How Does Engine Power Affect Fuel Mass Flow Rate in Diesel Engines?

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Discussion Overview

The discussion revolves around the relationship between engine power and fuel mass flow rate in diesel engines, specifically examining how engine power at a fixed RPM influences fuel consumption. Participants explore the linearity of this relationship and the implications of observed data trends.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant, Alex, notes a linear trend in the Willans line up to about 75% engine power, after which the fuel mass flow rate increases more dramatically.
  • Another participant questions whether it is the power or the fuel flow that increases dramatically and suggests that high fuel flow may lead to inefficiencies due to longer injection times.
  • Alex provides a graph showing that at full load, the fuel mass flow rate increases significantly, suggesting that engine friction may also increase at higher loads.
  • A different participant interprets the graph as showing a gentle exponential curve, attributing the curvature to the need for longer injection periods at higher fuel volumes, and raises the possibility of measurement errors at high power levels.
  • This participant also discusses estimating mechanical losses by extrapolating the low power end of the Willans line to zero fuel consumption, indicating that the mechanical power loss could be between 2 kW and 4 kW.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the relationship between engine power and fuel mass flow rate, with some suggesting linearity and others proposing exponential behavior. The discussion remains unresolved regarding the exact nature of this relationship and the implications of the observed data.

Contextual Notes

Limitations include potential measurement errors in the high power data points and the absence of extrapolated data from the low power end of the graph, which complicates the estimation of mechanical losses.

Alex91
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Hi

I have been plotting a Willans line, (engine power against fuel mass flow rate) and I noticed that the line is fairly linear up to about 75% and then it starts to increase a bit more dramatically.

  • So I was wondering how does engine power at a fixed RPM effect fuel mass flow rate?
  • Is it directly proportional or is it squared? And how would you prove this?
  • Is there an equation that you can use that shows how the two affect each other?

Any Help is much appreciated.

Cheers

Alex
 
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Alex91 said:
… then it starts to increase a bit more dramatically.
Which increases, the power or the fuel flow?
It would help if you could post a copy of the graph with annotations on the scales.

High fuel flow will require a greater time to inject so it will not be as efficient.
 
Hi,

Thanks for the reply.

I have attached a graph of the power against fuel mass flow rate at 1000rpm.

As the engine reaches it's full load, the fuel mass flow rate starts to increase a lot more dramatically. As you can see from the graph, the last four points don't really follow the linear trend of the rest of the graph..

It's almost as if at the very highest loads the engine friction increases a lot more for some reason.

Cheers

Alex
 

Attachments

  • Fuel against power.jpg
    Fuel against power.jpg
    12.3 KB · Views: 654
Your graph shows what looks like a very gentle exponential curve. The curvature is I believe due to the higher fuel volumes requiring a greater period of injection. The line should not be expected to be straight.

Alex91 said:
It's almost as if at the very highest loads the engine friction increases a lot more for some reason.
As the two end points fall below the exponential trend, an opposite conclusion is also possible. I cannot explain those two or three points at the high kW end. It is possible that there could be a significant error in the 14 kW measurement. Whatever the interpretation, it is the wrong end of the graph to yield an estimate of the mechanical losses at the test RPM.

The mechanical losses can be estimated by extrapolating the low power end of the Willans line to zero fuel consumption. The negative x–axis intercept then represents the mechanical power loss. That is the friction of the motor at the test RPM. The extension about the origin is missing from your graph so the extrapolation is not easy. See my attached approximation that shows mechanical losses are somewhere between 2 kW and 4 kW.
 

Attachments

  • extrapolated.jpg
    extrapolated.jpg
    10.9 KB · Views: 697

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