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Lect- 11 · • In a multi-stage compressor,a small departure from the design point at the first...
Transcript of Lect- 11 · • In a multi-stage compressor,a small departure from the design point at the first...
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1
Lect- 11
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 2
Lect-11
In this lecture...
• Performance characteristics of axial flow compressors• Single stage characteristics• Multi-stage characteristics
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 3
Lect-11
Single stage performance characteristics
• Let us consider a typical axial compressor stage comprising of a set of rotor blades followed by a set of stator blades.
U
C1C2
V1 V2
Rotor Stator
U
C3
α3
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 4
Lect-11
Single stage performance characteristics
U
C1
C2
Ca
V1
V2
β1
β2α2
α1
ΔCw
Vw2
Vw1
Cw2
Cw1
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 5
Lect-11
Single stage performance characteristics
• From the above velocity triangles,
( )[ ]
( )2120
210
0
122
tantan1,
tantan Since,
tantan
βα
βα
αβ
+−==∆
+−=∆=
=−=
UC
UΔh
UCor
CUUΔhCUΔh
CCandCUC
aw
a
w
awaw
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 6
Lect-11
Single stage performance characteristics
• Change in the design mass flow rate affects Ca, change in rotor speed affects U.
• Change of either Ca or U changes the inlet angle β1 at which the flow approaches the rotor.
• The above equation shows that the blade performance depends upon the ratio Ca/U.
) , ,f( eperformanc Stage Thus,
.efficiency the and tcoefficien flow t,coefficien loading the of function a is eperformanc stage The
ηφψ=
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 7
Lect-11
Single stage performance characteristics
UC
Uh w∆
=∆
20
design
UCa
design
UCa
UCa
UCa
stηMeasured
Measured
1.0
( )2120 tantan1 βα +−==
∆UC
UΔh
UC aw
( )design21 tantan βα +1
Stage loading
Stage efficiency
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 8
Lect-11
Single stage performance characteristics
U
C1
V1
β1
V1
β1α1
Ca
design
operation Normal :conditionDesign
=
UC
UC aa
U
C1
V1
β1
V1
β1α1
Ca
U
C1
V1
β1
V1
β1α1
Ca
design
separation flow incidence Positive :conditiondesign -Off
<
UC
UC aa
design
separation flow incidence Negative :conditiondesign -Off
>
UC
UC aa
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 9
Lect-11
Multi-stage performance characteristics
• Let us know consider a multi-stage compressor. Inlet station is denoted by 1 and exit of the compressor by 2.
• Therefore the overall pressure ratio of the compressor is P02/P01.
• The compressor outlet pressure, P02, and the isentropic efficiency, ηC, depend upon several physical variables
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 10
Lect-11
Multi-stage performance characteristics
=
ΩΩ=
Ω=
0101
01
01
02
2
012
01
01
01
02
010102
,,
toreduces above theTherefore fixed. are and Also, tly.significan eperformanc affect thenot do and that assumecan wedesign,given aFor
design,,,,,
,parameters essdimensionl-non of In termsdesign,,,,,,,,(,
TN
PTm
fPP
RD
DRTD
DPRTm
fPP
D)RTPmfP
C
C
C
η
νγ
γνγ
γη
νγη
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 11
Lect-11
Multi-stage performance characteristics
( ) ( )( ) ( ) kPaPandKT
PP
TT
NmfPP
C
325.10115.288
andWhere,
,,
re. temperatuand pressureday standard theof in terms processedfurther is thisUsually,
day Std.01day Std.01
day Std.01
01
day Std.01
01
01
02
==
==
=
δθ
θδθη
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 12
Lect-11
Multi-stage performance characteristics
01
02
PP
δθm
η
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 13
Lect-11
Multi-stage performance characteristics
η
01
02
PP
δθm
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 14
Lect-11
Multi-stage performance characteristicsMulti-stage performance characteristics
• In a multi-stage compressor, a small departure from the design point at the first stage causes progressively increasing departure from design conditions from the first stage onwards.
• Thus, a small reduction in (ca/U)design at the first stage could lead to positive incidence separation at the last stage.
• Similarly, a small increase in (ca/U)design could lead to negative incidence separation in the last stage.
• The most extreme mismatching of the front and rear stages occur during starting.
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 15
Lect-11
Multi-stage performance characteristicsMulti-stage performance characteristics
U
C1
C2
Ca
V1
V2
β1
β2α2
α1
U
C1
C2
Ca
V1
V2
β1
β2α2
α1
Design velocity triangles
First stages Last stages
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 16
Lect-11
Multi-stage performance characteristicsMulti-stage performance characteristics
• Decreased Ca with α1 and β2 constant, results in increased α2 and β1 or increased loading on both rotor and stator blades.
• In the case of increased Ca, it results in the opposite effect.
• Designers use several solutions to allow compressors to self-start: use of bleed valves allowing some of the incoming air to escape, variable IGVs, multi-spooling.
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 17
Lect-11
Multi-stage performance characteristicsMulti-stage performance characteristics
• Axial compressors suffer from two possible modes of unstable operation– Rotating stall: non-axisymmetric, aperiodic – Surge: axisymmetric, periodic
• Rotating stall: progression around the blade annulus of a stall pattern, in which one or more adjacent blade passages are instantaneously stalled, then are cleared for unstalled flow as the stall cell progresses.
• Rotating stall causes alternate loading and unloading of the blades: fatigue failure.
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 18
Lect-11
Multi-stage performance characteristicsMulti-stage performance characteristics
01
02
PP
δθm
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 19
Lect-11
Multi-stage performance characteristicsMulti-stage performance characteristics
Stage characteristicsThrottle characteristics
UCa
20
UP
ρ∆
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 20
Lect-11
In this lecture...
• Performance characteristics of axial flow compressors• Single stage characteristics• Multi-stage characteristics