Blade angles, Reaction, Diffusion

roldy

I'm really confused about an in class example my professor did to show how to obtain the hub and tip degrees of reaction of a free-vortex compressor stage and the diffusion factor for the rotor tip

Given:
[tex]\frac{\Delta P_t}{\rho {W_0}^2}=0.9[/tex]

[tex]\frac{r_t}{r_h}=2.646[/tex]

[tex]^{\circ}R_m=0.5[/tex]

[tex]\sigma_m=1.0[/tex]

[tex]\frac{\omega r_h}{W_0}=0.5[/tex]

His results:

[tex]D_{rotor,hub}=-.179[/tex]

[tex]D_{rotor,tip}=0.56[/tex]

[tex]D_{stator,hub}=.74[/tex]

[tex]D_{stator,tip}=0.55[/tex]

[tex]^{\circ}R_{tip}=0.714[/tex]

[tex]^{\circ}R_{hub}=-1.0[/tex]


The only values that I found where the [tex]^{\circ}R_{tip}[/tex] and [tex]^{\circ}R_{hub}[/tex].

For now, I'm just concentrating on figuring out the rotor tip diffusion. The equation that I have for the Diffusion of the rotor is as follows.

[tex]
D_{rotor}=1-\frac{cos(\beta_1)}{cos(\beta_2)}+\frac{1}{2\sigma}(tan(\beta_1)-tan(\beta_2))cos(\beta_1)
[/tex]

I would assume that the beta angles are the beta tip angles. This is where I got stumped. I don't have [tex]\omega[/tex] or [tex]W_0[\tex] to help me solve for the missing things.