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22-Mec-A6 Fluid Machinery · Undated paper

Question 7 of 8: Turbine Blade Flow

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

Notes on this paper

Paper format. National Examinations — 16-Mec-A6 Fluid Machinery, May 2019. Closed-book, three hours. Section A is calculative (5 questions) and Section B is descriptive (3 questions); candidates answer four questions from Section A and two from Section B (six questions, 60 marks, 10 marks each). All eight questions are solved as a study resource.

Reference texts. Dixon & Hall, Fluid Mechanics and Thermodynamics of Turbomachinery (7th ed.); Cohen, Rogers & Saravanamuttoo, Gas Turbine Theory (6th ed.); Fox & McDonald, Introduction to Fluid Mechanics (10th ed.); F. M. White, Fluid Mechanics (8th ed.); Çengel & Boles, Thermodynamics: An Engineering Approach (9th ed.).

Paper. This is the 16-Mec-A6, May 2019 Fluid Machinery examination.

Question 7: Turbine Blade Flow (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 — pressure and velocity through a pressure-compounded (Rateau) turbine. In pressure-compounding the total pressure drop is divided among several stages, each a nozzle (fixed) row followed by a moving row. In every stage the pressure falls only across the nozzle, where enthalpy is converted to kinetic energy, and stays constant across the moving row (the defining feature of impulse blading). The absolute steam velocity therefore rises sharply in each nozzle and falls back in each moving row as the steam gives up its kinetic energy to the blades.

P, Cdistance through 4 stages (F=fixed/nozzle, M=moving)steam pressure (impulse: falls only in nozzles)steam velocityFMFMFMFM
Part I: through four stages the pressure (solid) falls as a descending staircase — a step down in each nozzle (F), flat across each moving row (M) — while the absolute velocity (dashed) is a sawtooth, accelerating in every nozzle and decelerating in every moving row.

The result is the classic staircase-and-sawtooth: modest, repeated velocity peaks keep the blade speed ratio near optimum in every stage, which is exactly why pressure-compounding is used for large pressure drops instead of a single impulse stage (which would demand an impractically high jet velocity and blade speed).

Part II(a) — why the blade lengthens and twists toward the exhaust. As steam expands through the turbine its pressure and density fall, so the same mass flow occupies a much larger volume, $\dot V=\dot m/\rho$. The annulus flow area must grow to pass it at a sensible axial velocity, $A=\pi D\,h=\dot V/C_a$; with the mean diameter roughly fixed, the blade height $h$ must increase markedly toward the low-pressure end. Once the blade is long, the blade speed $U=\omega r$ differs substantially between root and tip (the tip radius can be 1.5–2× the root), so a single fixed blade angle cannot suit the whole span. The blade is therefore twisted so that its angle matches the local velocity triangle at every radius — a free-vortex design keeps the whirl-times-radius product constant and the axial velocity uniform.

UC1W1(i) Rootsmall U, C1 nearly radialUC1W1(ii) Midmoderate UUC1W1(iii) Tiplarge U, blade tangential
Part II(b): velocity triangles from root to tip. The blade speed $U=\omega r$ grows with radius while the axial velocity stays roughly constant, so the relative inlet angle $\beta_1$ opens out and the absolute angle $\alpha_1$ closes toward the tangential — the blade must twist from a steep, nearly radial root to a shallow, nearly tangential tip.

Part II(b) — how the diagram changes. At the root the small $U$ makes the relative velocity nearly aligned with the absolute flow, so the blade inlet angle is steep. At mid-height the larger $U$ swings the relative velocity round. At the tip, the large $U$ leaves a long tangential base, so the relative flow is much more inclined to the tangential and the blade section is shallow and flattened. Tracing these three triangles from root to tip defines the continuous twist of the aerofoil.