2. Compressor - Engsoft Power Lab - Engineering, … · · 2015-05-18The basic requirements of...
Transcript of 2. Compressor - Engsoft Power Lab - Engineering, … · · 2015-05-18The basic requirements of...
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2. Compressor
Axis of
rotation
Inflow
Outflow Shroud
Hub
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Compressor Thermodynamics and Fluid Dynamics 18 2
Basic Principles of an Axial Compressor 2 1
Contents
Degree of Reaction 89 6
Compressor Losses 95 7
Compressor Blade Shapes 77 5
Basic Sizing Parameters 68 4
2-D Design of Compressor Blades 106 8
Stall and Surge 113 9
Centrifugal Compressor 147 10
Dimensionless Numbers 55 3
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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
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Basic Requirements of Compressor
The basic function of a compressor is to utilize shaft work to increase the stagnation pressure of the air.
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 55% 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.
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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 to 60 percent of the total work produced in the turbine is consumed by
axial compressor. Consequently, maintaining a high compressor efficiency is very important.
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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 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 1.05:1 to 1.3:1, 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
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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
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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 gas turbine 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. (18 stages at 1.19 per stage gives a factor of
22.9 1.1918).
Pressure Ratio [1/3]
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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 [2/3]
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Flow
Pre
ssu
re H
ea
d
Positiv
e d
ispla
cem
ent
com
pre
ssor
Centrifugal compressor
Axial compressor
• Positive displacement compressors such as gear type units are used for lubrication systems in gas
turbines.
• They give low flow and high pressure (head).
• Centrifugal compressors are used for medium flow and medium head.
• Axial compressors are well suited for high flow rates.
Pressure Ratio [3/3]
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7EA, GE
Configuration of a Typical Axial Compressor
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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 equipped
with up to three rows of VIGVs
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 [1/2]
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When designing a compressor with the reaction blades, the first stage
must be preceded by 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.
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.
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 [2/2]
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A stage consists of a rotor/stator combination.
Rotor and Stator [1/4]
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Compressor rotor stacking Stator buildup Rotor buildup
Rotor and Stator [2/4]
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Axial-compressors, which are composed of successive
diffusing blade rows, employ a number of stages to give
the cycle pressure ratio.
The permissible stage work of the axial compressors is
less than that of axial turbines, and the stage outlet Mach
number is much lower. Therefore, leaving loss of the
axial compressor is lower than that of axial turbines.
Rotors add energy to the working fluid and hence causes
an increase in pressure and temperature of it.
Stators are fixed and do not rotate.
The job of the stators is to increase static pressure by
decreasing the fluid and keep the flow from spiraling
around the axis by bringing the flow back parallel to the
axis.
This process is then repeated as many times as
necessary to get the required pressure ratio.
Cantilever style stator vanes are used in compressors
where stage loading is relatively light.
Rotor and Stator [3/4]
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Rotor and Stator [4/4]
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Compressor Thermodynamics and Fluid Dynamics 2
Basic Principles of an Axial Compressor 1
Stall and Surge 9
Centrifugal Compressor 10
Basic Sizing Parameters 4
Dimensionless Numbers 3
Degree of Reaction 6
Compressor Losses 7
Compressor Blade Shapes 5
2-D Design of Compressor Blades 8
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The compressor is composed of several rows of airfoil cascades.
The blades of an axial compressor are close to one another, which seriously alters the flow around each
blade.
Therefore, several blades are placed in a row to simulate a compressor rotor or stator.
Such a row is called a cascade. That is, several blades placed in a row is called as cascade.
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.
Rotor blades Stator blades
High
pressure
Low
pressure
IGVs
Dire
ctio
n o
f R
ota
tio
n
H
H
H
H
L
L
L
L
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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
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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
(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]
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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, • The angle formed by air inlet angle and air exit angle ( = 1 2)
Compressor Cascade Nomenclature [3/3]
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z
r
Sta
tor
Ro
tor
Flow direction
CL
1 2 3
Velocity Triangles in Axial Flow Compressors [1/4]
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Velocity Triangles in Axial Flow Compressors [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 turbine.
The absolute velocity ( ) is the fluid velocity relative
to some stationary point and is usually parallel to the
nozzle (stationary blade).
When considering the flow across a rotating element
like a bucket, the relative velocity ( ) is important and
is usually parallel to the rotating element.
Vectorially, the relative velocity is defined as:
where is the tangential velocity
of the bucket.
ucw
u
w
c
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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 in Axial Flow Compressors [3/4]
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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 in Axial Flow Compressors [4/4]
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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
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.
Variation of Velocity and Pressure
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Blade
direction Turbine
blades
Compressor
blades
c1 w1
u
w2 c2
u
u c2 w2
u
w3 c3 Axial
direction
Compressor Turbine
Flow path Diverge (diffuser) Converge (nozzle)
Absolute velocity of flow Increase through a rotor
Decrease through a stator
Increase through a nozzle
Decrease through a bucket
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
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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
op
1
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 [1/2]
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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.
The stator also guides the flow smoothly into the next rotor.
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 [2/2]
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
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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 [1/5]
dpdhTds pp c
T
s
T
T
(h)
s
ds
dT
p = const.
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Polytropic efficiency is another concept of efficiency often used in compressor evaluation. 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 [2/5]
po
T
(h)
s
To
To+dTo
po+dpo
Tos+dTos
dhs
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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 [3/5]
Polytropic Efficiency [2/2]
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1 11
85
80
75
70
65
60
Pressure ratio
Isentr
opic
effic
iency,
%
55
50
95
90
6 21 16 31 26 41 36
90% polytropic efficiency
85% polytropic efficiency
80% polytropic efficiency
75% polytropic efficiency
70% polytropic efficiency
Compressor Efficiency [4/5]
Compressor Isentropic and Polytropic Efficiency Relationship
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Compressor efficiency is very important in the overall performance of the gas turbine, as it consumes 47-
60% 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
wo
rk
Tu
rbin
e w
ork
Com
pre
ssor
wo
rk
Net
work
Steam turbine Low efficient gas
turbine
High efficient gas
turbine
Compressor Efficiency [5/5]
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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 [1/3]
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
Combined Cycle Power Plants 2. Compressor 37 / 153
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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 [2/3]
Euler equation
Combined Cycle Power Plants 2. Compressor 38 / 153
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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 [3/3]
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
Combined Cycle Power Plants 2. Compressor 39 / 153
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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
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Temperature Rise per Stage [1/2]
Temperature increase per stage can be obtained using equation (5).
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
Combined Cycle Power Plants 2. Compressor 41 / 153
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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]
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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
Combined Cycle Power Plants 2. Compressor 43 / 153
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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.
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
Combined Cycle Power Plants 2. Compressor 44 / 153
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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
Combined Cycle Power Plants 2. Compressor 45 / 153
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[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
Combined Cycle Power Plants 2. Compressor 46 / 153
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Design Deflection [1/2]
Figure shows typical results for wind tunnel test of
cascade.
The losses increase with both positive and negative
incidence, but there is a wide range of incidence
having quite low losses.
The deflection increases with incidence up to the
stalling incidence s, where the maximum deflection is
obtained.
At this point the loss has about twice the minimum
value. This correspondence is not exact, but since the
losses increase rapidly beyond this, a stage is
designed for a nominal deflection of *=0.8s, which
also corresponds to an incidence at which the loss is
near its minimum.
As shown in the figure, at this condition the incidence
is slightly negative. But for another cascade it may be
zero, or slightly positive.
-20 -10 -5 10 -15
0.075
0.050
0.025
0
*
s
Incidence i, degrees
Lo
ss c
oe
ffic
ien
t
0 5
40
30
20
10
Me
an
de
flection
, d
egre
es
min
2min
The loss coefficients have been defined as
The conclusion from a large number of experimental tests is the the nominal deflection is mainly a function
of the air outlet angle and solidity of the cascade.
2
1
2,1,
2
1
22
5.05.0 w
pp
w
hhw
oosR
2
2
3,2.
2
2
33
5.05.0 c
pp
c
hhw
oosS
[ Mean deflection and mean total-head pressure loss
for cascade of fixed geometrical form ]
Combined Cycle Power Plants 2. Compressor 47 / 153
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Design Deflection [2/2]
From a large number of experimental tests a universal correlation, shown in figure, that relates the
deflection to the air exit angle with solidity as a parameter was developed by Howell (1945).
It is clear that the nominal deflection increases with solidity. This is because the flow follows the blade better
as the solidity increases.
A curve fitting for the nominal deflection is
50
40
30
20
10
0 -10
2
Air outlet angle 2 (or 3), degrees
No
min
al d
eflection
*, d
egre
es
0 10 20 30 40 50 60 70
1
= 2/3
1.64.367.810
0.103.546.12100
3.42.1768.3 222
2
22*
[ Nominal deflection as a function of air outlet angle
and solidity ]
An alternative to above equation is the tangent
difference formula, which for the rotor is
and for the stator is
R
/5.11
55.1tantan 12
S
/5.11
55.1tantan 32
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After completion of the stage design, the stage performance has to
be checked, particularly in regard to the efficiency which for a given
work out will completely govern the final pressure ratio.
This efficiency is dependent on the total drag coefficient for each of
the blade rows comprising the stage, and in order to evaluate these
quantities it will be necessary to revert to the loss measurements in
cascade tests.
The static pressure rise across the blades is given by
(1)
where, is stagnation pressure loss.
The axial force per unit length of each blade is sp.
The force acting on the cascade in tangential direction is
(2)
12 ppp
2
11,
2
22,2
1
2
1cpcpp oo
2
2
1
222
2
2
1 tantan2
1
2
1 zvccp
)tan(tan)tantan( 21
2
21 zzz vsvvmF
Cascade Aerodynamics [1/6]
c1
c2
2
1
m
s
[ Forces acting on a cascade ]
m Fz
C cm
L D
F
sp D
sp
2,1, oo pp
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The coefficient CL (lift coefficient) and CDp (profile drag coefficient) are based on an arbitrary defined vector
mean velocity cm where
where m is given by
If drag and lift forces along and perpendicular to the direction of the vector mean velocity, the drag gives
(3)
Put the equation (1) & (2) into equation (3) gives
(4)
Since
The first two terms in the expression for CDp are equal and the equation reduces to
(5)
Also, lift force can be expressed by
(6)
mzm vc sec 21 tantan2
1tan m
mmmDp psFCcCD cossin2
1 2
mmzmzmDp svsvsCcC coscostantan2
1sintantan
2
12
2
1
22
21
22
m tantantan2tantantantantantan 2121212
2
1
2
2
cos2
m
mDp
cC
sC
2
3cos2
z
mDp
vC
sC
1
2
3
2
1 cos
cos2
m
DpcC
sC
mmmL psFCcCL sincos2
1 2
Cascade Aerodynamics [2/6]
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Therefore,
This finally gives
(7)
The value of CDp and CL can be calculated with the cascade experimental data using equation (5) and (7). Since
1 is known from the geometry of the blade row, the following data can be found for any incidence angle I,
mmzmzmL svsvsCcC sinsintantan2
1costantan
2
12
2
1
22
21
22
mDpmL CCsC tancostantan)/(2 21
i 11 *
12 21
1 tantan5.0tan
m
Then, by using values of /0.5c12 read from the curve and the known value of s/C for the cascade, CDp and
CL can be calculated.
-20 -10 -5 10 -15
0.075
0.050
0.025
0
*
s
Incidence i, degrees
Lo
ss c
oe
ffic
ien
t
0 5
40
30
20
10
Me
an
de
flection
, d
egre
es
min
2min
[ Mean deflection and mean total-head pressure loss
for cascade of fixed geometrical form ] [ CDp and CL for cascade of fixed geometrical form ]
-20 -10 -5 10 -15
0.075
0.050
0.025
0
CDp
Incidence i, degrees
Dra
g c
oe
ffic
ient C
Dp
0 5
1.5
1.0
0.5
0
Lift co
eff
icie
nt C
L
CL
Cascade Aerodynamics [3/6]
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In addition to profile drag coefficient, three additional factors must be taken into account. These are caused by
the walls of the compressor annulus, the secondary flow, and tip clearance.
The drag coefficient for annulus loss is given by
where h is blade height, and the annulus loss becomes a small fraction of the total losses as the blade height
increases.
)/(020.0 hsCDA
2018.0 LDS CC
5.129.0 Lt
Dt Ch
hC
DtDSDADpD CCCCC
For typical axial compressor designs, the following empirical formula for the
additional drag coefficient arising from secondary losses has been derived,
The tip loss arises from a tip vortex and clearance. The empirical relation is
given by
where ht is blade height,
The total loss coefficient is then obtained by summing these
Cascade Aerodynamics [4/6]
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The theoretical pressure rise through the blade row is
Therefore,
The efficiency of the blade row (b) is defined as the ratio of the actual pressure rise to the theoretical
pressure rise.
If p1 and p2 are the static pressures at inlet and outlet of the rotor,
where p2 denotes the ideal pressure at outlet with no losses. If the stage efficiency (s) is defined as the ratio
of the isentropic static temperature rise to the actual static temperature rise, the pressure ratio gives
2
2
1
22 secsec5.0 zth vp
1
2
2
2
1
22 sec
sec1
sec5.0
z
th
v
p
2
2
1
2
2
1 cos
cos1
5.0
c
pth
th
bp
1
12
12
' pp
ppb
Cascade Aerodynamics [5/6]
1
11
2
21
T
T
p
p ss
Combined Cycle Power Plants 2. Compressor 53 / 153
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because Ts/2 will be the temperature rise in the rotor of 50% reaction.
Also
Therefore,
After expanding and neglecting second order terms this reduces to
But, T1 >> Ts,
If the degree of reaction is not 50%, then the stage efficiency becomes
12
112
11'
1
)1(
1
)1(
11
2
1
2
T
T
T
T
p
p
p
p sssb
s
ssb
T
T
1
41
11
1
sb
statorbrotorbs ,, 1
1
11
2
21
'
T
T
p
p s
Cascade Aerodynamics [6/6]
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Deviation Angle
Before the blade angle can be set, the deviation angle at the exit of the blade row should be determined.
Deviation angle, which is regarded as incomplete turning of the flow, is caused by the inviscid flow effect
and not related to viscosity.
In order to obtain the desired turning, therefore, blades need to be curved more than in the absence of
deviation angle.
It is recommended that deviation can be calculated using following equation at the design conditions.
where is camber angle, a is the maximum thickness of the blade, and *2 is given in degrees.
m*
50092.0
*
2
2
2
C
am
1
2
1
2 c2
c1
i
C
Point of max.
camber
a
s
Combined Cycle Power Plants 2. Compressor 55 / 153
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Compressor Thermodynamics and Fluid Dynamics 2
Basic Principles of an Axial Compressor 1
Stall and Surge 9
Centrifugal Compressor 10
Basic Sizing Parameters 4
Dimensionless Numbers 3
Degree of Reaction 6
Compressor Losses 7
Compressor Blade Shapes 5
2-D Design of Compressor Blades 8
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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.
Combined Cycle Power Plants 2. Compressor 57 / 153
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Degree of Reaction
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
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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 [1/2]
Combined Cycle Power Plants 2. Compressor 59 / 153
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22
1,2,
2
1,2,
2 u
Tc
u
TTc
u
hh
u
w opoopoor
mm DLF sincos
CwCL mL
2
2
1 CwCD mD
2
2
1
m
L
DmLm
C
CCCwF tan1cos
2
1 2
m
L
DmLz
C
CCCvF tan1sec
2
1 2
m
uFhw or
m
L
DmL
z
C
CC
s
C
u
v tan1sec
2
w1
w2 2
1
m
L
D
s
m
F
F
Fz
F
C
wm
21 tantan2
1tan m
[ Forces acting on a cascade ]
Loading Coefficient [1/2]
Combined Cycle Power Plants 2. Compressor 60 / 153
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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
1212 tantantantan
Combined Cycle Power Plants 2. Compressor 61 / 153
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[ Smith chart ]
Smith Chart
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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
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Pressure Rise Coefficient
Another dimensionless parameter is the pressure rise coefficient.
If axial velocity is assumed constant and the working fluid is assumed to be incompressible, then the
pressure rise coefficient can also be expressed as a function of the de Haller number. This is done by
applying Bernoulli’s principle.
where dH = de Haller number
11,
12
pp
ppC
o
p
2
22
2
112
1
2
1VpVp
2
111,2
1Vppo
2
2
1
2 11 dHV
VCp
Combined Cycle Power Plants 2. Compressor 64 / 153
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1
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
1
= 1.5
0.75
= 1.5
0.75
Pressure
surface
Suction
surface
0.9 1.0
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2
-1.4
11,
1
pp
ppC
o
p
Under ideal conditions at low Mach number, the
spike in the pressure coefficient of the pressure
surface should reach unity at stagnation point
located near the leading edge.
From there the pressure falls as the flow
accelerates to a location of maximum blade
thickness followed by diffusion toward the trailing
edge.
Near the trailing edge the flow may accelerate
slightly due to its orientation and camber.
On the suction surface of the blade, the negative
spike is caused by stagnation point, which is not
formed at the leading edge, but just downstream
along pressure surface.
Pressure then increases sharply from the suction
spike all the way to the trailing edge as the flow
diffuses.
This diffusion must be kept within acceptable limits.
[ Pressure coefficient for a cascade with different solidities ]
Diffusion Factor [1/4]
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Since the blade force is obtained by integrating the pressure acting on the blade surface, the area
described by the curves represents the blade force normal to the chord.
As the solidity increases, this force is reduced, but now with reduced pitch, more blade can be fitted to the
rotor wheel to carry the load.
Increased solidity lifts the value of the minimum pressure occurred on the suction surface, with the result
that the pressure gradient decreases. Therefore, the flow can be turned by a greater amount without danger
of flow separation.
However, compressor efficiency decreases as the solidity increases. This is because the profile loss
increases as the solidity increases.
In axial compressors, relative flow diffusion occurs in rotor rows and absolute flow diffusion occurs in stator
rows. The diffusion ratios, also call as de Haller number, which control the boundary layer behavior are
w2/w1 and c3/c2 for the rotor and stator, respectively.
The boundary layer growth in the region of adverse pressure gradient controls the static pressure rise. The
boundary layer thickness at the trailing edge is controlled by diffusion factor, defined as
where, wmax is the velocity at the location of minimum pressure.
This definition would be useful, if the profile shape were known and wmax could be easily calculated.
max
2max
w
wwDF
Diffusion Factor [2/4]
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It can be done quickly with a computer code for inviscid flows. But before this became a routine task, an
alternative was sought by Lieblein (1965).
1
2,1,
1
2
1
2
2,1,
1
1
2max
21
w
ww
w
w
w
www
fw
w
wwDF
The equation is valid for both rotor flows (compressible and
two-dimensional) and stator flows. For stator, relative
velocities are replaced by corresponding absolute
velocities.
The first part is similar to the local diffusion factor, and the
second part accounts for the amount of turning and higher
solidity of the blade row.
Since both reduced turning and higher solidity contribute to
lighter loading on blades, diffusion is expected to diminish
by both effects.
The Lieblein diffusion factor for the rotor and stator can be
expressed as
121
2
12 costantan2
1
cos
coscos
R
RDF 232
3
23 costantan2
1
cos
coscos
S
SDF
Diffusion Factor [3/4]
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The diffusion factor should be less than 0.4 for the rotor tip and less than 0.6 for the rotor hub and the stator.
The efficiency is less in the rear stages due to distortions of the radial velocity distributions in the blade
rows.
[ Dependence of momentum thickness () of the
boundary layer on diffusion factor ]
Experimental investigations show that even
though efficiency is less in the rear stages, as
long as the diffusion loading limits are not
exceeded, the stage efficiencies remain relatively
high.
The boundary layer thicken faster in a flow with
an adverse pressure gradient than when there is
none. A relationship may be developed between
diffusion and the boundary layer thickness. The
figure is a plot of the diffusion factor as a function
of the ratio of the momentum thickness of the
boundary layer to the chord length / C.
The curve shown in the figure begins its upward
bend at the momentum thickness-to-chord ratio of
about 0.007, and this corresponds to DF = 0.45.
Thus below these give good designs.
For larger DF values the stagnation pressure
losses grow appreciably.
[ Velocity distribution in a 12-stage compressor ]
max,/ zz vv
Diffusion Factor [4/4]
/C
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Compressor Thermodynamics and Fluid Dynamics 2
Basic Principles of an Axial Compressor 1
Stall and Surge 9
Centrifugal Compressor 10
Compressor Thermodynamics and Fluid Dynamics 2
Basic Principles of an Axial Compressor 1
Stall and Surge 9
Centrifugal Compressor 10
Basic Sizing Parameters 4
Dimensionless Numbers 3
Degree of Reaction 6
Compressor Losses 7
Compressor Blade Shapes 5
2-D Design of Compressor Blades 8
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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
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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
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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]
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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]
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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]
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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]
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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]
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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.
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Compressor Thermodynamics and Fluid Dynamics 2
Basic Principles of an Axial Compressor 1
Stall and Surge 9
Centrifugal Compressor 10
Basic Sizing Parameters 4
Dimensionless Numbers 3
Degree of Reaction 6
Compressor Losses 7
Compressor Blade Shapes 5
2-D Design of Compressor Blades 8
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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]
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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]
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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
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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
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Multiple circular arc (MCA) profile developed by NASA in the 1960s.
In NASA’s MAC 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]
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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]
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(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.
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It is desirable to achieve high pressure rise across each stage to reduce the number of stages need for the
total pressure rise across the entire compressor. This can be achieved through high speed blade, high inlet
Mach number, and advanced blade design.
Higher relative velocity at the inlet results in higher temperature and pressure rise in a compressor.
When the relative Mach number becomes greater than unity, the qualitative and quantitative behavior of the
flow changes substantially.
Shock waves are formed at the leading edge or inside the passage, resulting in higher static and
temperature rise as well as higher stagnation pressure and viscous losses.
In present-day compressors, the axial and total Mach number of absolute flow at inlet is always subsonic.
Some compressors have higher blade speeds and higher radii, thus the relative Mach numbers(w = c-u)
may reach supersonic near the outer sections of the rotor, while the relative flow near the inner radii remains
subsonic.
A transonic compressor is one where the relative flow remains subsonic (MR 1) at inner radii and
supersonic (MR 1) at outer radii, with transonic region in the middle. This is especially true for high aspect
ratio or low hub/tip ratio compressors.
In some low-aspect-ratio and compact compressors, there may be cases where the entire flow, hub to tip,
has supersonic relative flow. Such as compressor is known as a supersonic compressor.
There are major differences among a subsonic, transonic, and supersonic compressor.
Transonic and Supersonic Compressor [1/4]
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Transonic and Supersonic Compressor [2/4]
Transonic Compressor Blades
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The leading edge and the blade shape differ considerably when the entry flow is supersonic. To avoid
detached shocks, sharp-nosed leading edges are used with supersonic entry. The flow is expanded
smoothly over the suction surface with expansion waves; and a shock wave occurs within the passage,
originating on the pressure side.
There is a jump in static pressure and static temperature across a shock wave, and thus the relative flow
distribution takes place suddenly across a shock wave. This is beneficial in increasing the pressure rise as
compared to purely subsonic flow where the diffusion is carried out across a finite length cascade. The
disadvantage of such a diffusion is that, associated with localized large pressure rise, there are boundary
layer shock interaction effects which results in most cases with flow separation. This feature, combined with
entropy rise across a shock wave, results in higher pressure losses and lower efficiency.
Mixed flow from hub to tip results in large radial pressure gradients (sometimes discontinuous) in the radial
directions. This results in three-dimensional flow in a passage. The validity of two-dimensional analyses for
turbomachinery flows with shocks is somewhat questionable.
The shocks respond to changes in downstream conditions. This brings about a drastic change in the flow
behavior with variation in downstream conditions. Both the location and the strength of the shock are altered.
The upstream should be shock-free or should consist of alternate weak shocks and expansion waves.
Otherwise, there would be large turning upstream of the flow, a condition which is unacceptable. There is
only one incidence (at a given operating condition) when the flow at the entry is smoothly guided through the
blade suction surface, and there would be no upstream shocks or expansion waves. Such a condition is
called a unique incidence condition. Operating the compressor below or above this condition results in large
losses. Hence, the characteristic () is very steep for a supersonic flow. This is one of the most critical
limitations of a supersonic compressor.
Transonic and Supersonic Compressor [3/4]
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Associated with the shock wave is blade choking, which controls the mass flow that can be passed through
a compressor.
The designer has to incorporate the shock losses (both direct and indirect effects) in the process.
Higher static pressure ratio as well as pressure jumps cause rapid area changes and blade curvature. This
has to be incorporated in the design procedure.
Early transonic and supersonic compressor designs were failures. The efficiencies were poor and the
reliability was not good. It was initially believed that the low efficiencies obtained were due to the shock
pattern alone. It was recognized that the losses were more a result of flow disturbances caused by shocks.
Major improvements have been made in blade design, shock optimization, and hub-to-tip design. The most
successful designs are the ones custom designed, based on controlled diffusion airfoil and shock-free airfoil
design concepts. The efficiency of a supersonic compressor (single stage) which was as low as 40% during
1940s has been increased to nearly 90%. The highest relative Mach number has increased up to 2.4 in
experimental compressor stages. This has been achieved through a careful design of blade, choice of
aspect ratio, radial variation of blade shape, and other blade and flow parameters.
The present trend is toward low aspect ratio and higher Mach number blade, so as to achieve supersonic
flow at most radial locations.
The Mach numbers in stators have not increased as rapidly as rotor Mach numbers.
Transonic and Supersonic Compressor [4/4]
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Compressor Thermodynamics and Fluid Dynamics 2
Basic Principles of an Axial Compressor 1
Stall and Surge 9
Centrifugal Compressor 10
Basic Sizing Parameters 4
Dimensionless Numbers 3
Degree of Reaction 6
Compressor Losses 7
Compressor Blade Shapes 5
2-D Design of Compressor Blades 8
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%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 [2/6]
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
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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
Degree of Reaction [3/6]
c1
w1
c,1
1 1
vz,1
u1
w2 c2
c,2
2 2
vz,2
u2
c3
Shaft CL
IGV
rotor
stator
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Symmetrical stage has 50% reaction, and it is widely used.
With a high tangential velocity component maintained by each succeeding stationary row, the magnitude of
w1 is decreased.
Thus, higher blade speeds and axial-velocity components are possible without exceeding the limiting value
of 0.70 to 0.75 for inlet Mach number.
Higher blade speeds result in compressor of smaller diameter and less weight.
Another advantage is the equality of static pressure rises in the rotors and stators, resulting in a maximum
static pressure rise for the stage.
Therefore, a given pressure ratio can be achieved with a minimum number of stages.
The big disadvantage is the high exit loss resulting from the high axial-velocity component.
However, the advantages are important factors in aircraft applications, thus the symmetrical compressor
has been employed widely in aviation.
The symmetrical compressors have also being used in stationary applications because number of
compressor stages and mass flow rates are also important in them.
When designing a compressor with reaction blades, the first stage must be preceded by inlet guide vanes to
provide pre-swirl and the correct velocity entrance angle to the first stage rotor.
1) Symmetrical Stage
Degree of Reaction [4/6]
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Asymmetrical stage has reaction other than 50%.
The axial-inflow stage is a special case of an asymmetrical stage.
The rotor gives swirl to the velocity of the leaving flow, which is removed by the following stator.
The majority of stage pressure rise occurs in the rotor with the degree of reaction varying from 60% to 90%.
The stage is designed for constant energy transfer and axial velocity at all radii so that the vortex flow
condition is maintained in the space between blade rows.
The advantage of a stage with greater than 50% reaction is the low exit loss resulting from lower axial
velocity and blade speeds. Therefore, the efficiency of this type is higher than symmetrical stage because of
reduced exit loss.
The disadvantage resulting from a low static pressure rise in the stator is that it requires a greater number
of stages to achieve a given pressure ratio, thus it becomes heavier.
The lower axial velocities and blade speed, necessary to keep within inlet Mach number limitations, results
in large diameter.
In stationary applications where the increased weight and frontal area are not important, this type is used
frequently to take advantage of the higher efficiency.
2) Asymmetrical Stage [1/2]
Degree of Reaction [5/6]
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In the axial-outflow stage, the absolute exit velocity is in an axial direction, and all the static pressure rise
occurs in the rotor.
A static pressure decreases in the stator so that the degree of reaction exceeds 100%.
The advantages of this stage are low axial velocity and blade speed, resulting in the lowest possible exit
loss.
This design produces a heavy machine of many stages and of large diameter.
To keep within the allowable limit of the inlet Mach number, extremely low values must be accepted for the
blade velocity and axial velocity.
Although a reaction of less than 50% is possible, such a design results in high inlet Mach numbers to the
stator row, causing high losses.
The maximum total divergence of the stators should be less than approximately 20 degrees to avoid
excessive turbulence.
Combining the high inlet for the limiting divergence angles produces a long stator, thereby producing a
longer compressor.
2) Asymmetrical Stage [2/2]
Degree of Reaction [6/6]
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Compressor Thermodynamics and Fluid Dynamics 2
Basic Principles of an Axial Compressor 1
Stall and Surge 9
Centrifugal Compressor 10
Basic Sizing Parameters 4
Dimensionless Numbers 3
Degree of Reaction 6
Compressor Losses 7
Compressor Blade Shapes 5
2-D Design of Compressor Blades 8
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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
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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
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층류저층: 난류경계층에서 벽면 가까운 곳의 층으로서 층류와 유사
Boundary Layer
Profile Loss [1/5]
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Boundary Layer
Profile Loss [2/5]
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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 [3/5]
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.
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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 [4/5]
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.
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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 [5/5]
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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
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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
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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 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
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Compressor Thermodynamics and Fluid Dynamics 2
Basic Principles of an Axial Compressor 1
Stall and Surge 9
Centrifugal Compressor 10
Compressor Thermodynamics and Fluid Dynamics 2
Basic Principles of an Axial Compressor 1
Stall and Surge 9
Centrifugal Compressor 10
Basic Sizing Parameters 4
Dimensionless Numbers 3
Degree of Reaction 6
Compressor Losses 7
Compressor Blade Shapes 5
2-D Design of Compressor Blades 8
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Step 1: Choose the stage pressure ratio.
• Stage pressure ratio can be chosen in terms of the number of stages and total pressure ratio of the
compressor.
• Assume other important variables.
- stage efficiency = 90%
- stagnation temperature and pressure of air at compressor inlet = 15C, standard atmospheric press.
- degree of reaction = 50%
Step 2: Determine a suitable value of the stage temperature rise.
• 10~30K for subsonic compressors, but as high as 45K for transonic compressors.
• The value chosen will largely depend on such factors as allowable size and weight of the whole
compressor, the desired rotational speed and, within limits, the designer’s own particular preference.
Step 3: Calculate the air angles at a design diameter – the mean diameter is usually the most convenient.
• In order to calculate the air angles, some variable have to be chosen. Following values are used in
this calculation.
- rotor blade mean diameter = 1.2 m (rm = 0.6 m)
- rotor blade length = 0.2 m (mass flow rate can be used instead of blade length)
- Mach number of compressor inlet air = 0.5
- rotor speed = 3600 rpm
2112 tantantantan
p
z
p
zo
c
uv
c
uvdT
Simple Design Method [1/6]
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Step 4: Calculate the air angles along blade height.
• Assume that the axial velocity and specific work input are constant along radial direction.
• Firstly, use the free vortex design method.
• Free vortex design rnc,1 = rnvz tan1 = constant.
• Secondly, use the constant reaction method to compare with the results obtained from free vortex
design method.
rm
rn
dh
Hub
Tip
Simple Design Method [2/6]
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0.8 0.9 1.0 1.1 1.2
60
50
40
30
20
10
0
-10
1
2
1
2
Radius ratio, rn/rm
Air a
ngle
, deg.
0.80 0.85 0.90 0.95 1.0 1.05 1.10 1.15 1.20
1 29.6 28.1 26.8 25.5 24.4 23.4 22.4 21.5 20.7
1 26.4 30.8 34.7 38.2 41.2 44.0 46.4 48.6 50.6
2 47.6 45.9 44.2 42.7 41.2 39.8 38.5 37.3 36.1
2 -1.8 5.7 12.6 18.9 24.4 29.4 33.7 37.5 40.9
c1
w1
c,1
1
1 vz,1
u1
w2 c2
c,2
2 2 vz,2
u2
c3
Shaft CL
IGV
rotor
stator
Results for Free Vortex Design
Simple Design Method [3/6]
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0.8 0.9 1.0 1.1 1.2
60
50
40
30
20
10
0
-10
1, 2
1, 2
Radius ratio, rn/rm
Air a
ngle
, deg.
0.80 0.85 0.90 0.95 1.0 1.05 1.10 1.15 1.20
1, 2 15.0 17.6 20.0 22.3 24.4 26.4 28.4 30.2 31.9
2, 1 38.5 39.1 39.8 40.5 41.2 42.0 42.7 43.5 44.2
c1
w1
c,1
1
1 vz,1
u1
w2 c2
c,2
2 2 vz,2
u2
c3
Shaft CL
IGV
rotor
stator
Results for Constant Reaction Design
Simple Design Method [4/6]
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Step 5: Determine the blade outline.
• Determine the blade shape having minimum stagnation pressure loss in blade passage.
• Calculate the value of pitch/chord.
• Assume the aspect ratio of the rotor blade. (AR = 3 is used in this calculation)
• Determine the number of blades. (Commonly, a prime number is chosen for rotor blades, and an even
number for stator blades)
• Recalculate the values previously determined with newly determine number of blades.
• Determine the chord along blade height using the determined pitch. The tapered blade shape, which
is desirable for centrifugal force, can be determined using flow angles at this design step.
Simple Design Method [5/6]
50
40
30
20
10
0 -10
2
Air outlet angle 2 (or 3), deg.
Nom
ina
l de
flection
*, d
eg.
0 10 20 30 40 50 60 70
1
= 2/3
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Step 6: Determine the deviation angle.
Step 7: Determine the blade shape.
• Choose the shape of camber line.
• Both circular arc and parabolic arc
can be employed for camber line.
Step 8: Check the stage performance.
• CFD can be employed at this step.
• Wind tunnel test can also be used at
this step. However, this method is
very expensive and time consuming.
• Investigate the efficiencies for both
rotor and stator rows. Typical losses
occurred in a cascade, such as
profile loss, secondary flow loss, and
leakage loss can be included.
• Calculate stage efficiency.
Simple Design Method [6/6]
statorbrotorbs ,, 1
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Compressor Thermodynamics and Fluid Dynamics 2
Basic Principles of an Axial Compressor 1
Degree of Reaction 6
Compressor Blade Shapes 7
Compressor Losses 8
Stall and Surge 9
Centrifugal Compressor 10
2-D Design of Compressor Blades 5
Basic Sizing Parameters 4
Dimensionless Numbers 3
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Compressor Stall [1/10]
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.
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c : absolute velocity of inlet air
w : relative velocity entering rotor
u : rotor peripheral velocity
c
u
incidence
rotor
rotation
[Increased rotational velocity]
w
c
u
incidence
rotor
rotation
u
rotor
rotation
[Normal inlet velocity] [Low inlet velocity]
w
w c
incidence
Compressor Stall [2/10]
Flow separation
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1) Compressor stall occurs most frequently whenever there is unusually high compressor speed and a low air-
inlet velocity (low mass flow rate)
2) Excessive fuel flow caused by abrupt engine acceleration (reduces the velocity vector by increasing
combustor back pressure)
3) Excessively lean fuel mixture caused by abrupt engine deceleration (increases the velocity vector by
reducing combustor back pressure)
4) Contaminated or damaged compressor (increases the velocity vector by reducing compression)
5) Damaged turbine components, causing loss of power to the compressor and low compression (increases
the velocity vector by reducing compression)
6) Engine operation above or below designed RPM
7) Reduced surge margin caused by increased performance of compressor
Cause of Compressor Stall
Compressor Stall [3/10]
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Stall is the breakaway of the flow from the suction side of the blade.
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 [6/10]
Flow separation
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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]
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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.
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Rotating Stall [3/3]
Compressor Stall [7/10]
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 ]
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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 [9/10]
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Flutter regions on the compressor map of a
transonic compressor
Stall Flutter [2/2]
Compressor Stall [10/10]
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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.
Many design features affect the surge line shape, however, there is a general tendency for this line to be
higher at intermediate flows for compressors, such as low solidities, low radius ratios (blade tip radius/root
radius), and a rising hub line.
Surge [1/4]
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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.
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.
Surge [2/4]
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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 [3/4]
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Tear out of blades after high vibration trip (7FA)
Surge [4/4]
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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
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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]
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Choke
point
Constant
speed (rpm)
line
Operating range
Compressor Map [Sample 1]
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.
Combined Cycle Power Plants 2. Compressor 130 / 153
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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 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)
Characteristics of Constant Speed Line
u
rotor
w c
Angle of
attack
rotation
Flow separation
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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.
Compressor Map [Sample 2 & 3]
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Compressor Map [Sample 4]
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Compressor Map [Sample 5 & 6]
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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 [1/6]
General Notes
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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 [2/6]
Combined Cycle Power Plants 2. Compressor 136 / 153
HIoPE
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 [3/6]
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.
Combined Cycle Power Plants 2. Compressor 137 / 153
HIoPE
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.
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 [4/6]
Combined Cycle Power Plants 2. Compressor 138 / 153
HIoPE
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 [5/6]
Combined Cycle Power Plants 2. Compressor 139 / 153
HIoPE
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 [6/6]
Combined Cycle Power Plants 2. Compressor 140 / 153
HIoPE
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
Combined Cycle Power Plants 2. Compressor 141 / 153
HIoPE
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.
Combined Cycle Power Plants 2. Compressor 142 / 153
HIoPE
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
Combined Cycle Power Plants 2. Compressor 143 / 153
HIoPE
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
Combined Cycle Power Plants 2. Compressor 144 / 153
HIoPE
축류압축기 중간단 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]
Combined Cycle Power Plants 2. Compressor 145 / 153
HIoPE
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]
Combined Cycle Power Plants 2. Compressor 146 / 153
HIoPE
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]
Combined Cycle Power Plants 2. Compressor 147 / 153
HIoPE
Compressor Thermodynamics and Fluid Dynamics 2
Basic Principles of an Axial Compressor 1
Degree of Reaction 6
Compressor Blade Shapes 7
Compressor Losses 8
Stall and Surge 9
Centrifugal Compressor 10
2-D Design of Compressor Blades 5
Basic Sizing Parameters 4
Dimensionless Numbers 3
Combined Cycle Power Plants 2. Compressor 148 / 153
HIoPE
Principle
Combined Cycle Power Plants 2. Compressor 149 / 153
HIoPE
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
Combined Cycle Power Plants 2. Compressor 150 / 153
HIoPE
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.
Combined Cycle Power Plants 2. Compressor 151 / 153
HIoPE
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
Combined Cycle Power Plants 2. Compressor 152 / 153
HIoPE
Combination Compressor
Combined Cycle Power Plants 2. Compressor 153 / 153
HIoPE
질의 및 응답
작성자: 이 병 은 (공학박사) 작성일: 2015.02.11 (Ver.5) 연락처: [email protected]
Mobile: 010-3122-2262 저서: 실무 발전설비 열역학/증기터빈 열유체기술