Download Blade Performance - Turbomachinery Aerodynamics - Lecture Slides and more Slides Turbomachinery in PDF only on Docsity!

1

2

In this lecture...

• Performance parameters: cascade

analysis

• 2-D losses in axial compressor stage –

primary losses

4

Performance parameters

• Blade performance/loading can be

assessed using static pressure coefficient:

• The C

P

distribution (usually plotted as C

P

vs. x/C ) gives an idea about the

chordwise load distribution.

at the cascade inlet)

P is thereference staticpressure(usually measured

Where,P is the blade surface staticpressure and

V

P P

C

ref

local

local ref P (^2) 2 1

1 ρ

5

Performance parameters

Deflection, degrees

Total pressure loss coefficient

Position along cascade

Location of the blade trailing edge

7

Performance parameters

Incidence angle, degrees

Total pressure loss coefficient

8

Losses in a compressor blade

• Nature of losses in an axial compressor

• Viscous losses
• 3-D effects like tip leakage flows, secondary

flows etc.

• Shock losses
• Mixing losses

• Estimating the losses crucial designing loss

control mechanisms.

• However isolating these losses not easy and

often done through empirical correlations.

• Total losses in a compressor is the sum of

the above losses.

10

Losses in a compressor blade

• The loss manifests itself in the form of stagnation

pressure loss (or entropy increase).



 

 

 



= =

=



 

 

 

 = +

 

  

 = − = − −

01

2 1

2 2 1

1

01 2 2 1

1

01

2

01 01

01 01

02

2

2

1

1

P

V

R

s or,

V

P

R

s

V

( P ) Since,

P

( P )

R

s Neglectinghigher order terms,

... P

( P )

P

( P )

R

s

Expandingtheaboveequationinaninfinite series,

P

( P ) ln P

P ln R

s

o loss

o loss

o loss o loss

o loss

Δ ωρ

ρ

Δ

ρ

Δ ω

Δ Δ

Δ Δ Δ

Δ Δ

11

Losses in a compressor blade

• The overall losses in a turbomachinery can be

summarised as:

:Endwall losses

:tip leakage loss

:secondary flow loss

:shock losses

Where, :profile losses

E

L

s

sh

P

P sh s L E

13

2-D Losses in a compressor blade

• 2-D losses can be classified as:

• Profile loss due to boundary layer, including

laminar and/or turbulent separation.

• Wake mixing losses
• Shock losses
• Trailing edge loss due to the blade.

14

2-D Losses in a compressor blade

• The profile loss depends upon:

• Flow parameters like Reynolds number,

Mach number, longitudinal curvature of the

blade, inlet turbulence, free-stream

unsteadiness and the resulting unsteady

boundary layers, pressure gradient, and

shock strength

• Blade parameters like: thickness, camber,

solidity, sweep, skewness of the blade,

stagger angle and blade roughness.

16

2-D Losses in a compressor blade

• At far downstream, the flow becomes

uniform.

• Theoretically, the difference between the

stagnation pressure far downstream and the

trailing edge represents the mixing loss.

• Most loss correlations are based on

measurements downstream of the trailing

edge (1/2 to 1 chord length) and therefore

do not include all the mixing losses.

• If there is flow separation, the losses would

include losses due to this zone and at its

eventual mixing downstream.

17

2-D Losses in a compressor blade

boundary layer at the trailing edge.

displacement andmomentum thickness of the blade

the static pressure difference and velocities to the

To determine the above,it is necessary to relate

V

(P P )

streamline canbe written as:

The profile andmixinglosses along a

t p m 2 1

(^2002)

ρ

ω

−

19

2-D Losses in a compressor blade

• Thus, in a simplified manner, we see that

the profile loss can be estimated based on

the momentum thickness.

• The above loss correlation includes both

profile and wake mixing loss.

• If flow separation occurs, additional losses

are incurred. This is because the pressure

distribution is drastically altered beyond

the separation point.

• The losses increase due to increase in

boundary layer displacement and

momentum thicknesses.

20

2-D Losses in a compressor blade

• In addition to the losses discussed above,

boundary layer growth and subsequent decay of

the wake causes deviation in the outlet angle.

• An estimate of this is given as:
• Hence, viscous effect in a turbomachine always

leads to decrease in the turning angle.

• The values of displacement and momentum

thicknesses, depend upon, variation of freestream

velocity, Mach number, skin friction, pressure

gradient, turbulence intensity and Reynolds

number.

t

tan α ≈ ( 1 − Θ − Δ)tanα

2