22-Mec-A6 Fluid Machinery · May 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
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.
The three common methods are damper (throttle) control, variable inlet guide vanes, and speed control; any two may be described. Damper control partially closes a valve or louvre in the duct. This adds resistance, so the system curve becomes steeper (h rises faster with Q); its intersection with the unchanged fan curve moves up and to the left, reducing the flow. It is simple and cheap but wasteful, because the throttled pressure is dissipated as heat — the fan still works high on its curve. Speed control (variable-speed drive or, on steam turbine drives, changing turbine speed) lowers the whole fan characteristic: by the affinity laws Q ∝ N, H ∝ N², so the fan curve slides down and the operating point follows the fixed system curve to a lower flow at lower head. This is the most efficient method because the fan is not throttled — the power drops roughly with the cube of speed. (The third method, inlet guide vanes, pre-swirls the flow into the impeller in the direction of rotation, which reduces the work input and reshapes the fan curve; it is more efficient than a damper but less than full speed control.)
Each compressor blade is an aerofoil that turns and diffuses the flow. It works well only over a limited range of incidence (the angle between the incoming relative velocity and the blade chord). Stall occurs when the incidence becomes too large and the boundary layer on the suction surface separates, just as an aircraft wing stalls at high angle of attack. The blade then no longer turns the flow or raises its pressure; lift collapses and losses rise sharply.
Stall is provoked whenever the axial velocity falls relative to the blade speed — that is, at flows below design (throttling toward the surge line), at off-design speeds, or during rapid transients. Because a compressor works against a rising pressure, a stalled row cannot sustain the delivery pressure and the flow can break down violently (surge) or into rotating-stall cells that travel around the annulus and fatigue the blades. The front stages tend to stall at low speed and the rear stages at high speed, because the fixed blade geometry cannot match the changing density ratio across the machine.
Stalling dominates axial-compressor design. Because each stage can only produce a modest, stall-limited pressure rise (a limited amount of flow turning before separation), a high overall pressure ratio needs many stages in series — far more than a turbine of the same pressure ratio, where the accelerating (favourable) pressure gradient suppresses separation. Designers also stagger the stall margin (blade stagger, variable stator vanes, and bleed valves) so that no row is driven into stall during starting and part-speed operation, and they keep a comfortable margin between the operating line and the surge line.
