Thermodynamics Question (Centrifugal Compressor)

[Noisia]

Hi there guys,

Sorryto make my first post on here a request, but i am a little puzzled at the moment by this latest question I have been set! My lecture notes do not seem to cover this in any detail at all, and resources on the internet are either avoiding me or i am just plain blind!

1. Inlet blade angle : -55 degrees, Outlet blade angle : 0 degrees, mass flow rate of air : 4.32 kg/s, rotor inlet radius : 45mm, rotor radius at tip : 0.14m, outlet dimensions are r2 : 0.2m and h2 : 22mm, rotor has 21 blades, rotation speed is 15000rpm. Air enters compressor at temperature of 300K and pressure of 1.0atm.

Starting with a guessed value for c1, and using an iterative process, find Ma1 and the inlet velocity triangle satisfying the prescribed mass flow rate


2. As for equations I am not even sure what i should be using. These are what i have so far:

c = u + v

M1 = V1 / ([gamma]*R*T)^1/2

Then using v = V(flow rate) / A



I think that there is a fundamental error in my working so far, whether the equations are totally in the wrong direction i don't know! If you guys could just set me in the right direction it would be much appreciated as this has been doing my head in for a while now!

Regards

 

[NateD]

The equations you started with are on the right track, but you need to use a few more equations to solve this problem. As you know, the mass flow rate is equal to the product of density, velocity, and area. You can use this equation to calculate the velocity at the inlet and outlet of the compressor. Additionally, you need to use Bernoulli's equation to calculate the pressure at the inlet and outlet. Finally, you need to use the equation of state to calculate the temperature at the inlet and outlet of the compressor. Once you have all of these values, you can use the velocity triangles to calculate the Mach number. Hope this helps!