DESIGN OF CASCADE for AXIAL FLOW COMPRESSORS Arrangement of aerofoils for best Group Performance… P M V Subbarao Professor Mechanical Engineering Department.

DESIGN OF CASCADE for AXIAL FLOW COMPRESSORS

Arrangement of aerofoils for best Group Performance…

P M V SubbaraoProfessor

Mechanical Engineering Department

Module 1: Rotor-inlet Triangle

• When starting the calculation, the geometry from the inlet calculations is used.

• The calculation for the entire stage is repetative.• Conside the rotor-inlet conditions, i.e. station 1, will have

the same velocity and radius as the stator-outlet, i.e. station 3, for the previous stage.

1)3(i1

1)f,3(if,1

1)rms,3(irms,1

αα

VV

rr

Flow Angles &Velocities

Inlet Velocity Triangle

Va1

Va1

Vr1

Vr1

INLET CONDITIONS

Static Properties

Static properties:

Now that the velocity is known, the static enthalpy can be calculated. With help from the entropy other fluid dynamic properties like pressure, temperature, density etc. can be found.

To be able to move from the rotor-inlet towards the outlet of the rotor a relationship between these must be used.

Rothalpy Based Design

Define the rothalpy which is constant throughout the rotor.

The rothalpy is useful for calculating the outlet conditions of the rotor.

2

U

2

VhI

22r

Further in to the calculations the relative Mach number and the axial Mach number will be used.

Module 2, Rotor-outlet/stator-inlet

•There are two separate modules in module 2. •The first, 2.1, is for the calculation of the entropy rise in the rotor. •The second, 2.2, calculates the mean radius of rotor-outlet. •Both of these are iteration processes where an approximated value is first guessed and then a new value is calculated to adjust the approximated first value.

Iteration Loop:Flow angles and velocities : The mean radius at rotor-outlet in unknown so a value for this must be approximates to be able to find out the blade speed. A new value for this will be calculated further on in the calculation.

Since a change in radius throughout the rotor is occurring a modification to the definition of the stage load coefficient must be made. A modification is made based on the blade velocity at the rotor-outlet.

Outlet Velocity Triangle

Irreversible Flow through Cascades

Performance of Aerofoil

Camber angle,

Naca 65 : in

Circula rarc : in

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.

12 Deflection Fluid

Fluid Deflection

r1

r2maxr,

V

VVDfactor, Diffusion

100, s

csolidity

12 Deflection Fluid

Loss coefficient

Outlet flow Angle

Deflection

Cascade Testing

Cascade Testing

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,

K b1U2

ρσ 22

tb

maxct,

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

Multi Stage Compression

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

Radial Variation of Blade Angles

Thermodynamics of Irreversible Compressor

p

2a3

2c

V

p

2a2

2c

V

p

2a1

2c

V

Multi Stage Compressor

p03

p02

Compressor Maps

oi

stp

stp

o1

p

p

T

Tm

01

o3act

p

p