I'm creating a world with different oxygen density, about 15%. When given same fuel and air pressure, how will the fire burn up in this 15% oxygen density atmosphere compared to our world? And the world atmosphere is composed with 0.2% of Carbon Dioxide, and 1% of Methane. (Nitrogen? Same.)
Considering that oxygen is still present in the atmosphere, the fuel will definitely ignite. However, due to 35% lesser oxygen, the combustion reaction of fuel and oxygen will be 35% slower.
That is to say, that the flame will be 35% smaller in that environment, than the flame produced on Earth now. However, you also have 1% methane in the environment and the flame will burn atmospheric methane too. It is difficult to say exactly how much positive effect it will have on the flame, so let us do some math here.
CH$_4$ (16 grams) + 2O$_2$ (64 grams) ---------> CO$_2$ (44 grams) + 2H$_2$O (36 grams)
The reaction posted above (with given quantity of methane and oxygen) produces 810 KJ of energy. Also note that every one molecule of methane requires 2 molecules of oxygen to burn. However, since methane is present as only 1% of the atmosphere, it will use up only 2% of the oxygen which would be otherwise available for burning the fuel.
It depends on the type of fuel to decide if the fuel combustion process will take priority over methane combustion or methane combustion will take priority. For most types of common fuels in use today (gasoline, diesel, kerosine etc), methane combustion takes priority.
So, all in all we could say that the flame produced will be 65% (fuel burning part) + 2% (methane burning part) = 67% of the flame we have in our atmosphere.