Axial Flow Compressors - Turbomachinery Aerodynamics - Lecture Slides, Slides of Turbomachinery

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In this lecture...

• Axial flow compressors and fans
  • Thermodynamics of compression
    • P-v and T-s diagrams of compressors
    • Thermodynamics of compression process
    • Multi-stage compression
  • Basic operation of axial compressors/fans
  • Velocity triangles
  • Work and compression

Thermodynamics of compression

(i) Adiabatic (process 1-2/^ ) , Pvγ=c (ii) Isothermal process (1-2//^ ), Pv=c (iii) Isochoric (Process 1-2///^ ), Pv =c^ ∞

Thermodynamics of compressors

i) Isentropic process (1-2 /) ii) Polytropic process (1-2) iii) Isothermal process (1-2 //) iv) Isochoric Process (1-2 ///)

Thermodynamics of compressors

X 1 , X 2 are the losses in the rotor and the stator respectively

Compression in terms of static parameters

Thermodynamics of compressors

Compression in terms of total parameters

Basic operation of axial compressors

• Axial flow compressors usually consists of a

series of stages.

• Each stage comprises of a row of rotor

blades followed by a row of stator blades.

• The working fluid is initially accelerated by

the rotor blades and then decelerated in the

stator passages.

• In the stator, the kinetic energy transferred

in the rotor is converted to static pressure.

• This process is repeated in several stages to

yield the necessary overall pressure ratio.

Basic operation of axial compressors

• The compression process consists of a series of diffusions.
• This occurs both in the rotor as well as the stator.
• Due to motion of the rotor blades two distinct velocity components: absolute and relative velocities in the rotor.
• The absolute velocity of the fluid is increased in the rotor, whereas the relative velocity is decreased, leading to diffusion.
• Per stage pressure ratio is limited because a compressor operates in an adverse pressure gradient environment.

Velocity triangles

• Elementary analysis of axial compressors begins with velocity triangles.
• The analysis will be carried out at the mean height of the blade, where the peripheral velocity or the blade speed is, U.
• The absolute component of velocity will be denoted by, C and the relative component by, V.
• The axial velocity (absolute) will be denoted by C (^) a and the tangential components will be denoted by subscript w (for eg, C (^) w or Vw )
• α denotes the angle between the absolute velocity with the axial direction and β the corresponding angle for the relative velocity.

Velocity trianglesVelocity triangles

U C 1 C^2

V (^1) V (^2) C (^3)

V (^2)

C (^2)

Rotor Stator

1 2 3

β 1

β 2

α 2

α 3

U

V (^1)

C U V

 (^)   = +

Property changes across a stage

Total enthalpy

Absolute velocity

Static pressure

C 1 C (^2) C (^3)

h 01 h 02 h (^03)

P 1 P 2 P 3

Work and compression

• Assuming C a =C a1 =Ca2 , from the velocity

triangles, we can see that

• By considering the change in angular

momentum of the air passing through the

rotor, work done per unit mass flow is

α 1 β (^1) C tanα 2 tanβ 2

U

tan tan and C

U

a a

rotor,respective ly.

components of the fluid velocity before andafter the

w = UCw 2 −Cw 1 , whereCw 1 andCw 2 are the tangential

Work and compression

01

0 01

03

03 01

03 01

03 02

01 01

0 02 01

02 01

T

T

T

T

This canbe expressedas

h h

h h

Let us define stage efficiency, , as

the fluidpasses through the stator, T T

Since the flow is adiabatic andno work is done as

c T

U C

T

T

c

U C

T T

h h U C

st

s

s st

st

p

w p

w

w

η

η

η

Work and compression

( )

( 1 )

01 01

03

1

01

0 01

03

0 03 01

−

−

γ γ

γ γ

η

η

/

p

w st

/ st

c T

U C

P

P

to give,

This canbe combined with the earlier equation

T

T

P

P

Interms of pressureratio,

Inthe above equation, ΔT T T