
:html_theme.sidebar_secondary.remove:

.. py:currentmodule:: cantera


.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/python/onedim/diffusion_flame_extinction.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_python_onedim_diffusion_flame_extinction.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_python_onedim_diffusion_flame_extinction.py:


Diffusion flame extinction strain rate
======================================

This example computes the extinction point of a counterflow diffusion flame.
A hydrogen-oxygen diffusion flame at 1 bar is studied.

The tutorial makes use of the scaling rules derived by Fiala and Sattelmayer
(doi:10.1155/2014/484372). Please refer to this publication for a detailed
explanation. Also, please don't forget to cite it if you make use of it.

Requires: cantera >= 3.2, matplotlib >= 2.0

.. tags:: Python, combustion, 1D flow, diffusion flame, strained flame, extinction,
          saving output, plotting

.. GENERATED FROM PYTHON SOURCE LINES 20-28

.. code-block:: Python


    from pathlib import Path
    import numpy as np
    import matplotlib.pyplot as plt

    import cantera as ct









.. GENERATED FROM PYTHON SOURCE LINES 29-33

Initialization
--------------
Set up an initial hydrogen-oxygen counterflow flame at 1 bar and low strain
rate (maximum axial velocity gradient = 2414 1/s)

.. GENERATED FROM PYTHON SOURCE LINES 33-80

.. code-block:: Python


    reaction_mechanism = 'h2o2.yaml'
    gas = ct.Solution(reaction_mechanism)
    width = 18.e-3  # 18mm wide
    f = ct.CounterflowDiffusionFlame(gas, width=width)

    # Define the operating pressure and boundary conditions
    f.P = 1.e5  # 1 bar
    f.fuel_inlet.mdot = 0.5  # kg/m^2/s
    f.fuel_inlet.X = 'H2:1'
    f.fuel_inlet.T = 300  # K
    f.oxidizer_inlet.mdot = 3.0  # kg/m^2/s
    f.oxidizer_inlet.X = 'O2:1'
    f.oxidizer_inlet.T = 500  # K

    # Set refinement parameters
    f.set_refine_criteria(ratio=3.0, slope=0.1, curve=0.2, prune=0.03)

    # Define a limit for the maximum temperature below which the flame is
    # considered as extinguished and the computation is aborted
    temperature_limit_extinction = max(f.oxidizer_inlet.T, f.fuel_inlet.T)

    # Initialize and solve
    print('Creating the initial solution')
    f.solve(loglevel=0, auto=True)

    # Define output locations
    output_path = Path() / "diffusion_flame_extinction_data"
    output_path.mkdir(parents=True, exist_ok=True)

    hdf_output = "native" in ct.hdf_support()
    if hdf_output:
        file_name = output_path / "flame_data.h5"
        file_name.unlink(missing_ok=True)

    def names(test):
        if hdf_output:
            # use internal container structure for HDF
            file_name = output_path / "flame_data.h5"
            return file_name, test
        # use separate files for YAML
        file_name = output_path / f"{test}.yaml".replace("-", "_").replace("/", "_")
        return file_name, "solution"

    file_name, entry = names("initial-solution")
    f.save(file_name, name=entry, description="Initial solution", overwrite=True)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Creating the initial solution




.. GENERATED FROM PYTHON SOURCE LINES 81-85

Compute Extinction Strain Rate
------------------------------
Exponents for the initial solution variation with changes in strain rate
Taken from Fiala and Sattelmayer (2014)

.. GENERATED FROM PYTHON SOURCE LINES 85-111

.. code-block:: Python

    exp_d_a = - 1. / 2.
    exp_u_a = 1. / 2.
    exp_V_a = 1.
    exp_lam_a = 2.
    exp_mdot_a = 1. / 2.

    # Set normalized initial strain rate
    alpha = [1.]
    # Initial relative strain rate increase
    delta_alpha = 1.
    # Factor of refinement of the strain rate increase
    delta_alpha_factor = 50.
    # Limit of the refinement: Minimum normalized strain rate increase
    delta_alpha_min = .001
    # Limit of the Temperature decrease
    delta_T_min = 1  # K

    # Iteration indicator
    n = 0
    # Indicator of the latest flame still burning
    n_last_burning = 0
    # List of peak temperatures
    T_max = [np.max(f.T)]
    # List of maximum axial velocity gradients
    a_max = [np.max(np.abs(np.gradient(f.velocity) / np.gradient(f.grid)))]








.. GENERATED FROM PYTHON SOURCE LINES 112-118

Simulate counterflow flames at increasing strain rates until the flame is
extinguished. To achieve a fast simulation, an initial coarse strain rate
increase is set. This increase is reduced after an extinction event and
the simulation is again started based on the last burning solution.
The extinction point is considered to be reached if the abortion criteria
on strain rate increase and peak temperature decrease are fulfilled.

.. GENERATED FROM PYTHON SOURCE LINES 118-176

.. code-block:: Python

    while True:
        n += 1
        # Update relative strain rates
        alpha.append(alpha[n_last_burning] + delta_alpha)
        strain_factor = alpha[-1] / alpha[n_last_burning]
        # Create an initial guess based on the previous solution
        # Update grid
        # Note that grid scaling changes the diffusion flame width
        f.flame.grid *= strain_factor ** exp_d_a
        # Update mass fluxes
        f.fuel_inlet.mdot *= strain_factor ** exp_mdot_a
        f.oxidizer_inlet.mdot *= strain_factor ** exp_mdot_a
        # Update velocities
        f.flame.set_values("velocity", f.flame.velocity * strain_factor ** exp_u_a)
        f.flame.set_values("spreadRate", f.flame.spread_rate * strain_factor ** exp_V_a)
        # Update pressure curvature
        f.flame.set_values(
            "Lambda", f.flame.radial_pressure_gradient * strain_factor ** exp_lam_a)
        try:
            f.solve(loglevel=0)
        except ct.CanteraError as e:
            print('Error: Did not converge at n =', n, e)

        T_max.append(np.max(f.T))
        a_max.append(np.max(np.abs(np.gradient(f.velocity) / np.gradient(f.grid))))
        if not np.isclose(np.max(f.T), temperature_limit_extinction):
            # Flame is still burning, so proceed to next strain rate
            n_last_burning = n
            file_name, entry = names(f"extinction/{n:04d}")
            f.save(file_name, name=entry, description=f"Solution at alpha = {alpha[-1]}",
                   overwrite=True)

            print('Flame burning at alpha = {:8.4F}. Proceeding to the next iteration, '
                  'with delta_alpha = {}'.format(alpha[-1], delta_alpha))
        elif ((T_max[-2] - T_max[-1] < delta_T_min) and (delta_alpha < delta_alpha_min)):
            # If the temperature difference is too small and the minimum relative
            # strain rate increase is reached, save the last, non-burning, solution
            # to the output file and break the loop
            file_name, entry = names(f"extinction/{n:04d}")
            f.save(file_name, name=entry, overwrite=True,
                   description=f"Flame extinguished at alpha={alpha[-1]}")

            print('Flame extinguished at alpha = {0:8.4F}.'.format(alpha[-1]),
                  'Abortion criterion satisfied.')
            break
        else:
            # Procedure if flame extinguished but abortion criterion is not satisfied
            # Reduce relative strain rate increase
            delta_alpha = delta_alpha / delta_alpha_factor

            print('Flame extinguished at alpha = {0:8.4F}. Restoring alpha = {1:8.4F} and '
                  'trying delta_alpha = {2}'.format(
                      alpha[-1], alpha[n_last_burning], delta_alpha))

            # Restore last burning solution
            file_name, entry = names(f"extinction/{n_last_burning:04d}")
            f.restore(file_name, entry)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Flame burning at alpha =   2.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =   3.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =   4.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =   5.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =   6.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =   7.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =   8.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =   9.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  10.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  11.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  12.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  13.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  14.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  15.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  16.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  17.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  18.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  19.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  20.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  21.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  22.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  23.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  24.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  25.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  26.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  27.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  28.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  29.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  30.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  31.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  32.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  33.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  34.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  35.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  36.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  37.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  38.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  39.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  40.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  41.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  42.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  43.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  44.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  45.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  46.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  47.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  48.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  49.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  50.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  51.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  52.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  53.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  54.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  55.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  56.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  57.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  58.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  59.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  60.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  61.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  62.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  63.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  64.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  65.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  66.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  67.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  68.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  69.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  70.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  71.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  72.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  73.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  74.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  75.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  76.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  77.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  78.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  79.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  80.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  81.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  82.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  83.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  84.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  85.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  86.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  87.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  88.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  89.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  90.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  91.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  92.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  93.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  94.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  95.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  96.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  97.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  98.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha =  99.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 100.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 101.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 102.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 103.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 104.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 105.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 106.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 107.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 108.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 109.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 110.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 111.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 112.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 113.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 114.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 115.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 116.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 117.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 118.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 119.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 120.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 121.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 122.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 123.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 124.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 125.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 126.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 127.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 128.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 129.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 130.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 131.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 132.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 133.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 134.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 135.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 136.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 137.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 138.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 139.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 140.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 141.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 142.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 143.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 144.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 145.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 146.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 147.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 148.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 149.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 150.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 151.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 152.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 153.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 154.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 155.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 156.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 157.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 158.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 159.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 160.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 161.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 162.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 163.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 164.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 165.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 166.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 167.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 168.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 169.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 170.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 171.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 172.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 173.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 174.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 175.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 176.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 177.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 178.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 179.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 180.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 181.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 182.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 183.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 184.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 185.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 186.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 187.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 188.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 189.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 190.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 191.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 192.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 193.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 194.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 195.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 196.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 197.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 198.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 199.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 200.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 201.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 202.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 203.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 204.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 205.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 206.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 207.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 208.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 209.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 210.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 211.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 212.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 213.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 214.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 215.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 216.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 217.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 218.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 219.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 220.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 221.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 222.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 223.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 224.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 225.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 226.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 227.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 228.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 229.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 230.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 231.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 232.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 233.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 234.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 235.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 236.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 237.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 238.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 239.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 240.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 241.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 242.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 243.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 244.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 245.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 246.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 247.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 248.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 249.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 250.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 251.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 252.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 253.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 254.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 255.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 256.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 257.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 258.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 259.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 260.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 261.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 262.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 263.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 264.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 265.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 266.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 267.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 268.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 269.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 270.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 271.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 272.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 273.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 274.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 275.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 276.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 277.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 278.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 279.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 280.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame burning at alpha = 281.0000. Proceeding to the next iteration, with delta_alpha = 1.0
    Flame extinguished at alpha = 282.0000. Restoring alpha = 281.0000 and trying delta_alpha = 0.02
    Flame burning at alpha = 281.0200. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.0400. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.0600. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.0800. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.1000. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.1200. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.1400. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.1600. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.1800. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.2000. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.2200. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.2400. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.2600. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.2800. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.3000. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.3200. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.3400. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.3600. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.3800. Proceeding to the next iteration, with delta_alpha = 0.02
    Error: Did not converge at n = 301 
    *******************************************************************************
    CanteraError thrown by OneDim::timeStep:
    Took maximum number of timesteps allowed (500) without reaching steady-state solution.
    *******************************************************************************

    Flame burning at alpha = 281.4000. Proceeding to the next iteration, with delta_alpha = 0.02
    Error: Did not converge at n = 302 
    *******************************************************************************
    CanteraError thrown by OneDim::timeStep:
    Took maximum number of timesteps allowed (500) without reaching steady-state solution.
    *******************************************************************************

    Flame burning at alpha = 281.4200. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.4400. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.4600. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.4800. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.5000. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.5200. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.5400. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.5600. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.5800. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.6000. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.6200. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.6400. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.6600. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame burning at alpha = 281.6800. Proceeding to the next iteration, with delta_alpha = 0.02
    Flame extinguished at alpha = 281.7000. Restoring alpha = 281.6800 and trying delta_alpha = 0.0004
    Flame burning at alpha = 281.6804. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6808. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6812. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6816. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6820. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6824. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6828. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6832. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6836. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6840. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6844. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6848. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6852. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6856. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6860. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6864. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6868. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6872. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6876. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6880. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6884. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6888. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6892. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6896. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6900. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6904. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6908. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6912. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6916. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6920. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6924. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6928. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6932. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6936. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6940. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6944. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6948. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6952. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6956. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6960. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6964. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6968. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6972. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6976. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6980. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6984. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6988. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame burning at alpha = 281.6992. Proceeding to the next iteration, with delta_alpha = 0.0004
    Flame extinguished at alpha = 281.6996. Restoring alpha = 281.6992 and trying delta_alpha = 8e-06
    Flame burning at alpha = 281.6992. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6992. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6992. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6992. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6992. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6992. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6993. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6993. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6993. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6993. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6993. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6993. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6993. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6993. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6993. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6993. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6993. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6993. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6994. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6994. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6994. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6994. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6994. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6994. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6994. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6994. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6994. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6994. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6994. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6994. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6994. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6995. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6995. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6995. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6995. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6995. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6995. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6995. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6995. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6995. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6995. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6995. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6995. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6996. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6996. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame burning at alpha = 281.6996. Proceeding to the next iteration, with delta_alpha = 8e-06
    Flame extinguished at alpha = 281.6996. Restoring alpha = 281.6996 and trying delta_alpha = 1.6e-07
    Flame burning at alpha = 281.6996. Proceeding to the next iteration, with delta_alpha = 1.6e-07
    Flame burning at alpha = 281.6996. Proceeding to the next iteration, with delta_alpha = 1.6e-07
    Flame extinguished at alpha = 281.6996. Restoring alpha = 281.6996 and trying delta_alpha = 3.2e-09
    Flame extinguished at alpha = 281.6996. Abortion criterion satisfied.




.. GENERATED FROM PYTHON SOURCE LINES 177-181

Results
-------
Print some parameters at the extinction point, after restoring the last burning
solution

.. GENERATED FROM PYTHON SOURCE LINES 181-197

.. code-block:: Python

    file_name, entry = names(f"extinction/{n_last_burning:04d}")
    f.restore(file_name, entry)

    print('----------------------------------------------------------------------')
    print('Parameters at the extinction point:')
    print('Pressure p={0} bar'.format(f.P / 1e5))
    print('Peak temperature T={0:4.0f} K'.format(np.max(f.T)))
    print('Mean axial strain rate a_mean={0:.2e} 1/s'.format(f.strain_rate('mean')))
    print('Maximum axial strain rate a_max={0:.2e} 1/s'.format(f.strain_rate('max')))
    print('Fuel inlet potential flow axial strain rate a_fuel={0:.2e} 1/s'.format(
          f.strain_rate('potential_flow_fuel')))
    print('Oxidizer inlet potential flow axial strain rate a_ox={0:.2e} 1/s'.format(
          f.strain_rate('potential_flow_oxidizer')))
    print('Axial strain rate at stoichiometric surface a_stoich={0:.2e} 1/s'.format(
          f.strain_rate('stoichiometric', fuel='H2')))





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    ----------------------------------------------------------------------
    Parameters at the extinction point:
    Pressure p=1.0000000000000007 bar
    Peak temperature T=1552 K
    Mean axial strain rate a_mean=1.58e+05 1/s
    Maximum axial strain rate a_max=6.54e+05 1/s
    Fuel inlet potential flow axial strain rate a_fuel=3.12e+05 1/s
    Oxidizer inlet potential flow axial strain rate a_ox=1.01e+05 1/s
    Axial strain rate at stoichiometric surface a_stoich=2.71e+05 1/s




.. GENERATED FROM PYTHON SOURCE LINES 198-199

Plot the maximum temperature over the maximum axial velocity gradient

.. GENERATED FROM PYTHON SOURCE LINES 199-205

.. code-block:: Python

    plt.figure()
    plt.semilogx(a_max, T_max)
    plt.xlabel(r'$a_{max}$ [1/s]')
    plt.ylabel(r'$T_{max}$ [K]')
    plt.savefig(output_path / "figure_T_max_a_max.png")
    plt.show()



.. image-sg:: /examples/python/onedim/images/sphx_glr_diffusion_flame_extinction_001.png
   :alt: diffusion flame extinction
   :srcset: /examples/python/onedim/images/sphx_glr_diffusion_flame_extinction_001.png, /examples/python/onedim/images/sphx_glr_diffusion_flame_extinction_001_2_00x.png 2.00x
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (3 minutes 57.468 seconds)


.. _sphx_glr_download_examples_python_onedim_diffusion_flame_extinction.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: diffusion_flame_extinction.ipynb <diffusion_flame_extinction.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: diffusion_flame_extinction.py <diffusion_flame_extinction.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: diffusion_flame_extinction.zip <diffusion_flame_extinction.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_
