3. Compressor Turbines for Power Plants 3. Compressor 2 / 136 2 Compressor Thermodynamics and Fluid Dynamics 18 1 Basic Principles of an Axial Compressor 2 Contents

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3. Compressor

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Compressor Thermodynamics and Fluid Dynamics 18 2

Basic Principles of an Axial Compressor 2 1

Contents

Degree of Reaction 73 6

Compressor Losses 80 7

Compressor Blade Shapes 65 5

Basic Sizing Parameters 56 4

Stall and Surge 89 8

Centrifugal Compressor 122 9

Dimensionless Numbers 48 3

Developmental Trends 128 10


7FA, GE A compressor is a device that pressurizes a working fluid

Starter &

Gear Box

Air Inlet Compressor Combustor

Turbine Exhaust

VIGV

Air Extraction

Ports Diffuser

Transition

Piece

Cold Section Hot Section

Configuration of a Gas Turbine


Basic Requirements of Compressor

The basic function of a compressor is to utilize shaft work to increase the stagnation pressure of the air before

it is expanded through the turbine.

The basic requirements of compressors for power generation gas turbine application are high efficiency, high

air flow capacity per unit frontal area, and high pressure ratio per stage.

Compressors consume about 50% of mechanical energy produced by turbine. Therefore, compressor

efficiency is essential factor to overcome high energy price.

The larger the gas turbine, the higher the efficiency of gas turbine, and the lower gas turbine price per unit

power output.

The higher pressure ratio per stage, the shorter the compressor length.

In addition, the mechanical design should be simple, so as to reduce manufacturing time and cost. The

resulting structure should be mechanically rugged and reliable.


Gas Turbine Output (MW) Air Flow Rate

(lbs/s)

Compressor

Power (MW)

Total Turbine

Output (MW) WC/WT

Typhoon 5.1 39 8.1 13.5 0.59

Centaur 50 4.5 42 6.3 11.1 0.56

Mars 100 10.5 92 17.9 29.0 0.61

MS5371PA 26.1 269 39.0 66.3 0.59

RB-211 26.7 199 41.2 69.3 0.60

MS6581B 41.5 321 50.7 94.2 0.54

Trent 50 51.0 340 84.3 136.5 0.61

GT 8C2 56.3 429 77.6 136.1 0.57

MS6101FA 70.1 450 74.2 147.1 0.50

MS7121EA 82.2 655 105.3 192.5 0.55

13E2 160.7 1153 190.2 354.1 0.54

MS7241FA 172.7 971 164.4 340.7 0.48

MS9351FA 255.4 1429 229.7 490.3 0.47

Mean 0.55

Gas Turbine Matching

In a gas turbine, approximately 50 percent of the total work produced in the turbine is consumed by axial

compressor. Consequently, maintaining a high compressor efficiency is very important.


If pressure rise is small and mass flow is large, the device is a called a fan, whereas if the pressure rise is

high, the device is called a compressor. Sometimes a middle-range pressure rise device is termed a blower.

The compressors in most gas turbine applications, especially units over 5 MW, use axial flow compressors.

The axial compressor is the most complicated component to design in an aerodynamic point of view.

An axial flow compressor is one which the flow enters the compressor in an axial direction (parallel with the

axis of rotation), and exits from the gas turbine also in an axial direction.

The axial-flow compressor compresses its working fluid by first accelerating the fluid and then diffusing it to

obtain a pressure increase.

The axial flow compressor consumes around 50% of the power produced by the turbine section of the gas

turbine.

The increase in gas turbine efficiency is dependent on four basic parameters: pressure ratio, TIT, compressor

efficiency, and turbine efficiency.

In an axial flow compressor, air passes from one stage to the next, each stage raising the pressure slightly.

However, by producing low-pressure increases on the order of 1.1 : 1 to 1.4 : 1, very high compressor

efficiency can be obtained. The use of multiple stages permits overall pressure increases up to 40:1.

The industrial gas turbine has been conservative in the pressure ratio and TIT. This is because the industrial

gas turbines given up high performance for both rugged operation and long life.

However, this has all changed in the last 10 years. The performance of the industrial gas turbines improved

dramatically to overcome the increased energy cost. In addition, the performance gap between aerospace

engines and industrial ones reduced dramatically.

Introduction to Compressor


Type Pressure Ratio per Stage

Efficiency (%) Operational Range

(Surge to choke) Industrial Aviation Research

Centrifugal 1.2 - 1.9 2.0 - 7.0 13 75 - 87 Large, 25%

Axial 1.05 - 1.3 1.1 - 1.45 2.1 80 - 91 Narrow, 3 - 10%

Types of Compressor

Stage

Axis of

Rotation

Inflow

Outflow Shroud

Hub

A Centrifugal Compressor An Axial Flow Compressor


Pressure ratio = total pressure at compressor inlet

total pressure at compressor outlet

The expression “compression ratio” is not used for gas

turbines because this is a ratio of air density rather than air

pressure by definition.

Compressor pressure ratio of a

gas turbine engine is an extremely

important design parameter.

In general, the higher the pressure

ratio, the greater thermal

efficiency.

The growth of both the pressure

ratio and TIT parallel each other,

as both growths are necessary to

achieving the increase in thermal

efficiency in gas turbines.

Currently, some engines have

compressor pressure ratio of 23:1

(40:1 for aircraft gas turbines).

Year

Pre

ssu

re r

atio

1940 1950 1960 1970 1980 1990 2000 2010

45

40 Aircraft

Industrial 35

30

25

20

15

10

5

0

Pressure Ratio [1/4]


A typical axial flow compressor consists of a

series of stages; each stage has a row of rotor

blades followed by a row of stator blades which is

stationary.

The length of the blades and the annulus area,

which is the area between the blade root and tip,

decreases throughout the length of the

compressor.

This reduction in flow area compensates for the

increase in fluid density as it is compressed,

permitting a constant axial velocity.

In the heavy duty gas turbines, pressure ratio per

stage is reduced to provide stable operation. For

example, GE’s H-class gas turbine with 18 stages

of compressor has a pressure ratio per stage of

1.19.

In the multistage compressor, the pressure ratio is

obtained by multiplying the all pressure ratio per

stage. (GE HA gas turbine with 14 stages at

1.245 per stage gives a factor of 21.5 1.24514).



Process Component Heat Work Process

12 Compressor q12 = qC = 0 w12 = wC = (h2h1) Power in (adiabatic compression)

23 Combustor q23 = qB = h3h2 w23 = wB = 0 Heat addition at constant pressure

34 Turbine q34 = qT = 0 w34 = wT = h3h4 Power out (adiabatic expansion)

41 Exhaust q41 = qE = (h4h1) w41 = wE = 0 Heat release at constant pressure

121212 whhq

p

2

1

T

(h)

s

qin

3

4 1

2

3

4

qout

win wout

win

wout

qin

qout

Simple Cycle Analysis [1/2]



0 5 10 15 20Pressure Ratio [r]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Th

erm

alE

ffic

ien

cy

Thermal efficiency in a simple cycle gas

turbine increases with pressure ratio

and specific heat ratio.

The increasing rate of the thermal

efficiency is getting smaller as the

pressure ratio increases.

4

3

1

2

p

p

p

pr

crth

111

/1

1

rc

2

1

23

14

23

1423

23

4123

23

3412 11T

T

TT

TT

hh

hhhh

q

qq

q

ww

q

w

inputheat

ouputworknet

in

sys

th

Simple Cycle Analysis [2/2]



7EA, GE

Configuration of a Typical Axial Compressor


Task 1: When designing a compressor with the reaction blades, the first

stage must be preceded by pitch variable blades, known as variable

inlet guide vanes, to provide pre-swirl and the correct velocity entrance

angle to the first stage rotor. This means that VIGVs serve to direct the

axially approaching flow correctly into the first row of rotor blades

because those are very sensitive to any small change in incidence in

flow angle or non-uniformity in velocity.

Task 2: Additionally, its position affects the quantity of compressor inlet

air flow. Therefore, VIGVs are one of the useful tools to control stall

occurred in compressors.

Task 3: IGVs also serve the purpose of preventing the injection of

foreign objects into the engine.

Similar vanes, often known as the EGVs (Exit Guide Vanes) are placed

at the compressor exit to remove the rotational moment imparted to the

air during compression.

6.5

51.5 45

Engine Center

Line

VIGV

1st Stage

Compressor

Blade

Variable Inlet Guide Vanes [1/2]


IGV Pinion Gear Gear Ring

VIGV

The gas turbine output is controlled by a combination of VIGV control, and TIT control.

The TIT is controlled by a combination of the fuel flow admitted to the combustor and the VIGV setting.

Modern gas turbines are allowing a high gas turbine exhaust gas temperature down to approximately 40% GT

load.

Below that level, the turbine inlet temperature is further reduced because the airflow cannot be further

reduced.

Variable Inlet Guide Vanes [2/2]


Rotor and Stator [1/3]


Compressor rotor stacking Stator buildup Rotor buildup




The axial compressor is a multi-stage unit as the amount

of pressure rise by each stage is small; a stage consists

of a row of rotor blades followed by a row of stator vanes.

The entering air is accelerated in the rotor, that is, kinetic

energy is transferred to the air, and then it is diffused in

the stator to convert the kinetic energy into a pressure

rise.

The job of the rotors is to increase pressure using

mechanical energy transmitted from turbine. Stage

The stator vanes are placed to the rear of the rotor blades to receive the air at high velocity and act as a

diffuser, converting kinetic energy to pressure energy.

The stator also have a secondary function of directing airflow to the next stage of compression as the desired

angle.

From the front to rear of the compressor, i.e. from the low to high pressure end, there is a gradual reduction of

annulus area between to rotor hub and the stator casing. This is necessary to maintain a near constant air

axial velocity as the density increases through the length of the compressor.

The convergence of the air annulus is achieved by the tapering of the casing or rotor. A combination of both is

also possible, with the arrangement being influenced by manufacturing problems and other mechanical

design factors.


Compressor Thermodynamics and Fluid Dynamics 2

Basic Principles of an Axial Compressor 1

Basic Sizing Parameters 4

Dimensionless Numbers 3

Degree of Reaction 6

Compressor Losses 7

Compressor Blade Shapes 5

Stall and Surge 8

Centrifugal Compressor 9

Developmental Trends 10


The compressor is composed of several rows of airfoil cascades. That is, several blades placed in a row is

called as cascade.

The high pressure zone air of the first stage blade being pumped into the low pressure zone of its stator.

The high pressure zone of the first stage stator vane then pumps into the low pressure zone of the second

stage rotor blade.

This cascade progress continues to the last stage of compression.

It might appear that the rotor blade high and low pressure zone might cancel each other out as they blend

together; but the overall effect of the divergent shape of the flow path results in a net decrease in velocity and

an increase in static pressure.

Cascade

First Stage

Rotor Blades

Stator

High

Pressure

Low

Pressure

IGVs

Direction o

f R

ota

tion

H

H

H

H

L

L

L

L

Second Stage

Rotor Blades

Stator

Blades

H

H

H

H

L

L

L

L

H

H

H

H

L

L

L

L


1 = blade inlet angle

2 = blade exit angle

1 = air inlet angle

2 = air exit angle

c1 = air inlet velocity

c2 = air exit velocity

C = chord

s = pitch (or space)

= blade camber angle

= 1 2 = deflection

= 1 2

= stagger or setting angle

i = incidence angle

= 1 1 = deviation angle

= 2 2

= solidity (= C/s)

AR = aspect ratio (= h/C)

Compressor Cascade Nomenclature [1/3]

1

2

1

2 c2

c1

i

C

Point of max.

camber

a

s


Nomenclature Description

Camber line • A line drawn halfway between the two surfaces, pressure and suction

Camber • The distance between the camber line and the chord line

Camber angle, • The turning angle of the camber line (= 1 2)

Blade shape • The blade shape is described by specifying the ratio of the chord to the camber at some

particular length on the chord line, measured from the leading edge

Aspect ratio, AR

• Aspect ratio is the ratio of the blade length (height) to the chord length

• The term “hub-to-tip ratio” is used frequently instead of aspect ratio

• It is important when 3-D flow characteristics are discussed

Pitch, s

(blade spacing)

• The pitch of a cascade is the distance between blades, usually measured between the camber

lines at the leading edges or trailing edges of the blades

Solidity,

• The ratio of the chord length to the pitch is the solidity of the cascade ( = C/s)

• It measures the relative interference effects of one blade with another

• 0.5~0.7: isolated airfoil test data can be applied with considerable accuracy

0.7~1.0: isolated airfoil test data can be applied with reduced accuracy

1.0~1.5: cascade data are necessary (majority of present designs belong to)

1.5 : channel theory can be employed

Blade inlet angle,

1

• The angle formed by a line drawn tangent to the forward end of the camber line and the axis of

the compressor

Blade exit angle,

2

• The angle formed by a line drawn tangent to the rear of the camber line and the axis of the

compressor



Nomenclature Description

Stagger angle

(setting angle ),

• The angle formed by a chord line and the axis of the compressor

• It is also called as setting angle of the blade

• High aspect ratio blades often are pretwisted so that at full speed centrifugal forces acting on

the blades will untwist the blades to the designed angle.

• The pretwist angle at the tip for blades with AR of about 4 is between 2~4.

Absolute air inlet

angle, 1 • Angle between absolute incoming velocity and axial direction.

Absolute air exit

angle, 2 • Angle between absolute leaving velocity and axial direction.

Relative air inlet

angle, 1 • Angle between relative incoming velocity and axial direction. (not shown in the figure)

Relative air exit

angle, 2 • Angle between relative leaving velocity and axial direction. (not shown in the figure)

Incidence angle, i • The difference between the blade inlet angle and air inlet angle (i = 1 1)

Angle of attack, • The angle between the inlet air direction and the blade chord ( = 1 )

Deviation angle,

• As the air is turned by the blade, it offers resistance to turning and leaves the blade at an angle,

greater than 2, so called air exit angle, 2

• The deviation angle is defined as the difference between the blade or the camber angle and the

average flow angle ( = 2 2)

Deflection angle, • The angle formed by air inlet angle and air exit angle ( = 1 2)



z

r

Sta

tor

Ro

tor

Flow direction

CL

1 2 3

Velocity Triangles [1/4]



Most axial compressors 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

w : relative velocity

u : tangential velocity

of blade

c1

w1

c,1

1 1

vz,1

u1

w2 c2

c,2

2 2

vz,2

u2

c3

Shaft CL

IGV

Rotor

Stator

3

Fluid velocity is an important variable governing the

flow and energy transfer within a compressor.

The absolute velocity ( ) is the fluid velocity relative

to some stationary point and is usually parallel to the

stator (stationary blade).

When considering the flow across a rotating element

like a rotor, 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 rotor.

ucw

u

w

c


The air approaches the rotor blades with an absolute velocity c1 at an inlet angle 1 to the axial direction.

In combination with the tangential velocity of the rotor blades u, its relative velocity will be w1 at an inlet angle

1. (w1 = c1 u)

The relative velocity w1 should align closely with the rotor blade angle at the inlet.

After passing through the diverging passages formed between two adjacent rotor blades which do work on

the air and increase its absolute velocity (from c1 to c2), the air will have relative velocity w2 at an exit angle 2

which is less than 1. This turning of the air towards the axial direction is necessary to provide the increase of

effective flow area.

The rotor blade turns the relative velocity w1 to w2, thereby imparting angular momentum to the air and thus

increasing the absolute tangential velocity.

For a rotor, c2 c1 and w2 w1. This is because the kinetic energy is added by the shaft in the absolute

frame, and rotor blade passage acts like a diffuser in relative frame. The fact of c2 c1 can be explained by

the fact that the mechanical energy transmitted from the turbine will be transferred to the air through the rotor

and the absolute velocity of the air increases.

The exit relative velocity w2 is nearly parallel to the blade at exit.

The relative velocity w2 in combination with u gives the absolute velocity c2 at exit of the rotor at an angle 2.

The absolute velocity at rotor exit should line up with the stator blades.

The air then pass through the passages formed by the stator blades wherein it is further diffused to velocity c3

at an exit angle 3. In most designs, it is equal to 1 so that it is prepared for entry to the next stage. (c3=c1,

and 3=1)



c1

w1

u

w2

c2

u

Shaft CL

IGV Rotor 1 Stator 1

c3

w3 u

Rotor 2

ho, po, To

h, p, T

The basic principle of acceleration of

the working fluid, followed by diffusion

to convert acquired kinetic energy into a

pressure rise, is applied in the axial

compressor

Air is turned through the proper angle

by the VIGVs before it impinges on the

rotor blade of the first stage.

Work transmitted from the turbine is

added to the air by the rotor blades,

thereby increasing its stagnation

enthalpy, pressure, temperature, and

kinetic energy.

The flow is discharged at a proper

angle of attack to stator blades where

the static pressure is further increased

by flow diffusion.

The stagnation pressure remains nearly the same through the stator (except for losses), but the static

pressure is further increase while the kinetic energy decreases.

The air is directed to the second stage rotor, and the process repeats itself.



1212

2

1

2

2112212122

1wzzgccppuuq

012 q

012 uu

012 zz

12

2

11

2

222

1

2

1wcpcp

121,2, wpp oo

1,2, oo pp

12w

Change of Stagnation Pressure

In an open system, the first law of thermodynamics is as follows,

(adiabatic process)

(the change of the internal energy can be ignored)

(the change of the potential energy can be ignored)

(1)

The equation (1) can be reduced as follows,

The sign of the is negative because it is a supplied work to the compressor.

Therefore, the following conclusion can be obtained.

In order to investigate the change of stagnation pressure during the air pass through the rotor passage, we

can consider energy equation.

In the stator passage, there is no work supplied and produced. Therefore, =0 12w

Therefore, the following conclusion can be obtained.

1,2, oo pp


An axial flow compressor compresses its

working fluid by first accelerating the fluid

and then diffusing it to obtain a pressure

increase.

The fluid is accelerated by a row of rotor

and diffused by a row of stator.

The diffusion in the stator converts the

velocity increase obtained in the rotor to a

pressure increase.

Even though the pressure is rising

dramatically, the velocity is held relatively

constant.

Compressor exiting velocity is lower than

compressor entering velocity for flame

stability in combustion chambers.

2

2

1chho

2

2

1cTcTc pop 2

2

1c

cTT

p

o

It should be noted that total conditions for pressure, temperature, and enthalpy increase only in the rotor

where energy is inputted to the system.

It is common in an multistage axial flow compressor that the enthalpy rise per stage is constant, rather than

that the pressure rise per stage is constant.

Variation of Velocity and Pressure

IGV

Roto

r

Roto

r

Roto

r

Sta

tor

Sta

tor

Sta

tor

ho, po, To: total values

h, p, T: static values

c: absolute velocity

CL


Compressor Turbine

Blade flow path Diverge (diffuser) Converge (nozzle)

Absolute velocity of flow Increase Decrease

Relative velocity of flow Decrease Increase

Pressure Rise Drop

Work transfer Input (through rotor) Output (through bucket)

Enthalpy (Temperature) Increase Decrease

Airfoil shape Slender Thick (and composed of many circular arcs)

Flow in a blade passage Decelerate (thick boundary layers) Accelerate (thin boundary layers)

Possibility of flow separation Large Small

Flow turning Small (typically 30 to avoid flow separation) Large (typically 100)

Number of stages Large (because of small flow turning) Small (because of large flow turning)

Blade height Decrease Increase

Flow through a Cascade

Blade

Direction Turbine

Blades

Compressor

Blades

c1 w1

u

w2 c2

u

u

c2 w2

u

w3 c3

Axial

Direction

Blade

Direction

Axial

Direction

Compressor Turbine


Brayton Cycle

1 2

3 4

Compressor Work [1/3]

Technical Work: 2

112 dpw

p

2

1

3

4

win

(a)

p

2

1

3

4

wout

(b)

p

2

1

3

4

wsys

(c)

b

a

b

a


Compressor

Fuel Combustor

Turbine

Air

Power

Exhaust gas 1

2 4

3

cooc hhw /1,2, coop TTc /1,2,

11

1

1,

2,1,

1,

2,1,

o

o

c

op

o

o

c

op

p

pTc

T

TTc

1

1

1,

r

Tc

c

op1

1,

2,

1,

2,

o

o

o

o

T

T

p

pr

c

p

o

o

o

c

h

T

p

= total pressure

= total temperature

= specific stagnation enthalpy

= specific heat

= specific heat ratio

= isentropic efficiency of compressor

h

s

1

2

3

4

3

4 2


1) 압축기로 유입되는 공기의 온도가 증가할수록 압축기에서 소모하는 일의 크기가 증가 가스터빈 출력 저하

2) 각 단에서 동일한 압력비를 얻기 위해서는 압축기 앞부분 단보다 뒷부분 단에서 더 큰 일이 필요

축류압축기 뒷부분 단이 앞부분 단에 비해 효율이 낮음

압력비가 증가할수록 압축기 효율이 낮아짐


The rotor compresses the air from p1 (or po,1) to p2 (or po,2).

The purpose of the stator is to convert kinetic energy from

c22/2 to c3

2/2 and to further increase the static pressure.

The static pressure increases from p2 to p3 along the line 2-

3, and the stagnation pressure decreases from po,2 to po,3

due to viscous losses.

A large increase in velocity at the exit of the stage is thus

avoided.

In the compression process certain losses are incurred that

result in an increase in the entropy of the air. Thus, in

passing through a compressor, the velocity, the pressure,

the temperature, the density, the entropy of the air are

changed.

[ Compression line ]

Compression Line


p1

po,1

1

o,1

1/2 c12

p2

p3

po,3

po,2

1/2 c32

2

3

o,2 o,3

T

(h)

s

Roto

r S

tato

r

Ide

al co

mp

resso

r w

ork

Pra

ctica

l co

mp

resso

r w

ork

1/2

c22

3s

o,3s

2s

3ss

o,3ss


1,2,

1,2,

1,3,

1,3,

,

,

oo

oso

oo

oso

actualc

idealc

chh

hh

hh

hh

w

w

Work input to an isentropic compressor c =

Work input to an actual compressor

Isentropic Efficiency

A constant pressure line has a varying slope proportional to the temperature.

This fact can be demonstrated by Gibbs’ equation,

This equation shows that the slope of a constant pressure line increases with temperature.

Additionally, the equation gives the fact that the vertical distance between two different constant pressure

lines increases with temperature. This means that two different constant pressure lines diverge as the

entropy increases.

In the axial compressor, the work input needed for a given pressure rise is greater for the rear stages than

front ones. This is because temperature is higher at the rear stages, and thus the work input required by the

rear stages is increased.

This is the reason why the isentropic efficiency becomes lower as the overall pressure ratio increases.

Compressor Efficiency [1/4]

dpdhTds pp c

T

s

T

T

(h)

s

ds

dT

p = const.


Polytropic efficiency is another concept of efficiency often used in compressor evaluation. It is the true

aerodynamic efficiency exclusive of the pressure ratio effect. It is defined as the isentropic efficiency of an

infinitesimally small step in the compression process(Walsh and Fletcher, 1998). Therefore, it is often referred

as small stage or infinitesimal stage efficiency. It is defined by

From Gibbs’ equation and the definition of specific heat at constant pressure

Therefore,

Integrating between 1 and 2 (initial and final state), it can be obtained

dh

dhsp

0 dpdhTds s

dTcdh p

TdT

pdp

dTc

dp

p

p/

/1

1,

2,

1,

2,

ln

ln1

o

o

o

o

p

T

T

p

p

Polytropic Efficiency [1/2]

[ Infinitesimal compression process ]


po

T

(h)

s

To

To+dTo

po+dpo

Tos+dTos

dhs


Polytropic efficiency is not used directly in design point calculation. However, it is important for comparison

of the compressors having different pressure ratio.

Although exactly same technologies and frontal area are used in the design of two compressors having

different pressure ratio, the isentropic efficiency of the compressor having low pressure ratio is higher than

that having high pressure ratio.

This is because the rear stages require more work input for the same pressure rise. Therefore, compressor

having lager number of stages shows lower isentropic efficiency than that having smaller number of stages.

Therefore, isentropic efficiency decreases as the pressure ratio increases.

However, if those two compressors are designed using same technology level, average stage loading, and

geometric such as frontal area, they will have the same polytropic efficiency regardless of pressure ratio.

Polytropic efficiency for axial compressors increases as the size and technology level increase.

The isentropic efficiency can be expressed with the polytropic efficiency.

1

1/1

/1

pr

rc

1,

2,

o

o

p

pr


Polytropic Efficiency [2/2]


Compressor efficiency is very important in the overall performance of the gas turbine, as it consumes around

50% of the power produced by the gas turbine. Currently, the efficiency of the compressor is in the 85 to 90%

range.

In general, the higher the compressor pressure ratio, the better the thermal efficiency of the gas turbine.

Considerable effort has being done to improve compressor efficiency, which has led to a decrease in the ratio

of (compressor / turbine) stages.

Tu

rbin

e w

ork

Com

pre

ssor

wo

rk

Net Work

Tu

rbin

e w

ork

Net

Work

Pu

mp

Work

Tu

rbin

e w

ork

Com

pre

ssor

wo

rk

Net

Work

Steam Turbine Low Efficient Gas

Turbine

High Efficient Gas

Turbine



R

Reaction Action

F

V

A

, Nozzle

F = mV = V2A

m = VA (mass flow rate)

Fluid Dynamic Force

Euler Equation [1/4]


Air enters the rotor with an absolute velocity (c1) and

an angle 1. However, it enters the rotor finally with a

relative velocity (w1) and an angle 1 because rotor

rotates.

Air passing through the rotor passage is given a

relative velocity w2 at an angle 2, which is less than

1 because of the camber of the blade. In addition, w2

is less than w1 because air is diffused in the rotor

passage.

The combination of the relative exit velocity and blade

velocity produce an absolute velocity c2 at the exit of

the rotor.

In the case of compressor, the convention chosen is

that the absolute and relative velocities and angles

are positive when measured in the direction of

rotation. Therefore, c,1, c,2, 1,2 are positive; w,1,

w,2, 1, 2 are negative.


Velocity Triangles

c1

w1

c,1

1 1

vz,1

u1

w2 c2

c,2

2 2

vz,2

u2

c3

Shaft CL

IGV

Rotor

Stator

3


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

acting on the rotor.

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 rotor.

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 on rotor = force length =

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

Net power on rotor,

Therefore, Euler’s equation can be derived.

(1)

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

1θ,cm

11θ, rcm

11θ, rcm

2θ,21θ,122θ,11θ,12 cucumrcrcmW

2θ,21θ,11212 / cucumWw


Euler equation


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

thermodynamics gives,

This means that the mechanical energy transferred to the air through a rotor blades is represented by the

stagnation enthalpy increase.

(3)

The first law of thermodynamics is,

(2)

2,1,12 oo hhw

1212

2

1

2

2112212122

1wzzgccppuuq

1212

2

1

2

212122

1wzzgcchhq

12121,2,12 wzzghhq oo

121,2,12 whhq oo


Therefore, following relationship can be obtained from Euler equation,

or (4)

It is clear that the stagnation enthalpy and pressure rise in a compressor 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

(5)

2,21,12,1,12 cucuhhw oo θucddho

θdcudho

c1

c2 q

w z1

z2

1

2


Rothalpy

The rothalpy is a function that remains constant throughout a

rotating machine.

Rothalpy can be derived from the Euler’s equation.

It can be found out from the rothalpy notation that stagnation

enthalpy is constant in a non-rotating machine.

The general notation of rothalpy is

Icuhcuh oo 2,22,1,11,

ucchI 2

2

1

c

w

c

vz

u

rotor

This expression can be reformulated by expressing the velocities in the relative frame of reference .

= constant along a streamline

wuc

wuc

222222 2 uuwwvcvc zz

2222222

2

1

2

12

2

1uwvhuuwuuwwvhI zz

22

2

1

2

1uwhI


Temperature Rise per Stage [1/2]

Temperature increase per stage can be obtained using equation (4).

And assuming that the blade speeds at the inlet and exit of the compressor are same,

Enthalpy change can be written when the axial velocity remains constant (vz = vz,1 = vz,2 ):

(6)

[from velocity triangle, ] (7)

Therefore, above equation can be expressed by

(8)

Practically, the stage temperature rise will be less than this because of three dimensional effects in the

compressor annulus. It has been demonstrated from experimental investigations that the actual temperature

rise can be obtained by the multiply of work done factor () which is less than unity.

11,22, tantan zzo vvudh

2112 tantantantan p

z

p

zo

c

uv

c

uvdT

1,12,2 cucudho

11z,1θ, tanvc

22z,2θ, tanvc

2112 tantantantan zzo uvuvdh

2211 tantantantan zz vv


This is a really a measure of the ratio of the actual work absorbing capacity of the stage to its ideal value as

calculated from the equation.

The explanation of this is based on the fact that the radial distribution of axial velocity is not constant across

the annulus but becomes increasingly peaky as the flow proceeds, settling down to a fixed blade at about

the fourth stage.

Therefore, equation (8) is expressed in the real world as follows:

(9)

Vz mean

First Stage

Fourth Stage

Blade

Height

Blade

Height

Vz

[ Axial Velocity Distributions ]

Me

an

wo

rk d

on

e fa

cto

r (

)

Number of stage

4 8 12 16 20

1.0

0.9

0.8

2112 tantantantan

p

z

p

zo

c

uv

c

uvdT

Temperature Rise per Stage [2/2]


Pressure Ratio per Stage

Enthalpy rise in a stage can be expressed as follows:

(10)

Therefore, pressure ratio across the rotor can be written:

(11)

Where r is a pressure ratio, and are total pressure at inlet and exit of the rotor row.

Equation can be expressed in terms of stage temperature rise. from equation (10) following relation can be

derived.

(12)

Practical stage pressure ratio includes stage isentropic efficiency (s).

(13)

1

1

1,

2,

1,1,2,1,2,

o

o

opoopooop

pTcTTchhdh

1

1,1,

2,1

o

o

o

o

T

dT

p

pr

1

1,1,

2,1

o

os

o

o

T

dT

p

pr

1,op 2,op

1

21

1,

1

12

1,1,

2,tantan1tantan1

op

z

op

z

o

o

Tc

uv

Tc

uv

p

pr


1

12

1,1,

2,tantan1

op

z

o

o

Tc

uv

p

p

12

1,1,

2,tantan1

op

z

o

o

Tc

uv

T

T

Pressure and Temperature Rise

From equation (11),

Both stagnation pressure rise and temperature rise are strong functions of

blade speed, axial velocity or axial Mach number (or mass flow), inlet and

exit flow angles, and the absolute or relative turning angles.

For a given blade angle (2) and inlet angle (1), the pressure and

temperature rise depend strongly on the flow coefficient( = vz/u).

Furthermore, the pressure rise depends on the efficiency as well as the

flow coefficient.

A compressor with 1, 2, and u are constant, the pressure and

temperature rise decrease as the mas flow (or ) increases.

On the other hand, if 1, 2, and u are constant, the pressure and

temperature rise increase with u. Therefore, high blade speed and low

mass flow contribute to higher pressure and temperature rise.

Furthermore, higher flow turning (12) or (12) contributes to higher

pressure and temperature rise. However, there is limiting value that leads

to flow separation.

c1

w1

c,1

1 1 vz,1

u1

w2 c2

c,2

2 2 vz,2

u2

c3

Shaft CL

IGV

rotor

stator

3

1

122

1

122

1,

2,tantan

11tantan

11

Mv

u

Mp

p

zo

o


The rule of thumb, the energy rise per stage would be constant for a multiple stage gas turbine compressor,

rather than the commonly held perception that the pressure rise per stage is constant.

= total enthalpy at inlet and exit of compressor (kJ/kg, or Btu/lbm)

= number of stages

Assuming that the air is thermally and calorically perfect (cp and are constant), stage temperature rise can be

obtained using the pressure ratio from equation (12).

Energy Increase

N

hhh

inletoexito

o

,,

inletoh , exitoh ,

N

1

1

1,

rTdT oo


[Exercise 3.1] Calculate the stage temperature rise and pressure ratio of a compressor .

The design conditions at the mean diameter are:

u = 180 m/s, vz = 150 m/s, 1 = 15, 2 = 45

Use the work done factor of 0.86 and stage isentropic efficiency of 0.9. the inlet temperature is 15C.

[Solution]

The stage temperature rise can be obtained using the equation (9),

dTo = (0.86180 m/s 150 m/s)(tan45tan15)/(1.0047 kJ/kgK)

= {0.861801500.7321 (kgm/s2)mK}/1004.7 J

= 16.92K

The stage pressure ratio can be obtained using the equation (13),

PR = (0.916.92/288 +1)3.5

= 1.198

Exercise







Compressor Losses 7


Stall and Surge 8




Dimensionless Numbers

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 compressors and turbines are degree of reaction, loading

coefficient, flow coefficient, etc.

In addition to these, corrected mass flow, and corrected speed are also important dimensionless numbers in

compressors.

A set of dimensionless numbers will give a useful guidance in designing a compressor stage.


%10013

12

hh

hh

%10013

12

pp

pp

dpdhq

Thermodynamic process occurred in compressor and

turbine is adiabatic process. And ignoring density

changes.

dpdh

Degree of Reaction [1/2]

static enthalpy rise across the rotor

static enthalpy rise across the stage = x 100 (%)

Sta

tor

Ro

tor

Flow

direction

CL

1 2 3

The pressure rise occurs at both rotor and stator rows. As a measure of the extent to which the rotor

itself contributes to pressure rise, the term degree of reaction is used, defined as the ratio of the static

enthalpy rise in the rotor to that in the whole stage.

%10013

12

TT

TT


The pressure rise occurs at both rotor and stator rows. As a

measure of the extent to which the rotor itself contributes to

pressure rise, the term degree of reaction is used, defined as

the ratio of the static enthalpy rise in the rotor to that in the

whole stage.

21 tantan2

u

vz

u

v

hh

hh

hh

hh z

2

tantan11 21

13

23

13

12

From Euler equation and the first law of thermodynamics, the

following equation can be derived.

p1

po,1

1

o,1

1/2 c12

p2

o,3s

p3

po,3

po,2

1/2 c32

2

3

o,2 o,3

h

s

Roto

r S

tato

r

Ide

al co

mp

resso

r w

ork

Pra

ctica

l co

mp

resso

r w

ork

1/2

c22

2111 tantantantan2

u

vz

zv

u 11 tantan

21 tantan2

1

2

1

u

vz

Degree of Reaction [2/2]


The most important performance variable in turbomachinery is the amount of work input or extraction.

Loading is a measure of how much work is demanded of the compressor or stage. Its dimensionless form is

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

The loading coefficient reflects the pressure/temperature rise across a compressor or 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 rotor speed, that is,

where wr is the isentropic work.

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

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

Normally, the value of loading coefficient is kept fairly low to prevent flow separation, with design range 0.35

to 0.50. As a result, the amount of turning is about 20, and does not exceed 45.

The allowable loading coefficient is much lower for a compressor stage than a turbine. This is because, in a

compressor, the intrinsic pressure rise provides an adverse pressure gradient for the blade surface

boundary layers. Thus the boundary layers become thicker more quickly and are liable to separate after only

a small amount of flow turning. Hence, axial compressors have many more stages than axial turbines.

2

2,21,1

2

2,1,

2 u

cucu

u

hh

u

w oor

u

v

u

ccz 212,1, tantan

Loading Coefficient


The flow coefficient is a non-dimensional axial velocity.

This is defined by the ratio of the axial velocity entering to the mean rotor speed, that is,

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

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

stage.

It also varies with radius.

However, in a simple velocity diagram, the flow coefficient is constant.

Normally, the value of flow coefficient has the range of between 0.4 and 0.7 in axial compressors.

It is often at the lower end of this range for the last stage to achieve acceptable exit Mach number.

Euler equation can be rewritten in a nondimensional from by dividing both sides by u2, leading to

It can be found from this equation that the loading coefficient and flow coefficient are closely related to the

flow turning.

Flow Coefficient

11 tantan

1

u

vz

21 tantan


[ Smith chart ]

Smith Chart


In most compressor stages both rotor row and stator row

are designed to diffuse the working fluid, and hence

transform its kinetic energy into an increase in static

enthalpy and static pressure.

The more the fluid is decreased, the larger pressure rise,

but boundary layer growth and flow separation is limiting

the process.

To avoid this, de Haller proposed that the overall

deceleration ratio, i.e. w2/w1 for rotor and c3/c2 for stator,

should not be less than 0.72 in any row.

That is, the de Haller criterion is used as a criterion to

ensure that the diffusion in the flow passage would not

be strong enough to cause separation of the boundary

layers.

1

2

w

wdHR

de Haller Number

c1

w1

c,1

1 1

vz,1

u1

w2 c2

c,2

2 2

vz,2

u2

c3

Shaft CL

IGV

Rotor

Stator

3

2

3

c

cdH S









Compressor Losses 7


Stall and Surge 8




1. Mean inlet Mach number

• This is calculated using the known inlet flow, pressure, temperature, and frontal area of the compressor.

• Commonly, this value has a range of between 0.4 and 0.6.

2. Tip relative Mach number

• The trend in compressor design is to increase the tip speed and relative Mach number.

• Tip relative Mach number can be evaluated by drawing the velocity triangle.

• The highest tip relative Mach number occurs on the first stage.

• Conservative and ambitious design levels are 0.9 and 1.3, respectively.

• The latter requires high diffusion relative to the blade to achieve subsonic conditions, which increases

pressure losses. VIGVs may be employed to reduce these levels.

• The transonic compressor blades, airflow over some parts of the blade is allowed to exceed sonic velocity,

have been developed with an aid of the new design skills and material development.

• The pressure rise coefficient for a compressor blade is given by

• Therefore, the pressure rise can be controlled by the value of Cp or DF (diffusion factor), and the inlet

relative Mach number. The value of Cp is limited by the boundary layer phenomena.

• For a fixed value of Cp or DF, the pressure rise can be increased by increasing the relative Mach number.

Basic Sizing Parameters [1/8]

2

1

12

1

2

1

12

2

1

12 1/222

RR

pM

pp

pM

pp

w

ppC

2

1

1

2

2

11 Rp MC

p

p


2. Tip relative Mach number (continued)

• The potential advantages of higher tip speed

have been investigated from the experimental

tests for the pressure rise at various tip speeds

(Mt). They are

1) The pressure rise increases rapidly as the

blade tip speed increases.

2) The gradient, (po3/po1)/Mt, also increases

with Mach number.

3) Efficiency as high as 89% has been

achieved at Mt = 1.3.

• Efficiencies decrease with blade tip Mach

number due to higher losses caused by shocks

and shock-boundary layer interaction. This

decrease in efficiency is more dominant at

higher Mach numbers.

• Mass flow also increases with blade speed.

Mass flow is important in power generation gas

turbines in terms of competitiveness because a

unit price decreases as the unit capacity

increases.


[ Variation of pressure rise, efficiency, and max with

tip speed ]

Tip Mach Number

0.4 0.8 1.2 1.6 2.0 2.4

5

4

3

2

1

0

0

0.8

0.4

max

C = 0.9 C = 0.8

80%

90%

C

DF=0.5

max

po,3/po,1

Compressor with swept blades


3. Stage loading

• Loading is a measure of how much work is needed of the compressor or stage.

• Stage loading can also be calculated at radial positions other than the pitch line.

• A key design issue is its value at the hub of the first stage where it has highest value due to the lower

blade speed.

• Here to maintain acceptable diffusion rates a value of 0.6 would be conservative and 0.9 ambitious.

4. Rotational speed

• For single shaft engines directly driving a generator, the speed must be either 3000rpm or 3600rpm.

• However, small engines may have higher rpm than large ones to get higher compressor efficiency. ( =

cx/u 0.5 for higher efficiency)

• The significance of higher velocity is that mass airflow can be increased without increasing the diameter of

the engine.

• The turbine is often the dominant factor due to its high temperature and stress levels.



5. Pressure ratio

• Invariably the stage pressure ratio falls from front to rear

because of increasing temperature.

• The achievable pressure ratio for a given number of stages is

governed by many factors, however, the most important are

achieving satisfactory part speed surge margin and good

efficiency.

• In general, the front stages of a multi-stage axial flow

compressor are pushed towards stall at low speed.

• The larger the number of stages, and pressure ratio per

stage, the worse this phenomenon.

• To deal with this, variable geometry such as VIGVs and

VSVs, or bleed valves must be employed.

• The higher the overall pressure ratio in a given number of

stages, and hence loading, the lower the efficiency.

• The 1.4:1 per stage pressure ratio achievable in the high

performance compressor is accomplished by supersonic

diffusion.

• Some compressor being installed in the newest engines, or

being developed for future aviation engines, are running

pressure ratios as high as 1.5 to 1.6 per stage.



6. Hub-tip ratio

• Hub-tip ratio means that the ratio of the hub radius to tip radius (=

rhub/rtip).

• This is considered as aspect ratio frequently.

• At high values of hub-tip ratio, tip clearance becomes a more significant

percentage of the blade height. This leads to reduced efficiency and

surge margin.

• At low hub-tip ratios, disc and blade stress become critical and

secondary flows become stronger.

• To balance these two effects hub-tip ratio of the first stage should be

greater than 0.65, and become as high as 0.92 for rear stages on high

pressure ratio compressors.

Shaft center

line

Compressor

disc

Hub

Tip

Flow

rhub

rtip

7. Aspect ratio

• Aspect ratio is defined by blade height divided by blade chord.

• Where weight is important high aspect ratio blade is desirable, but at the expense of reduced surge

margin and more blades leading to high cost.

• Typical design levels are 1.5-3.5, based on axial chord, the lower values being more prevalent for small

engines where mechanical stresses dominate.

• Aspect ratio is established when the mass flow and axial velocity have been determined



8. Hade angle

• The hade angle is the angle formed between the inner or outer annulus line to the axial.

• The air passes through rotors and stators to increase the stagnation pressure of the air to the degree

required in the gas turbine engine cycle. As the air is compressed, the density of the air is increased and

the annulus area is reduced to correspond to the decreasing volume. This change is area may be

accomplished by means of varying tip or hub diameter or both.

• For industrial engines, a falling tip line and zero inner hade angle is better because it allows some

commonality of discs and root fixings reducing cost.

• For aero-engines, a rising hub line and zero outer hade angle is better because it minimizes number of

stages, weight, and frontal area. This also simplifies the mechanical design for achieving good tip

clearance control.

• A hade angle of up to 10 may be used for the outer annulus design, but preferably less than 5. The inner

annulus line hade angle should be kept to less than 10.



9. Blade gapping

• The axial gap between a blade row and its downstream stator row must be large enough to minimize the

vibratory excitation due to the upstream wake and also to avoid clipping in the event of surge moving the

tip of the rotor blade forward.

• Conversely, it should be minimized for engine length and cost.

• Typically, the gap is set to 20% of the upstream chord.

10. Exit Mach number

• These values must be minimized to prevent excessive downstream pressure loss.

• Mach number of the air leaving the compressor should not be higher than 0.35 and ideally 0.25.

• Exit swirl should be zero but certainly less than 10. Otherwise, EGVs must be considered.



z

Wake

Core flow

Velocity variation

across blade spacing

w1

1

s w2 2

Suction

surface

Pressure

surface


Flow in the Wake of a Compressor Cascade

The wake is a velocity defect generated by the

boundary layers of the blade surfaces. If 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.







Compressor Losses 7


Stall and Surge 8




The purpose of compressor blade is to achieve

the necessary flow turning while minimizing

losses.

The lift coefficient can be directly related to the

blade camber angle.

The nature and type of blade employed in

compressors depends on the application and the

Mach number range.

Basically, therefore, the blade shapes of axial

compressors are governed by the camber line

shape and thickness distribution.

The representative camber lines are polynomial,

exponential, circular arc, and multiple circular arc.

Subsonic blades usually consist of circular arcs,

parabolic arcs, or combination of those.

% Chord 1.0 0.5

Loca

l re

lative

Ma

ch n

um

ber

3.0

2.0

1.0

0

% Chord 1.0 0.5

Loca

l re

lative

Ma

ch n

um

ber

3.0

2.0

1.0

0

Forward position of maximum

thickness or camber

Rearward position of

maximum thickness or camber

The blade having small thickness is generally desirable for aerodynamic reasons. However, mechanical

considerations require a minimum level in terms of blade strength and vibration.

A significant test results conducted using blades of 10% tb/C. Recently, however, most compressor blades

have a maximum thickness of around 5% chord (tb/C).

Generals [1/2]


The position of the maximum thickness has a significant influence on

the performance of the blade row.

The forward locations of blade maximum thickness result in the same

performance features with the forward cambered blades.

It can be seen that the forward positions of blade maximum thickness

or camber tend to amplify the suction surface velocity. Such blades

can support lower loadings as the flow is more prone to separation

due to the significant adverse pressure gradient after the velocity

peak.

Transonic compressor: the velocity relative to a moving row of blades

is supersonic over part of the blade height. In addition, although the

entry flow is subsonic, a supersonic region can be formed inside the

passage by flow acceleration on suction surface.

Supersonic compressor: the velocity at entry is everywhere

supersonic, from hub to tip.

For blades operated in supersonic flows, leading and trailing edges

are very thin and blade thickness is very small.

For supersonic inlet flow, proper control of supersonic and subsonic

turning is essential. With such control, the loss can be minimized.

Generals [2/2]


NACA 65- 8 10

NACA 65- (12)10

NACA 65- (15)10

NACA 65- (18)10

NACA 65- (21)10

NACA 65- (24)10

(a) NACA 65 series

Most modern axial flow compressors are designed with NACA airfoils.

NACA 65 series blade profile has a maximum thickness at 40% chord and

developed by modification of aircraft wing airfoils in the late 1940s.

One of the representative modification is a slightly thicker trailing edge for

easier blade manufacture.

The number 65-(15) 10 means that the blade has a lift coefficient (CL) of

1.5, a profile shape 65, and a thickness/chord ratio of 10%.

This profile was used extensively by GE up to the late 1950s

NACA 65 series blades had been used until 1990 in most commercial

axial flow compressors.

The C-series blade profiles had been widely used in UK.

The C4 is similar to the NACA 65 series profiles, however the location of

maximum thickness is slightly forward at 30% chord.

In addition, C4 have more blunt leading edge. Thus, it has better erosion

resistance but less high speed performance.

Both blade types were replaced by the double circular arc blades.

NACA 65 (x)y, where x is 10

times the design lift coefficient of

an isolated airfoil and y is the

maximum thickness in percent of

chord.

NACA 65 Series & C Series


Double circular arc (DCA) profile developed in the late

1950s.

DCA profile has a superior high speed performance

because it has a maximum thickness at 50% chord.

This blade showed equal to or better performance

even lower speeds.

This blade has a large shock loss in transonic flow

regime.

It can be found from the figure that both NACA 65

series and C4 blades suffer from low pressures on the

pressure surface leading edge. Sudden acceleration

and deceleration are undesirable from the point of view

of boundary layer growth.

DCA has much better pressure distribution than NACA

65 blades and C4 blades, but the suction peak is aft of

the leading edge and the adverse pressure gradient on

the suction side toward the trailing edge is much

greater, an undesirable feature from the point of view

of flow separation.

DCA blades were replaced by controlled diffusion

airfoils.

Double Circular Arc

0

z/c

Pre

ssure

co

eff

icie

nt

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

CDA

NACA 65

C4

0.9 1.0

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

tb=5%C

rb=0.5%C

(b) Double circular arc


Multiple circular arc (MCA) profile developed by NASA in the 1960s.

In NASA’s MCA blades have the centerline consisting of two circular arcs

having different curvature.

It has been demonstrated that MCA blade has less total pressure losses

than DCA blades in transonic stators.

A detached bow shock is formed at the front of the blunt leading edge.

The fluid behind the bow shock expands over the suction surface to

supersonic speed until it reaches a normal shock formed in the blade

passage.

Total pressure losses caused by the shock in the blade passage are

related to the strength of the shock, and thus the Mach number

immediately upstream of the shock.

In order to reduce the pressure losses caused by the shock, the strength

of the normal shock should be reduced.

In MCA blades, this is accomplished by limiting the turning of the inlet

section of the blade.

After the shock, the blade turning is increased to achieve the total turning

necessary for the compressor design.

(c) Multiple circular arc

r1

r2

[ Camber line of a MCA blade ]

Multiple Circular Arc [1/2]


Passage

Shock

Bow Shock Bow Shock

Stagnation

Streamline

Supersonic

Upstream Flow

Sonic Line

Expansion Waves

[ A typical shock structure around a transonic cascade ]

Multiple Circular Arc [2/2]


(d) Controlled diffusion airfoil shape and

Mach number distribution

The present trend is toward the use of custom-tailored

airfoils rather than the standardized series of blades.

The new advanced compressor rotors have fewer

blades with higher loadings, thinner, larger. Those

blades are designed using advanced radial equilibrium

theory, which create three dimensional and controlled

diffusion-shaped airfoils (3D/CDA), with smaller

clearances and higher loading per stage.

In the case of controlled diffusion airfoils (CDA), which is

designed for the required loading, the particular blade

thickness distribution is not specified.

CDA usually have a significant region of laminar flow on

the suction surface leading edge which gives low profile

loss. It is generally agreed that CDA gives around 1%

higher efficiency than conventional blades.

CDA are designed to avoid flow separation near the

trailing edge, thus they can tolerate much higher

loadings.

Continuous acceleration on LE to avoid

laminar boundary layer separation

Low peak Mach number to avoid

shock induced separation

Controlled diffusion near

trailing edge to avoid

turbulent boundary layer

separation

Constant subsonic Mach

number on pressure surface

% Chord

1.0 0.5

Ma

ch

nu

mb

er

1.5

1.0

0

0.5

0

Controlled Diffusion Airfoils

There has been considerable research in recent years to design shock free and controlled diffusion airfoils

for high-speed as well as multistage compressor applications.

Controlled diffusion airfoils are designed and optimized specifically for subsonic and transonic applications,

by minimizing boundary layer separation and by diffusing the flow from supersonic to subsonic velocities

without a shock wave.







Compressor Losses 7


Stall and Surge 8




21 tantan2

1

2

1

u

vz

1) Low reaction stages ( < 50%)

• A low reaction stage has a smaller static pressure rise in its rotor than that in the stator.

• In such a stage the quantity (tan1-tan2) is positive. Thus, 1 > 2.

• In a low-degree reaction stage, the stator rows are burdened by a comparatively larger static pressure rise

which is not desirable for obtaining higher efficiencies.

2) 50% reaction stages

• 1 = 2.

• 2 = 1. from

• Therefore, w1 = c2 and w2 = c1.

• These relations show that the velocity triangles at the entry and exit of the rotor of a fifty per cent stage are

symmetrical.

• The whirl or swirl components at the entries of the rotor and stator rows are also same.

3) High reaction stages ( > 50%)

• A high reaction stage has a larger static pressure rise in its rotor than that in the stator.

• In such a stage the quantity (tan1-tan2) is negative. Thus, 1 < 2.

• Since the rotor blade rows have relatively higher efficiencies, it is better to have a slightly larger pressure

rise in them compared to the stator.

2211 tantantantan1

u

vz

Degree of Reaction


c1 w1

u w

vz c2 w2

u c

(a) Symmetrical velocity triangle for

50% reaction stage

c1 w1

u w

c2 w2

u c

(b) Velocity triangle for axial-entry

stage

c1 w1

u

w

c2 w2

c

u

(c) Velocity triangle for axial-outflow

stage

Comparison of Velocity Triangles

c1

w1

c,1

1 1

vz,1

u1

w2 c2

c,2

2 2

vz,2

u2

c3

Shaft CL

IGV

rotor

stator


1) 가장 적은 압축기 단 수를 이용하여 가스터빈에 요구되는 압력비 달성

• 대칭형 속도삼각형을 적용하면 로터와 스테이터에서 상승하는 정압 크기 동일

• 따라서 단에서 최대의 정압 상승 가능

• 이를 통해 가장 적은 압축기 단 수를 이용하여 가스터빈에서 요구하는 압력비를 얻을 수 있음

• 축류압축기 단 수가 줄어들면 가스터빈 제작비 절감, 진동특성 향상, 무게 감소

2) 압축기 운전안정성 향상

• 로터와 스테이터에서 상승하는 정압 크기 동일

• 어떤 주어진 단 압력비를 얻기 위해 로터나 스테이터에서 정압 상승 크기 최소로 유지 가능

• 이로 인해 압축기가 실속으로부터 상대적으로 자유로워 짐

3) 동일한 직경을 가지는 가스터빈으로 유입되는 공기의 질량유량 증가

• 로터 회전속도가 증가하더라도 로터로 유입되는 공기의 상대속도 작게 유지 가능

• 로터로 유입되는 공기의 절대속도 유입각(1)이 양()이고, 상대속도 유입각 (1)이 음()으로써 이들 부호가 서로 다르기 때문에 가능

• 따라서 입구 마하수 0.70~0.75를 초과하지 않으면서 로터 회전속도와 축방향 속도를 증가시킬 수 있음

• 로터 회전속도가 증가하면 압축기로 유입되는 공기의 질량유량 증가

• 따라서 동일한 크기의 질량유량이 요구되는 경우 로터 회전속도 증가를 통해 압축기 직경을 축소할 수 있기 때문에 대칭형 속도삼각형은 소형화가 요구되는 항공용 가스터빈 설계에 적합

Symmetrical Stage [1/2]

반동도 50%를 가지는 축류압축기의 장점 [1/2]


3) 동일한 직경을 가지는 가스터빈으로 유입되는 공기의 질량유량 증가 (계속)

• 일정한 rpm으로 회전하는 발전용 가스터빈의 경우 로터 회전속도 증가는 압축기 직경 확대를 의미하기 때문에 대형 발전용 가스터빈의 설계에 있어서 반동도 50%를 가지는 축류압축기는 큰 장점 보유

• 참고로, 로터로 유입되는 공기의 상대속도가 작아지면 로터 블레이드에서 발생하는 형상손실이 작아지기 때문에 고효율 축류압축기 설계 가능

4) 로터와 스테이터 블레이드 형상 동일

• 속도삼각형이 대칭이기 때문에 나타나는 현상

• 로터와 스테이터 블레이드 형상이 동일하면 블레이드 데이터 관리 및 제작 측면에서 유리

반동도 50%를 가지는 축류압축기의 장점 [2/2]

반동도 50%를 가지는 축류압축기의 단점

1) 배기손실(exhaust loss, or exit loss) 증가

• 압축기를 빠져나가는 공기의 축방향 속도성분이 크기 때문에 압축기에서 발생하는 배기손실 증가

• 그러나 압축기를 빠져나가는 고속의 압축공기는 압축기와 연소기 사이에 위치한 디퓨저에서 운동에너지가 압력에너지로 변환되기 때문에 큰 문제가 되지 못함

2) IGVs 필요

• 1단 로터에 유입되는 공기 유입각을 정확하게 맞추어주기 위하여 IGVs 설치 필요

• 그러나 대부분의 축류압축기는 부분부하운전특성 향상, 부분부하운전성능 향상, 외부 이물질의 가스터빈 유입 방지 등을 위해 VIGVs를 설치하기 때문에 이 또한 큰 문제가 되지 않음

Symmetrical Stage [1/2]


반동도가 50%가 아닌 압축기 단에 대한 속도삼각형은 모두 비대칭

비대칭 속도삼각형을 적용하는 경우 로터와 스테이터 블레이드 형상이 달라짐

비대칭 속도삼각형 가운데 하나인 그림 (b)에 나타나 있는 축방향 유입 속도삼각형의 경우 축방향으로 유입된 공기는 로터를 빠져나오면서 선회속도를 얻으며, 스테이터를 빠져나오면서 다시 축방향으로 진행

이렇게 설계된 압축기의 반동도는 60~90% 범위, 이로 인해 대부분의 압력상승이 로터에서 발생

이렇게 설계된 압축기 단은 반경방향을 따라서 일정한 에너지 전달과 축방향 속도를 가지며, 로터와 스테이터 열 사이에 와유동(vortex flow) 형성

50%보다 큰 반동도를 가지는 단의 장점: 낮은 블레이드 회전속도 및 축방향 속도로 인해 배기손실이 작기 때문에 50% 반동도를 가지는 단보다 높은 효율 보유

축방향 유입 속도삼각형의 단점:

• 스테이터에서 정압 상승이 작게 일어나기 때문에 상대적으로 많은 단 필요, 이로 인해 압축기 무거워짐

• 아울러 블레이드 회전속도와 축방향 속도가 작기 때문에 입구 마하수 한계를 지키기 위해 압축기 직경 증가

그러나 육상용 가스터빈의 경우 가스터빈의 무게 및 전면면적 증가는 중요하지 않음

따라서 이런 형태의 속도삼각형은 효율을 우선적으로 중시하는 발전용 가스터빈 압축기에 적용 가능

Asymmetrical Stage [1/2]


그림 (c)에 나타나 있는 축방향 배출 속도삼각형, 즉 축방향과 평행한 방향으로 로터를 빠져나가는 속도삼각형을 적용한 단의 경우 모든 정압 상승이 로터에서 발생

그리고 스테이터에서는 정압이 오히려 줄어들며, 이로 인해 100%를 초과하는 반동도 가짐

축방향 배출 속도삼각형을 적용한 단의 장점: 축방향 속도와 블레이드 회전속도가 작기 때문에 배기손실이 가장 작게 발생

단점: 많은 단 수와 큰 지름으로 인해 압축기가 무거워짐

반동도가 50%보다 작아지면 스테이터로 유입되는 입구 마하수가 커지기 때문에 큰 손실 발생

일반적으로 스테이터의 확장 각도는 약 20°보다 작아야 함

이렇게 확장 각도가 제한되기 때문에 입구 마하수가 증가하는 경우 스테이터 길이가 증가하며, 이로 인해 압축기가 길어지고 무거워지는 문제 발생

Asymmetrical Stage [2/2]







Compressor Losses 7


Stall and Surge 8




The calculation of the performance of an compressor at both design and off-design conditions requires the

knowledge of the various flow losses encountered in the compressor.

The flow losses are as follows:

Flow Loss Description

Shaft loss • Disc friction loss and bearing loss are belong to this.

• Disc friction loss is caused by the skin friction on the discs.

Incidence loss • This loss occurs when the incidence is different from design condition.

Profile loss

• This loss occurs because of the growth of boundary layer on blade surface,

flow separation usually occurred on the suction side of the blades.

• The effect of this loss is an increase of entropy due to the viscous heat

developed by the energy dissipation within the boundary layers. This results in

a stagnation pressure loss.

• The wake loss and shock loss are belong to this.

Secondary flow loss • This loss is caused by the generation of secondary flow in the flow path.

Annulus loss • This loss occurs because of the growth of boundary layer on the annular walls.

• It is also called as endwall loss.

Leakage loss • This loss is due to the clearance between blade tips and the casing.

• This loss also occur due to the clearance between stator and disc.

Exit loss • This loss is due to the kinetic energy head leaving the stator.

Performance Losses


Energy from the

turbine (100)

Isentropic work (82)

Shaft losses

(2)

Rotor aerodynamic losses (9)

Stator aerodynamic losses (7)

Disc friction loss

Bearing loss Profile loss

Annulus loss

Secondary loss

Tip leakage

Profile loss

Annulus loss

Secondary loss

Tip leakage

Energy Balance in a Compressor


Profile loss is caused by the effect of blade boundary layer growth, including flow separation, and wakes

through turbulent and viscous dissipation.

As the term indicates, this loss is associated with the growth of the boundary layer on the blade profile.

The boundary layer growth on the blade surfaces and walls of the compressor limit the pressure rise. The

energy contained in the working fluid is dissipated into heat within boundary layer and this increases the

entropy and results in total pressure loss, even though the stagnation enthalpy is constant for adiabatic flow.

Separation of the boundary layer occurs when the adverse pressure gradient on the surfaces becomes too

steep and this increases the profile loss.

The pattern of the boundary layer growth and its separation depend on the geometries of the blade and the

flow.

In general, the suction surface of a blade is more prone to boundary layer separation.

Tip leakage

Profile loss

Endwall loss

Cooling loss

Profile Loss [1/3]

The profile loss on a typical subsonic profile is mainly

governed by the flow behavior on the suction side

because of higher velocity and the occurrence of

adverse pressure gradients (typically more than 80%

of the skin friction loss occurs on the suction side).

If the flow is initially supersonic or becomes

supersonic on the blade surface additional losses

occur due to the formation of shock waves resulting

from the local deceleration of supersonic flow to

subsonic.


The wake is a velocity defect generated by the boundary

layers of the blade surfaces. If 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.

Profile Loss [2/3]

The profile loss includes the loss due to the wake through viscous and

turbulent dissipation.

The non-uniform velocity profiles in the wake are smoothed out by viscous

and turbulence effects.

Furthermore, the trailing vortex systems in the blade wake and its eventual

mixing and dissipation give rise to additional losses.


The loss due to viscous dissipation across the shock is

called “shock loss”.

This loss, in principle, could be estimated theoretically, but

the estimate of indirect loss associated with boundary-layer-

shock interaction has to be based on computation or

correlations.

Sudden jump in static pressure across the shock results in

thickening of the boundary layer and flow separation.

This loss could be substantial portion of total profile losses,

depending on Mach number and Reynolds number.

In general, this loss is normally the smallest loss

component.

Shock Loss

Profile Loss [3/3]


The majority of blade rows in turbomachinery are housed in casings.

In stationary blade rows, energy loss is occurred as the boundary layer is grown on the end walls.

This also occurs in the rotation blade rows but the flow on the end walls is affected by the rotation of the

cascade.

The boundary layer on the hub of the blade passages is subjected to centrifugal force, whereas that on the

ceiling (outer casing) is scrapped by the moving blades.

Motion of blade (scraping)

Tip leakage

Scrapped

flow

Annulus Loss


Hub

Tip

High

efficiency

area

Rad

ial h

eig

ht

Bucket efficiency

Secondary flow in a blade cascade Secondary vortices in short and long blades

Secondary Flow Losses


At blade ends there is a clearance, such as rotor ends

(casing) and unshrouded stator tips (hub), and the flow on

the pressure surface tends to escape over the blade tip

because of static pressure difference and interacts with the

suction surface flow.

This leakage vortex dominates the flow behavior near such

regions. Its influence can be mitigated by minimizing the

clearance. It is generally agreed that the optimum clearance

is around 1% chord, however, this level of precision is difficult

to achieve in the rear stages due to the small blade sizes.

The magnitude of tip clearance is small in proportion to the

blade height in the initial blade rows, however, this clearance

occupies an ever greater percentage of the blade span as

the blade rows become smaller towards the rear of the

compressor.

Hence, tip clearance flow has the greatest influence on

compressor flow behavior in the latter stages, and it affects

the occurrence of surge.

The tip clearance and secondary flows are closely related to

each other and it is often convenient to estimate them

together.

Tip Clearance Loss







Compressor Losses 7


Stall and Surge 8




Compressor Stall [1/9]

Flow Separation on a Blade

The value of the pressure coefficient at which stall occurs depends on the condition of the boundary layer

(whether separated or unseparated on the walls and blade surfaces), the presence of shock waves, and the

Reynolds number, as well as on compressor parameters, such as aspect ratio, stagger angle, chord length,

blade spacing, etc.

Because the boundary layer encountered in compressors are very complex, the prediction of inception of stall

and other phenomena is usually empirical in nature.


c : absolute velocity of inlet air

w : relative velocity entering rotor

u : rotor peripheral velocity

c

u

incidence rotor

rotation

(c) Increased rotational velocity

w

c

u

incidence

rotor

rotation

u

rotor

rotation

(a) Normal inlet velocity (b) Low inlet velocity

w

w c

incidence


Stall

(d) Flow separation


Stall is the breakaway of the flow from the suction side of the blade.

Compressor stall occurs most frequently whenever there is unusually high

compressor speed and a low air-inlet velocity (low mass flow rate)

1) Excessive fuel flow caused by abrupt engine acceleration (reduces the

velocity vector by increasing combustor back pressure)

2) Excessively lean fuel mixture caused by abrupt engine deceleration

(increases the velocity vector by reducing combustor back pressure)

3) Contaminated or damaged compressor (increases the velocity vector by

reducing compression)

4) Damaged turbine components, causing loss of power to the compressor

and low compression (increases the velocity vector by reducing

compression)

5) Engine operation above or below designed RPM

6) Reduced surge margin caused by increased performance of compressor

Cause of Compressor Stall


Flow separation


There are three distinct stall phenomena, such as individual blade stall, rotating stall, and stall flutter.

Individual stall and rotating stall are aerodynamic phenomena.

Stall flutter is an aeroelastic phenomenon.

Individual blade stall occurs when all the blades around the compressor annulus stall simultaneously without

the occurrence of a stall propagation.

The circumstances under which individual blade stall is established are unknown at present.

It appears that the stall of a blade row generally manifests itself in some type of propagating stall and that

individual stall is an exception.

In some instances of extremely severe compressor stall or surge, caused by fuel system malfunction or FOD,

a reversal of airflow occurs with such force that bending stresses on the rear of compressor blades can cause

them to contact the stator vanes. At that point a series of material failure can result in total disintegration of the

rotor system and complete engine failure.

Individual Stall



Rotating stall is a mechanism which allows a

compressor to adapt to a lower mass flow for the given

blade geometry. In such an operating regime, the flow

is shared unequally within the annulus.

Two types of rotating stall have been observed, part-

span and full-span stall.

Part span stall, which is milder of the two, is common

in the front stages of compressors at sub-idle speeds,

however, it usually disappears as the compressor

accelerates towards the normal operating range.

The reason of the occurrence of the rotating stall at low

speeds is because of stage mismatching at off-design

condition.

At low compressor speeds, the density ratio across the

compressor decreases rapidly. At low values of density

ratios, the flow annulus area at the rear of the

compressor limits the flow through the compressor.

This forces the front stages to operate at higher

loadings and finally stall occurs.

Rotating Stall [1/3]




The higher loadings in the front stages may allow the tip leakage vortex

to disrupt the boundary layer formed on the suction side, and this

causes a large scale tip stall. This may extend through several adjacent

blade passages forming a stall cell. The number of stall cell increases

with blade loading.

Further loading of the front stages may cause the stationary stall cell

detach and rotate around the compressor annulus. The stall cell moves

right to left, opposite to the direction of rotation. This speed of

propagation of the stall is found to be 50-70% of the blade speed.

Part span stall occupies a small part of the blade length and thus has a

limited impact on the overall performance of the compressor.

Part span stall may transition to the much more disturbing full span stall.

Full span stall is characterized by a large stall cell extending throughout

the blade length, thus it is more prone in the rear stages of the

compressor having lower aspect ratios.


[ Full span stall ] [ Part span stall ]




Full span stall results in severe vibration which may lead to rapid high cycle fatigue failure.

The efficiency, pressure ratio, and flow capacity of the compressor may diminish by up to 50% when

compared to normal operation.

Therefore, harmful effects, such as audible noise, fluctuation in RPM, and increase in TIT/EGT because of

less available air for cooling.

Full span stall occurs in the medium range, and its effect is much more damaging because it is much more

difficult to recover from it.

Pockets of rotating stall on front stages

moving in the direction of rotation at

between 40% and 70% of compressor

speed

[ Part span stall ]

Channel of rotating stall on all stages

moving in the direction of rotation at

approximately 50% of compressor speed

[ Full span stall ]


Stall flutter occurs due to the stalling of the flow around a blade.

Blade stall causes Karman vortices(1) in the airfoil wake. Whenever the frequency of these vortices coincides

with the natural frequency of the airfoil, flutter will occur.

Stall flutter is a major cause of compressor blade failure.

Several types of flutter have been identified and these are indicated as various flutter boundaries on the

compressor map. (see next slide)

(1) The term von Kármán vortex street is used in fluid dynamics to describe a repeating pattern of swirling vortices caused by the unsteady separation of flow of a fluid over bluff bodies. It is named after the engineer and fluid dynamicist, theodore von Karman and is responsible for such phenomena as the “singing” of suspended telephone or power lines, and the vibration of a car antenna at certain speeds.

Stall Flutter [1/2]


http://en.wikipedia.org/wiki/File:Vortex-street-animation.gif


Flutter regions on the compressor map of a

transonic compressor

Stall Flutter [2/2]



A compressor operates a wide range of flow and speed. Therefore, it should be designed to operate in a

stable condition at low rotational speeds and full speed as well.

There is an unstable limit of operation known as surge, that should be avoided for stable operation of

compressor, and it is given on the compressor map as the surge line.

The surge occurs when the compressor back pressure is high and the compressor cannot pump against this

high head, causing the flow to separate and reverse its direction.

Surge is a reversal of flow and is a complete breakdown of the continuous steady flow through the whole

compressor.

It results in mechanical damage to the compressor due to the large fluctuations of flow, which results in

changes in direction of thrust forces on the rotor, creating damage to the blade and the thrust bearings.

A decrease in the mass flow rate, an increase in the rotational speed of rotors, or both can be causes of

compressor surge.

Whether surge is caused by a decrease in flow velocity or an increase in rotational speeds, the rotors or

stators can stall.

Although, extensive investigations have been conducted on surge, it is not fully understood yet. Poor

quantitative universality or aerodynamic loading capacities of different rotors and stators, and an inexact

boundary layer behavior make the exact prediction of flow in the compressor at off-design stage difficult.

Surge can occur throughout the speed range if the surrounding components force the compressor operating

point up a speed line such that the pressure ratio is increased to the surge line value.

It is the point where blade stall becomes so severe that the blade can no longer support the adverse pressure

gradient, and with a lower pressure rise now being produced the flow instantaneously breaks down.

Surge [1/3]


The result is a loud bang with part of the flow reversing through the compressor from high to low pressure.

Additionally, when the surge is occurred, rapid changes in the mass flow lead to alternating stall and unstalled

behavior resulting in violent oscillations in pressure, propagation of pressure waves, and the failure of the

entire compression system.

In an engine a flame will often be visible at the engine intake and exhaust as combustion moves both

forwards and rearwards from the combustor.

If action is not taken immediately to lower the working line and hence recover from surge, such as opening

bleed valves or reducing fuel flow, then the compressor flow will re-establish itself and then surge again.

The surge cycle would continue at a frequency of between five and ten times a second eventually leading to

engine damage.

Usually surge, or near surge is accompanied by several indications, such as general and pulsating audible

noise (bang), excessive vibration, axial shaft position changes, higher discharged gas temperatures,

compressor differential pressure fluctuations, and lateral vibration amplitude increases.

Frequently, with high pressure compressors, operation in the incipient surge range is accompanied by the

emergence of a low frequency, asynchronous vibration signal that can reach predominant amplitudes, as well

as excitation of various harmonics of blade passing frequencies.

Extended operation in surge causes thrust and journal bearing failures.

Failures of blades are also experienced due to axial movement of the shaft causing contact of rotor with stator.

Due to the large flow instabilities experienced, severe aerodynamic stimulation at one of the blade natural

response frequencies is caused, leading to rotor blade failure.

Surge [2/3]


Tear out of blades after high vibration trip (7FA)

Surge [3/3]


Compressor Performance Parameters [1/2]

For a gas compressor, the compressor performance can be expressed as follows:

where po,exit is the compressor exit stagnation pressure, c is the adiabatic compressor efficiency, m dot is the

air mass flow, po,in is the compressor inlet stagnation pressure, To,in is the compressor inlet stagnation

temperature, N is rpm, is the kinematic viscosity, R is gas constant, is specific heat ratio, D is the tip

diameter of the compressor, and design means the geometry of machine.

Use of dimensional analysis reduces the complexity.

For a given compressor and for inlet conditions for which does not vary, above equation reduces to:

DdesignRNTpmfp inoinocexito ,,,,,,,,, ,,,

,,,,

2

,

2

,

, ND

RT

ND

Dp

RTmfPR

inoino

ino

c

2

,,

,,,,ND

T

N

p

TmfPR

inoino

ino

c


At high enough Reynolds number (3x105), changes in this number have little effect on compressor

performance so that (PR,c) can be correlated in terms of:

As no functional dependence is implied if the non-dimensional variables on the RHS are scaled by a

constant, we can thus choose to replace them by the corrected mass flow rate and corrected speed so that

The reference temperature and pressure are taken to be the sea level value for the standard atmosphere, Tref

= 15C (59.6F), pref = 101 kPa (14.7 psi).

The advantage of using these corrected variables is that their numerical magnitude is similar to the actual

value so the its significance is not disappeared.

inoino

ino

cT

N

p

TmfPR

,,

,,,

ccc NmfNm

fPR ,,,

refp

inop ,

= corrected mass flow rate

= compressor inlet total pressure

= reference pressure (14.7 psi)

cm

refT

inoT ,

= corrected speed

= compressor inlet total temperature

= reference temperature (15C)

cN

Compressor Performance Parameters [2/2]

refino TT /,refino pp /,


The overall performance of the compressor is depicted on the compressor map, which

includes family of constant speed (rpm) lines. The efficiency islands are included to show

the effects of operating on- and off-design point.

Operating Range

Constant

Speed (rpm)

Line

Surge

Margin

Choke

Point

Partial Span

Stall

Full Span

Stall

Surge

40%

60%

80%

100%

Pre

ssu

re R

atio

Mass Flow

Constant

Efficiency

Line

Sample 1

Compressor Map [1/11]


c

u

Angle of

attack

rotor

rotation

[Normal inlet velocity]

w

[Low inlet velocity]

The velocity relative to the rotor blade is composed of two

components: the axial one depending on the flow velocity of the air

through the compressor, and tangential one depending on the

sped of rotation (rpm) of the compressor.

Therefore, if the flow for a given speed of rotation is reduced, the

direction of the air approaching each blade is changed so as to

increase the angle of attack.

This results in more lift and pressure rise until the compressor

airfoil goes into stall.

Discuss about that why and how the compressor reaches the

choke point?

• Air flow increase angle of attack decrease PR decrease

• Air flow increase flow reaches M = 1 at the blade throat (flow

choking occurs)

u

rotor

w c

Angle of

attack

rotation

Flow separation

Characteristics of Constant Speed Line



A compressor map is plotted on the same non-dimensional

basis, i.e. pressure ratio and isentropic efficiency against

the non-dimensional mass flow for fixed values of non-

dimensional speed.

It can be seen from the compressor map that a speed line

covers narrow range of mass flow. Especially, the speed

lines become very steep at high rotational speeds.

The same limitations occur at either end of the speed lines

due to surge and choking.

Sample 2 & 3



Sample 4


Surge Margin

Working Line

Pre

ssure

Ratio

cm

c

cN

Surge Line


Sample 5 & 6



Once the compressor geometry has been fixed at the design point then the compressor map is produced to

define its performance under all off-design conditions. For a fixed compressor geometry, the map is unique.

The compressor map displays the variation of total pressure ratio across a compressor, as a function of

corrected mass flow (usually expressed as percent of design value), at a series of constant corrected speed

lines (Nc).

Traditionally, corrected speeds and corrected mas flow rates have been used in the compressor map to make

the curve general.

Pressure ratio and isentropic efficiency are plotted versus referred flow for a series of constant referred

speed.

On a given corrected speed line, the corrected mass flow rate is reduced as the pressure ratio increases until

it reaches a limiting value on the surge line.

The surge line is a locus of unstable compressor operating points, such as stall or surge, and is to be

avoided. To cope with this instability, the surge margin is considered.

For each corrected speed line there is a maximum flow which can not be exceeded, no matter how much

pressure ratio is reduced. This operating regime is termed choke and it is caused by the flow reaching sonic

velocity in one or more blade throats.


General Notes


Each compressor in a gas turbine engine has an compressor map, which is also called as operating map. A

complete maps is either based on compressor rig test results or is predicted by a special computer program.

Alternatively the map of a similar compressor can be suitably scaled. Compressor map is important, since it is

an integral part of predicting the performance of a gas turbine engine, both at design and off-design conditions.

Flow Axis

• The x-axis is usually some function of compressor entry mass flow, usually corrected mass flow (usually

expressed as percent of design value) or non-dimensional flow, as opposed to real flow.

• This axis can be considered a rough measure of the axial Mach number of the flow through the device.

Pressure Ratio Axis

• Normally the y-axis is pressure ratio (po,exit/po,inlet), where po is stagnation (or total head) pressure.

• ΔTo/To (or similar), where To is stagnation (or total head) temperature, is also used.

mmc

ref

ino

p

p ,

refp

inop ,

= corrected mass flow rate

= compressor inlet total pressure

= reference pressure (14.7 psi)

cm

ref

ino

T

T ,

refT

inoT , = compressor inlet total temperature

= reference temperature (15C)



Speed Lines

• The slightly curved, near vertical, lines on the main part of the map are the (constant rotational) corrected

speed lines. They are a measure of rotor blade tip Mach number.

• Note on the illustration that the speed lines are not distributed linearly with flow. This is because this

particular compressor is fitted with variable stators, which open progressively as speed increases, causing

an exaggerated increase in flow in the medium to high speed region.

• At low speed, the variable stators are locked, causing a more linear relationship between speed and flow.

• On a given corrected speed line, as the corrected mass flow is reduced the pressure ratio usually

increases until it reaches a limiting value on the surge line.

• For an operating at or near the surge line the orderly flow (i.e., nearly axi-symmetric) in the compressor

tends to break down (flow becomes asymmetric with rotating stall) and can become violently unsteady.

• Thus the surge line is a locus of unstable compressor operating points to be avoided.

• Also note that beyond 100% flow, the speed lines close up rapidly, due to choking. Beyond choke, any

further increase in speed will generate no further increase in airflow.

NNc = constant corrected speed lines cN


Surge Line

• The surge line is a locus of unstable compressor operating points, such as stall or surge, and is to be

avoided. Above this line is a region of unstable flow, which should be avoided.

• A compressor surge, typically, causes an abrupt reversal of the airflow through the unit, as the pumping

action fails because of the airfoils stalls.


Surge Margin

• To cope with this instability, the surge margin is considered.

• As the name suggests, surge margin provides a measure of how close an operating point is to surge. The

definitions of surge margin are as follows:

• For operation on the constant corrected speed line, an alternative definition for surge margin in terms of

corrected mass flow on the working line and on surge line at the same corrected speed would be

preferable.

• During the life of the compressor, the surge line tends to lower because of blade tip clearance increase due

to casing/rotor rubbing. Such rubbing occurs during transients owing to the differential thermal expansion

of the different components.

• In addition, the working line also tends to rise because of component deterioration, such as fouling, FOD,

SPE, and WDE.

• One of the goals of the compressor designer is to increase the surge margin.

w

sw

m

mmSM

working

workingsurge

PR

PRPRSM

wm

smwm

= mass flow at the operating point, be it steady state or transient

= the mass flow at surge, at same corrected speed as

PR = pressure ratio



Efficiency Axis

• A sub-plot shows the variation of isentropic (i.e. adiabatic) efficiency with flow, at constant speed. Some

maps use polytropic efficiency. Alternatively, for illustrative purposes, efficiency contours are sometimes

cross-plotted onto the main map.

• Note that the locus of peak efficiency exhibits a slight kink in its upward trend. This due to the choking-up of

the compressor as speed increases, with the variable stators closed-off. The trend line resumes, once the

variables start to move open.

Working Line

• Compressors usually are operated at a working line, separated by some safety margin from the surge line.

• A typical steady state working (or operating/running) line is a locus of the operating points of the engine, as

it is throttled.

• If the unit had no variable geometry, there would be handling problems, because the surge line would be

very steep and cross the working line at part-flow.

• Compressor surge is a particular problem during slam-accelerations and can be overcome by suitable

adjustments to the fuelling schedule and/or use of blow-off (bleeding air off the compressor, for handling

purposes).



Choke Line

• As the flow increased at a constant speed, the compressor characteristic curve reaches an choke point.

• The choke point is the point when the flow reached a value of Mach = 1.0 at the blade throat, the point where

no more flow can pass through the compressor.

• When choke occurs, the efficiency of the compressor decreases significantly, but does not lead to

destruction of the unit.

• In addition, operation at or near choke point will result in over-temperature condition in the turbine section.

Operating Range

• The operational range is the range between the surge point and the choke point.

• The pressure ratios of the industrial gas turbines are lower than those of aviation units because the operating

range needs to be large.

• It is important to note that with the increase in pressure ratio and the number of stages, the operating range

is narrowed.

• The more stages, the higher the pressure ratio, the smaller the operational range between surge and choke

regions of the compressor.



6.5

51.5 45

Engine

center line VIGV

Inlet flow

angle Inlet flow

angle

VIGV

1st stage

compressor

blade

1st stage

compressor

blade

VIGV

Stall Control [1/7]

1) 압축기 유입 공기 질량유량 조절 – Surge control

2) 압축기 반동도 유지 – 1단 rotor로 유입하는 공기의 유동각 조절 VIGV 역할

1. VIGVs


2. Variable Stator [1/3]

Stall Control [2/7]

Variable stators were developed by GE in the early 1950s when designing the J79.

The front stages are forced to operate at higher loading at part speed. This tends to stall these stages and

thus variable geometry my be used to alleviate such higher loadings. Variable stators are employed on one or

more of the front stages of axial compressors to off-load the front stages.

They are closed at low speed to reduce the mass flow passing through the front stages. When the variable

stators are closed, re-match the compressor stages to perform better performance at lower speed.

However, the flow area reduces as the variable stators are closed, and choking limits compressor operation

drastically.

Hence, variable stators are designed to open as the compressor accelerates to higher speeds.

Variable stators are thought to be necessary when the pressure ratio from a single spool exceeds about 7.


c1

c3

= const.

Stator

Rotor

u

1 2 3

c2

w3

w1

w2

[ Fixed Stator ] [ Variable Stator ]


Stall Control [3/7]

1 2

3 ()

c1

c2

c3

1 2

1 2 3

Stator

Rotor

u

w3 w1

w2

유입 공기량 1: 설계조건 2: 설계조건보다 작은 경우 3: 설계조건보다 많은 경우



Stall Control [4/7]

축류압축기 전단부 몇 개 단에 가변 스테이터 적용

가변 스테이터는 엔진 회전속도에 의해서 자동적으로 각(피치) 조절

가변 스테이터를 적용하면 작동기구로 인하여 압축기가 복잡해지지만 가스터빈 전체적으로는 다축식보다 간단

https://www.google.co.kr/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0CAcQjRxqFQoTCILr-uzJw8gCFUccpgodw3EDXw&url=https://commons.wikimedia.org/wiki/File:Variable_guide_vanes_on_compressor_case.jpg&bvm=bv.105039540,d.dGY&psig=AFQjCNEvKltpoYuazl-GdTDnCZkqgI6TJg&ust=1444967574383865


축류압축기 중간 단 또는 후방에 브리드 밸브를 설치하여 기관 시동시 및 저출력 작동시 이 밸브가 자동적으로 열리도록 하여 압축공기를 대기중으로 방출

방출된 공기량 만큼 축방향 속도가 작아짐에 따라 로터 유입각이 작아져서 실속 방지.

u

c

c’

w

w’

3. Bleed Valve [1/2]

Stall Control [5/7]


Bleed valves are used to dump compressed air. This is wasteful because the air has had work input.

However, bleed valves are a lower cost and a more reliable option when compared to variable stators.

Bleed air can, depending on the application point, lower the working line or even modify the surge line.

As much as 5 to 25% of the compressed air may be bled off whilst starting. Consequently, the TIT increases

significantly as the available cooling air reduces.

Bleed valves are seldom used as a sole means of controlling the off design performance of the compressor

and are mostly used in conjunction with variable geometries to optimize the benefits of them.

Stall Control [6/7]

Pre

ssure

Ratio

Working Line with

Bleed Valve Open

Working Line

with Bleed

Valve Closed Surge Line

TN /

pTm /

3. Bleed Valve [2/2]


LP Compressor

(MS6001FA)

Standard Annular

Combustor

IP Turbine

HP Turbine

(CF6-80E)

HP Compressor

(CF6-80C2)

Power Turbine

LPC exit diffuser

scroll case

HPC inlet collector

scroll case

Hot end drive shaft

to generator

Exhaust diffuser

축류압축기의 안정운전 범위는 대개 압력비 5 이하

다축식 구조에서는 압축기 각 축당 압력비를 5 이하로 제한 가능

다축식으로 하면 고압력비와 고효율 가능

베어링 증가에 따라 구조가 복잡해지고 중량도 증가

4. Multi-Spool Engine

Stall Control [7/7]







Compressor Losses 7


Stall and Surge 8




Principle


Centrifugal compressors, they are still used on small gas turbines, are less efficient than axial compressors.

Recent development have produced compression ratios as high as 10:1 from a single centrifugal compressor.

When the pressure ratio exceeds 5:1, the flows entering the diffuser from the rotor are supersonic. This

requires a special design of the diffuser.

In a centrifugal compressor, the fluid is forced through the impeller by rapidly rotating impeller blades. The

velocity of the fluid is converted into pressure, partially in the impeller and partially in the diffusers.

Most of the velocity leaving the impeller is converted into pressure energy in the diffuser.

Generals

장 점 단 점

1) 단당 압축비가 크다

- 10:1 (15:1 in a dual stage)

2) 아이들에서 최대출력까지 넓은 운전영역에서 효율이 좋다

3) 축류식에 비해 구조가 간단하여 제작이 쉽고 가격이 저렴하다

4) 무게가 가볍다

5) 시동파워가 낮다

6) FOD 저항성이 크다

1) 압축효율이 낮다

2) 동일추력의 경우 전면면적이 커서 저항이 크다

3) 단 사이의 손실 때문에 2단 이상으로 하기 곤란하다


Centrifugal vs. Axial Compressor

1. The centrifugal and axial compressors are comparable in weight.

2. Aerodynamically, the axial compressor has better flow characteristics. Real fluid effects in centrifugal

compressors are much larger, and therefore centrifugal ones have a lower efficiency.

3. The advantage of the centrifugal compressor lies in the simplicity of manufacture, especially when the

turbomachine is miniaturized.

4. For moderate stagnation pressure ratios and low mass flow, centrifugal compressors are superior to the axial

ones. The multistage centrifugal compressors involve larger aerodynamic losses. Thus, axial compressor is

preferred for high pressure ratios and large mass flow.

5. Recent interest in centrifugal compressors for use in (a) small gas turbines for cars, (b) space power plants,

(c) rocket engines, and (d) artificial heart pumps has revived the aerodynamic investigation of this machine.

6. For industrial applications, such as natural gas pumping and rocket engines, safety and reliability are more

important and thus centrifugal compressors are sometimes preferred.

7. Gas turbines for power generation, where large mass flow and large pressure ratio are encountered, utilize

axial flow compressors.


2 Stage Impeller

It is much more difficult to produce an

efficient multistage centrifugal compressor

because the flow has to be ducted back to

the axis at each stage.

2 stage centrifugal compressors - Kawasaki

PR = 10.5, Output = 1.68 MW

th = 26.6% (blade cooling is possible because it

adopts axial turbine although it is a small GT)

Multistage Centrifugal Compressor


Combination Compressor

A compressor has an axial-flow compressor combined with a centrifugal compressor as the last stage.







Compressor Losses 7


Stall and Surge 8




Increased pressure ratio

• Higher engine efficiency requires higher engine pressure ratio.

• Higher pressure ratios will also increase the number of stages and potentially longer rotors.

• The number of turbine stage has been changed from three to four as the pressure ratio increases.

• Variable stator has adopted to control compressor stall and to increase efficiency during part load

operation.

Increased specific flow

• Specific flow will continue to increase and approach aero-engine technology.

• Siemens: 820 kg/s (latest 50 Hz engine); MHI: 860 kg/s (J-class)

• GE: 745 kg/s (9FB.05), 440 kg/s (7FA), 558 kg/s (7H)

• The absolute maximum of today is around 1000 kg/s@3000 rpm, but this can be achieved only with multi

-spools.

• GE and Alstom have upgraded compressor with aero-engine technology.

All major OEMs have on-line compressor vibration measurements and associated protection system.

Developmental Trends [1/7]


Previous Designs New Designs Risk

2D double circular arc or NACA 65 profiles 3D or Controlled Diffusion-shaped Airfoil

(CDA) profiles

Large number of airfoils Reduced airfoils

Repeating stages Stages unique

Shorter chords Longer chords

Low/modest aspect ratios High aspect ratios

Large clearances Small clearances

Low/modest pressure ratios Much high pressure ratios

Low/modest blade loading per stage High blade loading per stage

Wider operating margin Narrow operating margin

Thicker leading edges Thinner leading edges

Dry operation Wet operation

Lower costs Higher costs

Developmental Trends [2/7]


Pre

ssure

ratio

7E/9E

501ATS

7EA/9EC

V84.2/V94.2

7H/9H

V84.3A/

V94.3A

V84.3

501F/701F

7F/9F

7FA/9FA

GT24/GT26

GT13E2

GT11N2

501G/701G

35

30

25

20

15

10

5

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

501D5A

/701D

GE

Siemens

Alstom

WH/MHI

Pressure Ratio


10

Pre

ssu

re r

atio

8

66 70 78 74 86 82 98 94 90 02

14

12

18

16

22

20

24

MS9001E

MS5001M

MS7001H

MS6001B

MS9001H

MS7001EF MS9001F MS7001EA

MS9001B

MS7001C

MS7001B MS7001A

MS5001P

MS7001E

MS5001N

MS9001FA

Pressure Ratio - GE


200

0

66 70 78 74 86 82 98 94 90 02

600

400

1000

800

1400

1200

1600

MS9001E

MS5001M/R

MS7001H

MS6001B MS6001A

MS9001H

MS7001EF

MS7001FA

MS9001FA

MS7001EA

MS9001B

MS7001C

MS7001B

MS7001A

MS5002A MS5001P MS5002B

MS5001N

Air flo

w, lb

/se

c

MS7001E

Air Flow - GE


200

0

1940 1950 1970 1960 1990 1980 2010 2000

600

400

1000

800

1400

1200

Air m

ass flo

w, kg

/se

c

TIT

, C

TIT

Air mass flow

Air Flows and TITs


Sealing became an important issue

as the pressure ratio increases

Brush seals

• Minimize air leakage

• Tolerant of misalignments

• More durable than labyrinth seals

High Pressure Packing


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

Documents

3. Compressor Turbines for Power Plants 3. Compressor 2 / 136 2 Compressor Thermodynamics and Fluid Dynamics 18 1 Basic Principles of an Axial Compressor 2 Contents