The interaction of fan and system characteristic curves
A system of ductwork and plant has a characteristic behaviour that can be shown by a curve relating the total pressure loss with the air quantity flowing through it. Equation (15.3) showed that pressure drop depends on the square of the air velocity and equation (15.12) allows us to extend this idea and say that the total pressure drop, Apt, is proportional to the square of the volumetric airflow rate, Q. A system characteristic curve is thus a parabola, passing through the origin, expressed by
Apt2 = Aai(C2/<2i)2 (15.39)
The behaviour of a fan also be shown by a characteristic curve that relates fan total pressure with volumetric airflow rate but this can only be established by test. Figure 15.18 shows how the shape of the fan curve depends on the type of impeller and it can be seen that an impeller with many, shallow, forward-curved blades has a point of inflection but one with a few, deep, backward-curved blades does not.
When a duct system is coupled with a fan running at a particular speed the duty obtained is seen by the intersection of their respective, characteristic pressure-volume curves. Such an intersection defines a point of rating on the fan characteristic, shown by P, or P2 in Figure 15.19. Changes in the fan speed do not alter the position of the point of rating on the fan curve but cause it to take up different positions on the system curve, in accordance with the fan laws (see section 15.16). Thus, in Figure 15.19, P! and P2 are the same point
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CB Q. Q> 3 In <n 2! Q. O Ra U> |
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Pressure-volume fan characteristic for a given speed of rotation |
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Fig. 15.18 Pressure-volume diagrams for fans with forward — and backward-curved impeller blades.
Of rating on the fan curve but occupy different positions on the system curve, depending on the speed at which the fan runs.
EXAMPLE 15.8
Plot the pressure-volume characteristic for the system forming the basis of example 15.7.
Answer
From example 15.7 the total pressure loss in the system for a flow rate of 3 m3 s_1 is 542.74 Pa, which is 543 Pa, for all practical purposes. Using equation (15.39) we can write Apl2 = 543(<22/3)2 and the following table is compiled:
<2(m3s-‘) 0.5 1.0 1.5 2.0 2.5 2.75 3.0 3.25
/tyt(Pa) 15 60 136 241 377 456 543 637
This information is plotted in Figure 15.19.
A fan should be chosen that has a characteristic, for a given running speed, that passes through the system curve at the desired duty, namely, 3.0 m3 s_1 and 543 Pa, in the cases of examples 15.7 and 15.8. If, for some reason, the fan curve does not intersect the system curve at the right point then the fan speed may be changed, in accordance with the fan laws (section 15.16), to give the correct duty.
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Volumetric airflow rate m3 s 1 Fig. 15.19 The point of rating on a fan characteristic curve is fixed but it slides down the system characteristic curve as the fan speed is reduced. |
EXAMPLE 15.9
A fan has a pressure—volume characteristic given by the following information, obtained from a test, when running at 1144 rev min"1 (19.1 rev s-1):
Q (m3 s-1) 1.5 2.0 2.5 3.0 3.5
Pee (Pa) 542 520 488 443 388
Determine the quantity of air handled if it is installed in the system forming the subject of examples 15.7 and 15.8.
Answer
The data are plotted in Figure 15.19 and show an intersection with the system characteristic at Pi, yielding a duty of 2.77 m3 s-1 at a fan total pressure of 463 Pa.
Posted in Engineering Fifth Edition