velocity triangles
TRANSCRIPT
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MAE 4261: AIR-BREATHING ENGINES
Velocity Triangles Example
November 3, 2009
Mechanical and Aerospace Engineering Department
Florida Institute of Technology
D. R. Kirk
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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
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VELOCITY TRIANGLES AT b
w
Start by drawing the axial velocity to some scale (10 units here)
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VELOCITY TRIANGLES AT b
wVb
b=75º
Draw the absolute velocity vector
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VELOCITY TRIANGLES AT b
wVb
b=75º
vb
Draw v in direction of rotation from the axis to absolute velocity vector
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VELOCITY TRIANGLES AT b
r
wVb
b=75º
vb
Add the rotational velocity (r) and remember Vabs=Vrel+Vcs
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VELOCITY TRIANGLES AT b
r
vb
wVb
b=75º
Draw in the velocity to the rotor as seen from the rotating frame
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VELOCITY TRIANGLES AT b
r
vb
wVb
b=75º
Stationary frame inletvelocity to rotor
relative frame inletvelocity to rotor
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VELOCITY TRIANGLES AT c
r
Either start with the fixed axial velocity or fixed rotational speed
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VELOCITY TRIANGLES AT c
r
c’=55º
w
Add the velocity from the rotor blades in the relative frame
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VELOCITY TRIANGLES AT c
r
c’=55º
w
vc
Add the velocity exiting the rotor in the absolute frame
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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
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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
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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
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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
,,
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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?
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ADDITIONAL QUESTION
Information abouthow to shapeleading edge ofrotor blade
Doesn’t come intoideal Euler equationbut obviouslyimportant foraerodynamicPurposes(rotor relative inflowangle)