centrifugal-Compressor-stage-design for impeller, diffuser and volute

Impeller, diffuser and volute

1. PEMP
RMD510
DesignofCentrifugalCompressor
-
1
Design
of

Centrifugal
Compressor
-
1
Session delivered by: Session delivered by:
Prof Q H Nagpurwala Prof Q H Nagpurwala Prof
.
Q
.
H
.
Nagpurwala Prof
.
Q
.
H
.
Nagpurwala
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
1

2. PEMP
RMD510
Session Objectives
To introduce the dele
g
ates to
g
• the procedure for aerodynamic design of centrifugal
compressors
• the methods for obtaining impeller geometry
•
theprocedureforthedesignofvanedandvanelessdiffusers the
procedure
for

the
design
of

vaned
and
vaneless
diffusers
• Effect of geometric parameters on centrifugal compressor
p
erformance
p
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
2

3. PEMP
RMD510
Nomenclature
C
Absol te elocit
C
Absol
u
te
v
elocit
y
n Number of vanes
ppressure
N
Rotational speed
N
Rotational

speed
r Radius
TTemperature
U
Im
p
eller s
p
eed at ti
p
pp p
U
e
Impeller speed at mean radius of eye
V, WRelative velocity

Relative flow angle

Slip facto
r

Power input factor

Angular velocity
Suffixes
a, x Axial component
aAmbient
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r Radial component
w,

Whirl component

4. PEMP
RMD510
Centrifugal Compressor
C
1
= C
a1
C
w2
W
w2
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4
Centrifugal compressor stage and velocity diagrams at impeller entry and exit

5. PEMP
RMD510
Centrifugal Impeller with Vaned Diffuser
WithoutSplitterBlades
WithSplitterBlades
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Without
Splitter
Blades
With
Splitter
Blades

6. PEMP
RMD510
Types of Impellers
C
C
C
Head – flow
characteristics
fif
or var
i
ous
outlet blade
angles
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6

7. PEMP
RMD510
Components of Fluid Forces on Blades / Vanes
Fluid particles flowing through a rotor experience forces in axial, radial
and
tangential
directions
radial
and
tangential
directions
.
Til
Ail
T
angent
i
a
l
component
Radial
A
x
i
a
l
component
Radial

component
Shaft
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7
Shaft

8. PEMP
RMD510
Velocity Triangles
Approximate blade shapes can be obtained from velocity triangles.
C
2
W
2
C
w2
U
2
C
r2
W
2
Outlet velocity triangle
U
e
C
a1
=C
1
W
1
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8
Inlet Velocity Triangle

9. PEMP
RMD510
Design Formulae
From Euler turbine equation of energy exchange,


h
h
C
U
C
U
W

Specificwork


01 03 1 2 2
h
h
C
U
C
U
W
w e w




Specific
work
,


01 03
T Tc
p


Diffuser
p
Im
p
eller
Vaneless
space
If the flow at inlet to the impeller is axial,
then C
w1
= 0, and
p

2 2w
CU W



01 03
T Tc
p


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9

10. PEMP
RMD510
C
Design Formulae
C
,
'
2
2
w
w
C
C


Slip Factor
2
Then
U
W


C’
w2
impeller radial for
2
U
C
w



Then
,
U
W


Introducing power input factor,

2
U
W



C
w2
C
ws
and temperature rise
U
W



U
T
T
2


Velocity triangle at
impeller exit
C
C
p
c
T
T
01 03

 





1
01
03
1
'
03
03
1
 






 

T
T
T
p
c
w
C
C





01
01
03
0103
0103
1








T T p
p
c


1
2







U
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10
01
1








Tc
U
p
c

11. PEMP
RMD510
Compression Process on h-s Diagram
Thefluidisacceleratedfrom The
fluid
is
accelerated
from

velocity C
0
to velocity C
1
and
the static pressure falls from
p
0
to p
1
.
0
1
Since the stagnation enthalpy
is constant in steady, adiabatic
flowwithoutshaftwork then flow
without
shaft
work

then

h
00
= h
01
2
2
1 1
C
h
C
h
o
r
2
1 1
20 0
2 2
C
h
C
h



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12. PEMP
RMD510
Design Procedure
•
Assume rotational speed, tip speed and air entry velocity
•
Determine the pressure ratio of the compressor and the power
id di i i h h li fh i ili
requ
i
re
d
to
d
r
i
ve
i
t, assum
i
n
g
t
h
at t
h
e ve
l
oc
i
t
y
o
f
t
h
e a
i
r at
i
n
l
et
i
s
axial,
•
Calculate
the
inlet
angle
of
the
impeller
vanes
at
the
root
and
tip
Calculate
the
inlet
angle
of
the
impeller
vanes
at
the
root
and
tip
radii of the eye assuming that the axial inlet velocity is constant acrosstheeye
•
Estimatethenumbe
r
ofvanes
•
Estimate the axial depth of the impeller channels at the periphery of the
impeller
the
impeller
•
Estimatetheinletangleofthediffuservanes,and
•
the
throat
width
of
the
diffuser
passages
which
are
assumed
to
be
of
09
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12
•
the
throat
width
of
the
diffuser
passages
,
which
are
assumed
to
be
of
constantdepth

13. PEMP
RMD510
Design Specifications
The following data are suggested as a basis for the design of a single-sided centrifugal compressor:
P
it
ft
1
04
P
owe
r
i
npu
t
f
ac
t
or,

1
.04
Slipfactor,

0.9
Rotational
speed
N
290
rev/s
Rotational
speed
,
N
290
rev/s
Overalldiameterofimpeller 0.5m Eye
tip
diameter
0
.3
m
Eye
tip
diameter
0
.3
m
Eye rootdiameter 0.15m
Airmassflow,m9kg/s
Inletstagnationtemperature,T
01
295K
Inletstagnationpressure,p
01
1.1bar
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Isentropicefficiency,

c
0.78

14. PEMP
RMD510
Design Requirements
Requirements are (a)
Todeterminethepressureratioofthecompressor
(a)
To
determine
the
pressure
ratio
of
the
compressor

and the power required to drive it assuming that
the velocit
y
of the air at inlet is axial
y
(b)To calculate the inlet angle of the impeller vanes
attherootandtipradiiof theeye,assumingthat at
the
root
and
tip
radii
of

the
eye,
assuming
that

the axial inlet velocity is constant across the eye
(c)
Toestimatetheaxialdepthoftheimpeller
(c)
To
estimate
the
axial
depth
of
the
impeller

channels at the periphery of the impeller
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15. PEMP
RMD510
Pressure Ratio and Power
(a) ImpellertipspeedU=

*0.5*290=455.5m/s
Tem
p
eraturee
q
uivalentofthewor
k
doneonunitmassflowofairis
p
q
193
5. 455 *9.0*04.1
2 2

K
U
T
T


193
*
78
0
193
10* 005.1
5.3
1
3
01 03






 



T
T
K
c
T
T
p


23.4
295
193
*
78
.
0
1 1
1
01
01 03
01
03
 


 
 



 

 



T
T
T
p
p
c
Power required = m c
p
( T
03
-T
01
) = 9*1.005*193 = 1746 kW
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16. PEMP
RMD510
Static Density at Inlet
(b) To find the inlet angle of the vanes it is necessary to determine the inlet
velocity, which in this case is axial, i.e. C
a1
= C
1
.
C
a
1
mustsatisfythecontinuityequation
m
=

1
A
1
C
a
1
,where
A
1
istheflow
C
a
1
must
satisfy
the
continuity
equation
m


1
A
1
C
a
1
,
where

A
1
is
the
flow

area at inlet.
Since the density

1
depends upon C
1
and both are unknown, a trial and error
processisrequired process
is
required
.
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17. PEMP
RMD510
Design Procedure
•
The iterative procedure is not critically dependent on the initial value
assumed for the axial velocity, but clearly it is desirable to have some rational
basis for obtaining an estimated value for starting the iteration.
•
The simplest way of obtaining a reasonable estimate of the axial velocity is to calculate the density on the basis of the known stagnation temperature and pressure; in practice this will give a density that is too high and a velocity that is too low.
•
Having obtained an initial estimate of the axial velocity. The density can be recalculatedandhence theactualvelocityfromthecontinuityequation;if recalculated
and
hence

the
actual
velocity
from
the
continuity
equation;
if

the assumed and calculated velocities do not agree it is necessary to iterate
until agreement is reached.
•
Notethatitisnormaltodesignforanaxialvelocityofabout150m/s thus
•
Note
that
it
is
normal
to
design
for
an
axial
velocity
of
about
150
m/s
,
thus

providing a suitable compromise between high flow per unit frontal area and
low frictional losses in the intake.
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18. PEMP
RMD510
2
2
)
15
0
3
0
(
Iteration on C
a1
m kg
RT
p
/ 30.1
295
*
287
0
100 *1.1
3 01
1
  

Based on stagnation
diti
Annulus area of impeller eye, A
1
=
2
2
2
053.0
4
)
15.
0
3.
0
(
m



sm
A
m
C
RT
a
/ 131
053.0*30.1
9
295
287
.
0
1 1
1
01
  

con
diti
ons
C
K
c
C
p
5.8
201.0
31.1
10* 005.1*2
131
2
1
2
2
3
2
1
2
  
Since C
1
= C
a1
, the equivalent
dynamic temperature is





bar
T
T
p
p
K
c
C
T
T
p
992.0
5. 286 295
1.1
5. 286 5.8 295
2
5.3 1
1
01
01
1
1
01 1
  











m kg
RT
p
/ 21.1
5. 286 * 287.0
100 * 992.0
3
1
1
1
1
01
  

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sm
A
m
C
a
/ 140
053.0*21.1
9
1 1
1
  

Check on C
a1

19. PEMP
RMD510
Fi lt i l
Iteration on C
a1
(… contd.)
Fi
na
l
t
r
i
a
l
:
Try C
a1
= C
1
=145 m/s
Eiltd it t i
K 5.10
201.0
45.1
10* 005.1*2
145
2
2
3
2 2
1
  
c
C
p
E
qu
i
va
l
en
t
d
ynam
i
c
t
empera
t
ure
i
s
b
968
0
1.1
K 5. 284 5.10 295
2
01
2
1
01 1
    
p
c
C
T T
p





kg/m 185.1
5
.
284
*
287
.
0
100 * 968.0
b
a
r
968
.
0
5. 284 295
3
1
1
5.3 1
1 01
01
1
  




RT
m
T T
p
p 
 
m/s 143
053
0
*
185
1
9
5
.
284
287
.
0
1
1
  
A
m
C
RT
a

Check on C
a1
:
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053
.
0
185
.
1
1 1
A


20. PEMP
RMD510
Flow Angles at Inducer

This is a good agreement and a further trial using C
a1
= 143 m/s is
unnecessary because a small change in C
a1
has little effect upon
F hi i i h fi l l 143

.
F
or t
hi
s reason
i
t
i
s more accurate to use t
h
e
fi
na
l
va
l
ue
143

m/s, rather than the mean of 145 m/s (the trial value) and 143
m/s. The vane angles can now be calculated as follows:
Peripheral speed at the impeller eye tip radius
=

*
03
*
290
=
273m/s



0
.
3

290

273

m/s
and at eye root radius = 136.5 m/s


143


33 46
5 136
143
tan
1
.
.





65
27
273
143
tan
1
.



at root =

attip
=
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

65
27
273
tan
.

at
tip

21. PEMP
RMD510
Radial Velocity and Static Density at Exit
(c) To calculate the required depth of the impeller channel at the
periphery we must make some assumptions regarding both
hdil fli hidhdiiif
t
h
e ra
di
a
l
component o
f
ve
l
oc
i
ty at t
h
e t
i
p an
d
t
h
e
di
v
i
s
i
on o
f

losses between the impeller and the diffuser so that the
densit
y
can be evaluated. The radial com
p
onent of velocit
y

ypy
will be relatively small and can be chosen by the designer; a
suitable value is obtained by making it approximately equal to
theaxialvelocityatinlettotheeye the
axial
velocity
at
inlet
to
the
eye
.

To estimate the density at the impeller tip , the static pressure
and tem
p
erature are found b
y
calculatin
g
the absolute velocit
y

pyg y
at this point and using it in conjunction with the stagnation pressure which is calculated from the assumed loss up to this point
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21
point
.

22. PEMP
RMD510
Absolute Velocity at Exit
MakingthechoiceC
r2
=C
a1
,wehaveC
r2
=143m/s
C
w2
=U=0.9*455.5=410m/s
K 8.93
201.0
10.4 43.1
2 2
2 2 2
2
2
2
2
2





p
w r
p
c
C C
c
C
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23. PEMP
RMD510
Distribution of Total Loss
Assuming that half the total loss, i.e. 0.5(1-

c
) = 0.11, occurs in
the impeller, the effective efficiency of compression from p
01
to p
02
illb 089 th t
5.3
5.3
02
582.1
193 *89.0
1





p
w
ill
b
e
0
.
89
so
th
a
t
,
01
295


p
Now, (p
2
/p
02
) = (T
2
/T
02
)
3.5
K
2
394
8
93
488
22
C
T
T
2

02
2

02
and T
02
= T
03
= 193+295 = 488 K
th t
5.3
2
2. 394

 p
K
2.
394
8
.
93
488
2
2
02 2





p
c
T
T
so
th
a
t
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23
02
2
488



p

24. PEMP
RMD510
Impeller Width at Exit
Since (p
2
/p
01
) = (p
2
/p
02
) (p
02
/p
01
) 5.3
012
35.2
488
2. 394
* 582.1




pp
3 2
2201
k
g
/m 28.2
2
394
*
287
0
100 *58.2
58.21.1*35.2
488



 

 RT
p
bar p
p 
2
2
g
2
.
394
*
287
.
0
RT

The required flow area normal to the radial direction at the impeller tip is
2
9
m
2
2 2
m 0276 .0
143*28.2
9



r
Cm
A

Hence the depth of impeller channel at exit
5.0*
0276 .0

b
= 0.0176 m or 1.76 cm
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(This result will be used when discussing the design of the
diffuser in the next section)

25. PEMP
RMD510
Estimation of Number of Blades
The number of impeller vanes can be obtained from the correlations for slip factor
Stanitz correlationWiesner correlation
7.0
2
cos
1
Z
s



Stodola correlation
and

’
2
is measured from radial direction.

2
In the present case,

’
2
= 0
Hence, Stanitz correlation reduces to
Z
s


63.0
1
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25
Z
For

s
= 0.9, number of blades, Z= 19.79~
20

26. PEMP
RMD510
Generation of Blade Profile
Impeller vane profiles can be generated •by using softwares, like BLADEGEN
ProfileA
•by trial and error process, using CAD and CFD tools
Profile
A
Profile B Final Profile D
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26
Profile C

27. PEMP
RMD510
Types of Diffusers
•
Vaneless diffuser Cildiff
Angular momentum is conserved in the vaneless
space; i.e. r.C
w
= constant. C
r
also varies in the
vaneless space because of the change in radius.
Htitif
C
d
C
ill i ldth
•
C
on
i
ca
l
diff
user
H
ence, es
ti
ma
ti
on o
f
C
w
an
d
C
r
w
ill
y
i
e
ld
th
e
absolute velocity and flow angle at inlet to the
vaned /conical diffuser.
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
27

28. PEMP
RMD510
Types of Diffusers
Uniform thickness
curved vanes
Aerofoil shape
vanes
Uniform thickness
Wedge shape vanes
straight vanes
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
28

29. PEMP
RMD510
Types of Diffusers
• Straight wedge type •
Aerofoilshapedvanes
•
Aerofoil
shaped

vanes
(a) Straight wedge type
(b) Aerofoil shaped vanes
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
29

30. PEMP
RMD510
Types of Impellers and Diffusers
Impellers
•Radially ending
•
Backswept
Diffusers
•
Backswept
•Pre-swirl
•
Abovew/splitterblades
•Vaneless
•Vaned
Above

w/splitter
blades
–
Radial
–Wedge Di t
•
Di
scre
t
e-passage
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
30
NASA Glenn Research Center

31. PEMP
RMD510
Typical Diffuser Geometry
Throat
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
31
Flow regions of vaned diffuser

32. PEMP
RMD510
Diffuser Design
Radial width of vane less space = 5 cm
Approximate mean radius of diffuser throat = 0.33 m
Depth of diffuser passages = 1.76 cm Number of diffuser vanes = 12 Ii i d d i I
t
i
s requ
i
re
d
to
d
eterm
i
ne
:
(a) the inlet angle of the diffuser vanes, and
(b)thethroatwidthofthediffuserpassages which areassumedtobeof (b)
the
throat
width
of
the
diffuser
passages
,
which
are
assumed
to
be
of

constant depth.
For simplicity, it will be assumed that the additional friction loss in the short
distance between impeller tip and diffuser throat is small and therefore the 50 %
of the overall loss can be considered to ha ve occurred up to the diffuser throat.
For convenience, suffix 2 will be used to denote any plane in the flow after the
impellertip theconte tmakingitclear hich planeis nderconsideration
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
32
impeller
tip
,
the
conte
x
t
making
it
clear
w
hich
plane
is
u
nder
consideration
.

33. PEMP
RMD510
()
C id diti tth di fth diff l di d i t
Iteration on C
r2
at Diffuser Inlet
(
a
)
C
ons
id
er con
diti
ons a
t
th
e ra
di
us o
f
th
e
diff
user vane
l
ea
di
ng e
d
ge,
i
.e. a
t

r
2
= 0.25+0.05 = 0.3m. Since in the vaneless space C
w
r = constantfor
constant angular momentum,
25
.
0
The radial component of velocity can be found by trial and error. The
iteration ma
y
be started b
y
assumin
g
that the tem
p
erature e
q
uivalent of the
sm C
w
/ 342
30.0
25
.
0
* 410
2


yygpq
resultant velocity is that corresponding to the whirl velocity, but only the
final trial is given here.
Try
C
=97m/s
Try

C
r2
=
97
m/s
K 9.62
201.0
97.0 42.3
2
2 2 2
2



p
c
C
Ignoring any additional loss between the impeller tip and the diffuser vane
leading edges at 0.3m radius, the stagnation pressure will be that
calculated for the impeller tip, i.e.
p
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
33
5.3
01
02
582.1
p
p

34. PEMP
RMD510
Static Density at Diffuser Inlet
Proceeding as before we have
K
1
425
9
62
488
T
5.3
2
2
488
1. 425
K
1
.
425
9
.
62
488







pp
T
5.3
2
02
07.3
488
1. 425
* 582.1
488
 






ppp
2
01
100
*
38
3
bar 38.31.1*07.3
488
 


pp
3
2
kg/m 77.2
1. 425 * 287.0
100
*
38
.
3
 

09
@ M S Ramaiah School of Advanced Studies, Bengaluru
34

35. PEMP
RMD510
Diffuser Inlet Angle
Area of cross-section of flow in radial direction
2
9
= 2

*0.3*0.0176=0.0332 m
2
Check on C
r2
:
W
2
Taking
C
as979m/s theangleofthediffuservaneleading
s C
r
m/9.97
0332 .0*77.2
9
2


Taking
C
r
2
as
97
.9
m/s
,
the
angle
of
the
diffuser
vane
leading

edge for zero incidence should be

16
9.97
t
t
1
2
1




C

16
342
t
an
t
an
1
2
2
1




w
r
C
C
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
35

36. PEMP
RMD510
Static Density at Diffuser Throat
(b) The throat width of the diffuser ch annels may be found by a similar calculation
for the flow at the assumed throat radius of 0.33 m
/
311
25.0
*
410
C
2
2
22
2
m/s 83
m
/
s
311
33.0
*
410



CC
r
w
Try
2
2
2
2
K
5
436
5
51
488
K 5.51
201.0
83.0 11.3
2






T
C
C
p
5.3
012
2
37.3
488
5.436
* 582.1
K
5.
436
5
.
51
488








pp
T
3
2201
kg/m
96
.
2
100*71.3
bar 71.31.1*37.3


 


pp
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
36
2
kg/m
96
.
2
5. 436 * 287.0


37. PEMP
RMD510
Diffuser Angle at Throat
As a first approximation, we may neglect the thickness of the diffuser vanes
sothattheareaofflowintheradialdirection
=2*

*0.33*0.0176=0.0365m
2
m/s 3.83
0365
0
*
96
2
9
2
 
r
C
Check on
C
r2
:
0365.
0
*
96.
2
3
.
83
1

15
311
3
.
83
tan
1


Direction of flow =
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
37

38. PEMP
RMD510
Diffuser Throat Width
, or ,
2
2 2
2 2 2 2 2 2 2
C
CA
A CA CA
r r
r r
 
 
Now,
m
=
Hence, flow area in the direction of resultant velocity, i.e. total throat area of the
diffuser passages is
0.0365 sin 15
°
= 0.00945 m
2
Therefore, with 12 diffuser vanes, the widt h of the throat in each passage of depth 0.0176 m is,
cm
440
or
m
0440
0
00945 .0

cm
4
.
40
or

m
0440
.
0
0176 .0*12
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
38

39. PEMP
RMD510
Inducer Relative Mach Number on Ground Consider inlet Mach number at the tip radius of the impeller eye Inlet velocity = 143 m/s (axial)
Eye tip speed = 273 m/s
Relative velocity at tip = Velocityofsound
=


m/s 308 273 143
2 2
 


m/s
338
10
*
5
284
*
287
0
*
4
1
3
Velocity
of
sound

=

Maximum Mach number at inlet = 308/338 = 0.91


m/s
338
10
*
5.
284
*
287.
0
*
4
.
1
3

This would not be considered satisfactory even if it were actually the maximum
value likely to be reached. But, if the co mpressor is part of an aircraft engine
re
q
uired to o
p
erate at an altitude of 11000 m
, where the atmos
p
heric tem
p
erature
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
39
qp , pp
is only about 217 K, we must calculate the Mach number under these conditions.

40. PEMP
RMD510
Si th illb t t i d t th ff ti th i t k h th
Inducer Relative Mach Number in Flight
Si
nce
th
ere w
ill
b
e a
t
empera
t
ure r
i
se
d
ue
t
o
th
e ram e
ff
ec
t
i
n
th
e
i
n
t
a
k
e w
h
en
th
e
aircraft has a forward speed, the effect of drop in atmospheric temperature will
not be quite so great as might be expected. We will take 90 m/s (324 km/hr) as
beingtheminimumspeedlikelytobereachedathighaltitude being
the
minimum
speed
likely
to
be
reached
at
high
altitude
.
Temperature equivalent of forward speed = 4K
Inletstagnationtemperature
=
217
+
4
=
221K
Inlet
stagnation
temperature

217

4

221
K
Temperature equivalent of axial inlet
velocity from the first example = 10.5 K
Inlet static temperature at altitude = 210.5 K
5
284
21


Inlet Mach number at altitude =
06.1
5. 210
5
.
284
91.0
2





09
@ M S Ramaiah School of Advanced Studies, Bengaluru
40
This is clearly too high and we will find the Mach number when an inlet prewhirl
of 30°is introduced.

41. PEMP
RMD510
Effect of Inlet Prewhirl
I thi th b l t i l t l it ill b li htl hi h th b f th t th i l t
Try
C
=
150
m/s
I
n
thi
s case
th
e a
b
so
l
u
t
e
i
n
l
e
t
ve
l
oc
it
y w
ill

b
e s
li
g
htl
y
hi
g
h
er
th
an
b
e
f
ore, so
th
a
t

th
e
i
n
l
e
t

static temperature will be slightly lower. A new value for the axial velocity must be found
by the usual trial and error process. Reverting to the original sea-level static case:
Try
C
a1
=
150
m/s
C
1
= 150/cos 30 = 173.2 m/s
Temperature equivalent ofC
1
= 14.9 K
T
1
= 295-14.9 = 280.1K
p
1
= 0.918 bar and
9
3
1
/ 14.1m kg 

Check onC
a1
=
Whirl velocity at inlet, C
w1
= 149 tan 30
=
86
m/s
sm/ 149
053.0*14.1
9

30º
=
86
m/s
Maximum relative velocity =
= 239 m/s
239

2 2
86 273 149 
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
41
Hence maximum inlet Mach number atT
01
= 295 K is

71.0
10*1.280 * 287.0*4.1
239
3


42. PEMP
RMD510
U d ltit d diti thi ld i t littl th 0 8 H
Effect of Prewhirl on Pressure Ratio
U
n
d
er a
ltit
u
d
e con
diti
ons
thi
s wou
ld
r
i
se
t
o
littl
e more
th
an
0
.8
.
H
ence, a
prewhirl of 30°can be regarded as adequate.
To show the effect of 30°prewhirl on the pressure ratio, we will take the
worst case and assume that the prewhirl is constant over the eye of the
impeller.
Speed of impeller eye at mean radius,
m/s 8.204
2
5.136 237



e
U
2
e




1
2
 
e w
p
UC U
c


Actual temperature rise


K 175
10* 005.1
8.204 *86 5.455 *9.004.1
3
2



175
*
78
0
5.3
03


p
79.3
295
175
78
.
0
1
0103




 


p
p
This pressure ratio may be compared with the original value of 4.23 obtained
ithnopre hirl Itissometimesad antageo sto seadj stableinletg ide
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
42
w
ith
no
pre
w
hirl
.
It
is
sometimes
ad
v
antageo
u
s
to
u
se
adj
u
stable
inlet
g
u
ide

vanes to improve the performance under off-design conditions.

43. PEMP
RMD510
Mach Number at Impeller Exit
We next consider the relevant Mach numbers in the diffuser. The maximum
value will occur at the entry to the diffuse r, that is, at the impeller tip. Once
again the values calculated in the previous example will be used.
The temperature equivalent of the resultant velocity of the air leaving the impeller was found to be
2
K
C
C
p
8.93
2
22

and hence
C
2
= 434m/s
T
f d b3942K dh hMh b hi ll i l
T
2
was
f
oun
d
to
b
e
394
.2
K
an
d
t
h
us t
h
e
M
ac
h
num
b
er at t
h
e
i
mpe
ll
er t
i
p equa
l
s


09.1
10
*
2
394
*
287
0
*
4
1
434
3

09
@ M S Ramaiah School of Advanced Studies, Bengaluru
43


10
*
2
.
394
*
287
.
0
*
4
.
1

44. PEMP
RMD510
Mach Number at Diffuser Inlet
Now consider the leading edge of the diffuser vanes. The whirl velocity was
found to be 342 m/s and the radial component 97.9 m/s. The resultant velocity
at this radius is therefore 356 m/s. The static temperatures was 425.1 K at this radius so that the Mach number is
86.0
1
0
*1
.
42
5
* 2
87
.
0
*4
.
1
356
3

0
.
5
87
.
0
.
In the particular design under considera tion, the Mach number is 1.09 at the
impeller tip and 0.86 at the leading edges of the diffuser vanes. It has been
fdh l hdilli ibi h b f
oun
d
t
h
at as
l
ong as t
h
e ra
di
a
l
ve
l
oc
i
ty component
i
s su
b
son
i
c, Mac
h
num
b
ers
greater than unity can be used at the impeller tip without loss of efficiency. It
appears that supersonic diffusion can occur without the formation of shock
wavesifitiscarriedoutatconstantangularmomentumwithvortexmotionin waves
if
it
is
carried
out
at
constant
angular
momentum
with
vortex
motion
in

the vaneless space. But the Mach number at the leading edge of the diffuser
vanes is rather high and it would probably be advisable to increase the radial
widthofthevanelessspaceorthedepthofthediffuser
toreducethevelocityat
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
44
width
of
the
vaneless
space
or
the
depth
of
the
diffuser
to
reduce
the
velocity
at

this radius.

45. PEMP
RMD510
Comments
High Mach numbers at the leading edges of the diffuser vanes are undesirable, not
only because of the danger of the shock losses, but because they imply high air speeds
and relatively large pressures at the stagnation points where the air is brought to rest locally at the leading edges of the vanes. This causes a circumferential variation in static pressure, which is transmitted upstream in a radial direction through the vaneless space to excite the impeller tip. Although the variation would considerably reduce by the time it reaches the impeller it may well be large enough to excite the reduce
by

the

time

it

reaches

the

impeller
,
it

may

well

be

large

enough

to

excite

the

impeller vanes and cause mechanical failure due to vibrational fatigue cracks in the
vanes. This will occur when the exciting frequency, which depends on the rotational
speed and relative number of impeller and diffu ser vanes, is of the same order as one of
the natural frequencies of the impeller vanes. To reduce the likelihood of this, care is
taken to see that the number of vanes in the impeller is not an exact multiple of the
number in the diffuser; it is common practice to use a prime number for the impeller vanes and an even number for the diffuser vanes. vanes
and
an

even

number
for

the

diffuser

vanes.
The reason for the vaneless space will now be apparent: the dangers of both, shock
losses and excessive circumferential variation in static pressure, would be considerably
increased if the leadin
g
ed
g
es of the diffuser vanes were too near the im
p
eller ti
p
where
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
45
gg p p
the Mach numbers are very high.

46. PEMP
RMD510
Wih h di i
Further Work
Wi
t
h
t
h
ese
di
mens
i
ons
1. Create a geometric model of the Centrifugal compressor
usingaCADtool using
a
CAD

tool
.
2. Export the model to a CFD tool and carry out the fluid
flowanalysis flow
analysis
3. Using an FEM tool, carry out the structural dynamic
analysischoosingappropriatematerialproperties. analysis
choosing
appropriate
material
properties.
4. Create a shaft and choose bearings and carryout rotor
d
y
namic anal
y
sis
yy
5. Generate manufacturing drawings 6
Generatecompressoroperatingcharacteristicsusinga
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
46
6
.
Generate
compressor
operating
characteristics
using

a

suitable post processor.

47. PEMP
RMD510
Design Guidelines

Relative velocity ratio,
W
2
/W
sh1
> 0.75de Haller number

Exit absolute flow angle,

2
= 60º -65º

Sweep angle for backward swept impeller = 30º

Ratio of inducer tip diameter to
im
p
eller outer diameter
, d
sh
1
/
d
2
= 0.4 -0.55
cos

p,
sh
1
2

Number of impeller blades by Wiesner’s correlation,

Inducer hub-tip diameter ratio = 0.5 –0.6
7.0
2
cos
1
Z
s




09
@ M S Ramaiah School of Advanced Studies, Bengaluru
47

48. PEMP
RMD510
Effect of Geometric Parameters
Performance of the centrifugal compressor is affected
by the following geometric parameters:
•Impeller vane thickness
•
Splitterblades Splitter
blades
•Trailing end skew •
Exittrim
•
Exit
trim
•Inducer leading edge sweep •Vaned shroud at inducer •Impeller with integral shroud
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
48
•Inlet guide vanes

49. PEMP
RMD510
Impeller Vane Thickness
Because of manufacturing problems and physical necessity, impeller vanes have
definite thickness. When fluid leaves the impeller, the vanes no longer contain
theflow,andthemeridionalvelocitydecreases. Hence, boththerelativeand the
flow,
and
the
meridional
velocity
decreases.

Hence,

both
the
relative
and

absolute velocities also decrease with consequent change in exit flow angle.
C
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
49

50. PEMP
RMD510
Splitter Blades
Compressorspecifications
(a)
(b)
Inducer hub dia. 22 mm
Inducer tip dia. 65 mm
Impeller tip dia
87 mm
Compressor
specifications
Impeller

tip

dia
.
87
mm
Number of vanes 18 Rotational speed 81000 rpm Inlet pressure 0.98 bar
()
Inlet temperature 303 K
(a)LR- 0.81(b)LR-0.65(c)LR-0.50(d)LR-0.35
(
c
)
(d)
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
50
Geometric models of impellers with different splitter to main
blade length ratios (LR=0.81, 0.65, 0.50 and 0.35)

51. PEMP
RMD510
Splitter Blades

The optimum length of
s
p
litter blade is half the len
g
th
pg
of the main blade.
Maximum efficiency and
p
ressure ratio at 0.50 splitter
length.

iifi i

N
o s
i
gn
ifi
cant
i
mprovement
in performance when splitter
len
g
th is reduced further.
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
51
g

52. PEMP
RMD510
Trailing End Skew
HubHubHub
45
°
90°
45
°
45
-
45
°
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
52
45° Skew0° Skew -45° Skew

53. PEMP
RMD510
Trailing End Skew
OtiSd30000
0.95
Operating Speed 30,000 rpm
3.50
4.00
4.50
Pressure Ratio
2/P01)
O
pera
ti
ng
S
pee
d

30
,
000
rpm
0.85
0.90
ic Efficiency
1.4%
2.
00
2.50
3.00
Total to Total
(P0
2
45°
30°
0°
-30°
-45°
0.700.75
0.80
Isoentrop
45°
30°
0°
-30°
-45°
00
0.50 1.00 1.50 2.00 2.50
Corrected Mass flow rate (Kg/s)
0.70
1.00 1.50 2.00 2.50
Corrected Mass flow rate (Kg/s)
Effect of exit skew on impeller performance
09
@ M S Ramaiah School of Advanced Studies, Bengaluru
53

54. PEMP
RMD510
5
Leading End Skew
35
4
4.5
5
sure ratio
Baseline Back sweep 10˚ Back sweep 15˚
Stall margin has increased with
20º forward sweep
2
2.5
3
3
.
5
Total press
Back sweep 20˚ Back sweep 25˚ Forward sweep 10˚ Forward sweep 20˚
2
3 3.5 4 4.5 5 5.5 6 6.5 7
Corrected mass flow rate (kg/s)
5 4
re ratio
Baseline(0.5 mm tip clc.) Forward sweep 20˚(0.5 mm tip clc.)
3
Total pressur
Forward sweep 20˚(0.75 mm tip clc.)
Definition of leading end sweep
A higher tip clearance with forward
df btth
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54
2
34567
Corrected mass flow rate (kg/s)
sweep may re
d
uce per
f
ormance
b
u
t

th
e
compressor production cost will be low

55. PEMP
RMD510
Vaned Shroud at Inducer
Inducer leading
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55
Inducer
leading

end sweep
Barton M.T. et al: ASME J. of Turbomachinery,
Vol. 128, October 2006, pp 627-631

56. PEMP
RMD510
Vaned Shroud at Inducer
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56
Barton M.T. et al: ASME J. of Turbomachinery,
Vol. 128, October 2006, pp 627-631

57. PEMP
RMD510
Exit Trim
Radial exit
Altering the axial width of the ill titk
Exit width trim
i
mpe
ll
er vanes a
t
ex
it
,
k
nown as
Exit Trim, with respect to the
baseline design, helps the manu-
facturer in producing design variants to meet different customerrequirementswithout
Axialentry
customer
requirements
without

spending effort in carrying out an
ab initiodesign for a new product
ithi
ti f
Axial
entry
w
ithi
n a cer
t
a
i
n range o
f

specifications.
09
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57

58. PEMP
RMD510
Impeller with Integral Shroud
09
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58

59. PEMP
RMD510
Inlet Guide Vanes
•
Inlet Guide Vanes (IGV) provide
prewhirl to the flow entering the
impeller impeller
.
•
The inlet velocity triangle is altered.
•
Th k it fth
•
Th
e wor
k
capac
ity
o
f

th
e compressor
also changes due to introduction of whirl
component of velocity.
W = U
2
C
w2
+
U
1
C
w1
•
Introduction of IGVs is desired to
ihff
di f f
i
mprove t
h
e o
ff
-
d
es
ig
n per
f
ormance o
f

the compressor and to limit the inducer
tip Mach number; but the friction losses
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59
will tend to increase.

60. PEMP
RMD510
Session Summary
Thissessionhascovered: This
session
has
covered:
• Basic design methodology of centrifugal compressors.
• Calculation of aerod
y
namic and
g
eometric
p
arameters of the
ygp
impeller and generation of velocity triangles.
• Calculation of diffuser parameters, especially the diffuser inlet
angleandthethroatwidthofdiffuserpassage angle
and
the
throat
width

of

diffuser

passage
.
• Effect of geometric parameters on compressor performance.
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