Question 5 of 6: Brayton Cycle Modifications

Question 5: Brayton Cycle Modifications (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.

Reference basic cycle. In every panel below the grey line is the basic air-standard Brayton cycle 1–2–3–4: isentropic compression 1→2, constant-pressure heat addition 2→3 up to the limiting turbine inlet temperature \(T_{max}\), isentropic expansion 3→4, and constant-pressure heat rejection 4→1 back to the fixed atmospheric inlet temperature. The red dashed line is the modification. Two constraints are held throughout, as the question specifies: the turbine inlet temperature stays at \(T_{max}\), and the compressor inlet temperature stays at ambient. The efficiency of the basic cycle depends only on the pressure ratio, \(\eta = 1 - r_p^{-(k-1)/k}\), while the net work per kilogram depends on both the pressure ratio and the temperature limits — which is why some modifications raise one and lower the other.

Part (a) — T–s diagrams of the five modifications (10 marks)

Part (b) — Advantages, disadvantages, and effect on efficiency and output (5 marks)

(i) Increased pressure ratio. Raising the pressure ratio lifts the compressor discharge temperature \(T_2\) along the same isentrope, so with the turbine inlet temperature pinned at \(T_{max}\) the heat added 2→3 shrinks while the mean temperature of heat addition rises. Thermal efficiency therefore increases monotonically, since it depends on pressure ratio alone. Net work per kilogram, however, does not: it passes through a maximum at \(r_{p,opt} = (T_{max}/T_{min})^{k/2(k-1)}\), which for \(T_{max} = 1500\) K and \(T_{min} = 288\) K is about 18, and falls away on either side because the enclosed area of the cycle is squeezed as \(T_2\) climbs toward \(T_3\). The practical consequences are that a given power output needs a larger air flow and hence a physically larger machine, that the compressor needs many more stages with tighter surge margins and variable-geometry stators, and that the compressor delivery temperature eventually becomes too high to cool the turbine blades effectively. The trade-off is chosen differently in different markets: aero engines run overall pressure ratios of 40–50 because fuel burn dominates, whereas industrial machines designed for peaking duty use lower ratios near the work optimum to get the most megawatts out of a given frame size.

(ii) Regenerative heating. A counter-flow heat exchanger transfers heat from the turbine exhaust into the compressor discharge air, so the air enters the combustor at \(T_x\) instead of \(T_2\) and the fuel supplies only the remainder up to \(T_{max}\). Net work is completely unchanged — neither the compressor nor the turbine sees a different state — but the heat input falls, so thermal efficiency rises while power output stays constant. This is the only one of the five modifications that improves efficiency without any penalty in specific work. The limits are set by the second law: regeneration is possible only while the exhaust is hotter than the compressor discharge, that is at low pressure ratios, and it becomes useless and then harmful once \(T_2\) exceeds \(T_4\). The costs are a large, expensive and heavy heat exchanger, an added pressure drop on both sides that erodes part of the gain, and slower transient response. Regenerators are therefore standard on small industrial and microturbine sets (which run low pressure ratios and where a few points of efficiency justify the exchanger) and on marine recuperated units, but are absent from aero engines, where the weight and frontal area are unacceptable.

(iii) Compressor intercooling. Splitting the compression into two stages with a cooler between them returns the air toward ambient at the intermediate pressure, so the second stage compresses colder and hence denser air and the total compressor work falls — visible on the T–s diagram as the compression path bending back to the left. Since the turbine work is unchanged and the turbine inlet temperature is still \(T_{max}\), net work per kilogram increases substantially. But the compressor now delivers cooler air, so more fuel is needed to reach \(T_{max}\), and thermal efficiency actually falls unless a regenerator is added downstream to recover the extra exhaust heat. Intercooling is thus almost always paired with regeneration, and the intercooled-recuperated combination is the reason such engines exist at all: the classic example is the marine WR-21 and the intercooled aeroderivative LMS100, which reaches about 44% simple-cycle efficiency. The costs are the intercooler itself, its pressure drop, a cooling water or air circuit, and the need for a heat sink — readily available at sea, awkward inland.

(iv) Turbine reheating. Expansion is interrupted part-way and the gas is reheated back to \(T_{max}\) in a second combustor before completing its expansion. Because the second expansion begins at a much higher temperature, the two drops together exceed the single drop of the basic cycle, so like intercooling this raises net work per kilogram markedly. And like intercooling it lowers thermal efficiency, because the added heat is supplied at a lower pressure and the exhaust leaves hotter — again the remedy is a regenerator, for which reheat conveniently provides an ideally hot exhaust. Reheat also increases the exhaust temperature, which is a genuine advantage in a combined cycle where that heat feeds the steam bottoming cycle; the sequential-combustion GT26 and GT36 machines are built on exactly this logic and achieve very high combined-cycle efficiency despite the simple-cycle penalty. The disadvantages are a second combustor with its own controls and emissions behaviour, higher NO_x from a second high-temperature flame, and greater mechanical complexity.

(v) Exhaust afterburning. Fuel is burnt in the gas leaving the turbine, using the oxygen left over from the lean primary combustion, and the hotter gas is expanded through the propelling nozzle. No extra shaft work is produced at all — the turbine has already been passed — so this is not a way of making more power in a shaft-power sense; what it does is raise the jet velocity, and thrust can rise by 50% or more for a modest increase in engine mass. Thermal efficiency falls sharply, because heat is added at nearly atmospheric pressure where the expansion ratio available to convert it is small, and specific fuel consumption can double or worse. Afterburning is therefore reserved for short-duration needs where thrust matters more than fuel: military take-off, transonic acceleration and combat manoeuvre, and it was used on Concorde's Olympus 593 for take-off and transonic acceleration only. It has no place in a stationary power plant, where the equivalent idea — supplementary firing in a heat recovery boiler — is used instead, and is worthwhile there precisely because the added heat then goes into a steam cycle that can extract work from it.