Air power output

Bearing losses

Aerodynamic losses

Belt loss Motor loss

Electrical/electronic controller loss

Electrical power input

Q is proportional to D3 p is proportional to D2

N N2 ρ Power is proportional to D5 N3 ρ

Where D = fan impeller diameter, ρ = density of air and N = speed of fan rotation

Figure 2 – Losses from the whole fan subsystem (after BS 5801:2008)

by dividing air power (pressure, Pa x volume flowrate, m3

/s) by the shaft input

power. The actual shape of the curves will depend on the type of fan (and the shape of this example is typical of a ‘backward curved centrifugal’ fan). The manufacturer will often identify a ‘selection range’ that is recommended for the fan. This is shown as the yellow highlight in Figure 3. The fan efficiency varies across the operational range of the fan. The losses will be due to friction in the fan case; turbulence and ‘shock’ losses; losses in bearings and seals; and leakage and short- circuiting. The total losses (including the whole subsystem from electrical power compared to the air power being supplied) will be somewhat greater than those indicated on the fan curves due to external losses, as illustrated in Figure 2 for an example fan.

The fan meets the system As discussed in recent CPD articles, if the volume flow rate in the ductwork is varied the pressure loss will be related to the square of the volume flow rate. This may be simplified to ∆p = RQ2

where ∆p

is the system pressure drop (Pa), Q is the volume flow (m3

/s) and R is a constant for

the system relating to its resistance to air flow (the term resistance, should not be confused with system pressure drop). Using a calculated pressure drop at any

particular flow rate, the value of R may be determined and then a curve drawn for a range of volume flow rates against pressure drop, as in the system curve in Figure 4. This figure has also had the fan curve

from Figure 3 superimposed – the fan curve being a series of points at which the fan can operate at a constant speed. Likewise, a system curve is the series of points at which the system can operate. The operating point for the fan-system

62 CIBSE Journal November 2011

combination is where these two curves intersect, and this provides the flow rate for this particular fan running at a particular speed with this system. In this case the efficiency also appears to be almost at a maximum so the fan will be operating at its most effective. However, of course, this is not the required design flow rate (shown in green) – the fan, running at this speed, will deliver more air though the system than is required. Also the practicality of real system operation must not be forgotten. Although the system curve has been established from design calculations, the installed system is bound to differ from this due to installation vagaries and uncertainties in the design data. Also, while in use there will be continuous changes in the pressure profiles, both in the system and the building, so when considering the operating point, thought must be given to the potential range of conditions and the effect they may have on the fan output. The extremes of operation can be particularly significant when considering variable air volume (VAV) systems. The temperature of the air passing

across a fan will affect the mass flow rate of the air. For example, if a fan is simply passing fresh air through a system, then as the external temperature increases the air density will reduce and hence the mass flow rate of air will also reduce. This is shown in Figure 5 – note how the volume flow rate will remain constant.

A family of fan curves The performance of fans is determined by a number of relationships (known ‘fan laws’) that can be derived to examine what will affect a fan’s operation. In the ranges that would be expected in building services applications:

So the flow rate will alter with the cube of the impeller diameter, (and the pressure with the square of the diameter), so a change in a fan diameter will make a disproportionate alteration to the volume flow (compared with the swept area of the fan impeller). And the power (being the product of pressure and volume flow rate) will increase to the fifth order of the diameter, so a small change in fan diameter can produce a large increase in fan power and a consequent increase in motor power and supply electrical power. The fan’s diameter, D, and the air

density, ρ, are normally assumed to be constant when considering a specific fan and system combination, and so the three relationships are conveniently simplified to Q ∝ N, p ∝ N2

, and Power ∝ N3 . So,

for example, a 10% increase in fan speed means a 10% increase in air volume flow rate, a 21% increase in pressure and a 33% increase in power consumption. And using these relationships families

of fan curves can be drawn for operating the fan at different speeds as in Figure 6 – each of the fan speeds has its own operating point with the system but, in this case, only the low fan speed provides the required flow rate for this example.

Varying the flow The flow can also be altered (reduced) on the system side by adding restrictions (such as dampers) or by altering the way that air is fed into the fan using ‘guide vanes’ or ‘throttling discs’. Although these may be a capitally cheap option, and appropriate for infrequently used systems or for those where only minor regulation is required, their use for significant alterations to the operating point should be carefully considered as they are likely to severely reduce the potential savings available from the reduction of air volume flow rates. Multiple speed electrical motors can be used to provide efficient ‘step changes’ in fan output – this is where there are separate windings within a single motor that can be used to alter the speed to meet specific load requirements (for example, in a cooking area where there are quite different air supply requirements when preparing food, compared to when

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