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25-Nav-B5 Marine Control Systems · May 2017

Question 8 of 8: Fan Control

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format: National Examination 98-Mar-B5 Fluid Machinery, May 2017 — closed book, three hours, 60 marks. Section A is calculative (Q1–Q5) and Section B is descriptive (Q6–Q8); the rubric asks for four questions of Section A plus two of Section B (six questions, each of equal value, 10 marks). All eight questions are solved in full as a study resource. General constants supplied with the paper: g = 9.81 m/s², patm = 100 kPa, pvapour = 2.34 kPa (20 °C), ρwater = 1000 kg/m³, ρair = 1.21 kg/m³ (15 °C), cp,air = 1.005, cv,air = 0.718 kJ/kg·K.

Reference texts. S. L. Dixon & C. A. Hall, Fluid Mechanics and Thermodynamics of Turbomachinery (7th ed.); R. A. Sabersky, A. J. Acosta, E. G. Hauptmann & E. M. Gates, Fluid Flow: A First Course in Fluid Mechanics (4th ed.); H. Cohen, G. F. C. Rogers & H. I. H. Saravanamuttoo, Gas Turbine Theory; R. W. Fox, A. T. McDonald & P. J. Pritchard, Introduction to Fluid Mechanics.

Check: This paper, although listed under “Marine Control Systems”, is printed and headed “98-Mar-B5, Fluid Machinery” throughout, with zero marine-control-systems content (no PID loops, governors, or automation). It is solved here exactly as printed. Question 2's design method (annulus sizing from mass flow, 50% reaction symmetric velocity triangles) follows the standard preliminary axial-compressor design procedure of Dixon & Hall ch. 3–5; since no stage/compressor efficiency is supplied, the number of stages is obtained from the ideal (isentropic) overall temperature rise divided by the actual work done per stage — the standard simplification for this class of preliminary-design problem. Question 3 assumes zero exit whirl at the Francis runner outlet (design/best-efficiency condition), the standard assumption when no exit-blade data is given.

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.

All three methods move the fan away from its design operating point (the intersection of the original fan curve and the original system curve) to a new, lower-flow intersection — but each does so by moving a different one of the two curves, which is the key distinction between them.

(i) Duct dampersQHsystem curve steepens; new pt. moves down-left along the SAME fan curve(ii) Inlet vanesQHpre-whirl lowers the fan curve itself; system curve unchanged(iii) Fan speedQHwhole fan curve drops by N² (affinity laws); system curve unchanged
Fig. Q8 - Fan control methods, each starting from the same design operating point (green dot) and moving to a reduced-flow point (red dot): (i) dampers steepen the system curve along an unchanged fan curve; (ii) inlet vanes lower the fan curve itself against an unchanged system curve; (iii) reduced speed drops the whole fan-curve family (affinity laws) against an unchanged system curve.

(a)(i) / (b)(i) — Duct dampers

A damper is a variable restriction added in series with the existing ductwork. It does not alter the fan itself, so the fan curve is unchanged; instead it adds extra frictional resistance, which steepens the system-resistance curve $h=K_4Q^2$ (a larger effective $K_4$) at every flow. The new operating point is where this steeper system curve crosses the same, unmoved fan curve — necessarily at a lower Q and a higher H than before, since the fan curve is falling and the new system curve is steeper. Physically, the fan is still trying to deliver its full design flow, but the operator is throttling it by manufacturing an artificial extra pressure drop; the fan absorbs more head than it needs to for the reduced flow, which is thrown away as friction across the damper — this is why damper control is simple and cheap to install but the least energy-efficient of the three methods (the "wasted" head is fan power that still had to be supplied).

(a)(ii) / (b)(ii) — Inlet vanes

Inlet guide vanes swirl (pre-whirl) the air before it enters the impeller eye, so that it already has some tangential velocity component in the direction of impeller rotation before the blades act on it. From the Euler turbomachine equation, work input (and hence developed head) depends on the change in whirl velocity across the impeller, $w=U(C_{w2}-C_{w1})$; giving the flow a head-start of pre-whirl ($C_{w1}>0$) reduces $\Delta C_w$ for the same blade speed, which lowers the fan curve itself at every flow — the system curve is untouched. The new operating point is the intersection of this depressed fan curve with the same original system curve, again at lower Q. Because the fan curve is genuinely being modified to require less work (rather than throttled with extra friction downstream), inlet-vane control is markedly more efficient than damper control over its useful range, which is why it is common in larger HVAC and process fans.

(a)(iii) / (b)(iii) — Fan speed

Reducing the driving-motor speed changes the machine itself through the fan affinity (similarity) laws: for the same impeller and system, $Q\propto N$ and $H\propto N^2$, so the entire fan H–Q curve scales down and shifts toward the origin as speed falls — the fan-curve family moves, the system curve again stays fixed. The new operating point is again the intersection with the unchanged system curve, at reduced Q. Because no artificial friction (damper) or induced pre-swirl loss (vanes) is introduced — the fan is simply doing proportionally less work — speed control is the most energy-efficient of the three methods across the widest flow-turndown range, which is why variable-frequency-drive (VFD) motor speed control is now the preferred method wherever the extra drive cost is justified.

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