Fans and blowers (Fig. 39.1) are turbomachines which deliver air at a desired high velocity (and accordingly at a high mass flow rate) but at a relatively low static pressure. The pressure rise across a fan is extremely low and is of the order of a few millimeters of water gauge.The upper limit of pressure rise is of the order of 250mm of water gauge.The rise in static pressure across a blower is relatively higher and is more than 1000 mm of water gauge that is required to overcome the pressure losses of the gas during its flow through various passages. A blower may be constructed in multistages for still higher discharge pressure.

Figure 39.1 A centrifugal fan or blower

A large number of fans and blowers for relatively high pressure applications are of centrifugal type. The main components of a centrifugal blower are shown in Fig. 39.2. A blower consists of an impeller which has blades fixed between the inner and outer diameters. The impeller can be mounted either directly on the shaft extension of the prime mover or separately on a shaft supported between two additional bearings. Air or gas enters the impeller axially through the inlet nozzle which provides slight acceleration to the air before its entry to the impeller. The action of the impeller swings the gas from a smaller to a larger radius and delivers the gas at a high pressure and velocity to the casing. The flow from the impeller blades is collected by a spiral-shaped casing known as volute casing or spiral casing . The casing can further increase the static pressure of the air and it finally delivers the air to the exit of the blower.

Figure 39.2 Main components of a centrifugal blower

The centrifugal fan impeller can be fabricated by welding curved or almost straight metal blades to the two side walls (shrouds) of the rotor. The casings are made of sheet metal of different thickness and steel reinforcing ribs on the outside. Suitable sealing devices are used between the shaft and the casing.

A centrifugal fan impeller may have backward swept blades, radial tipped blades or forward swept blades as shown in Fig. 39.3. The inlet and outlet velocity triangles are also shown accordingly in the figure. Under

ideal conditions, the directions of the relative velocity vectors and are same as the blade angles at the entry and the exit. A zero whirl at the inlet is assumed which results in a zero angular momentum at the inlet. The backward swept blades are employed for lower pressure and lower flow rates. The radial tipped blades are employed for handling dust-laden air or gas because they are less prone to blockage, dust erosion and failure. The radial-tipped blades in practice are of forward swept type at the inlet as shown in Fig. 39.3. The forward-swept blades are widely used in practice. On account of the forward-swept blade

tips at the exit, the whirl component of exit velocity is large which results in a higher stage pressure rise.

The following observations may be noted from figure 39.3.

, if , backward swept blades

, if , radial blades

, if , forward swept blades

Figure 39.3 Velocity triangles at inlet and outlet of different types of blades of an impeller of a centrifugal blower

Parametric Calculations

The mass flow rate through the impeller is given by

(39.1)

The areas of cross sections normal to the radial velocity components and are and

(39.2)

The radial component of velocities at the impeller entry and exit depend on its width at these sections. For small pressure rise through the impeller stage, the density change in the flow is negligible and the flow can be assumed to be almost incompressible. For constant radial velocity

(39.3)

Eqs. (39.2) and (39.3) give

(39.4)

Work

The work done is given by Euler's Equation (refer to Module-1) as

(39.5)

It is reasonable to assume zero whirl at the entry. This condition gives

and hence,

Therefore we can write,

(39.6)

Equation (39.5) gives

(39.7)

For any of the exit velocity triangles (Figure 39.3)

(39.8)

Eq. (39.7) and (39.8)

(39.9)

where is known as flow coefficient

Head developed in meters of air =

(39.10)

Equivalent head in meters of water =

(39.11)

where and are the densities of air and water respectively.

Assuming that the flow fully obeys the geometry of the impeller blades, the specific work done in an isentropic process is given by

(39.12)

The power required to drive the fan is

(39.13)

v

Fan Laws

The relationships of discharge Q , head H and Power P with the diameter D and rotational speed N of a centrifugal fan can easily be expressed from the dimensionless performance parameters determined from the principle of similarity of rotodynamic machines as described before . These relationships are known as Fan Laws described as follows

(40.1)

(40.2)

(40.3)

where and are constants.

For the same fan, the dimensions get fixed and the laws are

and

For the different size and other conditions remaining same, the laws are

and

(40.4)

These relationships are known as the Fan-laws. The Fan-lows can be summarized as

For the same fan:

Discharge Speed

Head developed (Speed)2

Power (Speed) 3

For the fans of different sizes:

Discharge (Diameter)3

Head developed (Diameter)2

Power (Diameter)5

Performance of Fans

For all three cases (backward, radial and forward swept blades) in Figure 39.3, we can write

(40.5)

The work done is given by Euler's equation (refer to Modue-1) as

(40.6)

Noting that (zero whirl at the entry) we can write

or,

(40.7)

The volume flow rate (assuming no density change between the inlet and outlet)

Thus

By substitution in (40.7)

(40.8)

Let us define, Pressure Coefficient,

(40.9)

Volume Coefficient,

(40.10)

and Power Coefficient,

(40.11)

Substitution of (40.8) in the above yields

(40.12)

or,

(40.13)

(40.14)

Equations (40.13) and (40.14) are plotted in Fig 40.1 for different values of volume coefficient with as a parameter.

Figure 40.1 Performance curves of a Fan

The characteristics in Figure 40.1 depict the following

(i) Forward curved fans develop the highest pressure for a given impeller diameter and speed.

(ii) Power requirement of a forward curved fan increases steeply for a small change in flow rate.

(iii) Pressure developed decreases fast with increasing flow rate in a backward curved fan

In conclusion, the forward curved fans have large volume discharge and pressure rise but they demand higher power. However, forward curved fans are unstable for off-design operating conditions.

Backward curved fans are very efficient and the drooping power characteristic makes them suitable for a better off-design performance

Radial curved fans are preferred for dust-laden fluids. Due to their shape, the solid particles are not stuck and deposited on the blade surface.

Exercise

1) A centrifugal blower takes in 200 m3 /min of air at a pressure and temperature of 101 kN/ m2 and 45 C and delivers it at a pressure of 750 mm of water gauge. Assuming the coefficients of the blower and the drive as 80% and 82% respectively, determine (a) the power required to drive the blower and (b) the pressure and temperature of air at blower exit.

2) A backward-swept centrifugal fan develops a pressure of 80 mm of water gauge. It has an impeller diameter of 0.89 m and runs at 720 rpm. The blade angle at the tip is 39 and the width of the impeller is 0.1m. Assuming a constant radial velocity of 9.15 m/s and density of air as 1.2 kg/ m3 , determine the fan efficiency, discharge and power required.

3) A centrifugal fan discharges 400 m3 /min of air at a static pressure of 40 mm of water gauge when operating at 400 rpm. The power input is 4.5 kW. The diameter of the outlet duct is 60 cm. The pressure losses due to friction from inlet to outlet are negligible. Determine the static and total efficiencies of the fan. Assume pressure and temperatures as 1.013 bar and 200 C respectively. The density of air may be assumed 1.2 kg/m3 .