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Bigger turbo - More power?

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Among our friends we had a hot debate about whether a larger turbo on otherwise exactly same engine setup will make more power at certain rpm (say 4000rpm)? Lets take into consideration that boost pressure and manifold air temperature on that certain RPM are exactly the same. We both agree that backpressure is one factor that reduces volumetric efficiency, but is there anything else into that?

Personally I'm on the side that at same rpm in the same conditions, disregarding backpressure, the power output is the same. The other side of the debate is claiming that the amount of air a larger turbo can provide, is bigger.

Well intake to exhaust manifold pressure ratio is a mapping mode available on some ecus if that answers your question.

The reality is it is unlikely that two turbos will be operating at exactly the same intake temperature and turbine inlet pressure.

The sensitivity of an particular engine will also depend on compression ratio and cam/port timing. It isn't just exhaust stroke pumping loss but intake dilution which can rob power.

I think the practical answer is for a mild motor with two "well suited" turbos that are one size apart with similar turbine housing A/R is not much difference/within the noise of other factors at mid range engine speed. I think Raceonly did a test like this on an extend or Bridgeport 13b with a BW EFR8374 and a EFR9180 and claimed no difference in peak power, just a wider powerband with the smaller turbo. Obviously you need two turbos which flow enough on both sides not to choke the engine.

The question is more theoretical than practical, as you said, it is unlikely that two turbos will be operating at the same iat and turbine inlet pressure. Changes in both hot and cold side have always an effect on the opposite side.

The answer I'm after, is that if there is anything more that will rob power on a smaller turbo, other than hotter iat, exhaust stroke pumping loss and excessive combustion gasses left in the cylinder due to high egp? Is there something more that I am missing from the "equasion" what a larger compressor wheel and housing can provide, compared to a smaller one.

The correct answer is - it depends...

Some vehicle applications may be expected to make a smallish gain, others may make a small loss - depends on the engine assembly (intake opening to exhaust tailpipe outlet) and what was originally there.

Two, related, possible issues with going larger - there is more 'leakage' around the exhaust turbine until the gas volume is sufficient to apply pressure to the vanes and apply torque (power) to drive the impellor. Similarly, if the impellor is too large, it may not be as efficient compressing the charge because of internal leakage until it gets to the gas flow required.

Charge air density is charge air density, if you take pressure and remove temperature it's kind of an 'eh' data point so removing the adiabatic efficiency of the compressors as a factor kinds of defeats the purpose of comparison in the real world.