# 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. – alephzero 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? – user145760 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/… – user145760 Jul 7 '17 at 20:16

## 1 Answer

It is usually a completely different group of people doing compressor aerodynamic design versus overall thermodynamic cycle design. The compressor aero group, using a variety of computer simulation codes (ranging from simple spreadsheets all the way up to 3 dimensional unsteady CFD) are going to generate a "compressor map". The compressor map gives the pressure ratio, mass flow through the compressor, and efficiency for given rotor speeds (and perhaps other variables). This allows the thermodynamic cycle guys to treat the entire compressor with just a few simple numbers. All of the details like the number of blades, the number of vanes, the stagger angles of the blades, etc, etc get boiled down to a simple map. That way the thermodynamics guy does not have to know or even care about how many blades there are. He doesn't even care how many stages are in the compressor. He just knows that at 10,000 rpm the compressor is giving him 10 lbm/s, 15:1 pressure ratio and is 90% efficient (or whatever), and at 12,000 rpm it's giving 13 lbm/s at 18:1 ratio, etc. etc. The thermodynamic cycle then takes that compressor map, along with similar input from the turbine aerodynamics guys, the combustor aerodynamics guys, the inlet and exhaust aerodynamics guys, and combines it into an overall picture of the engine performance. There will be iteration between those groups. For example, the cycle guy may determine that he has more than enough thrust but he needs more efficiency. So the compressor aero guy then changes number of blades or something, now maybe it is 9.5 lbm/s at 14.5:1 ratio but 93% efficient at 10,000 rpm.

• Thank you very much!! This is exactly the answer I was hoping for. – user145760 Jul 8 '17 at 8:55
• "He doesn't even care how many stages..." - in real life, design is always an iterative process. Until you have taken a guess at how many stages you need, you don't know if an axial compressor is even feasible to physically fit in the space available! And the thermo guy should certainly take account of "details" like variable-angle stators (to improve stall margins etc) in a general way - but not in terms of the detailed design. – alephzero Jul 8 '17 at 22:23
• Actually, these days nobody gets paid to do the sort of calculations that use formulas like the OP quotes. Computers can do all that much faster. The fastest time I've seen in real life to do the basic design of a complete aircraft jet engine - to the level where we could give the customer (i.e. airline) a guarantee of the basic parameters like weight, thrust, fuel consumption, and price - was less than 48 hours. We got the contract, because the other companies involved couldn't match that speed of response - and the engine is now flying, so it wasn't just a hypothetical case study! – alephzero Jul 8 '17 at 22:30
• I must work for one of your competitors. We can't do anything in 48 hours ;) – Daniel K Jul 9 '17 at 3:00