Gas Power Systems

The air-standard idealisation

In a gas power system there is no closed working fluid: air comes in, fuel is burned inside it, and exhaust goes out. To analyse such engines with the tools of cycles, Moran and Shapiro use the air-standard analysis:

• The working fluid is a fixed mass of air, treated as an ideal gas.
• Combustion is replaced by heat transfer from an external source.
• The exhaust and intake are replaced by heat rejection to the surroundings, closing the cycle.
• All processes are internally reversible.

With constant specific heats evaluated at room temperature, this is the cold-air standard: approximate, but it reveals what controls efficiency with a minimum of algebra.

Spark and squeeze: Otto and Diesel

A reciprocating engine is characterised by its compression ratio $r = V_\text{max}/V_\text{min}$ and its mean effective pressure — the constant pressure that, acting over the stroke, would give the same net work.

The Otto cycleOtto cycleThe ideal cycle of a spark-ignition engine, with heat added at constant volume. Its efficiency depends only on the compression ratio. idealises the petrol engine: isentropic compression, heat added at constant volume (the spark ignites a premixed charge that burns almost instantly at top dead centre), isentropic expansion, heat rejected at constant volume. Its cold-air efficiency depends only on the compression ratio:

$\eta_\text{Otto} = 1 - \frac{1}{r^{\gamma - 1}}.$

The Diesel cycleDiesel cycleThe ideal cycle of a compression-ignition engine, with heat added at constant pressure. idealises the compression-ignition engine: air alone is compressed until it is hot enough to ignite fuel injected near top dead centre, and the fuel burns as it is sprayed in — roughly at constant pressure while the piston moves down.

At the same compression ratio, the Otto cycle wins: all its heat goes in at the highest temperature. But a petrol engine cannot raise its compression ratio much above 10–12, because the premixed fuel–air charge would ignite on its own and knock. The diesel compresses only air, so it has no such limit — it needs 15–22:1 just to ignite its fuel — and that is why diesels are more efficient in practice.

The Brayton cycle: the gas turbine

A gas turbine does the same thing in a continuous flow. The Brayton cycleBrayton cycleThe ideal cycle of a gas turbine: compressor, combustor (constant pressure), turbine, heat rejection (constant pressure). idealises it: isentropic compression in a compressor, heat addition at constant pressure in a combustor, isentropic expansion through a turbine, and (in the closed idealisation) heat rejection at constant pressure. With cold-air properties the efficiency depends on the pressure ratio:

$\eta_\text{Brayton} = 1 - \frac{1}{r_p^{(\gamma-1)/\gamma}}.$

Moran and Shapiro's Example 9.4 — ten-to-one pressure ratio, 1400 K turbine inlet — gives 45.7% with variable properties; the lab reproduces it.

The striking number is the back-work ratioBack work ratioThe fraction of the turbine work consumed by the pump or compressor: about 1% in a steam plant, 40–60% in a gas turbine.. Compressing a gas is expensive (Lesson 4), and the compressor of a gas turbine typically consumes 40–60% of the turbine's work. That makes the whole machine brutally sensitive to component efficiencies: a few points lost in the compressor or turbine come straight out of a much smaller net work. Gas turbines became practical only in the 1940s, when aerodynamics and metallurgy finally made both components good enough.

Hence the obsession with turbine inlet temperature. Higher $T_3$ means more turbine work for the same compressor work. Modern machines run their first-stage blades in gas at 1600–1900 K, well above the melting point of their nickel alloys, kept alive by internal cooling passages and ceramic coatings.

Regeneration, intercooling and reheat

• Regeneration. At modest pressure ratios, the turbine exhaust is hotter than the compressed air. A heat exchanger, the regenerator, uses the exhaust to preheat the air before the combustor, cutting the fuel needed. At high pressure ratios the exhaust is cooler than the compressed air, and regeneration is useless.
• Intercooling. Compressing in two stages with cooling in between reduces the compressor work, since cooler gas has a smaller $v$ and $w = \int v\,dp$.
• Reheat. Expanding in two stages with a second combustor in between increases the turbine work.

Intercooling and reheat raise the net work; on their own they lower the efficiency, because they add heat at lower temperatures and reject it at higher ones. Combined with regeneration, they push the cycle toward the Ericsson cycle, which has the Carnot efficiency.

Jet engines

An aircraft gas turbine is a Brayton cycle in which the turbine produces only enough work to drive the compressor; the rest of the gas's enthalpy is expanded in a nozzle to make a fast jet. A turbofan uses part of the turbine work to drive a large fan, accelerating a lot of air gently, which is far more propulsively efficient. The thermodynamics is the same; the product is thrust instead of shaft power.

Combined cycles: the best of both

A gas turbine receives its heat very hot — over 1600 K — but throws its exhaust away at 850–900 K. A steam plant rejects its heat beautifully cold, near 300 K, but can only take heat in below about 900 K. Put them together and you get a cycle that receives heat at the gas turbine's temperatures and rejects it at the steam plant's:

The gas turbine's exhaust flows through a heat-recovery steam generator that raises steam for a Rankine cycle. Overall,

$\eta_\text{cc} = \eta_\text{gt} + (1 - \eta_\text{gt})\,\eta_\text{boiler}\,\eta_\text{steam},$

and two cycles of about 40% and 35% combine to around 60%. The combined-cycleCombined cycleA gas turbine whose hot exhaust raises steam for a steam turbine, reaching efficiencies above 60%. plant is the most efficient way yet devised to make electricity from fuel, and it is what most new gas-fired stations are.

Next: run a cycle backwards and it pumps heat uphill. How can a heat pump deliver three units of heat for one of electricity?