MAE 4261: AIR-BREATHING ENGINESVelocity Triangles Example

April 12, 2012

Mechanical and Aerospace Engineering DepartmentFlorida Institute of Technology

D. R. Kirk

EXAMPLE: SEE SECTION 8.2 FROM H&PDraw velocity triangles assuming that wr = 2 times the axial velocity w (w = constant)abc

VELOCITY TRIANGLES AT bwStart by drawing the axial velocity to some scale (10 units here)

VELOCITY TRIANGLES AT bwVbbb=75Draw the absolute velocity vector

VELOCITY TRIANGLES AT bwVbbb=75vqbDraw vq in direction of rotation from the axis to absolute velocity vector

VELOCITY TRIANGLES AT bwrwVbbb=75vqbAdd the rotational velocity (wr) and remember Vabs=Vrel+Vcs

VELOCITY TRIANGLES AT bwrvqbwVbbb=75Draw in the velocity to the rotor as seen from the rotating frame

VELOCITY TRIANGLES AT bwrvqbwVbbb=75Stationary frame inletvelocity to rotorrelative frame inletvelocity to rotor

VELOCITY TRIANGLES AT cwrEither start with the fixed axial velocity or fixed rotational speed

VELOCITY TRIANGLES AT cwrbc=55wAdd the velocity from the rotor blades in the relative frame

VELOCITY TRIANGLES AT cwrbc=55wvqcAdd the velocity exiting the rotor in the absolute frame

VELOCITY TRIANGLES AT cwrbc=55wvqcrelative frame exitvelocity of rotorstationary frame exitvelocity of rotorAgain, draw vq in the direction of rotation to the absolute velocity vector

COMPOSITE TRIANGLEwrvqbwbb=75bc=55vqcTo draw the composite velocity triangle, overlay the rotational velocity wFixed or metal blade angles

QUESTIONSIs 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

QUESTIONSIs 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 rowOn 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 rowsIn 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 QUESTIONwrvqbwVbbb=75Stationary frame inletvelocity to rotorrelative frame inletvelocity to rotorSo 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?Why draw this?

ADDITIONAL QUESTIONInformation abouthow to shapeleading edge ofrotor blade

Doesnt come intoideal Euler equationbut obviouslyimportant foraerodynamicPurposes(rotor relative inflowangle)