Problem 0
- Read the notes here on mixture fraction
- And here on adiabatic flame temperatures
- State if you did this
Problem 1
Plot reactants and products of complete combustion versus mixture fraction for $\xi\in[0,1]$.
Problem 2
A series of one-dimensional turbulence flame simulation was performed. For each simulation we have a position, temperature, enthalpy, and set of species mass fractions. This simulation was performed with species having their own diffusivities. Hence, different mixture fraction definitions will have different values for a given composition.
The data for all simulations were concatenated into a single file, scatter.dat, whose columns represent the variables above. (If you plot column 1, you will notice a zig-zag pattern which just means that the domain repeats itself for each of the simulations that are stacked on top of each other in the file.) The data were reduced by only keeping 1 out of 100 of the original rows.
There are 19 chemical species. A Cantera mechanism file is available as c2h4red.yaml.
The streams are at 550 K with compositions:
- Fuel
- $y_{C2H4}$=0.25486817
- $y_{N2}$=0.74513183
- Oxidizer
- $y_{O2}$=0.29073905
- $y_{N2}$=0.70926095
Part a
For each point in the file, compute mixture fractions $\xi_C$, $\xi_H$, $\xi_O$, $\xi_N$, $\xi_B$, with $\xi_B$ being the Bilger mixture fraction. Plot each of the elemental mixturee fractions veresus the Bilgr mixturee fraction. This is a scatter plot, so use very small points for plotting, and don’t connect the points with lines. You can do this on a single plot with different colors for each mixture fraction; or you can do four different plots. Which elemental mixture fraction is “best?”
Part b
For each point in the file you have a temperature and a composition. These should correspond directly to the enthalpy in the file. At each point, you computed a Bilger mixture fraction (Part a). Use this mixture fraction to compute the corresponding enthalpy from simple mixing between the two streams. How do the two enthalpies compare? (This is best answered by plotting $h_B$ versus $h$ as a scatter plot.)
Problem 3
Derive the mixture fraction transport equation starting from the species transport equation.