# Power-volume and efficiency-volume characteristics

Two further characteristic curves, power-volume and efficiency-volume, are also used to express the performance of a fan at a given speed and these are shown in Figure 15.20(a),

(b) and (c), for three different types of fan. In Figure 15.20(a), for a centrifugal fan with backward-curved blades on its impeller, we see that peak efficiency corresponds to a point on the pressure-volume curve to the right of its maximum pressure where it is beginning to slope downwards fairly sharply. This is an advantage in that changes in fan total pressure (or system resistance) do not give large changes in the volume delivered. The curve for the power absorbed is seen to reach a maximum value just after the position of greatest efficency and to fall away thereafter.

The performance of a fan with forward-curved impeller blades is quite different (Figure 15.20(b)). Not only is peak efficiency to the left of the hump on the pressure-volume curve but the power absorbed goes on rising as the airflow increases. Moreover, if selection is to the right of the highest efficiency, small changes in fan total pressure give comparatively large changes in the air volume handled.

Figure 15.20(c) illustrates the behaviour of an axial flow fan and we see there is a non­overloading power characteristic, like that of a backward-curved fan. Maximum efficiency also corresponds to a steeply sloping position on the pressure-volume characteristic.

The point of rating chosen on the pressure-volume curve for a fan running at a certain speed identifies a particular total efficiency. When the fan is installed in a duct system, having a characteristic intersecting that of the fan at the chosen point, this point of rating stays in a fixed position on the fan curve, even if the speed is changed (see section 15.16). It follows that the fan efficiency will then remain constant at the original value as the speed is altered. The fan power absorbed can then be calculated according to the third law in group A when the speed is changed.

EXAMPLE 15.12

(a) For the case of examples 15.10 and 15.11 determine the fan power when the fan is running at 1239 rev min-1 (20.6 rev s-1) handling air (i) at 0°C and 101.325 kPa and (ii) at 35° and 85 kPa.

 Percentage fan total pressure Percentage fan total pressure Percentage fan total pressure Percentage airflow

 Percentage airflow

 Percentage airflow Fig. 15.20 The characteristic performance of various types of fan.   (b) Specify a suitable duty for the fan in (i), above, and estimate the probable power of the driving motor, assuming that the fan impeller has backward-curved blades.

(a) (i) At 0°C and 101.325 kPa:

Using fan law 3 in group A we have

Fan power = 1.527 x (1239/1144)3 = 1.94 kW

Alternatively, law 2 could be used to calculate the fan total pressure:

P, F = 463 x (1239/1144)2 = 543 Pa

Since the point of rating is unchanged (otherwise the fan laws could not have been applied) the efficiency remains at 84 per cent and, by equation (15.20), we then have

Wf = 3.0 x 0.543/0.84 = 1.94 kW

(ii) At 35°C and 85 kPa:

Using fan law 3 in group B we have

Fan power = 1.94 x x _1|_ = L44kw

Alternatively, law 2 in group B could be used to calculate the fan total pressure:

Pw = 543 X (273 + 35) X 10L325 = 404 Pa

Since the point of rating is unchanged and the volume handled remains at 3.0 m3 s-1 (by fan law 1 in group B), the fan power is determined from equation (15.20):

Wf = 3.0 x 0.404/0.84 = 1.44 kW

(b) Applying the margins suggested earlier and considering the operating conditions at 0°C and 101.325 kPa the duty specified would be

1.05 x 3.0 = 3.15 m3 s’1 and 1.1 x 543 = 597 Pa

It is reasonable to assume the same total fan efficiency as before and, applying a factor of 1.25 (because the impeller is backward-curved) the motor power can be estimated as

1.25 x 3.15 x 0.597/0.84 = 2.8 kW

This would be rounded up to a motor size of 3 kW.

 XI (c)  Vector diagrams at the blades of impellers and a picture of the blades of a backward — curved impeller with aerofoil section blades. Fig. 15.21 An impeller with backward-curved blades must run faster than one with forward-curved blades to give the same volumetric airflow rate, as Figure 15.21 shows. In the vector diagram we see that the tip speed vector at the blade tip must be greater for the backward — curved impeller than for the forward-curved, if the resultant vectors are to have equal lengths, implying the former must run at a greater rotational speed. The consequences are that fans with forward-curved impeller blades are smaller, cheaper, slower running and quieter than those having backward-curved blades for the same airflow rate, although the latter are more efficient. The forward-curved impeller can only develop fan total pressures up to about 750 Pa but there is virtually no limit with backward-curved fans. The usual

Choice for conventional low velocity systems is consequently the forward-curved fan. For medium and high velocity systems a backward-curved blade with an aerofoil section (Figure 15.21(c)) is commonly used.

To achieve the required performance from a centrifugal fan it is essential that the ductwork approach to the inlet eye is smooth and straight. The greater the departure from this ideal the more the reduction in performance. When single or double inlet fans are mounted in chambers, or air handling units (see section 15.21 and Figure 15.24), without ducted connections, at least three-quarters of an inlet diameter should be allowed between the inlet eye and the nearby wall of the chamber and at least 1.5 inlet eye diameters between the adjoining inlets of pairs of fans. The duct connection to the discharge side of the fan must also be straight and smoothly expanding. Ths is to give the airstream leaving the fan outlet a chance to expand and become less turbulent. The full effective length of straight duct (L) to achieve this, according to Keith Blackman (1980), depends on the mean velocity of airflow (V) in the duct and is given in equivalent diameters by

L/De = 2.5 + 0.2(V — 12.5) (15.40)

Where De is the equivalent duct diameter of the fan outlet, subject to a minimum length of 2.5 equivalent diameters.

Figure 15.22 illustrates the pattern of airflow at the outlet from a centrifugal fan. The true picture is more complicated than the figure suggests: there are many rotational components in the airstream and a complete recovery of their kinetic energy and a conversion to useful static pressure is difficult, if not impossible (as much as eighteen equivalent diameters may be needed). It is only the static pressure of an airstream that is immediately available to offset frictional losses, and it follows that it is highly desirable to convert as much as possible of the velocity pressure into static pressure. A measure of recovery occurs as the air flows through the rest of the supply system because the air velocity is progressively reduced in the process of duct sizing and, if this is done in a well engineered manner, significant static regain will result.

However, steps for recovery should be taken as soon as the air leaves the fan, the aim being to smooth the airflow into a fully developed, symmetrical profile as soon as possible. Equation (15.40) shows that this can mean the provision of quite a long length of straight duct.

 Velocity profiles Fully developed Fig. 15.22 Velocity profiles and effective duct lengths for the recovery of velocity pressure and conversion to useful static pressure at the outlet from a centrifugal fan.

The presence of a damper too close to the fan discharge greatly upsets the airflow and gives much higher pressure losses. Similarly, bends should not be too close to the fan outlet and, in the case of a branch it is especially important to have an adequately long section of straight duct between it and the fan.

The axial flow fan may appear to offer advantages in plant layout because of the straight through direction of airflow. However it is often convenient to use a centrifugal fan because the change of direction through 90°, suffered by the airflow, tends to reduce the length of plant room needed. Nevertheless axial flow fans can often be useful, provided that gradual reducers and expanders, of adequate straight length, are fitted at inlet (especially) and outlet. Axial flow fans invariably require silencers, particularly if the fan total pressure exceeds about 70 Pa.

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