How does turbine efficiency compare with internal combustion engines if all the turbine power is converted to mechanical energy?
When looking at conversion from chemical energy into mechanical energy: very favourably. The early turbojets had low thrust efficiency, they could not convert their gas generator power into thrust in an efficient way. When comparing energy efficiencies we start with the chemical energy in the fuel, and won't be working backwards from available thrust.
If all gas generator power is converted to mechanical energy we're talking about turboshafts. The best way to compare the fuel efficiency of the engine only and not get engaged in a discussion about thrust conversion, is a listing of engine brake horsepower, which directly measures the shaft torque1 applied to a propeller, fan, set of truck wheels, ships propeller etc.
- As can be seen, a large gas turbine engine like the GE LM6000 (a converted aeroplane turbofan engine) is among the most frugal engines around, with a brake specific fuel consumption of 0.329 lbs/(hp * h) = 200 g/kWh = 42% efficiency.
- Diesels can get efficiencies of over 50%, mainly the large, low RPM 2-stroke diesels generating a huge amount of torque. The Wärtsilä-Sulzer RTA96-C runs at 22-120 RPM, which would be problematic for automobile and aircraft propulsion.
- The highest efficiency of all is the combined cycle with 62.2%, a gas turbine combined with a steam turbine to utilise the exhaust energy.
The low specific fuel consumption is for large gas turbine engines, they don’t scale down well because of the boundary layer effects: a smaller engine has relatively a larger circumference. Also, they only operate efficiently at full power, piston engines have the advantage at lower rpm percentage.
So the smaller the engine, the more advantageous are the circumstances for the piston engine: they scale down much more favourably than the gas turbines. But given enough volume, gas turbines are not inherently wasteful with fuel at all.
If an aircraft mounted the exact same propeller on a supercharged piston engine and a turbine, and flew under identical conditions at the same pitch and rpm, how much more fuel would the turbine use
We're taking about aero engines now, and should leave unsuitable 2-stroke low RPM ship diesels out of the comparison. Also, since the propellers and flight conditions are identical, we can leave the whole thrust conversion mechanism out of the equation. As mentioned earlier, size matters when talking about gas turbine efficiency. Let's take 2 sizes:
The absolute largest turboprop engine was the Kuznetsov NK-12, developed just after WWII. A more modern large turboprop is the Europrop TP400, only slightly smaller, used for the A400, 2 with a maximum power output of 11,000 hp = 8,203 kW.
- Cruise shaft power specific fuel consumption: 0.167 kg/kWh (0.275 lb/hp/h) = 51.5% efficiency.
- Cruise propulsive power specific fuel consumption: 0.213 kg/kWh (0.350 lb/hp/h)
But it may be seen that large gas turbine engines are very fuel efficient, and are not inferior to piston engines in frugality.
I could not find fuel consumption data on a comparable piston engine that delivers 11,000 hp. The only reference is to a drag racing engine, which is not very concerned with fuel economy.
Largest piston powered prop
The largest piston engine ever produced was the Lycoming XR-7755, producing 5,000 hp at a fuel economy of .38-.41lb/hp-hour, 231-249 g/kWh or 35.5-32.5% efficiency. And that with 1947 technology.
Also from the 1940s: the Allison T40 turboprop with 5,100 hp and specific fuel consumption at 0.63 lb/(she*h) = 383 g/kWh = 22% efficiency. Low compression ratio, no FADEC.
The Q400 has two PW150A turboprops of 5,000 hp each. Could not find the SFC of this modern gas turbine engine. The Rolls Royce Tyne is from the 1950s and does not have the latest technology.
It is hard to find equivalent piston and gas turbine engines for a fair comparison:
- Time of development. Avgas pistons were highly developed after WWII, afterwards development of large engines stopped, now only used in smaller aeroplanes. Turboprops now have 3-axes, very high compression ratio and inlet temperatures, FADEC.
- Engine rated horsepower. Turbines don't scale down well, and the comparison HP rating will have a large influence on the outcome.
1: The gross power delivered by the engine is the torque Q at the shaft times the angular speed $\Omega$. This is the pure engine power, the Shaft(!) Horse Power of piston engine specifications. To measure the gross shaft power, connect an eddy current damper to the output shaft and measure the amps required to run at constant $\Omega$
2: By Matti Blume - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=68573331