Question 8 of 8: Fan Control

Question 8: Fan Control (10 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Part (a) — what moves on each diagram. In every case the operating point is the intersection of the fan characteristic with the system characteristic, so reducing the flow means moving one of the two curves. Figure 8.1 reproduces the three attachment diagrams with the design curves broken and the changed curve solid.

(i) Duct dampers. The system curve steepens while the fan curve stays where it is; the new operating point slides up and to the left along the unchanged fan characteristic, at a higher head and a lower flow. (ii) Inlet vanes. The fan curve is depressed, most strongly at high flow, while the system curve is untouched; the new point slides down and to the left along the unchanged system characteristic. (iii) Fan speed. The fan curve is again the one that moves, this time falling as a whole family of geometrically similar parabolas; the new point again slides down the unchanged system curve. The visual signature that distinguishes damper control from the other two is therefore simply which curve is redrawn, and whether the head at the new point is higher or lower than at design.

Part (b)(i) — effect of duct dampers. A damper is a deliberately introduced throttling loss. The system characteristic is $h=K_4Q^2$, and closing a damper raises $K_4$; the parabola through the origin becomes steeper and intersects the fan curve at a smaller flow. The fan itself is unaware that anything has changed — it simply moves back along its own curve to a point of higher head and lower flow. Taking the Question 5 fan and system as a worked illustration, reducing the flow from 528 to 423 m³/s requires the system constant to rise from $5.5\times 10^{-6}$ to $17.6\times 10^{-6}$, more than trebling the resistance. The whole of the extra head is dissipated across the damper vane as turbulence and heat: the air power at the duty point rises from about 415 kW, which is what the ducting genuinely needs, to about 1329 kW, so roughly 900 kW is thrown away. Damper control is therefore the cheapest to install, the simplest and most robust in service, and by a wide margin the least efficient. It also pushes the fan towards its stall line, since the operating point migrates up the characteristic towards the region of positive slope, and it can generate considerable noise across the throttling element.

Part (b)(ii) — effect of inlet vanes. Inlet guide vanes work on the machine rather than on the duct. Angling them imparts a swirl to the air in the direction of impeller rotation before it reaches the blades, so the fluid arrives with a pre-existing whirl component $C_{w1}>0$ instead of entering radially. Euler's equation for the work is

$$w=U_2C_{w2}-U_1C_{w1}$$

and the second term, which is zero for radial entry, now subtracts directly from the work transferred. The head the fan can produce at any given flow falls, and the whole characteristic is pushed down — more so at high flow, where the inlet velocity and hence the pre-whirl velocity are largest, so the curve is depressed and slightly flattened rather than merely shifted. The inlet velocity triangle shows the same thing geometrically: with the axial component fixed by the flow, adding a tangential component in the direction of rotation reduces the relative velocity's turning angle across the blade and therefore the change of whirl the impeller can impose. Because the reduction is achieved by transferring less energy in the first place rather than by destroying energy afterwards, inlet-vane control is markedly more efficient than damping — typically recovering half of the damper's excess at moderate turndown. Its weaknesses are that the saving falls away at deep turndown, that the pre-whirl introduces incidence mismatch and hence some loss of its own, and that the vane mechanism sits in a dirty gas stream and needs maintenance. Counter-rotating pre-whirl would increase the head, which is occasionally used for a modest boost but is not a control method here.

Part (b)(iii) — effect of fan speed. Reducing the driver speed rescales the entire fan characteristic according to the fan laws: at a given point on the homologous curve the flow varies as $N$, the head as $N^2$ and the power as $N^3$. The characteristic $H=K_1-K_3Q^2$ keeps its shape but its shut-off head drops as the square of speed, so the family of curves shrinks toward the origin, and each intersects the unchanged system parabola at a smaller flow and a lower head. Where the system curve is itself a parabola through the origin, as it is for pure friction, the operating point moves along the same homologous line, so the fan stays at its design efficiency point throughout the turndown — a considerable advantage. Continuing the Question 5 illustration, the same reduction to 423 m³/s needs only 924 rev/min against 1155, and the air power falls to $0.8^3=51\ \%$ of design, that is 415 kW — the same 415 kW the duct actually requires, with nothing thrown away. Speed control is thus the most efficient of the three by a factor of about three at this turndown, and it reduces noise and blade stress as well; its drawbacks are the capital cost and harmonic distortion of a variable-frequency drive or fluid coupling, reduced motor cooling at low speed, and the need to avoid shaft critical speeds within the operating range. On a large boiler ID fan the energy saving usually repays the drive within a year or two of part-load operation, which is why speed control has displaced damper control on new plant almost universally.