MAE 4261: AIR-BREATHING ENGINES

Velocity Triangles Example

April 12, 2012

Mechanical and Aerospace Engineering DepartmentFlorida Institute of Technology

D. R. Kirk

EXAMPLE: SEE SECTION 8.2 FROM H&P

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

a

b

c

VELOCITY TRIANGLES AT b

w

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

VELOCITY TRIANGLES AT b

wVb

b=75º

Draw the absolute velocity vector

VELOCITY TRIANGLES AT b

wVb

b=75º

vb

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

VELOCITY TRIANGLES AT b

r

wVb

b=75º

vb

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

VELOCITY TRIANGLES AT b

r

vb

wVb

b=75º

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

VELOCITY TRIANGLES AT b

r

vb

wVb

b=75º

Stationary frame inletvelocity to rotor

relative frame inletvelocity to rotor

VELOCITY TRIANGLES AT c

r

Either start with the fixed axial velocity or fixed rotational speed

VELOCITY TRIANGLES AT c

r

c’=55º

w

Add the velocity from the rotor blades in the relative frame

VELOCITY TRIANGLES AT c

r

c’=55º

w

vc

Add the velocity exiting the rotor in the absolute frame

VELOCITY TRIANGLES AT c

r

c’=55º

w

vc

relative frame exitvelocity of rotor

stationary frame exitvelocity of rotor

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

COMPOSITE TRIANGLE

r

vb

w b=75º

c’=55º

vc

To draw the composite velocity triangle, overlay the rotational velocity

w

Fixed or ‘metal’ blade angles

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

QUESTIONS• Is this a compressor or a turbine?

– This is a turbine. The stationary frame tangential velocity (v) 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.

TP

VVrmT inout

,,

ADDITIONAL QUESTION

r

vb

wVb

b=75º

Stationary frame inletvelocity to rotor

relative frame inletvelocity to rotor

• So far, we have looked at trailing edge angles of the blades (b and c’)• Why do we care about exit velocities from stator in the relative frame? Why do we

even draw this on velocity triangles?

Why draw this?

ADDITIONAL QUESTION

Information abouthow to shapeleading edge ofrotor blade

Doesn’t come intoideal Euler equationbut obviouslyimportant foraerodynamicPurposes(rotor relative inflowangle)