I want to ask about the torque experienced by a axial flow turbine, in relation to the pitch angle or angle of attack. If you can suggest an equation, will greatly help.

(I'm new to technical terms, please bear with me)

  • $\begingroup$ You'd also need to know the flow speed of material. $\endgroup$ – Olin Lathrop Mar 9 '15 at 14:04
  • $\begingroup$ Okay then as a function of flow speed and angle of attack, can u suggest an equation? $\endgroup$ – Alexander Mar 9 '15 at 16:10

This topic is much larger than just a simple equation involving the angle of attack of turbine blades.

There have been many university papers writen about topics involving turbine design and properties. Two of these are: angle of attack and tidal turbine.

The blades are designed as airfoils, so the details of the blades are important. The speed of the fluid as well as the speed of the turbine rotation combine to determine if the blades stall. In addition to this, the Reynolds number is another important factor as with all fluid modeling.

Reading through these two papers shows that even with equations and computer models, physical model testing is still required. Looking at these papers might be a place to start looking for background information.

Basically this is a very big topic that can not be reduced to a single equation.


Answering this question simply is not feasible, you are asking a question which is enormously difficult to answer without a large number of parameters. The biggest issue which you face is that there are many, many correct solutions to this question without constraints, but only one physically correct solution.

It is similar to the question "how big does my radiator need to be to cool my engine?": the question is simple enough, you might even know the power which you need to extract to prevent overheating, but for a given duct there is a whole range of mathematically correct inlet/outlet velocities and pressures, but only one physically correct solution. Our problem has not been sufficiently constrained.

To nudge you in the correct direction, there are two big factors to consider here:

  1. what happens to the flow passing through your turbine?
  2. how does the design of your turbine affect the torque at the shaft?

The first question can be greatly simplified by imposing the maximum efficiency we can, or perhaps some factor of that, and assume that this is feasible. This is governed by Betz's Law.

Once you apply this constraint, it had ought to be trivial to obtain the power produced at your turbine using basic information about the flow. You know that for this to be achieved you must have zero loses in the flow as a result of your turbine (beyond the energy extracted of course), so for a given number of blades there is only one solution. Now create a model in which the physics impose zero loses at this solution; the closer to a real world model this is, the more accurate your answer will be. Now vary AoA to see how your loses change within your model. Your model should account for separation but there are plenty of 2D open source codes you could try.

The above method will not get you the answer, as it assumes that the solution you start with is optimum and works from there, but it will give you an idea of how AoA changes affect your torque in an arbirary system, and it is simple enough that most people with basic knowledge of fluid dynamics and some time could do it.

  • $\begingroup$ I currently want a rough relation, so u suggest I try and work on the losses? And can you give me the link or keywords that might help me find the codes? $\endgroup$ – Alexander Apr 9 '15 at 15:07

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