Centrifugal Compressors

1
Main Topics
•
•
•
•
•

Introduction
Impeller Design
Diffuser Design
Performance
Examples

2
3
Introduction
• Slightly less efficient than axial-flow compressors
• Easier to manufacture
• Single stage can produce a pr...
EULER EQUATION
Torque T = m (Cθ2r2 – Cθ1r1)
Power P = Tω
= m (U2Cθ2 – U1Cθ1)

5
RELAVANT UNIT

6
Introduction
• Isentropic Stagnation State
2

V
h0 = h +
2

7
Introduction
• For an ideal gas with constant specific heat
2

V
h0 = h +
2

kRT  T0 
V = 2( h0 − h ) = 2C p ( T0 − T ) ...
Introduction
• For an ideal gas with constant specific heat
2

2c  T0 
V =
 − 1
k −1 T 
2
V
2  T0 
2
=M =
 − 1
2...
Introduction
• For an isentropic process

 T0 
 
T 

k ( k −1 )

 T0 
 
T 

p0
= ,
p

p0  ( k − 1) 2 
= 1 +...
Introduction
• For the critical state (M=1)
*

T
2
=
T0 k + 1
*

p  2 
=

p0  k + 1 

ρ  2 
=
ρ 0  k + 1

*

k...
Introduction

12
Introduction

E = η m ( h03 − h01 ) = U 2Vt 2′
p03
h

p02

02
i’

p3
03

p2

i

3

p1
2

V12

01
1

2
s

13
Introduction
• The Specific Shaft Work into the Compressor

The specific shaft work = E ηm

ηm = 0.96

14
Introduction
• Compressor Efficiency:
– The ratio of the useful increase of fluid energy divided by the
actual energy inpu...
Introduction

Ei = hi − h01 = C pT01 [ Ti T01 − 1]
 p 
 03 
= C pT01 

 p01 


( k −1)

k


− 1


16
Introduction
• The Compressor Efficiency

Ei Ti − T01
ηc = =
E T03 − T01
• No external work or heat associated with the di...
Introduction
• The Overall Pressure Ratio

p03  U 2Vt 2'η c 

= 1 +
p01  C pT01η m 



k k −1

• The compressor ef...
Introduction
• The Slip Coefficient (Stanitz Equation)

0.63π
µ s = 1−
nB



1


 1 − ϕ 2 cot β 2 



• More relat...
Introduction
• Total pressure ratio from:
–
–
–
–

Ideal velocity triangle at the impeller exit
The number of vanes
The in...
Impeller Design
• The impeller design starts with a number of
unshrouded blades (Pfleiderer)
• Flow is assumed axial at th...
Impeller Design
• The angle β1 varies over the leading edge, since V1
remains constant while U1 (and r) varies (V1 assumes...
Impeller Design
• Choose a relative Mach number at the inlet
Vrb1S = M R1S a1
Acoustic Speed :
Static Temperature :

a1 = ...
Impeller Design
• Calculation of V1 and U1S

V1 = Vrb1S sin 32

0

U1S = Vrb1S cos 32

0

• Calculation of the shroud diam...
Impeller Design
• Calculation of the hub diameter by applying the mass
flow equation to the impeller inlet

D1H

 2

4m ...
Impeller Design
• Calculation of static temperature and static pressure

T01
T1 =
2
1 + ( k − 1) M 1 2


p01
p1 = 

2
...
Impeller Design
• The fluid angle at the hub

β1H

 V1
= tan 
U
 1H
−1






• The vane speed at the hub

U 1H

ND...
Impeller Design
• The outlet diameter D2
&
Inlet flow rate: Q1 = m ρ1
Output head H:

H = Ei g
1

Dimensional specific spe...
Impeller Design
• The ideal and actual tangential velocities
From Table 3 in appendix A :

ηC

η m Ei
The Energy transfer ...
Impeller Design
• The vane angle and the number of vanes

Vrb 2t = U 2 − Vt 2

( 0.23 ≤ ϕ 2 ≤ 0.35)

Vrb 2 n = ϕ 2U 2
Vrb ...
Impeller Design
• The impeller efficiency

1 −η I
χ=
1 − ηC

( 0.5 ≤ χ ≤ 0.6)

Ti′ − T01
ηI =
T02 − T01
31
Impeller Design
• The static temperature T2 is used to determine density
at the impeller exit
2
2′

V
T2 = T02 −
2C p

&
m...
Impeller Design
• The optimal design parameters by Ferguson (1963)
and Whitfield (1990) from Table 5.1
• Table 5.1 Should ...
Diffuser Design
• A vaneless diffuser allows reduction of the exit Mach number
• The vaneless portion may have a width as ...
Diffuser Design

35
Diffuser Design
• Vanes are preferred where size limitations matter
• Vaneless diffuser is more efficient
• Number of diff...
Diffuser Design
• The mass flow rate at any r (in the vaneless diffuser)

( r2 ≤ r ≤ r3 )
Vr = Vn
&
m = 2πrbρVn
37
Diffuser Design
• For constant diffuser width b

ρrVn = constant
ρrVn = ρ 2 r2Vn 2
• The angular momentum is conserved in ...
Diffuser Design
• Typically, the flow leaving the impeller is supersonic

M 2′ > 1
• Typically, the flow leaving the vanel...
Diffuser Design
• Denote * for the properties at the radial position at which M=1
(The absolute gas angle, α, is the angle...
Diffuser Design
• The angular momentum equation

rV sin α = r V sin α
*

*

*

• Dividing momentum by continuity relations...
Diffuser Design
• Assuming an isentropic flow in the vaneless region

T  ρ 
= *
*
ρ 
T
 
• For M=1

k −1

,

T0
T=...
Diffuser Design
• Substituting in the density relation

ρ  2  k − 1 2 
=
M 
1 +
*
ρ
2

 k +1

1 ( k −1)

• Sub...
Diffuser Design
• The angle α* is evaluated by

α = α 2′
M = M 2′
r sin α
V V a
T 
= *=
= M * 
*
r sin α
V
aa
T 
*

...
Diffuser Design
• The radial position r* is determined by

 2  k − 1 2 
r sin α
= M 2′ 
M 2′ 
1 +
r2 sin α 2
2

...
Diffuser Design
• Finally r3 is determined by

 2  k − 1 2 
r sin α
= M3
M 3 
1 +
r3 sin α 3
2

 k +1 
*

*

−...
Performance
• Typical compressor characteristics

ηmax

C

B
A

p01
p02

η = cte.

Surge line

Choke line

N
= cte.
T01
&
...
Performance
• The sharp fall of the constant-speed curves at higher mass
flows is due to choking in some component of the ...
Performance
• In the stationary passage of the inlet The sharp fall of the
constant-speed curves at higher mass flows is d...
a=

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

a = kRT
• The temperature...
a=

Performance
• By setting M=1

 2 
T = T0 
= Tt

 k + 1
*

• The chocking (maximum) flow rate

1

 k 
&
m = At ...
a=

Performance
• The throat pressure (isentropic process)
k ( k −1)

 Tt 
pt = pin  ÷
 Tin 

• The chocked flow rate...
a=

Performance
• The critical temperature


U 2  2T01
T * = 1 +
= Tt
÷
 2C pT01 ÷( k + 1)



• The throat mass flow...
Performance
• The chocked mass flow rate in stationary components is
independent of impeller speed
• The point A in the ch...
Performance
• The at some point in the impeller leads to change of direction of
Vrb 2
and an accompanying decrease in head...
Example 5.1

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 5.2

63
Example 5.2

64
Example 5.2

65
Example 5.3

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
Practice- Sheet 3

76
Practice- Sheet 3

77
TURBOMACHINERY BASICS
CENTRIFUGAL COMPRESSOR
Hasan Basri
Jurusan Teknik Mesin
Fakultas Teknik – Universitas Sriwijaya

Pho...
79
EULER EQUATION
Torque T = m (Cθ2r2 – Cθ1r1)
Power P = Tω
= m (U2Cθ2 – U1Cθ1)

80
RELAVANT UNIT

81
PREWHIRL OR PREROTATION

82
PART-LOAD CONTROL

83
SLIP FACTOR

84
IMPELLER EXIT BLADE ANGLE

85
EFFICIENCY

86
ROTHALPY & TOTAL ENTHALPY

87
ENERGY TRANSFER

88
SPECIFIC SPEED

89
90
91
92
VANED DIFFUSER

93
VANED DIFFUSER

94
LSD (Low Solidity Diffuser)

95
AXIAL VANED DIFFUSER

96
VOLUTE/SCROLL

97
PERFORMANCE MAP

98
PERFORMANCE MAP

99
CORRECTED CONDITIONS

100
IMPELLER INCIDENCE

101
DIFFUSER INCIDENCE

102
SPLITTER BLADES

103
SPLITTER BLADES

104
IMPELLER BLADE GEOMETRY

105
SOME ANGLES

106
IMPELLER CFD

107
108
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pengetahuan tentang sentrifugal

  1. 1. Centrifugal Compressors 1
  2. 2. Main Topics • • • • • Introduction Impeller Design Diffuser Design Performance Examples 2
  3. 3. 3
  4. 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) 4
  5. 5. EULER EQUATION Torque T = m (Cθ2r2 – Cθ1r1) Power P = Tω = m (U2Cθ2 – U1Cθ1) 5
  6. 6. RELAVANT UNIT 6
  7. 7. Introduction • Isentropic Stagnation State 2 V h0 = h + 2 7
  8. 8. Introduction • For an ideal gas with constant specific heat 2 V h0 = h + 2 kRT  T0  V = 2( h0 − h ) = 2C p ( T0 − T ) = 2  − 1 k −1 T  2 c = kRT 2 8
  9. 9. Introduction • For an ideal gas with constant specific heat 2 2c  T0  V =  − 1 k −1 T  2 V 2  T0  2 =M =  − 1 2 c k −1 T  T0 k −1 2 = 1+ M T 2 2 9
  10. 10. Introduction • For an isentropic process  T0    T  k ( k −1 )  T0    T  p0 = , p p0  ( k − 1) 2  = 1 + M  p  2  ρ 0  ( k − 1) 2  = 1 + M  ρ  2  1 ( k −1 ) ρ0 = ρ k ( k −1 ) 1 ( k −1 ) 10
  11. 11. Introduction • For the critical state (M=1) * T 2 = T0 k + 1 * p  2  =  p0  k + 1  ρ  2  = ρ 0  k + 1  * k ( k −1 ) 1 ( k −1 ) 11
  12. 12. Introduction 12
  13. 13. Introduction E = η m ( h03 − h01 ) = U 2Vt 2′ p03 h p02 02 i’ p3 03 p2 i 3 p1 2 V12 01 1 2 s 13
  14. 14. Introduction • The Specific Shaft Work into the Compressor The specific shaft work = E ηm ηm = 0.96 14
  15. 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 15
  16. 16. Introduction Ei = hi − h01 = C pT01 [ Ti T01 − 1]  p   03  = C pT01    p01   ( k −1) k  − 1   16
  17. 17. Introduction • The Compressor Efficiency Ei Ti − T01 ηc = = E T03 − T01 • No external work or heat associated with the diffuser flow, i.e. h02 = h03 , T02 = T03 17
  18. 18. Introduction • The Overall Pressure Ratio p03  U 2Vt 2'η c   = 1 + p01  C pT01η m    k k −1 • The compressor efficiency from experimental data • Slip exists in compressor impeller Vt 2 ' = µ sVt 2 18
  19. 19. Introduction • The Slip Coefficient (Stanitz Equation) 0.63π µ s = 1− nB   1    1 − ϕ 2 cot β 2    • More relations in Appendix E • But, Stanitz equation is more accurate for the practical range of vane angle; i.e. 45 < β 2 < 90 0 0 19
  20. 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 20
  21. 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 21
  22. 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+U12)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) 22
  23. 23. Impeller Design • Choose a relative Mach number at the inlet Vrb1S = M R1S a1 Acoustic Speed : Static Temperature : a1 = kRT1 T1 = Absolute inlet Mach no : T01 1 + ( k − 1) M 12 2 V1 M 1 = = M R1S sin β1S a1 23
  24. 24. Impeller Design • Calculation of V1 and U1S V1 = Vrb1S sin 32 0 U1S = Vrb1S cos 32 0 • Calculation of the shroud diameter 2U1S D1S = N 24
  25. 25. Impeller Design • Calculation of the hub diameter by applying the mass flow equation to the impeller inlet D1H  2  4m   =  D1S −  πρ1V1    1 2 • Calculation of density from the equation of state of a perfect gas p1 ρ1 = RT1 25
  26. 26. Impeller Design • Calculation of static temperature and static pressure T01 T1 = 2 1 + ( k − 1) M 1 2   p01 p1 =   2 1 + ( k − 1) M 1 2  k ( k −1) 26
  27. 27. Impeller Design • The fluid angle at the hub β1H  V1 = tan  U  1H −1     • The vane speed at the hub U 1H ND1H = 2 27
  28. 28. Impeller Design • The outlet diameter D2 & Inlet flow rate: Q1 = m ρ1 Output head H: H = Ei g 1 Dimensional specific speed: Ns = NQ1 2 H 3 4 1 D2 = DS Q1 2 H 1 4 (DS from Table 3 in appendix A) 28
  29. 29. Impeller Design • The ideal and actual tangential velocities From Table 3 in appendix A : ηC η m Ei The Energy transfer : E= ηC The actual tangential velocity : Vt 2 ' = E U 2 Vt 2 ' ( µ s = 0.85 − 0.9) The ideal tangential velocity : Vt 2 = µs 29
  30. 30. Impeller Design • The vane angle and the number of vanes Vrb 2t = U 2 − Vt 2 ( 0.23 ≤ ϕ 2 ≤ 0.35) Vrb 2 n = ϕ 2U 2 Vrb 2 n β 2 = tan Vrb 2t −1 0.63π µs = 1 − nB   1    1 − ϕ cot β  2 2   30
  31. 31. Impeller Design • The impeller efficiency 1 −η I χ= 1 − ηC ( 0.5 ≤ χ ≤ 0.6) Ti′ − T01 ηI = T02 − T01 31
  32. 32. Impeller Design • The static temperature T2 is used to determine density at the impeller exit 2 2′ V T2 = T02 − 2C p & m b2 = 2πρ 2 r2V2 n 32
  33. 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 33
  34. 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 34
  35. 35. Diffuser Design 35
  36. 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 36
  37. 37. Diffuser Design • The mass flow rate at any r (in the vaneless diffuser) ( r2 ≤ r ≤ r3 ) Vr = Vn & m = 2πrbρVn 37
  38. 38. Diffuser Design • For constant diffuser width b ρrVn = constant ρrVn = ρ 2 r2Vn 2 • The angular momentum is conserved in the vaneless space rVt = r2Vt 2′ 38
  39. 39. Diffuser Design • Typically, the flow leaving the impeller is supersonic M 2′ > 1 • Typically, the flow leaving the vaneless diffuser is subsonic M 3 < 1.0 39
  40. 40. Diffuser Design • Denote * for the properties at the radial position at which M=1 (The absolute gas angle, α, is the angle between V and Vr) Vr = Vn = V cos α • The continuity equation ρrV cos α = ρ r V cos α * * * * 40
  41. 41. Diffuser Design • The angular momentum equation rV sin α = r V sin α * * * • Dividing momentum by continuity relations tan α tan α = * ρ ρ * 41
  42. 42. Diffuser Design • Assuming an isentropic flow in the vaneless region T  ρ  = * * ρ  T   • For M=1 k −1 , T0 T= k −1 2 1+ M 2 2T0 T = k +1 * 42
  43. 43. Diffuser Design • Substituting in the density relation ρ  2  k − 1 2  = M  1 + * ρ 2   k +1 1 ( k −1) • Substituting in the absolute gas angle relation  2  k − 1 2  tan α = tan α  M  1 + 2   k +1 −1 ( k −1) * 43
  44. 44. Diffuser Design • The angle α* is evaluated by α = α 2′ M = M 2′ r sin α V V a T  = *= = M *  * r sin α V aa T  * * 1 2  2  k − 1 2  r sin α =M M  1 + r sin α 2   k +1 * * −1 2 44
  45. 45. Diffuser Design • The radial position r* is determined by  2  k − 1 2  r sin α = M 2′  M 2′  1 + r2 sin α 2 2   k +1  * * −1 2 • The angle α3* is evaluated by  2  k − 1 2  tan α 3 = tan α  M 3  1 + 2   k +1  −1 ( k −1) * 45
  46. 46. Diffuser Design • Finally r3 is determined by  2  k − 1 2  r sin α = M3 M 3  1 + r3 sin α 3 2   k +1  * * −1 2 • The volute is designed by the same methods outlined in chapter 4 46
  47. 47. Performance • Typical compressor characteristics ηmax C B A p01 p02 η = cte. Surge line Choke line N = cte. T01 & m T01 p01 47
  48. 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 48
  49. 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 49
  50. 50. a= Performance • In the stationary passage of the inlet or diffuser for a Mach number of unity a = kRT • The temperature at this point  ( k − 1) 2  T = T0 1 + M  2   50
  51. 51. a= Performance • By setting M=1  2  T = T0  = Tt   k + 1 * • The chocking (maximum) flow rate 1  k  & m = At pt  ÷  RTt  2 51
  52. 52. a= Performance • The throat pressure (isentropic process) k ( k −1)  Tt  pt = pin  ÷  Tin  • The chocked flow rate in impeller (use relative velocity instead of absolute velocity) 2 rb1 2 1 V U h01 = h + − 2 2 52
  53. 53. a= Performance • The critical temperature  U 2  2T01 T * = 1 + = Tt ÷  2C pT01 ÷( k + 1)   • The throat mass flow rate (isentropic process) 1 ( k +1)   2( k −1) 2  2   k  U & m = At p01  1 + ÷ ÷  RT01   k + 1  2C pT01 ÷     2 53
  54. 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 Vn 2 Vt 2 • Causes increase in head or pressure • Further increase in external system produces a decrease in impeller flow (beyond point C) and surge phenomena results 54
  55. 55. Performance • The at some point in the impeller leads to change of direction of Vrb 2 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. 55
  56. 56. Example 5.1 56
  57. 57. Example 5.1 57
  58. 58. Example 5.1 58
  59. 59. Example 5.1 59
  60. 60. Example 5.1 60
  61. 61. Example 5.1 61
  62. 62. Example 5.1 62
  63. 63. Example 5.2 63
  64. 64. Example 5.2 64
  65. 65. Example 5.2 65
  66. 66. Example 5.3 66
  67. 67. Example 5.3 67
  68. 68. Example 5.3 68
  69. 69. Example 5.3 69
  70. 70. Example 5.3 70
  71. 71. Example 5.3 71
  72. 72. Example 5.3 72
  73. 73. Example 5.3 73
  74. 74. Example 5.3 74
  75. 75. Example 5.3 75
  76. 76. Practice- Sheet 3 76
  77. 77. Practice- Sheet 3 77
  78. 78. TURBOMACHINERY BASICS CENTRIFUGAL COMPRESSOR Hasan Basri Jurusan Teknik Mesin Fakultas Teknik – Universitas Sriwijaya Phone: 0711-580739, Fax: 0711-560062 Email: hasan_basri@unsri.ac.id 78
  79. 79. 79
  80. 80. EULER EQUATION Torque T = m (Cθ2r2 – Cθ1r1) Power P = Tω = m (U2Cθ2 – U1Cθ1) 80
  81. 81. RELAVANT UNIT 81
  82. 82. PREWHIRL OR PREROTATION 82
  83. 83. PART-LOAD CONTROL 83
  84. 84. SLIP FACTOR 84
  85. 85. IMPELLER EXIT BLADE ANGLE 85
  86. 86. EFFICIENCY 86
  87. 87. ROTHALPY & TOTAL ENTHALPY 87
  88. 88. ENERGY TRANSFER 88
  89. 89. SPECIFIC SPEED 89
  90. 90. 90
  91. 91. 91
  92. 92. 92
  93. 93. VANED DIFFUSER 93
  94. 94. VANED DIFFUSER 94
  95. 95. LSD (Low Solidity Diffuser) 95
  96. 96. AXIAL VANED DIFFUSER 96
  97. 97. VOLUTE/SCROLL 97
  98. 98. PERFORMANCE MAP 98
  99. 99. PERFORMANCE MAP 99
  100. 100. CORRECTED CONDITIONS 100
  101. 101. IMPELLER INCIDENCE 101
  102. 102. DIFFUSER INCIDENCE 102
  103. 103. SPLITTER BLADES 103
  104. 104. SPLITTER BLADES 104
  105. 105. IMPELLER BLADE GEOMETRY 105
  106. 106. SOME ANGLES 106
  107. 107. IMPELLER CFD 107
  108. 108. 108

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