# Axial compressor - change of temperature not proportional to number of blades and their geometrical properties?

I'm learning theory of axial compressors for my summer internship and I find some of the equations puzzling, although I do understand the way they were derived.

The equation bellow is for temperature increase on rotor.

Could someone elaborate on why isn't the $\Delta T$ proportional to other factors like the number of blades? Is it correct to assume that even one blade is considered to be able to accelerate all the fluid going through the compressor to the tangential velocity considered in this equation, given by $U =\omega$r? This would then mean that the number of blades and their geometry, except the main angles, will only play a role in energy losses and distribution of load on individual blades?

• Can you identify some variables?
– JMac
Jul 7 '17 at 19:49
• " Is it correct to assume that even one blade is considered to be able to accelerate all the fluid going through the compressor to the tangential velocity considered in this equation"... why would you think that could possibly be true? The point is that you decide on the optimum number of blades per stage after you have decided on the overall thermodynamics - and it depends on several other factors as well as the thermodynamics. An answer attempting to explain the mechanical design of the compressor would be far to long for this forum of course. Jul 7 '17 at 19:50
• Thanks for your reply. I didn't think that one blade could do that. That's why I submitted this question in the first place - to look after some correlations. I'm sorry if I made myself unclear. I can see that my question wasn't very well thought through. Sorry about the confusion. So if I'm understanding this correctly, we are assuming that a certain number of blades of a certain geometry is able to swirl the fluid to a speed U. How is this calculated? Are there equations we can use or is it necessary to use computer simulations or something else? Jul 7 '17 at 20:11
• @JMac Sure! U is the velocity of fluid, given to it by rotor, Tt2 and Tt1 are temperatures and Cz is axial velocity of the fluid, as for the angles, I think it's safer to point you at my resource - you can just search "DEFINITION OF FLOW ANGLES" safaribooksonline.com//library/view/aircraft-propulsion-2nd/… Jul 7 '17 at 20:16