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MAE 4261: AIR-BREATHING ENGINES

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MAE 4261: AIR-BREATHING ENGINES

Velocity Triangles Example

April 12, 2012

Mechanical and Aerospace Engineering Department

Florida Institute of Technology

D. R. Kirk

a

b

- Draw velocity triangles assuming that wr = 2 times the axial velocity w (w = constant)

c

w

Start by drawing the axial velocity to some scale (10 units here)

Vb

w

bb=75º

Draw the absolute velocity vector

Vb

w

bb=75º

vqb

Draw vq in direction of rotation from the axis to absolute velocity vector

Vb

w

bb=75º

wr

vqb

Add the rotational velocity (wr) and remember Vabs=Vrel+Vcs

Vb

w

bb=75º

wr

vqb

Draw in the velocity to the rotor as seen from the rotating frame

relative frame inlet

velocity to rotor

Stationary frame inlet

velocity to rotor

Vb

w

bb=75º

wr

vqb

wr

Either start with the fixed axial velocity or fixed rotational speed

bc’=55º

w

wr

Add the velocity from the rotor blades in the relative frame

bc’=55º

w

wr

vqc

Add the velocity exiting the rotor in the absolute frame

stationary frame exit

velocity of rotor

bc’=55º

relative frame exit

velocity of rotor

w

wr

vqc

Again, draw vq in the direction of rotation to the absolute velocity vector

Fixed or ‘metal’ blade angles

bc’=55º

w

bb=75º

w

wr

vqb

vqc

To draw the composite velocity triangle, overlay the rotational velocity

- Is this a compressor or a turbine? How can you tell?
- On which blade row(s) is there a torque applied? Why?
- Describe in words the energy exchange process in each of the two blade rows

- Is this a compressor or a turbine?
- This is a turbine. The stationary frame tangential velocity (vq) in the direction of rotor motion is reduced across the moving blade row

- On which blade row(s) is there a torque applied? Why?
- Torque is applied to both blade rows since there is a change in angular momentum across each of them. However, power is extracted only from the moving blades.

- Describe in words the energy exchange process in each of the two blade rows
- In the first blade row, fluid internal energy is converted to swirling kinetic energy by accelerating the flow through a nozzle. No additional energy is added or removed from the flow.
- In the second blade row, swirling kinetic energy is extracted from the flow reducing the overall level of energy in the flow and transferring it to the spinning rotor blades.

- So far, we have looked at trailing edge angles of the blades (bb and bc’)
- Why do we care about exit velocities from stator in the relative frame? Why do we even draw this on velocity triangles?

relative frame inlet

velocity to rotor

Stationary frame inlet

velocity to rotor

Vb

w

bb=75º

Why draw this?

wr

vqb

Information about

how to shape

leading edge of

rotor blade

Doesn’t come into

ideal Euler equation

but obviously

important for

aerodynamic

Purposes

(rotor relative inflow

angle)