5. turbine - engsoft · 2017-12-21 · gas turbines for power plants 5. turbine 2 / 122 4 impulse...

Gas Turbines for Power Plants 5. Turbine 1 / 122

5. Turbine


Impulse and Reaction Turbines 45 4

Introduction 2 1

Dimensionless Numbers 28 3

Thermodynamics and Fluid Dynamics for Turbines 10 2

Advanced Vortex Blades 74 6

Blade Materials 83 7

Stage Efficiency 70 5

Contents

Blade Cooling 97 8

Developmental Trends 116 9


Air inlet Compressor Combustors

Turbine

Exhaust

Cold section Hot section

The function of the turbine is to extract energy from the working fluid and convert it to

mechanical energy, thereby enabling the turbine to drive the compressor and generator.

Turbine


Compressor blades operate at a relatively low temperature but are highly stressed. The combustor operates

at a relatively high temperature and low stress conditions. The turbine blades operate under extreme

conditions of stress, temperature, and corrosion.

The turbine has the task of producing power to drive the compressor and generator.

It does this by extracting energy from the hot gases released from the combustion system and expanding

them to a lower pressure and temperature.

The design of the nozzle and turbine bucket is broadly based on aerodynamic techniques.

The desire to produce a high engine efficiency demands a high turbine inlet temperature, but this causes

problems as the turbine blades would be required to perform and survive long operating periods at

temperatures above their melting point.

These blades, while glowing red-hot, must be strong enough to carry the centrifugal loads due to rotation at

high speed.

Therefore, turbine blade material should have excellent creep characteristics and should be cooled

effectively.

Nickel alloys are used to construct the turbine blades and the nozzle guide vanes because these materials

demonstrate good properties at high temperatures.

Fundamentals of Turbines


Compressor vs. Turbine

Turbines are easier to design because large pressure drop can be achieved per stage without the danger of

flow separation. Therefore, the permissible work extracted per stage within the turbine is much greater than

that correspondingly put in the compressor. This is because the accelerating flow within the turbine is much

more tolerant to flow separation than the diffusing flow in compressors.

Therefore, fewer stages are required in operating turbines as compared to compressors to achieve the same

change in pressure.

Therefore, much higher efficiencies can be achieved in the turbine stages.

However, the turbine has other problems that are not present in compressors. For example, the presence of

high-temperature gases causes reduced life expectancy and requires the materials having good creep

characteristics. In addition, the presence of particle in combustion products results in erosion problems.

Sometimes, combustion products contain corrosive compounds.

The analysis of a turbine is very similar to that of a compressor stage. Many of equations and physics

developed are common to both, with the exception of major differences in the property changes listed below.

1) In a turbine the parameter po, ho, and To decrease through the bucket, while they increase across a

compressor rotor.

2) The compressor operates at lower temperatures than a turbine.

3) The flow turning is much higher (50-180) in a turbine than in a compressor (20-35).

4) The blade thickness and profiles differ considerably.

5) The annulus area increases in a multistage turbines and decreases in a multistage compressor.

6) Material considerations (high temperature and stress) are much more critical in a turbine.


Configuration


Nozzle (or Stationary Blade)

Nozzle

• The primary function of the nozzle guide vanes is to

convert the pressure energy of the hot gases released

from combustors into kinetic energy. The nozzle guide

vanes are of an airfoil shape with the passage between

adjacent vanes forming a convergent duct.

• A secondary purpose of the turbine stator is to direct the

gases at the optimum angle into the turbine blade so the

wheel will turn with the maximum efficiency.

• The nozzle guide vanes are usually of hollow form and

may be cooled by passing compressor delivery air through

them.

Turbine Components

https://www.google.co.kr/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=&url=https://www.linkedin.com/company/gas-turbine-journal-llc-&bvm=bv.105841590,d.dGo&psig=AFQjCNGTJcghqlmlskKflgiO9vyb7E1EPg&ust=1445930337139908

https://www.google.co.kr/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0CAcQjRxqFQoTCLG7gJTN38gCFQblpgodRzMKdg&url=https://www.gasturbinejournal.com/coupon-replacement-technology/&psig=AFQjCNGTJcghqlmlskKflgiO9vyb7E1EPg&ust=1445930337139908


Bucket: The function of the bucket is to convert

kinetic energy of the hot gases into mechanical

energy to drive compressor and generator.

Cover (Shroud)

• Shroud is present to minimize gas leakage

over the blade tips.

• Normally, the first-stage blades are

unshrouded and have the cooling holes on

the top of the blades.

• However, the rear stage blades are

shrouded.

Dovetail: Lock the bucket on the rotor disk.

Shank

• Shank prevents heat transfer from turbine

blade to dovetail.

• Vibration control.

• Reduce stress.

Dovetail

Shank

Turbine Components


[ Shrouded blade ] [ Free tip blade ]

Shrouded 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 ]


Impulse and Reaction Turbines 4

Introduction 1

Dimensionless Numbers 3

Thermodynamics and Fluid Dynamics for Turbines 2

Advanced Vortex Blades 6

Stage Efficiency 5

Blade Materials 7

Blade Cooling 8

Developmental Trends 9


Heat and Work in a Gas Turbine

754 MJ/s

(100%)

205 MW

(27.2%)

203 160 119 MW = 482 MW (63.9%)

277 MW (net output)

(36.7%)

272 MJ/s

(36.1%)

Q1. 터빈 각 단의 출력을 이 그림에 나타나 있는 것처럼 앞 단에서는 크게 하고 뒷 단에서는 작게 하려면 터빈 단 설계에 있어서 일차적으로 고려해야 할 요소가 무엇인가?

Q2. 터빈 앞 단에서 뒷 단보다 많은 출력을 발생시키면 가스터빈 가격 측면에서 어떤 장점을 가지는가?


Most axial-flow turbines consist of more than one stage; the front stages are

usually impulse and the later stages are 50% reaction.

Because the temperature drop is higher for low/zero-reaction turbines, the

nozzle of subsequent stages have lower temperatures and thus require less

cooling air.

The impulse stages produce about twice the output of a reaction stage,

whereas the efficiency of an impulse stage is less than that of a reaction

stage. This is because all the flow acceleration occurs within a nozzle

passage, and this increases losses.

The final stage exit Mach number should be around 0.3. the highest

allowable is 0.55.

The final stage turbine exit swirl angle should be less than 20, and ideally 5

on the pitch line to minimize downstream duct pressure loss.

The hade angle is normally kept to less than 15 to avoid flow separation.

Flow Characteristics


4,3, oopT TTc

1

3,

4,

3,

3,

4,

3, 11o

o

opT

o

o

opTp

pTc

T

TTc

1

3, 1 TPRTc opT

1

3,

4,

3,

4,

o

o

o

o

T

T

p

pTPRT

p

o

o

o

c

h

T

p

= total pressure

= total temperature

= specific stagnation enthalpy

= specific heat

= specific heat ratio

= isentropic efficiency of compressor

= Turbine Pressure Ratio

Turbine Thermodynamics [1/2]

4,3, ooT hhTW

h

s

1

2

3

4

3

4 2

Compressor

Fuel Combustor

Turbine

Air

Power

Exhaust gas 1

2 4 3

1) 터빈으로 유입되는 공기의 온도(TIT)가 증가할수록 터빈에서 생산되는 일의 크기가 증가 가스터빈 출력 증가

2) TPR이 작아질수록 터빈에서 생산되는 일의 크기가 증가 축류압축기 압력비 증가

TPR


High temperature and pressure gas enters the first stage nozzle axially at less than Mach number of 0.2 and

is then accelerated across the nozzle which reduces flow area. The mean nozzle exit Mach number may be

around 0.8. And the nozzle exit angle will be between 65 and 73.

There is no work or heat transfer, and only a small loss in total pressure due to friction and turbulence losses.

Total temperature remains unchanged, except by addition of cooling air, while static pressure and

temperature reduce due to the flow acceleration.

Power is extracted across the bucket via the change in tangential velocity. As the flow passes through the

bucket, the total pressure and temperature decrease.

The decrease in pressure is measured by the turbine pressure ratio (TPR), which is the ratio of the air

pressure exiting the turbine to the air pressure entering the turbine. This number is always less than 1.0.

Since no external heat is being added to or extracted from the turbine during this expansion process, the

process is adiabatic (isentropic).

From the first law of thermodynamics, the turbine work (TW) is equal to the change in the enthalpy of the flow

from the entrance to the exit of the turbine. The enthalpy at the entrance and exit is related to the total

temperature at those stations.

The work done by the turbine is related to the turbine pressure ratio, the incoming total temperature, some

properties of the gas, such as specific heats (cp) and specific heat ratio (), and an efficiency factor (T).

The efficiency factor is included to account for the actual performance of the turbine as opposed to the ideal,

isentropic performance.

Turbine Thermodynamics [2/2]


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.

Flow Behavior in a Turbine Stage

Velocity Triangle in a Turbine Stage [1/4]


Most axial flow turbines are designed on the basis of

constant axial velocity throughout the stages because

of the simplifications of design procedure of the

subsequent stage.

c : absolute velocity of fluid

w : relative velocity of fluid to blade

u : tangential velocity of blade

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

u

u

c2

w2

2

2

w3

3 c3

p1

p2

p3

u

1

c1

3

Nozzle Row

Bucket Row




Velocity Triangle at Root

Root

Tip

rRoot rTip




w : velocity of fluid relative to blade

u

u

c2

w2

2

2

w3

3 c3

p1

p2

p3

u

1

c1

3

Nozzle Row

Bucket Row

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.


Velocity Triangle at Tip

Root

Tip

rRoot rTip


u

u

c2

w2

w3

p1

p2

p3

u

1

c1

Nozzle Row

Bucket Row

2

2

3 c3

3


https://www.google.co.kr/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0CAcQjRxqFQoTCJOf_vDG38gCFcMZlAodxWoMoQ&url=http://www.bine.info/en/topics/energy-generation/power-plants/news/effizientestes-kraftwerk-der-welt-eroeffnet/&psig=AFQjCNFnhF5xmx81y1CCGvGER1e7oDiKOA&ust=1445928429165284

https://www.google.co.kr/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0CAcQjRxqFQoTCMjSwL_H38gCFUuglAodDloB1A&url=https://commons.wikimedia.org/wiki/File:Gas_Turbine_Blade.jpg&psig=AFQjCNFnhF5xmx81y1CCGvGER1e7oDiKOA&ust=1445928429165284


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.

Expansion Lines

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 ]

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


Notation for Flow in a Bucket Row

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

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.


R

Reaction Action

F

V

A

, Nozzle

F = mV = V2A

m = VA (mass flow rate)

Fluid Dynamic Force

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 compressor/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 in the turbine.

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 aerospace gas turbines operate at highest possible speed allowed by stress limits.

• 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 turbine which takes 600 kg/s of gas at

1550C and 20 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 680 m/s, as given in figure, and discharges it from

the bucket (rotor) without swirl (c,2 = 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.


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,

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

smrn

u /5.18860

22

smcc /639sin 222,

23,2, /452,120 smhh oo

kWs

m

s

kghhmhmW oo 271,72120452600

2

2

3,2,23

MWWW turbinenet 6523,23


232,3,23 whhq oo

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

3,2,23 oo hhmhmW



Introduction 1




Stage Efficiency 5

Blade Materials 7

Blade Cooling 8



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 turbomachinery are degree of reaction, loading coefficient, and flow

coefficient.

Generals


Loading Coefficient [1/2]

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.

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 output to the

square of mean bucket speed, that is,

where ws is the isentropic stage work output, subscript 2 and 3 mean bucket inlet and outlet, respectively.

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

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

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.

Typically, most gas turbines have loading coefficient of 1.3~2. In general, the front stages have higher values.

2

3,32,2

2

3,2,

2 u

cucu

u

hh

u

w oos

32

3,2,tantan

u

v

u

ccz


(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)

Loading Coefficient [2/2]

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


Flow Coefficient

The flow coefficient reflects the effect of the mass flow as well as bucket 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

32 tantan


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.

Smith Chart [1/2]

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.

For power generation gas turbines, it is preferable to operate at lower loading and low flow coefficient to

achieve higher efficiency.

The turbine must provide the required shaft work (ho) and run at the same speed as the compressor. Hence,

the loading coefficient is essentially fixed. The Smith chart is then used to guide the choice of flow coefficient

in the preliminary turbine design.


Smith chart gives contours of constant isentropic efficiency versus loading coefficient and 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, no cooling air affecting gas path aerodynamics, 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.

Smith Chart [2/2]

In the case of small gas turbine (around 0.1 kgK/skPa),

approximately three points should be reduced further. The losses

increase rapidly as the gas turbine size decreases.

Cooling air also lowers the attainable efficiency. The values

obtained from the chart should be reduced for each percent of

bucket cooling air.

• 1.5% per 1% suction surface film cooling

• 0.5% per 1% of bucket shroud cooling by upstream injection

• 0.5% per 1% trailing edge cooling

• 0.25% per 1% of leading edge or pressure surface film cooling

In the case of nozzle cooling, approximately half of the above can

be used.


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

[ Expansion line in a turbine stage ]

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

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



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

[ Velocity triangle in a turbine stage ]

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

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 zb uvwwuw

2

2

3

222

2

2

332 tantan2

1

2

1 zvwwhh

32 tantan2

2/tan 3

31

32

hh

hh

32 tantan

2/tan 2

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



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 buckets, and the bucket force

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

w2

c2

u

c1 1

2

2

Nozzle row

u

Bucket row

c3

w3

u 3

3

p1

p2

p3


[ Velocity triangle ]


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

loa

din

g c

oe

ffic

ien

t

2 3=5 10

20

40

60

80

100 120

140

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. [ 50% reaction stage ]

1tan2tan21 23

50% Reaction Stage [2/2]




Introduction 1




Stage Efficiency 5

Blade Materials 7

Blade Cooling 8



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) ]


Impulse vs. Reaction

u

u

c2

w2

2

2

w3

3 c3

p1

p2

p3

u

1

c1

3

Nozzle Row

Bucket Row

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.


w : velocity of fluid relative to blade


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

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



The impulse turbine has its

entire enthalpy drop in the

nozzle, therefore, it has a very

high velocity entering the

bucket.

Multistage Impulse Turbine

Pressure

Absolute

velocity

Distance through turbine

Nozzle Bucket Nozzle Bucket Nozzle Bucket


Pressure

Absolute

velocity

Distance through turbine

Nozzle Bucket Nozzle Bucket Nozzle Bucket

half of impulse turbine

Multistage Reaction Turbine


Evolution of Steam 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


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 Leakage [1/2]

[ Impulse stage ] [ Reaction stage ]

Gas turbines have internal sealing systems between the rotating buckets and the stationary casing.

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 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 efficiency 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.


증기터빈과 달리 가스터빈 노즐에서는 누설손실 발생하지 않음

이는 가스터빈을 통과하는 연소가스 온도가 터빈 블레이드 냉각이 요구될 정도로 높기 때문에 터빈 디스크 내부로 유입되면 안 되기 때문임

가스터빈에서는 압축기로부터 추출한 냉각공기를 버켓 허브(루트)와 노즐 사이 틈을 통해 주유동에 합류시킴으로써 고온의 작동유체가 터빈 디스크 내부로 유입되는 것을 방지

결론적으로 가스터빈 노즐에서는 누설손실이 발생하지 않으며, 이로 인해 증기터빈과 달리 노즐 실에서의 누설은 가스터빈 효율에 영향을 미치지 못함

Comparison of Leakage [2/2]


Comparison of the Number of Turbine Stages [1/3]

The number of turbine stage of the reaction turbine is double of the impulse turbine.

The less the number of turbine stages, the less gas turbine cost. This is because the cost of the gas turbine

blade is very high.

In addition, the vibration characteristics of the gas turbine becomes worse as the number of turbine stage

increases.

The number of turbine stage can be minimized by the employment of impulse turbine. This is because the

pressure and temperature of the working fluid decrease more rapidly when it pass through an impulse stage

than reaction stage. Therefore, the number of turbine stages operated under the high temperatures can be

reduced by the employment of impulse stages.

In general, the blade cost operated under high temperatures is very high because of both cooling problems

and high cost base materials.

However, the problem is that the impulse turbine shows less turbine efficiency than reaction turbine.

In the case of four stages turbine, therefore, front two stages are designed by impulse turbine and rear two

stages are designed by reaction turbine to reduce gas turbine cost and to obtain high turbine efficiency.

In addition, impulse blades are thicker than reaction ones. Therefore, impulse blades have advantages of

installation of cooling passage inside the blades.


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



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



• 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 Flow Parameters

Impulse-Reaction Turbine [1/4]

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.

The amount of reaction in a blade varies to accommodate the natural variation of reaction with blade height.

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



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

Better flexibility with respect to operating range

Lower staging loading

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

Reaction Blades

Advantages Alstom

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.

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


The pitch line reaction should be around 0.5 for best efficiency. The efficiency decreases as the reaction

reduces. This is because profile loss increases as the reaction reduces.

However, it may be reduced as low as 0.3 when the blade temperature is borderline with respect to creep or

oxidation.

This will increase the nozzle exit velocities and bucket inlet relative velocities, reducing the static temperature

and hence also the bucket metal temperatures.

It also reduce the rearwards axial thrust load.

Hub reaction should ideally always be greater than 0.2.

Degree of Reaction in Practical Turbines



Introduction 1




Stage Efficiency 5

Blade Materials 7

Blade Cooling 8



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


2

2

u

c2 w3

w2

3

c3

3

(a) < sin2

w3

w2

c2

u

c3

(b) = sin2

c2 w3

u

w2 c3

(c) > sin2

w2

c2

u

w3 c3

2

2

3


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


Velo

city

Number of revolution

1 2

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.

Wake and Core Flow

Impulse

bucket Reaction

bucket



Introduction 1




Stage Efficiency 5

Blade Materials 7

Blade Cooling 8



Endwall

Le

ad

ing e

dge

of

bla

de

s1 s2

Formation of Horseshoe Vortex

Horseshoe vortex formed around a

square bar

Horseshoe vortex formed around a

round bar

Nozzle Profile

(15%)

Bucket

Profile

(15%)

Nozzle

Secondary

(15%) Bucket Secondary

(15%)

Tip

Leakage

(22%)

Shaft Packing

Leakage

(7%)

Root Leakage (4%) Rotation (3%) Carryover (4%)


Endwall flow produces endwall boundary layer.

Endwall flow is one of major sources of turbine losses,

especially in cascades with short length blades and

high flow turning.

The endwall losses occupy a substantial part of the

total aerodynamic losses in a nozzle or bucket row,

even as high as 30~50%.

The boundary layer fluid upstream of the leading edge

is decelerated by the adverse pressure gradient and

separates at a saddle point s1.

The boundary layer fluid elements form a reverse

recirculating flow just before the leading edge.

Formation of Horseshoe Vortex

Stream Surface

Inlet

Boundary

Layer

Endwall

Crossflow

Endwall

Counter Vortex

Passage Vortex

This reverse flow produces another saddle point s2.

The upstream boundary layer is rolled-up in the recirculating zone and it is divided into two legs at the leading

edge saddle point of the blade and forms the so-called horseshoe vortex.

Then, one leg goes into suction side and the other leg goes into pressure side in axial cascades.


Secondary flow means various vortices

passing through blade-to-blade passage in

axial turbines.

The pressure side leg moves towards the

suction side of neighboring blade in the

passage due to the tangential pressure

gradient and becomes the passage vortex.

The suction side leg called as the counter

vortex rotates in the opposite direction to the

larger passage vortex.

There are two distinct (but arising from the

same physical phenomena) vortices are

present on the suction side of blades and

they may merge, interact or stay separate.

Counter vortex is also called as “stagnation

point vortex”, or “leading edge vortex”, or

“horseshoe vortex”.

Secondary Flow

Stream

surface Inlet

boundary

layer

Endwall

crossflow

Endwall

Counter vortex

Passage vortex


Free vortex design Advanced vortex design

Hub

Tip

High

efficiency

area

Rad

ial h

eig

ht

Bucket efficiency

Secondary Flow Loss

Stream surface

Inlet

boundary

layer

Endwall

crossflow

Endwall

Counter vortex

Passage vortex


Free vortex blade

Leaned blade

Compound leaned blade

(Advanced vortex blade)

Concepts

Advanced Vortex Blade


[ M501G stage 3 vane segment ]

[ M501G stage 4 vane segment ]

Evolution of Turbine Blades

In order to reduce the secondary flow losses in

turbine stages, radial velocity components are

accounted for by using CFD techniques.

Radial flow distribution is biased toward the

more efficient mid-section of the bucket by the

redistribution of the exit angle of nozzle blade.

According to the open literature from GE,

stage efficiency of the steam turbine can be

improved 0.5 to 1.2% by the employment of

advanced vortex blades.

Nozzle solidity is reduced to allow use of more

efficient blade profiles.

Root reaction is moderately increased to

increase efficiency, and tip reaction is

decreased to reduce bucket tip leakage

losses.


The efficiency of an axial-

flow turbine, which in

modern new advanced

gas turbine, reaches

about 92%.

Evolution of the First Stage Bucket

Design c

Increased c

Reduced c u

u

u

w

Increased

inlet angle

Decreased

inlet angle Hub

Tip

Annulus

height mean

actual

Inlet Middle ~ Exit


Source: Siemens

Secondary flow loss can be reduced remarkably

by the adoption of leaned blades

Efficiency Gain with 3D Blades



Introduction 1




Stage Efficiency 5

Blade Materials 7

Blade Cooling 8



Creep [1/4]

o

Permanent

elongation

a b

c

d

Str

ess

Strain

a: yield stress

c: ultimate stress

d: fracture

o-a: elastic behavior

a-d: plastic behavior

e

The failure mechanism of a turbine blade is

related primarily to creep and corrosion and

secondarily to thermal fatigue.

Over a period of operational time the turbine

blades slowly grow in length.

Creep is a term used to describe the permanent

elongation which occurs to rotating parts.

Creep is most pronounced in turbine blades

because of the heat loads and centrifugal loads

imposed during operation.

Each time a turbine blade is heated, rotated, then

stopped (referred to as engine cycle), it remains

slightly longer than it was before.

The additional length may be only millions of an

inch under normal circumstances or, after an

engine over temperature or, over speed condition,

very much longer.


Schematic of material placed in

tension with a small elastic

extension

The effect of extended service on material structure at an

elevated temperature, with the material subject to a tensile

stress

Creep [2/4]


Creep [3/4] S

train

Primary

phase

Tertiary

phase

Time

Secondary

phase

Tensile force


Nevertheless, if the blade remains in service long enough, changes are that it will eventually make contact

with its shroud ring and begin to wear away.

When this occurs, an audible rubbing can be heard on engine.

Creep can be thought of as occurring in three stages: Primary, secondary, and tertiary.

The primary and tertiary stages occur relatively quickly. Primary creep occurs during the engine’s first run,

tertiary during operating overloads.

But the secondary creep stage occurs quite slowly (flat portion on the strain/time graph). It is within the

secondary creep region that the engine manufacturer bases the turbine’s service life.

Causes for accelerated (tertiary) creep:

- Over temperatures;

- Extended operation at high power;

- Erosion of the blades from ingestion of foreign objects.

Creep [4/4]


Thermal Fatigue

Thermal fatigue of turbine blades is a secondary failure mechanism.

Temperature differentials developed during the starting and stopping of the turbine produce thermal stress.

The cycling of these thermal stresses is thermal fatigue.

Thermal fatigue is low cycle and similar to a creep-rupture failure.

The analysis of thermal fatigue is essentially a problem in heat transfer and properties such as modulus of

elasticity, coefficient of thermal expansion, and thermal conductivity.

The most important metallurgical factors are ductility and toughness. Highly ductile materials tend to be more

resistant to thermal fatigue. They also seem more resistant to crack initiation and propagation.

Turbine blade alloys tend to indicate low ductility at operating temperature. Thus, surface notches initiated by

erosion or corrosion and then cracks are propagated rapidly.

The number of starts per hour of operating time directly affects the blade life. It has been found that fewer

starts per operating time increases turbine life.


Corrosion

Corrosion causes the deterioration of blade materials and reduces component life.

Corrosion is described as hot corrosion and sulfidation process.

Hot corrosion is an accelerated oxidation of alloys caused by the deposition of Na2SO4 on turbine blades.

Oxidation results from the ingestion of salts in the engine and sulfur from the combustion of fuel.

Sulfidation corrosion is considered a form of hot corrosion in which the residue contains alkaline sulfates.

Hot corrosion is a rapid form of attack that is generally associated with alkali metal contaminants, such as

sodium and potassium, reacting with sulfur in the fuel to form molten sulfates.

The presence of only a few ppm of such contaminants in the fuel, or the equivalent in the air, is sufficient to

cause this corrosion.

Sodium can be introduced in many ways, such as slat contained in the liquid fuel, through the turbine air inlet

at sites near salt water, or as contaminants in steam/water injections.

High-temperature hot corrosion that has been known since 1950s occurs at temperature between 1500F

(816C) and 1700F (927C) in the presence of Na2SO4.

Low-temperature hot corrosion was recognized as a separate mechanism of corrosion attacks in the mid-

1970s. It occurs at temperature between 1100F (593C) and 1400F (760C) and requires a significant

partial pressure of SO2.

The two types of hot corrosion cause different type of attack. High-temperature hot corrosion features inter-

granular attack, sulfide particles, and a denuded zone of base metal.

Low-temperature hot corrosion characteristically shows no denuded zone, no inter-granular attack, and a

layered type of corrosion scale.


Superalloys are complex mixtures of many critical metals, such as nickel, chromium, cobalt, titanium,

tungsten, carbon, and other metallic elements.

General agreement on precise mixtures by manufacturers of turbine parts is still the subject of much debate.

One reason for this is that the strength properties these metals ultimately have depends on the mixture.

However, the stronger the metal, the more difficult and expensive it is to form and machine into the

complicated shapes necessary for turbine engine parts.

Superalloys were developed for use in high temperature areas where oxidation resistance is required and

where high thermal, tensile, and vibratory stresses are present.

Superalloys have a maximum temperature limit of 2000F when uncooled and 2600F when cooled internally.

Nickel-base superalloys contain little or no iron, are noncorrosive, and can be worked in thin weldable sheets.

Thus, nickel-base superalloys, often referred as inconel (a trade name), are used often to construct

combustor liners, turbine cases, and turbine blades.

Turbine nozzles and buckets are either forged by newer powder metallurgy technique or by traditional

methods, or investment cast from nickel-base alloys. They are also cast by single crystal methods. These

materials have very high temperature strength under centrifugal loads and are highly corrosion resistant.

Blade Materials [1/5]

Nickel-base Superalloys Source: Otis and Vosbury, “Aircraft gas turbine powerplants”, Jeppessen, 2001.


[ Directional solidification ]

[ Single crystal ]

Low Creep characteristics High

Ingot price: 1 2 5

Application in aviation: 1970 1982

Application in power generation: 1987 1990


The blades must be strong enough to carry the centrifugal loads due to rotation at high speed.

Turbine blades must also be resistant to fatigue and thermal shock, so that they will not fail under the

influence of high frequency fluctuations in the gas conditions, and they must also be resistant to corrosion and

oxidization.

In spite of all these demands, the blades must be made in a material that can be accurately formed and

machined by current manufacturing methods.


At elevated temperatures, component failure begins and progresses through grain boundaries. The equiaxed

process assures uniformity of the grain structure along all their axes.

DS blade has a grain structure that runs parallel to the major axis of the part and contains no transverse grain

boundaries. DS was introduced by P&W in 1965.

The elimination of these transverse grain boundaries improves creep and rupture strength on the alloy, and

the orientation of the grain structure provides a favorable modulus of elasticity in the longitudinal direction to

enhance fatigue life.

In addition to improved creep life, the DS blades possess more than 10 times the strain control or thermal

fatigue compared with aquiaxed blades.

Because grain boundaries remain the weak link in turbine blades, numerous techniques have been used to

strengthen them. Even better than strengthening grain boundaries is eliminating them by producing parts

consisting of a single crystal.

By eliminating all grain boundaries and the associated grain boundary strengthening additives, a substantial

increase in the melting point of the alloy can be achieved, thus providing a corresponding increase in high-

temperature strength.

In SC blades, all grain boundaries are eliminated from the material structure and a single crystal with

controlled orientation is produced in an airfoil shape. SC blades offer additional creep and fatigue benefits

through the elimination of grain boundaries.

The advantage of SC alloys compared with equiaxed and DS alloys in low-cycle fatigue (LCF) life is

increased by about 10%.



The directional solidification process results in large MC-type carbides in some alloys, and these carbides are

often precracked and initiate matrix fatigue cracks under cyclic loading conditions.

If some grain boundaries are not perfectly aligned with the solidification direction, creep cracks may initiate at

these boundaries where they intersect a free surface.

The removal of grain boundary strengthening

elements, including C, B, Zr, and Hf, might

improve the fatigue properties by elimination of

MC carbides and could increase the incipient

melting temperature and therefore the creep

resistance, because these elements are melting-

point depressants.

In the absence of grain boundaries, more

flexibility in alloying might be achieved that would

result in an optimum balance of creep-rupture

strength and oxidation and hot corrosion

resistance. Development of leaner alloys also

improves castability.

Equiaxed

DS

SC

Creep

strength

Thermal

fatigue

resistance

Corrosion

resistance

Re

lative

Life

0

2x

4x

6x

8x

10x



Single Crystal Blades

Directional Solidification

Blades

Equiaxed

Blades

Time

Elo

nga

tio

n

Fracture



Construction Process

1) Turbine disk forging by use of powder metals.

a) A forming case is filled with powder metal and placed in a vacuum chamber.

b) A forming case is vibrated to tightly pack the powder. The vacuum prevents air voids in the mixture.

c) The metal powder is subjected to very high mechanical pressure of approximately 25,000 psi. High heat

is supplied sufficient to melt the metal particles together into a disk-shaped piece.

2) Compressor rotor and stator blade investment casting.

a) Molten metal is poured into a ceramic mold in a furnace then taken out to cool.

b) The mold is broken away and the blade comes out in a near final shape.

c) The part is machined to its final shape.

3) Turbine blade casting by the “lost wax method” (see next page)

4) Turbine blade casting by the “single crystal method”

Accomplished as above for directional solidification except that the molten metal is drawn into the mold

through a small corkscrew channel at one end while the other end is chilled.

Source: Otis and Vosbury, “Aircraft gas turbine powerplants”, Jeppessen, 2001.


Blade Construction Process

Lost Wax Method

1) A wax copy of the piece is made in a

metal mold.

2) The wax piece is dipped in liquid

ceramic to form a coating.

3) Molten metal is poured into the

ceramic casting furnace and wax

leaves the mold.

4) During cooling, the casting is

centrifugally loaded in a spin-

chamber to provide a directional

solidification to the piece resulting in

a long grain structure. After

solidification the ceramic shell is

broken off and the piece is

processed into a finished part.



Introduction 1




Stage Efficiency 5

Blade Materials 7

Blade Cooling 8



The first stage blades of turbine must withstand the most severe temperature and stress, thus they are the

limiting component in the gas turbine.

TIT has been increased approximately 10C per year.

It is generally agreed that an increase of 100F (56C) in TIT can provide a corresponding increase of 8~13%

in output and 2~4% of improvement in simple-cycle efficiency.

One method of increasing both the power output and thermal efficiency of the gas turbine is to increase the

TITs. In advanced gas turbines of today, the TIT can be as high as 1600C.

Unfortunately, however, this temperature exceeds the melting temperature of the metal blades. Therefore, it is

essential that the blades should be cooled, so they can survive under these extreme temperatures.

Proper cooling must be provided to achieve blade metal temperatures between 1000F (537C) and 1300F

(704C), below the levels of the onset of hot corrosion.

The temperature of cooling air, which is extracted from compressor, is around 400C for advanced gas

turbines for power generation. This cooling air passes through the blades and the temperatures of the blades

can be lowered to approximately 704C, which is acceptable for reliable operation of the gas turbines

Cooling allows the components to operate in a thermal environment 500 to 700C above the temperature

limits of the alloys used for gas turbine blades.

Blade Cooling – Generals [1/4]


Te

mp

era

ture

, C

1800

Year

1950 1960 1970 1980 1990 2000 2010 2020

1700

1600

1500

1400

1300

1200

1100

1000

900

800

700

600

S-816

N80A M252

U500 U700 IN738 IN939 IN792 DS

Single crystal

Material improvement

TBC

Film cooling Turbine inlet temperature

Benefits of

cooling



Tip cap

cooling holes

Film cooling

holes

Trailing edge

cooling slots

Blade platform

cooling holes

Impingement

cooling

Dovetail

Cooling air

Squealer tip

Hot gas

Film

cooling

Rib turbulators

Shaped internal cooling passage

Trailing edge

ejection

Tip cap cooling

Rib turbulated

cooling

Pin-fin cooling

Cooling air

Hot gas

Stator-rotor

seal

Source: Recent Advances of Internal Cooling Techniques for Gas Turbine Airfoils Minking K Chyu and Sin Chien Siw, J. Thermal Sci. Eng. Appl. 5(2), 021008 (May 17, 2013)



Cooling Air Supply and Its Flow [1/2]

http://upload.wikimedia.org/wikipedia/commons/e/e1/GaTurbineBlade.svg


Cooling Air Extraction

Cooling Air Supply and Its Flow [2/2]


Impingement

cooling

Film

cooling

Rib turbulators

Shaped internal cooling passage

Trailing edge

ejection

Tip cap cooling

Rib turbulated

cooling

Pin-fin cooling

Cooling air

Hot gas

1. Convection Cooling [1/2]

This is the most widely used cooling concept in modern

gas turbines.

Cooling air flows inside the turbine blade and removes

heat from the walls of cooling air passages.

In order to increase the heat transfer surface area, single

pass has been change into multi-pass, that is serpentine

passages.

Additionally, in order to augment heat transfer coefficient,

heat transfer surface treatments have been employed,

such as rib-rougheners or turbulators, and pin-banks or

pin-fins.

TThAq w


1. Convection Cooling [2/2]

Due to manufacturing constraints in the very narrow

trailing edge of the blade, pin-fin cooling is typically used

to enhance the heat transfer in this region.

In a pin-fin array heat is transferred from both the

smooth channel endwall and the numerous pins.

Flow around the pins in the array is comparable to the

flow around a single cylinder.

As the cooling air flows past the pin, the flow separates

and wakes are shed downstream of the pin.

In addition to this wake formation, a horseshoe vortex

forms just upstream of the base of the pin, and the

vortex wraps around the pins. This horseshoe vortex

creates additional mixing, thus increases heat transfer.

There are two array structures commonly used. One is

the inline array and the other is the staggered array.

Pin-Fin Cooling

Pin-fin


2. Film Cooling [1/2]

Cooling air, which is extracted from the last stage of

compressor and passed through the internal cooling

passage of the blade, is injected through small holes

on the blade surface and forms an insulating layer

between the hot mainstream gas and the blade

surface.

This cooling air film protects the turbine blades from

hot gases with very high temperatures.

Additionally, this cooling air film acts as a heat sink,

consequently reducing heat transfer to the walls.


2. Film Cooling [2/2]

Temperature F

Turbine inlet 1630

Average metal 1613

Maximum surface 1700

Cooling T 17

Turbine inlet 1819

Average metal 1452


Cooling T 357

Turbine inlet 2025

Average metal 1390


Cooling T 635

Turbine inlet 2300

Average metal 1400


Cooling T 900

W501A

(1968)

And

W501AA

(1970)

W501B

(1973)

W501D5

(1980)

501F

(1990)


Impingement cooling is commonly used near the leading edge of the blades, where heat loads are the

greatest. Especially, the leading edge is well suitable for impingement cooling because it has a blunt shape.

Cooling air is impinged on the inner surface of the airfoil by high-velocity air jets, permitting an increased

amount of heat to be transferred to the cooling air from the metal surface.

This cooling method can be restricted to desired sections of the airfoil to maintain even temperatures over the

entire surface.

For example, the leading edge of a blade needs to be cooled more than the mid-chord section or trailing edge,

so the gas is impinged.

3. Impingement Cooling


Cooling requires the coolant flow to pass through the porous wall of the blade material.

The heat transfer takes place directly between the coolant and the hot gas.

This cooling is effective at very high temperatures, since it covers the entire blade with coolant flow.

4. Transpiration Cooling

Cooling

air film

Cooling air

Hot gas Porous

material


5. Thermal Barrier Coating [1/3]

Thermal barrier

coating (TBC):

100-300 m

Oxidation

resistant bond

coat: 20-30 m

Thermally

grown oxide

(TGO)

Hot

gases

Interior

cooling

air

Nic

ke

l

su

pp

era

lloy

su

bstr

ate

Te

mp

era

ture

Thermal barrier coating

100-150C

Cooling

air temp.

Hot gas

temp.

Distance


[ TBC Blades (Siemens) ]



The development of directional solidification and single crystal casting technologies have increased alloy

operation temperatures, thus contributed to increase TIT.

Then, gas turbine materials developments have moved to thermal barrier coating, as the temperature

capability of Ni-based superalloys approaches their intrinsic limit.

Ceramic is used as a coating material because it has very low thermal conductivity. Thus, coating layer can

reduce the blade surface temperature by insulating it from the hot gas.

TBCs are composed of two layers: a bond coat with diffusion aluminide or MCrAlY, and a top coat with

material having low thermal conductivity.

The aluminide coatings with platinum increase the oxidation resistance and also the corrosion resistance.

The thermal barrier coatings have an insulation layer of 100 to 300 m thick and are based on ZrO2-Y2O3 and

can reduce metal temperatures by 100~150C.

Coatings ensure that the lives of the blades are extended and in many cases are used as sacrificial layer,

which can be stripped and recoated.

Life of coatings depends on composition, thickness, and the standard of evenness where it has been

deposited.

Ceramic and aluminum alloy thermal barrier coating of superalloy parts are also processes which give high

surface strength and resistance to corrosion.

This coating is said to give the best protection against the scaling type corrosion or erosion which occurs at

high gas temperatures.

Scaling is caused by sodium in the air and sulfur in the fuel reacting chemically with the base metals.



The purpose of the blade cooling is to obtain the highest

overall cooling effectiveness with the lowest possible

penalty on the turbine efficiency.

The ejected coolant interacts with the external flow near

the both endwalls and blade surface. This increases

aerodynamic and thermodynamic losses in the stage.

In optimizing a cooling system, this has to be weighed

against the increase in cycle efficiency that can be

achieved through higher TITs.

In the case of porous blade, the disturbance to the flow

pattern and the wake thickness increases as the coolant

flow increases. Thus, the losses increase.

In a blade with trailing edge slots, the loss initially starts

to increase with coolant flow as the wake thickens.

However, as the coolant flow is increased it tends to

energize the wake and reduce losses. Flow a higher

coolant flow, the coolant pressures must be higher,

resulting in an energization of the flow.

Cooled Blade Aerodynamics


Heat transfer coefficient contours at tip: full-featured

geometry (left) and simplified geometry (right)

Squealer Blades

http://www.google.co.kr/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwis7Kqi3aTRAhUFGZQKHXvnBcAQjRwIBw&url=http://thermalscienceapplication.asmedigitalcollection.asme.org/article.aspx?articleid=1690809&psig=AFQjCNFggEJ7uSYiHfHwiuJ0H6gjJEykdw&ust=1483489779117353

http://www.google.co.kr/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&ved=0ahUKEwjr7Y7b3aTRAhWGpJQKHVtwBU4QjRwIBw&url=http://site.ge-energy.com/businesses/ge_oilandgas/en/techinsights/conjugate-heat-transfer-part-2-3.html&psig=AFQjCNFggEJ7uSYiHfHwiuJ0H6gjJEykdw&ust=1483489779117353


Hot blade

Warm blades

Temperature increase of blades is caused by the oxidation

blockage of cooling channels.

Creep life of the blade is a strong function of the material

temperature.

It is generally agreed that the life of a turbine blade can be

reduced by half if the blade temperature is higher only 30C than

design temperature.

Loss of coating, especially TBC, can reduce the life of the blade

significantly.

Measurement of Blade Temperature

[ Overheated blade ]

[ Coating erosion ]

[ Coating loss and oxidation damage of

HPT stage 1 bucket (LM6000) ]



Introduction 1




Stage Efficiency 5

Blade Materials 7

Blade Cooling 8



The TIT defines the technology level of the gas turbine. The primary objective of increasing the TIT is to allow

for higher power output for a given engine size. Due to the improvements in material science and blade

cooling techniques, the allowable TIT has steadily increased by 10 K every year over the last few decades

and there is hope that this trend will continue. Unfortunately, however, the life of the turbine blade is halved by

each 15 K rise in temperature, hence new technologies are always being sought to suppress creep, thermal

fatigue and oxidation which are the primary mechanisms that limit blade life.

Considerable effort has also been made in developing efficient cooling techniques and surface coating, so

that TITs can be increased.

The TIT will increase to 1600C to get higher combined cycle efficiency.

It seems that the engines have TIT higher than 1600C will little market penetration because of the necessity

of steam cooling. Steam cooling engines will not meet user’s requirements for rapid startup and steep ramp

rates.

The fact that 60 percent efficiency could be obtained only by employment of steam cooling has definitely

proven false.

Higher TITs force the steam turbine throttle temperature above 600C.

The number of turbine stage increased to four as the pressure ratio increase. There is an efficiency gain

associated with the fourth stage because the stage loading will be reduced and larger exhaust area.

Siemens H-class machines have reverted back to DS blades instead of SC blades because of cost problems.

Recent research activities have been focused in the area of new materials that can withstand higher

temperatures and higher stresses at the same time. This would enable improvement in cycle efficiencies,

decrease the number of turbine stages.

Developmental Trends


Tu

rbin

e In

let Te

mp

era

ture

, C

7E/9E

501ATS

7EA/9EC

V84.2/V94.2

7H/9H

V84.3A/V94.3A

V84.3

GT11N2

501F/701F

7F/9F

7FA/9FA

GT24/GT26 GT13E2

501G/701G

1600

1500

1400

1300

1200

1100

1000

80 78 84 82 88 86 92 90 96 94 00 98

501D5A/701D

GE

Siemens

Alstom

WH/MHI

Turbine Inlet Temperature

EGT increases with TIT. The HRSG efficiency increases with EGT.


Cooling Technologies

Te

mp

era

ture

, C

1500

1965

Allowable Gas

Temperature Film Cooling

Closed-loop

Cooling

U700

IN738 IN939

IN92DS

1st Gen. SX

2nd Gen. SX

Maximum Material

Temperature 1000

700

TBC; Thermal Barrier Coating

DS; Directional Solidification

SX; Single Crystal

1975 1985 1995 2005 2015

Benefits of

Cooling


Blade Tip Active Clearance Control


Turbine Case Cooling System

Turbine Case or Skin Temperature

Blade Tip Active Clearance Control


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

5. turbine - engsoft · 2017-12-21 · gas turbines for power plants 5. turbine 2 / 122 4 impulse...

Documents