Fan and Duct Network
In some instances the fan has a free discharge. Typical is the axial fan installed in a wall opening (wall fan). In most cases the fan is connected to a duct run; in this instance the total pressure difference and volume flow are determined from both the fan and duct network characteristics.
Consider the thermodynamic analysis for incompressible gas flow in a I 1 2 —i 1 2 2^ ““ i 2Cl (9 A 1.8) |
Where
C is the air velocity
Z is the height Equation (9.63) gives
(9.119)
For which Eq. (9.118) can be written as
1 2 » ‘ = Pi + 2f)t’2 + P8Zz + P’ |
(9.120) |
F2 . . .
The term Ap = pJi T ds is the entropy generation given as pressure loss.
In a straight duct where Zj = z2 and the cross-sectional area is uniform, then ct = c2. This gives Ap = pi — p2 > 0 . Ap is the duct pressure loss, which is a result of entropy generation. Entropy generation is due to the flow friction, which is the reason for pressure loss.
Consider the pressure Joss in a duct with straight, uniform cross-sectional area. The pressure loss is caused by friction. When different air sheets move against each other, friction is generated. The velocity and thermodynamic properties of air influence the friction. The duct wall has an overall roughness, which causes vortices to be formed with resulting friction in gas. The velocity has a pronounced effect; in flow with low velocity, the vortices are small. For a straight duct the pressure loss Apk can be determined from
(9.121)
Where
L is the duct length D is the inner diameter f is the flow friction factor
In velocity and gas property effects, the Reynolds number, Re, is taken into consideration as
(9.122) |
Re = —
V
Where p is the kinematic viscosity.
The kinematic viscosity is related to density by
Where p. is the dynamic viscosity.
Friction factor. |
Consider next the fan with its connected air duct characteristics when both are operating together. We indicate the fan leaving air by subscript 2 and the suction side by subscript 1.
Using Eq. (9.120) gives
Pi + pci = P + JPci + A/?, (9,127)
Where Ap = Apk + Apkv> the pressure difference in straight ducts, bends, etc. caused by the entropy generation.
Equation (9.127) can be rewritten as
A p = p2-p +^p{cj-c) = ApIot, (9.128)
Which means that the generated pressure loss is large—as much as the fan total pressure difference.
For a special fan situation, a straight air duct of uniform cross-sectional area is used on the leaving side. The outgoing velocity c3 is the same as the fan leaving velocity c2. The only minor loss is the outgoing loss = pc3. Another part of the pressure drop is the frictional pressure drop Apk. Equation (9.127) gives
A p = A pk + ^pcj = A pk + jpcj = A ptot, (9.129)
From which
&Pk = ^Pmt-jPci = Pi~Pi-pcl = pk. (9.130)
The pressure term pk in Eq. (9.130) is called the obtainable fan pressure.
In steady-state conditions, the mass and volume flow are constant through the fan and duct. If the duct consists of branches of different crosssectional area A(, then
Q„— c, A{ i=l,…,n (9.131)
Where n is the number of different cross-sectional areas At.
The duct pressure drop can be obtained from Eqs. (9.121) and (9.126) as
Ap = ’ (9.132)
The fan total pressure difference Aptox also depends on the volume flow. In practice, dependency is determined experimentally, Aptot = f(qv). Equations (9.128) and (9.132) give
Aprot = «?„) = • (9’1331
The fan volume flow qv and its corresponding Aptot can be found when a Apt0l — qv chart is drawn; the duct parabola and experimental Ap(0t both equal f{qv) (Fig. 9.47). The experimental curve Aptot = f{qv) is called the fan characteristic curve, and the duct static pressure drop dependency on the duct volume flow is the characteristic curve. The characteristic curve intersection point is called fan operating point.
Ivl FIGURE 9.47 Fan and duct operating point (Apv |
Example 5
The fan characteristic curve is given by
0 |
556 |
1111 |
1667 2222 |
2778 |
3333 |
||
APror, P* |
491 |
535 |
549 |
535 |
491 |
417 |
314 |
Pj, kw |
0.40 |
0.63 |
0.90 |
1.20 |
1.53 |
1.7 |
1.75 |
The duct pressure drop is 589 Pa; airflow is 1944 L s_1. Determine the fan total pressure, volume flow, shaft power, and total efficiency.
Solution. Draw into the Aptol — qv diagram the characteristic curve of the fan and the duct-pressure-drop volume flow dependency. The latter is a parabola passing through the origin with the following equation:
^ 1944 ‘^v ‘
(Here Aptot is in Pa and qv in L s_1.) At the curve’s intersection point, Ap = Apm = 520 Pa and qv = 1900 L s^1 = 1.9 m3 s_1. By interpolation from the above table, the shaft power is 1.34 kW. The total fan efficiency is
V = = 5201.9 _ 0.737 = 73.7% .
77 Pa 1340 U./O /0.//0.
It may be necessary in a given system to use more than one fan. The fans may be connected either in series or parallel.
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