25-Nav-B5 Marine Control Systems · May 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Examination 98-Mar-B5 Fluid Machinery, May 2015 — 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).
Reference texts. S. L. Dixon & C. A. Hall, Fluid Mechanics and Thermodynamics of Turbomachinery, 7th ed.; R. K. Turton, Principles of Turbomachinery, 2nd ed.; H. Cohen, G. F. C. Rogers & H. I. H. Saravanamuttoo, Gas Turbine Theory, 6th ed.; R. W. Fox, A. T. McDonald & P. J. Pritchard, Introduction to Fluid Mechanics, 8th ed.
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 — centrifugal fan flow control. A fan runs where its own head-flow characteristic crosses the system resistance curve. The three common controls are outlet (or inlet) damper throttling, inlet-guide-vane (swirl) control, and variable-speed drive; any two may be described. Damper throttling adds resistance to the duct, steepening the system parabola; the operating point slides up and to the left along the unchanged fan curve, so flow falls but at the cost of a throttled pressure drop and poor efficiency. Variable-speed control instead lowers the whole fan curve according to the fan laws ($Q\propto N$, $H\propto N^{2}$); the operating point moves down the fixed system curve, reducing flow with far less waste because no artificial resistance is introduced. Inlet-guide-vane control is intermediate: pre-swirl reshapes the fan curve and is more efficient than a damper but less so than speed control.
Part II — Francis turbine flow control. Power in a Francis turbine is regulated by wicket (guide) gates — a ring of pivoting vanes around the runner. Rotating the gates together changes the flow area and the swirl delivered to the runner, so both the flow and the power adjust to match the electrical load while the machine holds synchronous speed. The gates are driven by a governor through a servomotor so that the unit follows load automatically. A schematic shows water from the penstock entering a spiral casing, passing radially inward through the wicket gates onto the runner, and discharging down the draft tube to the tailrace.
Rapid gate movement raises serious hydraulic concerns. Closing the gates quickly decelerates the water column in the penstock and produces a water-hammer pressure rise that the penstock and casing must withstand; opening them quickly can cause the draft tube to see sub-atmospheric pressure and column separation. At low load (part gate) the runner operates off-design and sheds an unsteady swirling vortex rope in the draft tube, causing pressure pulsations, vibration and possible cavitation. Governors are therefore rate-limited, surge tanks or relief valves are fitted to absorb water-hammer, and prolonged very-low-load running is avoided.
