steam turbine

Mehran University of Engineering and Technology SZAB Campus Khairpur Mir’s

STEAM TURBINESTEAM TURBINE

THERMPDYNAMICSTHERMPDYNAMICS--IIII

AkashAkash Thahrani (MUET,SZAB KHAIRPUR)Thahrani (MUET,SZAB KHAIRPUR)

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LECTURE # 01

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ROTODYNAMIC MACHINARY: A machine in which transfer of energy between the fluid and the rotor takes place and change of angular momentum of fluid causes torque on rotor.

Turbine:a machine for producing continuous power in which a wheel or rotor, typically fitted with vanes, is made to revolve by a fast-moving flow of water, steam, gas, air, or other fluid.

Fan, Pump, Compressor:In all of these three machines transfer of energy takes place from rotor to fluid

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Classification of rotodynamic Machines:

A rotodynamic turbine or compressor may be classified in two ways:

1. By the direction of flow of fluid relative to the rotor.a. Parallel to the axis of rotorb. In radial direction (Centrifugal Compressor)b. In radial direction (Centrifugal Compressor)

2. By the way in which the rate of change of angular momentum of fluid is achieved.a. Impulseb. reaction

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Impulse turbine:

The most basic turbine takes a high pressure , high enthalpy fluid, expand it In a fixed nozzle, and then uses the rate of change of angular momentum of the fluid in a rotating

passage to provide the torque on the rotor, Such a machine is called an impulse turbine.

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Reaction Turbine:

Radial tubes which are connected to the supply tube Are free to rotate about a vertical axis The end of each tube is shaped as a nozzle and the steam from supply tube expands through the nozzles to atmosphere

in tangential direction

There is an increase in the velocity of steam,

And the rate of increase in the momentum is provided by the force on the steam from the nozzle walls provided by the force on the steam from the nozzle walls in the direction of the steam flow.

An equal and opposite force acts on the nozzle wallsIn the direction of the steam flow.

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RATE OF WORKDONE IN IMPULSE TURBINE

Figure: 01 Simple impulse turbine

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Absolute velocity at inlet = Cai

Absolute velocity at exit = Cae

Blade velocity = CbFig: 02 tangential flow on to moving blade

+ve

+ve

Force on fluid

Force on blade

Force on the fluid = - m’(Cai + Cae)

An equal and opposite force must act on the blades:

= m’(Cai + Cae)

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Fig : 03: Relative velocities for a moving

bladeblade

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Energy Transformation in Turbine

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LECTURE # 02

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Simple impulse Turbine

The most basic turbine.

It is the turbine which takeshigh enthalpy fluid, expands it ina nozzle , and then uses the rateof change of angular momentumof the fluid in a rotating passageof the fluid in a rotating passageto provide the torque on therotor.

This turbine is called simpleimpulse turbine because theexpansion of the steam takesplace in one set of the nozzles.

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Diagram: indicates one set of nozzles which is followed by a ring of moving blades

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Diagram indicates approximately changes in pressure and velocity during the flow of steam through the turbine.

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Symmetrical Blading:

Symmetrical blading means that relative inlet Velocity angle ( βi ) is equal to elative velocity angle at exit ( βe ).

SOME IMPORTANT TERMS RELATED TO VELOCITY TRIANGLES

velocity angle at exit ( βe ).

βi = βe

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Blade velocity co-efficient

Velocity of the steam relative to the blade is reduced by friction and this is expressed by :

Cre = K Cri Where,

K = the Blade velocity Co- efficient

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Whirl Velocity:

Horizontal Component of Absolute velocities at inlet and exit are called the Whirl velocities.

Cwi = Whirl velocity at inlet Cwi = Whirl velocity at inlet Cwe = Whirl velocity at exit

The change in Whirl velocity is responsible for the torque that is produced when steam strike the blades.

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Velocities of flow:

vertical components of the absolute velocities at inlet and exit are called velocities of flow

Cfi = flow velocity at inlet Cfi = flow velocity at inlet Cfe = flow velocity at exit

The change between these two components of absolute velocity is responsible for axial thrust.

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The steam supplied to a single wheel impulse turbine expands completely in thenozzles and leaves with a high absolute velocity. This is the absolute inlet velocity tothe blades as shown in fig:

IMPULSE STEAM TURBINE

The steam is delivered to the wheel at an angle αi.

The selection of angle αi is one of compromise since an increase in αi reduces thevalue of useful component (Cai Cos αi), and increases the value of the axial, or flowcomponent (Cai Sin αi).

The absolute velocity Cai can be considered as the resultant of blade velocity Cb andthe velocity of steam relative to the blade at inlet Cri.

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Absolute velocity at inlet = Cai

Absolute velocity at exit = Cae

Blade velocity = Cb

Relative velocity at inlet = Cri

Relative velocity at exit = Cre

βi = angle of Absolute velocity at inlet.

βe = angle of Absolute velocity at inlet.

SUPERIMPOSING VELOCIT TRIANGLES AT INLET AND EXIT

Blade velocity = Cb

α i = angle of Absolute velocity at inlet.

α e = angle of Absolute velocity at exit.

at inlet.

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Cb

βiαe

Velocity Diagram for First row of moving bladesC

fe

Cfi

∆Cw = Cwi + Cwe

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LECTURE # 03

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RATE AT WHICH WORK IS DONE ON THE IMPULSE TURBINE

The rate at which work is done on the wheel is given by the product of the driving force and the blade velocity.

DRIVING FORCE: From Newton’s Second Law the tangential force acting on the jet is given by

F= m’ × (Change of velocity in the tangential direction)

The tangential velocity of the steam relative to the blade at inlet is given by AE = Cri CosβiAE = Cri Cosβi

The tangential velocity of the steam relative to the blade at exit is given by AD = - Cre Cos β

Therefore Change in velocity in tangential direction

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The reaction to this force provides the driving thrust on the wheel:

Referring to the combined diagram :

The change in velocity is given as:

As we Know thatThe rate at which work is done on the wheel is given by the product of the driving force and the blade velocity.

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DIAGRAM EFFECIENCY

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LECTURE # 04

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The velocity of steam leaving the nozzles of an impulseturbine is 900 m/s and the nozzle angle is 20’. The bladevelocity is 300 m/s and the blade velocity co efficient is 0.7.calculate for a mass flow of 1 Kg /s , and symmetricalblading:

EXAMPLE NO : 01

(i) The blade inlet angle(ii) The driving force on the wheel(iii) The axial thrust(iv) The diagram power(v) The diagram effeciency

GIVEN DATA

Cai = 900 m/s

αi = 20’

Cb = 300 m/s

K = 0.7

m’ = 1 kg / s

And symmetrical blading (βi = βe)

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Cb = 300 m/s

Cai = 900 m/s

α = 20’

(i) The blade inlet angle

βi = ?

Applying Cosine Rule to OAB

E A DO

Applying Cosine Rule to OAB

Cri = 626.5

Using sine rule

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(ii) The driving force on the wheel

Driving Force on the Wheel = m’ ΔCw

Cre = k Cri = 626.5 × 0.7 = 438.5 m/s

AD = CriCosβi = 626.5 Cos 29˚24’ = 545.8 m/s AE = C Cosβe = 438.5Cos 29˚24’ = 381.9 m/s

ri

AE = CreCosβe = 438.5Cos 29˚24’ = 381.9 m/s

Cw = AD – (- AE) = 545.8 + 381.9 = 927.7 m/s

m’ ΔCw = 1 × 927.7 = 927.7 kg/s K-13ME-05

(iii) The axial thrust

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LECTURE # 05

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Optimum operating conditions from the blade velocity diagrams

For a given steam velocity Cai & a given blade velocity Cb:Rate of doing work is maximum when :

Rate of doing work per unit mass

= 2(Cai Cos αi - Cb) × Cb

Rate of doing work is maximum when :

• Cos α i = 1 when (α i = 0)

•At this angle Axial component becomes zero.

•But axial component is essential to allow the steam to reach the blades and to clear the blades on leaving.

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Effects of varying angle (α i ):Disadvantage•As α i increases rate of doing work on the blades is reduced.

Advantage•Surface area will be reduced and hence

friction will be less.friction will be less.

• Therefore selection of the inlet velocity angle must be made on the basis of these conflicting requirements.

• Usual values of α i lie b/w 15 to 30 degrees. K-13ME-05

Blade speed ratio or Condition for maximum diagram effeciency

Differentiating diagram effeciency with respect to (Cb/Cai). (Cb/Cai).

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Maximum Diagram Effeciency:

According to the condition of Max: Diagram Effeciency:

FIGURE: Diagram effeciency against blade speed ratio for a single-stage impulse turbine.

Substituting in Equation no: (i), we get,

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We know that Max: Diagram Effeciency is give as

Substituting this in equation no: (i)

Power output at maximum diagram effeciency

According to the condition of Max: Diagram Effeciency

from equation (ii) and (iii):

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LECTURE # 06

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Compounding (method of reducing the speed)

As discussed in the impulse turbine, that if the steam isexpanded from boiler pressure to condenser pressure in onestage the speed of the rotor becomes tremendously high whichcops up practical complicacies.

“All these methods utilize a multiple system of rotor in series, keyed on a common shaft and the steam pressure or jet velocity keyed on a common shaft and the steam pressure or jet velocity is absorbed in stages as the steam flows over the blades. This is known as compounding.”

There are several methods of reducing this rotor speed.

1. Velocity Compounding 2. pressure compounding3. Pressure -Velocity Compounding

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Velocity compounding (Curtis Stage)

Velocity compounded stage is called Curtis stage after itsdesigner.

In velocity compounding all the expansion takes place in asingle set of nozzles, and the steam then passes through aseries of blades attached to a single wheel or rotor.

Since the blades move in same direction it is necessary tochange the direction of the steam between one set of movingblades and the next.

For this purpose a stationary ring of blades is fitted betweeneach pair of moving blades.

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Sectional View of a Stage of Velocity Compounded impulse turbine

In a velocity compounded impulseturbine every stage consists of:

A SET OF NOZZLES:where the fluid expand from

boiler pressure to the condenserpressure.

TWO SETS OF MOVING BLADESSEPARATED BY A SET OF FIXEDBLADES :where in moving blades velocity isabsorbed and the fixed bladesthan redirect the steam oversecond row of moving blades

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PRESSURE COMPOUNDING (THE RATEAU TURBINE)

A turbine with a series ofsimple impulse stages iscalled Rateau Turbine

In pressure compoundingthe pressure drop availableto the turbine is used in ato the turbine is used in aseries of small incrementseach increment beingassociated with one stage ofturbine.

Boiler Pressure Condenser

PressureK-13ME-05

Cb

βi1 αe1

∆Cw1 = Cwi1 + Cwe1

Cfe

1

Cfi

1

First row

Velocity diagrams for a two-row velocity Compounded impulse turbine

∆Cw1 = Cwi1 + Cwe1

Cb

βi2 αi2

βe2

Cfe

2

Cfi2

∆Cw2 = Cwi2 + Cwe2

Second rowαe2

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LECTURE # 07

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The first stage of a turbine is a two-row velocity-compounded impulse wheel.The steam velocity at inlet is 600 m/s, the mean blade velocity is 120 m/s, andthe blade velocity coefficient for all blades is 0.9.The nozzle angle is 16o and the exit angles for the first row of moving blades,the fixed blades, and the second row of moving blades, are 18, 21, and 35o

respectively.

Calculate:

Problem: 02

1. The blade inlet angles for each row;

2. The driving force for each row of moving blades and the axial thrust onthe wheel, for a mass flow rate of 1 kg/s;

3. The diagram power per kg per second steam flow, and the diagramefficiency for the wheel;

4. The maximum possible diagram efficiency for the given steam inletvelocity and nozzle angle. K-13ME-05

Data:Cai1 = 600 m/s ; Cb = 120 m/s k = 0.9 ; αi1 =16’ ; βe1 = 18 ‘ βi1 = 20’ ; αe1 = 24.5’βi1 = 20’ ; αe1 = 24.5’

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1. The blade inlet angles for each row; (βi1 ,βi2 )

These angle can be determined by drawing the velocity triangles

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FIX

ED

BLA

DE

MOVING BLADE 1

FIX

ED

BLA

DE

MOVING BLADE 2

Cai2 = k Cae1 = 0.9 × 327 = 294 m/sExit angle for the fixed blade is 21’

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Cb =120 m/s

βi1 = 20’ αe1 = 24.5’

Velocity Diagram for First row of moving blades

Cfe

1 =

13

5 m

/s

Cfi

1 =

16

7 m

/s

From inlet triangle we get the values :βi1 = 20’ Cri1 = 486 m/sThen:

From exit triangle we get the values of:αe1 = 24.5’Cae1 = 327 m/s

∆Cw1 = Cwi1 + Cwe1 = 874 m/s

Cfi

1 =

16

7 m

/s

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Cb =120 m/s

βi2 = 34.5’

αi2 = 21’ βi2 = 35’

Cfe

2 =

97

m/s

Cfi2

= 10

6 m

/s

βi2 = 34.5’

∆Cw2 = Cwi2 + Cwe2 = 292.5 m/s

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Total Driving Force = m’ (∆Cw1 + ∆Cw2)

Driving Force for the 2nd row of moving blades = m’ ∆Cw2

Driving Force for the 1st row of moving blades = m’ ∆Cw1

(ii) Driving Force and Axial Thrust

Driving Force

Axial Thrust

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(iii) Diagram Effeciency

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Cri1 = βi1 = Cri2 = βi2 =

Cai1 = 600 m/s αi1 = 16o Cai2 =

Cwi1 = Cwi2 =

Cfi1 = Cfi2 =

Cb1 = 120 m/s Cb2 =

Cre1 = βe1 = Cre2 = βe2 =35o

K = 0.9, exit angle for fixed blades = 21 o

Cre1 = βe1 = Cre2 = βe2 =35

Cae1 = αe1 = 18o Cae2 =

Cwe1 = Cwe2 =

Cfe1 = Cfe2 =

Cb2=

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This is the type of turbine in which there is a gradualpressure drop and takes place continuously over the fixedand moving blades.

REACTION TURBINE

Fixed Blades: the function of fixed blades is that the alterthe direction of steam as well as it expand to a largervelocity.

Moving blades: they absorb the kinetic energy of thesteam

Reaction turbine (three stage)K-13ME-05

As the volume of steam increases at lower pressures therefore, the diameter of the turbine must increase after each group of blade rings.

Some important considerations about reaction turbine

Since the pressure drop per stage is small, therefore the number of stages required is much higher than an impulse turbine of same capacity.

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VELOCITY COMPOUNDED IMPULSE TURBINE

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