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.
Cavitation is the local boiling of a liquid caused not by heating but by a drop in pressure. A liquid contains microscopic gas and vapour nuclei; whenever the local static pressure falls to the vapour pressure corresponding to the liquid temperature, these nuclei grow explosively into vapour-filled cavities. In a hydraulic machine the low pressures occur where velocity is highest — at the eye and suction surfaces of pump impeller vanes, and at the runner exit and draft-tube entry of a reaction turbine. The controlling quantity is therefore the margin between the local pressure and the vapour pressure, expressed for pumps as the net positive suction head (NPSH) and for turbines through the Thoma cavitation coefficient.
The damage is done during collapse, not growth. When a vapour cavity is swept into a region of higher pressure (downstream on the vane, or where the flow decelerates) it condenses and implodes in less than a millisecond. If the bubble collapses against or very near a solid surface the implosion is asymmetric: the far side of the bubble accelerates through the cavity and forms a high-speed micro-jet that strikes the wall, while the rebound emits an intense shock wave. Repeated at thousands of cycles per second, these micro-jet impacts and shocks exceed the fatigue strength of the metal, pitting and eventually removing material, so that the surface takes on the characteristic spongy, honeycombed appearance. Accompanying symptoms are a crackling noise, vibration, and a fall in head, efficiency and flow.
The parts most at risk are those on the low-pressure side of the low-pressure passages: the suction (back) faces of pump impeller vanes near the leading edge and the impeller eye; and, in a reaction turbine, the runner blade suction surfaces near the trailing edge, the outer band, and the draft-tube inlet. Impulse (Pelton) wheels, which run at atmospheric pressure, are largely immune. The remedies are to raise the available suction head (mount the pump lower, set the turbine runner below tailwater), limit speed, and use cavitation-resistant stainless steels.
The number of vanes on a centrifugal impeller is a compromise. Vanes guide the flow so that it leaves at the design angle; ideal (Euler) theory assumes an infinite number of perfectly guiding vanes. Too few vanes guide the flow poorly: the fluid cannot follow the blade curvature, so a relative circulation (slip) develops between the blades, the actual outlet whirl and hence the head fall below the ideal, and the wide passages allow flow separation and recirculation that reduce efficiency and can make the head–flow curve unstable.
Too many vanes guide the flow well but at a cost: each vane has thickness, so many vanes block a large fraction of the flow area at the eye and crowd the passages, raising the local velocities; and the total wetted blade surface is large, so skin-friction losses climb. The passages also become long and narrow, adding frictional head loss. Both effects lower efficiency and reduce the flow the impeller can pass. The optimum — typically five to nine vanes for a normal centrifugal pump — balances good flow guidance (high head, little slip) against low blockage and friction. Empirical rules relate the best vane number to the blade angle and the ratio of inlet to outlet diameter, reflecting exactly this trade-off between guidance and losses.
