1 Introduction1. Introduction

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• Turbo machinery: is a device that exchanges energy with a fluid using continuously flowing fluid and rotating blades.g y g g

• Examples are : Wind turbines, Water turbines, Aircraft engines.

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Classification of TurbomachinesClassification of TurbomachinesTurbomachines can be classified in two main groups;

A Power Machines (Turbines): extract energy from flowA. Power Machines (Turbines):‐ extract energy from flowmedium and transfer it to shaft of the machine.

• According to the available kind of energy power machinescan be further classified as:

1. Water turbines :‐ convert pressure energy

2 Wind turbines: convert kinetic energy of the air2. Wind turbines:‐ convert kinetic energy of the air

3. Heat Turbines:‐ Convert heat energy of the gas or steama. steam turbines:

b. Gas turbines3

• Machines for Extracting Work (Power) from a Fluid

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B.  Working Machines (Pumps): deliver energy from the shaft of the machine to the flow medium.

• According to the kind of flow medium and pressure generated 

working machines are further classified into:working machines are further classified into:

1. Pumps (Liquid Medium)

2. Compressors (Gas Medium)

a. Fans ‐‐‐ Low pressure rise

b. Blowers ‐‐‐medium Pressure riseb. Blowers  medium Pressure rise

c. Turbo‐Compressors ‐‐‐high pressure rise

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• Machines for Doing Work on a Fluid

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Classification of Turbomachines base on the way in which th fl th h th tthe flow passes through the rotor:

I. Axial‐flow Machines:‐ the direction of the flow in the‘ idi i ’ i ll l h i f h‘meridian section’ is parallel to the axis of the rotor

Flow path ~ parallel to axis of rotation

II. Radial‐flow Machines: the direction of the flow in themeridian section is perpendicular to the rotor:

Flow path ~ perpendicular to axis of rotation

III. Mixed‐ flow Machines: The direction of the flow in themeridian section has a component parallel as well asperpendicular to the axis of the rotor.perpendicular to the axis of the rotor.

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8

9

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• Turbomachines have always a vaned rotor and often stationary y yvanes (guide vanes). The guide vanes are mostly located at the pressure end of the machine.

• Pressure end/flange: is the part at which the energy possessed by the fluid is a maximum:y

– In working machines, the exit end is the pressure end

– In power machines the inlet end is the pressure end

• Suction end/flange:‐ is the part at which the energy possessed b th fl id i i ib the fluid is a minimum.

– In working machines, the inlet end is the pressure end

I hi th it d i th d– In power machines the exit end is the pressure end

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The Specific Work Y [ ]2

2mThe Specific Work Y [    ]The difference of the useful specific energy content of the flow medium between the two ends of the machine is defined as

2s

medium between the two ends of the machine is defined as ‘ specific work done between inlet and outlet of the machine =Y’

• Regarding the energy transfer in a turbomachinery is to be noted that:

i /d f h f l f h fla. an increase/decrease of the useful energy content of the flow medium in the case of working/power machines,

b and always and increase of the non utilizable energy contentb. and always and increase of the non‐utilizable energy content 

of the flow medium.

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Energy absorbed by the flow medium due to flow losses. This energy is non-utilizable.

Useful energy rise of the

Total energy transferred from impeller to the

Flow energy transferred into torque

Total energy available (useful)

flow mediumflow medium torqueYY Y

Pump Turbine

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From Bernoulli Equation:

Pressure Energy

Velocity Energy

geodetic Energy

Total Energy += +

Thus specific energy can be given by the formula:

( )sDD mZZCCdY ⎥

⎤⎢⎡−

∫222

( )

geovelpr

SDsD

S

YYYYs

ZZgvdpY

++=

⎥⎦

⎢⎣

−++= ∫ 22

Where:                         specific pressure work ∫=D

Spr vdpY

kinetic energy

S ifi d ti

2

22sD

velCCY −

=

( )SD ZZgY −= Specific geodetic energy   ( )SDgeo ZZgY

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• Specific energy content of the flow medium between S and D ends of the machine can be expressed interms of ‘Head’ H.

[ ]HmmY ⎥⎤

⎢⎡

⎥⎤

⎢⎡ 2

• Note that the value of H will change if the machine works in

[ ]mHs

gs

Y ⎥⎦⎢⎣=⎥

⎦⎢⎣

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Note that the value of H will change if the machine works in another field of gravity contrary to the value of Y which does not change with g.

• Y is always measured between the suction and pressure ends of the machine In the case of water turbines the tail raceof the machine. In the case of water turbines the tail race surface is considered as the suction end.

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Often the equation for Y can be simplified:

• In the case of Wind turbines where only velocity energy is available, it is:

• In the case of steam turbines the velocity and geodetic

2

22sD

velCCY −

=

In the case of steam turbines, the velocity and geodetic energy can be neglected as both are very small compared with the pressure energy,

• In the case of pumps with equal diameters of suction and

∫==D

Spr vdpYY

• In the case of pumps with equal diameters of suction and pressure flanges, the velocity energy is zero.

geopr YYY +=16

Determination of the Pressure Energy prYDetermination of the Pressure Energy

The pressure energy represents the needed work to change h i f h fl di f P P b

pr

the static pressure of the flow medium from PS to PD by a 

process without losses.

In case of an incompressible medium the pressure energy is:

SDDD PPdp −∫∫

In case of a compressible medium the density is changing

ρρSD

SSpr

PPdpvdpY === ∫∫

In case of a compressible medium the density  is changing from  S to D. Ypr has to be determined by integration:

DD dp∫∫ ==SS

prdpvdpYρ

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Consider isentropic process AB’p p

The course AB’ is given by the equation:

PK CkwhereconstvP == ..

The value of the ‘const’ can be determined from the known inlet conditions:

VCkwhereconstvP ..

from the known inlet conditions:

KvPncompressio .:K

DD

ss

vPansion

vPncompressio

.:exp

.:

KDD

Kss

K vPvPvP ... == DDss

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Compression (Pumping Machine)p ( p g )

Integration:

KK

D

S

KKss

D

Sadpr dp

PvPvdpYY

⎤⎡⎤⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛===

−−

∫∫11

1

K

KK

S

DS

KK

S

Dssadpr P

PRTk

kPPvP

kkYY

⎤⎡⎞⎛

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

=⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

==

−

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11

1

11

PVP

K

S

DSPadpr CR

kkndCCRtconsgasas

PPTCYY =

−−=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛==

1tan1

NPi t ifthid lF :

Kkgkcal

KkgNmC

KkgNm

TPRAirFor

P 240.01005

9.286:

==

==ρ

KK

S

D

S

D givesthisPP

TT

processisentropicfortheorygasidealFrom

⎟⎟⎠

⎞⎜⎜⎝

⎛=

−

,,

:,1

Kkgkcal

KkgNmC

KkgKkg

V 171.09.715 ==( )SDPS

DSPadpr TTC

TTTCYY −=⎟⎟

⎠

⎞⎜⎜⎝

⎛−== 1

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Expansion (turbine)Expansion (turbine)

Integration:

⎤⎡⎤⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛===

−−

∫∫KK

D

S

KKDD

D

Sadpr dp

PvPvdpYY

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1

⎤⎡⎞⎛

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−==

−K

KK

D

sD

KK

D

sDDadpr P

PRTk

kPPvP

kkYY

1

11

11

11

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛−==

K

D

sDPadpr P

PTCYY 1

( ) gasesperfectForTTCYYTTTCYYSimilarly

D

sDPadpr

−==

⎟⎟⎠

⎞⎜⎜⎝

⎛−== 1

( )steamForiiYY

gasesperfectForTTCYY

SDadpr

sDPadpr

−==

==

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Ypr in T,s Diagram

a. Compression⎥⎥⎤

⎢⎢⎡

−⎟⎟⎠

⎞⎜⎜⎝

⎛==

−

1

1K

K

Dspadpr P

PTcYY

For isentropic process:

⎥⎥⎦⎢

⎢⎣

⎟⎠

⎜⎝ SP

KK

DK

K

D PPT⎟⎞

⎜⎛

⎟⎞

⎜⎛

−− 1

'

1'

For isentropic process:

( ) KK

DSSd

S

DS

S

D

S

PTTTtor

PPTThence

PP

T D

D

⎥⎥⎤

⎢⎢⎡

−⎟⎟⎞

⎜⎜⎛

=−=Δ

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛=

−

1

,

1

'

'

For adiabatic process:( )

adppr

SSSad

tcY

PTTTtor

D

Δ=⎥⎥⎦⎢

⎢⎣

⎟⎟⎠

⎜⎜⎝

Δ 1

∫∫ ===

==−= 0

Ppr dTcdiAsYvdpdi

vdpdiorvdpdidq

∫='

D

S

T

T Ppr dTcY21

Thus, Ypr is obtained if the integration is done from TS to T ’ along a line of constto TD  along a line of const. Cp for instance along the pressure PD:

Ypr =Yad=CPΔtad is represented by the area AB’B”C”C”

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B. Expansion

( )⎤⎡

−=Δ==−K

SDpadpadpr TTctcYY1

'

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛−=Δ

KK

D

Ssad P

PTtwhere

1

1⎥⎦⎢⎣

Ypr=Yad is represented by the area AB”C”C’B’the area AB”C”C’B’

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Y in i,s DiagramYpr in i,s Diagram

a Compression: dSD

iiiidivdpY D Δ=−=== ∫∫ '

'

a. Compression: adSDipr iiidivdpYS

Δ∫∫ '

d Y i t d band Ypr is represented by the distance AB.

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Y in i,s DiagramYpr in i,s Diagram

b expansion: dSD

iiiidivdpY D Δ=−=== ∫∫ 'b.  expansion: adSDipr iiidivdpY

S

Δ∫∫ ''

d Y i t d band Ypr is represented by the distance AB’.

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The powerp• The amount of the power change of the continuous flow 

which passes the machine is:which passes the machine is: 

[ ]WorNmVYMYN eff ⎥⎦⎤

⎢⎣⎡== ρ

• Coupling power = effective power for ideal machines that i h l

sff ⎥⎦⎢⎣

operate without any losses

• An actually machine involves losses Thus the coupling power• An actually machine involves losses . Thus the coupling power of the machine is:

m

ρ pumpsforVY⎪⎨⎧

mηρηρ

η VYturbinesforVY

pumpsforN =⎪⎩

⎪⎨=

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