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25-Nav-B5 Marine Control Systems · May 2017

Question 6 of 8: Blade Design (Descriptive)

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 6: Blade Design (Descriptive) (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 I — Forward- vs backward-curved vanes

The vane exit angle β2 (measured from the tangential direction) fixes the direction of the relative velocity leaving the impeller and therefore the whirl (tangential) component of the absolute velocity, V2T = VB2 − V2R/tanβ2. A backward-curved vane (β2 < 90°) points its trailing edge away from the direction of rotation, so the relative velocity subtracts a large amount from the blade speed and the absolute exit velocity V2 is modest. A forward-curved vane (β2 > 90°) leans toward the rotation, adding to the whirl, so V2 is large for the same blade speed. The outlet triangles below show this directly.

Outlet velocity trianglesUWV₂Backward-curved (β₂ < 90°)UWV₂Forward-curved (β₂ > 90°)
Fig. Q6-I(a) - Outlet triangles: forward-curved vanes give a larger absolute (whirl) velocity V₂ than backward-curved vanes at the same blade speed U.

The diffuser (or volute) converts the kinetic energy of the impeller discharge into pressure. Because a forward-curved vane leaves the fluid with a much higher absolute velocity, a larger fraction of the total head is present as velocity head that must be recovered in the diffuser. Diffusion is an inherently lossy, stall-prone process, so although forward-curved vanes generate a higher theoretical head, more of it is exposed to diffuser losses and the characteristic is peaky and less stable. Backward-curved vanes generate their head with less kinetic energy at the impeller exit, so the diffuser has less to recover and efficiency is higher and more stable.

The resulting head–flow characteristics differ markedly. The backward-curved curve falls steadily and monotonically with flow — a stable, self-limiting shape ideal for parallel operation and throttling control. The forward-curved curve rises to a higher peak but can droop or rise again at part flow, producing a region of positive slope that can cause surging or unstable operation.

Flow QHead HBackward-curved (stable)Forward-curved (rising/unstable)
Fig. Q6-I(b) - Typical head-flow characteristics. Backward-curved vanes give a steady falling (stable) H-Q curve; forward-curved vanes give a higher but rising/drooping (potentially unstable) curve.

Part II — Optimum number of vanes

The number of impeller vanes is a compromise. With too few vanes the blade passages are wide and the flow is poorly guided: the actual fluid outlet angle falls well short of the geometric blade angle (large slip), so the whirl and hence the developed head are lower than the Euler prediction. The flow can also separate on the suction side of the widely-spaced blades, and non-uniform loading increases hydraulic losses and can promote recirculation at part load.

With too many vanes the passages become narrow and the accumulated blade thickness blocks a significant part of the flow area at the eye, raising local velocities. The additional wetted surface increases skin-friction (disk-friction and passage-friction) losses, and the extra blockage reduces the effective throat, lowering efficiency and increasing the risk of choking at high flow. The optimum vane count (commonly 5–9 for a radial pump) balances good flow guidance and low slip against minimum friction and blockage.