1

Centrifugal Compressors

2

Main Topics

• Introduction

• Impeller Design

• Diffuser Design

• Performance

• Examples

3

4

Introduction

• Slightly less efficient than axial-flow compressors• Easier to manufacture• Single stage can produce a pressure ration of 5 times that of a

single stage axial-flow compressor• Application: ground-vehicle, power plants, auxiliary power units• Similar parts as a pump, i.e. the impeller, the diffuser, and the

volute• Main difference: enthalpy in place of pressure-head term• Static enthalpy (h) and total (stagnation) enthalpy (ho)

5

EULER EQUATION

Torque T = m (Cθ2r2 – Cθ1r1)

Power P = Tω = m (U2Cθ2 – U1Cθ1)

6

RELAVANT UNIT

7

Introduction• Isentropic Stagnation State

2

2

0

Vhh +=

8

Introduction

( ) ( )

kRTc

T

T

k

kRTTTChhV

Vhh

p

=

−

−=−=−=

+=

2

000

2

2

0

11

222

2

• For an ideal gas with constant specific heat

9

Introduction

20

022

2

02

2

2

11

11

2

11

2

Mk

T

T

T

T

kM

c

V

T

T

k

cV

−+=

−

−==

−

−=

• For an ideal gas with constant specific heat

10

Introduction

( ) ( )

( ) ( )

( ) ( )1120

120

0

11

00

1

0

2

11

2

11

,

−

−

−−

−+=

−+=

=

=

k

kk

kkk

Mk

Mk

p

p

T

T

p

p

T

T

ρρ

ρρ

• For an isentropic process

11

Introduction

( )

( )11

0

*

1

0

*

0

*

1

2

1

2

1

2

−

−

+=

+=

+=

k

kk

k

kp

p

kT

T

ρρ

• For the critical state (M=1)

12

Introduction

13

Introduction

( ) 220103 ′=−= tm VUhhE η

s

1

2

3

p1

p2

p3

p03

0302

01

p02

i

i’h

2

21V

14

Introduction

• The Specific Shaft Work into the Compressor

The specific shaft work

0.96

m

m

E η

η

=

=

15

Introduction

• Compressor Efficiency:– The ratio of the useful increase of fluid energy divided by the

actual energy input to the fluid

– The useful energy input is the work of an ideal, or isentropic, compression to the actual final pressure P3

16

Introduction

[ ]( )

−

=

−=−=−

1

1

1

01

0301

010101

kk

p

ipii

p

pTC

TTTChhE

17

Introduction

0103

01

TT

TT

E

E iic −

−==η

• The Compressor Efficiency

• No external work or heat associated with the diffuser flow, i.e.

03020302 , TThh ==

18

Introduction

1

01

'22

01

03 1

−

+=

kk

mp

ct

TC

VU

p

p

ηη

• The Overall Pressure Ratio

• The compressor efficiency from experimental data• Slip exists in compressor impeller

2'2 tst VV µ=

19

Introduction

−

−=22 cot1

163.01

βϕπµ

Bs n

• The Slip Coefficient (Stanitz Equation)

• More relations in Appendix E• But, Stanitz equation is more accurate for the practical

range of vane angle; i.e.

02

0 9045 << β

20

Introduction

• Total pressure ratio from:– Ideal velocity triangle at the impeller exit– The number of vanes– The inlet total temperature– The stage and mechanical efficiencies

• Mechanical efficiency accounts for– Frictional losses associated with bearing, seal, and disk

friction– Reappears as enthalpy in the outflow gas

21

Impeller Design

• The impeller design starts with a number of unshrouded blades (Pfleiderer)

• Flow is assumed axial at the inlet• Favorable to have large tangential velocity at outlet

(Vt2’)

• Vanes are curved near the rim of the impeller (β2 <90o)

• But, they are bent near the leading edge to conform to the direction of the relative velocity Vrb1 at the inlet

22

Impeller Design

• The angle β1 varies over the leading edge, since V1 remains constant while U1 (and r) varies (V1 assumes uniform at inlet)

• At D1S, the relative velocity Vrb1=(V12+U1

2)0.5 and the corresponding relative Mach number MR1S are highest

• For a fixed set of, N, m,Po1, and To1, the relative Mach number has its minimum where β1S is approximately 32o (Shepherd, 1956)

23

Impeller Design

• Choose a relative Mach number at the inlet

( )

SSR

SRSrb

Ma

VM

Mk

TT

kRTa

aMV

111

11

21

011

11

111

sin :noMach inlet Absolute

211 :eTemperatur Static

:Speed Acoustic

β==

−+=

=

=

24

Impeller Design

011

011

32cos

32sin

SrbS

Srb

VU

VV

=

=• Calculation of V1 and U1S

• Calculation of the shroud diameter

N

UD S

S1

1

2=

25

Impeller Design

21

11

211

4

−=

V

mDD SH πρ

• Calculation of the hub diameter by applying the mass flow equation to the impeller inlet

• Calculation of density from the equation of state of a perfect gas

1

11 RT

p=ρ

26

Impeller Design

• Calculation of static temperature and static pressure

( )

( )( )1

21

011

21

011

211

211−

−+

=

−+=

kk

Mk

pp

Mk

TT

27

Impeller Design

= −

HH U

V

1

111 tanβ

• The fluid angle at the hub

• The vane speed at the hub

21

1H

H

NDU =

28

Impeller Design

1 1

12

13

4

12

12 1

4

Inlet flow rate:

Output head H:

Dimensional specific speed:

( from Table 3 in appendix A)

i

s

SS

Q m

H E g

NQN

H

D QD D

H

ρ==

=

=

&

• The outlet diameter D2

29

Impeller Design

( )9.085.0 : velocityl tangentiaideal The

: velocityl tangentiaactual The

:nsferEnergy tra The

:Aappendix in 3 Table From

'22

2'2

C

−==

=

=

ss

tt

t

C

im

VV

UEV

EE

µµ

ηη

η

• The ideal and actual tangential velocities

30

Impeller Design

( )

−

−=

=

≤≤=−=

−

22

2

212

2222

222

cot1

163.01

tan

35.023.0

βϕπµ

β

ϕϕ

Bs

trb

nrb

nrb

ttrb

n

V

V

UV

VUV

• The vane angle and the number of vanes

31

Impeller Design

( )6.05.0 1

1 ≤≤−−= χ

ηηχ

C

I

• The impeller efficiency

0102

01

TT

TTiI −

−= ′η

32

Impeller Design

pC

VTT

2

22

022′−=

• The static temperature T2 is used to determine density at the impeller exit

Vr

mb

n2222 2πρ

&=

33

Impeller Design

• The optimal design parameters by Ferguson (1963) and Whitfield (1990) from Table 5.1

• Table 5.1 Should be used to check calculated results for acceptability during or after the design process

34

Diffuser Design

• A vaneless diffuser allows reduction of the exit Mach number

• The vaneless portion may have a width as large as 6 percent of the impeller diameter

• Effects a rise in static pressure• Angular momentum is conserved and the fluid path is

approximately a logarithmic spiral• Diffuser vanes are set with the diffuser axes tangent to the

spiral paths with an angle of divergence between them not exceeding 12o

35

Diffuser Design

36

Diffuser Design

• Vanes are preferred where size limitations matter

• Vaneless diffuser is more efficient

• Number of diffuser vanes should be less than the number of impeller vanes to:– Ensure uniformness of flow

– High diffuser efficiency in the range of φ2 recommended

37

Diffuser Design

• The mass flow rate at any r (in the vaneless diffuser)

( )n

nr

Vrbm

rrrVV

ρπ2

32

=≤≤=

&

38

Diffuser Design

222

constant

nn

n

VrrV

rV

ρρρ

==

• For constant diffuser width b

• The angular momentum is conserved in the vaneless space

22 ′= tt VrrV

39

Diffuser Design

12 >′M• Typically, the flow leaving the impeller is supersonic

• Typically, the flow leaving the vaneless diffuser is subsonic

0.13 <M

40

Diffuser Design

αcosVVV nr ==

• Denote * for the properties at the radial position at which M=1 (The absolute gas angle, α, is the angle between V and Vr)

• The continuity equation

**** coscos αραρ VrrV =

41

Diffuser Design

*

*tantan

ρα

ρα =

• The angular momentum equation

• Dividing momentum by continuity relations

*** sinsin αα VrrV =

42

Diffuser Design

2

0

1

**

21

1 ,

Mk

TT

T

Tk

−+=

=−

ρρ

• Assuming an isentropic flow in the vaneless region

• For M=1

1

2 0*

+=

k

TT

43

Diffuser Design

( )11

2* 2

11

1

2−

−+

+=

k

Mk

kρρ

• Substituting in the density relation

• Substituting in the absolute gas angle relation

( )11

2*

2

11

1

2tantan

−−

−+

+=

k

Mk

kαα

44

Diffuser Design

21

2**

21

***

**

2

2

2

11

1

2

sin

sin

sin

sin

−

′

′

−+

+=

===

==

Mk

kM

r

r

T

TM

a

a

a

V

V

V

r

r

MM

αα

αα

αα• The angle α* is evaluated by

45

Diffuser Design

21

222

22

**

2

11

1

2

sin

sin−

′′

−+

+= M

k

kM

r

r

αα

• The radial position r* is determined by

• The angle α3* is evaluated by

( )112

3*

3 2

11

1

2tantan

−−

−+

+=

k

Mk

kαα

46

Diffuser Design

21

233

33

**

2

11

1

2

sin

sin−

−+

+= M

k

kM

r

r

αα

• Finally r3 is determined by

• The volute is designed by the same methods outlined in chapter 4

47

Performance• Typical compressor characteristics

cte.01

=T

N

01

01

p

Tm&

02

01

p

p Surge line

.cte=ηmaxη

Choke line

C B

A

48

Performance

• The sharp fall of the constant-speed curves at higher mass flows is due to choking in some component of the machine

• The low flows operation is limited by the phenomenon of surge

• Smooth operation occurs on the compressor map at some point between the surge line and the choke line

• Chocking is associated with the attainment of a Mach number of unity

49

Performance

• In the stationary passage of the inlet The sharp fall of the constant-speed curves at higher mass flows is due to choking in some component of the machine

• The low flows operation is limited by the phenomenon of surge

• Smooth operation occurs on the compressor map at some point between the surge line and the choke line

• Chocking is associated with the attainment of a Mach number of unity

50

Performance

• In the stationary passage of the inlet or diffuser for a Mach number of unity

a =

a kRT=• The temperature at this point

( ) 20

11

2

kT T M

−= +

51

Performance

• By setting M=1

a =

12

t tt

km A p

RT

= ÷

&

• The chocking (maximum) flow rate

*0

2

1 tT T Tk

= = +

52

Performance

• The throat pressure (isentropic process)

a =

2 21 1

01 2 2rbV U

h h= + −

• The chocked flow rate in impeller (use relative velocity instead of absolute velocity)

( )1k k

tt in

in

Tp p

T

−

= ÷

53

Performance

• The critical temperature

a =

( )( )

11

2 12 2

0101 01

21

1 2

k

k

tp

k Um A p

RT k C T

+−

= + ÷ ÷ ÷+ &

• The throat mass flow rate (isentropic process)

( )2

* 01

01

21

2 1 tp

TUT T

C T k

= + = ÷ ÷ +

54

Performance

• The chocked mass flow rate in stationary components is independent of impeller speed

• The point A in the characteristic curve represents a point of normal operation

• An increase in flow resistance in the connected external flow system results in decrease in and increase in

• Causes increase in head or pressure• Further increase in external system produces a decrease in

impeller flow (beyond point C) and surge phenomena results

2nV

2tV

55

Performance

• The at some point in the impeller leads to change of direction of and an accompanying decrease in head.

• A temporary flow reversal in the impeller and the ensuing buildup to the original flow condition is known as surging.

• Surging continues cyclically until the external resistance is removed.

• Surging is an unstable and dangerous condition and must be avoided by careful operational planning and system design.

2rbV

56

Example 5.1

57

Example 5.1

58

Example 5.1

59

Example 5.1

60

Example 5.1

61

Example 5.1

62

Example 5.1

63

Example 5.2

64

Example 5.2

65

Example 5.2

66

Example 5.3

67

Example 5.3

68

Example 5.3

69

Example 5.3

70

Example 5.3

71

Example 5.3

72

Example 5.3

73

Example 5.3

74

Example 5.3

75

Example 5.3

76

Practice- Sheet 3

77

Practice- Sheet 3

78

TURBOMACHINERY BASICSCENTRIFUGAL COMPRESSOR

Hasan Basri

Jurusan Teknik MesinFakultas Teknik – Universitas Sriwijaya

Phone: 0711-580739, Fax: 0711-560062Email: hasan_basri@unsri.ac.id

79

80

EULER EQUATION

Torque T = m (Cθ2r2 – Cθ1r1)

Power P = Tω = m (U2Cθ2 – U1Cθ1)

81

RELAVANT UNIT

82

PREWHIRL OR PREROTATION

83

PART-LOAD CONTROL

84

SLIP FACTOR

85

IMPELLER EXIT BLADE ANGLE

86

EFFICIENCY

87

ROTHALPY & TOTAL ENTHALPY

88

ENERGY TRANSFER

89

SPECIFIC SPEED

90

91

92

93

VANED DIFFUSER

94

VANED DIFFUSER

95

LSD (Low Solidity Diffuser)

96

AXIAL VANED DIFFUSER

97

VOLUTE/SCROLL

98

PERFORMANCE MAP

99

PERFORMANCE MAP

100

CORRECTED CONDITIONS

101

IMPELLER INCIDENCE

102

DIFFUSER INCIDENCE

103

SPLITTER BLADES

104

SPLITTER BLADES

105

IMPELLER BLADE GEOMETRY

106

SOME ANGLES

107

IMPELLER CFD

108