Let's say I have the geometry of the rotor: the number of blades, the airfoils that make up each blade, their position, chord length and their twist angle. Would it be possible to use this information to determine the tip-speed ratio?
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$\begingroup$ Not normally from just rotor geometry, but you can estimate the free wheeling TSR of a well designed rotor using blade element theory. But they shouldn't ever be free spinning. You need a pretty good idea of the disc loading to get anything meaningful for decent high ratio designs. $\endgroup$– Phil SweetCommented Mar 28, 2018 at 23:19
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$\begingroup$ I'm actually modeling miniature wind turbine connected to a DC generator. Other than the viscous damping from the generator, I am assuming it is approximately free spinning. I do have the TSR for 3 blades, but I want to look at power coefficient vs. number of blades (where the number can be 2, 3, 4 and 6). I can't get the TSR for the other numbers so I need some way to calculate it, or at least get the RPM as a function of wind speed. $\endgroup$– Eric Q.Commented Mar 28, 2018 at 23:38
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$\begingroup$ Since TSR is the ratio of blade tip soeed and fluid speed -you need to have two fixed or known to find the third... See windynation.com/jzv/inf/… $\endgroup$– Solar MikeCommented Mar 29, 2018 at 4:50
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$\begingroup$ Yes, that's true, but from a theoretical point of view, TSR should depend on the rotor geometry. $\endgroup$– Eric Q.Commented Mar 29, 2018 at 6:22
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$\begingroup$ @EricQ. The ratio depends in two factors : the tip speed and the fluid speed - define any two and you get the third... $\endgroup$– Solar MikeCommented Mar 29, 2018 at 12:06
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Yes.
I would point you to the 2014 paper by M. Ragheb titled Optimal Tip Speed Ratio http://mragheb.com/NPRE%20475%20Wind%20Power%20Systems/Optimal%20Rotor%20Tip%20Speed%20Ratio.pdf which includes a fairly clear description of the factors affecting turbine efficency.
For a rotor with a variable pitch system, the rotational speed vs. power generated can be controlled by feathering the blades to accommodate varying wind speeds and therefore keep the system operating at the best TSR.
For a fixed pitch system, some method of governing the maximum RPM and will be required.
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$\begingroup$ I'm not looking to design for a particular TSR, I already have a 3d CAD model of a rotor and would like to know what its TSR would be approximately. EDIT: We can assume it will be able to spin freely and the pitch is already specified. $\endgroup$– Eric Q.Commented Mar 28, 2018 at 23:17