1. Fans and Blowers
Module V

2. Fans

3. Blowers
Centrifugal blower

4. Centrifugal fan or blower
Fans and blowers 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.
A centrifugal fan or blower
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.

5. 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.
A blower consists of an impeller which has blades fixed between the inner and outer diameters.
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.

6. Velocity triangle for centrifugal fan/blower
Velocity triangles at inlet and outlet of different types of blades of an impeller of a centrifugal blower

7. Velocity triangle
A centrifugal fan impeller may have backward swept blades, radial tipped blades or forward swept blades as shown.
The inlet and outlet velocity triangles are also shown accordingly in the figure.
Under ideal conditions, the directions of the relative velocity vectors Vr1 and Vr2 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.
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 (Vw2) is large which results in a higher stage pressure rise.

8. Effect of blade outlet angle
Outlet velocity triangles for different blade settings in a centrifugal pump
The head-discharge characteristic of a centrifugal pump depends (among other things) on the outlet angle of the impeller blades which in turn depends on blade settings.
Three types of blade settings are possible
the forward facing for which the blade curvature is in the direction of rotation and, therefore 2 > 900, (Fig. a),
radial, when 2 = 900 (Fig. b), and
backward facing for which the blade curvature is in a direction opposite to that of the impeller rotation and therefore, 2 < 900 (Fig. c).

9. Effect of blade outlet angle…
From the geometry of velocity triangle, the relationship between and can be written as.
In case of forward facing blade, 2 > 900 and hence cot2 is negative and therefore Vw2 > U2 .
In case of radial blade, 2 = 900 and Vw2 = U2
In case of backward facing blade 2 < 900 , and Vw2 < U2
The sign of K2 , the constant in the theoretical head-discharge relationship, depends accordingly on the type of blade setting as follows:
For forward curved blades, K2 < 0
For radial blades, K2 = 0
For backward curved blades, K2 > 0

10. Effect on velocity for different outlet angle
The following observations may be noted from figure

11. Parametric Calculations
The mass flow rate through the impeller is given by
The areas of cross sections normal to the radial velocity components Vf1 and Vf2 are A1 = D1b1 and A2 = D2b2
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 ,
Hence,

12. Flow Coefficient 
In flow turbomachines, an alternative to volume flow coefficient Q/( ND3) which is frequently used is the velocity (or flow) coefficient f = Vf/U where U is blade tip speed and Vf is the average axial velocity. Since
Q = Vf x flow area  VfD2
And Vf
then

13. Work The work done is given by Euler's Equation as
It is reasonable to assume zero whirl at the entry.
This condition gives
Therefore we can write,
Work done,
For any of the exit velocity triangles,

14. Work Therefore, where  = Vf2/U2 is known as flow coefficient
Head developed in meters of air =
Equivalent head in meters of water =
where a and w 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 2

15. Work The power required to drive the fan is
From any of the outlet velocity triangles
Work done per unit mass is also given by

16. Efficiency
The static pressure rise through the impeller is due to the change in centrifugal energy and the diffusion of relative velocity component. Therefore, it can be written as
The stagnation pressure rise through the stage can also be obtained as:
Therefore,
On account of losses, the isentropic work (p0)/ is less than the actual work.
Therefore the stage efficiency is defined by

17. Number of Blades
Too few blades are unable to fully impose their geometry on the flow, whereas too many of them restrict the flow passage and lead to higher losses. Most of the efforts to determine the optimum number of blades have resulted in only empirical relation given below,

18. Performance characteristic curves of a centrifugal blower or fan
The typical performance curves describing the variation of head, power and efficiency with discharge of a centrifugal blower or fan are shown in Figure

19. Fan Laws
Called affinity law derived using law of similitudes; provides three basic relationships
The process of arriving at the affinity laws assumes that the two operating points that are being compared are at the same efficiency.
Law 1: Flow vs. diameter and speed Or
Law 2: Total Head vs. diameter and speed Or
Law 3: Power vs. diameter and speed

20. Fan Laws Discharge  Speed Head developed  (Speed)2 Power  (Speed) 3
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

21. Performance of Fans
For all three cases (backward, radial and forward swept blades) in Figure, we can write
The work done is given by Euler's equation as
Noting that Vw1 = 0(zero whirl at the entry) we can write
The volume flow rate (assuming no density change between the inlet and outlet)
Thus,

22. Performance of Fans… Therefore, …(A)
Let us define, Pressure Coefficient,
Volume Coefficient,
and Power Coefficient,
Substitution of above coefficients in eqn (A) yields

23. effect of entire system
Performance of Fans…
(B)
(C)
Equations (B) and (C) are plotted for different values of volume coefficient  with 2 as a parameter.
Pump, dimensional form,
effect of entire system
Fan, non-dimensional form, only effect of angle

24. Assignment
Plot power coefficient and pressure coefficient vs. volume coefficient for different outlet angle β2 in MATLAB.

25. Performance of Fans…
The characteristics in Figure depict the following
Forward curved fans develop the highest pressure for a given impeller diameter and speed.
Power requirement of a forward curved fan increases steeply for a small change in flow rate.
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.

26. Degree of reaction

28. Another relation

30. Question
A centrifugal fan runs at 1450 RPM having inner and outer impeller diameter as 18 cm
and 20 cm. The flow rate is 0.5 kg/s. The relative and absolute velocities respectively
at entry and exit are 20 m/s, 21 m/s and 17 m/s, 25 m/s. If the motor efficiency is 78%,
Determine the following:
Stagnation or stage pressure rise
Degree of reaction
Power required to drive the fan.
The air density is 1.25 kg/m3
Answer
N/m2
0.457 W

33. Assignment
A backward-swept centrifugal fan develops a pressure of N/m2 . It has an impeller diameter of 89 cm and runs at 720 rpm. The blade angle at the tip is 39° and the width of the impeller is 10 cm. Assuming a constant radial velocity of 9.15 m/s and density of air as 1.2 kg/ m3 , determine the
(a) fan efficiency,
(b) discharge and
(c) power required.
(d) Degree of reaction
(e) Pressure coefficient
Answer
(a) 82.16%
(b) m3/s
(c) 2.29 kW
(d) 66.8%
(e) 1.328