22-Mec-B3 Energy Conversion and Power Generation · December 2014

Question 6 of 6: Cycle Performance Enhancement

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

Question 6: Cycle Performance Enhancement (15 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.

All three enhancements share one underlying idea, and it is worth stating before the individual cases. The efficiency of any heat engine is bounded by \(1 - T_L/T_H\), where the temperatures are the mean temperatures at which heat is taken in and rejected. A basic cycle falls short of its potential either because it takes in a great deal of heat at low temperature, or because it throws away heat that is still hot enough to be useful, or because it produces less work than its machinery could support. Feedwater heating attacks the first, recuperation attacks the second, and turbocharging attacks the third.

(a) Feedwater heating in a steam cycle. In a plain Rankine cycle the condensate arrives at the boiler at close to condenser temperature — 29 °C in the cycle of Question 2 — and the boiler must raise it all the way to saturation before any evaporation begins. That sensible heating is done at low temperature, and heat added at low temperature converts to work badly. Regeneration removes it from the boiler's account. Steam is bled from the turbine at intermediate pressures and used to heat the feedwater, either by direct mixing in an open (deaerating) heater or through tubes in a closed heater; by the time the water reaches the boiler it is already at, or near, the saturation temperature of the highest extraction pressure. In the Question 2 cycle a single 0.6 MPa heater raises the feed from 29 °C to 159 °C, and the cycle efficiency rises from 39.4 % to 42.0 %.

The bargain is explicit: the bled steam produces less work than it would have if it had expanded to the condenser, so the work per kilogram of throttle steam falls. But the heat input falls proportionately more, and the ratio — which is what efficiency measures — improves. Seen through the mean-temperature argument, the mean temperature of heat addition has risen because its coldest portion has been deleted. There are practical dividends too: the open heater deaerates the feedwater, protecting the boiler from oxygen corrosion; the extraction flows reduce the volumetric load on the low-pressure stages and the condenser; and the boiler's economiser sees a smaller temperature range. Real stations use six to eight heaters in series, each capturing a slice of the temperature rise, until the marginal gain no longer justifies the extra vessel, and Question 4's Belledune diagram shows exactly such a train.

(b) Recuperative heating in a gas turbine. The Brayton cycle has the opposite problem. Its exhaust leaves the turbine far hotter than the air leaving the compressor — in Question 1, 474 °C against 115 °C — so heat is thrown away at a temperature at which it could still do useful work, while the combustor is asked to supply heat over that same range from fuel. A recuperator is a gas-to-gas counter-flow heat exchanger that closes the gap: exhaust on one side, compressor delivery on the other, transferring heat from the stream that is leaving to the stream that is arriving.

Nothing about the work output changes at all — the compressor and turbine see the same pressures and temperatures — but the fuel input falls by the recuperated duty, which in the Question 1 cycle is 1763 kJ/kg out of a 2820 kJ/kg requirement. The efficiency accordingly rises from about 25 % to 46.5 %. Two conditions govern whether recuperation is worthwhile. First, the turbine exhaust must actually be hotter than the compressor delivery, which restricts recuperation to low pressure ratios; a high-pressure-ratio aero-derivative machine has a compressor delivery hotter than its exhaust and cannot be recuperated at all. Second, the exchanger's terminal temperature difference and pressure drop set how much of the theoretical gain survives — a tighter approach recovers more heat but costs surface area and pressure loss, and the pressure loss directly reduces turbine work. That trade is why the exam specifies a 20 °C terminal difference rather than assuming perfect recovery.

(c) Turbocharging a reciprocating engine. Feedwater heating and recuperation both improve a cycle's efficiency at fixed size. Turbocharging does something different: it uses waste exhaust energy to increase the amount of air — and therefore fuel — that a cylinder of given swept volume can burn, so that the same engine produces substantially more power. The mechanism is that the exhaust gas leaving the cylinder still has both pressure and temperature, and in a naturally-aspirated engine all of it is lost to the atmosphere. A turbocharger places a turbine in that stream and couples it directly to a compressor on the intake, so the exhaust does the work of raising the intake pressure. Crucially, the compressor is driven by energy that would otherwise be wasted, not by the crankshaft — that is what distinguishes turbocharging from supercharging.

Compression heats the charge, which partly undoes the density gain and raises the knock tendency of a spark-ignition engine, so an intercooler (charge-air cooler) is fitted between compressor and inlet manifold. With a 1.8 bar absolute boost and an intercooler removing 60 % of the compression temperature rise, the charge density is about 1.61 times ambient, so roughly 60 % more fuel can be burned per cycle in the same displacement. The efficiency benefits follow indirectly but are real: a smaller engine can now do the work of a larger one, so friction and pumping losses per unit of output fall — the “downsizing” effect that dominates modern automotive practice. On the gas exchange itself, a turbocharged engine can run with intake pressure above exhaust pressure over part of the cycle, giving positive pumping work where a throttled naturally-aspirated engine has a negative loop. In large marine and stationary diesels, where boost pressures reach 4 bar and more, turbocharging is not an option but a necessity: it is the single largest reason brake mean effective pressure has risen by a factor of three over the naturally-aspirated engine, and why the most efficient two-stroke diesels exceed 50 % brake thermal efficiency. The limits are mechanical and thermal — peak cylinder pressure, exhaust valve and piston-crown temperature, and, on the spark-ignition side, detonation, which is managed with lower compression ratio, richer mixture at full load, and modern direct injection and variable valve timing.