PEMP
RMD510
Design of Radial Turbines &
Turbochargers
Session delivered by:
Prof Q.
Prof.
Q H.
H Nagpurwala
14
@ M S Ramaiah School of Advanced Studies, Bengaluru
1
Session Objective
PEMP
RMD510
• To discuss the design of radial turbines using a
•
•
14
procedure based on optimum specific speed
To understand the basic construction and working
of turbochargers
To discuss the design of radial compressor and
radial turbine modules of a typical turbocharger
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2
PEMP
RMD510
Design of Radial Turbine
(Based on Specific Speed)
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3
PEMP
RMD510
Radial Turbine Layout and Expansion Process
Nozzle
blades
At rotor
t iinlet
l t
Expansion process in a
radial turbine
At rotor outlet
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Design Guidelines
PEMP
RMD510
From Euler turbine equation, specific work is given by:
 A significant contribution comes
from the first term. For an axial flow turbine,
where U2 = U1, no contribution to the specific work is obtained from this term.
 A positive contribution to the specific work is obtained from the second term
when w3 > w2. In fact, accelerating the relative velocity through the rotor is a most
useful aim of the designer as this is conducive to achieving a low loss flow.
 The third term indicates that the absolute velocity
y at rotor inlet should be larger
g
than at rotor outlet so as to increase the work input to the rotor.
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Design Guidelines
 The
Th
PEMP
RMD510
nominall design
d
i defined
is
d fi d by
b
 relative flow with zero incidence at rotor inlet, i.e. W2 = Cr2, and
 axial absolute flow at rotor exit,, i.e. C3 = Cx3
 Thus,
with Cw3 = 0 and Cw2 = U2, the specific work for the nominal design is
Spouting Velocity:
The term spouting velocity, C0 (originating from hydraulic turbine practice) is
ddefined
fi d as that
h velocity
l i which
hi h hhas an associated
i d ki
i energy equall to the
h
kinetic
isentropic enthalpy drop from turbine inlet stagnation pressure p01 to the final
exhaust pressure. When no diffuser is used
or
With complete recovery of the exhaust kinetic energy, and with Cw2 = U2,
At the best efficiency point, generally, 0.68 < U2 / C0 < 0.71.
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Design Guidelines
 The
PEMP
RMD510
blades are aligned along the radii for much of their length.
 Absolute
flow angle at rotor inlet = Nozzle outlet angle = ~ 70º.
 Absolute
Ab l
flow
fl angle
l at exducer
d
exit
i = 0º.
0º
Inlet relative velocity should be aligned to the blade direction at inlet, which
means that it should be radial. However,

 this may lead to high aerodynamic loading at the tip
 as the blade tips are open, such high pressure loading can not be maintained
Max. efficiency in radial inflow turbines is achieved when inlet flow angle is
modified by the concept of ‘slip’ or ‘deviation’ as applied to radial compressors.

 The
Th
recommended
d d slip
li correlation
l ti is
i that
th t given
i
by
b Wiesner
Wi
 Cu ,1,ac 
cos 1
w  
  1
0.7
C
Z
 u ,1,tl 
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Z = number of blades (incl. splitter blades)
1 = blade angle w.r.t
w r t radial direction
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Variation of Slip Factor with Z
PEMP
RMD510
The slip factor for radial bladed rotor varies with the number of blades:
14
Number of radial blades
on rotor pperiphery
p y
Slip factor
Cu,11/u1
9
11
13
15
17
19
0.785
0 813
0.813
0.834
0.850
0.862
0.873
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Design Data
Inlet temperature
: 1200 K
Inlet pressure
: 300 000 Pa
PEMP
RMD510
Rotor-outlet stagnation pressure : 110 000 Pa
Hot-gas inlet mass flow
: 0.5 kg/s
Fuel/Air ratio
: 0.02
Number of rotor blades
: 13 (radial)
Nozzle outflow angle
: 70° to radial direction
To find: Rotor diameter
Blade axial width at inlet
Rotational speed
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Inlet Velocity Triangle
act
c1
C1
1
PEMP
RMD510
W1
Cr,1
r1
Cu,1
u1
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PEMP
RMD510
Inlet Flow Parameters
• G
Guess S
Stagnation-to-Stagnation
i
S
i polytropic
l
i efficiency
ffi i
= 0.92
0 92
• For 13 blades w=  = 0.834
T0, 2
T0,1
 p0 , 2 

 

 p0,1 
 R

 cp


 p ,c


T0,2 = 961.36 K
Then, T  1080.68 K
c p  1194.64 J/kg K
Δh 0  C p ΔT 0 285,089 J/kg
act
C1
c1
1 W1
Cr,1
Δh 0  ψ u12  u1  584.7 m/s
Cu,1  487.6 m/s
C1  518.9 m/s
Cr,1  181.1 m/s
W1  206.4 m/s
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Cu,1
u1
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Optimum Specific Speed
Distribution of losses along envelope of
maximum total
total-to-static
to static efficiency
(Rohlik 1968)
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PEMP
RMD510
Typical performance of radial turbine
(Rohlik 1968)
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Optimum Specific Speed (… contd.)
PEMP
RMD510
Curves for specific speed for radial flow turbine indicate that the max.
efficiency should reach at non-dimensional Ns of 0.6.
N s,op  0.6 
2πN Vin
60 Δh 
2πN d1 πNd1
u1  ω r1 

60 2
60
2  b1 

Vin  Cr,1 π d1 b1  Cr,1 π d1  
 d1 
g c Δh0  ψ u1
34
2
ω Cr,1 π d1 b1 d1 
2
Ns 
ψ u 
2 34
1
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Rotor Inlet Width to Diameter Ratio
PEMP
RMD510
N s2ψ 3 2u13  N s2ψ 3 2   u1 
b1

 2 2



d1 ω d1 π C r,1  4π   C r,1 
tan αc,1  ψ u1 C r,1
2 12
b1 N s ψ tan αc,1


d1
4π
Inserting appropriate design inputs,
inputs we get
b1/d1 = 0.072
Bothh b1 andd d1 can be
B
b determined
d
i d by
b calculating
l l i volume
l
flow
fl rate at
rotor inlet.
C1
 0.8843
g c RT0 ,1
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Rotor Inlet Mach Number
PEMP
RMD510
Mach number can be determined
from the following relation or
the figure
g
0.8843
1
 
 
 
 
2
Cp  
M
C
 
 2


1
1
R  
 Cp   
g c RT 0
  2
 1  

 
 R
  

M 1  0.815
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Calculation of Density
ρ st,1
ρ0 ,1


 1 





2
M1

 Cp

 1 
2
 R

 C p
  
  R
PEMP
RMD510
 
 1
 
 0.729
The stagnation density at rotor inlet can be assumed equal to that at nozzle
inlet for this preliminary design
ρ0 ,1  p 0 ,1 RT0 ,1   300  10 3 286 .96  120 
 0 .8712 kg m 3
 ρ st,1  0.
0 6353 kg
k m3
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Rotational Speed
PEMP
RMD510
m  C r,1 ρ st,1π d1 b1  C r,1 ρ st,1 π d12 b1 d 1 
0 .5
d 
181.11  0 .6353  π  0 .072
2
1
d 1  138 .6 mm
b1  9 .98 mm
2 πN d 1
u1 
60 2
60  u1
N 
 80 560 rpm
πd 1
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PEMP
RMD510
Final Design
 Having found the basic geometric
parameters of the rotor (and inlet nozzle
vanes), the blade profiles can be generated by
Inlet
Exit
using analytic equations
using

i commercial
i l software,
f
like
lik
BLADEGEN
 The
final design has to be arrived at through
iteration between structural integrity
(considering aerodynamic and thermal
loading) and aerodynamic performance.
Finally, the mechanical design should be
carried out, taking due care of the component
manufacturing
g and assemblyy requirements.
q

14
Nozzle
vane
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Exducer
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PEMP
RMD510
Design of Turbocharger
(Based on Specific Speed)
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Schematic of a Turbocharger
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PEMP
RMD510
20
Turbocharger Components
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PEMP
RMD510
21
Working of Turbocharger
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PEMP
RMD510
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PEMP
RMD510
Turbocharger Design Data
Compressor
Turbine
1.0
1.04
Inlet stagnation
g
temperature,
p
,K
300 ((T0,1
0 1)
800 ((T0,4
0 4)
Inlet stagnation pressure, N/m2
1*105 (P0,1)
Find Engine back pressure (P0,4)
Outlet static pressure, N/m2
2* 105(Pst,3)
1.2* 105 (Pst,7)
Air
Combustion
Co
bust o products
p oducts 100%
00%
theoretical air
Cp J/(kg K ) & ( Cp /R )
1010 (3.52)
1172 (4084)
Blade angle
g at periphery
p p y
30° (2)
0 ° (5)
Specific speed, Ns
0.628
--
dhb,1/ dsh,1
0.60
--
0.82 (p,ts,1-3
0.8
p ts 1 3)
0.82 (p,ts,4-7
0.8
p ts 4 7)
Flow angle at rotor exit, c2 (deg)
60
0
Flow angle at rotor inlet, c1 (deg)
0
70
Number of rotor blades,
blades Z
17
13
0.96 (p,tt,1-2)
0.96 (p,tt,5-6)
Mass flow rate, kg/s
Fluid
ud
Polytropic
o y op c efficiency
e c e cy
Polytropic efficiency
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Calculations Planes
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PEMP
RMD510
24
Wiesner’s Correlation
PEMP
RMD510
This correlation, defining slip factor, , can be used to calculate
the number of blades, Z, in the radial turbine as well as in the
radial
di l compressor.
cos β
 Cu,1,ac 
1
σw  
  1
0
.
7
C
u
u,
1
,tl
tl
Z


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PEMP
RMD510
Compressor Design Calculations
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Compressor Velocity Triangles
PEMP
RMD510
u2
CCu,2,tl
u,2,tl
Cu,2
Outlet Velocity Triangle
Cr,2 W2
c2=60
60
2=30
30
ush,1
Cx,sh,1
x sh 1
14
h1
w,sh,1 Wsh,1
Inlet Velocity Triangle
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Enthalpy Rise
 R

  C p
 1

 η p,c,ts

PEMP
RMD510



T0 ,3  p 0 ,3 

 
T0 ,1  p 0 ,1 
p 0 ,3  p st,3 when η p,c,ts is used
T0 ,3
 2 0 .3484  1.2732
T0 ,1
ΔT 0 ,1 3  0 .2732  300  81.95 K
C pc  1010 J/kgK
Therefore,
and
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Δh 0 ,1 3  82722 J/kg
g c Δh0 ,13 3 4  4879 .9
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Inlet Volume Flow Rate
PEMP
RMD510
Guess inlet axial velocity
First iteration: 110 m/s
Second iteration: 127.3 m/s (all second iteration values are in parenthesis)
Cx
110

 0 .375 0 .434
293 .41
g c RT 0 ,1

For C p R  3 .52 , M 1  0 .32 0 .371 
C p R 1 




2
ρ0
M

 1 

ρ st
Cp

 1  
2 

 R


 1.0520 1.0703 
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From slide 15
29
Rotational Speed
PEMP
RMD510
p0 ,1
105

 1.1616 kg/m3
ρ0 ,1 
R T0 ,1 286.96  300
ρst,1  1.1042 kg/m3 ( 1.0853 )
m  ρ V
st,1 1
V1  0.9056 m 3 /s  V1  0.9516
V  0.9214 m /s,
V1  0.9599
60 N s g c Δh0 
N
2π V
 30767 rev/min 30500
3
1
34

1
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Compressor Outlet Velocity Diagram
PEMP
RMD510
u2
From Wiesner’s correlation (slide 25)
CCu,2,tl
u,2,tl
Cu,2
cos β2
Cu,ac
 σw  1
 0.872
0 .7
Cu,tl
Z
Cr,2 W2
c2=60
2=30
For cos β2  cos 30 , Z  17
1
1
Cu,2  tan β2
1

   0.676  ψ
u2
 tan αc 2 σ w 
0 .5
 g c Δh0 
 82772 
 u2  
 

 0.676 
 ψ 
d 2  60 u2 /N  219.2 mm
14
0 .5
 350.0 m/s
/
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PEMP
RMD510
Inlet Velocity Diagram
Th procedure
The
d
to
t select
l t minimum
i i
Wsh,1 is
i as follows
f ll
1. Choose a value of d sh,1
2 Calculate u sh,1  Nπ / 60d sh,1
2.


2
2
3. Calculate Aa  πd sh,
1 / 4 1  0.6

4 Calculate m RT0 ,1 /Aa p0 ,1
4.




2
m RT0 /g
/ c
M
M

1 
5. from the relation

AP0
 Cp 
R 
 1 
1
 2
calculate M1
Cp 
 R

6. Calculate  pst,1 /p0 ,1   pst,1  C x,1  Wsh,1
 Cp 

1 
 R 
This pprocedure is given
g
in tabular form in Slide 33,, in which the second iteration
values are given in brackets. The optimum value of dsh,1 is found to be 120 mm.
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PEMP
RMD510
Calculation of Optimum Shroud Parameter
dsh,1 (mm)
100
125
120
ush,1(m/s)
= 1610.97 dsh,1
(= 1575.22 dsh,1)
161.10
(157.22)
201.37
(199.64)
193.32
(191.65)
Aa (m2 )  0.5027dsh2 ,1 103
5 026
5.026
7 854
7.854
7 2389
7.2389
0.5838
0.3736
0.4053
0.61
0.34
0.37
0.836
0.944
0.934
204 93
204.93
116 06
116.06
127 31
127.31
260.7
(258.5)
232.4
(230.9)
231.5
(230.1)

m RT0 ,1 /A p0 ,1
M1
ρ st, 1 /ρ 0 ,1
C x,1 ( m/s ) 
0 .86088
Aa  ρ st,1 /ρ 0 ,1 
Wsh,1  Cx2,1  ush2 ,1
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Impeller-Diffuser Interface
PEMP
RMD510
 The minimum value of Wsh,1 is found to be 230.1 m/s.
 Hence, the de Haller velocity ratio, W2 / Wsh,1= 0.83.
 This should not lead to diffusion induced separation.
Impeller-Outlet and diffuser-inlet width, b2:
C2  ψu 2 sin αc,2  274.1 m/s
T0 ,2  381.95 K
C2
g c RT0 ,2  0.8281
M 2  0.740
ρst,2
 0.771
ρ0 ,2
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Inducer Hub-Tip Ratio
PEMP
RMD510
 Find
Fi d the
th rotor-outlet
t
tl t stagnation
t
ti pressure using
i the
th rotor
t efficiency
ffi i
 C
 p
 R
 




η p,c,tt,1 2




p0 ,2  T0 ,2 

 

p0 ,1  T0 ,1 
5
2
Therefore,, p0 ,2  2.262  10 N/m
ρ0 ,2  2.0635 kg/m 3
3
.
ρ st,

1
5909
kg/m
g
st 2
C r,2  C 2 cos 60   137 .1 m/s

b2  m πd 2 ρst,2C r,2   6.69 mm
Inducer hub diameter can be determined from hub-tip ratio
d hb,
hb 1
 0.60  d hb,1  0.60  120  72 mm
d sh,1
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Radial Diffuser Stability
PEMP
RMD510
C2 d 2 2 ρst,2
Re,2 
μst,2
for mean Tst,2  320 K
μ  2.020 10 5 Ns/m 2
Re,2  2.44 106
b2 r2  0.061
From the Stability limits in Jansen’s curves
b 2 / r2
0.125
0 08
0.08
0.061
14
(r3 / r2)mx
4.0
29
2.9
2.0 (by interpolation)
80 percent of 2.0 is 1.6
 d3 =11.6
6 x 219
219.22 = 350 mm
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Radial Diffuser Stability (… contd.)
PEMP
RMD510
Stable operating range of vaneless diffusers (Jansen, 1964)
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PEMP
RMD510
Turbine Design Calculations
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Turbine Design Calculations
Turbine Rotor Diameter:
Δh0 ,e
The turbine has
slightly increased
mass flow,
flow because
of fuel addition, and
must supply windage
and
d bearing
b i power in
i
addition to
compressor power.
PEMP
RMD510
2
u
1
02
.


5 Cu,5

82772 J/kg 

g c u5
1.04 
cos β5
Cu,5
 1
Z e0 .7
Cu,u 5 ,tltl
Cu,5 ,tl  u5 and β5  0 ; Z e  13
C u,5 ,ac
 0 .834
u5
1.02 82772 .4
u 
*
1.04 0 .834
u 5  312 .0 m/s
/  d 5  198 .1 mm
2
5
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Turbine Design Calculations
PEMP
RMD510
Turbine Pressure Ratio:
m e Δh 0 ,e  1.02 m c Δh 0 ,c
ΔT 0 ,e
1010
1
.
02

1
.
0


 81 .953  69 .27 K
1.04
1172
p 0 ,in  T0 ,in
 
p 0 ,,ex  T0 ,,ex
p 0 ,ex




 C p
 
  R
 800 


 730 .73 
 p st,ex
 1

 η p,e,ts
 C p
 
  R



 1

η
 p,e,ts



 1.570
 p 0 ,in  1.570  1.2  10 5  1.884  10 5 N/m
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40
Turbine Design Calculations
PEMP
RMD510
N l Outlet
Nozzle
O l Velocity:
Vl i
The following parameters have been calculated:
Blade speed = 312.0 m/s ; Work coefficient,  = 0.834 ; Nozzle angle = 70°
Cu,1 ψu1
tan 70 

Cr,1 Cr,1

Cr,1 0.834
φ

 0.3035
u1
tan 70
Cr,1  94.70 m/s
Cr,5
cos 70 
 C5  276.89 m/s
C5
C5
276.89

 0.5779
g c RT0
286.96*800
with C p R  4 .084  M  0 .513
14
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41
Turbine Design Calculations
PEMP
RMD510
C p R 1

ρ0 
M
 1.137
 1 

ρ st  2 C p R   1 
1.884  10 5
 0 .8207 kg/m 3  ρ st,5  0 .7215 kg/m 3
ρ0 ,5 
286 .96  800
2


The mass flow rate is 1.04 kg/s
Hence, the volume flow rate is 1.441 m3/s,
and the enthalpy drop is 81180 J/kg.
Vin
2 πN
Specific speed, N s 
60  g c Δh 0 3 4

14
2π  30500
1441

 0.797
0 797
3 4
60
81180 
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42
Velocity Function vs Mach Number for Perfect Gases
14
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PEMP
RMD510
43
Exit Width to Diameter Ratio
PEMP
RMD510
The optimum specific speed for radial-inflow turbine is about 0.65. The
specific speed of this turbine is high. We might expect that there might be a
problem arriving at an exducer in which the outlet diameter reduce.
Turbine inlet blade width to diameter ratio is calculated using the relation
 b1  N s2 tan αc1ψ 3 2 N s2 tan αc1ψ 1 2
  

4πψ
4π
 d1 
b5 N s2 tan αc 5ψ 1 2


d5
4π

0.797 

2
tan 70 0.834
 0.1269
4π
 1 7.9
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44
Optimum Specific Speed
Distribution of losses along envelope of
maximum total
total-to-static
to static efficiency
(Rohlik 1968)
14
PEMP
RMD510
Typical performance of radial turbine
(Rohlik 1968)
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45
Turbine Design Calculations
PEMP
RMD510
Outlet Static Density:
 The outlet static pressure is specified together with the stagnation
temperature
temperature.
 The Mach number here is low, and it will be sufficiently accurate to
guess the static temperature.
pst,6  1.2 105 N/m 2
T0 ,6  730.73 K
Tst,6  725 K
guess
1.2 105
ρst,6 
 0.577 kg/m 3
286.96  725
ρst,5 ρst,6  1.257 
14
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46
PEMP
RMD510
Results
The results of the calculations, made for an exducer hub-shroud ratio
of 0.3, are tabulated below:
---
0.8
0.9
1.0
---
0.935
0.881
0.836
---
1.15
1.208
1.314
αw,sh,6  tan1 d sh,6 d5  Cx,6 Cr,5 φ
Degrees
75.44
72.77
70.05
αw,hb,6  tan
t 1 Λdsh,6 d5  Cx,6 C5 φ
Degrees
49 12
49.12
44 06
44.06
39 51
39.51
Whb,,6 W5
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47
Diameter Ratio
PEMP
RMD510
 The diameter ratio and the relative flow acceleration are both
marginal at 0.8 velocity ratio. Both are satisfactory at a velocity ratio
of 0.9.
 We select
d sh,6
 0.881
d5
 The flow angles give a guide to the exducer blade angles.
 The exducer angles should be set to somewhat higher values to
allow for flow deviation.
 An approximate estimate of this deviation would be 33º at the
shroud and 5º at the hub.
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48
Turbine Hub and Tip Dimensions
PEMP
RMD510
d sh,6  0.881*198.1
 174.5 mm
2
34
 d hb , 6 
Ψ N s1
2


1   1 


πφ
φ
 d sh , 6 
0.8343 4  0.797
 0.712

π  0.3035
 2  1.0.506944    0.702
d hb,6  0.702 174.5  122.49 mm
b5
 0.1269
d5
b5  0.1269 198.1  25.138 mm
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49
Data for Modeling the Compressor
PEMP
RMD510
Inlet Velocity Triangle
At Shroud
At Hub
uhb,1
Cx,hb,1
Whb,1
ush,1 =191.65 m/s
uhb,1 = 114.98 m/s
Cx,sh,1 = 127.3
127 3 m/s
Cx,hb,1 = 127.3 m/s
Wsh,1= 230.1
Whb,1 = 171.53
w,sh,1 = 56.4º
14
w,hb,1
w,hb,1 = 42.1º
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50
Data for Modeling the Compressor
Outlet Velocity Triangle
PEMP
RMD510
=350 m/s
=271
271.3
3 m/s
=236.6 m/s
C2=274.1 m/s
=137.1 m/s
158.08 m/s
137.1
78.7
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51
Data for Modeling Turbine
PEMP
RMD510
Inlet Velocity Triangle
act
C5=276.89 m/s
c1=70°
w5=28.68°
Cr,5=94.7
W5=107.95 m/s
260.19
U5 =312.0 m/s
14
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52
Modeling Using CFX
PEMP
RMD510
Creating a Blade:
Radial Impeller Configuration
14
Initial Angle/Thickness Dialog
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53
Geometric Model - Compressor
PEMP
RMD510
Input Parameters:
Blade
Fluid Domain
14
Dsh = 14 mm
Dhb = 8.5 mm
D2 = 25 mm
D3 = 30 mm
2 = 30
Z = 10
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54
Geometric Model - Compressor
Blade
Fluid Domain
14
PEMP
RMD510
Input Parameters:
Dsh = 21 mm
Dhb = 5.25 mm
D5 = 30 mm
c5 = 70
Z=9
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55
3-D CAD Models
PEMP
RMD510
Compressor
Turbine
14
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56
Session Summary
PEMP
RMD510
• A procedure for design of radial turbines based on optimum
specific
ifi speedd is
i discussed.
di
d
• Salient constructional features and working principle of a
turbocharger are presented.
presented
• The design of radial machines is explained through step by step
design of compressor and radial turbine modules of a typical
turbocharger
14
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57