3. compressor turbines for power plants 3. compressor 2 / 136 2 compressor thermodynamics and fluid...
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Gas Turbines for Power Plants 3. Compressor 1 / 136
3. Compressor
Gas Turbines for Power Plants 3. Compressor 2 / 136
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
Gas Turbines for Power Plants 3. Compressor 3 / 136
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
Gas Turbines for Power Plants 3. Compressor 4 / 136
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 Turbines for Power Plants 3. Compressor 5 / 136
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.
Gas Turbines for Power Plants 3. Compressor 6 / 136
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
Gas Turbines for Power Plants 3. Compressor 7 / 136
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
Gas Turbines for Power Plants 3. Compressor 8 / 136
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]
Gas Turbines for Power Plants 3. Compressor 9 / 136
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).
Pressure Ratio [2/4]
Gas Turbines for Power Plants 3. Compressor 10 / 136
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]
Pressure Ratio [3/4]
Gas Turbines for Power Plants 3. Compressor 11 / 136
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
q
ww
q
w
inputheat
ouputworknet
in
sys
th
Simple Cycle Analysis [2/2]
Pressure Ratio [4/4]
Gas Turbines for Power Plants 3. Compressor 12 / 136
7EA, GE
Configuration of a Typical Axial Compressor
Gas Turbines for Power Plants 3. Compressor 13 / 136
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]
Gas Turbines for Power Plants 3. Compressor 14 / 136
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]
Gas Turbines for Power Plants 3. Compressor 16 / 136
Compressor rotor stacking Stator buildup Rotor buildup
Rotor and Stator [2/3]
Gas Turbines for Power Plants 3. Compressor 17 / 136
Rotor and Stator [3/3]
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.
Gas Turbines for Power Plants 3. Compressor 18 / 136
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
Gas Turbines for Power Plants 3. Compressor 19 / 136
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
Gas Turbines for Power Plants 3. Compressor 20 / 136
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
Gas Turbines for Power Plants 3. Compressor 21 / 136
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
Compressor Cascade Nomenclature [2/3]
Gas Turbines for Power Plants 3. Compressor 22 / 136
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)
Compressor Cascade Nomenclature [3/3]
Gas Turbines for Power Plants 3. Compressor 23 / 136
z
r
Sta
tor
Ro
tor
Flow direction
CL
1 2 3
Velocity Triangles [1/4]
Gas Turbines for Power Plants 3. Compressor 24 / 136
Velocity Triangles [2/4]
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
Gas Turbines for Power Plants 3. Compressor 25 / 136
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)
Velocity Triangles [3/4]
Gas Turbines for Power Plants 3. Compressor 26 / 136
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.
Velocity Triangles [4/4]
Gas Turbines for Power Plants 3. Compressor 27 / 136
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
Gas Turbines for Power Plants 3. Compressor 28 / 136
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
Gas Turbines for Power Plants 3. Compressor 29 / 136
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
Gas Turbines for Power Plants 3. Compressor 30 / 136
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
Gas Turbines for Power Plants 3. Compressor 31 / 136
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
Compressor Work [2/3]
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
Gas Turbines for Power Plants 3. Compressor 32 / 136
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
Compressor Work [3/3]
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
Gas Turbines for Power Plants 3. Compressor 33 / 136
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.
Gas Turbines for Power Plants 3. Compressor 34 / 136
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 ]
Compressor Efficiency [2/4]
po
T
(h)
s
To
To+dTo
po+dpo
Tos+dTos
dhs
Gas Turbines for Power Plants 3. Compressor 35 / 136
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
Compressor Efficiency [3/4]
Polytropic Efficiency [2/2]
Gas Turbines for Power Plants 3. Compressor 36 / 136
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
Compressor Efficiency [4/4]
Gas Turbines for Power Plants 3. Compressor 37 / 136
R
Reaction Action
F
V
A
, Nozzle
F = mV = V2A
m = VA (mass flow rate)
Fluid Dynamic Force
Euler Equation [1/4]
Gas Turbines for Power Plants 3. Compressor 38 / 136
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.
Euler Equation [2/4]
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
Gas Turbines for Power Plants 3. Compressor 39 / 136
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 [3/4]
Euler equation
Gas Turbines for Power Plants 3. Compressor 40 / 136
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
Euler Equation [4/4]
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
Gas Turbines for Power Plants 3. Compressor 41 / 136
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
Gas Turbines for Power Plants 3. Compressor 42 / 136
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
Gas Turbines for Power Plants 3. Compressor 43 / 136
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]
Gas Turbines for Power Plants 3. Compressor 44 / 136
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
Gas Turbines for Power Plants 3. Compressor 45 / 136
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
Gas Turbines for Power Plants 3. Compressor 46 / 136
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
Gas Turbines for Power Plants 3. Compressor 47 / 136
[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
Gas Turbines for Power Plants 3. Compressor 48 / 136
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
Gas Turbines for Power Plants 3. Compressor 49 / 136
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.
Gas Turbines for Power Plants 3. Compressor 50 / 136
%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
Gas Turbines for Power Plants 3. Compressor 51 / 136
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]
Gas Turbines for Power Plants 3. Compressor 52 / 136
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
Gas Turbines for Power Plants 3. Compressor 53 / 136
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
Gas Turbines for Power Plants 3. Compressor 55 / 136
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
Gas Turbines for Power Plants 3. Compressor 56 / 136
Compressor Thermodynamics and Fluid Dynamics 2
Basic Principles of an Axial Compressor 1
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
Gas Turbines for Power Plants 3. Compressor 57 / 136
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
Gas Turbines for Power Plants 3. Compressor 58 / 136
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.
Basic Sizing Parameters [2/8]
[ 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
Gas Turbines for Power Plants 3. Compressor 59 / 136
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.
Basic Sizing Parameters [3/8]
Gas Turbines for Power Plants 3. Compressor 60 / 136
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.
Basic Sizing Parameters [4/8]
Gas Turbines for Power Plants 3. Compressor 61 / 136
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
Basic Sizing Parameters [5/8]
Gas Turbines for Power Plants 3. Compressor 62 / 136
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.
Basic Sizing Parameters [6/8]
Gas Turbines for Power Plants 3. Compressor 63 / 136
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.
Basic Sizing Parameters [7/8]
Gas Turbines for Power Plants 3. Compressor 64 / 136
z
Wake
Core flow
Velocity variation
across blade spacing
w1
1
s w2 2
Suction
surface
Pressure
surface
Basic Sizing Parameters [8/8]
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.
Gas Turbines for Power Plants 3. Compressor 65 / 136
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
Gas Turbines for Power Plants 3. Compressor 66 / 136
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]
Gas Turbines for Power Plants 3. Compressor 67 / 136
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]
Gas Turbines for Power Plants 3. Compressor 68 / 136
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
Gas Turbines for Power Plants 3. Compressor 69 / 136
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
Gas Turbines for Power Plants 3. Compressor 70 / 136
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]
Gas Turbines for Power Plants 3. Compressor 71 / 136
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]
Gas Turbines for Power Plants 3. Compressor 72 / 136
(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.
Gas Turbines for Power Plants 3. Compressor 73 / 136
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
Gas Turbines for Power Plants 3. Compressor 74 / 136
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
Gas Turbines for Power Plants 3. Compressor 75 / 136
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
Gas Turbines for Power Plants 3. Compressor 76 / 136
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]
Gas Turbines for Power Plants 3. Compressor 77 / 136
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]
Gas Turbines for Power Plants 3. Compressor 78 / 136
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]
Gas Turbines for Power Plants 3. Compressor 79 / 136
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]
Gas Turbines for Power Plants 3. Compressor 80 / 136
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
Gas Turbines for Power Plants 3. Compressor 81 / 136
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
Gas Turbines for Power Plants 3. Compressor 82 / 136
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
Gas Turbines for Power Plants 3. Compressor 83 / 136
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.
Gas Turbines for Power Plants 3. Compressor 84 / 136
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.
Gas Turbines for Power Plants 3. Compressor 85 / 136
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]
Gas Turbines for Power Plants 3. Compressor 86 / 136
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
Gas Turbines for Power Plants 3. Compressor 87 / 136
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
Gas Turbines for Power Plants 3. Compressor 88 / 136
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
Gas Turbines for Power Plants 3. Compressor 89 / 136
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
Gas Turbines for Power Plants 3. Compressor 90 / 136
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.
Gas Turbines for Power Plants 3. Compressor 91 / 136
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
Compressor Stall [2/9]
Stall
(d) Flow separation
Gas Turbines for Power Plants 3. Compressor 92 / 136
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
Compressor Stall [3/9]
Flow separation
Gas Turbines for Power Plants 3. Compressor 93 / 136
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
Compressor Stall [4/9]
Gas Turbines for Power Plants 3. Compressor 94 / 136
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]
Compressor Stall [5/9]
Gas Turbines for Power Plants 3. Compressor 95 / 136
Rotating Stall [2/3]
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.
Compressor Stall [6/9]
[ Full span stall ] [ Part span stall ]
Gas Turbines for Power Plants 3. Compressor 96 / 136
Rotating Stall [3/3]
Compressor Stall [7/9]
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 ]
Gas Turbines for Power Plants 3. Compressor 97 / 136
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]
Compressor Stall [8/9]
Gas Turbines for Power Plants 3. Compressor 98 / 136
Flutter regions on the compressor map of a
transonic compressor
Stall Flutter [2/2]
Compressor Stall [9/9]
Gas Turbines for Power Plants 3. Compressor 99 / 136
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]
Gas Turbines for Power Plants 3. Compressor 100 / 136
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]
Gas Turbines for Power Plants 3. Compressor 101 / 136
Tear out of blades after high vibration trip (7FA)
Surge [3/3]
Gas Turbines for Power Plants 3. Compressor 102 / 136
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
Gas Turbines for Power Plants 3. Compressor 103 / 136
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 /,
Gas Turbines for Power Plants 3. Compressor 104 / 136
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]
Gas Turbines for Power Plants 3. Compressor 105 / 136
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
Compressor Map [2/11]
Gas Turbines for Power Plants 3. Compressor 106 / 136
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
Compressor Map [3/11]
Gas Turbines for Power Plants 3. Compressor 107 / 136
Sample 4
Compressor Map [4/11]
Surge Margin
Working Line
Pre
ssure
Ratio
cm
c
cN
Surge Line
Gas Turbines for Power Plants 3. Compressor 109 / 136
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.
Compressor Map [6/11]
General Notes
Gas Turbines for Power Plants 3. Compressor 110 / 136
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)
Compressor Map [7/11]
Gas Turbines for Power Plants 3. Compressor 111 / 136
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
Compressor Map [8/11]
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.
Gas Turbines for Power Plants 3. Compressor 112 / 136
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
Compressor Map [9/11]
Gas Turbines for Power Plants 3. Compressor 113 / 136
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).
Compressor Map [10/11]
Gas Turbines for Power Plants 3. Compressor 114 / 136
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.
Compressor Map [11/11]
Gas Turbines for Power Plants 3. Compressor 115 / 136
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
Gas Turbines for Power Plants 3. Compressor 116 / 136
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.
Gas Turbines for Power Plants 3. Compressor 117 / 136
c1
c3
= const.
Stator
Rotor
u
1 2 3
c2
w3
w1
w2
[ Fixed Stator ] [ Variable Stator ]
2. Variable Stator [2/3]
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
Gas Turbines for Power Plants 3. Compressor 118 / 136
2. Variable Stator [3/3]
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
Gas Turbines for Power Plants 3. Compressor 119 / 136
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]
Gas Turbines for Power Plants 3. Compressor 120 / 136
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]
Gas Turbines for Power Plants 3. Compressor 121 / 136
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]
Gas Turbines for Power Plants 3. Compressor 122 / 136
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
Gas Turbines for Power Plants 3. Compressor 124 / 136
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
Gas Turbines for Power Plants 3. Compressor 125 / 136
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.
Gas Turbines for Power Plants 3. Compressor 126 / 136
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
Gas Turbines for Power Plants 3. Compressor 127 / 136
Combination Compressor
A compressor has an axial-flow compressor combined with a centrifugal compressor as the last stage.
Gas Turbines for Power Plants 3. Compressor 128 / 136
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
Gas Turbines for Power Plants 3. Compressor 129 / 136
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]
Gas Turbines for Power Plants 3. Compressor 130 / 136
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]
Gas Turbines for Power Plants 3. Compressor 131 / 136
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
Gas Turbines for Power Plants 3. Compressor 132 / 136
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
Gas Turbines for Power Plants 3. Compressor 133 / 136
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
Gas Turbines for Power Plants 3. Compressor 134 / 136
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
Gas Turbines for Power Plants 3. Compressor 135 / 136
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
Gas Turbines for Power Plants 3. Compressor 136 / 136
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