Mel346-42.ppt

Analysis of Axial & Centrifugal Compressors

P M V Subbarao Professor Mechanical Engineering Department

To be Selected as per Specific Speed of Applications….

Multi Stage Hybrid Compressor

Static & Stagnation Scalars

Irreversible Adiabatic Stage of an Axial Flow Compressor p03s=p02s p02 p03 T03=T02 Rotor Losses

T02s

Total Losses T03s T

Pinput,a Pinput, s p01 T01

s

Gas dynamics of Irreversible Compressor p02s

Va23 2c p

Va22 2c p

Va21 2c p

Stage Efficiency The stage efficiency of an adiabatic compressor stage is:

h03s  h01  stage  h03  h01

For calorically perfect gas

T03s  T01  stage  T03  T01 Actual temperature rise of a fluid when compressed in an irreversible stage for a pressure ratio of p03/p01 is:

T03  T01 

T03s  T01

stage

p03   stageT0 S  1  p01  T01

  

       1 

System of Equations for Stage Design

p03,act p01

UV f cot 1  cot  2      stage  cp    1   T01      

       1 

Vr21  Vr22  2 Vr1  Vr22  Va22  Va21

U  cot 1  cot 1  cot  2  cot  2 Vf

Vr 2 

V f cot 1  cot 1  cot  2  sin  2

Selection of Global Stage Variables Stage load coefficient

Stage flow coefficient

Stage reaction

Δh ψ 2 U Vf φ U

h2  h1  h03  h01

The stage load distribution throughout the compressor

Selection of Design Parameters • A high pressure rise per stage will decrease the number of stages for a given overall pressure rise. • A high pressure rise per stage is obtained using: • High blade speed. • High inlet flow velocity. • High fluid deflection in rotor blades. 



Pstage  m c p T03a  T01   mUVf cot 1  cot  2 

Inlet Velocity Triangle & Flow Velocity

1

1

Selection of Inlet Angle

Va1

Vr1 Vr1

Va1

Blade Speed • For a given rotor speed the velocity of the blade at the tip will be maximum. • The centrifugal stress in the rotor blades depends on the rotational speed, the blade material and length of the blade. • The maximum centrifugal stress is given by,

 ct ,max 

b

• b, hub-tip diameter ratio. • K varies in the range 0.55 – 0.65.

2





U t2 1  b 2 K

Fluid Deflection

Fluid Deflection  cot 1  cot 2  c solidity ,   100 s

Vr,max  Vr2 Diffusion factor, D  Vr1

Performance of Aerofoil

Camber angle, q

Naca 65 : inl Circula rarc : inl

Clues to Invent an Aerofoil Outlet flow Angle

Deflection

Loss coefficient

Current Design Practice Fan or low pressure Compressor

Parameter Pressure ratio for single stage Pressure ratio for two stages Pressure ratio for three stages Inlet mass flow rates Tip speed Diffusion factor

Range 1.5 – 2.0 2.0 – 3.5 3.5 – 4.5 195 – 205 kg/m2.s 427 – 457 m/s 0.5 – 0.55

Current Design Practice High pressure Compressor

Parameter Stage loading coefficient Flow coefficient Hub/tip ratio Inlet mass flow rates Tip speed Diffusion factor

Range 0.3 – 0.35 0.45 – 0.55

0.6 – 0.75 175 – 185 kg/m2.s 386 – 457 m/s 0.5 – 0.55

Compressor Maps

po 3act p01

   m To1 pstp   Tstp poi  

Multi Stage Compression

Loss in capacity due to variation of velocity is defined as work done factor. Work done factor, l, decrease with number of stages.

Multi Stage Axial-flow Compressor

Gas Dynamics of An Impeller Va2 Vf2

Vr2 Vw2 < U

Vw1 Vr1

Va1 Vf1

Thermodynamic View of an isentropic Compressor 





P  m Vw2 r2  Vw1r1   mh02  h01   m c p T02  T01  

P  m c p T03  T01  p03=p02

3

p3

2

1

Only Impeller can consume Power !!!

Va23 2c p

T

T03=T02 p2

Va22 2c p



P  m  Vw 2 r2  Vw1r1  p01 p1 Va21 2c p

T01 s

Irreversible Diffuser p03s=p02s

p02a

p03a

T03=T02 Impeller Losses Overall Losses T



P  mVw 2 r2  Vw1r1  p01 T01

s

Work consumed by A compressor = Increase in Stagnation Enthalpy of gas 





Pact   m Vw2 r2  Vw1r1   mh03  h01   m c p T03  T01 

For an irreversible compression, the actual pressure rise is less than isentropic pressure rise due to (T03-T01).

p03a  p03s

p03a  T03as     p01  T01 

Define, Adiabatic Efficiency of A Compressor:

       1  

 comp

 T03as  T01    1  T01  

T03as  T01  T03  T01

p03a   comp T03  T01     1  p01  T01 

       1  

       1  





Pact   m Vw2 r2  Vw1r1   m c p T03  T01 

Ur2  Vw1r1  cp

p03,act p01

 T03  T01 

 compUr2  Vw1r1     1    c T p 01  

       1 

Ns 

N Q H

3

4

for pumps

Erection of Pump

Hd

ps Hs

Hpump

Internals – Pump Vs Compressor

Compressor Impeller

Fan Impeller Pump Impeller