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Turbomachine – basic concepts

Appendices . . . . . . . . . . . . . . . . . . . . . . . A.1
Keywords . . . . . . . . . . . . . . . . . . . . . . . K.1
The article of online continued resource Transformační technologie; ISSN 1804-8293;
www.transformacni-technologie.cz; Copyright©Jiří Škorpík, 2006-2021. All rights reserved. This work was published without any linguistic and editorial revisions.
INTRODUCTION TO TURBOMACHINERY

Introduction

Turbomachine
Shaft
Blade (Vane)
Rotor (Impeller, Runner)
Blade passage

Turbomachines are a wide group of machines (eg steam turbines, combustion turbines, compressors, pumps, water turbines and etc.). Their characteristic feature is the rotor, which is a shaft circumferentially equipped with blades (vanes), sometimes called an impeller or a runner. The blades form passages called a called blade-to-blade passage (shortly blade passage), in which the working fluid flows – Figure 295, s. 11.1 shows the impeller of a water Kaplan turbine, on which the blade passges are clearly visible.. The energy transformation occurs due to the force interaction between the working fluid and the blades.

295:
Kaplan turbine – rotor
Kaplan turbine – rotor
A rotor of the Kaplan turbine from the Orlík Dam, made in ČKD Blansko (CZ).
Rotational speed

The blade passage principle works even for "sparse" rotors, or even with a large blade distance, as evidenced by wind turbine rotors, see Figure 981. Even single-blade rotors can be designed. In general, the smaller the number of blades, the higher the rotor speed for the same speed change as a rotor with more blades but lower speeds - this is the only way to process current across the rotor diameter with the same efficiency.

981:
Wind turbine – rotor
Wind turbine – rotor
ød [m] diameter of rotor; ω [rad·s-1] angular velocity.
11.2
Turbomachine – basic concepts

Principle of operation and basic clasifiacation of turbomachines

Principle of operation

The direction of the force causing the rotor to rotate
Turbine
Working machine
Ability to transform pressure, kinetic, potential and internal energy

The rotation of the rotor of the turbomachine is caused by the force acting on the blades. If the fluid transfers energy to the rotor, then the machine is called a turbine (the action force is from the flow, reaction force from the blades) - the machine does work[43.]. In rotordynamics pumps, turbocompressors, fans (working machines) the opposite process takes place and the fluid obtains energy (the action force is from the blades) - the machine consumes work. These forces are generated during the transformation of the energy of the fluid inside the blade passages to work and vice versa, the turbomachines being able to directly transform the pressure, kinetic, potential and internal energy according to the type of machine.

For turbomachines, the pressure difference before and after the machine (pressure drop) or the difference in the velocity of the w. fluid or a combination of both is typical, for example, of a Kaplan turbine, see Figure 270. This water turbine contains blades even outside the impeller, such blades are called stator blades and are used to direct the water in front of the impeller. In the stator row of blades, part of the pressure energy[43.] of the water of the water column above the turbine is also transformed into kinetic energy. Stator (stator blades) is included in most types of blade machines.

270:
Kaplan turbine – principle
Kaplan turbine – principle
Stator (Guide vanes),
Scroll casing (Volute)
a level in top tank; b level in low tank; c guide vanes (stator); d reinforcement of scroll casing (sometimes called volute). h [m] height difference between top and low level.

Another example is a small turbocharger of an internal combustion engine (ICE) whose purpose is to increase the pressure of the sucked air for ICE through an exhaust gas flow. The turbocharger consists of two impellers on a common shaft, see Figure 271, one is a turbine impeller that drives the compressor impeller. In this case, the combustion gas enters the turbine impeller through two spiral passages, which open into a vaneless confuser, which performs the same function as the guide vanes of a Kaplan turbine (the combustion gas flow is directed to the turbine impeller in a spiral path). The compressor impeller, air is compressed and simultaneously accelerates (increases its pressure and kinetic energy). At the outlet of the compressor wheel there is a vaneless diffuser, the task of which is to divert the air evenly from the wheel and decelerate before entering the scroll case (the transformation of kinetic energy to pressure energy).

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INTRODUCTION TO TURBOMACHINERY

see Figure 271, one is a turbine impeller that drives the compressor impeller. In this case, the combustion gas enters the turbine impeller through two spiral passages, which open into a vaneless confuser, which performs the same function as the guide vanes of a Kaplan turbine (the combustion gas flow is directed to the turbine impeller in a spiral path). The compressor impeller, air is compressed and simultaneously accelerates (increases its pressure and kinetic energy). At the outlet of the compressor wheel there is a vaneless diffuser, the task of which is to divert the air evenly from the wheel and decelerate before entering the scroll case (the transformation of kinetic energy to pressure energy).

271:
Turbocharger
Turbocharger
Vaneless confuser
Vaneless diffuser
a turbine impeller; b compressor impeller; c double scroll cas of turbine; d vaneless confuser; e exhaust; f inlet to compressor; g vaneless diffuser; h scroll casing of charger.
Wind turbine as an example of a turbomachine without cassing

A wind turbines are machines with the largest rotor diameter, see Figure 193. In this case, the kinetic energy of the wind is transformed to work. Wind turbines do not have a cassing, so the flow behind the turbine is affected by the ambient current with higher kinetic energy.

193:
Wind turbine
Wind turbine
c [m·s-1] wind speed in front of the affected turbine area.
11.4
Turbomachine – basic concepts

Basic clasifiacation

Clasification according to fluid compressibility
Hydraulic turbomachines
Heat turbomachines

The choice of the design method of the turbomachine is most influenced by the properties of the working fluid - its compressibility. For hydraulic machines, the change in the density of the working fluid is insignificant. In heat machines, the density of the working fluid changes. This means that, for example, water and wind turbines are considered hydraulic machines and turbochargers heat machines.

Basic types and applications of turbomachines

Turboset

The turbomachine is always part of a set

There are a large number of types and ways of using turbomachines and they are always connected to some other machine (eg turbine / generator, pump / drive, etc.). Assemblies of machines with the turbomachine are called turbosets.

Pumps

Machines for transport and increasing of pressure

Pumps are machines used to transport and increase the pressure of a liquid. Blade pumps can be classified into circulation, condensate and feed pumps according to operating conditions.

Circulation pumps are mainly used to ensure the circulation of liquid in a loop - it overcomes the pressure drop[38.] in the loop. The energy transferred to the liquid in the circulation pump is approximately 100 J·kg-1. Powers can be up to MW units (main circulation pump of a nuclear power plant[9.]). Figure 292 shows an example of a small circulation pump with a centrifugal impeller in a monobloc design, which is connected in a loop with a heat[43.] exchanger and a heat consumer. The fluid in the impeller, by the action of centrifugal forces, flows from the center of the rotor to its circumference. The liquid flows from the rotor into the volute, from where it flows to the discharge branch of the pump.

292:
Circulating pump
Circulating pump
a heat exchanger; b heat consumer; c circulating pump.
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INTRODUCTION TO TURBOMACHINERY
Condensate pump

The condensate pumps are used for pumping of the working liquid near its saturating (e.g. a condensate, liquefied gases). 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).

Multi-stage turbomachine

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 - several impellers in a row are needed to transfer such an amount of energy to the fluid, so we are talking about a multi-stage turbomachine. Figure 293, p. 11.6 is a schematic section of a multi-stage feed pump.

293:
Feed pump
Feed pump
Figure from [2].

Water turbines

Water turbines are among the most powerful types of turbomachines with outputs of up to 1000 MW. The most used are three types of water turbines: Pelton turbine, Francis turbine, Kaplan turbine. The water turbine needs a minimum water gradient[5.].

Pelton turbine

In a Pelton turbine, the potential energy of water is transformed into the kinetic energy in the nozzle in front of the impeller at first step. The stream of water from the nozzle rotates the impeller through contact with its blades, on which it transmits its kinetic energy to them.

Francis turbine

The Francis and Kaplan turbines are similar. In front of the stator row of blades is the water pressure corresponding to the water gradient. The water flow is accelerated in the stator row of blades, (due to the narrowing of the passges that the stator blades create) and the pressure decreasing. The water flow enters the blade passages of the turbine impeller, which rotates. The stator blades are adjustable, which allows power regulation. The Kaplan turbine has adjustable rotor blades also, see Figure 295, p. 11.1.

11.6
Turbomachine – basic concepts

Compressors

Increasing pressure in diffuser passage

Compressors are machines in which gases and vapors are compressed, more precisely the pressure energy is increased, and the internal energy[43.] is increased, if the compression is not cooled - the work in the compressor is transformed into enthalpy[43.]. The blade passages of the compressor have the shape of diffusers[41.], in which the kinetic energy of the gas is transformed into enthalpy. Multi-stage compressors are used for higher compression, see Figure 298 multi-stage compressor.

298:
Multi-stage compressors
Photo from [10].

Steam turbines

Vapor expansion to lower pressure and temperature

In a steam turbine, vapor (most often steam) expands from a higher pressure to a lower pressure, which is also associated with a decrease in temperature, more precisely enthalpy is transformed into work. Steam turbines are very widely used in the production of electricity not only in conventional thermal or nuclear power plants, but also in industrial plants, if there is a source of vapor.

Laval turbine as an example of enthalpy transformation to work

Figure 296, p. 11.8 is a section of a single-stage steam turbine (Laval turbine[1.]), In order to describe its function. The steam from state 0 first expands to state 1 in the Laval nozzle[40.] (Stator), in which the enthalpy is transformed into kinetic energy (steam velocity c1). The steam stream then enters the rotor nlade passages, in which the kinetic energy of the steam is converted to work. Behind the rotor, the kinetic energy is much lower than in front of the rotor (steam velocity c2), the difference is the work.

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INTRODUCTION TO TURBOMACHINERY
296:
Laval turbine (One-stage steam turbine)
Laval turbine (One-stage steam turbine)
a nozzle (guide vanes disk usually has several nozzles for higher mass flow rate and power); b rotor; c exit branche; d gearbox; e generator; f direction of rotation of the rotor. 0 inlet of steam; 1 gap between stator and rotor; 2 exit of steam from rotor; 3 výstup páry, p [Pa] pressure.
Multi-stage steam turbines and nozzles in the form of blade passages

It is advantageous to process higher enthalpy differences in several stages in a multi-stage steam turbine. Each stage includes a stator row of blades attached to the casing (creating a series of nozzles spaced around the circumference) and a rotor row of blades, see Figure 170.

170:
Multi-stage steam turbines
Multi-stage steam turbines
6 MW multi-stage steam turbine, 9980 min-1, input parameters: 36,6 bar, 437 °C, steam output pressure 6,2 bar. S stator row of blades; R rotor row of blades. Made in Alstom (factory PBS – CZ). Information source: [7].

High power turbines are divided into several smaller turbines (casings) - this solves the problem of large bearing distances in the case of multi-stage, the problem of large flow. The turbine casings are arranged one behind the other connected by couplings, or side by side without couplings, while steam distributions can be made between the casings in series or in parallel, see. chapter Basic multi-casing turbines[23.], see Figure 297.

11.8
Turbomachine – basic concepts
297:
Multi-casing turbine
Multi-casing turbine
4-casings steam turbine in Temelin nuclear power plant (Czech republic)
The length of turboset is 63 m, it means the leght including generator, the length of the rotor is 59,035 m (turbine rotor 36,45) and its weight 326,4 t (2000 t is total weight of turboset). 1x highpressure casing; 3x lowpressure casings. The last casing of turbine is closed. Made in Škoda (cz). Photo from [8].

Gas turbines

Compression, combustion and expansion in a combustion turbine

The working fluid of gas turbines is gas. Gas turbines with a combustion chamber[23.] are most often used (therefore they are often called combustion turbines). Combustion turbines contains a compressor part and a turbine part. Figure 133, p. 11.10 is a section of a combustion turbine illustrating the construction and function of the combustion turbine. Inside of the compressor is compressed intake air. The fuel and air are burned[1.] 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.

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INTRODUCTION TO TURBOMACHINERY
133:
Combustion turbine
Combustion turbine
Combustion turbine GE-9F series
a air inlet; b compressor; c combustion chambers; d turbine; e exhaust. power output 300 MW. Figure from [12], edited by author.
For energy and as the core of a jet engine without excess power on the shaft
Jet engine

Combustion turbines are not only used for electricity generation, but are also used to drive jet engines[23.] - in this case the power of the turbine part is equal to the power input of compressor section and the rest of the enthalpy gradient of the exhaust is used for expansion in the engine nozzle for a thrust.

Fans

Transport of gases with a small increase in pressure
Low, midle, high pressure f.

Fans are used to transport gases, or to slightly increase the gas pressure, when there are no changes in gas density. Depending on the compression value, the fans are called low pressure (0 to 1 kPa), middle pressure (up to 3 kPa) and high pressure (above 3 kPa).

Example of low pressure centrifugal fan operation

Na Figure 261 is a cross-sectional view of a low pressure centrifugal fan with forward leaning blades with a scroll casing. In this case, only the velocity of the working gas is increased in the rotor, because the blade passage have a constant flow area, the working gas pressure can be increased in the diffuser channel connected behind the scroll casing.

261:
Centrifugal low pressure f.
Centrifugal low pressure fan
b [m] width of impeller; h [m] width of scroll casing. Photo: Ebmpapst [6], the casing of cast aluminium alloy[24.].
11.10
Turbomachine – basic concepts

Turbomachines without casing

Propeller
Screw propeller
Flow tube

Machines without a housing very often contain only a rotor. Machines without a housing include wind Turbines[4.] (Figure 299), aircraft propellers or propellers. Machines without a housing are characterized by small pressure changes in front of and behind the rotor, as this would lead to instability of the rotor flow tube, see Figure 193.

299:
Wind turbine
Wind turbine
Rotor of wind turbine Vestas V90 with a column height of 105 m, a rotor diameter of 90 m and an installed power output of 2 MW. Drahany (CZ). r [m] radius of rotor.

Classification of turbomachines by stream direction

Classification of the turbomachines by a stream direction in relation to the axis of the shaft (Figure 276 – four main directions: axial, radial, mixed and tangential) informs about design of the machine. The predominant flow direction is usually reflected in the machine name.

276:
Axial, radial, mixed and tangential turbomachines
Axial, radial, mixed and tangential turbomachines
(a) to (d) are pumps, compressors or fans; (e) to (j) are turbines. (a) axial; (b)radial – with axial inlet; (c) mixed flow; (d) radial – flow (centrifugal); (e) axial; (f) radial – with axial outlet; (g) mixed flow; (h)radial – flow (in case with alternate rotors rotating opposite); (i) radial – flow (centripetal); (j) tangential – (Pelton turbine).

Each flow direction has its design advantages as well as advantages in properties. Usually, the selection of a suitable type of turbomachine by the direction of flow is made according to its required specific speed and operating parameters.

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INTRODUCTION TO TURBOMACHINERY

of turbomachine by the direction of flow is made according to its required specific speed and operating parameters.

Construction features of turbomachines

Flow parts
Machine parts

The individual parts of the turbomachines differ according to the type of turbomachine. However, common flow or blade and machine parts can be identified.

Most turbomachines contain inlet and outlet flow parts (so-called inlet/outlet branche) through which the working fluid enters and exits, rotor seals[24.], casing, shaft bearings[24.]. The turbomachines usually contains a regulate of quality and quantity of working fluid; an oil system, etc. All these parts are also included in the Kaplan turbine in Figure 189.

189:
Kaplan turbine
Kaplan turbine
Branche
1 inlet of water to turbine through spiral casing; 2 stator blades – are adjustable for regulation of mass flow rate; 3 rotor blades – are adjustable – for regulation of efficiency; 4 suction pipe – outlet branch; 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; 7 rotor seal (casing shaft passage).

Blade, blade passage and blade row

Root of blade
Shroud

The blades are usually made separately. The blades are fixed into the stator and the rotor through a root of blade[24.] or by other ways and they forms the blade passages (blade row) with a required size, see Obrázek 194. Some turbomachines contain the adjustable blades (these blades enable a change the size of the flow area of the passages or close of the flow) e.g. the Kaplan turbine. 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.

11.12
Turbomachine – basic concepts
194:
Example of a rotor disk composition of a single-stage steam turbine
Example of a rotor disk composition of a single-stage steam turbine
(a) blade; (b) blade passages are formed by blades; 1 root of blade; 2 shroud (may not always be); 3 spacer.
Pitch of blades
Straight blades
Twisted blades

As can be seen from Figure 1261, the size of the blade passages, or the spacing of the blades (so called pitch), depends on the radius at which it is measured. In this case 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 295, p. 11.6, 298, p. 11.7, 299, p. 11.11). The straight blades are usually used at radial machines or axial machines with short blades.

1261:
turbine rotor with blades
(a) turbine rotor with blades; (b) cylindrical sectional view through blade passages at radius r (profile row). r [m] mean radius of blade length; u [m·s-1] circumference velocity at radius r; s [m] pitch of blades.
Leading edge
Trailing edge
Suction edge
Pressure edge

Figure 195, p. 11.14 shows the names of the individual parts of the blade, which depend on the shape and orientation of the blade in the blade row. The edges of the blades through which the working fluid enters the row are referred to as leading edges NH, the exit edges by the trailing edge of the blade OH. The pressure changes along the curved surfaces of the blades (more in the article Fundamentals of aerodynamic of blade profiles and blade rows, p. 16.1) - the side of the blade with lower pressure is called the suction side of the blade SS and the side with higher pressure as the pressure side of the blade PS.

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INTRODUCTION TO TURBOMACHINERY
195:
Blade

Internal power output/input of turbomachine

Equation of internal power

Internal work

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 and is defined as the product of its specific internal work and mass flow, see Equation 289. The internal power is not the indicated shaft power, it is also influenced by mechanical losses. The relation between the internal power and shaft power is descripted in the chapter Power output/input of turboset, p. 17.1. If working fluid consumes work (working machine), then ai and Pi inside turbomachine be negative, but this sign "negative" is not usually used and is used term "power input".

289:
Equation of internal power
Pi [W] power output/input of turbomachine; ai [J·kg-1]specific internal work of turbomachine;  [kg·s-1] mass flow rate through turbomachine.

Specific internal work of 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[43.] is used for calculation ai. This equation take into account all these forms of energy.

Hydraulic turbomachines

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 fluid (hydraulic machine) the so-called Bernoulli equation for an incompressible fluid can be derived from the First Law of Thermodynamics for an open system, see Equation 543. n this case only transformations of pressure, kinetic and potential energies are acceptable and transformations of other types of energies are taken as internal losses - therefore the sum of specific pressure, specific kinetic and specific potential energy of a fluid is called specific total energy of liquid.

11.14
Turbomachine – basic concepts
Bernoulli equation
Total energy of liquid
Internal losses

an open system, see Equation 543. n this case only transformations of pressure, kinetic and potential energies are acceptable and transformations of other types of energies are taken as internal losses - therefore the sum of specific pressure, specific kinetic and specific potential energy of a fluid is called specific total energy of liquid.

543:
Bernoulli equation
ρ [kg·m-3] density; g [m·s-2] gravitational acceleration; yi, e [J·kg-1] specific total energy of liquid at inlet and at exit; Δyi-e [J·kg-1] change of specific total energy of working liquid between inlet and exit; zi-e [J·kg-1] specific internal losses of machine between inlet and exit; u [J·kg-1] specific internal heat; q [J·kg-1] specific heat of working fluid transmitted from surroundings; h [m] level of inlet/exit branche. index i denotes the inlet, index e denotes the exit.
Heat turbomachines

Any type of the above energies can be transformed in heat machines, however, the effect of potential energy changes is usually insignificant. Also, the effect of changes in pressure energy and internal thermal energy of the working fluid is not distinguished and instead the enthalpy value is worked, so the First Law of Thermodynamics for an open system for this case is written in the form corresponding to Equation 544, s. 11.16.

544:
ic [J·kg-1] specific stagnation enthalpy of fluid[43.].

The above special equations can be used both for very accurate calculations in the design of the machine and for complete energy balances of technological units or for the approximate calculation of the basic parameters of the machine, as shown in the following Problems 545 and 546.

Power input of pump
P.545: 20 t·h-1 of water is pumped from a lower tank to a higher tank through the turbopump. Pressure is 1 bar in the lower tank, 40 bar in the higher tank. The height difference of the levels is 7 m. What is approximate power input of the pump? The problem solving is shown in the 545.
Internal work of steam turbine
P.546: 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. The problem solving is shown in the Appendix 546.
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INTRODUCTION TO TURBOMACHINERY

Turbomachine stage

Definition and energy balance of stage

Turbine stage
Working machine stage

The turbomachine stage contains the stator (stator blade row) and the rotor (rotor blade row). Figure 192 shows a stage of a Francis pump turbine (reversible turbine) as an example of the composition of the turbomachine stage. The stage of the turbine is formed first by the stator row of blades then by the rotor, in working machines it is the opposite. Because the total energy of the fluid can be transformed to work only in the rotor, an index 1 in front of the rotor and an index 2 behind the rotor are used for the state of the working fluid. For turbines, the fluid level in front of the stator is indicated by an index of 0. For working machines, the fluid level in front of the stator is indicated by an index of 3. In multi-stage machines, the method of marking within one stage is exactly the same, see Figure 277.

192:
Turbomachine stage
277:
Turbomachine stage
Example of marking the state of working fluid by multi-stage turbomachine (longitudinal section)
(a) turbine stage; (b) compressor stage.
Internal work of one stage

External work (ai≠0) takes place only in the rotor row of blades. Conversely, in the stator row of blades, the energy content of the working fluid remains the same (of course only in case of adiabatic process.), so when applying Equation 543, p. 11.15 and Equation 544, p. 11.15 to the stator, its left side will be zero.

Vortex machines

Stages of turbomachines that do not contain a stator row of blades are referred to as vortex, because without the existence of directing the stream of the working fluid, a vortex must arise behind / in front of the rotor, for example a vortex water turbine, etc.

11.16
Turbomachine – basic concepts

Velocity triangle

Absolute velocity
Cylindrical coordinate system.

In Equations 543, p. 11.15 and 544, p. 11.15, the energy balances applied to the stage are velocities c in front of and behind the blade row. The velocity of a fluid c is called absolute and can be projected in three directions because it is a flow in space. In the case of turbomachines, a cylindrical coordinate system is used to describe these components, because is clearer to describe the axis movement than the conventional rectangular coordinate system, as shown in Figure 861. The velocity component in the axial direction is called axial a, the velocity component in the direction of rotation is called circumferential u, and the velocity component perpendicular to the axial direction is called radial r. The absolute velocity is thus the vector c(cr, cu, ca) – in the following text, the arrow indicating the vector is not shown for the sake of clarity. Figure 272 shows an example of the absolute velocities of the working gas in front of and behind the turbine turbine rotor and its components according to the proposed orientation of the cylindrical coordinate system.

861:
Absolute velocity
P point at which the velocity c is investigated; ν [°] azimuth.
272:
Absolute velocity
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Blade passage

When designing the turbomachine stage, the speed values c are important in energy balances and the speed directions c for the design of the shape of the blade passages or the shape of the blades - if the direction is known, the curvature of the passage can be designed, when the speed change is known, it is possible to suggest whether the channel is convergent or divergetic, etc.

Relative velocity

The absolute fluid velocity c is the vector sum of the relative fluid velocity w and the tangential velocity of the rotor u. The relative velocity of the fluid w is the velocity of the fluid observed by an observer moving with the stage rotor. Relative velocity can have three spatial components. To clarify the concept of relative speed, here is Figure 257, which shows a moving cyclist A speed v and a stationary observer B. While a stationary observer observes the absolute direction and magnitude of the wind c, the cyclist observes the direction and magnitude of the wind w, which is referred to as relative, i.e. relative to a moving point with respect to the reference (stationary) point.

257:
Relative velocity
v [m·s-1] velocity of cyclist; w [m·s-1] relative velocity of wind.
Tangential velocity of rotor

The tangential velocity is function of the rotating radius r and the angular velocity ω (see Equation 548). It has not any components in axial and radial direction. The tangential velocity lies in the plane which is perpendicular on the axial direction.

548:
Tangential velocity of rotor
n [s-1] shaft speed.
Laval turbine

The graphical representation of the absolute, relative fluid velocity and the tangetial velocity of the rotor is called the velocity triangle. In Figure 273 are shown the velocity triangles of rotor of Laval turbine from Figure 296, p. 11.8, where the working fluid (steam) inlet the rotor blade passages at a velocity of c 1 and outlet at c2.

273:
Laval turbine (Velocity triangle)
11.18
Turbomachine – basic concepts

of rotor of Laval turbine from Figure 296, p. 11.8, where the working fluid (steam) inlet the rotor blade passages at a velocity of c 1 and outlet at c2.

The velocity triangle is being usually portrayed separately from the picture of blade row (for better a overview and need of the calculations). In addition, the angles of the individual velocities are dimensioned into it, as shown in Figure 549, which also presents other rules for its construction. For example, the input and output velocity triangles are drawn in the flow plane. The positive direction of the individual velocity components is in the tangetial velocity direction. Angles are dimensioned counterclockwise (in this case, it is not necessary to pay attention to the positive direction of velocity in calculations due to the properties of the trigonometric function[42.] ), but other dimensioning of angles is possible, see [13, p. 26].

549:
Velocity triangle
α [°] angle of absolute velocity; β [°] angle of relative velocity.

The velocity triangle is valid for the specific examined point of the working fluid volume in the machine. The secondary point will already have a slightly different velocity triangle, so when designing the turbomachine stage, a certain degree of simplified flow description is approached according to the requirement for calculation accuracy. The basic flow simplification in a turbomachine stage is usually: 1. one-dimensional (1D) flow; 2. two-dimensional (2D) flow; 3. three-dimensional (3D) flow.

1D calculation of turbomachine stage 316.gif
Reference streamline
Reference radius of blade

1/3 Calculation of one streamline on reference radius of blade only. 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 base design. This type of calculation is described in the article Design of axials turbomachine stages, p. 19.1 and the article Design of radials and diagonals turbomachine stages, p. 20.1.

2D calculation of turbomachine stage

2/3 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 axials turbomachine stages, p. 19.1.

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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 axials turbomachine stages, p. 19.1.

3D calculation of turbomachine stage
FEM

3/3 The completely numerically calculation of whole volume of the stage using advanced programs based on finite element methods (FEM). This methods usually taking into account changes of the velocities 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.

Axial stage
P.706: Find tangential, absolute, relative velocity and its components and angles of a Laval turbines on diamater of the rotor 160 mm. The shaft speed is 29 625 min-1. Other parameters of velocity triangle are: u1=u2, c1=530 m·s-1, c2u=0 m·s-1, w1=w2. The problem solving is shown in the Appendix 706.
Radial stage
P.878: Find tangential, absolute, relative velocity and its components and angles of a radial turbines on Figure 272, p. 11.17. Outside diameter of wheel is 45 mm, mean outlet diameter is 23 mm. The shaft speed is 80 000 min-1. The angle of inlet absolute velocity is 26°. The tangential component of the outlet absolute velocity is -15 m·s-1, and its absolute size is 90 m·s-1. The problem solving is shown in the Appendix 878.

Trubomachine lifecycle

Demand – supply, proposals, contract

The reason for the existence of every turbomachine is its need in some application. The future owner publishes a demand for a machine with specific features, usually by contacting several manufacturers. The manufacturer submits a tender and usually competes with other manufacturers according to price, so it is important to emphasize in more detail the advantages of the design over the competition (lower operating and service costs, possible future expansion, longer life, etc.) [14], [15]. In the offer, it is better to focus on several quality parameters than on a large number of subordinates, which with a high degree of probability cannot be met without minor deviations, but which can cause litigation between the manufacturer and the customer.

Proposal engineer

Producers make more offers than realized works, nevertheless it is important to create offers not only quickly but also with quality, and the proposal engineer must comprehensively understand the problem of the offered machine and the product ecosystem and also be able to explain it.

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The design of the turbomachine is not routine and the universal process cannot be used, however, it can be stated that the subject of the design of the turbomachine is the design of individual parts of the turbomachine (see Figure 189, p. 11.12) and harmonization of these parts into a functional unit according to the customer requirements (use of work on the offer and order). The turbomachine is designed by a team of designers working in a firm with a tradition, and the process was created by continuous work on the development of a specific type of turbomachine.

Firm standardization

There is an effort to ensure that the production takes place in parallel with the design, or as soon as possible from the signing of the contract. This is especially a problem with custom-made machines with lower power outputs. This places high demands on the production, calculation and design of the structure. Therefore, most companies are gradually introducing modular concepts of turbomachines with standard firm components, which allowed parallel work on the design of the machine and its production (design and simultaneous production of parts that will certainly be part of the set). A machine built from standard firm components is often not optimally designed for a specific operating point, but this is balanced by lower price, speed of delivery and assembly. The advantage of firm standardization is also that standard firm components undergo continuous improvement, which would be difficult to achieve with the concept of "every machine is a prototype" - for standard components can perform detailed strength calculations, optimize production and assembly procedures, produce jigs, easier to detect deficiencies or causes of accidents, etc.

However, the extent of firm standardization of an individual producer is a limiting factor in offers, ie the smaller the variability of standard components, the smaller the market the relevant producer is able to cover with its products. This is related to the fact that with a high degree of firm standardization, it loses the ability to produce atyps (it does not have designers, production machines and employees capable of machining precisely atypical shapes or dimensions). There is room for small regional producers without firm standardization lines.

Delivery and installation

Turbomachines are often big machine and delivering them to the installation site can be a problem from the point of view of local infrastructure and sudden events and accidents, see Figure 542 , p. 11.22. The season can also be a problem (river navigability, snow showers, etc.), see restrictions on wind turbine installations listed in the article Use of wind energy [4.]. At present, supplies are also affected by changes in the political situation in the region. Therefore, it is necessary to clarify this issue when concluding the contract or in the offer, especially who should provide what.

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are also affected by changes in the political situation in the region. Therefore, it is necessary to clarify this issue when concluding the contract or in the offer, especially who should provide what.

542:
Blade of steam turbine
Minor damage during transport can increase costs by one percent.
Rotor balancing
Minor damage during transport can increase costs by one percent.
In this case, there was a slight damage to the blades of the steam turbine rotor under the tarpaulin - in the picture on the left you can see in the rear highest part of the rotor abrasion on the tarpaulin. The cost of changing the blades (transport, balancing, including vacuum balancing chamber) was 1 % of the original price.

Most turbomachines are part of technological units, so it is necessary to take into account that the operation of the machine will be connected to other machines in a regulatory, mechanical or working fluid manner. This places additional demands on the assembly schedule and on the delivery contract, because it is not always possible to identify which of the machines is the real cause of the problems when operating the machine. For example, it is the oscillation of machine sets of various suppliers, contamination of working fluids in the machine by a previous machine, etc.

Operation

For larger turbomachines, a test run is performed after installation, during which the parameters and reliability of the machine are verified. But even this does not have to end the cooperation between the manufacturer and the operator - there may be a contractual relationship between them for service and supply of spare parts or other services related to operation and remote monitoring. At present, remote monitoring of the condition of the machine (vibration, corrosion, etc.) using the terrestrial Internet or via the SDU unit (Satellite Data Unit [3, p. 269]) is also a standard service for aircraft engines.

Renovation or liquidation?

Turbomachines are machines with a very long life and their physical life is often longer than the moral life. In turbomachines, only some components wear significantly (bearings, blades from abrasion and erosion, see Figure 419). Both of the above properties are the reason for frequent renovations of turbomachines. The repaired machine can be operated on the original site or sold [17]. The renovation should take into account the experience of the previous operation and take the renovation as an opportunity to eliminate some problems and improve its parameters (so-called retrofit).

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only some components wear significantly (bearings, blades from abrasion and erosion, see Figure 419). Both of the above properties are the reason for frequent renovations of turbomachines. The repaired machine can be operated on the original site or sold [17]. The renovation should take into account the experience of the previous operation and take the renovation as an opportunity to eliminate some problems and improve its parameters (so-called retrofit).

419:
Blade of wind turbine
>Wind turbine blade after renovation of its surface
Wind turbine blade after renovation of its surface – the first after twenty years of operation

Renovations of turbomachines are also related to reverse engineering (see Figure 190 ), which is carried out due to a lack of production documentation, for example if it is not archived or the machine is being renovated by a company other than the one that manufactured it, etc. It is also necessary to take into account that the renovation of a paddle machine often changes its parameters and therefore it is necessary to take into account changes in the load of related technologies.

190:
Scroll cassing of water turbine
3D scanning is a modern tool for reverse engineering
3D scanning is a modern tool for reverse engineering
3D scanning with an Artec RAY scanner in the spiral cassing of a water turbine and the resulting digitized image intended for conversion to CAD format. The photo and picture were provided by ABBAS, a.s. [16], the author of the photo is Jan Burian.
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that the renovation of a paddle machine often changes its parameters and therefore it is necessary to take into account changes in the load of related technologies.

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Appendices

The article includes the following appendices:

no.  name page
545  Problem solving A.1
546  Problem solving A.1-A.2
706  Problem solving A.2-A.3
878  Problem solving A.3-A.5

The appendices are a paid part of the article and can be purchased in PDF format together with the article here:

Citation this article

ŠKORPÍK, Jiří. Lopatkový stroj – základní pojmy, Transformační technologie, 2021-10. Brno: Jiří Škorpík, [on-line] pokračující zdroj, ISSN 1804-8293. Dostupné z https://www.transformacni-technologie.cz/lopatkovy-stroj-zakladni-pojmy_112021.pdf. English version: Turbomachine – basic concepts. Web: https://www.transformacni-technologie.cz/turbomachine–basic-concepts_112021.pdf.

©Jiří Škorpík, LICENCE

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