What range of relative humidity is present in the combustion byproducts of a natural gas stove, immediately after combustion?

If I have a traditional gas range-top, burning natural gas (instead of LPG or propane), what is the typical range of humidity present in the combustion byproducts immediately above the flame? The combustion process adds water to the air, and the natural gas has an inherent humidity as well. However, the combustion process also dramatically raises the temperature, thus significantly drying the air.




Assuming ideal conditions starting from dry air, the theoretical mixture immediately after complete combustion contains $19\ \%$ $\ce{H2O}$ (molar fraction) since the oxygen from the air is replaced according to


$$\ce{CH4 + 2 O2 -> CO2 + 2 H2O}$$


However, the adiabatic flame temperature in air (not oxygen) is $2236\ \mathrm K$, which is well above the critical point temperature of $647\ \mathrm K$. Therefore, the relative humidity (i.e. the ratio of the partial pressure of water vapor to the saturation vapor pressure) is not defined at such temperatures immediately after combustion.


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