Real-Gas Properties and Modern Engine Trends

cp(T) of air and combustion products, why γ falls with temperature, the trends in pressure ratio, temperature and bypass ratio, and their limits

The GE9X

The engine of Lesson 1-1 again, this time from the inside. The GE9X squeezes its air 60 times — 27 times in the high-pressure compressor alone — behind a 3.4 m fan of 16 composite blades. Its combustor liners, two of its turbine nozzle rows and a turbine shroud are made of ceramic matrix composites, which tolerate temperatures nickel alloys cannot. GE designed it for 10 % better fuel efficiency than the GE90 (the GE9X). Every one of those choices pushes a trend this course has already met: higher pressure ratio for thermal efficiency, higher temperature for a smaller and more powerful core, higher bypass for propulsive efficiency. And at 60:1 and turbine temperatures near 2000 K, the constant gas properties of the earlier lessons are no longer good enough.

Why $c_p$ rises with temperature. At room temperature an air molecule stores energy in moving and rotating. Above a few hundred kelvin its atoms also begin to vibrate against each other, which soaks up energy — so it takes more heat to raise the temperature by one degree.

c_p

rises and

\gamma = c_p/c_v

falls. Combustion products make it stronger: CO₂ and H₂O have more ways to vibrate than N₂ and O₂.

📐Real air, from CoolProp

At atmospheric pressure (Lab 1):

250 K: $c_p = 1006$ J/(kg·K), $\gamma = 1.404$ .
1000 K: $c_p = 1141$ , $\gamma = 1.336$ .
2000 K: $c_p = 1250$ , $\gamma = 1.298$ .

The mean

c_p

over a compression from 288 to 850 K is 1049 J/(kg·K), not 1004.5. Over an expansion of air from 1700 to 900 K it is 1184.

📐What really leaves the combustor

Burn Jet A at a fuel–air ratio of 0.025 in air arriving at 850 K and 40 bar, and let Cantera find the equilibrium products (Lab 2):

Turbine entry temperature 1707 K.
Products: 76 % N₂, 12.8 % O₂ (real engines burn very lean), 5.1 % CO₂, 4.9 % H₂O by mole.
At $T_{t4}$ : $c_p = 1289$ J/(kg·K), $\gamma = 1.286$ .
At stoichiometric (f = 0.0675) the flame would reach 2673 K — far beyond any turbine, which is why the burner mixes in extra air.

The course's hot-section values, 1156 J/(kg·K) and 1.33, are averages over a turbine's whole expansion; at the turbine entry itself the gas is quite different. Real cycle codes use tables such as NASA's CEA or Cantera throughout.

💡Three trends

Seven airliner engines, from the JT9D-7R4 of 1982 to the GE9X, certified in 2020 (Lab 3):

Overall pressure ratio has risen by about 6.5 per decade, from 27 to 60. The ideal Brayton efficiency it allows rose from 61 % to 69 %.
Bypass ratio has risen by about 1.9 per decade, from 4.8 to 12.5.
Turbine entry temperature has risen too, made possible by turbine cooling and materials (Lesson 6-4) — the enabler of the other two, since a hotter core gives more power per kilogram, so a smaller core can drive a bigger fan.

💡Where the trends run out

Compressor exit temperature. Higher pressure ratio means hotter air entering the burner; the last compressor discs set a limit (Lesson 4-2).
Turbine materials and cooling air. Every kilogram of cooling air bled from the compressor is a kilogram that does no work in the cycle — the case for ceramics.
Core size. With a high bypass ratio and a high pressure ratio, the last compressor blades become small — only a centimetre or two tall. Tip clearances and manufacturing tolerances do not shrink with them, so losses rise. Alan Epstein, then of Pratt & Whitney, analysed this limit in the AIAA Journal in 2014.
Fan size. A bigger fan needs a bigger, heavier, draggier nacelle; past some bypass ratio, the aircraft loses more than the engine gains. Unit 10 follows the ways around it.

Nothing is too wonderful to be true, if it be consistent with the laws of nature; and in such things as these, experiment is the best test of such consistency.

– Michael Faraday, laboratory journal, 19 March 1849 (Wikiquote)

💡How much do constant properties matter?

For ranking designs, a two-gas model (cold and hot) is usually enough. For temperatures — the compressor exit limit, the turbine blade life — it is not: Lab 4-1c found 31 K of error at a 40:1 compressor exit, more than the margin a designer is allowed. Production cycle codes therefore always use real-gas tables.

💡Where you will use this

Lesson 6-4 explains turbine cooling and the materials behind rising temperatures. Lesson 7-1 uses Cantera again for flame temperatures, 7-4 for emissions. Lesson 10-2 looks at what comes after the trends: geared fans, open rotors, hydrogen.

📚Further reading

Sanford Gordon and Bonnie J. McBride, Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications, NASA RP-1311 (1994): the CEA program behind most cycle codes' gas tables.
Alan H. Epstein, 'Aeropropulsion for Commercial Aviation in the Twenty-First Century and Research Directions', AIAA Journal (2014).
The Cantera and CoolProp documentation.

↓But there is a problem

Every engine so far started at station 0, with the air delivered smoothly to its fan. At Mach 3 that is the hardest job on the aircraft. SR-71 crews knew the moment it went wrong: the shock system in front of one engine would jump forward out of its inlet, that engine's afterburner would often blow out, and the aircraft would yaw violently.