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- 1. Centrifugal Compressors 1
- 2. Main Topics • • • • • Introduction Impeller Design Diffuser Design Performance Examples 2
- 3. 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) 4
- 5. EULER EQUATION Torque T = m (Cθ2r2 – Cθ1r1) Power P = Tω = m (U2Cθ2 – U1Cθ1) 5
- 6. RELAVANT UNIT 6
- 7. Introduction • Isentropic Stagnation State 2 V h0 = h + 2 7
- 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. 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. 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. 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. Introduction 12
- 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. Introduction • The Specific Shaft Work into the Compressor The specific shaft work = E ηm ηm = 0.96 14
- 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. Introduction Ei = hi − h01 = C pT01 [ Ti T01 − 1] p 03 = C pT01 p01 ( k −1) k − 1 16
- 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Impeller Design • The impeller efficiency 1 −η I χ= 1 − ηC ( 0.5 ≤ χ ≤ 0.6) Ti′ − T01 ηI = T02 − T01 31
- 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. 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. 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. Diffuser Design 35
- 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. Diffuser Design • The mass flow rate at any r (in the vaneless diffuser) ( r2 ≤ r ≤ r3 ) Vr = Vn & m = 2πrbρVn 37
- 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. 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. 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. 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. 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. 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. 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. 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. 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. Performance • Typical compressor characteristics ηmax C B A p01 p02 η = cte. Surge line Choke line N = cte. T01 & m T01 p01 47
- 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. 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. 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. 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. 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. 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. 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. 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. Example 5.1 56
- 57. Example 5.1 57
- 58. Example 5.1 58
- 59. Example 5.1 59
- 60. Example 5.1 60
- 61. Example 5.1 61
- 62. Example 5.1 62
- 63. Example 5.2 63
- 64. Example 5.2 64
- 65. Example 5.2 65
- 66. Example 5.3 66
- 67. Example 5.3 67
- 68. Example 5.3 68
- 69. Example 5.3 69
- 70. Example 5.3 70
- 71. Example 5.3 71
- 72. Example 5.3 72
- 73. Example 5.3 73
- 74. Example 5.3 74
- 75. Example 5.3 75
- 76. Practice- Sheet 3 76
- 77. Practice- Sheet 3 77
- 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
- 80. EULER EQUATION Torque T = m (Cθ2r2 – Cθ1r1) Power P = Tω = m (U2Cθ2 – U1Cθ1) 80
- 81. RELAVANT UNIT 81
- 82. PREWHIRL OR PREROTATION 82
- 83. PART-LOAD CONTROL 83
- 84. SLIP FACTOR 84
- 85. IMPELLER EXIT BLADE ANGLE 85
- 86. EFFICIENCY 86
- 87. ROTHALPY & TOTAL ENTHALPY 87
- 88. ENERGY TRANSFER 88
- 89. SPECIFIC SPEED 89
- 90. 90
- 91. 91
- 92. 92
- 93. VANED DIFFUSER 93
- 94. VANED DIFFUSER 94
- 95. LSD (Low Solidity Diffuser) 95
- 96. AXIAL VANED DIFFUSER 96
- 97. VOLUTE/SCROLL 97
- 98. PERFORMANCE MAP 98
- 99. PERFORMANCE MAP 99
- 100. CORRECTED CONDITIONS 100
- 101. IMPELLER INCIDENCE 101
- 102. DIFFUSER INCIDENCE 102
- 103. SPLITTER BLADES 103
- 104. SPLITTER BLADES 104
- 105. IMPELLER BLADE GEOMETRY 105
- 106. SOME ANGLES 106
- 107. IMPELLER CFD 107
- 108. 108

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