Laminar Flame

This example shows how to simulate a freely-propagating, unstrained laminar flame.

#!/usr/bin/python
"""
An unstrained flame converges to a stable propagation rate for a slightly
lean methane/air mixture.
"""

from ember import *
import matplotlib as mpl
mpl.use('Agg')
import matplotlib.pyplot as plt

output = 'run/ex_lfs'

conf = Config(
    Paths(outputDir=output),
    InitialCondition(fuel='CH4:1.0',
                     oxidizer='O2:1, N2:3.76',
                     equivalenceRatio=0.9,
                     xLeft=0.0,
                     xRight=0.01),
    StrainParameters(initial=0,
                     final=0),
    General(fixedLeftLocation=True,
            fixedBurnedVal=False,
            nThreads=4),
    Grid(vtol=0.1, dvtol=0.15, gridMin=5e-6, gridMax=0.001),
    PositionControl(proportionalGain=2000, xInitial=0.005, xFinal=0.005),
    TerminationCondition(tolerance=1e-5),
    Times(profileStepInterval=50))

if __name__ == '__main__':
    conf.run()

    struct = utils.load(output + '/profNow.h5')

    plt.figure()
    plt.plot(struct.x, struct.V / struct.rho)
    plt.xlabel('Position [m]')
    plt.ylabel('Axial Velocity [m/s]')
    plt.twinx()
    plt.plot(struct.x, struct.T, 'r--')
    plt.tick_params( colors='r')
    plt.ylabel('Temperature (K)', color='r')
    plt.savefig(output+'/FinalProfiles.png')
    plt.close()

The following configuration parameters are particularly important for unstrained flames:

• StrainParameters should have both initial and final set to 0.

• General should have fixedLeftLocation set to True. Since the boundary condition on the burned side of the flame is an outflow condition, a zero-gradient boundary condition is appropriate, so we set fixedBurnedVal to False.

• PositionControl - Since an unstrained flame propagating into a stagnant mixture has no steady-state solution in the fixed reference frame, we use this option to vary the inlet velocity to the domain so that we end up in a reference frame that follows the flame. The values of xInitial and xFinal should be equal, and set to a point within the initially specified domain. The proportionalGain value needs to be set high enough so that the flame doesn’t move too far within the domain, but low enough to avoid numerical instabilities.