P. LIU ET AL.

2

vortex design, which was investigated by three dimen-

sional laser Doppler anemometer measurement [7].

In this paper, the radial flows at both the inflow and

the outflow have been considered for the improvement of

the design method. Two types of axial flow fans are de-

signed by the controlled vortex design by specifying the

constant tangential velocity both at inlet and outlet of the

rotor. One type is ducted axial flow fan which is usually

designed to prescribe almost uniform inflow and outflow

as if it was in the straight pipe. However, many axial

flow fans are not used in the straight pipe, such as the

application of using in the ventilation and cooling sys-

tems without pipe. Thus it is important to take the real

flow situation into account in design. Then the other type

which is half-ducted axial flow fan was designed to com-

pare with the traditional design of ducted ones by speci-

fying the flow angles according to the previous experi-

mental results of authors [8,9].

2. Design and Numerical Method

The quasi three-dimensional flow theory was applied to

investigate the flow of the axial flow fans. The merid-

ional flow and the revolutional flow between blades were

calculated by the method of streamline curvature. Based

on the theory, the meridional flow was calculated by

adopting the radial balance equations [10], while the

calculation of the blade to blade flow was obtained by

2D cascade data with the correction by a potential flow

theory so as to consider the axial flow velocity change

and the inclination of the flow surface [11].

In calculation of meridional flow, the following force

balance equation was evaluated at the quasi-orthogonal

direction on meridional plane:

2

2

d

d

m

m

V

qV Bq

q (1)

when the compressibility of the fluid is ignored,

1sinsind

2t

cos d

m

Aq rrq

an

(2)

d

d

1

2dd

t

tt

rV

PV

Bq qr q

(3)

2

expd expd

m

i

V

qqBqAqq C

(4)

The arbitrary constant Ci can be got by the relative

equation of mass flow rate and velocity. The energy per

second getting through outlet of the rotor can be calcu-

lated by the following equation on assumption of con-

stant Vt at inlet and outlet (0 at inlet):

222

cos d

c

h

q

th mt

Bq

m

EI rVuV

K

22

q

2t

(5)

So that Vt2 can be got. The total pressure rise is pre-

sumed to be able to calculate by the Euler equation as:

2t

PP uV

(6)

Therefore, the meridional velocity and the tangential

velocity can be obtained so that the calculation of merid-

ional flow is finished.

The blade profile on the revolutional plane was se-

lected by referring to the diagram of circular arc carpet.

Thus, the circular arc blade with equal thickness and

quadrilateral blade on the meridional plane was adopted.

Two types of axial flow fan were designed in this pa-

per. One is the ducted case as if it was in the straight pipe

and another is the half-ducted case with the radial inflow

and outflow. The blade shapes on top view were obtained

showing in Figure 1 on right side. The highly twisted

blades can be avoided by half ducted fan with the con-

trolled vortex design by specifying the flow angles. For

the ducted fan, the streamlines on the meridional plane

are uniform and parallel to each other, as shown in Fig-

ure 1(a). While the streamlines of half-ducted fan shown

in Figure 1(b) obviously differ from that of ducted fan

because the inclinations of inflow and outflow are given

based on the experimental data [8,9] so as to consider the

effect of radial velocity component on the internal flow

field. The flow angles of the streamlines are given 63, 16,

38 degrees respectively on tip streamline at inlet, on tip

streamline at outlet, on hub streamline at outlet.

Table 1 shows the designed parameters of ducted fan

and half-ducted fan. All these parameters are specified

the same value for both of the designed fans. Besides, the

blade shape near the hub and the casing is not straight

line but modified into spline curve, which can be seen in

Figure 7(a). The flow rate and pressure rise are repre-

sented with nondimensional form of flow coefficient and

pressure rise coefficient which are defined as:

22

4

πth

Q

DDU

t

(7)

2

2

t

p

U

(8)

and

s

pQ

T

(9)

The designed fan blade profile data were tackled in the

commercial software for the analysis of three-dimen-

sional flow. In order to increase the speed of the numeri-

cal simulation, the internal flw fields of the axial flow o

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