Expert: Paul Soderman - 10/17/2011

Question
QUESTION: Sir,
In turbo machinery, what exactly is the origin of the torque on rotor blades and torque on fluid passing through rotor? Why are these two torques equal in magnitude but opposite in direction?

ANSWER: Sangeeth
The primary torque of interest in turbomachinery is the torque of the drive shaft, which is primarily due to drag of the rotor blades.  That gives us the load and power required by the motor.  From a design standpoint, we also would like the torque of each rotor blade.  That torque is the sum total of the moments due to lift and drag and the pitching moment of the airfoil resolved at the point of interest, usually the root of the blade shaft.  From momentum theory we know that the forces and moments on an airfoil such as a rotor blade are equal and opposite to the momentum change imparted to the fluid.  That comes form Newton's law. Consider the lift on the airfoil to be upward.  That causes the flow to deflect downward.
Paul

---------- FOLLOW-UP ----------

QUESTION: Sir,
With your concepts and a little bit of reading and lots of thinking, I figured out a reasoning to my question. I hereby present it. Kindly correct me if I am wrong.

The rotor blades rotate with a constant angular velocity w. Hence no inherent torque acts on it if the flow it zero. When the flow starts, the rotor blades produces aerodynamic force ( I presume this is what you meant by " Drag of the rotor blades" in your reply). This aerodynamic force thus produces a torque about the blade root. This torque opposes the motion of the rotor blades at constant w( if power is not given to overcome this torque, it will eventually bring the rotor to rest!). Thus, a definite power is req by the shaft and is given by the relation T( torque) * w.

But simultaneously, the production of aerodynamic force also ensures that the rotor blades exerts force on the fluid ( 3rd law) and this force acts on the fluid ( this is the point where energy transfer takes place between rotor and fluid) and produces a torque opposite in nature ( but equal in magnitude) to the blade torque. This torque causes change in angular momentum of the fluid and therefore does work on the fluid ( through euler turbine equation).

Stator also produces the same kind of blade torque and opposing torque on the fluid and so also causes angular momentum change in the fluid ( only that it removes angular momentum that the rotor had previously added!) But, since stator does not rotate, there needn't be any work provided to it and in turn, it does no work on the fluid.

ANSWER: Yes Sangeeth, that is pretty close.  I like your analysis of shaft power and energy transfer to the fluid.  I am not sure if you really mean that the blades can rotate before the flow starts. Blade motion and flow occur simultaneously.  Lift also affects shaft power, but it is small compared to the drag because it is fairly parallel to the shaft.  The one thing I would differ with is your analysis of the stator.  Because the stator has drag, it removes energy from the flow and therefore does work on the flow.  The value of that power loss is D * V where drag (D) and velocity (V) are vectors and we use the dot product. We could include lift but any force acting perpendicular to the fluid velocity does no work. The power lost by the fluid goes into heat. This is true for all aerodynamic bodies of course and explains why we have to add propulsion to a body in flight.
Paul

---------- FOLLOW-UP ----------

QUESTION: 1.Blades can rotate before the flow ( independently) as in a compressor?
2. Lift is parallel, But it acts in the opposite direction to that of the rotor rotation. Thus it opposes the rotor motion right? Also, if you try to avoid this by rotating the rotor in the same direction as the lift, then the relative velocity faced by rotor would be absurdly pointing.
3.Well, I was actually considering only non viscous flow around the blades. That is why i neglected the frictional loss you have mentioned. But thanks for that insight ( of the real case of viscous flow over the blades).

Thanks a lot for your patience and your efforts in educating me. You are doing an supremely altruistic work of sharing your knowledge with those who need it most.

Answer
1.  I don't understand statement one.  Once a blade moves there is relative motion between the blade and fluid.  With a coordinate system attached to the blade, the usual case, the fluid flows around the blade, even in a compressor.

2.  Lift is perpendicular to the flow velocity vector, which is the vector sum of the axial flow through the compressor or fan and the rotational velocity of the blade (ignoring swirl).  This makes the lift fairly parallel to the drive shaft, which is the thrust direction.  Thus the lift is almost perpendicular to the rotor path, not opposed to it.  The drag is opposed to the rotor motion.

3.  If there is no viscosity there is no drag, and the torque required by the motor would be zero.
Paul