steam turbine

Steam TurbineSteam Turbine

The Impulse PrincipleThe Impulse Principle

The force on the plate, F is equal to the change in The force on the plate, F is equal to the change in momentum of the jet in +x directionmomentum of the jet in +x direction

( )0s s

m mF V V

g g

• •

= − =

where m is mass-flow rate of the jet, lbm/s or kg/s

Vs is velocity in horizontal direction, ft/s or m/s

Fixed flat plate


( )s B

mF V V

g

•

= −

( )B B S B

mW FV V V V

g

••

= = −

Moving flat plate

where VB is the plate velocity, ft/s or m/s

2

2

2

2

B Bplate

S SS

V VW

V VmVg

η•

•

= = − ÷ ÷

÷

Force on the plate

Power done by jet

Efficiency is ratio of power to initial power of the jet

Power is 0 if VB = 0 or (Vs-VB)=0

B

S

V

V


To find optimum VTo find optimum VBB, power is differentiated , power is differentiated

respect to Vrespect to VBB

( ) ( )2

,

2

max

2 0

2

4

S B B S BB B

SB opt

S

dW d m mV V V V V

dV dV g g

VV

mVW

g

• • •

••

= − = − =

=

=

Half of kinetic energy per unit time of jet

Half of jet velocity


Fluid relative entrance velocity = Fluid relative exit velocity

Fluid relative velocity = s BV V−

( )Absolute jet velocity at exit (+x direction) = - - 2B S B B SV V V V V= −

( ) ( )

( )2

22

2

4

S B S S B

B B S B

B Bb

S S

m mF V V V V V

g g

mW FV V V V

g

V V

V Vη

• •

••

= − − = −

= = −

= − ÷

For frictionless blade

By impulse and momentum principle

For 180o curved blade

Double of value on flat plate case


( ) ( )2

,

2

max

2 2 2 0

2

2

S B B S BB B

SB opt

S

dW d m mV V V V V

dV dV g g

VV

mVW

g

• • •

••

= − = − =

=

=

To find optimum VTo find optimum VBB, power is differentiated , power is differentiated

respect to Vrespect to VBB

Half of jet velocity

Equal to kinetic energy per unit time of jet

,max 100%Bη =


It is impossible to have 180It is impossible to have 18000 curved blade in actual curved blade in actual applicationapplication jet exit will impinging on the back of next bladejet exit will impinging on the back of next blade

Blade entrance angle and blade exit angle cannot be Blade entrance angle and blade exit angle cannot be zero, as shown in the figure belowzero, as shown in the figure below

The Velocity DiagramThe Velocity Diagram

Absolute velocity of fluid leaving the nozzle

Relative velocity of fluid (as seen by an observer riding on the blade)

Blade velocity

Absolute velocity of fluid leaving the bladeRelative velocity of fluid leaving the blade

Nozzle angle

Blade entrance angle

Blade exit angle

Fluid exit angle


( )

( )

( )

1 2

1 2

1 2

2

1 1 1

cos cos

cos cos

2 cos cos

S S

w w

BB S S

sB BB

s s s

mF V V

g

mF V V

g

mVW FV V V

g

VV V

V V V

θ δ

θ δ

η θ δ

•

•

••

= −

= −

= = −

= − ÷ ÷ ÷

Velocity of whirl, Vw


With no friction, expansion or contractionWith no friction, expansion or contraction

( )

r1 r2 1

2 1 1

V in + x direction = V in -x direction = cos

Absolute velocity of fluid leaving the blade in +x direction

cos cos 2 cos

s B

s B s B B s

V V

V V V V V V

θ

δ θ θ

−

= − − = −

( )

( ),

1

1,

2 2max 1

2cos

0

cos

2

2cos

2 B opt

Bs B

B

sB opt

s

mVW V V

g

dWbydV

VV

m mW V V

g g

θ

θ

θ

••

•

• ••

= −

=

=

= =

( ) 2max

,max21

cos

2

B

s

W

mVg

η θ•

•= =

÷ ÷


From first-law of thermodynamics, From first-law of thermodynamics, for adiabatic system and for adiabatic system and ΔΔPE = 0PE = 0

( )2 21 2

1 2 2 2s sV V

W H H mg g

• • = − + − ÷

where H1 and H2 are the enthalpy entering and leaving the blade

H1- H2 is obtained by considering fluid flow relative to the blade (observer is on the blade), where only relative velocities and no work are observed.

2 22 1

1 2 2 2r rV V

H Hg g

− = − ÷

( ) ( )2 2 2 21 2 1 22 s s r r

mW V V V V

g

••

= − − − Including friction, expansion or contraction


In case of pure impulse (no friction, no expansion In case of pure impulse (no friction, no expansion and no contraction), and no contraction), HH11 = H = H22 and V and Vr1r1 = V = Vr2r2

Friction is described by, Friction is described by, velocity coefficientvelocity coefficient, k, kvv

Stage efficiency is the ratio of work of the blade Stage efficiency is the ratio of work of the blade divided by the total enthalpy drop for the whole divided by the total enthalpy drop for the whole bladeblade

( )2 2 impulse 1 22

pure s s

mW V V

g

••

= −

2

1

rv

r

Vk

V=

Hs

s

W W

H m hη

• •

∆ •= =∆ ∆

Impulse TurbineImpulse Turbine

Blade is usually symmetrical.Blade is usually symmetrical. Entrance angle (Entrance angle (φφ ) and exit angle ( ) and exit angle (γγ) are around ) are around

2020oo.. Usually used in the entrance high-pressure stages Usually used in the entrance high-pressure stages

of a steam turbine.of a steam turbine. Enthalpy drop and pressure drop occur in the Enthalpy drop and pressure drop occur in the

nozzle.nozzle.

The Single-Stage The Single-Stage Impulse TurbineImpulse Turbine

De Laval turbineDe Laval turbine

• Steam is fed through one or several convergent-divergent nozzles.

• Pressure drop occurs in the nozzle (not in the blade)

•Maximum velocity (kinetic energy) occurs at nozzle exit.

Compounded-Impulse TurbineCompounded-Impulse Turbine

For single-stage impulse turbineFor single-stage impulse turbine

For modern boiler conditions, expansion in single For modern boiler conditions, expansion in single nozzle stage gives 1645 m/s.nozzle stage gives 1645 m/s.

Beyond the maximum allowable safety limits. (due to Beyond the maximum allowable safety limits. (due to centrifugal stress)centrifugal stress)

To overcome these difficulties,To overcome these difficulties, Velocity-compounded turbineVelocity-compounded turbine Pressure-compounded turbinePressure-compounded turbine

1,

cos

2s

B opt

VV

θ=

Velocity-Compounded Impulse TurbineVelocity-Compounded Impulse Turbine

Curtis stage turbineCurtis stage turbine

22 1 1

1

33 2 2

2

44 3 3

3

rr r v

r

ss s v

s

rr r v

r

VV V k

V

VV V k

V

VV V k

V

< =

< =

< =


( ) ( ) ( ) ( ){ }2 2 2 2 2 2 2 21 2 2 1 3 4 4 32 s s r r s s r r

c

mW V V V V V V V V

g

••

= − − − + − − −

1 1,

cos

2s

B opt

VV

n

θ=Nozzle angle

Number of stages


Work ratio Work ratio for 2 stages turbine 3:1for 2 stages turbine 3:1 for 3 stages turbine 5:3:1for 3 stages turbine 5:3:1 for 4 stages turbine 7:5:3:1for 4 stages turbine 7:5:3:1

Pressure-Compounded Impulse TurbinePressure-Compounded Impulse Turbine

Rateau turbineRateau turbine

1 2 ... 2 tots s c

hV V g

n

∆= = =

Δ htot = the total specific enthalpy drop of the turbine

n = the number of stages

Enthalpy drops per stage are the same

Pressure drops are not

Pressure-Compounded Impulse TurbinePressure-Compounded Impulse Turbine

Advantages of reduced blade velocity, reduced steam velocity (hence friction)

Equal work among the stages.

Disadvantages pressure drop across the fixed nozzles require leak-tight diaphragm to avoid steam leakage.

Reaction PrincipleReaction Principle

Fixed nozzle, a rocket, a whirling lawn sprinkle and turbine are Fixed nozzle, a rocket, a whirling lawn sprinkle and turbine are devices that cause a fluid to exit at high speeds.devices that cause a fluid to exit at high speeds.

The fluid beginning with zero velocity inside, creates a force in The fluid beginning with zero velocity inside, creates a force in the direction of motion F equal tothe direction of motion F equal to

c

VF m

g

•=

Reaction TurbineReaction Turbine

pressure

Absolute velocity

Nozzles with full steam admission

Unsymmetrical bladeSimilar shape to fixed blade (opposite direction curve)

Pressure continually drops through all rows of blades (fixed and moving)

Absolute velocity changes within each stage repeats from stage to stage

50 % Degree of reaction

-Half of enthalpy drop of the stage occurs at fixed blade

-Half of enthalpy drop of the stage occurs at moving blade


( )

( ) ( )

1

1

, 1

2 2

1

2 cos

2 cos 2 0

cos

cosopt

Bs B

c

s BB

B opt s

s Bc c

VW m V V

g

dWV V

dV

V V

m mW V V

g g

θ

θ

θ

θ

• •

•

• ••

= −

= − =

=

= =


( )2 21 0

0 1

, 0 1

12 s s

cN

f s s

V Vg h h

h h hη

− ÷ − = =∆ −

( )0 2

B

s ss

W W

m h m h hη

• •

• •= =∆ −

( )2 21 1

1 22 2

B

s sms s

c c

W W

V Vm h m h hg g

η• •

• •= =

+ ∆ + − ÷ ÷

Fixed-blade (nozzle) efficiency

Moving-blade efficiency

Stage efficiency

, isentropic enthalpy drop across fixed bladef sh∆ =

isentropic enthalpy drop across moving blademsh∆ =

isentropic enthalpy drop across entire stagesh∆ =

Enthalpy

Entropy


Reaction stage has pressure drop across the Reaction stage has pressure drop across the moving blade.moving blade.

Not suitable for high pressure stage because Not suitable for high pressure stage because pressure drop is very high and results in steam pressure drop is very high and results in steam leakage around the tips of the blades.leakage around the tips of the blades.

Impulse turbine is normally used for HP stages.Impulse turbine is normally used for HP stages. Reaction turbine is normally used for LP stages.Reaction turbine is normally used for LP stages.

Axial ThrustAxial Thrust

Impulse turbineImpulse turbine Little pressure drop on the moving blade from frictionLittle pressure drop on the moving blade from friction Change in axial component of momentum of the Change in axial component of momentum of the

steam from entrance to exitsteam from entrance to exit

For pure symmetrical impulse blades, VFor pure symmetrical impulse blades, V r1r1 = V = Vr2r2 and and φφ = =

γγ, axial thrust is zero., axial thrust is zero.

( )1 2sin sinaxial r rc

mF V V

gφ γ

•

= −

Axial ThrustAxial Thrust

Reaction turbineReaction turbine Change in axial momentum is zero.Change in axial momentum is zero. Large and continual pressure drop across the Large and continual pressure drop across the

moving blade.moving blade. Axial thrust is quite large.Axial thrust is quite large. Thrust bearing to support axial thrust.Thrust bearing to support axial thrust. Dummy piston (rings) to balance axial thrustDummy piston (rings) to balance axial thrust

Steam TurbineSteam Turbine

Twisted BladesTwisted Blades

Reaction blades are high, especially in the latter stages.Reaction blades are high, especially in the latter stages. VVBB increases with radius from base to tip of blade. increases with radius from base to tip of blade.

VVs1s1 and and θθ do not vary in radial direction. do not vary in radial direction.

Increase from root to tip

decrease from root to tip

Twisted BladesTwisted Blades

Combination TurbinesCombination Turbines

Case 1Case 1 Curtis stages (Velocity compounded impulse)Curtis stages (Velocity compounded impulse)

First two-rowsFirst two-rows

Rateau stages (Pressure compounded impulse)Rateau stages (Pressure compounded impulse) Latter stagesLatter stages

Case 2Case 2 Curtis stagesCurtis stages

First one or two-rowsFirst one or two-rows

Reaction stagesReaction stages

Combination TurbinesCombination Turbines

Impulse stageImpulse stage Suitable for high pressureSuitable for high pressure No pressure drop on moving bladeNo pressure drop on moving blade For same enthalpy drop, much larger pressure drop For same enthalpy drop, much larger pressure drop

occurs at high pressure.occurs at high pressure. Higher pressure drop = more possibility for leakage Higher pressure drop = more possibility for leakage

between blade tip and casingbetween blade tip and casing Reaction stageReaction stage

More efficient at low pressureMore efficient at low pressure

Turbine ConfigurationsTurbine Configurations

Tandem compound – single shaftTandem compound – single shaft Cross compound – two parallel shaftCross compound – two parallel shaft HP turbine – high pressure turbineHP turbine – high pressure turbine IP turbine – intermediate pressure turbineIP turbine – intermediate pressure turbine LP turbine – low pressure turbineLP turbine – low pressure turbine LSB – last stage bladeLSB – last stage blade

Turbine ConfigurationsTurbine Configurations

Steam Flow PathSteam Flow Path

Straight through Single reheat

Extraction Induction (or mixed flow)

Turbine RotorsTurbine Rotors

Almost all of turbines are placed face-to-face, Almost all of turbines are placed face-to-face, especially in IP and LP turbine, which comprise especially in IP and LP turbine, which comprise of reaction stages.of reaction stages.

What is the reason for this arrangement?What is the reason for this arrangement?

HP inlet

HP Exhaust

IP inlet

LP ExhaustIP Exhaust LP Exhaust LP ExhaustLP Exhaust

LP inlet LP inlet

IP Exhaust

What is the configuration type of this What is the configuration type of this steam turbine?steam turbine?

steam turbine

Engineering