Air flows in a axial flow fan of free vortex design with hub

Air flows in a axial flow fan of free vortex design, with hub radius r_h = 7.5 cm and casing radius 17cm. The fan operates at 2400 rpm. The volumetric flow rate Q = 1.1 m^3/s and the stagnation pressure rise is 3 cm H_2O. The fan efficiency is eta_tt - 0.86. (a) Find the axial velocity, (b) Find the work done on the fluid, (c) Find the absolute and relative flow angles at the inlet and exit of the rotor when the inlet is axial.

Solution

solution:

1)for given axial flow compressor as per design degree of reaction is 50% hence

inlet vane angle(relative) =flow angle at outlet(absolute)

a=m

outletvane angle=inlet flow direction

b=n

2)for axial flow fan we have flow rate as follows

Q=pi*(17*17-7.5*7.5)Cf*10^-4

where Q=1.1

hence Cf=15.0436 m.s

3)blade velocity is

D=Dh+Dt/2=.245 m

Cb=pi*D*N/60=30.7876 m/s

4)pressure rise is

P=1000*9.81*3*.01=294.3 N/m2

P=(Cwo-Cwi)Cb

Cwo-cwi=9.559 m/s

5)work done is given as

W=(Cwo-Cwi)*Cb=294.3 kj/kg

5)actual work=W/n=294.3/.86=342.209 kj/kg

6)here from velocity triangle for axial fan

we have

cwo-cwi=Cb-2*x

we get

x=Cwi=10.6143 m/s

where Cwo=20.1733 m/s

7)where Cf is given as

Cf=xcotm

m=b=35.20 degree

cf=(cb-x)cotn

n=a=53.28 degree