are in the article Heat turbine and turbocompressor.
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.
Wind turbines are the turbomachines without housing 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.
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...).
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 such as machine availability on the market, price and rate of return on investment etc. The efficiency of machine can be considered significant technical criterion. For the piston machines is characteristic higher efficiency at small power in several tens and hundreds kilowatts opposite the turbomachines.
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. Type of the turbomachine according to stream direction 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 (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.
The blades are usually made separately. The blades are fixed into the stator and the rotor through a blade root 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 or the cylindrical surface of the casing on the tip of the blades 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.).
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:
Enthalpy, kinetic energy and potential energy of 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 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 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 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 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:
The Equations 3. and the Equations 4. can be use for a simple calculation of basic parameters of the turbomachine:
ai [J·kg-1] -4168,7 Pi [W] 23159Results of Problem 1.
ii [kJ·kg-1·K] 3306,04 ie [kJ·kg-1·K] 2845,51 ai [kJ·kg-1] 460,53Results of Problem 2.
The turbomachine stage contains the stator (stator blade row) and the rotor (rotor blade row):
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 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):
In case of the heat machines, the equilibrium of stagnation enthalpy can be derived from the Equation 4.:
The sum of energy of working fluid is changed inside the rotor blade row. 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 working fluid (sum of energy at the inlet is lesser than at the exit of the rotor blade row). Inside the rotor blade row is true ai≠0 from the equation of First law thermodynamics for open system.
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 one flows with the velocity c2 from these passages.
The velocity of 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 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:
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:
A scheme, which shows of the absolute, relative and circumference 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).
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 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.
Inside of the turbomachine occurs losses, which influence its power output. There is an friction inside the stream of working fluid and on the surface of the parts machine. The working fluid can be flows 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-normal state of the turbomachine*. The turbomachine losses is 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 (decreasing of enthalpy /pressure/ potential gradient and kinetic energy of working fluid). (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.
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.
(1) Describe methods of calculation of turbomachine stages (3 methods). (2) Base classification of turbomachine losses.
This document is English version of 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.