3. flows in a steam path in steam path_v7.pdfsteam turbine 3. flow in steam path 29 / 112 the...

Steam Turbine 3. Flow in Steam Path 1 / 112

3. Flows in a Steam Path


Steam Turbine Flow Model 24 2

Dimensionless Numbers 49 4

Fluid Dynamics 2 1

Thermodynamics and Fluid Dynamics for Steam Turbines 35 3

Impulse Turbine and Reaction Turbine 65 5

Stage Efficiency 101 6

Blade Profile Enhancement 107 7


Incidence

Blade inlet

angle

Gas inlet

angle

Direction of

gas flow

Stagger angle

Camber

angle Deflection

Direction of

gas flow

Deviation

Angle

Gas outlet

angle

Blade outlet

angle

Pitch

Trailing edge

Leading edge

Blade thickness Suction side

Pressure side

Nomenclature of Turbine Blade


R

Reaction Action

F

V

A

, Nozzle

F = mV = V2A

m = VA (mass flow rate)

Fluid Dynamic Force


Speed of Sound [1/2]

dV p+dp

+d

p

V = 0

a

a

dp p

x

a dV p+dp

+d

p

dp

p

x

a

Stationary

observer

Observer

travelling with

wave front

RTp

a

2

a

VM


The effect of compressibility is important in high velocity regimes. Mach number is the ratio of velocity to

acoustic speed of a gas at a given temperature M V/ . Acoustic speed is defined as the ratio change in

pressure of the gas with respect to its density if the entropy is held constant:

cs

pa

2

With incompressible fluids, the value of the acoustic speed tends toward infinity. For isentropic flow, the

relation between pressure and density is as follows:

.constp

.lnln constp 0

d

p

dp 2ap

d

dp

RTp

a

2

Speed of Sound [2/2]


Consider a one-dimensional isentropic gas flow in a convergent-divergent nozzle. Since the mass flow rate is

constant, and taking logarithms and then differentiating gives

Since the stagnation enthalpy is constant in isentropic flow, differentiating the stagnation enthalpy gives

From Gibb’s equation

Thus,

Elimination of density term using the continuity equation gives

Isentropic Flow with Area Change

.constVAm

0A

dA

V

dVd

.2

1 2 constVhho VdVdh

0/ dpdhTds /dpdh

dad

pdpVdV

s

211

V

dVM

A

dA12

[ A Convergent-divergent Nozzle ]

Flow in a Convergent-Divergent Nozzle [1/5]


dA = (M21)

dV

V A

M 1

M 1 Convergent Nozzle

(Nozzle)

M 1 M 1 Divergent Nozzle

(Diffuser)

M 1

M 1 Convergent Nozzle

(Nozzle)

M 1 M M 1 Divergent Nozzle

(Diffuser)

Blade

direction

Axial

direction

Turbine

Blades Compressor

Blades



Convergent-divergent nozzle

x

M 1 [ Convergent-Divergent Nozzle ] M 1

M = 1

dA = (M21)

dV

V A

[ Supersonic Converging-Diverging Nozzle, GE ]

Blade Overlap



삼천포화력본부 #6 LSB (33.5”/3600 rpm)

LSB developed by Siemens (32”/3600 rpm)



Siemens



Choked Flow [1/11]

1

2

V1 0

p1 T1

1

A

M2

.constp

2

2212

11 MTT

12

1

2

22

1

1

2

11

MM

RT

Apm 0

2

dM

md 12 M

22222222 RTAMMAaAVm 22 RTa

2

22

RT

p

2

22

T

pM

RAm

Choked flow is also called as ‘choking of the flow’, or, ‘flow choking’, or ‘choke’.


02

dM

md 12 M

There is a maximum airflow limit that occurs when the Mach number is equal to one. The limiting

of the mass flow rate is called choking of the flow. If we substitute M2 = 1, we can determine the

value of the choked mass flow rate.

12

1

1

1

2

1

RT

Apm

Choked Flow [2/11]


V

p2/p1 1.0

a Sonic velocity

(p2/p1)critical

p1

p2

High pressure fluid

V2

1 2

A T2

Energy equation:

from dV2 / d(p2/p1) = 0, one can get maximum speed,

1212

2

1

2

2112212122

1wzzgVVppuuq

2122112 2 TTcppV

1

1

2112 1

12

p

ppV

2222111

2 aRTppVcritical

Choked Flow [3/11]


Mass flow rate:

Using isentropic relationship,

from dm / d(p2/p1) = 0, one can get a critical pressure ratio,

AVm 22

1

1

2

1

2

critical

p

pCritical pressure ratio

- superheated steam = 0.546 (=1.3)

- saturated steam = 0.577 (=1.135)

- air = 0.528 (=1.4)

(see K.C. Cotton, pp. 15)

1

1

2

2

1

2

1

1

1

2

p

p

p

ppAm

1

1

211

2

11

2p

pp

Am

Choked Flow [4/11]


Stop V/V

Control V/V

HP IP LP Gen

Condenser

Reheater Reheat Stop and

Intercept V/V

Main Steam

Hot Reheat

Cold

Reheat

Crossover

Ventilation

V/V

HRH bypass station

(HRH: Hot Reheat)

HP

byp

ass

sta

tio

n

Application of Choked Flow to Sparger

Choked Flow [5/11]


[ Typical layout showing dump tube diffusers fitted into the condenser inlet duct ]

Typical Turbine Bypass Dump to Condenser

Choked Flow [6/11]


Desuperheater section of a

steam conditioning valve

Spargers designed to spray out to end to

eliminate steam impinging upon the

condenser tubes


Choked Flow [7/11]


Pressure reducing

valve

Sparger


Choked Flow [8/11]


Choked Flow [9/11]


PWR System Outline

Choked Flow [10/11]


<Side View>

차세대원전에서1 비상시 원자로냉각재계통(RSC; Reactor Coolant System) 의 압력을 낮추어주기 위하여 POSRV(Pilot Operated Safety Relief Valve)를 통하여 고온고압의 증기를 IRWST(In-containment Refueling Water Storage Tank) 내부에 잠겨있는 sparger를 통하여 방출.

Computational Domain for IRWST

Choked Flow [11/11]


cc = 0.61

c = 0.98 cc = 1.00

c = 0.98

cc = 1.00

c = 0.82

Aj A0

cd = cc c

Aj = cc A0

Vactual = c Videal

m = Vactual Aj = ccc Videal A = cd Videal A

cd = discharge coefficient

(or flow coefficient)

cc = contraction coefficient

c = velocity coefficient

Flow of Fluids

(CRANE Co.)

Actual Flow

Fluid Flow


Steam Turbine Flow Model 2

Dimensionless Numbers 4

Fluid Dynamics 1

Thermodynamics and Fluid Dynamics for Steam Turbines 3

Impulse Turbine and Reaction Turbine 5

Stage Efficiency 6

Blade Profile Enhancement 7


Steam Turbine Flow Model

1

1

2

2

1

2

1

1

1

2

p

p

p

ppAcm d

1

1

2

2

1

21

1

2

p

p

p

pAacQ d

CV 1 2 3 4 5

SV = Stop Valves

CV = Control Valves

P = First Stage Shell Pressure

L-0 L-1

Con

de

nser

Stage Number

P

Steam

SV


The flow model is a series of orifices or nozzles in a pipe with a constant upstream pressure and downstream

pressure.

The pressure between any two of these orifices depends entirely on the quantity of steam and the nozzle

area following that point.

The first stage is represented as having four orifices to simulate a turbine with four control valves, while all the

other stages have only one orifice.

If all four control valves are opened, the flow will increase until an equilibrium condition is reached.

This steady state flow through each orifice in the model will be the same.

Therefore, the pressure upstream of each orifice will depend on the area of the downstream orifice.

As steam passes from throttle to the condenser, the areas of individual orifices are progressively larger.

Therefore, the pressure upstream of each stage is lower than the preceding stage.

A number of steam turbine stages can be classified into only three groups:

① The first stage or governing stage Variable flow area by control valve position

② The last stage (LSB) Flow choking is occurred

③ All the stages between Constant pressure ratio even during part load operation

In view of the specifics of the steam path design, all stages of a condensing steam turbine are divided into four groups,

① Governing stages

② Stages with high pressure and low volume discharge of steam (2D)

③ Intermediate stages with relatively low pressure and high volume discharge of steam (3D)

④ Last stages in the lowest-pressure range, characterized by a very high volume discharge.



1st s

tag

e s

he

ll

2nd s

tag

e b

ow

l

500

1000

1500

2000

Thro

ttle

Pre

ssure

, psig

2500

2nd s

tag

e s

he

ll

3rd

sta

ge

bo

wl

3rd

sta

ge

sh

ell

4th s

tag

e b

ow

l

4th s

tag

e s

he

ll

5th s

tag

e b

ow

l

5th s

tag

e s

he

ll

6th s

tag

e b

ow

l

1800

1500

1250

1042

868

1200

Th

rott

le p

ress

2400

900

750

625 521

434

Factor

of 2 Factor

of 2

0



For a throttle pressure of 2400 psig, the first stage

pressure with VWO would be 1800 psig and the

pressure downstream of the second stage would

be about 1500 psig. In this case, the pressure

ratio across the second stage is 1.2.

If throttle pressure decreases to 1200 psia, the

flow would decrease by a factor of 2 to 1. this

relationship holds true for all the stages until the

last stage. That is, the pressure ahead of the last

stage will decreases by a factor of 2 to 1.

All other stages, except HP first stage and LP last

stage, operate at a constant pressure ratio and

therefore a constant efficiency over the load range.

Velocity triangles for various

steam turbine loads

Intermediate Stage



The governing stage has the unique characteristic of variable area.

As control valve opens, the area allowing throttle steam to flow through the turbine increase and produce

more power.

In addition, the change in flow changes the first stage discharge pressure, resulting in the pressure ratio

across the first stage.

Therefore, the first stage efficiency changes with control valve position.

At valves wide open the first stage is designed for the ideal ratio of wheel velocity and steam velocity.

As control valves close, the first stage efficiency decreases.

Partial

Arc Full

Arc

HP 1st Stage



0 0.2 0.4 0.6 0.8 1.0

10

20

30

40

50

60

70

80

90

100

0

IP Turbine

LP Turbine

HP 2nd Stage to Cold Reheat

HP 1st Stage

Throttle Flow Ratio

Tu

rbin

e S

ectio

n E

ffic

ien

cy [%

]

HP 1st Stage



The last low pressure turbine stage is the only other

stage that experiences significant changes in

pressure ratio as a result of normal power plant

operation.

The pressure of upstream of the last stage changes

with control valve position and the downstream

pressure changes with condenser pressure.

Therefore, the last stage efficiency changes with both

control valve position and with condenser pressure.

The change in pressure ratio across the first and last

stage dictates the change in efficiency of the HP and

LP turbines, respectively.

LP Last Stage



Stage Extract Bowl P Shell P Press Remarks

(psia) (psia) ratio

Throttle 3514.7

1 3409.3 2627.4 1.30

2 2122.2 1.24

3 1704.1 1.25

4 1355.9 1.26

5 1 1067.7 1.27

6 830.0 1.29

7 2 639.0 1.30 HP turbine outlet

IV 581.6

8 570.0 438.1 1.30

9 336.0 1.30

10 3 254.0 1.32

11 184.0 1.38

12 4 135.7 1.36 IP turbine outlet

X-over pipe

13 5 131.7 74.8 1.76 LP turbine inlet

14 40.5 1.85

15 6 20.5 1.96 Exceeding a critical PR



18 0.74 5.50 Connected to condenser

Stage Pressure Ratio [Sample]


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19Stage number

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0P

ressu

rera

tio

HP IP LP

Exceeding critical pressure ratio

Extraction stage : 5, 7, 10, 12, 13, 15, 16, 17

Stage Pressure Ratio [Sample]



Discussion

Several LP turbine stages, 3rd to LSB, have higher than critical pressure ratio. Discuss the

following issues.

1) Possibility of choked flow

2) Flow area

3) Steam extraction

4) LSB in terms of degree of reaction

Critical pressure ratio

- superheated steam = 0.546 (=1.3)

- saturated steam = 0.577 (=1.135)

- air = 0.528 (=1.4)

(see K.C. Cotton, pp. 15)




Fluid Dynamics 1



Stage Efficiency 6



Flow Behavior in a Turbine Stage

Pressure E Kinetic E

Thermal E Thermal E Mechanical E

Nozzle Row Bucket Row

z

r

The flow behavior is investigated in a tangential plane.

Therefore, the flow velocity has two components, one is axial

component denoted by subscript z, and the other is

tangential component denoted by subscript implying a whirl

velocity.


Absolute vs. Relative Velocity

Fluid velocity is an important variable governing the

flow and energy transfer within a turbine.

The absolute velocity ( ) is the fluid velocity relative

to some stationary point and is usually parallel to the

nozzle (stationary blade).

When considering the flow across a rotating element

like a bucket, the relative velocity ( ) is important

and is usually parallel to the rotating element.

Vectorially, the relative velocity is defined as:

where is the tangential velocity

of the bucket.

ucw

u

w

c

[ Velocity Triangle in an Axial Turbine ]

u

u

c2

w2

2

2

w3

3 c3

p1

p2

p3

u

1

c1

3

Nozzle Row

Bucket Row


Velocity Triangle in a Turbine

Velocity Triangle at Root

Root

Tip

rRoot rTip


The absolute velocity increases from c1 to c2 across the nozzle.

The absolute velocity decreases from c2 to c3 across the bucket. This is because the kinetic energy entering

bucket is extracted by the bucket. Thus, bucket attains rotating power.

In the case of turbine, the convention chosen is that the angles are positive when measured in the direction of

rotation. Therefore, 2, 2 are positive; 3, 3 are negative.

c : absolute velocity of fluid

u : tangential velocity of blade

w : relative velocity of fluid to blade

u

u

c2

w2

2

2

w3

3 c3

p1

p2

p3

u

1

c1

3

Nozzle Row

Bucket Row


Velocity Triangle at Tip

Velocity Triangle in a Turbine

Root

Tip

rRoot rTip


u

u

c2

w2

w3

p1

p2

p3

u

1

c1

Nozzle Row

Bucket Row

2

2

3 c3

3


Expansion Lines

A nozzle is used to provide partial

expansion of the gas as well as to

guide the flow smoothly into a

bucket.

If the flow is isentropic in the nozzle,

condition 2s is achieved after

passing through the nozzle.

Practically, however, nozzle

expansion occurs along curve 1-2

because of losses occurred in the

nozzle path.

Change in stagnation pressure

(po,1po,2) is due to the losses,

because there is no work extraction

from the fluid inside the nozzles.

The process along 2-3 represents

the expansion through bucket.

If the flow is isentropic only in the

bucket, condition o,3s or 3s is

achieved.

p3

po3

1

o,3ss

p2

o,1

p1

po,2 po,1

1/2c12

2

1/2c22

h

s

1/2c32

3ss

2s

o,3s

3s

o,3

3

o,2

u

u

c2

w2

2

2

w3

3

c3

p1

p2

p3

u

1

c1

3

Nozzle Row

Bucket Row

[ Expansion Line in a Turbine Stage ]


Turbine Efficiencies

Total-to-static Efficiency Total-to-total Efficiency

• In many turbines (especially steam turbines), the

kinetic energy at the exit (c32/2) should be as small

as possible, because this represents aerodynamic

loss.

• Therefore, the design philosophy is to achieve as

low a velocity at the exit as possible. For this reason,

active length of LSB of steam turbines is very long.

• In such situations, a total-to-static efficiency is used.

• In most aeronautical applications gas turbines, the

exhaust energy is utilized for thrust generation.

Therefore, the exhaust energy is used to produce

useful power.

• Therefore, a more appropriate definition to

represent the performance of these turbines is the

total-to-total efficiency .

• The total-to-total efficiency is also defined as

isentropic efficiency.

• For a multistage turbine, total-to-total efficiency

should be used because the kinetic energy at the

exit of a stage (except the last stage) is not lost.

sso

oo

ssssossoo

oo

tshh

hh

hhhh

hh

31,

3,1,

33,3,1,

3,1,

ssoo

oo

tthh

hh

3,1,

3,1,


Notation for Flow in a Bucket Row

u

w3

3

c3

c2

w2

2 2

3

N B

w,3

c,2 c,3

w,2

dc = (c,2 c,3)

u

c: absolute velocities (velocities in the reference

frame of the nozzles)

w: relative velocities (velocities relative to moving

surface, the buckets)

u: tangential velocities of blades (in the positive

direction)

2, 2 are positive, and 3, 3 are negative.

r2 r3

w2 or c2 w3 or c3

Bucket

Row

u

u

c2

w2

2

2

w3

3 c3

p1

p2

p3

u

1

c1

3

Nozzle Row

Bucket Row

Euler Equation [1/7]



The change of momentum between the flow entering and leaving the bucket can be used to calculate the

force acting on the bucket.

There are three principal components of this force, axial, radial, and tangential.

The axial and radial components are important for the design of bearings and for the analysis of vibration

excitations, etc.

But, these two components cannot contribute to the work transfer between the working fluid and the bucket.

Only the tangential component of the force can produce a change in enthalpy through a work transfer.

Tangential force on rotor from entering fluid =

Work bucket = force length =

Power on bucket per unit time = work on rotor / time =

Net power on bucket,

Therefore, Euler’s equation can be derived.

(e.1)

Turbine has a positive work out, however, a pump, fan, and compressor will have negative work out.

2,cm

22, rcm

22, rcm

3,32,233,22,23 cucumrcrcmW

3,32,22323 / cucumWw

22, cc

Euler equation



For an adiabatic bucket row in the absence of external torques, or large changes in elevation, the first law of

thermodynamics gives,

(e.3)

The first law of thermodynamics is,

(e.2)

3,2,23 oob hhww

2323

2

2

2

3223323232

1wzzgccppuuq

2323

2

2

2

323232

1wzzgcchhq

23232,3,23 wzzghhq oo

232,3,23 whhq oo

Therefore, following relationship can be obtained from Euler equation,

or (e.4)

It is clear that the stagnation enthalpy and pressure drop in a turbine are directly proportional to the change

in tangential velocity and blade speed. This is the most useful single relation in turbine design.

In the preliminary design of axial flow machines, the change of radius of the mean flow can often be ignored,

so that a more restricted version of Euler’s equation becomes

(e.5)

θucddho

θdcudho

c2

c3 q

w z2

z3

2

3

3,32,23,2,23 cucuhhww oob



Pressure and Temperature Drop in a Bucket Row

2,23,32,3,2,3, cucuTTchh oopoo

11

1

2,

3,

2,

2,

3,

2,2,3,

o

o

op

o

o

opoop

pTc

T

TTchh

32222,3,2,23,3 tantancos ucccucucu

1

32

2,

22

2,

3,tantan

cos1

opo

o

Tc

uc

p

p

For simple diagram having constant u from stage inlet to outlet,

32

2,

22

2,

3,tantan

cos1

opo

o

Tc

uc

T

T

2,23,32,3,23 cucuhhww oob

1

322

2,

3,tantan

11

a

uv

p

pz

o

o

322

2,

3,tantan

11

a

uv

T

Tz

o

o


1

322

2,

3,tantan

11

a

uv

p

pz

o

o

322

2,

3,tantan

11

a

uv

T

Tz

o

o

The pressure drop and temperature drop in a turbine are strongly dependent on the blade speed, axial

velocity or mass flow, inlet and exit flow angles, and absolute (23) or relative flow turning angles (23).

Higher turning angles produce larger pressure and temperature drops, and thus a higher work output.

Unlike compressors, large flow turning can be accomplished without flow separation.

The effect of the mass flow (or flow coefficient) is opposite to that of a compressor. A turbine with 2 and 3

fixed and blade speed held constant, higher mass flow produces larger pressure and temperature drops.

If 2, 3, and mass flow held constant, higher blade speeds produce larger pressure or temperature drops and

higher work output per stage.

Therefore, higher speeds result in more compact power plants. (this is why fossil power plants adopt 3600

rpm instead of 1800 rpm)

Pressure and Temperature Drop in a Bucket Row



[Exercise 3.1] Use of the Euler’s equation

What is the power output (kW) of the first stage of an axial flow steam turbine which takes 600 kg/s of

steam at 600C and 250 bar stagnation conditions? After passing through the nozzle, the flow leaves

nozzle at a direction 70 degrees from that of axial, at a velocity of 500 m/s, as given in figure 1, and

discharges it from the bucket (rotor) without swirl (c,3 = 0). The pitch diameter of the bucket is 1 m, and

the shaft speed is 3600 rpm. The turbine has an isentropic stagnation-to-stagnation stage efficiency of

90 percent.

Figure 1


2=70



[Solution]

Power output of the stage can be obtained

The first law of thermodynamics is as follows,

The turbine can be treated as adiabatic. Therefore,

From the Euler equation,

From the given conditions,

Therefore,

smrn

u /5.18860

22

smcc /470sin 222,

23,2, /566,88 smhh oo

kWs

m

s

kghhmhmW oo 140,5388566600

2

2

3,2,23

MWWW turbinenet 8.4723,23

232,3,23 whhq oo

2,23,32,23,2, cucucuhh oo

2,3,23 oo hhw 3,2,23 oo hhmW

3,2,23 oo hhmhmW




Fluid Dynamics 1



Stage Efficiency 6



By means of dimensional analysis, a group of variables representing some physical state is reduced into a

small number of dimensionless groups.

This enables a unique representation of certain classes of machines based on pressure rise (or drop) and

mass flow. Most importantly, it enables reduction of laboratory testing effort by reducing the number of

variables.

Specifically, the following can be accomplished:

1) Prediction of a prototype performance from tests conducted on a scaled model (similitude).

2) Unique representation of the performance (e.g., Mach number, Reynolds number effect).

3) Determination of a best machine on the basis of efficiency for specific head, speed, and flow rate.

Most important dimensionless numbers in axial turbines are degree of reaction, loading coefficient, flow

coefficient, etc.

Generals


The most important performance variable is the work done on the fluid, or delivered by the machines. Its

dimensionless form is the loading coefficient, which is also called as work coefficient.

That is, the loading coefficient reflects the pressure/temperature drop across a turbine.

For an adiabatic stage, the loading coefficient is defined by the ratio of specific stage work input to the square

of mean bucket speed, that is,

where wb is the isentropic work done at bucket row.

For simple diagram having constant u from stage inlet to outlet,

The loading coefficient is positive for turbines, and negative for compressors and pumps.

Loading Coefficient [1/2]

2

3,32,2

2

3,2,

2 u

cucu

u

hh

u

w oob

32

3,2,tantan

u

v

u

ccz


Loading Coefficient [2/2]

(a) high-work turbine

( = 2.0, = 0.5, = 0.5) ( = 1.0, = 0.5, = 0.5) ( = 0.5, = 0.5, = 0.5)

(b) medium-work turbine (c) low-work turbine

( = work coefficient, = flow coefficient, = degree of reaction)

In turbines having the value of 1.5 are called as “highly-loaded” or “high-work” turbines (or turbine

sections). Values of 1.0 mean “low-work” or “lightly-loaded” turbine stages.

Normally, last stage blades of steam turbines have very high loadings at the hub, and light loadings at the tip.

The value of the loading coefficient for an impulse turbine with a maximum loading coefficient is two when the

exit swirl is zero. In a 50% reaction turbine with a maximum loading coefficient is one.

(a) 0% reaction velocity diagram

u

c2 w3

w2

c3

c,2 = 2u

w3

w2

c2

u

c3

c,2 = u

(b) 50% reaction velocity diagram


The flow coefficient reflects the effect of the mass flow as well as blade speed.

The flow coefficient is defined the ratio of the axial velocity entering to the mean bucket speed, that is,

In a simple velocity diagram, the flow coefficient is constant.

The flow coefficient can be different at rotor inlet and at rotor outlet where both cz and u vary through the

stage.

It also varies with radius.

The relationship between loading coefficient and flow coefficient is

u

vz

Flow Coefficient

32 tantan


Smith Chart

A useful investigation of turbine performance

characteristics was compiled by Smith with more

than 100 sets of data from 33 turbines.

Smith found that the efficiency of a turbine depends

strongly on the loading coefficient and the flow

coefficient.

The loading coefficient influences the pressure

gradient in the passage, and this increases the

losses.

The flow coefficient is a direct measure of the mass

flow, for a given speed and machine size.

Higher flow coefficient, and hence higher mass flow,

results in a higher pressure drop, and the

corresponding losses also increase.

Therefore, the highest efficiencies occur at low loading and low flow coefficient.

As well as being an excellent comparator for different design options, the chart may be used to give

preliminary judgment on the efficiency attainable for a given design.

The chart gives the highest efficiency. This means that it was produced under the assumption that the turbine

is designed with large blades, and zero tip clearance.

In a practical design which has all the above merits, the highest efficiency attainable would be 95%.

When the lower technology level blades are employed, three points may be reduced from the values obtained

from the chart.


Degree of Reaction [1/10]

The degree of reaction in the turbine is defined as,

In the nozzle path, the first law of thermodynamics is,

(1)

In the nozzle, adiabatic process occurs, and no work produces.

Therefore, equation (1) becomes,

(2)

From the first law of thermodynamics,

(3)

The following relationships are valid is a turbine stage.

; adiabatic process

; for a normal stage

; no work at nozzle row

Thus,

(4)

2

1

2

221 5.0 cchh

12

2

1

2

21212 5.0 wcchhq

31

21

31

32 1hh

hh

hh

hh

static enthalpy drop in the bucket

static enthalpy drop in the stage

= 100 (%)

13

2

1

2

31313 5.0 wcchhq

013 q

31 cc

23133,1,

2

33,

2

11,312

1

2

1wwhhchchhh oooo

23231213 wwww

p3

po3

1

o,3ss

1/2c12

p2

o,1

p1

po,2 po,1

1/2c12

2

1/2c22

h

s

1/2c32

3ss

2s

o,3s

3s

o,3

3

o,2

[ Expansion Line in a Turbine Stage ]



Using Euler equation,

(5)

Input the equations (2) and (5) into (1) gives,

From the velocity triangle,

For a simple velocity triangle,

Therefore, the degree of reaction becomes,

For a simple velocity diagram having constant u from stage inlet

to outlet.,

(6)

3,32,22331 cucuwhh

3,32,2

2

3

2

2

21

cucu

cc

2

2,

2

2,

2

2 cvc z

2

3,

2

3,

2

3 cvc z

3,32,2

2

3,

2

2,

21

cucu

cc

3,2, zz vv

32 uuu 32

3,2,tantan1

21

u

v

u

ccz

[ Velocity Triangle in a Turbine Stage ]

u

u

c2

w2

2

2

w3

3 c3

p1

p2

p3

u

1

c1

3

Nozzle Row

Bucket Row



Equation (6) becomes,

(7)

From Euler equation,

(8)

Divide equation (8) by u2 gives,

( ) (9)

From equation (7) and (9), an important result is obtained.

(10)

From equation (9) and (10), the unknown angles of the absolute velocity can be obtained.

(11)

Turbomachinery design initiated by experienced designers through the choice of the flow and loading

coefficients and the degree of reaction and then determine the flow angles using eq. (11). These are true

only for a normal stage. If the axial velocity does not remain constant, the proper equations need to be

redeveloped from the fundamental concepts.

32

32 tantan2

12

tantan1

u

vz

323,2, tantan zb ucccuw

u

cz2u

ws 32 tantan

13 tan12tan12

2/1tan 3

2/1tan 2

1tan2 2


Similar expressions can be developed for the flow angles

of the relative velocity.

The Euler equation can be written as

Divide equation (8) by u2 gives,

Since the stagnation enthalpy of the relative motion is

constant across the bucket. Thus,

Therefore, the unknown angles of the relative velocity can

be obtained.

(12)

323,2, tantan zs uvwwuw

2

2

3

222

2

2

332 tantan2

1

2

1 zvwwhh

31

32

hh

hh

32 tantan

u

w3

3

c3

c2

w2

2 2

3

N B

w,3

c,2 c,3

w,2

dc = (c,2 c,3)

u


32 tantan2

2/tan 3

2/tan 2



It shows that the loading increases as the reaction decreases.

A small reaction means that the pressure drop across the bucket

is small, but the large loading is the result of a large deflection.

In the nozzle, the flow leaves at high speed at large angle 2.

The high kinetic energy obtained this way becomes available for

doing work on the buckets.

The flow is then deflected back toward the axis and beyond to a

negative value of 3, so that the last term in equation (10) is

positive. (3 = 1 in most turbine stages)

Thus, for a fixed reaction, an increase in the absolute value of 3,

obtained by increasing it in the opposite direction of u, leads to a

large deflection and a large value of loading coefficient.

Thus, a fairly low value of reaction and high turning gives heavily

loaded blades and a compact design.

(10)

u

u

c2

w2

2

2

w3

3 c3

p1

p2

p3

u

1

c1

3

Nozzle Row

Bucket Row

13 tan12tan12

1tan2 2


(a) 0% reaction velocity diagram

u

c2 w3

w2

c3

c,2 = 2u

w3

w2

c2

u

c3

c,2 = u

c2

w3

u

w2 c3

c,2 c,3

(b) 50% reaction velocity diagram

(c) 100% reaction velocity diagram



0% Reaction 50% Reaction

• A zero reaction turbine is called an impulse turbine

because there is no expansion or acceleration of

the flow through the rotor blades, and the rotor

torque comes wholly from the impulse of the nozzle

stream.

• With no pressure drop across the bucket row,

pressure seals are not required.

• A frequently used impulse diagram has axial stage

entry and exit flows and the reasonably high loading

coefficient of 2.0.

• In 50% reaction velocity diagrams, the bisector of

the line joining the apexes of the absolute and

relative velocity triangles crosses u in the middle,

which is why the diagrams become symmetric.

• Such diagrams are frequently favored for turbines

because they have accelerating flow to an equal

extent in nozzle and bucket passages, which leads

to lower losses.

• The rectangular turbine stage diagram shown in

above has the additional advantage of having axial

flow at stage inlet and outlet. Also tests show this

gives the highest efficiency for turbine stages.

u

c2 w3

w2

c3

c,2 = 2u

w3

w2

c2

u

c3

c,2 = u



0% Reaction Stage


u

u

c2

w2

2

2

w3 3

c3

p1

p2

p3

u

c1

Nozzle Row

Bucket Row

All of the static enthalpy drops across the nozzle in a 0%

reaction stage. For such a stage, from eq. (12),

or

It can be assumed that the axial velocity is constant at the

inlet and exit of the stage. In this case,

w2 = w3

If the flow angles are equal to the blade angles, then the

bucket has a symmetric shape.

The blades having low reaction are heavily loaded.

For a normal stage with axial entry and with degree of

reaction of 0, the relation reduces to

For an impulse stage, the flow angles for absolute and

relative velocity are reduced to

32 tantan 32

3tan12

2

u

w3 3 c3

c2

w2

2 2

N B

w,3

c,2

w,2

dc = (c,2 c,3)

u

2/1tan 3

2/1tan 2

2tan 3

2tan 2



50% Reaction Stage [1/2]

3

3

u

w3 c2

c3

2

w2

2

N

w,3

c,3 c,2

w,2

dc = (c,2 c,3)

B

A 50% reaction stage has equal static enthalpy drops across the

nozzle and bucket. For such a stage

In order to get a high efficiency, the flow angle at the inlet is kept

only slightly negative, but if some of the efficiency is sacrificed to

achieve higher performance, the inlet flow angle may reach 1 =

45.

For such a stage, a flow coefficient may have a value of = 0.75,

which gives = 2.5.

For a 50% reaction stage, the flow angles for absolute and relative

velocity are reduced to

From these it can be seen that

Therefore, the velocity triangles formed at the inlet and exit of the

bucket are symmetrical each other. Thus,

1tan2tan21 23

2

1tan 3

2

1tan 2

2

1tan 3

2

1tan 2

32 tantan 23 tantan

32 wc 32 cw [ Velocity Triangle ]

w2

c2

u

c1 1

2

2

Nozzle Row

u

Bucket Row

c3

w3

u 3

3

p1

p2

p3


1tan2tan21 23

50% Reaction Stage [2/2]


The stage loading coefficient for 50% reaction stage is,

The figure gives the design and off-design performance of

50% reaction stage, based on above equation.

It is clear from the figure that increases linearly with for a

given 2.

The loading coefficient increases with 2 for a given flow

coefficient.

The present trend in the design of the nozzle is to use as high

an 2 as possible. But it should be realized that increasing 2

increases w2 for a given blade speed, and thus the flow is

likely to reach supersonic speeds and limit the mass flow.

Therefore, the designer has to vary 2, u, , and vz (or ) to

get an optimum design for a given turbine inlet temperature.

The curves in this figure are for ideal conditions. That is,

viscous losses, shock losses, or three-dimensional effects are

not included.

0.0 0.2 0.4 0.6 0.8 1.0

2.5

2.0

1.5

1.0

0.5

0.0

-0.5

-1.0

Flow Coefficient

Sta

ge

Lo

ad

ing C

oe

ffic

ient

2 3=5 10

20

40

60

80

100 120

140

[ 50% Reaction Stage ]




Fluid Dynamics 1



Stage Efficiency 6



유체유동에 의해 발생하는 힘

2

1

Axial

Tangential

1Vm

2211 sinsin VVm

2Vm

1V

2V

터빈 동력생산 원리


NACA 4412

2

222

2

1112

1

2

1VpVppo

Velocity Distribution around an Airfoil

Flow Behaviors around an Airfoil [1/3]

Pressure distribution

Velocity distribution


pdALift

Lift

Pressure surface

Suction surface

x

p

(AOA = 5 deg.)

There is an angle of attack that produces

the optimum lift force. If this angle is

exceeded, the airfoil stalls and the drag

force increases rapidly.

Lift



c1

2 c2

P S S P

p2 p1 p

po

½ c12

½ c22

p2

1

b

Direction

of rotation

P: Pressure surface

S: Suction surface

Lifting Force Acting on a Turbine Blade



Degree of Reaction

%10031

32

hh

hh

%10031

32

TT

TT

%10031

32

pp

pp

dpdhq

Thermodynamic process occurred in compressor and turbine is adiabatic process.

And ignoring density changes.

dpdh

static enthalpy drop in the bucket

static enthalpy drop in the stage

= 100 (%)


Impulse Turbine

The pressure and velocity of the gases passing through the

bucket of the impulse turbine remain essentially the same,

and the only change thing is the direction of flow.

Therefore, the degree of reaction of the impulse turbine is

zero.

The turbine absorbs the energy by the change of the direction

of the high velocity gases.

[ Impulse Turbine, = 0% ]

Vj U

Vj U Bucket

F

U

Nozzle Row

Bucket Row

[ LSB (GE) ]


Reaction Turbine

Nozzle Row

Bucket Row

A reaction turbine changes the velocity and pressure of the gases.

The cross-sectional area formed between two adjacent buckets

decreases. Thus, gas velocity increases and pressure decreases

during passing through the passage.

Therefore, reaction turbine extracts energy by the reaction force

produced by the acceleration of the flow through the convergent

duct.

The degree of reaction of the reaction turbine is 50%.

[ Reaction Turbine , = 50% ]

Vi

Convergent

nozzle

Ve

U

F

[ LSB (Siemens) ]


Evolution of Turbine Blade

Siemens GEC AEI Rateau SCAM BBC Sulzer AEG

GE USA IMPULSE

Siemens-KWU D REACTION

W/H USA REACTION

BBC CH REACTION

Alsthom F IMPULSE

GEC UK IMPULSE 1970

2000 GE USA IMPULSE

Siemens-Westinghouse D REACTION

ABB-Alsthom F REACTION

MHI J REACTION

Ansaldo

Toshiba

Doosan

Hitachi

1998

N. Piignone

BHEL

Parsons

Fuji

MHI

ABB GEC-Alsthom

1989 1987

CEM

LMZ

Zamech

ASEA STAL

F. Tosi

De Pretto

1999


Impulse vs. Reaction

The impulse turbine has its entire enthalpy drop in

the nozzle. Therefore, it has a very high velocity

entering the bucket.

Ideally there is no change in the magnitude of the

relative velocity w between inlet and exit (which

are denoted by subscripts 2 and 3, respectively).

The large inlet velocity c2 has been reduced to a

small absolute exit velocity c3, which ideally is in

the axial direction.

u : tangential velocity of blade

w : velocity of fluid relative to blade

c : absolute velocity of fluid

The reaction turbine divides its enthalpy drop in both

nozzle and bucket.

Therefore, velocities are accelerated when the steam is

passing through both the nozzle and the bucket.

Impulse Turbine Reaction Turbine

u

u

c2

w2

2

2

w3

3 c3

p1

p2

p3

u

1

c1

3

Nozzle Row

Bucket Row

w2

c2

u

c1 1

2

2

Nozzle Row

u

Bucket Row

c3

w3

u 3

3

p1

p2

p3


Velocity Diagram


c1

u

2

c2

p1

p2

u

w2

w2

Nozzle Bucket

A1

A2N 2

A2B A3B

w3

u

c3

3 = 0

A2N A1

A2B = A3B

|2| = |3|

|w2| = |w3|

c2 4c1

p3

T1

T2 T3

c2

c1

w2

w3

3

c1

U

2

c2

p1

p2

u

w2 w2

Nozzle Bucket

A1

A2N 3

w3

c3

3 = 0

p3 T1

T2

T3

c2

A2B

A3B

u

w3

2 = 0

A2N A1

A3B A2B

|c2| |c1|

|w3| |w2|

c2 2c1

c1

w2


Multistage Impulse Turbine

Pressure

Absolute

Velocity

Distance through Turbine

Nozzle Bucket Nozzle Bucket Nozzle Bucket

The impulse turbine has its

entire enthalpy drop in the

nozzle, therefore, it has a very

high velocity entering the

bucket.


Multistage Reaction Turbine

Pressure

Absolute

Velocity

Distance through Turbine

Nozzle Bucket Nozzle Bucket Nozzle Bucket

half of impulse turbine


Question

1. Compare the impulse and reaction turbine in terms of SPE.

2. Compare the impulse and reaction turbine in terms of profile loss.

3. Suggest the equation to calculate the thrust produced in a stage.

4. Which type of turbine requires bigger thrust bearings?

5. Single stage supersonic impulse turbine is shown in the figure.

1) Discuss the shape of nozzle path.

2) What is the purpose of the increasing nozzle exiting velocity up to supersonic velocity?

Single Stage Supersonic Impulse Turbine

31 ppdlT

T = Thrust

d = mean diameter of blade row

l = active length of blade

p1 = pressure at the inlet of stage

p3 = pressure at the exit of stage

= degree of reaction at the mean dia.


Comparison of Velocity Triangle

F = mV = m(c2sin2 + c3sin3)

= mc2sin2

P = mc2sin2u

F = mV = m(c2sin2 + c3sin3)

= mc2sin2

P = mc2sin2u


2

2

3

3

w3

w2

c2

u

u

c3

w2sin2

w3sin3

u u

2u = c2sin2

2

3

w3

w2

c2

u

u

c3

u = c2sin2

w3sin3

u u


Comparison of the Number of Turbine Stages

Impulse Reaction

Let us consider a nozzle row only. This is

because there is no heat addition

and work out as well.

Neglecting inlet velocity,

Assume,

• h across fixed blades in reaction turbine is only 1/4 that of impulse turbine.

• Reaction turbines, however, have an additional equivalent h across the moving blades.

• Therefore, total h in reaction turbine is a half of impulse turbine.

• This means that reaction turbine needs twice number of stages to generate same output.

outin wPEKEFEuq outin wchchq 2

22

2

112

1

2

1

2

1

2

2212

1

2

1cchh

2

221 ch 2

221 ch

o902

uc 22 uc 2

22uh 25.0 uh


Smaller Rotor and Wheel Diameter Single Flow Control Stage

Design Change of HP Turbine - GE


The length of the rotor shaft is almost same. The reasons for this are

1) Pressure drop across the nozzle path in the impulse turbine is double of the reaction turbine. Therefore,

the diaphragms of the impulse turbine should be stronger than those of the reaction turbine.

2) Turbine buckets of the impulse turbine have to work twice of the reaction turbine. Thus, turbine buckets

should be much stronger than those of the reaction turbine.

Another important thing is that the active length of the reaction bucket is longer than that of impulse bucket.

The longer active length of buckets, the higher the turbine efficiency.

Design Change of HP Turbine - GE


Newly Designed HP Turbine [GE]

ALSTOM HP Turbine


Steam Turbines for CCPP Application GE

D-11 for Combined Cycle Units

207D-17 Steam Turbine


Reaction Type HP Turbine – 200 MW Steam

Turbine for the K-Power. (Hitachi)

Number of Turbine Stages

Impulse Type Steam Turbine

The number of stages of reaction turbine is twice of impulse turbine.

1) Suggest the method that make the number of stages of reaction turbine is equal to that of

impulse turbine.

2) The answer of the above question is not applied in the practical reaction turbine. Discuss the

reason for that.


Velocity Diagram

Reaction Stage

u = 0.65v0

c3 = 0.24v0

w2 = 0.24v0

u = 0.65v0

p1

p2

p3

Steam Flow

20

Impulse Stage

p1

u = 0.5v0

p2

u = 0.5V0

c3 = 0.23v0 p3

Steam Flow

13


The velocity increase about four times in

the nozzle and its direction changes from

axial to about 77 off axial.

Vo is the velocity of stream expanded from

the pressure upstream of a stage to the

downstream pressure without loss.

In a pure impulse stage the optimum u/c2 is

0.5.

The velocity leaving the stage should be

close to axial to minimize the stage leaving

loss.

Impulse Stage

In a 50% reaction stage, half of the

pressure drop is across the nozzle and

another half is across the bucket.

The flow turning in the nozzle of reaction

stage is smaller than that of impulse stage.

The inlet velocity of bucket in the reaction

stage is smaller than that in the impulse

stage.

The lower velocity results in lower friction

loss and lower erosion.

The shape of nozzle and bucket is same in

a 50% reaction stage.

Reaction Stage

Velocity Diagram


Comparison of Leakage

Impulse Reaction

Bucket

Tip

Diaphragm

Root

cylindrical

drum type

rotor

disc wheels

shrunk on to a

rotor shaft


Turbines have internal sealing systems between the rotating buckets and the stationary casing and between

the stationary nozzles and the rotor.

The rotating bucket to stationary casing seal is more critical in a reaction turbine than in an impulse turbine

since the reaction turbine has higher pressure drop across the buckets.

The stationary nozzle to rotor seal is more critical in the impulse turbine because of the higher pressure drop

across the impulse stationary nozzle.

However, the impulse turbine has a smaller rotor and thus a smaller sealing diameter, offsetting the effects of

the higher pressure drop.

In addition, the wheel design of the impulse turbine rotor allows the installation of rotor seal leakage steam

passages (holes) in the wheel, minimizing leakage steam interference with the main steam flow from the

stationary nozzle to the rotating bucket.

The rotor-mounted bucket design of the reaction turbine does not allow the installation of these leakage

passages.

However, because of the higher reaction at the root of the bucket, the reaction stage is less affected by re-

entering leakage from the stationary low.

The reaction stage has a higher profile (aerodynamic) efficiency than an impulse stage.

The impulse stage has higher efficiency on stages with small blade heights because the difference in leakage

losses offsets the higher profile of the reaction stage.

As the blade height increases, the influence of leakage losses decreases and a point is reached where the

reaction stage is more efficient.

Comparison of Leakage


• Velocity and pressure distribution along radial direction are uniform at the inlet and outlet of the stage.

• Velocity decreases along radial direction between nozzle and bucket.

• Pressure increases along radial direction between nozzle and bucket.

Radial Variation of Pressure and Absolute Velocity

Impulse-Reaction Turbine [1/6]

c1 c3

p1 p2 p3

c2

w2R

w2M

w2T

uR

uM

uT

c2R

c2M

c2T


노즐의 역할은 작동유체의 압력에너지를 운동에너지로 변환시키는 것이다. 따라서 노즐을 통과한 작동유체의 속도는 크게 증가한다. 그러나 노즐 출구에서의 축방향 속도는 노즐 입구에서와 동일하기 때문에 접선방향 속도만 크게 증가한다. 이로 인해 노즐 출구를 빠져 나온 작동유체는 큰 선회유동으로 인해 원심력이 발생하여 유체는 버켓 팁(tip) 쪽으로 집중되는 경향을 가진다.

유동이 버켓 팁 쪽으로 편중되면 버켓과 케이싱 사이에서 누설손실이 증가하며, 버켓 팁 근처에서 이차유동손실이 증가할 뿐만 아니라 반경방향을 따라서 버켓에서 생산하는 동력도 균일하지 못하게 된다.

이런 문제를 해결하기 위해서 버켓 팁 입구 쪽의 압력을 루트(root, or hub) 입구 쪽 압력보다 높게 유지시킨다. 이 경우 버켓 입구의 팁부분 압력이 루트부에 비해 높기 때문에 팁 쪽에서 루트 방향으로 진행하는 유동이 형성된다.

즉 버켓 팁 쪽에 형성되는 높은 압력으로 인해 루트 쪽으로 진행하려는 힘과 원심력에 의해 루트에서 팁 쪽으로 진행하려는 두 힘은 서로 방향이 반대이기 때문에 두 힘의 크기를 비슷하게 해주면 노즐과 버켓 사이에서 유동은 축방향으로 평행하게 흘러가며, 앞서 언급된 제반 문제점들이 사라지게 된다.

따라서 노즐과 버켓 사이에 형성되는 유동의 특징은 반경방향을 따라서 속도는 줄어들고, 압력은 증가한다.

한편, 축류형 다단 터빈은 버켓 입구에서 뿐만이 아니라 출구에서도 압력과 속도는 반경방향을 따라서 일정하게 유지되어야 한다.

따라서 버켓은 루트에서 팁 쪽으로 가면서 반동도가 증가하기 때문에 버켓 루트는 충동형, 팁은 반동형으로 설계한다.

이런 이유 때문에 터빈 버켓은 하나의 블레이드에 충동형과 반동형이 혼재된 충동-반동 블레이드(impulse-reaction blade)이다.



1000

psia

1000

psia

1000

psia

859.4 psia

844.1 psia

828.7 psia

819.7

psia

819.7

psia

819.7

psia

Free vortex design impulse type

HP turbine stage

22% @ tip

13.5%

@ pitch

5% @ root

[ Example of Pressure Variation in Radial Direction ]

버켓 팁으로의 유동편중 해결 방법



True impulse stages having 0% reaction and reaction stages that always have 50% reaction do not exist in

practical turbine design. In practice, the reaction varies from hub to tip.

Normally, reaction turbine stages are designed to operate at 50% reaction at midspan, with outer and inner

radii operating at higher and lower reactions, respectively.

Impulse stages typically have 3% to 5% reaction at the root of bucket in order to avoid zero or negative

reaction that results in efficiency loss and may lead to flow separation in the bucket.

For long reaction stage buckets, the degree of reaction at the mean diameter may be as low as 40%.

Thus, impulse and reaction stages in the classical definition do not exist in practical turbines.

Characteristics of flow behaviors in multistage axial turbine stage:

1) Pressure and velocity distributions along radial direction are uniform at the entry of a stage.

2) This is same as at the exit of a stage.

3) Centrifugal forces are caused by the tangential component of flow in the nozzle discharge.

4) This is same as in the reaction turbine.

5) The variation of reaction in radial direction is needed to partially cancel the centrifugal forces in the stage.

6) Otherwise, the flow would migrate to the tip, resulting in a poor stage efficiency due to as followings.

• Increase of bucket tip leakage loss

• Increase of secondary flow loss near bucket tips

• Bucket vibration characteristics becomes worse because of non-uniform load acting on the bucket

along radial direction



1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 1 2 3 4 5 6

0

10

20

30

40

50

60

70

Root Root Root

Root

Tip

Impulse Turbine

50% Reaction Turbine

Tip

HP IP LP

Degre

e o

f R

ea

ctio

n (

%)

Stage Number

Degree of Reaction in Fossil Power



Degree of Reaction in Nuclear Power



Stack-Up of Blade (LSB)

p1 = 6 psia

= 70% @ tip

p2 = 4.5 psia

p3 = 1 psia

p2 = 1.25 psia

= 5% @ root

Root

Tip


Comparison of Rotor Shaft

The simplest difference between impulse and reaction turbines is rotor shaft.

Impulse design has a little pressure drop across the buckets. Therefore, the buckets can be mounted on the

periphery of a wheel without generating significant axial thrust.

Impulse turbines do not have thrust concern, and the buckets are mounted on disk extension of the rotor

(wheels), resulting in larger overall diameters, small rotor diameters, and fewer stages than reaction turbines.

On the contrary, blades of reaction turbines are mounted directly at the shaft surface because of steam

pressure difference between upstream and downstream of blades.

This may create a large thrust (axial) force at the shaft caused large bend stress in the discs.

In addition, reaction turbines have more stages than impulse ones.

Wheel and diaphragm construction for impulse

blades Drum rotor construction for reaction blades


Balance Piston

Welding Balance Piston

The reaction design has a significant pressure drop across

the buckets and high thrust. Therefore, a balance piston,

which is normally built into the rotor, is installed in high-

pressure zones of single-flow turbines to offset the thrust.

Otherwise, the turbine is designed with double-flow. Some

designers also use a balance piston on impulse turbines that

have a high thrust. Balance Piston

(Siemens)


What are the major advantages of double

flow structure?

1) Larger capacity

2) Smaller thrust force

3) Shorter LSB

Double Flow

Double flow can be employed to avoid a balance piston in reaction turbines which have a higher

thrust than impulse turbine

31 ppdlT

T = Thrust

d = mean diameter of blade row

l = active length of blade

p1 = pressure at the inlet of stage

p3 = pressure at the exit of stage

= degree of reaction at the mean dia.


Reaction Blades

Advantages Alstom

Higher aerodynamic efficiency

• Lower turning and accelerating flow in both nozzle and bucket allow design of higher efficient and tolerant

profiles

• Lower acceleration of the flow through the nozzle and bucket leads lower profile loss

Lower staging loading

Many stage can be designed with 50% reaction (all HP and IP stages, and front stages of LP turbine)

Symmetric velocity triangle (50% reaction stage)

• Use of same profile in the nozzle and bucket and it may contribute to cost down

• Near-zero interstage swirl

Because of the lower pressure drop, there is no need for costly diaphragm construction

It leads larger number of stages because of lower stage loading (roughly twice that of impulse stages for 50%

reaction stages).

Increase of axial thrust which leads higher dummy balance piston, i.e. increased leakage loss.

Drum-type rotor is suitable for reaction turbine and it leads higher leakage area at the hub section.

Degree of reaction at the hub and tip section is higher compared with impulse stage. Higher hub reaction

leads lower leakage loss, however higher tip reaction gives higher leakage loss.

Disadvantages




Fluid Dynamics 1



Stage Efficiency 6



Stage Efficiency

2, sin4ist

2

2

max,, sin ist

2c

u

ideal

actualst

p

p

버켓에서 생산하는 실제 동력

버켓에서 생산할 수 있는 이상 동력

=

( = velocity ratio)

(from ) 0,

d

ist

2

2

2,

sin21

sin22

rst

2

2

2

2

max,,sin1

sin2

rst

2c

u


w3

w2

c2

u

c3

(b) = sin2

c2 w3

u

w2 c3

(c) > sin2

w2

c2

u

w3 c3

2

2

3

2

2

u

c2 w3

w2

3

c3

3

(a) < sin2


0.25 0.50 0.75 1.00 1.25 1.50

Velocity ratio ( )

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Sta

ge

eff

icie

ncy

Impulse Reaction

2

2

2,

sin21

sin22

rst

2, sin4ist

2c

u

Stage Efficiency


Wake and Core Flow

Reaction stage has better adaptability for

core flow of nozzle and higher stage

efficiency

The wake is a velocity defect generated by the

boundary layers of the blade surfaces. If it is

undisturbed by other blades it would move

downstream along the direction of outlet-flow angle

while decaying slowly over three or four chord

lengths.

Velo

city

Number of revolution

1 2

Impulse

Bucket Reaction

Bucket


[연습문제 3.2]

증기터빈에 유입되는 주증기 조건(main steam conditions)이 30 MPa, 650C 이다. 이 증기는 1단 충동터빈(one-stage impulse turbine)을 등엔트로피 팽창(isentropic expansion)되어 350C로 빠져나간다. 이때 엔탈피 강하(isentropic enthalpy drop)가 540 kJ/kg 이다. 이 터빈을 single stage로 설계하는 데 따른 문제점을 검토하시오. 단, c2와 u가 이루는 각도는 13, 유량계수(flow coefficient)는 0.5, 노즐입구에서의 속도 c1은 매우 작다고 가정한다.

w2

c2

u

w3

u c3

Direction

of Rotation

c1

Number of Stages


[검토 결과]

노즐에서 발생하는 일은 없다. 아울러 노즐통로유동은 단열과정이기 때문에 노즐출구에서의 증기속도는 열역학 제1법칙을 이용하여 구할 수 있다.

편의상 노즐 입구속도는 0이라 가정하면, 열역학 제1법칙으로부터 다음 결과를 얻는다.

kJ/kg

1039.23 m/s

한편, c2와 u가 이루는 각도가 13 이며, 유량계수(flow coefficient) 0.5를 이용하여 u를 계산하면,

= cx/u

u = 1039.23 sin13 /0.5 = 467.6 m/s

증기터빈의 회전속도가 3,600 rpm인 경우, 블레이드 피치직경은 다음 식으로 구한다.

d = 2.48 m

따라서, 블레이드 회전속도와 피치직경이 매우 크기 때문에 블레이드는 큰 응력을 받게 되며, 큰 속도로 인해서 손실이 증가하게 된다. 결론적으로 이 조건에서는 증기터빈을 다단(multiple stages)으로 구성하는 것이 유리하다.

1212

2

1

2

212122

1wzzgcchhq

54022 21

2

2 hhc

60

)2/(2 ndu

2c

Number of Stages




Fluid Dynamics 1



Stage Efficiency 6



Impulse Blade vs. Reaction Blade

Conventional

1940

Laminar

1950

SCHLICT

1965

Super

1980

T

1937

VN

1953

T2

1968

T4

1980

TX

1995

GE

Siemens

Bucket Shape


Bucket Profile Enhancement

Siemens


Alstom

Bucket Profile Enhancement


Shrouded Blade

[ Shrouded Blade ] [ Free Tip Blade ]

Shrouded blades have reduced leakage losses because they have seal system at the blade tip.

Shrouded blades have better vibration characteristics because they are often interlocked to provide

mechanical damping.

Shrouded blades give better efficiency because they have better aerodynamic characteristics at the blade tip.

The tip vortex formed from open tip blade produce a large disturbed flow when it combined with secondary

flow in the blade passage.

However, the shroud creates increased stress levels.

[ Tip Vortex ]


질의 및 응답

작성자: 이 병 은 작성일: 2016.6.21 (Ver.7) 연락처: [email protected] Mobile: 010-3122-2262 저서: 실무 발전설비 열역학 증기터빈 열유체기술 발전용 가스터빈

3. flows in a steam path in steam path_v7.pdfsteam turbine 3. flow in steam path 29 / 112 the...

Documents