Question about "Example Laminar flame speed calculation"

[rdwor]

Hello everyone,

Quick question, for example, https://cantera.org/stable/examples/python/onedim/adiabatic_flame.html.

In the "Temperature and Heat Release Rate" image... the energy axis is given as MW/m³. Is the scale correct? compared to the heating values. 

[Ray Speth]

Hi,

Yes, the units are correct. To work through the relationship between this volumetric heat release rate and the heating value of the fuel, we can do the following:

As a rough estimate of the heat release rate per unit area of the flame surface, we can take the near-peak value of 2000 MW/m³ times the width of the heat release region, approximately 0.4 mm, to get a value of 800 kW/m². A more accurate integration using np.trapezoid tells me that the correct answer is 1113 kW/m².

This should be compared with the heating value of the fuel times its mass flux at the inlet. The lower heating value for hydrogen is 120 MJ/kg. The flame speed in the given example is 0.72 m/s, with an inlet density of 1.33 kg/m³, and the mass fraction of H₂ in this mixture is 0.0094783. Taken together, this is a mass flow rate of 0.009076 kg/s. Multiplying by the LHV of hydrogen gives a heat release rate per unit area of 1089 kW/m², consistent with the observed heat release rate.

Regards,
Ray

​

[Rene Dworschak]

Thanks for the answer and the hints. I now know where my error in my calculations was.

Greetings and thanks for your (and the community's) efforts on the Cantera Framework.

René

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