Exploring Diesel Engine Friction and Fuel Mass Flow Rate

[Alex91]

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

 

[Baluncore]

… 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.

 

[Alex91]

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

 

[Baluncore]

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.

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.