Question 7 of 8: Brayton Cycle Modifications

Question 7: Brayton Cycle Modifications (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.

The basic cycle is 1–2 isentropic compression, 2–3 constant-pressure combustion to the metallurgical limit, 3–4 isentropic expansion back to atmospheric pressure, and 4–1 the open-cycle rejection to atmosphere. With both end temperatures pinned, the only free variables are the pressure ratio and where in the cycle heat is added or removed. Each modification is sketched below and then assessed for its effect on specific work and on efficiency.

(i) Increased pressure ratio — efficiency up, specific work down. Raising the pressure ratio pushes the compressor delivery temperature up and, because the turbine inlet temperature is capped, pulls the expansion end temperature down. On the diagram the modified cycle is taller and narrower than the basic one. The air-standard result $\eta = 1 - r_p^{-(k-1)/k}$ rises monotonically with pressure ratio, so efficiency improves; but the enclosed area, which is the specific work, first rises and then falls, and beyond the optimum ratio $r_{p,opt} = (T_3/T_1)^{k/[2(k-1)]}$ the extra compression costs more than the extra expansion returns. So this modification buys fuel economy at the price of output per unit of air, and hence of a physically larger machine for the same megawatts. In the limit the cycle collapses to zero net work when the compression alone reaches the turbine inlet temperature.

(ii) Regenerative heating — efficiency up, power unchanged. A counterflow exchanger transfers heat from the turbine exhaust into the compressor delivery air before it reaches the combustor. On the T-s diagram the two states move along their existing pressure lines: air leaves the regenerator hotter than state 2, and exhaust leaves it colder than state 4, with the two shifts equal in enthalpy. Neither the compressor work nor the turbine work changes at all, so the specific work and hence the power output are identical; what changes is that part of the heat formerly bought from the fuel is now recycled, so the fuel input falls and the efficiency rises. The essential precondition is that the exhaust be hotter than the compressor delivery, which is true only at modest pressure ratios — and which is why regeneration and high pressure ratio are alternative strategies rather than complementary ones.

(iii) Compressor intercooling — power up, efficiency slightly down. Splitting the compression and cooling the air back towards ambient between the two stages reduces the total compression work, because the work of compression is proportional to the absolute temperature at which it is performed. On the diagram the modified compression line kinks back towards the low-temperature isobar before rising again. Less compressor work for the same turbine work means more net work per kilogram of air, so the power output rises — often substantially. Efficiency, however, usually falls slightly: the air now enters the combustor cooler than it would have done, so more fuel is needed to reach the same turbine inlet temperature, and that extra heat is added at a low mean temperature. Intercooling is therefore an output-boosting measure, and it only improves efficiency when combined with regeneration, which recovers the heat that the cooler combustor inlet would otherwise waste.

(iv) Turbine reheating — power up, efficiency slightly down. Expansion is split, and the gas is reheated back to the limiting temperature between the two turbine stages. On the diagram the expansion line steps back up to the maximum temperature partway down. Because the constant-pressure lines diverge on T-s coordinates, expanding at a higher average temperature yields more work over the same overall pressure ratio, so the specific work rises. The additional heat, though, is again added at less than the peak of the cycle and the exhaust leaves hotter, so thermal efficiency slips a little. Reheating is the mirror image of intercooling, and like intercooling it becomes an efficiency measure only when a regenerator is fitted to recover the hotter exhaust — the combination of intercooling, reheat and regeneration is the classical route towards the Ericsson cycle.

(v) Exhaust afterburning — thrust or heat output up, cycle efficiency down. Fuel is burned in the turbine exhaust, downstream of the last rotating stage. On the diagram the modification appears as a constant-pressure temperature rise from state 4 along the atmospheric isobar, outside the work-producing part of the cycle. Because no expansion follows it in a shaft-power machine, none of that heat is converted to shaft work: the power output is unchanged while the fuel input rises, so the thermal efficiency falls. It is worth doing for two reasons that lie outside the simple cycle. In aviation the afterburner is followed by a propelling nozzle, so the extra enthalpy does become jet kinetic energy and thrust rises sharply — at a large penalty in specific fuel consumption. In a stationary combined-cycle or cogeneration plant, supplementary firing in the duct ahead of a heat-recovery steam generator raises steam production and lets the bottoming cycle recover the heat, so plant output rises even though the gas-turbine cycle efficiency considered alone is worse.