Axial Fans
Figure 9.43 shows the schematic diagram of an axial fan system. The air flows through a nozzle toward the impeller, where static pressure rises. The impeller is attached to a hub. The impeller is also called the propeller. The propeller is followed by a diffuser.
When the aim is to build a cheap fan system and have a small pressure rise, then the nozzle and diffuser are not usually installed in the system.
The performance of an axial fan is based on the external force to drive the propeller, whose blades change the direction of airflow when flowing from the inlet edge to the outlet edge.
Equation (9.59) is valid, but when ux = the power needed is
Pu = qmu(clucXu) = qmu Acu. (9.101)
Nozzle Diffllspr
Propeller Hub / C/Sing
/
Since Pu is positive, it must be that c2u > clu when the circumference speed is chosen as the positive direction. Equation (9.101) is valid for every circumference speed between the hub circumference and the outer impeller circumference.
In the following discussion, u is the average circumference speed. The absolute velocity in the shaft direction is denoted by ca.
The mass flow is constant in the shaft direction, so
Jo>i — 
(9.102,1 
J(D — Dl)cla = p
Where D, is the impeller diameter and D2 is the hub diameter.
Equation (9.102) gives cXa = c2a. The axial component does not change, but when clu > clu, then c2> cv Thus, the axial fan increases the absolute velocity of airflow.
Generally, Eq. (9.80) is valid, but when ut = u2, it gives the static pressure increase for an axial fan as
I, ■w 2) 
(9.103) 
1
&Ps = Pls~P = 2p(w
Equation (9.79) shows that the rise in circumference velocities at the entrance and exit leads to the static pressure p(u2 — mJ) increase but not in the axial fan. This results in the axial fan’s not having the same pressure rise as that of the centrifugal fan. Axial fans are applicable for large airflows, when the needed pressure increase is relatively small.
The reaction ratio of an axial fan for the isentropic case based on Eqs. (9.75), (9.81), and (9.103) is
W i — Wn
= 
(9.104)
2u{cu2cul) ‘
We restrict ourselves to investigate an axial fan, where there is only an impeller. The incoming air has the direction of the axis of the propeller.
The rotating of the impeller increases the absolute velocity of air. In order to increase the static pressure of the gas flow owing to the fan, the velocity relative to the blades should decrease according to Eq. (9.103).
The flow velocity diagrams on both sides of the impeller are shown in Fig. 9.44. The axial direction is the datum for all angles.
From the conditions c^, = cXa = wla — wXa and wx > w2, the relative velocity is smaller at the exit than at the inlet. There are two possibilities: the leaving flow direction angle is on the same axis side as that of the coming flow, or the leaving flow direction angle is on a different axis side. Figure 9.44 shows blades where both the relative velocity direction angles and j82 are on the same axis side.
The velocity triangle at the entrance gives
2
(9.105) (9.106) (9.107) (9.108) 
2 ? w = u~ + ca
And at the exit gives
2 , .2 2 IV2 = (M — C2«) + Ca.
From Eq. (9.103) the isentropic pressure rise is determined by
1 1 ‘ = ^p(2ucluclu) = pu
The exit velocity triangle gives
U — C,
Tan 02
From which
(9.109) 
^2« = 1 — — tan 0i, u u
And from Eq. (9.107)
Tan202 
(9.110) 
A p5 = pu
Using Eqs. (9.103) and (9.104), the reaction ratio is determined by
1 — ~2 tan~02 
2«" 
1 — — tan0i 
R = ,2Aft. = S 2 P«c2m 


/
1 + — tan m *• 
! , tan02 .
Tan0ly
7r/2,then cot01 > 0, tan02 > 0,
Because 0 < 0j < 7t/2 and 0 < 02 and r >
From the exit velocity triangle, it can be seen that the gas flow has a tangential velocity component. The gas rotates when it leaves the fan. Normally, the tangential velocity component is of no benefit if a duct is attached to the fan, since it disappears due to friction.
Example 2
The diameter of an axial fan impeller is Dx — 0.6 m, the hub diameter is D2 = 0.3 m, and the rotational speed is n — 960 rev min1. The axial velocity of airflow is cXa = 5.5 m s1, and the blade angle is 02 =10° (average) at the
Blade exit. Calculate the power, isentropic static pressure increase, and reaction ratio. The pressure of the coming air is I bar, and the temperature is 45 °C.
Solution. The average diameter is calculated by
D = j(D, + D2) = (0.6 + 0.3) = 0.45 m.
The average circumference speed is u = tt Dn = 22.6 m s1. The velocity trian
Gle on the entrance side as shown in Fig. 9.45a gives
Tan/3, = — = — = = 4.11 =*0! = 76.3°.
C1 ^ ‘I *
The velocity triangle at exit has /32 = 10°, w2a = c2a — 5.5 m s_I, which gives
Lli 
Tan/3i = tan 10° Wj
‘ Wla
Wlu = w2a ■ tan)32 = 5.5 tan 10° = 0.97 m s’ c2u = u ~ wiu = 22.6 — 0.97 = 21.6 m s’1.
Using ideal gas law, the air density is calculated as
Л = Ш= 105 28.964 = I nqr b 3
P RT 8314.31 (273 + 45) g ‘
The flow area is
A = — D2) = f(0.62 — 0.32) = 0.212 m2.
The mass flow through the fan is
Qm = pcuA = 1.095 ■ 5.5 • 0.212 = 1.277 kgs1. Equation (9.101) gives the power as
Pu = <3»,U(C2UC 1«) = йпгис2u = 1277 ■ 22.6 ■ 21.6 = 623 W
(a) 
(b) 
^21.6 1 21.6^ 22.6 2 22.6Z 
/ 2 C2u 1 C2u U 2M2 
= 267 Pa 
Aps = pu2 Equation (9.111) gives the reaction ratio as 
= 1.095 22.6′ 

1 + 
Tan 10° Tan 76.3° 
= 0.521 
At the exit the absolute velocity has velocity component c2u on the large circumference parallel to the shaft of Example 3. Component c2ll is of no advantage if a duct is connected to the axial fan, since it disappears due to the friction between the walls of the duct and gas flow.
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