22-Mec-A6 Fluid Machinery · May 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Examination 07-Mec-A6-1 Fluid Machinery (May 2014) — closed book, three hours, 60 marks. Section A is calculative (Q1–Q5) and Section B is descriptive (Q6–Q8); the rubric asks for four 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. K. Turton, Principles of Turbomachinery; H. Cohen, G. F. C. Rogers & H. I. H. Saravanamuttoo, Gas Turbine Theory (for the axial compressor stage); R. W. Fox, A. T. McDonald & P. J. Pritchard, Introduction to Fluid Mechanics (pump energy equation and affinity laws).
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 disparity in stage count comes down to one fact of fluid mechanics: a compressor works against a rising (adverse) pressure gradient, whereas a turbine works with a falling (favourable) one. Diffusing a flow — raising its static pressure — is intrinsically difficult because the boundary layers on the blades are moving into higher pressure and are prone to separate and stall. Accelerating a flow in a turbine passage is easy and stable by comparison, so a turbine stage can safely handle a far larger enthalpy change than a compressor stage.
Why the compressor needs many stages. To avoid boundary-layer separation and stall, each axial-compressor stage is limited to a modest pressure rise — a stage pressure ratio of only about 1.2–1.4 (exactly the 1.33 found in Question 4). Achieving an overall pressure ratio of 14:1, as in the Acacia/Port Rex machines, therefore requires the ratios to multiply up over many stages: $1.3^{n}\approx 14$ needs roughly ten stages. Each stage adds only a small temperature and pressure increment because the flow must be diffused gently to keep it attached; pushing a single stage harder would stall the blades, collapse the pressure rise and risk surge. The minimum number of stages is thus set by the overall pressure ratio divided among the maximum safe per-stage ratio.
Why the turbine needs multiple (but fewer) stages. The turbine expands the hot gas back down, and because the pressure gradient is favourable each stage can take a much larger enthalpy drop without any separation problem — so far fewer stages are needed to return the same energy. Yet a single turbine stage still cannot do it all: the whole expansion in one stage would demand blade speeds and gas velocities that are structurally and aerodynamically impractical (very high blade stress and near-sonic relative velocities), and the work per stage is limited by the allowable blade loading $w=U\,\Delta C_w$. Splitting the expansion over two or three stages keeps blade speeds, stresses and Mach numbers within limits while still extracting the power efficiently. The gas generator turbine also only has to drive the compressor (and the separate free/power turbine drives the load), so its stage count is matched to that lighter duty.
Selecting the stage numbers. For both machines the number of stages is chosen to keep each stage within its safe loading: the compressor is limited by the stall-driven maximum pressure ratio per stage, the turbine by blade-stress and Mach-number limits on work per stage. Because a compressor stage can raise pressure by only a fraction of what a turbine stage can drop it, the compressor inevitably carries several times as many stages for the same overall pressure ratio.
