Velocity Triangle

1. Velocity Triangles Example
Velocity Triangles Example
April 12, 2012
Mechanical and Aerospace Engineering Department

2. EXAMPLE: SEE SECTION 8.2 FROM H&P
• Draw velocity triangles assuming that ωr = 2 times the axial velocity w (w = constant)
a
b
c

3. VELOCITY TRIANGLES AT b
w
Start by drawing the axial velocity to some scale (10 units here)

4. VELOCITY TRIANGLES AT b
w
Vb
βb=75º
Draw the absolute velocity vector

5. VELOCITY TRIANGLES AT b
w
Vb
βb=75º
vθb
Draw vθ in direction of rotation from the axis to absolute velocity vector

6. VELOCITY TRIANGLES AT b
ωr
w
Vb
βb=75º
vθb
Add the rotational velocity (ωr) and remember Vabs=Vrel+Vcs

7. VELOCITY TRIANGLES AT b
ωr
vθb
w
Vb
βb=75º
Draw in the velocity to the rotor as seen from the rotating frame

8. VELOCITY TRIANGLES AT b
ωr
vθb
w
Vb
βb=75º
Stationary frame inlet
velocity to rotor
relative frame inlet
velocity to rotor

9. VELOCITY TRIANGLES AT c
ωr
Either start with the fixed axial velocity or fixed rotational speed

10. VELOCITY TRIANGLES AT c
ωr
βc’=55º
w
Add the velocity from the rotor blades in the relative frame

11. VELOCITY TRIANGLES AT c
ωr
βc’=55º
w
vθc
Add the velocity exiting the rotor in the absolute frame

12. VELOCITY TRIANGLES AT c
ωr
βc’=55º
w
vθc
relative frame exit
velocity of rotor
stationary frame exit
velocity of rotor
Again, draw vθ in the direction of rotation to the absolute velocity vector

13. COMPOSITE TRIANGLE
ωr
vθb
w βb=75º
βc’=55º
vθc
To draw the composite velocity triangle, overlay the rotational velocity
w
Fixed or ‘metal’ blade angles

14. 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

15. QUESTIONS
• Is this a compressor or a turbine?
– This is a turbine. The stationary frame tangential velocity (vθ) 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
ω
θθ
=
−= ,,


16. ADDITIONAL QUESTION
ωr
vθb
w
Vb
βb=75º
Stationary frame inlet
velocity to rotor
relative frame inlet
velocity to rotor
• So far, we have looked at trailing edge angles of the blades (βb and βc’)
• 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?

17. 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)