Transcript ME 423 - Middle East Technical University

ME 423
Chapter 4
Centrifugal Compressors
Prof. Dr. O. Cahit ERALP
Centrifugal Compressors
4. CENTRIFUGAL COMPRESSORS
Attention was focused on the simple turbojet unit
during the Second World War.
It was recognized that development time was critical
and much experience had been gained on the design
of small high – speed centrifugal compressors for
supercharging reciprocating engines.
As power requirements grew for aircrafts, it became
clear that the axial flow compressor was more suitable
large engines.
By the late fifties, it became clear that smaller gas
turbines would have to use centrifugal compressors.
Centrifugal Compressors
Advantages;
 Primarily, suitable for handling small volume flows,
 Shorter length than an equivalent axial compressor,
 Better resistance to “Foreign Object Damage” (FOD),
 Less susceptibility to loss of performance by build – up
of deposits on blade surface,
 Ability to operate over a wider range of mass flows at a
particular rotational speed.
Centrifugal Compressors
 A pressure ratio of around 4:1 can readily be obtained
from a single–stage compressor made of aluminium
alloys.
 The advent of titanium alloys, permitting much higher
tip speeds, combined with advances in aerodynamics
now permit pressure ratios of greater than 8:1 to be
achieved in a single–stage.
 When higher pressure ratios are required, the
centrifugal compressor may be used in conjunction
with an axial flow compressor, or as a two–stage
centrifugal.
Centrifugal Compressors
4.1 PRINCIPLE OF OPERATION
The centrifufal compressor consists essentially of a
stationary casing containing a rotating impeller, which
imparts a high velocity to the air and a number of fixed
diverging passages in which the air is decelerated with
the consequent rise in static pressure. The part of the
compressor containing the diverging passages is
known as the Diffuser.
A increase ; V decrease ⇨ P increase
Centrifugal Compressors
4.1 PRINCIPLE OF OPERATION
Width of Diffuser
Channel
Vaneless
Space
Impeller
Eye
Diffuser
Throat
90° Bend
taking air to
combustion
chambers
Mean
Radius of
Diffuser
Throat
Centrifugal Compressors
4.1 PRINCIPLE OF OPERATION
 Air is sucked into the impeller eye and whirled
around at a high speed by the values of the
impeller disc.
 The static pressure of the air increases from the
eye to the tip because of the centrifugal effects.
 The remainder of the static pressure rise is
obtained in the diffuser, where high velocity air
leaving the impeller tip is reduced.
Centrifugal Compressors
4.1 PRINCIPLE OF OPERATION
 The normal practice is to design the
compressor so that about half the pressure rise
occurs in the impeller and half in the diffuser.
 Shrouds have been used on some
superchargers but not in GT practice.
 It should be noted that straight radial vanes are
normally used because the impellers are very
highly stressed.
Centrifugal Compressors
4.2 WORK DONE & PRESSURE RISE
 Since no work is done on the air in the diffuser, the
energy absorbed by the compressor will be determined
by the conditions of air at the inlet and exit of the
impeller.
 In the first instance it will be assumed that the air enters
the impeller eye in the axial direction so that the initial
angular momentum of the air is zero.
Centrifugal Compressors
4.2 WORK DONE & PRESSURE RISE
Ideal conditions at impeller tip
V2
Vr2
VΘ2 =U
V2
Vr2
ω (rad /s)
Eye Tip
r2
Eye Root
Velocity relative to
the impeller
VΘ2 < U
r1
Centrifugal Compressors
4.2 WORK DONE & PRESSURE RISE
 The axial portion of the vanes must be curved so that
the air can pass smoothly into the eye.
 The angle which the leading edge of a vane makes with
the tangential direction β1 will be given by the relative
velocity of the air at inlet w1.
Centrifugal Compressors
4.2 WORK DONE & PRESSURE RISE
V2 : Absolute velocity with which the air leaves
the impeller tip.
Vθ2 : Tangential or whirl component
Vr2 : Radial velocity component
Under ideal conditions Vθ2 = U
Centrifugal Compressors
4.2 WORK DONE & PRESSURE RISE
 Due its inertia, the air trapped between the
impeller vanes is reluctant to move around with
the impeller, and we have already noted that
this results in a higher static pressure on the
leading face of a vane than the trailing face.
 It also prevents the air from acquiring a whirl
velocity equal to the impeller speed. This effect
is known as slip.
Centrifugal Compressors
4.2 WORK DONE & PRESSURE RISE
 Thus, slip is, how far the whirl velocity at the impeller tip
falls short of the tip speed.
 This depends largely upon the number of vanes on the
impeller.
 Greater the number of vanes, the smaller the slip.
Vθ2 ⇒ U as # of vanes (n) increase



Slip Factor ;
V 2

U
an emprical relation;
0.63
  1
n
Centrifugal Compressors
4.2 WORK DONE & PRESSURE RISE
 For unit mass flow of air, the theoretical torque which is
applied to the impeller :
(theoretical torque/ ṁ) = Vθ2r2
 Thus the work done on the air :
(Wdone)theor = Vθ2r2Ω = Vθ2U = σU2
 Due to friction between the casing and the air carried
around by the vanes, and other losses which have a
braking effect such as disc friction or "windage“ ;
the applied torque and therefore the actual work input is
greater than this theoretical value.
Centrifugal Compressors
4.2 WORK DONE & PRESSURE RISE
 A power input factor "ψ" can be introduced to take
account of this, so that the actual work done on the air
becomes
Work done = ψ σ U2
U 2
T03  T01  T02  Ta 
Cp
ψ = 1.03 1.04 (typical value)
 For an isentropic efficiency of ηc;
(T03-T01) = (T’03-T01)/ ηc
Centrifugal Compressors
4.2 WORK DONE & PRESSURE RISE
 Overall pressure ratio;
So:
P03  c U 2 
 1 

P01 
T01C p 
P03
P01
  


  1 
 T03 
 
 T01 
 T03  T01 
 1 

T
01


  


  1 
  


  1 
 ψ and σ are neither independent of one another
nor of ηc
 ψ ⇨ frictional loss ⇨ degraded into thermal energy
⇨ net effect is an increase in outlet T.
ψ decrease ⇨ η increase
Centrifugal Compressors
4.2 WORK DONE & PRESSURE RISE
 σ should be as large as possible. It is limited since the
number of vanes (n) is limited.
 As n increases the solidity of the impeller eye increases,
the effective flow area decreases, which causes an
increase in frictioanal losses.
 So a suitable compromise must be found, and the
present day practice is to use the number of vanes
which will give a slip factor of about 0.9.
 The other factor that influence the pressure ratio are the
tip speed U and the inlet temperature T01.
 T01 depends on ambient conditions.
Centrifugal Compressors
4.2 WORK DONE & PRESSURE RISE
 Centrifugal stresses in a rotating disc are proportional to
the square of rim speed.
 For a single sides impeller of light alloy, U is limited to
about 460 m/s by the maximum allowable centrifugal
stresses. Such a speed yields a pressure ratio of 4:1.
 Higher compression ratios mean more expensive
materials such as titanium alloys.
Centrifugal Compressors
4.3. THE DIFFUSER
 The problem of designing an efficient combustion
system is eased, if the velocity of the air entering
the combustion chamber is low.
 It is therefore necessary to design the diffuser so
that only a small part of the stagnation
temperature at the compressor outlet corresponds
to kinetic energy.
 It is much more difficult to arrange for an efficient
deceleration of flow than an efficient acceleration.
Centrifugal Compressors
4.3. THE DIFFUSER
 There is a natural tendency in a diffusing process, for air to
breakaway from the walls of the diverging passage, reverse
its direction and flow back in the direction of pressure
gradient.
 If the divergence is too rapid, this may result in the
formation of eddies with consequent transfer of some KE
into internal energy and a reduction in useful pressure rise.
 Experiments have shown that the maximum permissible
included angle of divergence of a rectangular channel with
one pair of sides diverging is about 11o. At angles greater
than this, the losses increase sharply.
Centrifugal Compressors
4.3. THE DIFFUSER
 Diffusing flows (declerating)
 Expanding Flows (Accelerating)
 The angle of the diffuser vanes at the leading edge must
be designed to suit the direction of absolute velocity of
the air at the radius of the leading edge, so that the air
will follow smoothly over the vanes.
 As there is always a radial gap between the impeller tip
and the leading edges of the vanes, this direction will
not be that the air leaves the impeller tip.
Centrifugal Compressors
4.3. THE DIFFUSER
 To find the correct inlet angle for the diffuser vanes, the
flow in the vaneless space must be considered.
 After the air leaves the impeller (neglecting friction)
Angular Momentum = V r = constant
"in the vaneless Space“
 V decreases from the impeller tip to diffuser vanes
(as r increase)
 In accordance with the equation of continuity;
Vr decreases with the increase in r.
 The Net result : V decreases with increasing r.
Centrifugal Compressors
4.3. THE DIFFUSER
 When Vr and V have been calculated at the radius of
the leading edges of diffuser vanes, then the direction of
the resultant velocity " V " can be found, hence the inlet
angle of the vanes.
 Once the Number of Vanes and the depth of the
passage have been decided upon, the throat width can
be calculated to suit the mass flow required under given
conditions of T and P.
 The Length of the Diffuser passages will be determined
by the maximum permissible angle of divergence
and the amount of diffusion required.
Centrifugal Compressors
4.3. THE DIFFUSER
 After leaving the diffuser vanes, the air may be passed into
a Volute and hence to a single Combustion Chamber
"CC". For aircraft GT, each (or few) diffuser passage can
be connected to a seperate "CC", or the stream could be
fed into an "annular CC" surrounding the shaft connecting
the Turbine compressor.
Aθ
θ
C.G.
_
r
Centrifugal Compressors
4.4. COMPRESSIBILITY EFFECTS
 We know that a breakdown of flow and excessive
pressure loss can be incurred if the velocity of a
compressible fluid relative to the surface over which it is
moving reaches the speed of sound in the fluid.
 When effort is made to obtain the maximum possible
mass flow from the smallest possible compressor (as in
aircraft practice), the air speeds are very high. It is of the
utmost importance that the Mach numbers at certain
points in the flow do not exceed the value beyond which
the losses increase rapidly due to the formation of shock
waves.
Centrifugal Compressors
4.4. COMPRESSIBILITY EFFECTS
 The “critical Mach number” is usually less than unity
when calculated on the basis of the mean velocity of the
fluid relative to the boundary because the actual relative
velocity near the surface of a curved boundary may be
in access of the mean velocity. As a general rule, unless
tests indicate otherwise, The Mach numbers are
restricted to about 0.8.
 At the intake, the air is deflected through a certain angle
before it passes into the radial channels on the impeller.
There is always a tendency for the air to break away
from the convex face of the curved part of the impeller
vane. Here then is a point at which the Mach number
will be extremely important.
Centrifugal Compressors
4.4. COMPRESSIBILITY EFFECTS
W1
 The Mach number is given by: M1 
 RT1
Where T1 is the static temperature at the inlet.
Breakaway commencing at
rear shockwave
W1
Centrifugal Compressors
4.4. COMPRESSIBILITY EFFECTS
U1
W1
a
W1
V1
W1’
Fixed inlet guide vane
V1 Va1
Angle of
prewhirl
Centrifugal Compressors
4.4. COMPRESSIBILITY EFFECTS
 It is possible to reduce the relative velocity w1 and
hence the Mach number by introducing Prewhirl at the
intake.
 This is achieved by allowing the air be drawn into the
impeller eye over curved IGV's attached to the
compressor casing, For the same axial velocity and
hence approximately the same mass flow, the relative
velocity is reduced as shown by the modified Velocity D.
 This method of reducing Mach number, unfortunately
reduces the work capacity of the compressor.
Centrifugal Compressors
4.4. COMPRESSIBILITY EFFECTS
 The air now has an initial whirl component V1 so that, the
rate of change of angular momentum per unit mass flow is
:
H = V2r2 - V1r1 if V1 is constant over the impeller eye.
 But the Mach number is only high at the tip of the eye. It is
clearly preferable to vary the prewhirl, gradually reducing
it from a maximum value at the tip, to zero at the root of
the eye. This may be done if the IGV are suitably twisted.
Centrifugal Compressors
4.4. COMPRESSIBILITY EFFECTS
Impeller Exit:
 It has been found that, as long as the radial velocity
component is subsonic, Mach numbers greater than 1
can be used at the impeller without loss of efficiency.
 It appears that supersonic diffusion can occur
without the formation of shock waves if it is carried
out at constant angular momentum with vortex
motion in the vaneless space.
 But if the Mach number at the leading edge of the
diffuser vanes are rather high, and it would probably be
advisable to increase the radial width of the
VANELESS SPACE or the depth of the diffuser to
reduce the velocity at that radius.
Centrifugal Compressors
4.4. COMPRESSIBILITY EFFECTS
 High M (at the leading edge diffuser) is not desirable
because of air resonance considerations.
 Static pressure differences around the circumference
from due to locally high pressures at stagnation points.
The danger is the instability created convects upstream
causing mechanical danger as well as spoiling the flow.
To take care of this the # of impeller vanes and diffuser
channels are selected properly.
 Exciting frequency f [rpm,# impeller vanes / # diffuser vanes] =
a natural frequency of impeller channels .
# diffuser channels are selected to be prime number
# impeller vanes selected to be even number
Centrifugal Compressors
4.4. COMPRESSIBILITY EFFECTS
 As a result:
The Vaneless space both
 Decreases the danger of shock losses
 Decrease the danger of excessive variations in static
pressure due to Higher M near the impeller tip.
Centrifugal Compressors
Centrifugal Compressors
Centrifugal Compressors
Centrifugal Compressors
Centrifugal Compressors
4.6. COMPRESSOR CHARACTERISTICS
 The performance of a compressor may be specified by
curves of delivery pressure and temperature (as a
measure energy transfer) against mass flow for various
fixed values of rotational speeds.
 These characteristics (¢), however are dependent on
other variables such as conditions of pressure and
temperature at the entry of the compressor, and the
physical properties of the working medium.
 Any attempt to allow for full variations of all these
quantities over the working range would involve an
excessive number of experiments, and make concise
presentation of the results impossible.
Centrifugal Compressors
4.6. COMPRESSOR CHARACTERISTICS
 Most of this complication may be eliminated by using the
technique of “Dimensional Analysis” by which the
variables involved may be combined to form a smaller
number of more managable "Dimensionless Groups“
 By Dimensional analysis the following groups may be
formed
R  T01
P02
T02
N D
...,..
...,...m 2
...,..
P01
T01
D  P01
R  T01
Centrifugal Compressors
4.6. COMPRESSOR CHARACTERISTICS
 When we are concerned with the performance of a
machine of Fixed Size, compressing a Specified Gas,
R and D in the above groups may be omitted from the
groups, Leaving Dimensional Groups such that
T01
P02
T02
N
...,..
...,...m
...,..
P01
T01
P01
T01
 If these are the variables affecting the performance, it is
only necessary to plot two sets of curves in order to
describe the performance of a compressor (at a fixed
speed) completely.
Centrifugal Compressors
4.6. COMPRESSOR CHARACTERISTICS
T01
N
 P02 /P01 plotted vs m
for fixed values of
P01
T01
 T02/T01
plotted vs m
T01
P01
for fixed values of
 from these 2 sets curves it is possible to construct
isentropic efficiency curves at constant speed.
 1

T02  T01  P02 / P01   1


T02  T01
T02 / T01   1
N
T01
Centrifugal Compressors
4.6. COMPRESSOR CHARACTERISTICS
Pressure Ratio
po25 /po1
4
Surge
Line
3
1.0
0.9
Locus of Points of
Maximum
Efficiency
0.8
2
N/√To1
Relative to
Design Value
0.7
0.6
1
0
0.2
0.4
0.6
0.8
m√To1/po1
1.0
1.2
Centrifugal Compressors
4.6. COMPRESSOR CHARACTERISTICS
Isentropic
efficiency
ηc %
5
4
3
0.6
0.7
0.8
0.9
1.0
N√To1/po1 (relative to
design value)
2
1
0
0.2
0.4
0.6
0.8
1.0
m√To1/po1 (relative to
design value)
1.2
Centrifugal Compressors
4.6. COMPRESSOR CHARACTERISTICS
 Consider what might be expected to occur when a valve
placed at the delivery line slowly operated.
Theoretically
A : Valve is shut; m =0;
P02/P01 pressure head (for the air trapped)
B :  and P02/P01 is maximum
C : All the power is absorbed in overcoming internal friction
resistance (hypothetical case)
In Actual Case
Point A could be obtained if desired but most of the curve
between A and B could not, owing to the phenomenon of
SURGING.
Centrifugal Compressors
4.6. COMPRESSOR CHARACTERISTICS
Pressure ratio
Theoretical Characteristics
D
B
Constant
speed curve
A
E
Mass flow
1
0
C
Centrifugal Compressors
4.6. COMPRESSOR CHARACTERISTICS
 Surging is associated with a sudden drop in delivery
pressure and with violent aerodynamic pulsations which
are transmitted throughout the whole machine.
 If we suppose that the compressor is operating at some
point D on the positive sloped part of the ¢ , then a
decrease in mass flow will be accompanied by a fall in
delivery pressure.
 If the pressure of air downstream of the compressor
does not fall quickly enough the air will tend to reverse
its direction and flow back in the direction of resulting
pressure gradient.
Centrifugal Compressors
4.6. COMPRESSOR CHARACTERISTICS
 When this occurs, the pressure ratio P02/P01 drops
rapidly. Meanwhile the pressure downstream of the
compressor has fallen as well, so that the compressor
will now be able to pick up again to repeat the cycle of
events which occur at high (!) frequency.
 Rotating Stall: When there is any non-uniformity in the
flow or geometry of the channels between blades or
vanes, a breakdown in the flow in one channel (say B),
cause the air to be deflected in such a way that channel
C receives fluid at a reduced angle of incidence.
Centrifugal Compressors
4.6. COMPRESSOR CHARACTERISTICS
 Channel A then stalls (air flow reduces) resulting in a
reduction of incidence to channel B enabling the flow in
that channel to recover.
 Thus the stall propagates in a direction opposite to the
blade rotation relative to the blades, from channel to
channel.
 This results in aerodynamic vibrations → fatigue failure.
 Passage blockage → Loss of performance
Centrifugal Compressors
4.6. COMPRESSOR CHARACTERISTICS
Centrifugal Compressors
4.6. COMPRESSOR CHARACTERISTICS
 Choking: On theoretical ¢ curve, actually point C can
not be reached, since some where beyond point E the
flow will be choked. (i.e. maximum possible flow rate.)
 The temperature ratio curve will be similar to the one
for-pressure ratio since
T02
P02
 f ( ,c )
T01
P01
 From P02/P01 and T02/T01 one can plot c vs
m  T01
P01
Centrifugal Compressors
4.6. COMPRESSOR CHARACTERISTICS
 In some cases equivalent flow
and equivalent speed
N

m 

are employed instead of the above
T01
P01
Here:  
, 
Tref
Pref
Generally: Tref = 288oK Pref = 1.013 bar
(ISA)
Centrifugal Compressors
TURBINE CHARACTERISTICS
 Similar to compressor ¢ Turbine performance is
expressed in terms of similar dimensionless (or
dimensional) groups
P03 m  T03 N
, ,
,
P04
P03
T03
 Turbine performance is plots are given by plotting
&
m  T03
P03
vs
P03
P04
for various
N
T03
Centrifugal Compressors
TURBINE CHARACTERISTICS
 The efficiency plot is constant over a wide range of N and
RT. This is because of the accelerating flow through the
turbine blades permit an operation over a wide range of
incidence without much loss.
m  T03 / P03 corresponds to a
 The maximum
choking condition at the existing pressure ratio. This
choking might occur in the NGV nozzle (or sometimes at
the outlet of the turbine depending on the design).
 Even when unchoked, the constant N / T
curves do not
03
seperate very much. Especially for multistage turbines, the
N / T03 curves converge to a single one.
 This is very important especially for the part load
performance of a gas turbine.
Centrifugal Compressors
TURBINE CHARACTERISTICS
Centrifugal Compressors
Problem on Centrifugal Compressors
 A centrifugal compressor which is fitted to an aircraft has
the following data;








Mass flow rate of air
Rotational speed
Total pressure ratio
Slip factor (σ)
Power input factor
Isentropic efficiency
Inner radius of impeller eye
Outer radius of impeller eye
:
:
:
:
:
:
:
:
6 kg/s
15000 rpm
4.0
0.9
1.04
0.82
8 cm
16 cm
Centrifugal Compressors
Problem on Centrifugal Compressors

Ambient conditions
Pa
:
0.3565 bar
Ta
:
236 K
 Forward speed of the aircraft
:
240 m/s
 Inlet prewhirl(constant for all radii) :
300
 At the impeller exit blades are straight β2v= 900
FIND:
a) Maximum Mach No at the impeller inlet
b) Maximum Mach No at the impeller inlet for no prewhirl.
For both a and b sketch velocity triangles
c) The diameter of the impeller
Centrifugal Compressors
Problem on Centrifugal Compressors
d) Assume that meridional velocity is constant throughout
the impeller,
Vm1= Vm2  Va1= Vr2
 Find the impeller exit width b2, sketch velocity triangles.
e) If the diffuser inlet radius r3= 1.2r2 and the width of the
vaneless space at the diffuser inlet is 2mm in excess of
impeller exit width, find the diffuser inlet Mach No.
Centrifugal Compressors
Solution :
3
b3
2
b2
r2
1
r1t
r1h
a)
Vac 2
2402
T01  Ta 
 236 
 265K
2c p
2010
P01  T01 
 
Pa  Ta 
k / k 1
 265 


 236 
3.5
 1.5
Centrifugal Compressors
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