Homework 4

Problem 1

Calculate the flame length for a propane-air and hydrogen-air jet flame. Assume ambient and fuel temperatures of 300 K, and a jet exit diameter of 5 mm. Assume a momentum dominated jet.

Problem 2

For a momentum dominated jet, if you double the exit diameter, what happens to the flame length? What happens if you double the stoichiometric mixture fraction? Do these results make sense?

Problem 3

Estimate the Kolmogorov length scale and Re during combustion in an autombile engine. (Yep, that’s it.)

Now, if that feels like you don't have enough information, here are a few hints. Take the integral scale as the space between the top of the cylinder head and the top of the cylinder at "top dead center" (TDC). Take the integral velocity as the piston velocity for some appropriate engine RPM and some appropriate piston stroke length. Use some appropriate kinematic viscosity (like the average of the value before and after burning).

Problem 4

Compute the flame speed and flame thickness for a premixed propane-air flame at an equivalence ratio of 0.8. For the flame speed, use the correlation in the notes and Cantera. For the flame thickness, just use Cantera. Take reactants at 298 K and 1 atm.

Note, gri30.yaml has propane in it, but the mechanism is not meant to be used with propane as a fuel. We’ll use it here, but the results won’t be as accurate as for a propane mechanism.
To compute the flame thickness, you can use the shape of the temperature profile, or the shape of the heat release rate profile.
- For heat release rate, something like the full width at half max (FWHM). For temperature, consider using $$\delta=\frac{(\Delta T)\_{max}}{(dT/dx)\_{max}}$$.

Problem 5

For the conditions of Problem 4, compute the turbulent flame speed using the Damkohler, Klimov, and Clavin/Williams expressions. Use $u^\prime_{rms}=500$ cm/s. Take $S_L$ from the correlation.