Axial Turbine Performance - Turbomachinery Aerodynamics - Lecture Slides, Slides of Turbomachinery

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1

In this lecture...

• Axial flow turbine

• Performance characteristics

• Axial turbine blades

• Exit flow matching with nozzle

Axial turbine performance

the turbine, respectively.

Where, subscripts and denote the inlet and exit of

T

, N

P

, f m T P

P

fluid at asufficientlyhighReynoldsnumber,

Therefore, for agiven turbine operatingwith agiven

characteristics for aturbine as well.

Inasimilar manner, we candefine performance

C

01 02

(^0101)

01 01

02 

η

Axial turbine performance

01

02

P

P

01

01 P

m T

N/ T 01

Choking mass flow

Axial turbine performance

• The efficiency plot shows that it is constant

over a wide range of rotational speeds and

pressure ratios.

• This is because the accelerating nature of

the flow permits turbine blades to operate

with a wide range of incidence.

• Maximum mass flow is limited by choking of

the turbine.

• The mass flow characteristics tend to merge

into a single curve independent of speed,

for larger number of stages.

Axial turbine performance

• When the turbine operates close to its

design point (low incidence), the

performance curves can be reduced to a

single curve.

• As the number of stages are increased,

there is a noticeable tendency for the

characteristic to become ellipsoidal.

• With increase in the number of stages, the

choking mass flow also reduces.

• Stodola (1945) formulated the “ellipse law”,

which has been used extensively by

designers.

Axial turbine performance

• The performance of turbines is limited by two

factors:

• Compressibility

• Stress

• Inlet temperature

• Compressibility limits the mass flow that can

pass through a turbine.

• Stress limits the rotational speed.

• It is also known that the performance also

strongly depends upon temperature.

• Temperature in turn affects the stress.

• Hence, in a design exercise, there must be a

compromise between the maximum

temperature and the maximum rotor speed.

Axial turbine performance

• For a given pressure ratio and adiabatic

efficiency, the turbine work per unit mass is

proportional to the inlet stagnation

temperature.

• Therefore typically a 1% increase in the turbine

inlet temperature can produce 2-3% increase in

the engine output.

• Therefore there are elaborate methods used for

cooling the turbine nozzle and rotor blades.

• Turbine blades with cooling can withstand

temperatures higher than that permissible by

the blade materials.

Axial turbine blades

• Profiles can be generally classified as:

• Profiles derived from various agencies like

NACA, AGARD etc.

• Profiles with circular arc and parabolic arc

camber.

• Profiles derived graphically or empirically

from a specified pressure or Mach number

distribution.

• Each industry has developed their own

proprietary profiles to meet their

requirements.

• Recent trend towards custom-designed or

custom-tailored airfoils.

Axial turbine blades

NACA basic turbine profiles

Profile for subsonic inlet and supersonic outlet

Axial turbine blades

C (^1)

C (^2)

α 1

α 2

PS SS

SS PS

P 2 P^1 21 ρC^1

21 ρC^22 P 2 P^0

Pressure distribution around a typical turbine blade

Axial turbine blades

• Spacing between blades is a critical parameter

in turbomachine performance.

• Closer spacing means lower loading per blade,

but more number of blades, increased weight

and frictional losses.

• Larger spacing means higher blade loading and

lower weight, losses etc.

• Optimum number of blades usually empirical.

This canbe simplifiedasZ VFC cos CS (tan tan )

Zwifel( )criterion: Z VFC F :bladeforce; C:chord W

W W

22 2 2 1 2

22 (^22)

1945 2

ρ α α^ α

ρ = = −

=

Exit flow matching

• The operation of a turbine is affected by

components upstream (compressor) and

downstream (nozzle).

• The compressor and turbine performance

characteristics form an important part of

this performance matching.

• It was discussed earlier that turbines do not

exhibit any significant variation in non-

dimensional mass flow with speed.

• However the turbine operating region is

severely affected by the nozzle.

Exit flow matching

• The nozzle exit area has a significant influence

on the off-design operation of a turbine and the

engine in general.

• The operation of the nozzle under choked or

unchoked condition also influences the

matching.

• The similarity between the flow characteristic of

a nozzle and a turbine is the fact that

thermodynamically, both are flow expanders.

• The matching between the turbine and the

nozzle is identical to that between a free-

turbine / power-turbine and the main turbine.