109 e3b against spitfire II

[Viper2000]

Go back to the paper given by Lovesey which I posted earlier.

Engine shaft power is proportional to mass flow rate.

Mass flow rate, W, is given by

W=0.422*Ncylinders*(Pcharge-(1/6)*Pexhaust)/Tcharge

Charge temperature & pressure are measured in the intake manifold. In this equation, W is in lb/minute; piston engines are tiny.

You will note that Lovesey cites a 7% improvement in supercharger pressure ratio from injecting fuel into the eye of the supercharger.

This is very significant given the pretty awful isentropic efficiency of the supercharger.

You can go through the data, and calculate the supercharger work from the efficiency curves in Figure 11.

You can calculate the actual engine air consumption iteratively by assuming that the FAR is about 1/12 at high power. Hence, given the SFC curve and the full throttle power vs altitude curve, you can use the fuel flow to calculated the total rate of charge consumption.

You can use the total rate of charge consumption to calculate the supercharge power consumption as a function of inlet temperature. You must of course add this supercharger power consumption to the brake power in order to calculate the shaft power, because it is the shaft power, not the brake power, which is directly proportional to fuel flow.

This means that you'll need to iterate in order to achieve convergence.

Try this with and without fuel injection into the eye of the supercharger, which may be modelled as a 25 K temperature reduction exchanged for a 1/12 mass flow rate increase.

Because the supercharger work is W*Cp*deltaT, you will find that injecting fuel into the eye of the supercharger results in a considerable reduction in the supercharger power required for any given boost pressure, which naturally improves brake power and brake SFC.

Your argument regarding cylinder temperature is spurious because the engine has a cooling system to maintain CHT, and because the reduction in induction manifold temperature results in a considerable reduction in the charge temperature during the compression stroke because compression through a fixed volume ratio results in a fixed temperature ratio rather than a fixed absolute temperature increment.

This means that there is less compression work.

Peak cycle temperature is essentially fixed by dissociation, and therefore the reduction in charge temperature translates directly into an increase in BMEP.

Alternatively, you could hold constant charge temperature and reduce the size of the aftercooler. Either way, you're still getting a benefit from the latent heat of evaporation of the fuel; but this benefit is greater overall when the fuel is injected into the eye of the supercharger.

Arguments about stoichiometry as less important for an aero-engine at high power than for a car engine because you're not bothered about emissions (at least in this period). Therefore you run the whole thing rich of peak.

Cylinder to cylinder variation in FAR will be small so long as the induction manifold temperature is kept reasonably high; this may be seen from the discussion about lead fouling towards the end of Lovesey's paper; charge distribution is good down to intake manifold temperatures of about 35ºC.

Cylinder to cylinder charge consumption will vary due to intake manifold aerodynamics.

But this actually means that if you go for 1940s DI you'll get a variation in FAR from cylinder to cylinder because the injection system would give each cylinder equal fuel irrespective of its actual air consumption. Modern engines would use an oxygen sensor in the exhaust to maintain stoichiometry. However, this would preclude operations rich of stoichiometric, so the benefit is to BSFC and emissions rather than to absolute power.

I have flown a Citabria with modern after-market engine instrumentation. Obviously the CHTs vary because it's air cooled; you're never going to get the back cylinders as cool as the front ones. Likewise, mixture distribution will always be questionable for a naturally aspirated engine, even on a hot day in South Carolina.

That sort of engine would obviously benefit from DI; and in the modern world, the philosophy is to turbo-normalise if altitude performance is wanted. The convenience of maintaining a fixed engine operating point independent of altitude is considerable. Modern compressors are very much more efficient than those from the 1940s, and therefore there is less compressor work to save in the first place. Additionally, with substantial exhaust energy being dumped out of the waste-gate, there is obviously less motivation to reduce compressor work. So there are a variety of factors driving modern engines towards DI.

This does not mean that single point injection upstream of a supercharger does not have advantages, especially if you have a high degree of supercharge.

Modern piston engines simply have different design goals than the high-powered piston aero-engines of the 1940s.