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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. EXAMPLE: SEE SECTION 8.2 FROM H&P. a. b.

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MAE 4261: AIR-BREATHING ENGINES

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Mae 4261 air breathing engines l.jpg

MAE 4261: AIR-BREATHING ENGINES

Velocity Triangles Example

April 12, 2012

Mechanical and Aerospace Engineering Department

Florida Institute of Technology

D. R. Kirk


Example see section 8 2 from h p l.jpg

EXAMPLE: SEE SECTION 8.2 FROM H&P

a

b

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

c


Velocity triangles at b l.jpg

VELOCITY TRIANGLES AT b

w

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


Velocity triangles at b4 l.jpg

VELOCITY TRIANGLES AT b

Vb

w

bb=75º

Draw the absolute velocity vector


Velocity triangles at b5 l.jpg

VELOCITY TRIANGLES AT b

Vb

w

bb=75º

vqb

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


Velocity triangles at b6 l.jpg

VELOCITY TRIANGLES AT b

Vb

w

bb=75º

wr

vqb

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


Velocity triangles at b7 l.jpg

VELOCITY TRIANGLES AT b

Vb

w

bb=75º

wr

vqb

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


Velocity triangles at b8 l.jpg

VELOCITY TRIANGLES AT b

relative frame inlet

velocity to rotor

Stationary frame inlet

velocity to rotor

Vb

w

bb=75º

wr

vqb


Velocity triangles at c l.jpg

VELOCITY TRIANGLES AT c

wr

Either start with the fixed axial velocity or fixed rotational speed


Velocity triangles at c10 l.jpg

VELOCITY TRIANGLES AT c

bc’=55º

w

wr

Add the velocity from the rotor blades in the relative frame


Velocity triangles at c11 l.jpg

VELOCITY TRIANGLES AT c

bc’=55º

w

wr

vqc

Add the velocity exiting the rotor in the absolute frame


Velocity triangles at c12 l.jpg

VELOCITY TRIANGLES AT c

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


Composite triangle l.jpg

COMPOSITE TRIANGLE

Fixed or ‘metal’ blade angles

bc’=55º

w

bb=75º

w

wr

vqb

vqc

To draw the composite velocity triangle, overlay the rotational velocity


Questions l.jpg

QUESTIONS

  • 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


Questions15 l.jpg

QUESTIONS

  • 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.


Additional question l.jpg

ADDITIONAL QUESTION

  • 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


Additional question17 l.jpg

ADDITIONAL QUESTION

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)


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